COST OF CAPITAL Applications and Examples Third Edition SHANNON P. PRATT ROGER J. GRABOWSKI
John Wiley & Sons, Inc.
Cost of Capital Applications and Examples
COST OF CAPITAL Applications and Examples Third Edition SHANNON P. PRATT ROGER J. GRABOWSKI
John Wiley & Sons, Inc.
1 This book is printed on acid-free paper. Copyright # 2008 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008, or online at http://www.wiley.com/go/permissions. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services, or technical support, please contact our Customer Care Department within the United States at 800-762-2974, outside the United States at 317-572-3993 or fax 317-5724002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our Web site at http://www.wiley.com. Library of Congress Cataloging-in-Publication Data: Pratt, Shannon P. Cost of capital: applications and examples/Shannon P. Pratt, Roger J. Grabowski.—3rd ed. p. cm. ‘‘Published simultaneously in Canada.’’ Previous editions had subtitle: Estimation and applications. Includes bibliographical references and index. ISBN 978-0-470-17115-8 (cloth: alk. paper) 1. Capital investments. 2. Business enterprises—Valuation. 3. Capital investments—United States. 4. Business enterprises—Valuation—United States. I. Grabowski, Roger J. II. Title. HG4028.C4P72 2008 658.15’2—dc22 2007020132 Printed in the United States of America 10 9
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To our families for their support and encouragement, without which our careers and this book would not have been possible Millie Son Mike Pratt Daughter-in-law Barbara Brooks Randall Kenny Portland, OR
Daughter Susie Wilder Son-in-law Tim Wilder John Calvin Meg Springfield, VA Daughter Georgia Senor Son-in-law Tom Senor Elisa Katie
Son Steve Pratt Daughter-in-law Jenny Pratt Addy Zeph Portland, OR
Graham Fayetteville, AR Mary Ann Son Roger Grabowski Jr. Daughter-in-law Misako Takahashi Rob Tokyo, Japan
Daughter Sarah Harte Son-in-law Mike Harte Kevin Evanston, IL
Daughter Julia Grabowski, MD San Diego, CA
Son Paul Grabowski New York, NY
Contents About the Authors Foreword Preface
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Acknowledgments Introduction
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Notation System and Abbreviations Used in This Book Part 1. Cost of Capital Basics
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1. Defining Cost of Capital 3 2. Introduction to Cost of Capital Applications: Valuation and Project Selection 3. Net Cash Flow: Preferred Measure of Economic Income 15 4. Discounting versus Capitalizing 23 5. Relationship between Risk and the Cost of Capital 39 Appendix 5A. FASB’s Concepts Statement No. 7: Cash Flows and Present Value Discount Rates 48 6. Cost Components of a Company’s Capital Structure 51 Part 2. Estimating the Cost of Equity Capital and the Overall Cost of Capital
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7. Build-up Method 69 8. Capital Asset Pricing Model 79 9. Equity Risk Premium 89 Appendix 9A. Bias Issues in Compounding and Discounting 114 10. Beta: Differing Definitions and Estimates 117 Appendix 10A. Formulas and Examples for Unlevering and Levering Equity Betas 143 Appendix 10B. Examples of Computing OLS Beta, Sum Beta, and Full-Information Beta Estimates 151 11. Criticism of CAPM and Beta versus Other Risk Measures 161 Appendix 11A. Example of Computing Downside Beta Estimates 176 12. Size Effect 179 13. Criticisms of the Size Effect 209 Appendix 13A. Other Data Issues Regarding the Size Effect 220 14. Company-Specific Risk 225 15. Alternative Cost of Equity Capital Models 243 16. Implied Cost of Equity Capital 255 17. Weighted Average Cost of Capital 265 Appendix 17A. Iterative Process Using CAPM to Calculate the Cost of Equity vii
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Component of the Weighted Average Cost of Capital When Capital Structure Is Constant 283 Appendix 17B. Iterative Process Using CAPM to Calculate the Cost of Equity Component of the Weighted Average Cost of Capital When Capital Structure Is Changing 297 18. Global Cost of Capital Models 309 19. Using Morningstar Cost of Capital Data 331 Part 3. Corporate Finance Officers: Using Cost of Capital Data 20. 21. 22. 23. 24.
Capital Budgeting and Feasibility Studies 363 Cost of Capital for Divisions and Reporting Units 369 Cost of Capital in Evaluating Acquisitions and Mergers 385 Cost of Capital in Transfer Pricing 393 Central Role of Cost of Capital in Economic Value Added 409
Part 4. Cost of Capital for Closely Held Entities 25. 26. 27. 28. 29.
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Handling the Discount for Lack of Marketability for Operating Businesses 419 Private Company Discount 429 Cost of Capital of Interests in Pass-Through Entities 437 Cost of Capital in Private Investment Companies 449 Relationship between Risk and Returns in Venture Capital Investments 469
Part 5. Other Topics
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30. Minority versus Control Implications of Cost of Capital Data 481 31. How Cost of Capital Relates to the Excess Earnings Method of Valuation 32. Adjusting the Discount Rate to Alternative Economic Measures 501 33. Estimating Net Cash Flows 505 Appendix 33A. Estimating the Value of a Firm in Financial Distress 518 34. Common Errors in Estimation and Use of Cost of Capital 529 35. Cost of Capital in the Courts 539 Part 6. Real Estate and Ad Valorem
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36. Cost of Capital of Real Property–Individual Assets 561 Appendix 36A. Valuing Real Property 580 37. Cost of Capital of Real Estate Entities 587 Appendix 37A Valuing Real Estate Entities 615 38. Cost of Capital in Ad Valorem Taxation 623 Part 7. Advice to Practitioners
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39. Dealing with Cost of Capital Issues 641 40. Questions to Ask Business Valuation Experts 647 Appendices
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I. Bibliography 655 II. Data Resources 683
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III. International Glossary of Business Valuation Terms 693 IV. Sample Report Submitted to U.S. Tax Court by Roger J. Grabowski V. ValuSource Valuation Software 725 VI. Review of Statistical Analysis 733 Index
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About the Authors Dr. Shannon P. Pratt, CFA, FASA, MCBA, CM&AA is the chairman and CEO of Shannon Pratt Valuations, Inc., a nationally recognized business valuation firm headquartered in Portland, Oregon. He is also the founder and editor emeritus of Business Valuation Resources, LLC, and one of the founders of Willamette Management Associates, for which he was a managing director for almost 35 years. He has performed valuation assignments for these purposes: transaction (acquisition, divestiture, reorganization, public offerings, public companies going private), taxation (federal income, gift, and estate and local ad valorem), financing (securitization, recapitalization, restructuring), litigation support and dispute resolution (including dissenting stockholder suits, damage cases, and corporate and marital dissolution cases), and management information and planning. He has also managed a variety of fairness opinion and solvency opinion engagements. Dr. Pratt has testified on hundreds of occasions in such litigated matters as dissenting stockholder suits, various types of damage cases (including breach of contract, antitrust, and breach of fiduciary duty), divorces, and estate and gift tax cases. Among the cases in which he has testified are Estate of Mark S. Gallo V. Commissioner, Charles S. Foltz, et al. V. U.S. News & World Report et al., Estate of Martha Watts V. Commissioner, and Okerlund V. United States. He has also served as appointed arbitrator in numerous cases. PREVIOUS EXPERIENCE Before founding Willamette Management Associates in 1969, Dr. Pratt was a professor of business administration at Portland State University. During this time, he directed a research center known as the Investment Analysis Center, which worked closely with the University of Chicago’s Center for Research in Security Prices. EDUCATION Doctor of Business Administration, Finance, Indiana University Bachelor of Arts, Business Administration, University of Washington PROFESSIONAL AFFILIATIONS Dr. Pratt is an Accredited Senior Appraiser and Fellow (FASA), Certified in Business Valuation, of the American Society of Appraisers (their highest designation). He is also a Chartered Financial Analyst (CFA) of the Institute of Chartered Financial Analysts, a Master Certified Business Appraiser (MCBA) of the Institute of Business Appraisers, a Master Certified Business Counselor (MCBC), and is Certified in Mergers and Acquisitions (CM&AA) with The Alliance of Merger and Acquisition Advisors. Dr. Pratt is a life member of the American Society of Appraisers, a life member of the Business Valuation Committee of that organization and teaches courses for the organization. He is also a lifetime member emeritus of the Advisory Committee on Valuations of The ESOP Association. He is a recipient of the magna cum laude award of the National Association of Certified Valuation Analysts for service to
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the business valuation profession. He is also the first life member of the Institute of Business Appraisers. He is a member and a past president of the Portland Society of Financial Analysts, the recipient of the 2002 Distinguished Achievement Award, and a member of the Association for Corporate Growth. Dr. Pratt is a past trustee of The Appraisal Foundation and is currently an outside director and chair of the audit committee of Paulson Capital Corp., a NASDAQ-listed investment banking firm specializing in small initial public offerings (usually under $50 million). PUBLICATIONS Dr. Pratt is the author of Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th edition (New York: McGraw-Hill, 2007); coauthor, Valuing Small Businesses and Professional Practices, 3rd edition with Robert Schweihs and Robert Reilly (New York: McGraw-Hill, 1998); coauthor, Guide to Business Valuations, 18th edition with Jay Fishman, Cliff Griffith and Jim Hitchner (Fort Worth, TX: Practitioners Publishing Company, 2008); coauthor, Standards of Value, with William Morrison and Jay Fishman (New York: John Wiley & Sons, 2007); coauthor, Business Valuation and Taxes: Procedure, Law, and Perspective, with Judge David Laro (New York: John Wiley & Sons, 2005); author, Business Valuation Discounts and Premiums (New York: John Wiley & Sons, 2001); Business Valuation Body of Knowledge: Exam Review and Professional Reference, 2nd edition (New York: John Wiley & Sons, 2003); The Market Approach to Valuing Businesses, 2nd edition (New York: John Wiley & Sons, 2005); and The Lawyer’s Business Valuation Handbook (Chicago: American Bar Association, 2000). He has also published nearly 200 articles on business valuation topics. Roger Grabowski, ASA, is a managing director of Duff & Phelps, LLC. Mr. Grabowski has directed valuations of businesses, partial interests in businesses, intellectual property, intangible assets, real property, and machinery and equipment for various purposes including tax (income and ad valorem) and financial reporting; mergers, acquisitions, formation of joint ventures, divestitures, and financing. He developed methodologies and statistical programs for analyzing useful lives of tangible and intangible assets, such as customers and subscribers. His experience includes work in a wide range of industries including sports, movies, recording, broadcast and other entertainment businesses; newspapers, magazines, music, and other publishing businesses; retail; banking, insurance, consumer credit, and other financial services businesses; railroads and other transportation companies; mining ventures; software and electronic component businesses; and a variety of manufacturing businesses. Mr. Grabowski has testified in court as an expert witness on the value of closely held businesses and business interests, matters of solvency, valuation, and amortization of intangible assets, and other valuation issues. His testimony in U.S. District Court was referenced in the U.S. Supreme Court opinion decided in his client’s favor in the landmark Newark Morning Ledger income tax case. Among other cases in which he has testified was Herbert V. Kohler Jr., et al., v. Comm. (value of stock of The Kohler Company); The Northern Trust Company, et al., v. Comm. (the first U.S. Tax Court case that recognized the use of the discounted cash flow method for valuing a closely held business); Oakland Raiders v. Oakland-Alameda County Coliseum Inc. et al. (valuation of the Oakland Raiders); ABCNACO, Inc. et al., Debtors, and The Official Committee of Unsecured Creditors of ABC-NACO v. Bank of America, N.A. (valuation of collateral); Wisniewski and Walsh v. Walsh (oppressed shareholder action); and TMR Energy Limited v. The State Property Fund of Ukraine (arbitration on behalf of world’s largest private company in Stockholm, Sweden, on cost of capital for oil refinery in Ukraine in a contract dispute).
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PREVIOUS EXPERIENCE He was formerly managing director of the Standard & Poor’s Corporate Value Consulting practice, a partner of PricewaterhouseCoopers, LLP and one of its predecessor firms, Price Waterhouse (where he founded its U.S. Valuation Services practice and managed the real estate appraisal practice). Prior to Price Waterhouse, he was a finance instructor at Loyola University of Chicago, a cofounder of Valtec Associates, and a vice president of American Valuation Consultants. EDUCATION Mr. Grabowski received his B.B.A.—Finance from Loyola University of Chicago and completed all coursework in the doctoral program, Finance, at Northwestern University, Chicago. PROFESSIONAL AFFILIATIONS He serves on the Loyola University School of Business Administration Dean’s Board of Advisors. Mr. Grabowski is an Accredited Senior Appraiser of the American Society of Appraisers (ASA) certified in business valuation. PUBLICATIONS Mr. Grabowski coauthors the annual Duff & Phelps’ Risk Premium Report. He lectures and publishes regularly. He is the coauthor of three chapters (on equity risk premium, valuing pass-through entities, and valuing sports teams) in Robert Reilly and Robert P. Schweihs, The Handbook of Business Valuation and Intellectual Property Analysis (New York: McGraw-Hill, 2004). He teaches courses for the American Society of Appraisers including Cost of Capital, a course he developed. He is the editor of the Business Valuation Review, the quarterly Journal of the Business Valuation Committee. David Fein is the CEO and president of ValuSource, which for over 20 years has been the leading provider of business valuation software, data, and report writers for CPAs, M&A professionals, and business owners. Mr. Fein’s mission is to create state-of-the-art technology to automate and standardize complex financial analysis and reporting tasks. He has a bachelor’s degree in computer science and an MBA. You may reach him at 1.800.825.8763 100, or at
[email protected]. William H. Frazier is a principal and founder of the firm of Howard Frazier Barker Elliott, Inc, and manages its Dallas office. He has 30 years of experience in business valuation and corporate finance. Mr. Frazier has been an Accredited Senior Appraiser of the American Society of Appraisers (ASA) since 1987 and serves on the ASA’s Business Valuation Committee as secretary. He has participated as an appraiser and/or expert witness in numerous U.S. Tax Court cases, including testimony in Jelke, McCord, Dunn and Gladys Cook. Mr. Frazier has written numerous articles on the subject of business valuation for tax purposes, appearing in such publications as the Business Valuation Review, Valuation Strategies, BV E-Letter, Shannon Pratt’s Business Valuation Update, and Estate Planning. He is the coauthor of the chapter on valuing family limited partnerships in Robert Reilly and Robert P. Schweihs, eds., The Handbook of Business Valuation and Intellectual Property Analysis (New York: McGraw-Hill, 2004). Mr. Frazier serves on the Valuation Advisory Board of Trusts & Estates Journal. James Harrington, MBA, is a product manager in Morningstar’s Individual Investor Business segment. He leads the group that produces the widely used and cited SBBI Classic and Valuation Yearbooks, the Cost of Capital Yearbook, the Beta Book, and various international and domestic reports.
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At Morningstar since March of 2006, Mr. Harrington has expanded the product offerings and increased sales for Morningstar publications and reports and is an accomplished financial writer and analyst. Immediately prior to his tenure at Morningstar, he was a product manager in the financial communications group at Ibbotson Associates. Before that, he was a bond and bond portfolio analyst, worked at the Chicago Board of Trade in the bond options pit for a filling group, managed inbound and outbound dock workers at a large trucking firm, and was even a Teamster for a year. Mr. Harrington holds a bachelor’s degree in marketing from Ohio State University and an MBA in both finance and economics from the University of Illinois at Chicago, where he graduated at the top in his class. Carl Hoemke started in valuation when he accepted a position as a tax appraiser for the local tax assessor’s office. His education is in architecture and business. After working for the tax assessor’s office for a period of about eight years, he joined a property tax consulting firm. He later became a partner at one of the big four accounting firms, first as a tax partner then ultimately as a corporate finance partner responsible for valuations primarily in energy and telecommunications. He is currently a managing director with Duff & Phelps, where he leads the firm’s State & Local Tax practice while continuing to provide valuation for other purposes including financial reporting and litigation support. Jim MacCrate, MAI, CRE, ASA owns his own boutique real estate valuation and consulting company, MacCrate Associates, LLC, located in the New York City Metropolitan area, concentrating on complex real estate valuation issues. Formerly, he was the Northeast regional practice leader and director of the Real Estate Valuation/Advisory Services Group at Price Waterhouse LLP and PricewaterhouseCoopers LLP. He received a B.S. Degree from Cornell University and M.B.A. from Long Island University, C. W. Post Center. He has written numerous articles for Price Waterhouse LLP, ‘‘The Counselors of Real Estate,’’ and has contributed to the Appraisal Journal. He initiated the Land Investment Survey that has been incorporated into The PricewaterhouseCoopers Korpacz Real Estate Investor Survey. He is on the national faculty for the Appraisal Institute and adjunct professor at New York University. Harold G. Martin, Jr., MBA, CPA, ABV, ASA, CFE, is the principal-in-charge of the Business Valuation, Forensic, and Litigation Services Group for Keiter, Stephens, Hurst, Gary & Shreaves, P.C. He has over 25 years of experience in financial consulting, public accounting, and financial services. He has appeared as an expert witness in federal and state courts, served as a court-appointed neutral business appraiser, and also served as a federal court-appointed accountant for a receivership. Mr. Martin is an adjunct faculty member of The College of William & Mary Mason Graduate School of Business and teaches valuation and forensic accounting in the Master of Accounting program. Prior to joining Keiter Stephens, he was affiliated for 13 years with Price Waterhouse and Coopers & Lybrand. He is a former member of the American Institute of Certified Public Accountants Business Valuation Committee and is a two-time recipient of the AICPA Business Valuation Volunteer of the Year Award. He is an editorial advisor for the AICPA CPA Expert, a national instructor for the AICPA’s valuation education program, an AICPA faculty member for the National Judicial College, a former member of the Appraisal Standards Board USPAP BV Task Force, and former editor of the AICPA ABV e-Alert. He is a frequent speaker and author on valuation topics and is a coauthor of Financial Valuation: Applications and Models, 2nd edition, published by John Wiley & Sons. Mr. Martin received his A.B. degree in English from The College of William and Mary and his M.B.A. degree from Virginia Commonwealth University. James Morris is a professor of finance at the University of Colorado at Denver, where he teaches courses in business valuation and financial modeling. He is an AM and holds a Ph.D. in Finance
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from University of California, Berkeley. In addition to teaching, he provides valuation services to the business community. Mark Shirley is a licensed certified public accountant and has earned advanced accreditations: Accreditation in Business Valuation (BV), Certified Valuation Analyst (CVA), Certified Forensic Financial Analyst (CFFA), and Certified Fraud Examiner (CFE). After leaving the Internal Revenue Service in 1984, Mr. Shirley’s consulting practice has concentrated on the disciplines of business valuation, forensic/investigative accounting, and financial analysis/modeling. Professional engagements have included business valuation, valuation of options/warrants, projections and forecasts, statistical sampling, commercial damage modeling, personal injury loss assessment, and the evaluation of proffered expert testimony under Daubert and the Federal Rules of Evidence. Since 1988, technical contributions have been published by Wiley Law Publications, Aspen Legal Press, and in professional periodicals, including The Valuation Examiner, BewertungsPraktiker Nr. (a German-language business valuation journal), The Practical Accountant, CPA Litigation Services Counselor, The Gatekeeper Quarterly, The Journal of Forensic Accounting, and local legal society publications. Since 1997 Mr. Shirley has authored courses for NACVA’s Fundamentals, Techniques & Theory; Forensic Institute, and Consultant’s Training Institute. He also has developed several advanced courses for the NACVA in applied statistics and financial modeling. A charter member of the LA Society of CPA’s Litigation Services Committee, Mr. Shirley has remained active since the committee’s formation. He is an adjunct faculty member at the National Judicial College, University of Nevada, Reno, since 1998. Mr. Shirley also serves on the Advisory Panel for Mdex Online; The Daubert Tracker, an online Daubert research database; and the Ethics Oversight Board for the NACVA. Since 1985, Mr. Shirley has provided expert witness testimony before the U.S. Tax Court, Federal District Court, Louisiana district courts, Tunica-Biloxi Indian Tribal Court, and local specialty courts. Court appointments have been received in various matters adjudicated before the Louisiana Nineteenth Judicial District Court. The NACVA has recognized Mr. Shirley’s contributions to professional education by awarding him the Circle of Light in 2002, Instructor of the Year in 2000/2001, and multiple recognitions as Outstanding Member and Award of Excellence. David M. Ptashne, CFA, is a Senior Associate with the Chicago office of Duff & Phelps and has worked directly with Roger Grabowski since 2003. Mr. Ptashne has performed numerous valuation studies of businesses and interests in businesses and intangible assets across various industries including advertising and communications, consumer products, technology, financial services, integrated oil and gas, retail, and healthcare. Mr. Ptashne enjoys researching international cost of capital issues and currently manages Duff & Phelps’ international cost of capital model. Mr. Ptashne is a member of the CFA Institute and CFA Society of Chicago. He received a Bachelor of Science degree in Finance with High Honors from the University of Illinois at Urbana-Champaign.
Foreword Given the central role of the cost of capital in discounted cash flow valuation, it is surprising how little discussion there is on the central inputs that go into its estimation. Shannon Pratt and Roger Grabowski have not only brought together all of the issues in the cost of capital computation but have done so in a way that melds timely advice for practitioners with serious debate about the best practices in the area. Both authors have decades of experience, and their expertise and knowledge show not only in how they present the material but also in the examples they use. The book has been significantly updated from the second edition, both in the numbers and also in the coverage of issues. In general, books on valuation-related topics take one of two paths. One is to follow the cookbook style and provide the reader with the ‘‘right answers’’ to questions, even though there may be debate about what is ‘‘right.’’ The other is to present the alternatives, explain the pros and cons, and trust the reader to make the right choices at the end. This book adopts the latter approach and provides comprehensive discussions not only of the standard inputs—risk-free rates, risk premiums, and debt ratios—but also of issues that come up infrequently in valuations but often enough that practitioners look for guidance. While this book is grounded in solid theory, it is a book for practitioners, and consequently it provides practical solutions to estimation problems. In the process, though, it respects their intelligence and capacity to handle ambiguity by providing a balanced discussion of the choices. It belongs on the bookshelves of serious valuation practitioners, and I would expect it to be widely referenced in the coming years. ASWATH DAMODARAN
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Why did we undertake writing this book? In a recent speech, Geoff Colvin, Senior Editor at Large with Fortune, stated that one of the four traits of great executives is their understanding of the fundamental reality of wealth creation—successful organizations invest to earn a rate of return in excess of their cost of capital.1 These executives ingrain that understanding in the organization, and the managers at all levels come to understand their cost of capital. Our experience tells us that practitioners need assistance in better understanding and estimating the cost of capital and in communicating their results, not from the view of portfolio management but from the view of business owners and managers. No other valuation text designed for the practitioner treats the cost of capital in the breadth and depth that this one does. In terms of breadth, this text treats cost of capital for uses in business valuation, project assessment and capital budgeting, divisional cost of capital, reporting unit valuation and goodwill impairment testing, transfer pricing, utility and other regulated industry rate setting, and ad valorem (property) taxation. Emphasis is on the cost of equity capital. In addition to detailed exposition of the build-up and Capital Asset Pricing Models for estimating the cost of capital, we present in-depth analysis of the components, including the equity risk premium, beta, and the size effect. We also analyze criticism of major models for developing estimates of the cost of capital in use today and present procedures for a number of alternative models. We discuss the Duff & Phelps Risk Premium studies, which are becoming more widely used tools in estimating the cost of equity capital.
WHAT’S NEW IN THIS EDITION Throughout the book, we summarize the results and practical implications of the latest research, much of which has been gleaned from unpublished academic working papers. EQUITY RISK PREMIUM 4 TO 6 PERCENT Importantly, based on empirical research on the magnitude of the equity risk premium, we conclude that it is in the range of 4% to 6% rather than above the 7% that many analysts have used in recent years. We believe that readers will find this research convincing, as we did. PRIVATE COMPANY DISCOUNTS OVER 25 PERCENT We were surprised to find academic research that concludes that the typical private company sells for about a 25% discount compared with otherwise comparable public companies. This is after controlling for variables such as size and industry. The authors of the studies surmise that the reasons for this phenomenon could relate to lack of exposure to the market and lower quality of information (e.g., lack of a track record of audited financial statements). 1
Summarized from a series of Fortune articles on ‘‘Lessons in Leadership.’’
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MUCH NEW DATA AND LITERATURE We not only describe the practical procedures that can be used to apply the various theories but also describe in detail the databases available to derive the numbers to put into the models. We summarize the most important and convincing of the proliferation of literature, both published and unpublished, in recent and prior years. The footnotes and bibliography tell the reader who wishes to get the original studies where to find them. We also added a chapter on global cost of capital models. Much of the new research cited in this book is from working papers, to locate a working paper, search online using any major search engine (i.e., Google or Yahoo) by author and title. An example: the first link provided using the Google search engine when a search for ‘‘Adrian, Tobias, and Francesco Franzoni. Learning About Beta: an Explanation of the Value Premium’’ will be ‘‘SSRN–Learning About Beta: An Explation of the Value Premium by. . .’’ This link will direct you to the Social Science Research Network, where the article is downloadable. CORPORATE FINANCE AND ADVICE TO PRACTITIONERS We have added a five-chapter section specifically for corporate finance officers. This includes, for example, capital budgeting and feasibility studies, cost of capital for divisions and reporting units, and valuation in mergers and acquisitions. There is also a chapter on advice from the authors about dealing with controversial cost of capital issues, a major chapter on cost of capital in the courts, and a chapter on cross examining experts on cost of capital.
AUDIENCES FOR THE BOOK In addition to the traditional professional valuation practitioner, this book is designed to serve the needs of:
Attorneys and judges who deal with valuation issues in mergers and acquisitions, shareholder and partner disputes, damage cases, solvency cases, bankruptcy reorganizations, property taxes, rate setting, transfer pricing, and financial reporting Investment bankers for pricing, public offerings, mergers and acquisitions, and private equity financing
Corporate finance officers for pricing or evaluating mergers and acquisitions, raising private or public equity, property taxation, and stakeholder disputes Academicians and students who wish to learn anywhere from the basic theory to the latest research
CPAs who deal with either valuation for financial reporting or client valuations issues
PRACTICAL APPLICATIONS The book is designed to enhance the insights of users of cost of capital applications as well as originators of such applications. Most formulas are accompanied by examples. Several chapter appendices present detailed expositions of the more complex procedures.
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Finally, the book is comprehensively indexed to serve as a reference for specific concepts and procedures within the general topic of cost of capital. Please contact the authors with any questions, comments, or suggestions for the next edition. Shannon P. Pratt, CFA, FASA, MCBA, CM&AA Shannon Pratt Valuations, Inc. 6443 S.W. Beaverton Hillsdale Highway, Suite 432 Portland, Oregon 97221 (503) 459-4700 E-mail:
[email protected] www.shannonpratt.com Roger J. Grabowski, ASA Duff & Phelps, LLC 311 S. Wacker Drive, Suite 4200 Chicago, Illinois 60606 (312) 233-6820 E-mail:
[email protected] www.duffandphelps.com
Acknowledgments This book has benefited immensely from review by many people with a high level of knowledge and experience in cost of capital and valuation. These people reviewed the manuscript, and the book reflects their invaluable efforts and legions of constructive suggestions: Thomas Blake CRA International Inc Boston, MA
Mark Lee Eisner LLP New York, NY
Stephen J. Bravo The Financial Valuation Group Framingham, MA
Gilbert E. Matthews Sutter Securities, Inc. San Francisco, CA
James Budyak Valuation Research Corp. & Company Milwaukee, WI
Dan McConaughy Grobstein, Horwath LLP Sherman Oaks, CA
Donald A. Erickson Erickson Partners, LLC Dallas, TX
Professor James Morris University of Colorado Denver, CO
Professor Thomas J. Frecka University of Notre Dame Notre Dame, IN
George Pushner Duff & Phelps LLC New York, NY
Michael Hamilton FTI Consulting New York, NY
Jeffrey Tarbell Houlihan Lokey Howard & Zukin San Francisco, CA
Jim Hitchner The Financial Valuation Group Atlanta, GA
Richard M. Wise Wise, Blackman, LLP Montreal (Quebec), Canada
In addition, we thank:
Kimberly Short of Shannon Pratt Valuations, Inc., for assistance with editing and research, including updating of the bibliography; updating and shepherding the manuscript among reviewers, contributors, authors, and publisher; typing; obtaining permissions; and other invaluable help. David Turney of Duff & Phelps, LLC, for preparing numerous tables and calculations that appear throughout the book. Harold Martin of Keiter, Stephens, Hurst, Gary & Shreaves, P.C., for contributing Appendix 17.1 on using the weighted average cost of capital with a constant capital structure. Professor James Morris, University of Colorado at Boulder, for contributing Appendix 17.2 on using the weighted average cost of capital with a changing capital structure. David Ptashne, CFA, of Duff & Phelps, LLC, for contributing Appendices 10.1, 10.2, and 11.1 on beta calculations. James Harrington with Morningstar for contributing Chapter 19 on using Morningstar Inc. cost of capital data as well as assisting in obtaining permissions for Morningstar exhibits used herein. xxiii
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Joel M. Stern, G. Bennett Stewart III, and Donald H. Chew Jr. for contributing Chapter 24 on economic value added. William Frazier of Howard Frazier Barker Elliott, Inc., for contributing Chapter 28 on the cost of capital in private investment companies. Jim MacCrate, MAI, of MacCrate Associates, LLC, for his contribution of Chapters 37, Appendix 37.1, and Chapter 36 and Appendix 36.1 on the cost of capital in real estate. Carl Hoemke of Duff & Phelps, LLC, for contributing Chapter 38 on the cost of capital in ad valorem taxation. David Fein of ValuSource for contributing the revised and updated Appendix E on ValuSource Pro. Mark Shirley of V & L Consultants, LLP, for contributing Appendix F on statistical analysis. Noah Gordon of Shannon Pratt Valuations, Inc., for assistance with researching and updating legal cases, as well as general editorial assistance.
For the granting of permissions, we would like to thank:
Professor Edwin Burmeister, Duke University
Business Valuation Resources, LLC Center for Research in Security Prices, University of Chicago
Professors Elroy Dimson, Paul Marsh, and Mike Staunton
Duff & Phelps, LLC John D. Emory Sr. and John D. Emory Jr., Emory & Co.
FactSet Mergerstat, LLC FMV Opinions, Inc.
Professor Arthur Korteweg, University of Chicago
Jim MacCrate, MacCrate Associates, LLC The McGraw-Hill Companies, Inc.
Morningstar, Inc. Glen Mueller, Dividend Capital Group
National Association of Real Estate Investment Trusts Pluris Valuation Advisors, LLC
PricewaterhouseCoopers, LLP
Standard & Poor’s (a division of McGraw-Hill) Thomson Corporation
Valuation Advisors, LLC
Thank you to those whose ideas contributed to several of the analyses incorporated herein:
David King, Mesirow Financial Consulting LLC
Professor Timothy Leuhrman, Harvard University
We thank all of the people singled out above for their assistance of course, any errors herein are our responsibility. Shannon Pratt Roger Grabowski
Introduction
PURPOSE AND OBJECTIVE OF THIS BOOK The purpose of this book is to present both the theoretical development of cost of capital estimation and its practical application to valuation, capital budgeting, forecasting of expected investment returns, and rate-setting problems encountered in current practice. It is intended both as a learning text for those who want to study the subject and as a handy reference for those who are interested in background or seek direction in some specific aspect of cost of capital. The objective is to serve two primary categories of users: 1. The practitioner who seeks a greater understanding of the latest theory and practice in cost of capital estimation 2. The reviewer who needs to make an informed evaluation of another party’s methodology and data used to produce a cost of capital estimate
OVERVIEW In this text, the reader can expect to learn about:
The theory of what drives the cost of capital
The models currently in use to estimate cost of capital The data available as inputs to the models to estimate cost of capital
How to use the cost of capital estimate in: Valuation
Feasibility studies Corporate finance decisions
Forecasting expected investment returns
How to reflect minority/control and marketability considerations Explanation of terminology, with its unfortunately varied and sometimes ambiguous usage in current-day financial analysis
IMPORTANCE OF THE COST OF CAPITAL The cost of capital estimate is the essential link that enables us to convert a stream of expected income into an estimate of present value. Doing this allows us to make informed pricing decisions for purchases and sales and to compare one investment opportunity against another.
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Introduction
COST OF CAPITAL ESSENTIAL IN THE MARKETPLACE In valuation and financial decision making, the cost of capital estimate is just as important as the estimate of the expected amounts of income to be discounted or capitalized. Yet we continually see income estimates laboriously developed and then converted to estimated value by a cost of capital that is practically pulled out of thin air. In the marketplace, better-informed cost of capital estimation will improve literally billions of dollars’ worth of financial decisions every day. For example, small differences in discount rates, and especially small differences in capitalization rates, can make very large differences in concluded values.
SOUND SUPPORT ESSENTIAL IN THE COURTROOM In the courts, billions of dollars turn on experts’ disputed cost of capital estimates in many contexts:
Gift, estate, and income tax disputes
Dissenting stockholder suits Corporate and partnership dissolutions
Marital property settlements Employee stock ownership plans (ESOPs)
Ad valorem (property) taxes
Utility rate-setting Damages calculations
Fortunately, courts are becoming unwilling to accept the statement ‘‘Trust me, I’m a great expert’’ in these disputes and instead are carefully weighing the quality of supporting evidence presented by opposing sides. Because cost of capital is critical to the valuation of any ongoing business, the thorough understanding, analysis, and presentation of cost of capital issues will go a long way toward carrying the day in a battle of experts in a legal setting.
ORGANIZATION OF THIS BOOK PART I. COST OF CAPITAL BASICS Chapter 1 defines the concept of cost of capital. Chapter 2 describes, in a general sense, how it is used in business valuation and capital budgeting. Chapter 3 defines net cash flow, explains why it is the preferred economic income variable for valuation and capital budgeting, and discusses issues relative to measuring expected net cash flow. Chapter 4 explains the difference between discounting and capitalizing. Chapter 5 addresses the concept of risk and the impact of risk on the cost of capital. Chapter 6 discusses the various components of a company’s capital structure. PART II. ESTIMATING THE COST OF EQUITY CAPITAL The second part explores cost of capital estimation. We begin with the build-up model (Chapter 7) and the Capital Asset Pricing Model (CAPM) (Chapter 8), two of the most widely used models for estimating cost of equity capital. With the backgrounds of those chapters, we then discuss a major input into these
Introduction
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models (and in all other cost of capital models), the equity risk premium, in Chapter 9. We then discuss other inputs into these models: making beta estimates for CAPM (Chapter 10) and one correction to the CAPM called the size effect (Chapter 12). In Chapter 11 we discuss the criticism of CAPM and beta as sole risk measures, and present alternative risk measures, while in Chapter 13 we discuss the criticisms of the size effect. In Chapter 14 we discuss company-specific risk. In Chapter 15 we then present alternative cost of equity capital models, such as the Fama-French 3-factor model. In Chapter 16 we present methods for deriving implied cost of capital estimates using discounted cash flow (DCF) and residual income models. In Chapter 17 we discuss the overall cost of capital based on the concept of a weighted average of the cost of each component of the capital structure (commonly referred to as the weighted average cost of capital) and how changes in the capital structure affect the cost of equity capital. We include appendices with detailed explanations of the iterative process for cost of equity capital estimation for nonpublic businesses (divisions, reporting units, closely held firms) in the context of the weighted average cost of capital. The models presented thus far are based on estimating the cost of equity for companies and investments in developed economies. In Chapter 18 we discuss alternative models for estimating the cost of equity capital for companies and investments in developing economies. Chapter 19 contains a discussion of the various data sources available from Ibbotson Associates, now part of Morningstar, for use in estimating the cost of capital. PART III. CORPORATE FINANCIAL OFFICERS—USING COST OF CAPITAL DATA The third part explores use of the cost of capital data in capital budgeting and feasibility studies in Chapter 20, determining cost of capital for divisions and reporting units in Chapter 21, using the data in evaluating mergers and acquisitions in Chapter 22, cost of capital in transfer pricing in Chapter 23, and using the data within the framework of an Economic Value Added (EVA1) financial management system in Chapter 24. PART IV. COST OF CAPITAL FOR CLOSELY HELD ENTITIES Part IVaddresses commonly encountered variations in cost of capital application particularly within the context of closely held entities. Chapter 25 covers handling discounts for lack of marketability. Chapters 26 to 28 address cost of capital for pass-through entities: partnerships, limited liability corporations, S corporations, and private investment companies. Chapter 29 focuses on venture capital investments. PART V. OTHER TOPICS Chapter 30 discusses minority versus controlling interest valuations. In Chapter 31 we discuss how the cost of capital relates to the excess earnings valuation method. Chapter 32 discusses adjusting the discount rate when the measure of economic income is some measure other than net cash flow. While this book is not a treatise on forecasting, we discuss issues in estimating net cash flows in Chapter 33. Chapter 34 covers common errors in estimating discount rates and future economic income, and Chapter 35 presents court case examples of cost of capital issues. PART VI. REAL ESTATE AND AD VALOREM Given the specialized nature of real estate, we present information on developing cost of capital estimates for real property investments, real estate investment trusts, and are within the context of ad valorem taxation in Chapters 36 through 38.
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Introduction
PART VII. ADVICE TO PRACTITIONERS Chapter 39 provides issue-by-issue advice on handing real-world cost of capital estimation issues. Chapter 40 provides questions for attorneys to use in cross-examining experts on cost of capital. APPENDICES The appendices provide sources for follow-up to this book, including a detailed bibliography in Appendix I, sources for the current data needed to implement cost of capital estimation in Appendix II, a glossary of business valuation terms in Appendix III, a sample report in Appendix IV, information on how to use ValuSource valuation software in Appendix V, and a review of statistical analysis in Appendix VI.
SUMMARY The book is designed to serve as both a primer and a reference source. Part I covers cost of capital basics. Part II covers the methods generally used to estimate cost of equity capital. Part III covers a variety of topics commonly encountered by the corporate financial officer. Part IV covers issues peculiar to closely held entities. Part V covers a variety of topics integral to users of cost of capital data. Part VI covers real property cost of capital issues. Part VII covers real-world cost estimation issues. The appendices provide a directory for further study and data sources.
Notation System and Abbreviations Used in This Book A source of confusion for those trying to understand financial theory and methods is that financial writers have not adopted a standard system of notation. The notation system used in this volume is adapted from the fifth edition of Valuing a Business: The Analysis and Appraisal of Closely Held Companies, by Shannon P. Pratt (New York: McGraw-Hill, 2007).
VALUE AT A POINT IN TIME PV ¼ Present value (seen as Pi in Chapter 19) PVb ¼ Present value of net cash flows due to business operations before cost of financing PVeu ¼ Present value of unlevered equity PVTSD ¼ Present value of tax savings on debt PVe ¼ Present value of equity FV ¼ Future value MVIC ¼ Market value of invested capital ¼ Enterprise value ¼ Me þ Md þ M p BV ¼ Book value of net assets FVRU ¼ Fair value of reporting unit FVNWCRU ¼ Fair value of net working capital of the reporting unit FVICRU ¼ Fair value of invested capital of the reporting unit FVFARU ¼ Fair value of fixed assets of the reporting unit FVIARU ¼ Fair value on intangible assets, identified and individually valued, of the reporting unit FVUIVRU ¼ Fair value of unidentified intangibles value (i.e., ‘‘goodwill’’) of the reporting unit FVdRU ¼ Fair value of debt capital of the reporting unit FVeRU ¼ Fair value of equity capital of the reporting unit FMVBE ¼ Fair market value of the business enterprise FMVNWC ¼ Fair market value of net working capital FMVFA ¼ Fair market value of fixed assets FMVIA ¼ Fair market value on intangible assets FMVUIV ¼ Fair market value of unidentified intangibles value (i.e., ‘‘goodwill’’) FMVe ¼ Fair market value of equity capital
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Notation System and Abbreviations Used in This Book
COST OF CAPITAL AND RATE OF RETURN VARIABLES k ¼ Discount rate (generalized) kc ¼ Country cost of equity ke ¼ Discount rate for common equity capital (cost of common equity capital) (seen as ki in Chapter 19). Unless otherwise stated, it generally is assumed that this discount rate is applicable to net cash flow available to common equity. ke500 ¼ Cost of equity for the S&P 500 keu ¼ Cost of equity capital, unlevered (cost of equity capital assuming firm financed with all equity) kni ¼ Discount rate for equity capital when net income rather than net cash flow is the measure of economic income being discounted kð ptÞ ¼ Discount rate applicable to pretax cash flows keð ptÞ ¼ Cost of equity prior to tax affect k p ¼ Discount rate for preferred equity capital kd ¼ Discount rate for debt (net of tax affect, if any) (Note: For complex capital structures, there could be more than one class of capital in any of the preceding categories, requiring expanded subscripts.) ¼ kdð ptÞ (1 – tax rate) kdð ptÞ ¼ Cost of debt prior to tax effect kTS ¼ Rate of return used to present value tax savings due to deducting interest expense on debt capital financing kNWCð ptÞ ¼ Rate of return for net working capital financed with debt capital (measured pretax) and equity capital kFAð ptÞ ¼ Rate of return for fixed assets financed with debt capital (measured pretax) and equity capital kdRU ¼ After-tax rate of return on debt capital of the reporting unit ¼ kdð ptÞRU (1 – tax rate) kdð ptÞRU ¼ Rate of return on debt capital of the reporting unit without taking into account the tax deduction on interest expense (pretax cost of debt capital) keRU ¼ After-tax rate of return on equity capital of the reporting unit kNWC ¼ Rate of return for net working capital kNWCRU ¼ Rate of return for net working capital of the reporting unit financed with debt capital (return measured after-tax) and equity capital kNWCð ptÞRU ¼ Rate of return for net working capital of the reporting unit financed with debt capital (measured pretax) and equity capital kFA ¼ Rate of return for fixed assets kFARU ¼ Rate of return for fixed assets financed with debt capital (return measured after tax) and equity capital kFAð ptÞRU ¼ Rate of return for fixed assets of the reporting unit financed with debt capital (measured pretax) and equity capital
Notation System and Abbreviations Used in This Book
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kIA ¼ Rate of return for intangible assets kIARU ¼ Rate of return for identified and individually valued intangible assets financed with debt capital (return measured after tax) and equity capital kUIV ¼ Rate of return for unidentified intangibles value kUIVRU ¼ Rate of return for unidentified intangibles value of the reporting unit financed with debt capital (return measured after tax) and equity capital kIAþUIV ¼ After-tax rate of return on all intangible assets, identified and individually valued, plus the unidentified intangible value kIAþUIVð ptÞ ¼ Pretax rate of return on all intangible assets, identified and individually valued, plus the unidentified intangible value financed with debt capital (measured pretax) and equity capital kIAþUIVRU ¼ After-tax rate of return on all intangible assets, identified and individually valued, of the reporting unit plus the unidentified intangible value of the reporting unit kIAþUIVð ptÞRU ¼ Pretax rate of return on all intangible assets, identified and individually valued, plus the unidentified intangible value of the reporting unit financed with debt capital (measured pretax) and equity capital kTSRU ¼ Rate of return used to present value tax savings due to deducting interest expense on debt capital financing of the reporting unit c ¼ Capitalization rate ce ¼ Capitalization rate for common equity capital. Unless otherwise stated, it generally is assumed that this capitalization rate is applicable to net cash flow available to common equity. Cni ¼ Capitalization rate for net income cð ptÞ ¼ Capitalization rate on pretax cash flows c p ¼ Capitalization rate for preferred equity capital cd ¼ Capitalization rate for debt (Note: For complex capital structures, there could be more than one class of capital in any of the preceding categories, requiring expanded subscripts.) D=P ¼ Dividend yield on stock DR j ¼ Downside risk in the local market (U.S. dollars) DRw ¼ Downside risk in global (‘‘world’’) market (U.S. dollars) Pn ¼ Stock price in period n P0 ¼ Stock price at valuation period R ¼ Rate of return R f ¼ Rate of return on a risk-free security R f ;n ¼ Risk-free rate in current month R f local ¼ Return on the local country government’s (default-risk-free) paper R f u:s: ¼ U.S. risk-free rate Rlocaleuro$issue ¼ Current market interest rate on debt issued by the local country government denominated in U.S. dollars (‘‘euro-dollar’’ debt), same maturity as debt issued by the local country government denominated in U.S. dollars
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Notation System and Abbreviations Used in This Book
Rn ¼ Return on individual security subject stock in current month Rm ¼ Historical rate of return on the ‘‘market’’ RP ¼ Risk premium RPm ¼ Risk premium for the ‘‘market’’ (usually used in the context of a market for equity securities, such as the NYSE or S&P 500) RPs ¼ Risk premium for ‘‘small’’ stocks (usually average size of lowest quintile or decile of NYSE as measured by market value of common equity) over and above RPm RPmþs ¼ Risk premium for the market plus risk premium for size (Duff & Phelps Risk premium report data for use in build-up method) RPu ¼ Risk premium for company specific or unsystematic risk attributable to the specific company RPw ¼ The equity risk premium on a ‘‘world’’ diversified portfolio RPi ¼ Risk premium for the ith security (seen in Chapter 19 as IRPi) RPlocal ¼ Equity risk premium in local country’s stock market RIi ¼ Risk index (full-information beta) for industry i RIiL ¼ Full-information levered beta estimate of the subject company EðRÞ ¼ Expected rate of return EðRm Þ ¼ Expected rate of return on the ‘‘market’’ (usually used in the context of a market for equity securities, such as the New York Stock Exchange [NYSE] or Standard & Poor’s [S&P] 500) EðRi Þ ¼ Expected rate of return on security i EðRdiv Þ ¼ Expected rate of return on dividend EðRcapgains Þ ¼ Expected rate of return on capital gains B ¼ Beta (a coefficient, usually used to modify a rate of return variable) BL ¼ Levered beta for (equity) capital BU ¼ Unlevered beta for (equity) capital BLS ¼ Levered segment beta Bd ¼ Beta for debt capital BUi ¼ Beta unlevered for industry (or guideline companies) equity capital BLi ¼ Beta levered for industry (or guideline companies) equity capital Be ¼ Beta (equity) expanded Bop ¼ Operating beta (beta with effects of fixed operating expense removed) Bi ¼ Beta of company i (F-F Beta) Bn ¼ Estimated market coefficient based on sensitivity to excess returns on market portfolio in current month Bn1 ¼ Estimated lagged market coefficient based on sensitivity to excess returns on market portfolio last month Blocal ¼ Market risk of the subject company measured with respect to the local securities market Bw ¼ Market or systematic risk measured with respect to a ‘‘world’’ portfolio of stocks
Notation System and Abbreviations Used in This Book
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bcw ¼ Country covariance with world bcr ¼ Country covariance with region K1 :::Kn ¼ Risk premium associated with risk factor 1 through n for the average asset in the market (used in conjunction with arbitrage pricing theory) si ¼ Small-minus-big coefficient in the Fama-French regression SMBP ¼ Expected small-minus-big risk premium, estimated as the difference between the historical average annual returns on the small-cap and large-cap portfolios hi ¼ High-minus-low coefficient in the Fama-French regression HMLP ¼ Expected high-minus-low risk premium, estimated as the difference between the historical average annual returns on the high book-to-market and low book-to-market portfolios Fd ¼ Face value of outstanding debt WACCð ptÞ ¼ Weighted average cost of capital (pretax) WACCBE ¼ Overall rate of return for the business enterprise WACCð ptÞBE ¼ Pretax WACC of the business enterprise WACCRU ¼ Overall rate of return for the reporting unit WACCð ptÞRU
¼ Weighted average cost of capital for the reporting unit ¼ Pretax WACC of the reporting unit
Me ¼ Market value of equity capital (stock) Md ¼ Market value of debt capital M p ¼ Market value of preferred equity s 2 ¼ Variance of returns for subject company stock s 2M ¼ Variance of the returns on the market portfolio (e.g., S&P 500) s 2e ¼ Variance of error terms s ¼ Standard deviation s B ¼ Standard deviation of operating cash flows of business before cost of financing s rev ¼ Standard deviation of revenues of output s local ¼ Volatility of subject (local) stock market s u:s: ¼ Volatility of U.S. stock market s stock ¼ Volatility of local country’s stock market s bond ¼ Volatility of local country’s bond market dr ¼ Regional risk not included in RPw CCRc ¼ Country credit rating of country l ¼ Company’s exposure to the local country risk t ¼ Tax rate (expressed as a percentage of pretax income) ti ¼ Federal and state income tax rate for industry (or guideline companies) r ¼ Property tax rate (expressed as a percentage of total fair market value) C ¼ Proportion of the entity that is assessed property tax h ¼ Holding period
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Notation System and Abbreviations Used in This Book
INCOME VARIABLES E ¼ Expected economic income (in a generalized sense; i.e., could be dividends, any of several possible definitions of cash flows, net income, etc.) F ¼ Fixed operating assets (without regard to costs of financing) Fc ¼ Fixed operating costs of the business NI ¼ Net income (after entity-level taxes) CF ¼ Cash flow for a specific period NCFe ¼ Net cash flow (free cash flow) to equity NCF f ¼ Net cash flow (free cash flow) to the firm (to overall invested capital, or entire capital structure, including all equity and long-term debt) NCFue ¼ Net cash flow to unlevered equity PMT ¼ Payment (interest and principal payment on debt security) D ¼ Dividends T ¼ Tax (in U.S. dollars) TS ¼ Present value of tax savings due to deducting interest expense on debt capital financing GCF ¼ Gross cash flow (usually net income plus noncash charges) EBT ¼ Earnings before taxes EBIT ¼ Earnings before interest and taxes EBITD ¼ Earnings before depreciation, interest, and taxes (‘‘Depreciation’’ in this context usually includes amortization. Some writers use EBITDA specifically to indicate that amortization is included.) EBITDA ¼ Earnings before interest, taxes, depreciation, and amortization V ¼ Variable operating assets
PERIODS OR VARIABLES IN A SERIES i ¼ ith period or ith variable in a series (may be extended to the jth variable, the kth variable, etc.) n ¼ Number of periods or variables in a series, or the last number in a series 0 ¼ Period 0, the base period, usually the latest year immediately preceding the valuation date py ¼ Partial year of first year following the valuation date
WEIGHTINGS W ¼ Weight We ¼ Weight of common equity in capital structure WeRU
¼ Me =Me þ Md ¼ Weight of equity capital in structure of reporting unit
Notation System and Abbreviations Used in This Book
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¼ Fair value of equity capital/FVRU W p ¼ Weight of preferred equity in capital structure ¼ M p =Me þ Md þ M p Wd ¼ Weight of debt in capital structure ¼ Md =Me þ Md (Note: For purposes of computing a weighted average cost of capital [WACC], it is assumed that preceding weightings are at market value.) Wdi ¼ Weight of interest-bearing debt in capital structure at market for industry (or guideline companies) WdRU ¼ Weight of debt capital in capital structure of reporting unit ¼ Fair value of debt capital/FVRU Wei ¼ Weight of common equity in capital structure at market for industry (or guideline companies) Ws ¼ Weight of segment data to total business (e.g., sales, operating income) WNWC ¼ Weight of net working capital in FMVBE ¼ FMVNWC =FMVBE WNWCRU ¼ Weight of net working capital in FVRU ¼ FVNWCRU =FVRU WFA ¼ Weight of fixed assets in FMVBE WFARU WIA
¼ FMVFA =FMVBE ¼ Weight of fixed assets in FVRU ¼ FVFARU =FVRU ¼ Weight of intangible assets in FMVBE ¼ FMVIA =FMVBE
WIARU ¼ Weight of intangible assets in FVRU ¼ FVIARU =FVRU WUIV ¼ Weight of unidentified intangibles value FMVBE ¼ FMVUIV (i.e., ‘‘goodwill’’)=FMVBE WUIVRU ¼ Weight of unidentified intangibles value FVRU WIAþUIV
WIAþUIVRU
¼ FVUIVRU (i.e., ‘‘goodwill’’)=FVRU ¼ Weight of intangible assets in FMVBE plus the weight of unidentified intangible value in FMVBE ¼ ðFMVIA þ FMVUIV Þ=FMVBE ¼ Weight of intangible assets in FVRU plus the weight of unidentified intangible value in FVRU
¼ ðFVIARU þ FVUIVRU Þ=FVRU WTS ¼ Weight of TS in FMVBE WTSRU
¼ TS=FMVBE ¼ Weight of TS in FVRU ¼ TS=FVRU
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Notation System and Abbreviations Used in This Book
GROWTH g ¼ Rate of growth in a variable (e.g., net cash flow) gni ¼ Rate of growth in net income
MATHEMATICAL FUNCTIONS S ¼ Sum of (add all the variables that follow) \ ¼ Product of (multiply together all the variables that follow) X ¼ Mean average (the sum of the values of the variables divided by the number of variables) G ¼ Geometric mean (product of the values of the variables taken to the root of the number of variables) a ¼ Regression constant e ¼ Regression error term 1 ¼ Infinity
NOTATION FOR REAL PROPERTY VALUATION (CHAPTER 36) DSCR ¼ Debt service coverage ratio EGIM ¼ Effective gross income multiplier NOI; Ip ¼ Net operating income OER ¼ Operating expense rates ke ¼ Equity discount or yield rate (dividend plus appreciation) km ¼ Mortgage interest rate kp ¼ Overall property discount rate cp ¼ Overall property capitalization rate ce ¼ Dividend to equity capitalization rate cm ¼ Mortgage capitalization rate or constant cn ¼ Terminal or residual or going-out capitalization rate cB ¼ Building capitalization rate cL ¼ Land capitalization rate cLF ¼ Leased fee capitalization rate cLH ¼ Leasehold capitalization rate A ¼ Change in income and value (adjustment factor) P ¼ Principal paid off over the holding period 1=Sn ¼ Sinking fund factor at the equity discount or yield rate (ke ) D0 ¼ Change in value over the holding period SC% ¼ Cost of sale PGI ¼ Potential gross income PGIM ¼ Potential gross income multiplier
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EGI ¼ Effective gross income Fd =PVp ¼ Face value of debt (loan amount outstanding) to value ratio ½1 ðFd =PVp Þ ¼ Equity to value ratio MB ¼ Building value Mm ¼ Mortgage value ML ¼ Land value MLF ¼ Leased fee value MLH ¼ Leasehold value Ip ¼ Overall income to the property IL ¼ Residual income to the land IB ¼ Residual income to the building Ie ¼ Equity income Im ¼ Mortgage income ILF ¼ Income to the leased fee ILH ¼ Income to the leasehold
ABBREVIATIONS ERP ¼ Equity risk premium (usually the general equity risk premium for which the benchmark for equities is either the S&P 500 stocks or the NYSE stocks) WACC ¼ Weighted average cost of capital WARA ¼ Weighted average return on assets T-Bill ¼ U.S. government bill (usually 30-day, but can be up to one year) STRIPS ¼ Separate trading of registered interest and principal of securities CRSP ¼ Center for Research in Security Prices, at the University of Chicago PIPE ¼ Private Investment in Public Equity SBBI ¼ Stocks, Bonds, Bills, and Inflation, published annually by Ibbotson Associates (now Morningstar) in both a ‘‘Classic edition’’ and a ‘‘Valuation edition’’ CAPM ¼ Capital Asset Pricing Model DCF ¼ Discounted cash flow DDM ¼ Discounted dividend model TIPS ¼ Treasury Inflation-Protected Security NCF ¼ Net cash flow (also sometimes interchangeably referred to as FCF, free cash flow) BE ¼ Business enterprise or reporting unit NWC ¼ Net working capital FA ¼ Fixed assets IA ¼ Intangible assets UIV ¼ Unidentified intangible value (i.e., ‘‘goodwill’’) NOPAT ¼ Net operating profit after taxes
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Notation System and Abbreviations Used in This Book
PAT ¼ Profit after tax ¼ Net Income RI ¼ Residual income EVA ¼ Economic value added DY ¼ Dividend yield RE ¼ Residual earnings AEG ¼ Abnormal earnings growth ROCE ¼ Return on common equity RNOA ¼ Return on net operating assets FLEV ¼ Net financial obligations/(Net operating assets net financial obligations) (i.e., financial leverage) SPREAD ¼ RNOA Net borrowing costs [(financial expense financial income, after tax)/(financial obligations financial assets)] io ¼ Implicit interest charges on operating liabilities (other than deferred taxes) OI ¼ Operating income OA ¼ Operating assets OL ¼ Operating liabilities OI ¼ Operating income NICE ¼ Nonmarketable investment company evaluation REIT ¼ Real estate investment trusts
Part 1
Cost of Capital Basics
Chapter 1
Defining Cost of Capital Introduction Components of a Company’s Capital Structure Cost of Capital is a Function of the Investment Cost of Capital is Forward Looking Cost of Capital is Based on Market Value, Not Book Value Cost of Capital is Usually Stated in Nominal Terms Cost of Capital Equals the Discount Rate Discount Rate is Not the Same as Capitalization Rate Summary
INTRODUCTION Cost of capital is the expected rate of return that the market participants require in order to attract funds to a particular investment. In economic terms, the cost of capital for a particular investment is an opportunity cost—the cost of forgoing the next best alternative investment. In this sense, it relates to the economic principle of substitution—that is, an investor will not invest in a particular asset if there is a more attractive substitute. The term market refers to the universe of investors who are reasonable candidates to provide funds for a particular investment. Capital or funds are usually provided in the form of cash, although in some instances capital may be provided in the form of other assets. The cost of capital usually is expressed in percentage terms, that is, the annual amount of dollars that the investor requires or expects to realize, expressed as a percentage of the dollar amount invested. Put another way: Since the cost of anything can be defined as the price one must pay to get it, the cost of capital is the return a company must promise in order to get capital from the market, either debt or equity. A company does not set its own cost of capital; it must go into the market to discover it. Yet meeting this cost is the financial market’s one basic yardstick for determining whether a company’s performance is adequate.1
As the quote suggests, most of the information for estimating the cost of capital for any company, security, or project comes from the investment markets. The cost of capital is always an expected (or forward-looking) return. Thus, analysts and would-be investors never actually observe it. We analyze many types of market data to estimate the cost of capital for a company, security, or project in which we are interested.
1
Mike Kaufman, ‘‘Profitability and the Cost of Capital,’’ in Chapter 8 of Handbook of Budgeting, 4th ed., ed. Robert Rachlin (New York: John Wiley & Sons, 1999), 8–3.
3
4
Cost of Capital
As Roger Ibbotson put it, ‘‘The Opportunity Cost of Capital is equal to the return that could have been earned on alternative investments at a specific level of risk.’’2 In other words, it is the competitive return available in the market on a comparable investment, with risk being the most important component of comparability.
COMPONENTS OF A COMPANY’S CAPITAL STRUCTURE The term capital in this context means the components of an entity’s capital structure. The primary components of a capital structure include:
Debt capital Preferred equity (stock or partnership interests with preference features, such as seniority in receipt of dividends or liquidation proceeds) Common equity (stock or partnership interests at the lowest or residual level of the capital structure)
There may be more than one subcategory in any or all of the listed categories of capital. Also, there may be related forms of capital, such as warrants or options. Each component of an entity’s capital structure has its unique cost, depending primarily on its respective risk. The next quote explains how the cost of capital can be viewed from three different perspectives: On the asset side of a firm’s balance sheet, it is the rate that should be used to discount to a present value the future expected cash flows. On the liability side, it is the economic cost to the firm of attracting and retaining capital in a competitive environment, in which investors (capital providers) carefully analyze and compare all return-generating opportunities. On the investor’s side, it is the return one expects and requires from an investment in a firm’s debt or equity. While each of these perspectives might view the cost of capital differently, they are all dealing with the same number.3
When we talk about the cost of ownership capital (e.g., the expected return to a stock or partnership investor), we usually use the phrase cost of equity capital. When we talk about the cost of capital to the firm overall (e.g., the average cost of capital for both equity ownership interests and debt), we commonly use the phrases weighted average cost of capital (WACC) or blended cost of capital overall cost of capital. Simply and cogently stated, ‘‘The cost of equity is the rate of return investors require on an equity investment in a firm.’’4 Recognizing that the cost of capital applies to both debt and equity investments, a well-known text states: Since free cash flow is the cash flow available to all financial investors (debt, equity, and hybrid securities), the company’s Weighted Average Cost of Capital (WACC) must include the required return for each investor.5 2 3 4
5
Ibbotson Associates, Cost of Capital Workshop (Chicago: Ibbotson Associates, 1999). Stocks, Bonds, Bills and Inflation Valuation Edition 2007 Yearbook (Chicago: Morningstar, 2007), 23. Aswath Damodaran, Investment Valuation: Tools and Techniques for Determining the Value of Any Asset, 2nd ed. (Hoboken, NJ: John Wiley & Sons, 2002), 182. Tim Koller, Marc Goedhart, and David Wessels, Valuation: Measuring and Managing the Value of Companies, 4th ed. (Hoboken, NJ: John Wiley & Sons, 2005), 291.
Cost of Capital is Forward Looking
5
COST OF CAPITAL IS A FUNCTION OF THE INVESTMENT As Ibbotson puts it, ‘‘The cost of capital is a function of the investment, not the investor.’’6 The cost of capital comes from the marketplace. The marketplace is the universe of investors ‘‘pricing’’ the risk of a particular asset. Allen, Brealey, and Myers state the same concept: ‘‘The true cost of capital depends on the use to which the capital is put.’’7 They make the point that it would be an error to evaluate a potential investment on the basis of a company’s overall cost of capital if that investment were more or less risky than the company’s existing business. ‘‘Each project should in principle be evaluated at its own opportunity cost of capital.’’8 When a company uses a given cost of capital to evaluate a commitment of capital to an investment or project, it often refers to that cost of capital as the hurdle rate. The hurdle rate is the minimum expected rate of return that the company would be willing to accept to justify making the investment. As noted, the hurdle rate for any given prospective investment may be at, above, or below the company’s overall cost of capital, depending on the degree of risk of the prospective investment compared to the company’s overall risk. The most popular focus of contemporary corporate finance is that companies should be making investments, either capital investments or acquisitions, from which the returns will exceed the cost of capital for that investment. Doing so creates economic value added, economic profit, or shareholder value added.9
COST OF CAPITAL IS FORWARD LOOKING The cost of capital represents investors’ expectations. There are two elements to these expectations: 1. The risk-free rate, which includes: The ‘‘real’’ rate of return—the amount (excluding inflation) investors expect to obtain in exchange for letting someone else use their money on a risk-free basis. Expected inflation—the expected depreciation in purchasing power while the money is in use. 2. Risk—the uncertainty as to when and how much cash flow or other economic income will be received. It is the combination of the first two items that is sometimes referred to as the time value of money. While these expectations, including assessment of risk, may be different for different investors, the market tends to form a consensus with respect to a particular investment or category of investments. That consensus determines the cost of capital for investments of varying levels of risk. The cost of capital, derived from investors’ expectations and the market’s consensus of those expectations, is applied to expected economic income, usually measured in terms of cash flows, in order to estimate present values or to compare investment alternatives of similar or differing levels of risk. Present value, in this context, refers to the dollar amount that a rational and well-informed investor 6 7
8 9
Ibbotson Associates, Cost of Capital Workshop (Chicago: Ibbotson Associates, 1999). Richard A. Brealey, Stewart C. Myers, and Franklin Allen, Principles of Corporate Finance, 8th ed. (Boston: Irwin McGrawHill, 2006), 216. Ibid. See, for example, Tim Koller, Marc Goedhart, and David Wessels, Valuation: Measuring and Managing the Value of Companies, 4th ed. (Hoboken, NJ: John Wiley & Sons, 2005); also see Alfred Rappaport, Creating Shareholder Value, rev. ed. (New York: The Free Press, 1997).
6
Cost of Capital
would be willing to pay today for the stream of expected economic income. In mathematical terms, the cost of capital is the percentage rate of return that equates the stream of expected income with its present cash value (see Chapter 4).
COST OF CAPITAL IS BASED ON MARKET VALUE, NOT BOOK VALUE The cost of capital is the expected rate of return on some base value. That base value is measured as the market value of an asset, not its book value. For example, the yield to maturity shown in the bond quotations in the financial press is based on the closing market price of a bond, not on its face value. Similarly, the implied cost of equity for a company’s stock is based on the market price per share at which it trades, not on the company’s book value per share of stock. It was noted earlier that the cost of capital is estimated from market data. This data refers to expected returns relative to market prices. By applying the cost of capital derived from market expectations to the expected cash flows (or other measure of economic income) from the investment or project under consideration, the market value can be estimated.
COST OF CAPITAL IS USUALLY STATED IN NOMINAL TERMS Keep in mind that we have talked about expectations, including inflation. The return an investor requires includes compensation for reduced purchasing power of the dollar over the life of the investment. Therefore, when the analyst or investor applies the cost of capital to expected returns in order to estimate value, he or she must also include expected inflation in those expected returns. This obviously assumes that investors have reasonable consensus expectations regarding inflation. For countries subject to unpredictable hyperinflation, it is sometimes more practical to estimate cost of capital in real terms rather than in nominal terms.10
COST OF CAPITAL EQUALS THE DISCOUNT RATE The essence of the cost of capital is that it is the percentage return that equates expected economic income with present value. The expected rate of return in this context is called a discount rate. By discount rate, the financial community means an annually compounded rate at which each increment of expected economic income (e.g., net cash flow, net income, or some other measure of economic benefits) is discounted back to its present value. A discount rate reflects both time value of money and risk and therefore represents the cost of capital. The sum of the discounted present values of each future period’s incremental cash flow or other measure of return equals the present value of the investment, reflecting the expected amounts of return over the life of the investment. The terms discount rate, cost of capital, and required rate of return are often used interchangeably. The economic income referenced here represents total expected benefits. In other words, this economic income includes increments of cash flow realized by the investor while holding the investment as well as proceeds to the investor upon liquidation of the investment. The rate at which these expected future total returns are reduced to present value is the discount rate, which is the cost of capital (required rate of return) for a particular investment. 10
We discuss the problems with estimating cash flows and cost of capital in real terms in Chapter 18.
Summary
7
DISCOUNT RATE IS NOT THE SAME AS CAPITALIZATION RATE Because some practitioners confuse the terms, we point out here that discount rate and capitalization rate are two distinctly different concepts. As noted in the previous section, discount rate equates to cost of capital. It is a rate applied to all expected incremental returns to convert the expected return stream to a present value. A capitalization rate, however, is merely a divisor applied to one single element of return to estimate a present value. The only instance in which the discount rate is equal to the capitalization rate is when each future cash flow is equal (i.e., no growth), and the expected returns are in perpetuity. One of the few examples would be a preferred stock paying a fixed amount of dividend per share in perpetuity. The relationship between discount and capitalization rates is discussed in Chapter 4.
SUMMARY As stated in the introduction, ‘‘The cost of capital estimate is the essential link that enables us to convert a stream of expected income into an estimate of present value.’’ Cost of capital has several key characteristics:
It is market driven. It is the expected rate of return that the market requires to commit capital to an investment.
It is a function of the investment, not a particular investor; to make the discount rate a function of the particular investor would imply changing the standard of value to what is commonly termed investment value rather than fair market value. It is forward looking, based on expected returns. Past returns are, at best, to provide guidance as to what to expect in the future.
The base against which cost of capital is measured is market value, not book value. It is usually measured in nominal terms, that is, including expected inflation. It is the link, called a discount rate, that equates expected future returns for the life of the investment with the present value of the investment at a given date.
Chapter 2
Introduction to Cost of Capital Applications: Valuation and Project Selection Introduction Net Cash Flow is the Preferred Economic Income Measure Cost of Capital is the Proper Discount Rate Present Value Formula Example: Valuing a Bond Applications to Businesses, Business Interests, Projects, and Divisions Summary
INTRODUCTION Cost of capital has many applications, the two most common being valuation and capital investment project selection. These two applications are very closely related. This chapter discusses these two applications in very general terms so the reader can quickly understand how a proper estimation of the cost of capital underlies valuations and financial decisions worth billions of dollars every day. Later chapters discuss these applications in more detail.
NET CASH FLOW IS THE PREFERRED ECONOMIC INCOME MEASURE For the purpose of this chapter, we will assume that the measure of economic income to which cost of capital will be applied is net cash flow (sometimes called free cash flow). Net cash flow represents discretionary cash available to be paid out to stakeholders of a firm (providers of capital to the firm) (e.g., interest, debt payments, dividends, withdrawals, discretionary bonuses) without jeopardizing the projected ongoing operations of the business. We will provide a more exact definition of net cash flow in Chapter 3. Net cash flow to equity is that cash flow available to the equity holders, usually common equity. Net cash flow is the measure of economic income on which most financial analysts today prefer to focus for both valuation and capital investment project selection. Net cash flow represents money available to stakeholders, assuming the business is a going concern and the company is able to support the projected operations. Although the contemporary literature of corporate finance widely embraces a preference for net cash flow as the relevant economic income variable to which to apply cost
9
10
Cost of Capital
of capital for valuation and decision making, there is still a contingent of analysts who prefer to focus on reported or adjusted accounting income.1
COST OF CAPITAL IS THE PROPER DISCOUNT RATE At the end of Chapter 1, we said that the cost of capital is customarily used as a discount rate to convert expected future returns to a present value. This concept is summarized succinctly by Allen, Brealey, and Myers: ‘‘When you discount [a] project’s expected cash flow at its opportunity cost of capital, the resulting present value is the amount investors would be willing to pay for the project.’’2 In this context, let us keep in mind critical characteristics of a discount rate: Definition: A discount rate is a yield rate used to convert anticipated future payments or receipts into present value (i.e., a cash value as of a specified valuation date). A discount rate represents the total expected rate of return that the investor requires to realize on the amount invested. The use of the cost of capital to estimate present value thus requires two sets of estimates: 1. The numerator. The expected amount of return (e.g., the net cash flow) on the investment in each future period over the life of the investment. 2. The denominator. A function of the discount rate, which is the cost of capital, which, in turn, is the required rate of return. This function is usually written as ð1 þ kÞn . where: k ¼ Discount rate n ¼ Number of periods into the future when the returns are expected to be realized Usually analysts and investors make the simplifying assumption that the cost of capital is constant over the life of the investment and use the same cost of capital to apply to each increment of expected future return. There are, however, special cases in which analysts might choose to estimate a discrete cost of capital to apply to the expected return in each future period. (An example is when the analyst anticipates a changing weighted average cost of capital because of a changing capital structure.) Notwithstanding, well-known author, professor, and consultant Dr. Alfred Rappaport espouses a constant cost of capital in his book Creating Shareholder Value: The appropriate rate for discounting the company’s cash flow stream is the weighted average of the costs of debt and equity capital. . . . It is important to emphasize that the relative weights attached to debt and equity, respectively, are neither predicated on dollars the firm has raised in the past, nor do they constitute the relative proportions of dollars the firm plans to raise in the current year. Instead, the relevant weights should be based on the proportions of debt and equity that the firm targets for its capital structure over the long-term planning period.3
The latter view is most widely used in practice. 1
2
3
See, for example, Z. Christopher Mercer, Valuing Financial Institutions (Homewood, IL: Business One Irwin, 1992), Chapter 13; and his article ‘‘The Adjusted Capital Asset Pricing Model for Developing Capitalization Rates,’’ Business Valuation Review (December 1989): 147ff. Franklin Allen, Richard A. Brealey, and Stewart C. Myers, Principles of Corporate Finance, 8th ed. (Boston: Irwin McGrawHill, 2006), 20. Alfred Rappaport, Creating Shareholder Value: A Guide for Managers and Investors, rev. ed. (New York: The Free Press, 1997), 37.
Example: Valuing a Bond
11
PRESENT VALUE FORMULA Converting the concepts just discussed into a mathematical formula, we have the following formula, which is the essence of using cost of capital to estimate present value. (Formula 2.1) PV ¼
NCF1 NCF2 NCFn þ þ þ ð1 þ kÞ ð1 þ kÞ2 ð1 þ kÞn
where: PV ¼ Present value NCF1. . . NCFn ¼ Net cash flow (or other measure of economic income) expected in each of the periods 1 through n, n being the final cash flow in the life of the investment k ¼ Cost of capital applicable to the defined stream of net cash flow n ¼ Number of periods The critical job for the analyst is to match the cost of capital estimate to the definition of the economic income stream being discounted. This is largely a function of reflecting in the cost of capital estimate the degree of risk inherent in the expected cash flows being discounted. The relationship between risk and the cost of capital is the subject of Chapter 5.
EXAMPLE: VALUING A BOND A simple example of the use of Formula 2.1 is valuing a bond for which a risk rating has been estimated. Let us make five assumptions: 1. The bond has a face value of $1,000. 2. It pays 8% interest on its face value. 3. The bond pays interest once a year, at the end of the year. (This, of course, is a simplifying assumption. Some bonds and notes pay only annually, but most publicly traded bonds pay interest semiannually.) 4. The bond matures exactly three years from the valuation date. 5. As of the valuation date, the market yield to maturity (i.e., total rate of return, including interest payments and price appreciation) for bonds of the same risk grade as the subject bond is 10%. Note three important implications of this scenario: 1. The issuing company’s embedded cost of capital for this bond is only 8%, although the market cost of capital (yield to existing, sometimes referred to as nominal, maturity) at the valuation date is 10%. The discrepancy may be because the general level of interest rates was lower at the time of issuance of this particular bond, or because the market’s rating associated with this bond was lowered between the date of issuance and the valuation date. 2. If the issuing company wanted to issue new debt on comparable terms as of the valuation date, it presumably would have to offer investors a 10% yield, the current market-driven cost of capital for bonds of that risk grade, to induce investors to purchase the bonds.
12
Cost of Capital
3. For purposes of valuation and capital budgeting decisions, when we refer to cost of capital, we mean market cost of capital, not embedded cost of capital. (Embedded cost of capital is sometimes used in utility rate-making, but this chapter focuses only on valuation and capital budgeting applications of cost of capital.) Substituting numbers derived from the preceding assumptions into Formula 2.1 gives us: (Formula 2.2) PV ¼
$80 $80 $80 $1;000 þ þ þ 2 3 ð1 þ :10Þ ð1 þ :10Þ ð1 þ :10Þ ð1 þ :10Þ3
$80 $80 $80 $1;000 þ þ þ ð1:10Þ ð1:21Þ ð1:331Þ ð1:331Þ ¼ $72:73 þ $66:12 þ $60:11 þ $751:32 ¼ $950:28 ¼
In this example, the fair market value of the subject bond as of the valuation date is $950.28. That is the amount that a willing buyer would expect to pay and a willing seller would expect to receive (before considering any transaction costs).
APPLICATIONS TO BUSINESSES, BUSINESS INTERESTS, PROJECTS, AND DIVISIONS The same framework can be used to estimate the value of an equity interest in a company or a company’s entire invested capital. You project the cash flows available to the interest to be valued and discount those cash flows at a cost of capital (discount rate) that reflects the risk associated with achieving the particular cash flows. Details of this procedure for valuing entire companies or interests in companies are presented in later chapters. Similarly, the same construct can be applied to evaluating a capital budgeting decision, such as building a plant or buying equipment. In that case, the cash flows to be discounted are incremental cash flows (i.e., cash flows resulting specifically from the decision that would not occur absent the decision). The early portions of the cash flow stream may be negative while funds are being invested in the project. The primary relationship to remember is that cost of capital is a function of the investment, not of the investor. Therefore, the analyst must evaluate the risk of each project under consideration. If the risk of the project is greater or less than the company’s overall risk, then the cost of capital by which that project is evaluated should be commensurately higher or lower than the company’s overall cost of capital. Although some companies apply a single ‘‘hurdle rate’’ to all proposed projects or investments, the consensus in the literature of corporate finance is that the rate by which to evaluate any investment should be based on the risk of that investment, not on the company’s overall risk that drives its cost of capital. We agree with this consensus. If the company invests in something riskier than its normal operations, the company’s risk will increase marginally. When this increased risk is recognized and reflected in the market, it will raise the company’s cost of capital. If the returns on the riskier new investment are not great enough to achieve higher returns commensurate with this higher cost of capital, the result will be a decrease in the stock price and a loss of shareholder value.
Summary
13
SUMMARY The most common cost of capital applications are valuation of an investment or prospective investment and project selection decisions (the core component of capital budgeting). In both applications, returns expected from the capital outlay are discounted to a present value by a discount rate, which should be the cost of capital applicable to the specific investment or project. The measure of returns generally preferred today is net cash flow, as discussed in the next chapter.
Chapter 3
Net Cash Flow: Preferred Measure of Economic Income
Introduction Defining Net Cash Flow Net Cash Flow to Common Equity Net Cash Flow to Invested Capital Net Cash Flows Should Be Probability-Weighted Expected Values Why Net Cash Flow Is the Preferred Measure of Economic Income Residual Earnings Summary Additional Reading
INTRODUCTION Cost of capital is a meaningless concept until we define the measure of economic income to which it is to be applied. Based on the tools of modern finance, the variable of choice for most financial decision making is net cash flow. This, obviously, poses two critical questions: 1. How do we define net cash flow? 2. Why is net cash flow considered the best economic income variable to use in net present value analysis? There are two general frameworks for valuing a business: valuing net cash flow to common equity and valuing net cash flow to invested capital. When valuing net cash flow to common equity, the discount rate should be the cost of equity capital. When valuing net cash flow to invested capital, the discount rate should be the overall cost of capital (commonly referred to as the weighted average cost of capital, or WACC).
DEFINING NET CASH FLOW Net cash flow is generally defined as cash that a business or project does not have to retain and reinvest in itself in order to sustain the projected levels of cash flows in future years. In other words, it is cash available to be paid out in any year to the owners of capital without jeopardizing the company’s expected-cash-flow-generating capability in future years. It must be distributed or dividended to the investors or reinvested in some incremental project not reflected in the cash flows that have been discounted to become incremental value. (Net cash flow is sometimes called free cash flow. It is 15
16
Cost of Capital
also sometimes called net free cash flow, although this phrase seems redundant. Finance terminology being as ambiguous as it is, minor variations in the definitions of these frequently arise.)
NET CASH FLOW TO COMMON EQUITY In valuing equity by discounting or capitalizing expected cash flows (keeping in mind the important difference between discounting and capitalizing, as discussed elsewhere), net cash flow to equity (NCFe in our notation system) is defined as: (Formula 3.1) Net income to common equityðafter taxÞ þ Noncash chargesðe:g:; depreciation; amortization; deferred revenue; deferred taxesÞ Capital expenditures Additions to net working capital Dividends on preferred stock Changes in long-term debtðþcash from borrowing; repaymentsÞ ¼ Net cash flow to common equity
NET CASH FLOW TO INVESTED CAPITAL In valuing the entire invested capital of a company or project by discounting or capitalizing expected cash flows, net cash flow to invested capital (NCFf in our notation system) is defined as: (Formula 3.2) Net income to common equityðafter taxÞ þ Noncash chargesðe:g:; depreciation; amortization; deferred revenue; deferred taxesÞ Capital expenditures Additions to net working capital þ Dividends on preferred stock þ Interest expenseðnet of the tax deduction resulting from interest as a tax-deductible expenseÞ ¼ Net cash flow to invested capital In other words, NCFf includes interest (tax effected, because interest is a deductible expense for tax purposes), because invested capital includes the debt on which the interest is paid, whereas net cash flow to equity does not. Occasionally an analyst treats earnings before interest, taxes, depreciation, and amortization (EBITDA) as if it were free cash flow. This error is not a minor matter, since the analyst has added back the noncash charges without deducting the capital expenditure investments, not to mention additions to working capital necessary to keep the operation functioning as expected. When we discount net cash flow to equity, the appropriate discount rate is the cost of equity capital. When we discount net cash flow to all invested capital, the appropriate discount rate is the WACC.
Only
amounts necessary to support projected revenues:
Net Cash Flows Should be Probability-Weighted Expected Values
17
NET CASH FLOWS SHOULD BE PROBABILITY-WEIGHTED EXPECTED VALUES Net cash flows to be discounted or capitalized should be statistical expected values, that is, (mean) probability-weighted cash flows. In the real world, it is far more common for realized net cash flows to be below forecast than above. A valuation that does not take this factor into account will overvalue a business. If the distribution of possible cash flows in each period is symmetrical above and below the most likely cash flow in that period, then the most likely cash flow is equal to the probability-weighted cash flow (the mathematical expected value of the distribution). However, many distributions of possible cash flows are skewed. This is where probability weighting comes into play. Exhibit 3.1 tabulates the probability-weighted expected values of projected cash flows under a symmetrically distributed scenario and a skewed distribution scenario. Exhibit 3.2 portrays the information in Exhibit 3.1 graphically. In both scenario A and scenario B, the most likely cash flow is $1,000. In scenario A, the expected value (probability weighted) is also $1,000. But in scenario B, the expected value is only $901. In scenario B, $901 is the figure that should appear in the numerator of the discounted cash flow formula, not $1,000. Most analysts do not have the luxury of a probability distribution for each expected cash flow, and it is not a common practice. However, they should be aware of the concept when deciding on the amount of each expected cash flow to be discounted.
Exhibit 3.1
Cash Flow Expectation Tables Scenario A—Symmetrical Cash Flow Expectation
Expected Value of Cash Flow $1,600.00 1,500.00 1,300.00 1,000.00 700.00 500.00 400.00
Probability of Occurrence
Weighted Value
0.01 0.09 0.20 0.40 0.20 0.09 0.01
$16 135 260 400 140 45 4
100%
$1,000
Scenario B—Skewed Cash Flow Expectation Expected Value of Cash Flow $1,600.00 1,500.00 1,300.00 1,000.00 700.00 500.00 (100.00) (600.00)
Probability of Occurrence
Weighted Value
0.01 0.04 0.20 0.35 0.25 0.10 0.04 0.01 100%
$16 60 260 350 175 50 (4) (6) $901
18
Cost of Capital
Probability of Occurrence
Scenario A—Symmetrical Cash Flow Expectation 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 $ 400
Expected value (mean)
500
700
1,000
1,300
1,500
1,600
Expected Cash Flow
Probability of Occurrence
Scenario B—Skewed Cash Flow Expectation 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 $ –600
Expected value (mean)
–100
500
700
901 1,000
1,300
1,500
1,600
Expected Cash Flow
Exhibit 3.2
Cash Flow Expectation Graphs
As we pointed out in Chapter 2, in calculating the present value of economic benefits, the numerator is the expected economic benefits. We have suggested that net cash flow is the preferred measure of economic income. While this is not a course in forecasting, the analyst may need to facilitate the preparation of expected net cash flows and/or test the reasonableness of net cash flows projected. In Chapter 33 we discuss projections of expected future economic benefits, focusing on net cash flows.
WHY NET CASH FLOW IS THE PREFERRED MEASURE OF ECONOMIC INCOME There are two reasons why the financial community tends to focus on net cash flow as the preferred measure of economic income to be discounted by the opportunity cost of capital. They are: 1. Conceptual. Net cash flow is what an investor actually expects to receive in a discrete period of time. In a valuation context, it is important that the numerator gives the most accurate estimate of what the investor expects to get. 2. Empirical. It is the economic income measure that best matches the historical data available to estimate a discount rate by ex post (historical) methods.
Residual Earnings
19
Morningstar in the Stocks, Bonds, Bills and Inflation (SBBI) 2007 Valuation Edition Yearbook clearly state the case for preferring what they term ‘‘free cash flows’’ (i.e., net cash flows after tax) as the appropriate economic income measure to discount: Several things can be noted about free cash flow. First, it is an after-tax concept.. . . Secondly, pure accounting adjustments need to be added back into the analysis .. . . Finally, cash flows necessary to keep the company going forward must be subtracted from the equation . These cash flows represent necessary capital expenditures to maintain plant, property, and equipment or other capital expenditures that arise out of the ordinary course of business. Another common subtraction is reflected in changes in working capital. The assumption in most business valuation settings is that the entity in question will remain a long-term going concern that will grow over time. As companies grow, they accumulate additional accounts receivable and other working capital elements that require additional cash to support. Free cash flow is the relevant cash flow stream because it represents the broadest level of earnings that can be generated by the asset. With free cash flow as the starting point, the owners of a firm can decide how much of the cash flow stream should be diverted toward new ventures, capital expenditures, interest payments, and dividend payments. It is incorrect to focus on earnings as the cash flow stream to be valued because earnings contain a number of accounting adjustments and already include the impact of the capital structure.1
If the SBBI data or Duff & Phelps data are used to develop a common equity discount rate—using either the build-up model or the Capital Asset Pricing Model (CAPM)—the discount rate is applicable to net cash flow available to the common equity investor. This is because the SBBI and Duff & Phelps return data have two components: 1. Dividends to the common stock 2. Change in common stock prices The investor receives the dividends, so their utilization is entirely at the investor’s discretion. For actively traded stock, the investor’s realization of the change in stock price is equally discretionary because the stocks are highly liquid (i.e., they can be sold at their market price at any time, with the seller receiving the proceeds in cash within three business days).
RESIDUAL EARNINGS An alternative formulation of economic income that has arisen in the literature is residual earnings (RE)2 and abnormal earnings growth (AEG)3 models. The RE and AEG models always yield the same valuation and yield the same value as does the discounted net cash flow method when applied with the same valuation assumptions. Both the RE and AEG models begin with adjusted statements of accounting income. RE is the return on common equity (expressed in dollars) in excess of the cost of equity capital. AEG is earnings (assuming reinvestment of dividends) in excess of earnings growing at the cost of equity capital. (Formula 3.3) NIn ðke BVn1 Þ RE ¼ BVn1 1 2 3
SBBI Valuation Edition Yearbook (Chicago: Morningstar, 2007), 13. Stephen H. Penman, Financial Statement Analysis and Security Valuation, 3rd ed. (New York: McGraw-Hill, 2007), Chapter 5. J. Feltham and J. Ohlson, ‘‘Valuation and Clean Surplus Accounting for Operating and Financing Activities,’’ Contemporary Accounting Research, vol. 11 (1995): 689–731.
20
Cost of Capital
where: RE ¼ Residual earnings NI ¼ Net income BV ¼ Book value of net assets ke ¼ Cost of equity capital The RE is based on clean-surplus accounting statement: (Formula 3.4) BVn ¼ BVn1 þ NIn Dn where: D ¼ Dividends NIn ¼ not reported earnings, but rather comprehensive income, which includes income terms reported directly in the equity account rather than in the income statement (Formula 3.5) AEG ¼ REn REn1 where: AEG ¼ Abnormal earnings growth In Chapter 4 we demonstrate the conditions for equality between valuations using net cash flow and residual earnings. While theoreticians and practitioners alike accept the primacy of cash flows in valuation,4 it is the subject of recent studies. In one study, the authors question whether multiples developed from earnings per share or from operating cash flows per share (net income plus depreciation and amortization plus net working capital divided by the weighted average number of common shares outstanding for the year) more accurately reflect stock prices. Their results suggest that valuations based on earnings forecasts provide better valuations where consensus earnings forecasts of analysts are available.5 Another study examines whether accounting variables explain stock price movements by assisting users of accounting information to better forecast cash flows.6 They find that changes in four accounting variables explain about 20% of the differences in stock returns. Finally, another study finds that when investors are provided complete cash flow data, stock prices fully reflect that data.7
4
5
6
7
See, for example, Steven J. Kaplan and Richard S. Ruback, ‘‘The Valuation of Cash Flow Forecasts: An Empirical Analysis,’’ Journal of Finance 50, No. 4 (1995): 1059–1093. Jing Liu, Doron Nissim, and Jacob Thomas, ‘‘Is Cash Flow King in Valuations?’’ Financial Analysts Journal 63, No. 2 (2007): 56–68. Peter F. Chen and Guochang Zhang, ‘‘How Do Accounting Variables Explain Stock Price Movements? Theory and Evidence,’’ Journal of Accounting and Economics (July 2007): 219–244. Keren Bar-Hava, Roni Ofer, and Oded Sarig, ‘‘New Tests of Market Efficiency Using Fully Identifiable Equity Cash Flows,’’ Working paper, February 2007.
Additional Reading
21
SUMMARY Net cash flow is the measure of economic income that most financial analysts prefer to use today when using the cost of capital for valuation or project selection. If valuing cash flows to equity, the discount rate should be the cost of equity capital. If valuing cash flows to debt, the discount rate should be the cost of the debt capital. If valuing cash flows available for all invested capital, the discount rate should be the weighted average cost of capital. Net cash flows should be measured as the mathematical expected value of the probabilityweighted distribution of expected outcomes for each projected period of returns, not the most likely value. In Chapter 5 we define risk as uncertainty of possible outcomes, a definition intended to encompass the entire range of possible returns for each future period.
ADDITIONAL READING Brief, Richard P. ‘‘Accounting Valuation Models: A Short Primer.’’ Abacus, 43 no. 4 (2007): 429–437. Estridge, Juliet, and Babara Lougee. ‘‘Measuring Free Cash Flows for Equity Valuation: Pitfalls and Possible Solutions.’’Journal of Applied Corporate Finance (Spring 2007): 60–71.
Chapter 4
Discounting versus Capitalizing Introduction Capitalization Formula Example: Valuing a Preferred Stock Functional Relationship between Discount Rate and Capitalization Rate Major Difference between Discounting and Capitalizing Constant Growth or Gordon Growth Model Combining Discounting and Capitalizing (Two-Stage Model) Equivalency of Discounting and Capitalizing Models Midyear Convention Midyear Discounting Convention Midyear Capitalization Convention Midyear Convention in the Two-Stage Model Seasonal Businesses Matching Projection Periods to Financial Statements: Partial First Year Capitalized Residual Earnings Summary
INTRODUCTION The first two chapters explained that the cost of capital is used as a discount rate to discount a stream of future economic income to a present value. This valuation process is called discounting. In discounting, we project all expected economic income (cash flows or other measure of economic income) from the subject investment to the respective class or classes of capital over the life of the investment. Thus, the percentage return that we call the discount rate represents the total compound rate of return that an investor in that class of investment requires over the life of the investment. There is a related process for estimating present value, which we call capitalizing. In capitalizing, instead of projecting all future returns on the investment to the respective class (es) of capital, we focus on the return of just one single period, usually the return expected in the first year immediately following the valuation date. We then divide that single number by a divisor called the capitalization rate. As will be seen, the process of capitalizing is really just a shorthand form of discounting. The capitalization rate, as used in the income approach to valuation or project selection, is derived from the discount rate. (This differs from the market approach to valuation, where capitalization rates for various economic income measures are observed directly in the marketplace.) A common error is to use the discount rate as a capitalization rate. This is correct only if the expected cash flows are the same from the year following the valuation date into perpetuity, as in the case of a perpetual preferred stock. The balance of this chapter presents the differences between discounting and capitalizing and alternative discounting and capitalizing conventions.
23
24
Cost of Capital
CAPITALIZATION FORMULA Putting the capitalization concept into a formula, we have: (Formula 4.1) PV ¼
NCF1 c
where PV ¼ Present value NCF1 ¼ Net cash flow expected in the first period immediately following the valuation date c ¼ Capitalization rate
EXAMPLE: VALUING A PREFERRED STOCK A simple example of applying Formula 4.1 uses a preferred stock for which a risk rating has been estimated. Let us make five assumptions: 1. The preferred stock pays dividends of $5 per share per year. 2. The preferred stock is issued in perpetuity and is not callable. 3. It pays dividends once a year, at the end of the year. (This, of course, is a simplifying assumption. Some privately owned preferred stocks pay dividends only annually, but most publicly traded preferred stocks pay dividends quarterly.) 4. As of the valuation date, the market yield for preferred stocks of the same risk grade as the subject preferred stock is 10% per annum. (We also must assume comparable rights, such as voting, liquidation preference, redemption, conversion, participation, cumulative dividends, etc.) 5. There is no prospect of liquidation. Note that the par value of the preferred stock is irrelevant, since the stock is issued in perpetuity and there is no prospect of a liquidation. The entire cash flow an investor can expect to receive over the life of the investment (perpetuity in this case) is the $5 annual per-share dividend. Substituting numbers derived from the preceding assumptions into Formula 4.1 produces: (Formula 4.2) $5:00 0:10 ¼ $50:00
PV ¼
In this example, the estimated fair market value of the subject preferred stock is $50 per share. That is the amount a willing buyer would expect to pay and a willing seller would expect to receive (before considering any transaction costs).
FUNCTIONAL RELATIONSHIP BETWEEN DISCOUNT RATE AND CAPITALIZATION RATE The preceding example presented the simplest possible scenario in which to apply the cost of capital using the capitalization method: a fixed cash flow stream in perpetuity. This is the one unique situation in which the discount rate (cost of capital) equals the capitalization rate. The discount rate equals
Functional Relationship between Discount Rate and Capitalization Rate
25
the capitalization rate because no growth or decline in the investor’s cash flow is expected. Most realworld investments are not quite that simple. In the case of an investment in common stock, a partnership interest, or a capital budgeting project in an operating company, investors often are expecting some level of growth over time in the cash flows available to pay dividends or partnership withdrawals. Even if unit volume is expected to remain constant (i.e., no real growth), investors still might expect cash flows to grow at a rate approximating expected inflation. If the expected annually compounded rate of growth is stable and sustainable over a long period of time, then the discount rate (cost of capital) can be converted to a capitalization rate. As stated earlier, the capitalization rate is a function of the discount rate. This obviously raises the question: What is the functional relationship between the discount rate and the capitalization rate? Assuming stable long-term growth in net cash flows available to the investment being valued, the capitalization rate equals the discount rate minus the expected long-term growth rate. In a formula, this functional relationship can be stated as: (Formula 4.3) c¼kg where: c ¼ Capitalization rate k ¼ Discount rate (cost of capital) for the subject investment g ¼ Expected long-term sustainable growth rate in the cash flow available to the subject investment The critical assumption in this formula is that the growth in the net cash flow available to the capital is relatively constant over the long term (technically in perpetuity). Caveat: As explained in Chapter 3, in estimating the net cash flow to capitalize, we deduct investments such as capital expenditures and additional net working capital needed to realize the projected future revenues of the existing business investment. In this formulation, we are valuing the existing business, not currently unknown investments that may be made in future years from investing these net cash flows in new business ventures. Now we know two essential things about using the cost of capital to estimate present value using the capitalization method, assuming relatively stable long-term growth in the return available to the investor: 1. Present value equals the next period’s expected cash flow divided by the capitalization rate. 2. The capitalization rate is the discount rate (cost of capital) less the sustainable expected long-term rate of growth in the cash flow. (Technically, sustainable growth in this context means in perpetuity. However, after 15 or 20 years, the remaining rate of growth has minimal impact on the present value, due to very small present value factors.) We can combine these two relationships into a single formula as: (Formula 4.4) PV ¼
NCF1 kg
where: PV ¼ Present value NCF1 ¼ Net cash flow expected in period 1, the period immediately following the valuation date
26
Cost of Capital
k ¼ Discount rate (cost of capital) g ¼ Expected long-term sustainable growth rate in net cash flow to investor A simple example of substituting numbers into Formula 4.4 is an equity investment with a constant expected growth in net cash flow. Let us make three assumptions: 1. The net cash flow in period 1 is expected to be $100. 2. The cost of capital (i.e., the market-required total return or the discount rate) for this investment is estimated to be 13%. 3. The sustainable rate of growth in net cash flow from year 1 to perpetuity is expected to be 3%. Substituting numbers from the preceding assumptions into Formula 4.4 gives us: (Formula 4.5) $100 PV ¼ 0:13 0:03 $100 ¼ 0:10 ¼ $1;000 In this example, the estimated fair market value of the investment is $1,000. That is the amount a willing buyer would expect to pay and a willing seller would expect to receive (before considering any transaction costs).
MAJOR DIFFERENCE BETWEEN DISCOUNTING AND CAPITALIZING From the preceding discussion, we can now deduce a critical insight: The difference between discounting and capitalizing is in how we reflect changes over time in expected future cash flows. In discounting: Each future increment of return is estimated specifically and included in the numerator. In capitalizing: Estimates of changes in future returns are lumped into one annually compounded growth rate, which is then subtracted from the discount rate in the denominator. If we assume that there really is a constant compounded growth rate in net cash flow to the investor in perpetuity, then it is a mathematical truism that the discounting method and the capitalizing method will produce identical values. (See the section in this chapter titled ‘‘Equivalency of Discounting and Capitalizing Models’’ for an illustration of how this equality works.)
CONSTANT GROWTH OR GORDON GROWTH MODEL One frequently encountered minor modification to Formulas 4.4 and 4.5 is to use as the ‘‘base period’’ the period just completed prior to the valuation date, instead of next period’s estimate. The assumption is that cash flows will grow evenly in perpetuity from the period immediately preceding the valuation date. This scenario is stated in a formula commonly known as the Gordon Growth Model (named for Professor Myron Gordon who popularized this formulation): (Formula 4.6) PV ¼
NCF0 ð1 þ gÞ kg
Combining Discounting and Capitalizing (Two-Stage Model)
27
where: PV NCF0 k g
¼ ¼ ¼ ¼
Present value Net cash flow in period 0, the period immediately preceding the valuation date Discount rate (cost of capital) Expected long-term sustainable growth rate in net cash flow to investor
Note that for this model to make economic sense, NCF0 must represent a normalized amount of cash flow from the investment for the previous year, from which a steady rate of growth is expected to proceed. Therefore, NCF0 need not be the actual cash flow for period 0 but may be the result of certain normalization adjustments, such as elimination of the effect of one or more nonrecurring factors. In fact, if NCF0 is the actual net cash flow for period 0, the valuation analyst must take reasonable steps to be satisfied that NCF0 is indeed the most reasonable base from which to start the expected growth embedded in the growth rate. Furthermore, the valuation report should state the steps taken and the assumptions made in concluding that last year’s actual results are the most realistic base for expected growth. Mechanistic acceptance of recent results as representative of future expectations is one of the most common errors in implementing the capitalization method of valuation. For a simple example of using numbers in Formula 4.6, accept all assumptions in the previous example, with the exception that the $100 net cash flow expected in period 1 is instead the normalized base cash flow for period 0. (The $100 is for the period just ended, rather than the expectation for the period just starting.) Substituting the numbers with these assumptions into Formula 4.6 produces: (Formula 4.7) $100ð1 þ 0:03Þ 0:13 0:03 $103 ¼ 0:10
PV ¼
¼ $1;030 In this example, the estimated fair market value of the investment is $1,030. That is the amount a willing buyer would expect to pay and a willing seller would expect to receive (before considering any transaction costs). Note that the relationship between this and the previous example is simple and straightforward. We backed up the receipt of the $100 by one period, and the value of the investment was higher by 3%, the growth rate. In a constant growth model, assuming that all of the available cash flows are distributed, the value of the investment grows at the same rate as the rate of growth of the cash flows. The reason is that, in defining net cash flow (as we did in the previous chapter), we have already subtracted the amount of capital expenditures and additions to net working capital necessary to support the projected growth. The investor in this example thus earns a total rate of return of 13%, comprised of 10% current return (the capitalization rate) plus 3% annually compounded growth in the value of the investment.
COMBINING DISCOUNTING AND CAPITALIZING (TWO-STAGE MODEL) For many investments, even given an accurate estimate of the cost of capital, there are practical problems with either a pure discounting or a pure capitalizing method of valuation.
28
Cost of Capital
Problem with discounting. There are few equity investments for which returns for each specific incremental period can be projected with accuracy many years into the future. Problem with capitalizing. For most equity investments, it is not reasonable to expect a constant growth rate in perpetuity from either the year preceding or the year following the valuation date.
This dilemma typically is dealt with by combining the discounting method and the capitalizing method into a two-stage model. The idea is to project discrete cash flows for some number of periods into the future and then to project a steady growth model starting at the end of the discrete projection period. Each period’s discrete cash flow is discounted to a present value, and the capitalized value of the projected cash flows following the end of the discrete projection period is also discounted back to a present value. The sum of the present values is the total present value. The capitalized value of the projected cash flows following the discrete projection period is called the terminal value or residual value. The preceding narrative explanation of a two-stage model is summarized in seven steps: Step 1. Decide on a reasonable length of time for which discrete projections can be made. Step 2. Estimate specific amounts of expected cash flow for each of the discrete projection periods. Step 3. Estimate a long-term sustainable rate of growth in cash flows from the end of the discrete projection period forward. Step 4. Use the Gordon Growth Model (Formulas 4.6 and 4.7) to estimate value as of the end of the discrete projection period. Step 5. Discount each of the increments of cash flow back to a present value at the discount rate (cost of capital) for the number of periods until it is received. Step 6. Discount the terminal value (estimated in step 4) back to a present value for the number of periods in the discrete projection period (the same number of periods as the last increment of cash flow). Step 7. Sum the value derived from steps 5 and 6. These steps can be summarized in the next formula, which assumes that net cash flows are received at the end of each year: (Formula 4.8) NCFn ð1 þ gÞ NCF1 NCF2 NCFn kg þ þ þ PV ¼ nþ 2 ð1 þ kÞ ð1 þ kÞ ð1 þ kÞ ð1 þ kÞn where: NCF1. . . NCFn ¼ Net cash flow expected in each of the periods 1 through n, n being the last period of the discrete cash flow projections k ¼ Discount rate (cost of capital) g ¼ Expected long-term sustainable growth rate in net cash flow, starting with the last period of the discrete projections as the base year The discrete projection period in the two-stage model is commonly between 5 and 10 years. However, for simplicity in applying Formula 4.8, we will just use a three-year discrete projection period. Let us make three assumptions: 1. Expected net cash flows for years 1, 2, and 3 are $100, $120, and $140, respectively. 2. Beyond year 3, cash flow is expected to grow fairly evenly at a rate of about 5% in perpetuity. 3. The cost of capital for this investment is estimated to be 12%.
Equivalency of Discounting and Capitalizing Models
29
Substituting numbers derived from these assumptions into Formula 4.8 produces: (Formula 4.9) $140ð1 þ 0:05Þ $100 $120 $140 PV ¼ þ þ 0:12 0:053 þ ð1 þ 0:12Þ ð1 þ 0:12Þ2 ð1 þ 0:12Þ3 ð1 þ 0:12Þ $147 $100 $120 $140 þ þ þ 0:07 ¼ 1:12 1:2544 1:4049 1:4049 $2;100 ¼ $89:30 þ $95:66 þ $99:65 þ 1:4049 ¼ $89:30 þ $95:66 þ $99:65 þ $1;494:77 ¼ $1;779 Thus, the estimated fair market value of this investment is $1,779. This is the amount a willing buyer would expect to pay and a willing seller would expect to receive (before considering any transaction costs). A common error is to discount the terminal value for n þ 1 periods instead of n periods. The assumption we have made is that the nth period cash flow is received at the end of the nth period, and the terminal value is the amount for which we estimate we could sell the investment as of the end of the nth period. The end of one period and the beginning of the next period are the same moment in time, so they must be discounted for the same number of periods. Note that, in the preceding example, the terminal value represents 84% of the total present value ($1,495 $1,779 ¼ 0.84). The analyst should always keep in mind two relationships when using cost of capital in a two-stage model for valuation: 1. The shorter the projection period, the greater the impact of the terminal value on the total present value. The length of the projection period should be the number of periods until the company is expected to reach a steady state, that is, until the company is expected to reach a normalized level of cash flow that it can grow at a more or less constant rate over a long period of time. There is no ‘‘magic’’ in using 5 years or 10 years for the projection period. 2. The closer the estimated growth rate is to the cost of capital, the more sensitive the model is to changes in assumptions regarding the growth rate. (This is true for the straight capitalization model as well as the two-stage model.) Of course, if the assumed growth rate exceeds the cost of capital, the model implodes and is useless. In some cases, the terminal value may not be a perpetuity model. For example, you might assume liquidation at that point, and the terminal value could be a salvage value. For example, the license to operate the business may have a finite life at which the operating business ends.
EQUIVALENCY OF DISCOUNTING AND CAPITALIZING MODELS As stated earlier, if all assumptions are met, the discounting and capitalizing methods of using the cost of capital will produce identical estimates of present value. Let us test this on the example used in Formula 4.5. Recall that we assumed cash flow in period 1 of $100, growing in perpetuity at 3%.
30
Cost of Capital
The cost of capital (the discount rate) was 13%, so we subtracted the growth rate of 3% to get a capitalization rate of 10%. Capitalizing the $100 (period 1 expected cash flow) at 10% gave us an estimated present value of $1,000 ($100 0.10 ¼ $1,000). Let us take these same assumptions and put them into a discounting model. For simplicity, we will only use three periods for the discrete projection period, but it would not make any difference how many discrete projection periods we used. (Formula 4.10) $100ð1:03Þ3 $100 $100ð1:03Þ $100ð1:03Þ þ þ 0:13 0:03 þ PV ¼ ð1 þ 0:13Þ ð1 þ 0:13Þ2 ð1 þ 0:13Þ3 ð1:13Þ3 2
$109:27 $100 $103 $106:09 þ þ þ 0:10 ¼ 1:13 1:2769 1:4429 1:4429 $1;092:73 ¼ $88:50 þ $80:66 þ $75:53 þ 1:4429 ¼ $88:50 þ $80:66 þ $73:53 þ $757:31 ¼ $1; 000 This example, showing the equivalency of using cost of capital in either the discounting or the capitalizing model, when all assumptions are met, demonstrates the point that capitalizing is really just a shorthand form of discounting. Capitalization usually is used when we do not have enough information to implement a discounting model. Nevertheless, when using a capitalizing model, the analyst should consider whether the answer would work out the same if it were expanded to a full discounting model. If not, it may be propitious to review and possibly adjust certain assumptions. If the discounting and capitalization models produce different answers using the same cost of capital and the same inputs, there may be some kind of internal inconsistency.
MIDYEAR CONVENTION In all of our previous examples, we have assumed that cash flows are received at the end of each year. Even if a company realizes cash flows throughout the year, payouts to the investors may be made only at the end of the year when the managers have seen the results of the entire year and have an idea about next year’s projections. For some companies or investments, however, it may be more reasonable to assume that the cash flows are distributed more or less evenly throughout the year. To accommodate this latter assumption, we can modify our formulas for what we call the midyear convention. MIDYEAR DISCOUNTING CONVENTION We can make a simple modification to Formula 2.1 (discounting) to what we call the midyear discounting convention. We merely subtract a half year from the exponent in the denominator of the equation. Formula 2.1, the discounting equation, now becomes: (Formula 4.11) PV ¼
NCF1 ð1 þ kÞ0:5
þ
NCF2 ð1 þ kÞ1:5
þ þ
NCFn ð1 þ kÞn0:5
Midyear Convention
31
MIDYEAR CAPITALIZATION CONVENTION Similarly, we can make a modification to the capitalization formula to reflect the receipt of cash flows throughout the year. The modification to Formula 4.4, the capitalization equation, is handled by accelerating the returns by a half year in the numerator:1 (Formula 4.12) PV ¼
NCF1 ð1 þ kÞ0:5 kg
Formula 4.12 is a mathematical equivalent of Formula 4.13. (Formula 4.13) NCFn ð1 þ gÞ NCF1 NCF2 NCFn kg PV ¼ þ þ þ þ ð1 þ kÞ0:5 ð1 þ kÞ1:5 ð1 þ kÞn0:5 ð1 þ kÞn0:5
MIDYEAR CONVENTION IN THE TWO-STAGE MODEL Combining discrete period discounting and capitalized terminal value into a two-stage model as shown in Formula 4.8, the midyear convention two-stage equation becomes: (Formula 4.14) NCFn ð1 þ gÞð1 þ kÞ0:5 NCF1 NCF2 NCFn kg PV ¼ þ þ þ þ 0:5 1:5 n0:5 ð1 þ kÞn ð1 þ kÞ ð1 þ kÞ ð1 þ kÞ Using the same assumptions as in Formula 4.9 (where the value using the year-end convention was $1,779) produces: (Formula 4.15) $140ð1 þ 0:05Þð1 þ 0:12Þ0:5 $100 $120 $140 0:12 0:05 þ þ þ PV ¼ 0:5 1:5 ð1 þ 0:12Þ3 ð1 þ 0:12Þ ð1 þ 0:12Þ ð1 þ 0:12Þ2:5 $155:527 $100 $120 $140 ¼ þ þ þ 0:07 1:0583 1:1853 1:3275 1:4049 $2;221:81 ¼ $94:49 þ $101:24 þ $105:46 þ 1:4049 ¼ $94:49 þ $101:24 þ $105:46 þ $1;581:47 ¼ $1;883
1
Proof of the accuracy of this method was presented in Todd A. Kaltman, ‘‘Capitalization Using a Mid-Year Convention,’’ Business Valuation Review (December 1995): 178–182. Also see, Michael Dobner, ‘‘Mid-year Discounting and Seasonality Factors,’’ Business Valuation Review (March 2002): 16–18; Jay B. Abrams, and R.K. Hiatt, ‘‘The Bias in Annual (Versus Monthly) Discounting is Immaterial,’’ Business Valuation Review (September 2003): 127–135.
32
Cost of Capital
In this case, using the midyear convention increased the value by $104 ($1,883 $1,779 ¼ $104) or 5.8% ($104 $1,779 ¼ 0.058). An alternative version of the terminal value factor in the two-stage model actually is equivalent to that used in the preceding formula. Instead of using the modified capitalization equation in the numerator of the terminal value factor, the normal terminal value capitalization equation is used, and the terminal value is discounted by n – 0.5 years instead of n years. This equation reads: (Formula 4.16) NCFn ð1 þ gÞ NCF1 NCF2 NCFn kg þ þ þ þ PV ¼ 0:5 1:5 n0:5 ð1 þ kÞ ð1 þ kÞ ð1 þ kÞ ð1 þ kÞn0:5 Using the same numbers as in Formula 4.15, this works out to: (Formula 4.17) $140ð1 þ 0:05Þ þ þ þ 0:12 0:05 PV ¼ 0:5 1:5 2:5 ð1 þ 0:12Þ ð1 þ 0:12Þ ð1 þ 0:12Þ ð1 þ 0:12Þ2:5 $100
$120
$140
$147 $100 $120 $140 þ þ þ 0:07 ¼ 1:0583 1:1853 1:3275 1:3275 $2;100 ¼ $94:49 þ $101:24 þ $105:46 þ 1:3275 ¼ $94:49 þ $101:24 þ $105:46 þ $1;581:92 ¼ $1;883 (The difference is a matter of rounding.) Note that using the midyear convention will always produce a higher value when the annual projected cash flows are the same, because of the time value of money. The assumption underlying the midyear convention is that investors receive the cash flows earlier than is the case under the year-end convention. A quick way to handle the midyear convention is simply to multiply the value without midyear discounting by (1 + k)0.5. SEASONAL BUSINESSES The midyear convention formulas can be modified for seasonal businesses. For example, assume that you analyze monthly income and cash flows and determine that springtime is the period which is the weighted average of the monthly cash flows during the year. You can substitute n ¼ 0.3 for n ¼ 0.5 in the midyear convention formula. The important point is that you need to understand the timing of the cash flows through the year before adopting any convention, annual, midyear, or other.
MATCHING PROJECTION PERIODS TO FINANCIAL STATEMENTS: PARTIAL FIRST YEAR Often our valuation date is not at the beginning of an accounting year; rather the valuation date is in the middle of the accounting year. For presentation purposes, it is often helpful to match the projection periods to the financial statement fiscal years. For example, the company may assemble
Matching Projection Periods to Financial Statements: Partial First Year
0
Year 1
2
3
4
^
^
^
^
33
where: 0 ¼ Valuation Date ^ ¼ Point in year where cash flows assumed to be realized Exhibit 4.1
Timeline of Net Cash Flows Equivalent to Formula 4.8
long-range plans. Those projections typically match the periods included in future financial statement fiscal years. We can adapt the principles of midyear discounting to this special case. It is helpful to present the projection periods in terms of timelines. Exhibit 4.1 presents the timeline of net cash projections valued in Formula 4.8 (cash flows assumed to be realized at the end of each of the future years). Exhibit 4.2 presents the timeline of net cash flow projections valued in Formula 4.13 (cash flows assumed to be realized at the midpoint of each of the future years or uniformly during those future years). Now assume, for example, that the valuation date is at the beginning of the fifth month of the current financial reporting year and net cash flow projections are similarly assumed to be realized at the midpoint of each of the future periods. For the remaining ‘‘partial period’’ (matching the remainder of the current financial reporting year), the net cash flows are expected to be realized 3½ months after the valuation date and the net cash flows in the first full year following the partial period are expected to be realized 13 months (midpoint of 7 remaining months of the remaining financial statement fiscal year plus 6 months into the first full year thereafter) after the valuation date, the net cash flows in the second full year are expected to be realized 20 months after the valuation date, and each subsequent year’s net cash flows is expected to be realized 12 months thereafter. Exhibit 4.3 presents the timeline of net cash flows expected in this example. Formula 4.18, a variation of Formula 4.13, displays the calculation of present value of net cash flows where the first projection period is a partial year. (Formula 4.18) NCFn ð1 þ gÞ ðNCF1 pyÞ NCF2 NCFn ðk gÞ þ þ þ þ PV ¼ py pyþ0:5 pyþðn0:5Þ 2 ð1 þ kÞ ð1 þ kÞ ð1 þ kÞ pyþðn0:5Þ ð1 þ kÞ where: py ¼ months of partial first year expressed as a decimal Year 1 0
^
2 ^
3 ^
4 ^
where: 0 ¼ Valuation Date ^ ¼ Point in year where cash flows assumed to be realized Exhibit 4.2
Timeline of Net Cash Flows Equivalent to Formula 4.13
34
Cost of Capital
Partial Full Year Year 1
0 ^
^
2
^
3
^
4
^
where: 0 ¼ Valuation Date ^ ¼ Point in year where cash flows assumed to be realized Exhibit 4.3
Timeline of Net Cash Flows Equivalent to Formula 4.16
7 ¼ 0:5833 of the first year, and the partial year factor for In the example, the partial year represents 12 ð70:5Þ the present value of the net cash flows in the partial first year equals 12 ¼ 0:2917. That is, the firstperiod net cash flows are expected to be received 0.2917 of a year following the valuation date (3½ months following the valuation date). The exponent for the present value of the net cash flows expected during the first full year following the valuation date equals ð0:5833 þ 0:5Þ ¼ 1:0833. That is, the net cash flows are expected to be received 0.5 years after the end of the partial first year (7 months). Applying Formula 4.16 using the same assumptions as in Formula 4.15 except for the partial first year, we get: (Formula 4.19) 7 $140ð1 þ 0:05Þ $100 $120 $140 12 ð0:12 0:05Þ þ þ þ PV ¼ 7 7 7 0:2917 þ0:5 þð20:5Þ ð1 þ 0:12Þ ð1 þ 0:12Þ12 ð1 þ 0:12Þ12 ð1 þ 0:12Þ12þð20:5Þ
¼
$58:33 $120 $140 $2;100 þ þ þ 1:083 2:083 1:034 ð1 þ 0:12Þ ð1 þ 0:12Þ ð1 þ 0:12Þ2:083
¼ $56:41 þ
$120 $140 $2;100 þ þ 1:131 1:266 1:266
¼ $56:41 þ $106:14 þ $110:56 þ $1;658:43 ¼ $1;931:55
CAPITALIZING RESIDUAL EARNINGS As we discussed in Chapter 3, the literature includes an alternative formulation of the valuation of net cash flows based on residual earnings. The equivalent RE valuation to Formula 4.7 as applied to net cash flows to equity capital is: (Formula 4.20) RE1 PV ¼ BV0 þ ðke gÞ where: PV ¼ Present value BV0 ¼ Book value (net asset value) for period 0, the period immediately preceding the valuation date
Summary
35
RE1 ¼ Residual earnings for period 0 BV0 ¼ ke ke ¼ Cost of equity capital g ¼ Expected long-term sustainable growth rate in net cash flow to equity investors Exhibit 4.4 shows an example of valuation using residual earnings consistent with the example shown in Formula 4.7. The equivalent abnormal earnings growth (AEG)–based valuation to Formula 4.7 is applied to net cash flows to equity capital: (Formula 4.21) 1 AEG2 NI þ PV ¼ ðke gÞ ke where: AEG2 ¼ RE2 RE1. The other variables are as defined in Formula 4.20. Exhibit 4.5 continues the example in Exhibit 4.4 for abnormal earnings growth. We can also reconcile the two-stage model of valuation using net cash flows to equity and the capitalization and discounting of net cash flows to invested capital.2 Why would we use the residual earnings model? This formulation causes the analyst to focus on the amount of capital invested (net assets) and the return on that investment. It highlights whether the firm is earning returns in excess of its cost of equity capital. It also ties the valuation to the financial statements and treats investments ( use of cash) instead of simply reductions of net cash flow. Finally, it most often results in more of the value being attributed to the existing investments (net assets) than to the terminal or residual value. While some may criticize the approach because it appears to place too much relevance on the accuracy of the balance sheet and the net asset amount, the residual earnings will be reduced if the carrying components of net assets overstates their value, reducing the present value of residual earnings. The residual earnings model will always be equivalent to a dividend discount valuation and a DCF valuation if we somehow could forecast dividends and cash flow for very long (infinite) horizons, or if we somehow could get the correct (but different) growth rates for each model. However, in separating what we know from speculation, this model breaks down the components of the valuation differently. We now have a component (1), the book value, which we observe in the present. If mark-to-market accounting is applied, the book value gives the complete valuation, as in the case of an investment fund where one trades as net asset (book) value. More generally, book value is not sufficient so one adds forecasts of residual earnings for the near term, component (2), and speculation about the long term, component (3), to estimate the difference between value and book value.3
The cost of equity capital and the overall cost of capital are the same whether we are using the present value of net cash flow or the residual earnings formulation of valuation.
SUMMARY This chapter has shown the mechanics of discounting and capitalizing and has defined the difference between a discount rate and a capitalization rate. 2 3
Ronald S. Longhofer, ‘‘The Residual Income Method of Business Valuation,’’ Business Valuation Review (June 2005): 65–70. Stephen H. Penman, ‘‘Handling Valuation Models,’’ Journal of Applied Corporate Finance (Spring 2006): 51.
36
Cost of Capital
Exhibit 4.4
Example of Valuation Using Residual Earnings
For company A we have: Income Statement
Year 1
EBIT Interest Expense EBT Taxes NI
Growth Rate
$228 16 $212 85 $127
3% 3% 3% 3% 3%
where: EBIT ¼ Earnings before interest and taxes EBT ¼ Earnings before taxes NI ¼ Net income Balance Sheet
Year 0
Year 1
Growth Rate
Current Assets Fixed and Intangible Assets Total Assets Current Liabilities Long-term Debt Book Value of Equity (BV) Liabilities plus Equity
$300 900 $1,200 $200 200 800 $1,200
$309 927 $1,236 $206 206 824 $1,236
3% 3% 3% 3% 3% 3%
Applying Formula 4.20 we get:
$23 ð0:13 0:03Þ ¼ $800 þ $230 ¼ $1;030
PV ¼ $800 þ
where: RE1 ¼ NI1 (BV0 ke) ¼ $127 ($800 0.13) ¼ $127 $104 ¼ $23 This is the same result we obtained in Formula 4.7. Using the clean surplus accounting statement we get: NCF1 ¼ BV0 þ NI1 BV1 ¼ $800 þ $127 $824
¼ $103 where: NCF1 ¼ Net cash flow to equity in period 1 NI1 ¼ Net income in period 1 (comprehensive income) BVn ¼ Book value of equity This is the same NCF we capitalized in Formula 4.7.
Summary
Exhibit 4.5
37
Example of Valuation Using Abnormal Earnings Growth RE2 ¼ RE1 ð1:03Þ ¼ $23 ð1:03Þ ¼ $23:69
Applying Formula 4.21 we get: PV ¼
1 ð$23:69 $23Þ $127 þ 0:13 ð0:13 0:03Þ
1 ½$127 þ $6:9 0:13 1 ¼ ½$133:9 0:13 ¼
¼ $1;030 This is the same result as we obtained in Formula 4.7.
It has shown that capitalizing is merely a short-form version of discounting. The essential difference between the discounting method and the capitalizing method is how changes in expected cash flows over time are reflected in the respective formulas. All things being equal, the discounting method and the capitalizing method will yield identical results. However, the validity of the capitalizing method in the income approach to valuation depends on the assumption that the difference between the discount rate and the capitalization rate represents a long-term average rate of growth in the income variable being capitalized. Because many companies are likely to expect near-term changes in levels of their returns that are not expected to be representative of longer-term expectations, many analysts use a combination of discounting and capitalizing for valuation. To accomplish this, they implement five steps: Step 1. Project discrete amounts of return for some period of years until the company is expected to reach a stabilized level from which relatively constant growth may be expected to proceed. Step 2. Use the Gordon Growth Model (or some other method) to estimate a ‘‘terminal value’’ as of the end of the discrete projection period. Step 3. Discount each discrete projected cash flow to a present value at the cost of capital for the number of periods until it is expected to be received. Step 4. Discount the terminal value to a present value at the cost of capital for the number of periods in the discrete projection period (the beginning of the assumed stable growth period). Step 5. Add the values from steps 3 and 4. Most discounting and capitalization formulas reflect the implicit assumption that investors will realize their cash flows at the end of each year. If it is assumed that investors will receive cash flows more or less evenly throughout the year, the formulas can be modified by the midyear convention.
Chapter 5
Relationship between Risk and the Cost of Capital Introduction Defining Risk How Risk Impacts the Cost of Capital Valuation of Risky Net Cash Flows Estimating Risk of Company Operations and Assets Types of Risk Maturity Risk Market Risk Unique Risk Other Risk Cost of Equity Capital Cost of Invested Capital or Overall Cost of Capital Summary Appendix 5A
INTRODUCTION The cost of capital for any given investment is a combination of two basic factors1: 1. A risk-free rate. By ‘‘risk-free rate,’’ we mean a rate of return that is available in the market on an investment that is free of default risk, usually the yield to maturity on a U.S. government security, which is a ‘‘nominal’’ rate (i.e., it includes expected inflation). 2. A premium for risk. This is an expected amount of return over and above the risk-free rate to compensate the investor for accepting risk. The generalized cost of capital relationship is as: (Formula 5.1) EðRi Þ ¼ R f þ RPi where: E(Ri) ¼ Expected return of security i Rf ¼ Risk-free rate RP ¼ Risk premium for security i
1
A third factor is liquidity, but that is usually treated as a separate adjustment, as discussed in Chapter 25.
39
40
Cost of Capital
Quantifying the amount by which risk affects the cost of capital for any particular company or investment is arguably one of the most difficult analyses in the field of corporate finance, including valuation and capital budgeting. Estimating the cost of capital is first and foremost an exercise in pricing risk.
DEFINING RISK Probably the most widely accepted definition of risk in the context of business valuation is the degree of uncertainty (or lack thereof) of achieving future expectations at the times and in the amounts expected.2 This means uncertainty as to both the amounts and the timing of expected economic income. Note that the definition implies as the reference point expected economic income. By expected economic income, in a technical sense, we mean the expected value (mean average) of the probability distribution of possible economic income for each forecast period. This concept was explained in Chapter 3 in the discussion of net cash flow. The point to understand here is that the uncertainty encompasses the full distribution of possible economic income for each period both above and below the expected value. Inasmuch as uncertainty is within the mind of each individual investor, we cannot measure the risk directly. Consequently, participants in the financial markets have developed ways of measuring factors that investors normally would consider in their effort to incorporate risk into their required rate of return. Throughout this book we are equating risk with uncertainty, as does most of the literature. However, some analysts make a useful distinction between the two terms. That is, ‘‘risk’’ is present where the parameters of uncertainty are defined (i.e., when the generating function is known with certainty), as in a coin toss (e.g. if forecasters all agree that recession will occur next year then the subject company’s net cash flows will still vary, but within the forecast of recession). ‘‘Uncertainty beyond risk’’ is when analysts have the possibility of an infinite number of subjective inputs (e.g. wide divergence of opinions among forecasters as to whether there will be a recession next year or not).3 No matter how many probability distributions or Monte Carlo simulations are used to create the forecasts, all risk cannot be eliminated. Therefore, forecasts cannot be discounted at the risk-free rate.
HOW RISK IMPACTS THE COST OF CAPITAL As noted earlier, the cost of capital has two components:4 1. A risk-free rate, Rf 2. A risk premium, RP As the market’s perception of the degree of risk of an investment increases, the risk premium, RP, increases so that the rate of return that the market requires (the discount rate) increases for a given set 2
3
4
David Laro and Shannon P. Pratt, Business Valuation and Taxes: Procedure, Law, and Perspective (Hoboken, NJ: John Wiley & Sons, 2005), 160. Evan W. Anderson, Eric Ghysels, and Jennifer L. Juergens, ‘‘The Impact of Risk and Uncertainty on Expected Returns,’’ Working paper, April 11, 2007. As noted in note 1, a third element—lack of marketability or liquidity—may be embedded in the discount rate, but more often it is treated as a separate adjustment to value. This is covered in Chapter 25.
How Risk Impacts the Cost of Capital
41
of expected cash flows. The greater the market’s required rate of return, the lower the present value of the investment. Risk is the ultimate concern to investors. The risk-free rate compensates investors for renting out their money (i.e., for delaying consumption over some future time period and receiving back dollars with less purchasing power). This component of the cost of capital is readily observable in the marketplace and generally differs from one investment to another only to the extent of the time horizon (maturity) selected for measurement of the risk-free rate. The risk premium is due to the uncertainty of expected returns and varies widely from one prospective capital investment to another. We could say that the market abhors uncertainty and consequently demands a high price (in terms of required rate of return or cost of capital) to accept uncertainty. Since uncertainty as to timing and amounts of future receipts is greatest for equity investors, the high risk forces equity as a class to have the highest cost of capital. VALUATION OF RISKY NET CASH FLOWS In Chapter 3 we discussed measuring future net cash flows in terms of expected net cash flows, and in Chapter 4 we discussed the valuation processes of discounting and capitalization. Combining the concepts, we can better understand the valuation process under conditions of risk. For example, Exhibit 5.1 represents the valuation process for a series of expected cash flows over the life of a typical five-year business project. Each year the cash flows have the potential to vary (the distribution of net cash flows). When viewed in terms of the valuation date, these distributions generally can be expected to be increasingly risky (increasing variability of possible net cash flows). The goal of the valuation process is to estimate the ‘‘price the market would pay’’ for the distributions of estimated net cash flows. In terms of Exhibit 5.1, we are estimating how much the market will pay as of the valuation date for the distribution of net cash flows in periods n ¼ 1, n ¼ 2, and so on. Our task is to determine the marketplace’s pricing of risk as of the valuation date for the comparable distribution of expected net cash flows. We need to first measure the risk and then measure the market’s pricing of those risks (i.e., what is the cost of capital for the net cash flows with comparable risk characteristics). n= 0
n= 1
n= 2
n=3
n=4
n=5
PV1 PV2 PV3 PV4 PV5 PVTotal
Exhibit 5.1
Valuation of Increasingly Risky Net Cash Flows with Symmetric Distributions
42
Cost of Capital
n= 0
n= 1
n= 2
n=3
n=4
n=5
PV1 PV2 PV3 PV4 PV5 PVTotal
Exhibit 5.2
Valuation of Increasingly Risky Net Cash Flows with Skewed Distributions
Exhibit 5.2 represents the same process but for a series of expected skewed distributions of net cash flows. Often net cash flows of a business reach the upper limit because of capacity constraints, pricing limitation, and so on, making such skewed distributions more representative of possible outcomes. In either case, calculating a measure of central tendency (e.g., expected value) by probability weighting the expected cash flows does not eliminate the risk of the distributions. The appropriate discount rate is not a risk-free rate of return. Would the market only demand the risk-free rate of return for taking on the variability of the cash flows? The answer is no. The market will demand compensation (added return) for accepting the risk that the actual cash flows will differ from the expected cash flows in future periods and the added return will increase depending on the amount of expected dispersion that could occur. That is, one would expect that the greater the dispersion of expected cash flows the greater the discount rate. We discuss the Financial Accounting Standards Board’s Concepts Statement No. 7 (Con 7) in Appendix 5A; misreading that statement has added to this confusion. Con 7 is sometimes interpreted to advocate discounting at the risk-free rate when the expected value of a probability distribution is used in the numerator. This is not what it says, as explained in Appendix 5A. ESTIMATING RISK OF COMPANY OPERATIONS AND ASSETS Business risk is the risk of the company operations. Business risk can be thought of in terms of the various underlying business operations: sales risk (risk of decrease in unit sales or in unit sales growth), profit margin risk (pricing and expense risks), and operating leverage risk. It can also be expressed in terms of the risk of the underlying assets of the business. Operating leverage is the variability of net cash flow from business operations (i.e., without regard to the cost of financing the business) as output or revenues change. Net cash flow from operations can be broken down in terms of revenues, variable costs, and fixed costs. Variable costs are those that are dependent on the rate of output or revenues of the firm. Fixed costs occur regardless of the level of
How Risk Impacts the Cost of Capital
43
output or revenue of the firm. Business risk can be quantified in terms of variability of revenue in this way:5 (Formula 5.2) Fc s rev sB ¼ 1 þ PVb where: sB ¼ Standard deviation of operating cash flows of the business before cost of financing Fc ¼ Fixed operating costs of the business PVb ¼ Present value of net cash flows from business operations (before costs of financing) srev ¼ Standard deviation of revenues derived from output That is, as the level of fixed costs rise relative to total costs, the variability of operating cash flows increases. All else being equal, a firm with high operating leverage has high fixed costs and low variable costs; each dollar of revenue from each additional unit of output is offset by a relatively small increase in operating costs. Alternatively, any company can be thought of as a portfolio of assets. But we generally are unable to directly observe rates of return appropriate for the risk of the underlying assets of the business (particularly intangible assets, including the goodwill of the business). We can depict the risk hierarchy of the asset mix of a business generally as shown in Exhibit 5.3. Generally, the risks of investing in net working capital are the least risky of the business assets. Net working capital can be converted to cash over the shortest time frame and with the least expected variance from carrying values. Property, plant, and equipment typically can be utilized in a variety of businesses and in producing a variety of different products. Further, if need be, they can be sold to other businesses; but the proceeds from any such sale likely will vary more from their carrying values than will, for example, net working capital. Finally, the value of intangible assets are most often Risk to the Company Lower Rate of Return Lower Risk Net Working Capital
Property, Plant, and Equipment
Higher Rate of Return
Higher Risk Intangible Assets
Exhibit 5.3 5
Risk of Company’s Asset Mix
Hazem Daouk and David Ng, ‘‘Is Unlevered Firm Volatility Asymmetric?’’ AFA 2007 Chicago Meetings, January 11, 2007.
44
Cost of Capital
Risk to the Investor Lower Rate of Return
Lower Risk Senior Debt Mezzanine (Subordinate) Debt
Preferred Equity
Higher Rate of Return
Higher Risk Common Equity
Exhibit 5.4
Risks of the Components of the Company Capital Structure
dependent on the success of the specific operations of the subject business. They generally have little or no value outside of the existing going concern. How can we estimate an appropriate risk premium for a company as a whole and for its component assets? We can look at the capital structure of the company and the company’s overall cost of capital as a mirror of the business risk. Think of the mix of business assets as the left-hand side of the company balance sheet and the company capital structure as the right-hand side of the company balance sheet. By determining the overall company cost of capital, we can then impute the overall return required from the business operations in order to provide investors (the suppliers of capital to the company) with their expected returns. We can observe market returns investors have received in the past and impute implied returns expected by investors from investments in companies with similar business risks. We are imputing the risk of the investment (company business) from the risks of the securities used to supply the investment and the pricing of risk implied from the returns on those securities. The capital structure of the company adds another layer of risk, financial risk. Financial risk is the added volatility providers of equity capital will experience because returns to bond holders and other preferred investors generally are fixed and are senior to returns to common equity. The leverage of financing increases the volatility to returns on common equity. We can depict the risk hierarchy of the risk of the components of the company capital structure generally as shown in Exhibit 5.4. This book is about measuring and pricing the risks of the assets and components of the capital structure of a business. We discuss separating business risk and financial risks in Chapter 10.
TYPES OF RISK Although risk arises from many sources, this chapter addresses risk in the economic sense, as used in the conventional methods of estimating cost of capital. In this context, capital market theory divides risk into three components:
Types of Risk
45
1. Maturity risk 2. Market risk 3. Unique risk 6 MATURITY RISK Maturity risk (also called horizon risk or interest rate risk) is the risk that the value of the investment may increase or decrease because of changes in the general level of interest rates. The longer the term of an investment, the greater the maturity risk. For example, market prices of long-term bonds fluctuate much more in response to changes in levels of interest rates than do short-term bonds or notes. When we refer to the yields on U.S. government bonds as risk-free rates, we mean that we regard them as free from the prospect of default, but we recognize that they do incorporate maturity risk: The only part of the yield that is risk-free is the income return component. That is, the interest payments promised are risk-free. But the market price or value of the bonds move up or down as interest rates move, creating capital loss or gain. Thus there is a risk to capital embedded in these bonds. The longer the maturity, the greater the susceptibility to change in market price in response to changes in market rates of interest. With regard to interest rates, much of the uncertainty derives from the uncertainty of future inflation levels. MARKET RISK Market risk (also called systematic risk or undiversifiable risk) is the uncertainty of future returns due to the sensitivity of the return on a subject investment to variability in returns for the investment market as a whole. Although this is a broad conceptual definition, for U.S. companies, the investment market as a whole is generally limited to the U.S. equity markets and typically is measured by returns on either the New York Stock Exchange (NYSE) Composite Index or the Standard & Poor’s (S&P) 500 Index. Some theoreticians say that the only risk the capital markets reward with an expected premium rate of return is market risk, because unique or unsystematic risk can be eliminated by holding a well-diversified portfolio of investments. Recent research has shown that it may be difficult or nearly impossible to be fully diversified. The chapters on the various methods of estimating the cost of capital show that market risk is a factor specifically measured for a particular company or industry in some methods but not at all or not necessarily in others. For example, market or systematic risk is taken into consideration in the Capital Asset Pricing Model (CAPM), which is the subject of Chapter 8, and in other methods of estimating the cost of capital. The term that is commonly used for sensitivity to market risk is beta. While beta has come to have a specific meaning in the context of the CAPM, beta is used in the literature of finance as a more general term meaning the sensitivity of an investment to the market factor. Bonds have beta risks (e.g., to interest rates, to general economic conditions as reflected in the broad stock market, etc.). Individual stocks have beta risks (e.g., to general economic conditions as reflected in the broad stock market, to the relative risks of large company stocks to small company stocks, etc.). In the context of the CAPM, beta attempts to measure the sensitivity of the returns realized by a security in company or an industry to movements in returns of ‘‘the market,’’ usually defined as either the S&P 500 Index or the NYSE Composite Index.
6
See Richard A. Brealey, Stewart C. Myers, and Franklin Allen, Principles of Corporate Finance, 8th ed. (New York: McGrawHill, 2006), 162.
46
Cost of Capital
UNIQUE RISK Unique risk (also called unsystematic risk, residual risk, or company-specific risk) is the uncertainty of expected returns arising from factors other than those factors correlated with the investment market as a whole. These factors may include characteristics of the industry and the individual company. In international investing, they also can include characteristics of a particular country. Some of the unique risk of an investment may be captured in the size premium, which is an adjustment to the textbook CAPM and is the subject of Chapter 12. Fully capturing unique risk in the discount rate requires analysis of the company in comparison with other companies, which is discussed in Chapter 14. However, while the size premium captures many risk factors, the analyst must be careful to capture all the risk factors and at the same time avoid double-counting. OTHER RISK Capital market theory assumes efficient markets. That is, it assumes prices change concurrent with changes in the economic fundamentals (economy, industry, or company factors) such that the market prices of publicly traded stocks represent the consensus of investors as to the present value of cash flows and that changes in such fundamentals are ‘‘instantly’’ recognized in market prices. One recent study supports the rationality of stock prices where data on expected cash flows is available to investors.7 But market inefficiency can and does occur for publicly traded stocks, particularly for smaller company stocks that do not have the investor following such that their prices do not react to changes in fundamentals. We do recognize that market prices may not correctly or fully account for the fundamentals of a smaller, thinly traded public company at particular points in time. We point out problems with textbook theories that fall down in such circumstances. Capital market theory also assumes liquidity of investments. Many of the observations about risk and return are drawn from information for liquid investments. Investors desire liquidity and require greater returns for illiquidity. We specifically address issues pertaining to illiquidity risk in Chapter 25 for minority interests and Chapter 26 for entire businesses.
COST OF EQUITY CAPITAL When using the build-up method (Chapter 7), the Capital Asset Pricing Model (CAPM) (Chapter 8), or another model such as the Fama-French 3-factor model (FF) (Chapter 15), we estimate one or more components of a risk premium and add the total risk premium to the risk-free rate in order to estimate the cost of equity capital. When using publicly traded stock data to imply the cost of equity capital (e.g., the discounted cash flow (DCF) method discussed in Chapter 16) we get a total cost of equity capital without any explicit breakdown regarding how much of it is attributable to a risk-free rate and how much is attributable to the risk premium.
COST OF INVESTED CAPITAL OR OVERALL COST OF CAPITAL The cost of invested capital is a blending of the costs of each component, commonly referred to as the weighted average cost of capital (WACC). Chapter 6 discusses each component in the capital structure, and Chapter 17 addresses the weighted average cost of capital. 7
Keren Bar-Hava, Roni Ofer, and Oded Sarig, ‘‘New Tests of Market Efficiency Using Fully Identifiable Equity Cash Flows,’’ Working paper, February 2007.
Summary
47
SUMMARY The cost of capital is a function of the market’s risk-free rate plus a premium for the risk associated with the investment. Risk is the degree of uncertainty regarding the realization of the expected returns from the investment at the times and in the amounts expected. The authors observe a common error of discounting probability-weighted net cash flows using the risk-free rate number. The false assumption is that the probability weighting accounts for risk. It does not. In an economic sense, the market distinguishes between types of risks of a company or investment: market or systematic risk and unique or unsystematic risk. Market risk is the sensitivity of returns on the subject investment to returns on the overall market. Unique risk is the specific risk of the subject company or industry as opposed to the market as a whole (i.e., the risk that remains after taking into account the market risk). Risk impacts the cost of each of the components of capital: debt, senior equity, and common equity. Because risk has an impact on each capital component, it also has an impact on the weighted average cost of capital. As risk increases, the cost of capital increases, and value decreases. Because risk cannot be observed directly in the market, it must be estimated. The impact of risk on the cost of capital is at once one of the most essential and one of the most difficult analyses in corporate finance and investment analysis.
Appendix 5A
FASB’s Concepts Statement No. 7: Cash Flows and Present Value Discount Rates The Financial Accounting Standards Board’s Concepts Statement No. 7 (Con 7), Using Cash Flow and Present Value in Accounting Measures, addresses issues surrounding the use of cash flow projections and present value techniques in accounting measurement. Practitioners are reading the Statement especially for guidance on implementation of the Statement of Financial Accounting Standard (SFAS) No. 142. The guidance was clarified in SFAS No. 157 Fair Value Measurements, Appendix B of FASB No. 157. Two particular elements of the Con 7 seem to be generating confusion: 1. The comparisons of ‘‘traditional’’ and ‘‘expected cash flow’’ approaches to present value (and Con 7’s endorsement of the latter). [paragraphs 42–61]. 2. The use of the risk-free rate to discount expected cash flows [Appendix A and paragraphs 114– 116]. This second point is probably the more confusing. Con 7 observes that when values are uncertain, accountants are trained to use ‘‘most likely’’ values or ‘‘best estimates.’’ The Statement refers to this practice of using ‘‘most likely’’ values as the traditional method. Then it correctly points out that when probability distributions are asymmetric, the ‘‘most likely’’ cash flow is not the same as the ‘‘expected’’ cash flow (the probability-weighted mean of the distribution of all possible outcomes). Con 7 refers to the use of ‘‘expected’’ cash flows as the expected value method. Note, though, that the risk-free rate alone is generally not the correct discount rate for either method, though it works for other present value methods, as is discussed later. Further, all of the standard finance theory for estimating risk-adjusted discount rates that are most commonly applied in a present value analysis (weighted average cost of capital [WACC], Capital Asset Pricing Method [CAPM], betas, etc.) was developed for the so-called expected value method, not for the traditional method. In fact, most finance practitioners and academics would have presumed that ‘‘traditional method’’ referred to this body of work, not to what Con 7 is referring to. Applying standard finance tools to develop discount rates for ‘‘most likely’’ cash flows is flawed unless the probability distribution is symmetric. There are two alternative valid approaches to discounting uncertain future cash flows. Consistently applied, they give the same result. 1. The risk-adjusted discount rate approach adds a risk premium to the discount rate which is then applied to expected cash flows. (Formula 5A.1) Eðcash flowsÞ PV ¼ ð1 þ kÞ where: k ¼ Risk-adjusted discount rate. Where k > risk-free rate of return (Rf ). 48
FASB’s Concepts Statement No. 7: Cash Flows and Present Value Discount Rates
49
This is the approach most commonly presented in finance texts as the ‘‘standard’’ present value method. Risk premia are typically estimated using a model (e.g., the build-up method or CAPM). 2. The certainty-equivalent approach subtracts a cash risk premium from the expected cash flows and then discounts at the risk-free rate. This appears to be what Con 7 is advocating. (Formula 5A.2)
PV ¼
½Eðcash flowsÞ cash risk premium ð1 þ R f Þ
The approach, though rarely used in companies, also is a present value method. It is theoretically appealing. The numerator is called a certainty equivalent. Here also, CAPM or other models can be used to estimate the cash risk premium. Although Con 7 does not say so explicitly, this is the approach set forth in its Appendix A. What Con 7 calls traditional versus expected value is misleading from a finance perspective. The so-called traditional incorporates probabilities only to the extent of noting which outcome is most likely; all other information in the probability distribution is ignored. In contrast, ‘‘expected value’’ is a probability-weighted average of all possible values the random variable can reach at a given point in time. It uses all the information in the probability distribution. Performing the probability weighting to arrive at the expected value is not by itself a sufficient treatment of risk for discounted cash flow (DCF) purposes. It is necessary but not sufficient. Neither the ‘‘most likely’’ cash flow nor the ‘‘expected’’ cash flow may be discounted at the risk-free rate without further adjustment. Expected cash flows may be discounted at a risk-adjusted discount rate, or they may be charged a cash risk premium and then discounted at the risk-free rate. The ‘‘most likely’’ cash flow should not be incorporated in a present value analysis unless the probability distribution is plausibly symmetric or unless some other accommodation is made for the other possible outcomes. How is the cash risk premium determined? Either:
Conduct interviews with investors (e.g., ask ‘‘What lesser amount of risk-free cash would make you indifferent between the risky gamble and the risk-free cash?’’)
It can be computed formulaically using capital market data as shown in Formula 5A.3: (Formula 5A.3) Eðcash flowÞ ð1 þ kÞ ¼
½Eðcash flowÞ1 ðcash risk premiumÞ ð1 þ R f Þ ¼
Certainty Equivalent ð1 þ R f Þ
50
Cost of Capital
Therefore, to get from the expected cash flow to its certainty equivalent, just multiply the former by the ratio: ½ð1 þ Rf Þ=ð1 þ kÞ, where k is a risk-adjusted discount rate that can be computed in the usual way. (Formula 5A.4) ½Eðcash flowÞ1 ð1 þ R f Þ ¼ Certainty equivalent ð1 þ WACCÞ Con 7 does not explain this, but it is part of widely available and accepted corporate finance theory.1 It is not controversial. It works for all the examples shown here and for broad classes of distributions.
1
See, for example, Richard A. Brealey, Stewart C. Myers, and Franklin Allen, Principles of Corporate Finance, 8th ed. (Boston: Irwin McGraw-Hill, 2006), Chapter. 9.
Chapter 6
Cost Components of a Company’s Capital Structure
Introduction Debt Capital Estimating Current Market Yields on Debt Tax Effect Lowers Cost of Debt Leases Are Debt Personal Guarantees Postretirement Obligations Risky Debt Preferred Equity Convertible Debt and Preferred Equity Employee Stock Options Common Equity Summary
INTRODUCTION The capital structure of many companies includes two or more components, each of which has its own cost of capital. Such companies may be said to have a complex capital structure. The major components commonly comprising a company’s capital structure are:
Debt capital Preferred equity
Common equity
Similarly, a project being considered in a capital budgeting decision may be financed by multiple components of capital. In a complex capital structure, each of these general components may have subcomponents, and each subcomponent may have a different cost of capital. In addition, there may be hybrid or special securities, such as convertible debt or preferred stock, warrants, options, or leases. Ultimately, a company’s or project’s overall cost of capital is a result of the blending of the individual costs of each of these components. This chapter briefly discusses each of the capital structure components, and Chapter 17 shows the process of blending them into a company’s or project’s overall cost of capital, which is called the weighted average cost of capital (WACC). Estimation of the costs of conventional fixed-income components of the capital structure, that is, straight debt and preferred stock, is relatively straightforward, because costs of capital for securities of comparable risk usually are directly observable in the market and the company’s actual embedded 51
52
Cost of Capital
cost is often at or very close to current market rates. Although there can be many controversies surrounding costs of fixed-income capital, especially if unusual provisions exist, we discuss these components only briefly here. This book is not intended to be a comprehensive treatise of debt, preferred and hybrid capital instruments. The rest of this book deals primarily with the critically important but highly elusive and often controversial issue of the cost of equity.
DEBT CAPITAL Conceptually, only ‘‘long-term’’ liabilities are included in a capital structure. However, many closely held companies, especially smaller ones, use what is technically short-term interest-bearing debt as if it were long-term debt. In these cases, it becomes a matter of the analyst’s judgment whether to reclassify the short-term debt as long-term debt and include it in the capital structure for the purpose of estimating the company’s overall cost of capital (WACC). The ‘‘long-term’’ debt would include the current portion of long-term debt and short-term debt used as if it were long-term debt. ESTIMATING CURRENT MARKET YIELDS ON DEBT Usually the cost of debt is equivalent to the company’s interest expense (after adjusting for the tax deductibility of interest) and is readily ascertainable from the footnotes to the company’s financial statements (if the company has either audited or reviewed statements or compiled statements with footnote information). If the rate the company is paying is not a current market rate (e.g., long-term debt issued at a time when market rates were significantly different), then the analyst should estimate what a current market rate would be for that component of the company’s capital structure. The interest rate should be consistent with the financial condition of the subject company based on a comparative analysis of it’s average ratios. Standard & Poor’s publishes debt rating criteria along with the Standard & Poor’s Bond Guide. Standard & Poor’s Corporate Ratings Criteria indicates median ratios by rating. CreditScore is a Standard & Poor’s application that gives a hypothetical credit rating based on the financial metrics of a subject company. The analyst can see where the investment would fit within the bond rating system, then check the financial press to find the yields for the estimated rating. Exhibit 6.1 displays the statistics available on debt ratings for industrials and utilities from Corporate Ratings Criteria. Once you have a debt rating, you can estimate the cost of debt capital using yield curve analysis. If the subject company does not have rated debt, you must estimate the debt rating. Interest rates vary depending on the years to maturity. That relationship is called the yield curve. For example, if short-term U.S. government interest rates for bonds with one-year to maturity have a current yield-to-maturity less than the yield-to-maturity on U.S. government bonds with 10 years to maturity, the yield curve is upward sloping. This is the most common slope for the yield curve over the years. But the yield curve can be inverted or downward sloping at times. Exhibit 6.2 shows an example of determining the weighted average current yield to maturity for a company’s bonds using a yield curve analysis. Assume that the yield curve is represented in the top panel of the exhibit. As you see, the yield curve developed from the example market data is upward sloping. Assume that the subject company debt is rated in the lowest rating categories and that the company’s outstanding debt has maturities as shown in the first column of the bottom panel of Exhibit 6.2. You can estimate the weighted average current yield by applying the appropriate yield to maturity from the third line of the top panel of Exhibit 6.2 to the company’s debt, as shown in columns three and four of the bottom panel of the exhibit.
Debt Capital
Exhibit 6.1
53
Key Industrial and Financial Ratios, Long-term Debt
Table 1 Key Industrial Financial Ratios, Long-term Debt Three-year (2002–2004) medians AAA AA EBIT interest coverage (x) EBITDA interest coverage (x) FFO/total debt (%) Free operating cash flow/total debt (%) Total debt/EBITDA (x) Return on capital (%) Total debt/total debt þ equity (%)
23.8 25.5 203.3 127.6 0.4 27.6 12.4
Table 2 Key Utility Financial Ratios, Long-term Debt Three-year (2002–2004) medians AA EBIT interest coverage (x) FFO interest coverage (x) Net cash flow/capital expenditures (%) FFO/average total debt (%) Total debt/total debt þ equity (%) Common dividend payout (%) Return on common equity (%)
4.4 5.4 86.9 30.6 47.4 78.2 11.3
19.5 24.6 79.9 44.5 0.9 27.0 28.3
A
BBB
BB
B
CCC
8.0 10.2 48.0 25.0 1.6 17.5 37.5
4.7 6.5 35.9 17.3 2.2 13.4 42.5
2.5 3.5 22.4 8.3 3.5 11.3 53.7
1.2 1.9 11.5 2.8 5.3 8.7 75.9
0.4 0.9 5.0 2.1 7.9 3.2 113.5
A
BBB
BB
B
3.1 4.0 76.2 18.2 53.8 72.3 10.8
2.5 3.8 100.2 18.1 58.1 64.2 9.8
1.5 2.6 80.3 11.5 70.6 68.7 4.4
1.3 1.6 32.5 21.6 47.2 4.8 6.0
Table 3 Key Ratios Formulas EBIT interest coverage EBITDA interest coverage
Funds from operations (FFO)/ total debt Free operating cash flow/ total debt Total debt/total debt þ equity
Return on capital
Total debt/EBITDA
Earnings from continuing operations* before interest and taxes/gross interest incurred before subtracting capitalized interest and interest income Adjusted earnings from continuing operationsy before interest, taxes, depreciation, and amortization/gross interest incurred before subtracting capitalized interest and interest income Net income from continuing operations, depreciation and amortization, deferred income taxes, and other noncash items/long-term debtz þ current maturities þ commercial paper, and other short-term borrowings FFO- capital expenditures— (þ) increase (decrease) in working capital (excluding changes in cash, marketable securities, and short-term debt)/long-term debtz þ current maturities, commercial paper, and other short-term borrowings Long-term debtz þ current maturities, commercial paper, and other short-term borrowings/long-term debtz þcurrent maturities, commercial paper, and other short-term borrowings þ shareholders’ equity (including preferred stock) þ minority interest EBIT/Average of beginning of year and end of year capital, including short-term debt, current maturities, long-term debt,z non-current deferred taxes, minority interest, and equity (common and preferred stock) Long-term debtz þ current maturities, commercial paper, and other short-term borrowings/adjusted earnings from continuing operations before interest, taxes, and D&A
*Including interest income and equity earnings; excluding nonrecurring items. y Excludes interest income, equity earnings, and nonrecurring items; also excludes rental expense that exceeds the interest component of capitalized operating leases. z Including amounts for operating lease debt equivalent, and debt associated with accounts receivable sales/securitization programs. Source: Standard & Poor’s Corporate Ratings Criteria 2006 (New York: Standard & Poor’s, a division of McGraw-Hill Companies, Inc.) copyright # 2006: 20, 43. Used with permission. All rights reserved.
54 Exhibit 6.2
Cost of Capital Yield Curve Approach to Determining Current Cost of Debt Capital Year(s) Until Debt Matures
AAA, AA, A BBB BB, B, CCC, CC, C, D
One
Two
Three
Four
Five
Six+
6.49% 7.45% 9.36%
7.15% 8.10% 10.01%
7.29% 8.25% 10.16%
7.38% 8.33% 10.27%
7.44% 8.40% 10.31%
7.60% 8.56 10.47
Yield Curve Approach
Exhibit 6.2 Face Value 1 Year 2 Year 3 Year 4 Year 5 Year Over 5 Years
$180 $166 $45,978 $108 $48 $8,400 $54,880
Yield
Weighted Average
9.36% 10.01% 10.16% 10.27% 10.31% 10.47%
0.03% 0.03% 8.51% 0.02% 0.01% 1.60% 10.20%
The analyst should consider that smaller companies may have higher costs of debt than larger companies because, on average, larger companies have higher credit ratings than smaller companies. Also, smaller companies may not be able to borrow as great a proportion of their capital structure as larger companies. Some companies have more than one class of debt, each with its own cost of debt capital (e.g., senior, subordinate, etc.). Traditionally, the relevant market ‘‘yield’’ has been either the yield to maturity or the yield-to-call date. Either of these yields represents the total return the debt holder expects to receive over the life of the debt instrument, including current yield and any appreciation or depreciation from the market price, to the redemption of the debt at either its maturity or call date, if callable. If the stated interest rate is above current market rates, the bond would be expected to sell at a premium. The yield-to-call date likely would be the appropriate yield, because it probably would be in the issuer’s best interest to call it (redeem it) as soon as possible and refinance it at a lower interest cost. If the stated interest rate is below current market rates, then it usually would not be attractive to the issuer to call it, and the yield to maturity would be the most appropriate rate. Credit quality is not your only criteria when determining the appropriate yield for debt instruments. The period over which cash flows (principal and interest) are expected to be received is also important. If you are matching nontraded debt instruments to traded debt instruments to obtain market observations of yields, you need to estimate the credit quality and the length of time over which cash flows are expected to be received. Increasingly, the debt markets have introduced instruments with varying schedules for paying interest and repaying principal. For example, to compare zero-coupon bonds to bonds paying periodic interest payments, you need to measure the length of time over which you will receive cash flow (interest and principal). With the variety of debt instruments that have become common, you need a method to equate the various instruments. One measure of the length of time over which cash flows are expected is the duration of the cash flows:1
1
For an explanation of duration in the context of bond valuation, see, e.g., Richard A. Brealey, Stewart C., and Franklin Allen, Principles of Corporate Finance, 8th ed. (Boston: Irwin McGraw-Hill, 2006), 632–635; Aswath Damodaran, Investment Valuation: Tools and Techniques for Determining the Value of Any Asset, 2nd ed. (Hoboken, NJ: John Wiley & Sons, 2002), 891–892.
Debt Capital
55
(Formula 6.1) n X n Eðcash flowÞ
Duration ¼
ð1 þ kÞn
1
n X Eðcash flowÞ 1
ð1 þ kÞn
n
n
where: n ¼ Periods of expected receipt of the cash flow from 1 through n E(cash flow) ¼ Period cash flow expected from the security, project, or company k ¼ Discount rate used to convert security, project, or company expected cash flows to present value Exhibit 6.3 is a simple example of calculating the duration of a bond. The $1,000 face value bond, issued several years earlier, has a coupon rate of 10% and will mature in 10 years. (We use the simplifying assumption that interest is paid annually, although interest is typically paid made frequently.) The expected cash flows are $100 per year for 9 years and $1,100 in year 10. Make these assumptions:
Assume that the current market rate of interest, given current interest rates and the risk of the issuing company, is now 15%.
The duration is the weighted present value of the cash flows with the weights being the year. The duration of the bond, as shown in Exhibit 6.3, is 6.24 years. This differs from the maturity date.
The duration is an average time over which you expect to receive the cash flow.
Duration can be used as a tool to measure the effective time over which expected cash flows from any investment will be received. TAX EFFECT LOWERS COST OF DEBT Because interest expense is a tax-deductible expense to a company, the net cost of debt to the company is the interest paid less the tax savings resulting from the deductible interest payment. This after-tax cost of debt can be expressed by Formula 6.2: Exhibit 6.3 (1) Year
Example of Calculating Duration of a Bond (2) Expected Cash Flow
(3) Present Value Factor
1 $100 0.8696 2 $100 0.7561 3 $100 0.6575 4 $100 0.5718 5 $100 0.4972 6 $100 0.4323 7 $100 0.3759 8 $100 0.3269 9 $100 0.2843 10 $1,100 0.2472 Total Duration ¼ Sum of (5)/sum of (4) ¼ 6.24 Years
(4) Present Value of Expected Cash Flow
(5) (5) ¼ (1) (4)
86.96 75.61 65.75 57.18 49.72 43.23 37.59 32.69 28.43 271.90 749.06
86.96 151.23 197.25 228.70 248.59 259.40 263.16 261.52 255.84 2,719.03 4,671.67
56
Cost of Capital
(Formula 6.2) kd ¼ kdð ptÞ ð1 tÞ where: kd ¼ Discount rate for debt (the company’s after-tax cost of debt capital) kd(pt) ¼ Rate of interest on debt (pretax) t ¼ Tax rate (expressed as a percentage of pretax income) For decision-making purposes, most corporate finance theoreticians recommend using the marginal tax rate (the rate of tax paid on the last incremental dollar of taxable income) if that differs from the company’s effective tax rate.2 That makes sense, since the marginal rate will be the cost incurred as a result of the investment. However, the focus should be on the marginal rate over the life of the investment, if that is different from the marginal cost incurred initially. Common practice assumes that the top statutory rate is the applicable rate because the typical assumption is that with the long-term horizon, companies will be profitable and will pay income taxes. But we know from historical records that many companies do not pay the top marginal rate. Simulations of expected income tax rates for public companies are available through Professor John Graham.3 The simulations take into account expected taxable income from current operations, carryover of net operating losses from prior periods, and interest expense from outstanding debt.4 LEASES ARE DEBT Capitalized leases are included in reported debt. But operating leases are a substitute for debt. You should generally include all debt (including off-balance sheet leases) in measuring the debt capital of the company.5 Financial Accounting Standards (FAS) Statement No. 13, Accounting for Leases (October 1975), requires footnote disclosure for noncancellable long-term operating leases.6 The disclosure includes:
Aggregate future minimum payments
Minimum payments for first five fiscal years Aggregate future minimum sublease rentals
Historical rental expense
For example, the Standard & Poor’s Ratings Services group routinely capitalizes operating leases for purposes of calculating comparative ratios.7 An excerpt from their Web site describing their methodology follows.
2 3 4
5 6 7
See, e.g., Allen, Brealey, and Myers, Principles of Corporate Finance, 8th ed., 461.
[email protected] John R. Graham, ‘‘Debt and the Marginal Tax Rate,’’ Journal of Financial Economics, (May 1996): 41–73; John R. Graham and Mike Lemmon, ‘‘Measuring Corporate Tax Rates and Tax Incentives: A New Approach,’’ Journal of Applied Corporate Finance (Spring 1998): 54–65. Aswath Damodaran, Damodaran on Valuation, 2nd ed. (Hoboken, NJ: John Wiley & Sons, 2006), 71–72. FAS No. 13, Accounting for Leases, (October 1975), paragraphs 16, 122. See also ‘‘Off–Balance Sheet Leases: Capitalization and Ratings Implications,’’ Moody’s Investors Service (October 1999).
Debt Capital
57
Corporate Ratings Criteria 2006: To improve financial ratio analysis, Standard & Poor’s uses a financial model that capitalizes off-balancesheet operating lease commitments and allocates minimum lease payments to interest and depreciation expenses. Not only are debt-to-capital ratios affected, but so are interest coverage, funds from operations to debt, total debt to EBITDA, operating margins, and return on capital. . . . The operating lease model is intended to make companies’ financial ratios more accurate and comparable by taking into consideration all assets and liabilities, whether they are on or off the balance sheet. In other words, all rated firms are put on a level playing field, no matter how many assets are leased and how the leases are classified for financial reporting purposes. (We view the distinction between operating leases and capital leases as artificial. In both cases, the lessee contracts for the use of an asset, entering into a debt-like obligation to make periodic rental payments.) The model also helps improve analysis of how profitably a firm employs both its leased and owned assets. By adjusting the capital base for the present value of lease commitments, the return on capital better reflects actual asset profitability.
Exhibit 6.4 shows an example of the methodology. Exhibit 6.5 displays the lease disclosure for a public company and the analysis resulting from capitalizing operating leases.8 Capitalizing operating leases is essential to accurately determine the implied coverage, rating, and market interest rate on outstanding company debt. For some companies, no adjustment is needed because the amount of lease financing used is not significant. But for other companies (e.g., airlines), off-balance sheet lease financing is significant and you must make appropriate adjustments if you hope to calculate a reasonably accurate cost of capital.9 PERSONAL GUARANTEES When estimating the cost of debt for a closely held company, the analyst should ascertain whether the debt is secured by personal guarantees. If so, this is an additional cost of debt that is not reflected directly in the financial statements (or, in some cases, might not even be disclosed). Such guarantees would justify an upward adjustment in the company’s cost of debt to what it would be without the guarantees (assuming that the debt would be available without guarantees). That is, you are interested in the cost of company debt without the influence of guarantor’s pledge of personal assets. You can use the estimated ratings methodology in the earlier section on debt capital to estimate the current implicit credit rating on company debt, the appropriate interest rate, and the implicit market value of outstanding debt.10 For example, in the late 1990s, insurance companies offered guarantees on seller financing. That is, when a company was sold with some percentage of the price as a down payment and the buyer gave the seller a promissory note for the balance (a common procedure in the sale of small businesses and professional practices), the insurance company would guarantee the note to the seller. The required down payment was at least 30% of the purchase price, and the insurance premium was about 3% per annum of the face value of the note. Perhaps 3% can be used as a shortcut estimate for adding to the cost of debt to reflect personal guarantees. Without personal guarantees, many times no debt would be available, and all the company’s capital structure should be discounted at the cost of equity.
8 9
10
This example appeared in a report submitted by Roger Grabowski in a disputed matter. See, e.g., Kirsten M. Ely, ‘‘Operating Lease Accounting and the Market’s Assessment of Equity Risk,’’ Journal of Accounting Research (Autumn 1995): 397–415; and Eugene A. Imhoff, Jr., Robert C. Lipe, and David W. Wright, ‘‘Operating Leases: Income Effects of Constructive Capitalization,’’ Accounting Horizons (June 1997): 12–32. See, for example, Brealey, Myers, and Allen, Principles of Corporate Finance, 8th ed., 655–656.
58
Cost of Capital
Exhibit 6.4
Example of Operating Lease Capitalizations (2004)
Table 1 provides data that would typically appear in the financial statement disclosure. Table 1 Lease Model Calculation* Payment Period
Reporting Year 2004
2005
Year 1 Year 2 Year 3 Year 4 Year 5 Thereafter Total Payments
61.0 54.0 46.1 42.6 38.7 177.9 420.3
65.8 53.3 46.5 41.9 39.6 177.9 425
Source: Standard & Poor’s Corporate Ratings Criteria 2006 (New York: Standard & Poor’s, a division of McGraw-Hill Companies, Inc.) copyright # 2006: 93. Used with permission. All rights reserved. *Reported figures: Future minimum lease commitments (mil. $).
The debt equivalent of the leases is based on discounting future lease commitment data gathered from the notes to financial statements using (1) annual lease payments for the first five years are set forth in the notes; and (2) for the remaining lease years, the model assumes the lease payments approximate the minimum payment due in year five. The number of years remaining under the leases is simply the amount ‘‘thereafter’’ divided by the minimum fifth-year payment. The result is rounded to the nearest whole number. The present value of this payment stream is then determined. The interest rate used is generally the issuer’s average interest rate. Adjustments used in the Standard & Poor’s Ratings model for calculating financial ratios:
Selling, General, and Administrative Expenses (SG&A) adjustment
Average of first-year minimum lease payments in the current and previous years.
SG&A is then reduced by this amount.
Implicit interest *
*
Depreciation expense *
*
Multiply the average (current and previous years) PV of operating leases by the interest rate. In Table 2 we have ($336.5 + $318.7)/2 = $327.6. This figure is then added to the firm’s total interest expense.
Calculated by subtracting the implicit interest from the SG&A adjustment. The lease depreciation is then added to reported depreciation expense.
The interest and depreciation adjustments attempt to allocate the annual rental cost of the operating leases. There is ultimately no change to reported net income as a result of applying the Standard & Poor’s lease analytical methodology.
Table 2 demonstrates the adjustments of the Standard & Poor’s ratings lease model. Table 2 Calculation of Operating Lease Adjustments for 2004
Total debt (reported) Total interest (incl. capitalized interest) Implied interest rate
2004
2003
2002
659.4 36.2 5.5
664.9 40.2 5.6
766.8
Debt Capital
59
Future minimum lease commitments (mil. $) 2005 61 65.8 2006 54 53.3 2007 46.1 46.5 2008 42.6 41.9 2009 38.7 39.6 2010–2014 38.7 2009–2012 39.6 Net present value (NPV) 336.5 318.7 2004 implicit interest Avg. NPV ($327.6) interest rate (5.5%) ¼ $17.9 Lease depreciation expense Adjustment to SG&A* implicit interest ¼ $63.4 $17.9 ¼ $45.5 Adjustment to SG&A—rent Avg. first-year min. payments ($61.0 þ $65.8)/2 ¼ $63.4 Source: Standard & Poor’s Corporate Ratings Criteria 2006 (New York: Standard & Poor’s, a division of McGraw-Hill Companies, Inc.) copyright # 2006: 94. Used with permission. All rights reserved. *SG&A—Selling, general, and administrative expenses.
If you adjust the ‘‘debt’’ balance, you need to adjust the income statement. The imputed ‘‘rent’’ on these assets becomes imputed interest plus depreciation expense. This changes EBIT and EBITDA. (both go up). We can see the impact on the debt and ratios in Table 3. Table 3 Sample Calculation Results
Oper. income/sales (%) EBIT interest coverage (x) EBITDA interest coverage (x) Return on capital Funds from oper./total debt (%) Total debt/EBITDA (x) Total debt/capital (%)
Without Capitalization
With Capitalization
18.6 8.7 12.3 18.9 54.1 1.5 37.6
21.2 6.2 8.6 15.6 40.4 2.1 41.0
Source: Standard & Poor’s Corporate Ratings Criteria 2006 (New York: Standard & Poor’s, a division of McGraw-Hill Companies, Inc.) copyright # 2006: 95. Used with permission. All rights reserved.
POSTRETIREMENT OBLIGATIONS Unfunded liabilities relating to defined benefit pension plans and retiree medical plans are debtlike in nature.11 Employees become the equivalent of creditors of the company because they accepted a portion of their compensation as these deferred benefits. Defined benefit plans differ from defined contribution plans, which are funded on a current basis, because with the latter the sponsor company does not bear the risk of ongoing performance of the assets set aside to fund the obligations. Because of the assumptions necessary for their measurement, you must be cognizant of the relative uncertain nature of accounting for postretirement obligations. When assessing assumptions, you can focus on differences among companies’ disclosures. The analysis requires that you compare the current value of the company’s plan assets to the projected benefit obligation for pensions (PBO) and the accumulated postretirement benefit obligations for retiree medical obligations (APBO). The PBO may understate the true economic liability because it 11
This section is drawn from Standard & Poor’s Corporate Rating Critera 2006 (New York: Standard & Poor’s/McGraw-Hill, 2006), 96–111.
60
Cost of Capital
Exhibit 6.5
Sample Capitalization of Operating Leases
Leases The Company distributes petroleum products throughout its marketing areas through a combination of owned and leased terminals. Leases for product distribution terminals are generally for short periods of time and continue in effect until canceled by either party with contracted days of notice, generally 30 to 60 days. Most product distribution terminal leases are subject to escalations based on various factors. The Company subleases a portion of its leased product distribution terminals. During December 1997, the Company purchased the Riverhead Terminal pursuant to a purchase option in the lease. Additionally, the Company leases two of its refining processing units pursuant to long-term operating leases. The Company has long-term leases with special purpose entities for land and equipment at the Company’s BP California, Exxon Arizona, and certain 76 Products sites. These leases provide the Company the option to purchase, at agreed-upon contracted prices, (a) not less than all of the leased assets at annual anniversary dates, and (b) a portion of the leased assets for resale to unaffiliated parties at quarterly lease payment dates. The Company may cancel the leases provided that lessors receive minimum sales values for the assets. The contracted purchase option price and minimum guaranteed sales values decline over the term of the leases. Minimum annual rentals vary with a reference interest rate (LIBOR). The Company leases the majority of its stores and certain other property and equipment. The store leases generally have primary terms of up to 25 years with varying renewal provisions. Under certain of these leases, the Company is subject to additional rentals based on store sales as well as escalations in the minimum future lease amount. The leases for other property and equipment are for terms of up to 15 years. Most of the Company’s lease arrangements provide the Company an option to purchase the assets at the end of the lease term. The Company may also cancel certain of its leases provided that the lessor receives minimum sales values for the leased assets. Most of the leases require that the Company provide for the payment of real estate taxes, repairs and maintenance, and insurance. At December 31, 1997, future minimum obligations under non-cancelable operating leases and warehousing agreements are as follows: (Thousands of Dollars) 1998 $159,441 1999 $147,674 2000 $134,432 2001 (a) $107,610 2002 (a) $44,023 Thereafter $390,376 ———— Total Payments $983,556 Less future minimum sublease income $110,855 ———— Net Total Payments $872,701 ———— ———— (a) Excludes guaranteed residual payments, totaling $123,221,000 (2001) and $191,522,000 (2002) due at the end of the lease term, which will be reduced by the fair market value of the leased assets. Source: Tosco Corporation 10k, December 1997.
Using the data from the disclosure, we can calculate the discounted present value of lease commitments at 7% discount rate (current market rate for borrowing), net of sublease income and including guaranteed residual payments: Present Value of Lease Payments @ 7%
$702,703
Future Sublease Income as % of Total Lease Payments Estimated Value of Future Sublease Income
11.3% $79,405
Debt Capital
61
Present Value of Lease Payments @ 7% Less: Estimated Value of Future Sublease Income Plus: Present Value of Guaranteed Residual Payments @ 7% Present Value of Lease Commitments Net of Sublease Value Adjusting the balance sheet we get the following: Total Debt per Balance Sheet (12/97) Market Value of Balance Sheet Debt1 Value of Operating Leases Market Value of Debt Plus Operating Leases 1
$702,703 (79,405) 230,557 $853,855 $1,893,165 $2,075,200 853,855 $2,929,055
See Chapter 17 for calculation.
We can calculate the ratios of market value of invested capital (MVIC) to earnings before interest, taxes, depreciation, and amortization (EBITDA) and debt to MVIC as shown next: MVIC/EBITDA Debt/MVIC 1 2
Book1 9.4 24%
Adjusted2 9.0 33%
Using book value of debt and unadjusted EBITDA. Using market value of debt plus operating leases and EBITDA adjusted for lease rent expense.
does not take into account future benefit improvements, even if probable, unless provided for in the current labor agreement. The PBO may differ from the accumulated benefit obligation (ABO), which is a measure of the present value of all the benefits earned to date. It approximates the value of the benefits if the company were to terminate the plan (similar to a ‘‘shutdown’’ scenario). The PBO also accounts for the effect of salary and wage increases on benefit payouts that are linked to future compensation amounts by formula. The PBO measures the pension promise at the amount that will ultimately be settled as the company continues (a ‘‘going concern’’ scenario). Under FAS Statement No. 87, PBO is the basis for expense recognition but ABO serves as a basis for balance sheet recognition of the accumulated, but unfunded liability. PBO, though, is the better measure of the true economic liability. Standard & Poor’s Ratings Services considers that: Companies with the same funding ratios in their benefit plans do not, however, necessarily bear the same risks related to their plans. The size of the gross liability is also important because, where the gross liability is large relative to the company’s assets, any given percentage change in the liability or related plan assets will have a much more significant effect than if the gross liability had been less substantial.12
Any adjustment made for unfunded pension liabilities, health care obligations, and other forms of deferred compensation are similar to debt but differ from debt instruments because the full amount of the expense incurred in meeting the obligations will result in tax deductions when made. This is equivalent to being able to expense both interest and principal of a debt obligation. Thus you need to factor in such benefit liabilities on an after-tax basis. Exhibit 6.6 displays an example of the adjustment to the debt because of unfunded PBOs. In Exhibit 6.6, the debt is increased by the amount of the unfunded projected benefit obligations, with the effect of a reduction to equity. This causes the capitalization to change (increase in debt to book value of equity) and the company’s debt rating is likely to decline, raising the cost of debt capital.
12
Standard & Poor’s Corporate Rating Critera 2006 (New York: Standard & Poor’s/McGraw-Hill, 2006), 98.
62
Cost of Capital
Exhibit 6.6
Example of Adjustment to Debt Due to Unfunded PBO
Capitalization Adjustments XYZ Co.* Debt totals $1.0 billion and equity $600 million at Dec. 31, 200X. Tax rate: 33%-1/3%. Projected benefits obligation (PBO) exceeds fair value of plan assets by $1.1 billion at year-end 200X, up from $700 million at the previous year-end. Change in benefits obligation (Mil. $) PBO, beginning of year Current service cost Interest cost (7% 2,000) Actuarial adjustments Benefits paid
2,000.0 60.0 140.0 100.0 300.0
PBO, end of year
2,000.0
Change in plan assets Fair value of plan assets, beginning of year Actual return on plan assets Benefits paid Fair value of plan assets, end of year Unfunded PBO
1,300.0 100.0 300.0 900.0 1,100.0
Source: Standard & Poor’s Corporate Ratings Criteria 2006 (New York: Standard & Poor’s, a division of McGraw-Hill Companies, Inc.) copyright # 2006: 107. Used with permission. All rights reserved.
Assuming only $800 million of the $1.1 billion unfunded accumulated benefits obligation was recognized on the balance sheet at Dec. 31, 200X, adjusted debt leverage is computed as follows: Adjusted debt and debt-like liabilities¼ Adjusted equity¼
Adjusted debt and debt-like liabilities/total capitalization This compares with unadjusted total debt to capitalization of:
Total debt þ [(1 tax rate) (unfunded PBO)] Book equity [(1 tax rate) (unfunded PBO liability already recognized on balance sheet)]
$1.0 bil. þ (66 2/3% $1.1 bil.) ¼ $1.733 bil. $600 mil. [66 2/3% ($1.1 bil. $800 mil.)] ¼ $400 mil. $1.733 bil./($1.733 bil. þ $400 mil.) ¼ 81.2% $1.0 bil./($1.0 bil. þ $600 mil.) ¼ 62.5%
Source: Standard & Poor’s Corporate Ratings Criteria 2006 (New York: Standard & Poor’s, a division of McGraw-Hill Companies, Inc.) copyright # 2006: 107. Used with permission. All rights reserved. *XYZ Co. operates in a country where benefits plans are prefunded and plan contributions are tax-deductible. Any intangible pension asset account relating to previous service cost would be eliminated against equity. This would also be tax-affected.
RISKY DEBT While a common approach in estimating the cost of debt capital is to use the promised yield on newly issued debt of the company (or comparably rated debt of other companies) in theory, the expected return on debt should reflect the promised yield net of expected default loss. The expected default loss (net of expected recovery) should not be included in the cost of debt because it is not part of the expected return.
Convertible Debt and Preferred Equity
63
One commonly used approach to estimating net default loss is using studies of historical default rates and recovery rates. But market expectations may differ from historical rates.13 One can look upon the value of equity as a call option on the company’s assets and use volatility for public companies’ stock to infer the portion of the yield that equates to the expected default loss on debt.14 Alternatively, if one considers risky debt as a combination of a safe bond and a short position in a put option (i.e., the company has the option of defaulting when the value of the operations and assets decline to amounts below the face value of the debts), then one can use volatility of public debt to infer the portion of the yield that equates to expected default loss on debt (i.e., difference between face value and portion of market value representing return of principal).15
PREFERRED EQUITY If the capital structure includes preferred equity, the yield rate can be used as the cost of that component. If the dividend is at or close to the current market rate for preferred stocks with comparable features and risk, then the stated rate can be a proxy for market yield. If the rate is not close to a current market yield rate, then the analyst should estimate what a current market yield rate would be for that component of the company’s capital structure. Standard & Poor’s publishes preferred stock rating criteria along with the Standard & Poor’s Stock Guide. Using this publication, analysts can see where the company’s preferred stock would fit within the preferred stock rating system, then check the financial press to find the yields for preferred stocks with similar features and estimated rating. Analysts must adjust for any differences in features often found in privately issued preferred equity, such as special voting or liquidation rights. If the preferred stock is callable, the same analysis (of the market rate of dividend compared to the dividend relative to call price as discussed with respect to debt) applies to the preferred stock.16
CONVERTIBLE DEBT AND PREFERRED EQUITY Convertible debt and convertible preferred equity are hybrid instruments that are essentially two securities combined into one: a straight debt or preferred equity element plus a warrant. Typically the instrument is callable at the request of the issuer. This feature is for the benefit of the issuer. The call forces conversion of the bond or preferred instrument earlier than the investor might chose. The cost of capital for the convertible instrument is the sum of the costs of these two elements. A warrant is a long-term call option issued by a company on a specific class of its own common equity, usually at a fixed price. Convertibles are easiest to understand if they are analyzed first as debt or nonconvertible preferred equity and then the value is adjusted for the value of the warrants (long-term call options).17 We discuss the overall cost of capital for a firm with convertible debt or convertible preferred equity in Chapter 17. There are several theories why companies issue convertible instruments. One theory is that convertible instruments offer a cheaper source of financing than straight debt financing or preferred 13
14
15 16 17
Ian A. Cooper and Sergei A. Davydenko, ‘‘Estimating the Cost of Risky Debt,’’ Journal of Applied Corporate Finance (Summer 2007): 90–94. Jens Hilscher, ‘‘Is the Corporate Bond Market Forward Looking?’’ European Central Bank Working Paper Series No. 800 (August 2007). Ibid, 92–94. See, for example, Damodaran, Investment Valuation, 2nd ed., 212–213. Ibid, 806–914.
64
Cost of Capital
equity financing. The convertible feature offers the issuer (1) the probability of a hybrid price for common stock not just the common stock price at the time the convertible instrument is issued and (2) the possibility of issuing debt or preferred equity at a lower yield than would be the case were the instruments not convertible. But the issuer is giving up a valuable right: the right to buy stock in the future at a predetermined price (the conversion price, which may change over time). That right has value and the value given up must be balanced with the seeming benefits.18 New valuation models for these hybrid instruments are being studied employing advanced methodologies for measuring risk. For example, one study adapts simulation models to their valuation.19 Another study proposes use of advanced binomial warrant (option) pricing model.20 Another study compares various models to observed market prices.21
EMPLOYEE STOCK OPTIONS Employee stock options are equity. Outstanding employee stock options will generate capital for the company once they are exercised; they represent a part of the equity capital of the company. Issuing employee stock options is a company expense, and the income statement should reflect the cost of issuing options to employees. Employee stock options are part of the cost of attracting and retaining employees.22 The topic of employee stock option valuation has received considerable attention since the Financial Accounting Standards Board proposed and later adopted the requirement to expense employee stock options.23 Valuation models have been proposed: binomial lattice models, modified BlackScholes models, and so on, to incorporate the nuances of valuing employee stock options compared to traded options.24 Finally, integral to pricing options is the forecasting of volatilities of the common stock on which the option pricing models depend.25
COMMON EQUITY Part II of this book is devoted to estimating the cost of common equity capital. Unlike yield to maturity on debt or yield on preferred equity, the cost of common equity for specific companies or risk categories cannot be directly observed in the market. The cost of equity capital is the expected rate of return needed to induce investors to place funds in a particular equity investment. As with the returns on bonds or preferred stock, the returns on common equity have two components:
18
19
20
21
22 23 24
25
Igor Loncarski, Jenke ter Horst, and Chris Veld, ‘‘Why Do Companies Issue Convertible Bonds? A Review of Theory and Empirical Evidence,’’ in Advances in Corporate Finance and Asset Pricing, ed. L. D. R. Renneboog (Amsterdam: Elsevier, 2006), 311–339. Dmitri Lvov, Ali Bora Yigitbasioglu, and Naoufel El Bachir, ‘‘Pricing Convertible Bonds by Simulation,’’ Working paper, December 2004. Zhiguo Tan and Yiping Cai, ‘‘Risk Equilibrium Binomial Model for Convertible Bonds Pricing,’’ South West University of Finance and Economics, Working paper January 28, 2007. Yuriy Zabolotnyuk, Robert Jones, and Chris Veld, ‘‘An Empirical Comparison of Convertible Bond Valuation Models,’’ Working paper, June 18, 2007. See, e.g., Damodaran, note 6 above pages 72–73 and note 13 above pages 440–450. See, e.g., Mark H. Lang, ‘‘Employee Stock Options and Equity Valuation,’’ Research Foundation of CFA Monograph (2004). Jaksˇa Cvitanic´, Zvi Wiener, and Fernando Zapatero, ‘‘Analytic Pricing of Employee Stock Options,’’ Working paper, July 19, 2006. George J. Jiang and Yisong S. Tian, ‘‘Volatility Forecasting and the Expensing of Stock Options,’’ Working paper, November 21, 2005.
Summary
65
1. Dividends or distributions 2. Changes in market value (capital gains or losses) Because the cost of capital is a forward-looking concept, and because these expectations regarding amounts of return cannot be directly observed, they must be estimated from current and past market evidence. Analysts primarily use theoretical-based methods of estimating the cost of equity capital from market data, each with variations:
Build-up methods (Chapter 7)
Capital asset pricing model (Chapter 8)
Arbitrage pricing theory (Chapter 15) Fama-French 3-factor model (Chapter 15)
Market-derived capital pricing model (Chapter 15) Yield-spread model (Chapter 15)
Or they derive an implied cost of equity capital from the current market price of the common stock (for public companies) (Chapter 16).
SUMMARY The typical components of a company’s capital structure are summarized in Exhibit 6.7. In addition to the straight debt, preferred equity, and common equity shown, some companies have hybrid securities, such as convertible debt or preferred stock and options or warrants. Chapter 17 explains how to combine the costs of each of these components to derive a company’s overall cost of capital, the weighted average cost of capital. Whereas this chapter has addressed briefly the cost of each component, the rest of the book focuses primarily on the many ways to estimate the cost of equity capital.
Exhibit 6.7
Capital Structure Components
Short-term notes Long-term debt Capital leases Unfunded postretirement obligations Preferred equity Common equity Additional paid-in capital Retained earnings Off–balance sheet financing Warrants Operating leases
Not technically part of the capital structure, but may be included in many cases, especially if being used as if long term (e.g., officer loans) YES (including current portion) Normally YES Normally YES YES YES—all part of common equity YES—all part of common equity YES—all part of common equity Normally YES YES Normally YES
Part 2
Estimating the Cost of Equity Capital and the Overall Cost of Capital
Chapter 7
Build-up Method Introduction Formula for Estimating the Cost of Equity Capital by the Build-up Method Risk-free Rate Risk-free Rate Represented by U.S. Government Securities Components of the Risk-free Rate Why Only Three Specific Maturities? Selecting the Best Risk-free Maturity Equity Risk Premium Small-Company Premium Company-Specific Risk Premium Size Smaller than the Smallest Size Premium Group Incorporating an Industry Risk Factor into the Build-up Method Volatility of Returns Leverage Other Company-Specific Factors Example of the Build-up Method Using Morningstar Data Example of the Build-up Method Using Duff & Phelps Size Study Data Summary
INTRODUCTION Previous chapters discussed the cost of capital in terms of its two major components, a risk-free rate and a risk premium. This chapter examines these components in general, dividing the equity risk premium into three principal subcomponents. The typical ‘‘build-up model’’ for estimating the cost of common equity capital consists of two primary components, with three subcomponents: 1. A ‘‘risk-free’’ rate 2. A premium for risk, including any or all of these subcomponents:
A general equity risk premium A small company premium A company-specific risk premium
In international investing, there may also be a country-specific risk premium, reflecting uncertainties owing to economic and political instability in the particular country to the extent that the instability is greater than in the U.S. We discuss the cost of capital in developing economies in Chapter 8.
69
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Cost of Capital
FORMULA FOR ESTIMATING THE COST OF EQUITY CAPITAL BY THE BUILD-UP METHOD Stating the preceding concept in a formula, the equity cost of capital can be estimated by the build-up method as: (Formula 7.1) EðRi Þ ¼ R f þ RPm þ RPs þ RPu where: E(Ri) ¼ Expected (market required) rate of return on security i Rf ¼ Rate of return available on a risk-free security as of the valuation date RPm ¼ General equity risk premium (ERP) for the ‘‘market’’ RPs ¼ Risk premium for smaller size RPu ¼ Risk premium attributable to the specific company or to the industry (the u stands for unsystematic risk, as defined in Chapter 5) After discussing how to develop each of these four components, we will substitute some numbers into the formula to reach an estimated cost of equity capital for a sample company. An additional possible component, industry risk, is discussed in a later section in this chapter.
RISK-FREE RATE A ‘‘risk-free rate’’ is the return available as of the valuation date on a security that the market generally regards as free of the risk of default. RISK-FREE RATE REPRESENTED BY U.S. GOVERNMENT SECURITIES In the build-up method (as well as in other methods), analysts typically use the yield to maturity on U.S. government securities, as of the valuation date, as the risk-free rate. They generally choose U.S. government obligations of one of these maturities:
30 days 5 years
20 years
Sources for yields to maturity for maturities of any length as of any valuation date can be found in the daily financial press. (When it is not possible to find yields to match the exact length of maturity, choose the closest maturity available.) To obtain a yield on long-term government bonds—for example, a 20-year yield, which is commonly used as the default long-term government bond—most analysts go to the financial press (e.g., The Wall Street Journal or The New York Times) as of the valuation date and find the yield on a bond originally issued for 30 years with approximately 20 years left to maturity. The Federal Reserve Statistical Release tracks 20-year yields. The link to its Web site is http://federalreserve.gov/release/ h15. The St. Louis branch of the Federal Reserve Bank also tracks 20-year yields. The link to its Web site is: http://research.stlouisfed.org/fred2/series/GS20. Alternatively, you can use the returns on
Risk-free Rate
71
zero-coupon government STRIPS.1 Long-term government bonds make interim interest payments, which results in their duration being less than their stated maturity. COMPONENTS OF THE RISK-FREE RATE The so-called risk-free rate reflects three components: 1. Rental rate. A real return for lending the funds over the investment period, thus forgoing consumption for which the funds otherwise could be used. 2. Inflation. The expected rate of inflation over the term of the risk-free investment. 3. Maturity risk or investment rate risk. As discussed in Chapter 5, the risk that the principal’s market value will rise or fall during the period to maturity as a function of changes in the general level of interest rates. All three of these economic factors are embedded in the yield to maturity for any given maturity length. However, it is not possible to observe the market consensus about how much of the yield for any given maturity is attributable to each of these factors. Very importantly, note that this basic risk-free rate includes inflation. Therefore, when this rate is used to estimate a cost of capital to discount expected future cash flows, those future cash flows also should reflect the expected effect of inflation. In the economic sense of nominal versus real dollars, we are building a cost of capital in nominal terms, and it should be used to discount expected returns that also are expressed in nominal terms. WHY ONLY THREE SPECIFIC MATURITIES? The risk-free rate typically is chosen from one of only three specific maturities because the build-up model incorporates a general equity risk premium often based on historical data developed by Morningstar. Morningstar data provides short-term, intermediate-term, and long-term historical risk premium series, based on data corresponding to the aforementioned three maturities. Twenty years is the longest maturity because Morningstar’s data goes all the way back to 1926, and 20 years was the longest U.S. government obligation issued during the earlier years of that time period. Data in the Duff & Phelps Studies can be used as an alternative to using Morningstar data in the build-up method. The risk premiums for the build-up method in the Duff & Phelps Studies include a general equity risk premium and size premium in one number, measured in terms of a premium over long-term U.S. government bonds (20-year). SELECTING THE BEST RISK-FREE MATURITY In valuing ‘‘going-concern’’ businesses and long-term investments made by businesses, practitioners generally use long-term government bonds as the risk-free security and estimate the equity risk premium (ERP or notationally RPm) in relation to long-term government bonds. This convention represents a realistic, simplifying assumption. Most business investments have long durations and suffer from a reinvestment risk comparable to that of long-term government bonds. As such, the use of long-term government bonds and an ERP estimated relative to long-term bonds more closely matches the investment horizon and risks confronting business managers in capital decisions and valuators in valuation problems than reference to Treasury bills. 1
STRIPS stands for ‘‘Separate Trading of Registered Interest and Principal of Securities.’’ STRIPS allow investors to hold and trade the individual components of U.S. government bonds and notes as separate securities. See, e.g., Brian P. Sack, ‘‘Using Treasury STRIPS to Measure the Yield Curve,’’ FEDS Working Paper No. 2000-42 (October 2000).
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Cost of Capital Exhibit 7.1
Yields on 10-Year, 20-Year, and 30-Year U.S. Government Bonds Yields
Period 6/15/2007 4/6/2006 2005 2004 2003 2002 2001 2000 1999 1998 1997
10-Year
20-Year
30-Year
5.2 4.6 4.3 4.3 4.2 3.9 5.1 5.1 6.4 4.9 5.8
5.3 4.8 4.6 4.9 5.0 4.9 5.8 5.6 6.8 5.6 6.0
5.2 4.7 n/a n/a n/a n/a 5.5 5.4 6.4 5.2 5.9
The consensus of financial analysts today is to use the 20-year U.S. government bond yield to maturity as of the effective date of valuation because:
It most closely matches the often-assumed perpetual lifetime horizon of an equity investment. The longest-term yields to maturity fluctuate considerably less than short-term rates and thus are less likely to introduce unwarranted short-term distortions into the actual cost of capital.
People generally are willing to recognize and accept that the maturity risk is embedded in this base, or otherwise risk-free, rate.
It matches the longest-term bond over which the equity risk premium is measured in the Morningstar data series.
Many analysts use either a 10-year or a 30-year yield, but as a practical matter it usually does not differ greatly from the 20-year yield. Exhibit 7.1 summarizes the yields on 10-year, 20-year, and 30-year government bonds for the last decade. Sometimes analysts select a 5-year rate to match the perceived investment horizon for the subject equity investment. The 30-day rate is the purest risk-free base rate because it contains virtually no maturity risk. If inflation is high, it does reflect the inflation component, but it contains little compensation for inflation uncertainty.
EQUITY RISK PREMIUM On an equity investment, the return on investment that the investor will (or has the opportunity to) realize usually has two components: 1. Distributions during the holding period (e.g., dividends or withdrawals) 2. The capital gain or loss in the value of the investment (For an active public security, it is considered part of the return whether the investor chooses to realize it or not, because the investor has that choice at any time.) Obviously, these expected returns on equities are much less certain (or more risky) than the interest and maturity payments on U.S. government obligations. This difference in risk is well documented by
Company-Specific Risk Premium
73
much higher standard deviations (year-to-year volatility) in returns on the stock market compared with the standard deviation of year-to-year returns on U.S. government obligations. To accept this greater risk, investors demand higher expected returns for investing in equities than for investing in U.S. government obligations. As discussed earlier, this differential in expected return on the broad stock market over U.S. government obligations (sometimes referred to as the excess return, but not to be confused with the excess earnings method) is called the equity risk premium (ERP) (or interchangeably market risk premium). See Chapter 9 for a complete discussion on estimating the equity risk premium.
SMALL-COMPANY PREMIUM Studies have provided evidence that the degree of risk and corresponding cost of capital increase with the decreasing size of the company. The studies show that this addition to the realized market premium is over and above the amount that would be warranted solely for the companies’ systematic risk. Chapter 12 discusses the results of research on this phenomenon as well as the data sources. Many practitioners use the small-company premium in the build-up method (difference between the realized returns on small company stocks and large company stocks). Data in the Duff & Phelps studies can be used as an alternative to using Morningstar data in the build-up method. The risk premiums for the build-up method in the Duff & Phelps studies include a general equity risk premium and size premium in one number. The Duff & Phelps study is discussed in Chapter 12.
COMPANY-SPECIFIC RISK PREMIUM To the extent that the subject company’s risk characteristics are greater or less than the typical risk characteristics of the companies from which the equity risk premium and the size premium were drawn, a further adjustment may be necessary to estimate the cost of capital for the specific company. Such adjustment may be based on (but not necessarily limited to) analysis of five factors: 1. 2. 3. 4. 5.
Size smaller than the smallest size premium group Industry risk Volatility of returns Leverage Other company-specific factors
SIZE SMALLER THAN THE SMALLEST SIZE PREMIUM GROUP As will be seen in Exhibits 12.7 and 12.8 from the Duff & Phelps studies, the smallest size group for which we have specific size premium data averages $76 million in market value of equity, $54 million in sales, and so forth. If the subject company is somewhat smaller than this cutoff, most observers believe that a further size premium adjustment is warranted, but there have not yet been adequate empirical studies to quantify this amount. The Duff & Phelps studies do provide regressions of the observed relationships between size and returns to use for extrapolating to smaller firms. Alternatively, a conservative approach may be appropriate, perhaps adding a point or two to the discount rate for a significantly smaller company and leaving any greater adjustments to be attributed to other specifically identifiable risk factors.
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Cost of Capital
INCORPORATING AN INDUSTRY RISK FACTOR INTO THE BUILD-UP METHOD The SBBI Valuation Edition 2006 Yearbook presents an expanded alternative build-up model that includes a separate variable for the industry risk premium. This model is shown in Formula 7.2. (Formula 7.2) EðRi Þ ¼ R f þ RPm þ RPs þ= RPi þ RPu where: E(Ri) ¼ Expected rate of return Rf ¼ Risk-free rate of return RPm ¼ Equity risk premium (market risk) RPs ¼ Size premium RPi ¼ Industry risk premium RPu ¼ Company-specific risk premium (unsystematic risk) The industry in which the company operates may have more or less risk than the average of other companies in the same size category. This differential is very hard to quantify in the build-up model. However, if the company is obviously in a very low-risk industry (e.g., water distribution) or a very high-risk industry (e.g., airlines), a point or two adjustment, either downward or upward, for this factor may be warranted. In an attempt to make the build-up method more closely approximate the Capital Asset Pricing Method (CAPM), Morningstar since 2000 has published industry risk adjustment factors (see Chapter 14). These ‘‘industries’’ are based on Standard Industrial Classification (SIC) codes. The industry premia have been adjusted quarterly since 2005. Each company’s contribution to the adjustment shown is based on a full-information beta (see Chapter 10). Morningstar calculates each company’s contribution to the full-information beta based on the segment sales reported in the company’s 10-K for that SIC code. A listing of each company included in each industry is available for downloading for free from the Morningstar Web site, http://corporate.morningstar.com/ib/asp/detail .aspx?xmlfile¼1431.xml. These industry adjustments are valid only to the extent that the subject company’s risk characteristics are similar to the weighted average of the companies that make up the ‘‘industry’’ for the SIC code shown. Any analyst contemplating using the Morningstar industry adjustments in the build-up method should download the list of companies included in the industry and make a judgment as to whether the risk characteristics of the companies are substantially similar to the subject company to make the adjustment reliable. In order to aid this judgment, the analyst may wish to go to the 10-K filings for the companies included. The description of the companies included give the analyst a much better picture of the similarities of the companies included in the industry to the subject. Also, the segment information in the 10-K will show the proportionate contribution to earnings, which may be very different than the proportionate contribution to revenue. But stock returns are a function of profit, not revenue, and use of revenue may result in an overweight of a low-profit segment. VOLATILITY OF RETURNS High volatility of returns (usually measured by the standard deviation of historical returns over some period) is another risk factor. However, without comparable data for the average of the other companies in the size category and/or industry, it is not possible to make a quantified comparison. If the
Example of the Build-up Method Using Morningstar Data
75
analyst perceives that the subject company returns are either unusually stable or unusually volatile compared with others in the size category and/or industry, some adjustment for this factor may be warranted, which would be a factor to consider in the company-specific risk premium. LEVERAGE Leverage is clearly a factor that can be compared between the subject company and its size peers. Exhibit 12.7 gives the market value of equity for each size category. For example, the smallest size category averages $76 million in market value of equity with a capital structure of roughly 30% debt and 70% equity, at market value. Size breakdowns of other size measures show generally similar capital structures. If the subject company’s capital structure significantly departs from this average, some upward or downward adjustment to the cost of equity relative to the average company in the size category would seem warranted. For example, highly leveraged companies should have higher equity costs of capital compared with companies with lower debt levels, all else being equal. Of course, a decrease in the required equity return might be warranted if the subject’s capital structure has little or no debt. OTHER COMPANY-SPECIFIC FACTORS Other factors specific to a particular company that affect risk could include, for example:
Concentration of customer base Key person dependence
Key supplier dependence
Abnormal present or pending competition Pending regulatory changes
Pending lawsuits Volatility of returns
Strengths/weaknesses of company management
A wide variety of other possible specific factors
Because the size premium tends to reflect some factors of this type, the analyst should adjust further only for specific items that are truly unique to the subject company. Unfortunately, despite the widespread use by analysts and appraisers of a company-specific risk premium in a build-up (or CAPM) model, there is limited academic research on the topic, and the company-specific risk premium remains in the realm of the analyst’s judgment. We discuss the research in Chapter 14.
EXAMPLE OF THE BUILD-UP METHOD USING MORNINGSTAR DATA Now that we have discussed the factors in the build-up model, we can substitute some numbers into the method. We start with five assumptions about Shannon’s Bull Market (SBM), a closely held, regional steakhouse chain with excellent food and drink and noted for its friendly service. We first use the Morningstar data in Formula 7.2: EðRi Þ ¼ R f þ RPm þ RPs þ= RPi þ RPu
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Cost of Capital
1. Risk-free rate. We will use the 20-year U.S. government bond, for which the yield to maturity at the valuation date of December 31, 2005, was 4.6%. 2. Equity risk premium. We will use the results of the research on the expected equity risk premium discussed in Chapter 9 and use an RPm estimate of 5.0% for this example. 3. Size premium. The SBBI Valuation Edition 2006 Yearbook shows that the size premium for the tenth decile—smallest 10% of New York Stock Exchange (NYSE) stocks with American Stock Exchange (AMEX) and Nasdaq Stock Market (Nasdaq) stocks included—over and above the return estimated by CAPM is 6.36%.2 4. Industry adjustment factor. SBM is in the SIC code 58, Eating and Drinking Places. The Industry Risk premia for that industry, developed using the full-information beta with contributions to that beta from eighty companies, is 2.07%. 5. Company-specific risk premium. SBM is considerably smaller than the average of the smallest 10% of NYSE stocks, and our analyst perceives that the restaurant industry is riskier than the average for the companies included in the subject company industry adjustment factor. Although the assessment is somewhat subjective, our analyst recommends adding a company-specific risk factor of 3.0% because of risk factors identified as unique to this company. Substituting the preceding information in Formula 7.2 we have: (Formula 7.3) EðRi Þ ¼ 4:6% þ 5:0% þ 6:36% þ ð2:07%Þ þ 3:0% ¼ 16:89%; rounded to 17% The indicated cost of capital for SBM is approximately 17%. Some analysts prefer to present these calculations in tabular form, as shown.
Build-up Cost of Equity Capital for SBM Using Morningstar Data Risk-free rate Equity risk premium Size premium Industry risk premium Company-specific risk premium SBM indicated cost of equity capital
4.6% 5.0% 6.36% 2.07% 3.00% 17% (rounded)
EXAMPLE OF THE BUILD-UP METHOD USING DUFF & PHELPS SIZE STUDY DATA As an alternative to Formula 7.2 for the build-up method, EðRi Þ ¼ R f þ RPm þ RPs þ RPu , where a general risk premium is added for the ‘‘market’’ (equity risk premium) and a risk premium for small size to the risk-free rate, you can use the Size Study to develop a risk premium for the subject company that measures risk in terms of the total effect of market risk and size.
2
Morningstar recommends using the size premium (return in excess of CAPM) analysis for both the build-up and CAPM cost of equity estimates. These data can be seen in the SBBI Valuation Edition 2006 Yearbook, at 38–39. See Chapter 12 in this volume for more information.
Example of the Build-up Method Using Duff & Phelps Size Study Data
77
The formula then is modified to be: (Formula 7.4) EðRi Þ ¼ R f þ RPmþs þ RPu where: E(Ri) ¼ Expected (market required) rate of return on security i Rf ¼ Rate of return available on a risk-free security as of the valuation date RPm+s ¼ risk premium for the ‘‘market’’ plus risk premium for size RPu ¼ Risk premium attributable to the specific company or to the industry The Size Study sorts companies by eight size measures (see Chapter 12 for a list of the measures), breaking the NYSE universe of companies into 25 size-ranked categories or portfolios and adding AMEX- and Nasdaq-listed companies to each category based on their respective size measures. We use four assumptions: 1. Risk-free rate. We will use the 20-year U.S. government bond, for which the yield to maturity at the valuation date of December 31, 2005, was 4.6%. 2. Risk premium. The Size Study incorporates both the equity risk premium and the size premium into a single number. The Duff & Phelps Risk Premium Report Size Study indicates that the risk premium for the smallest companies are as shown in the table. We use only six of the eight size measures listed in the report because SBM is closely held. Size as Measured by Book Value of Common Equity 5-year Average Net Income Total Assets 5-year Average EBITDA Sales Number of Employees Median Risk Premium
Risk Premium 12.34% 13.10% 12.72% 12.93% 12.21% 12.57% 12.6% (rounded)
3. Industry adjustment factor. You might consider applying this adjustment as listed in the SBBI Yearbook since the Size Study contains no comparable data. SBM is in the SIC code 58, Eating and Drinking Places. The industry risk premia for that industry was developed using the full-information beta with contributions to that beta from eighty companies is 2.07%. For purposes of this example, we are including this risk adjustment and adding it as part of the company-specific risk premium. 4. Company-specific risk premium. SBM is considerably smaller than the average of the smallest 10% of NYSE stocks, and our analyst perceives that the subject company is riskier than the average for the companies included in the industry adjustment. Although the assessment is somewhat subjective, our analyst recommends adding a company-specific risk factor of 3.0% because of risk factors identified as unique to this company. Substituting the preceding information in Formula 7.5, we have:
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Cost of Capital
(Formula 7.5) EðRi Þ ¼ 4:6% þ 12:6 þ ð2:07%Þ þ 3:0% ¼ 18:13%; rounded to 18% The indicated cost of capital for SBM is approximately 18%. Some analysts prefer to present these calculations in tabular form, as shown. Build-up Cost of Equity Capital for SBM Using Duff & Phelps Size Study Data Risk-free rate Risk premium (ERP plus size premium) Industry risk premium Company-specific premium SBM indicated cost of equity capital
4.6% 12.6% 2.07% 3.0% 18% (rounded)
If we were using the Capital Asset Pricing Model (CAPM) (the subject of Chapter 8), a portion of the size premium and probably the entire industry portion of the specific risk premium would be captured in the ‘‘beta’’ factor, which is the difference between CAPM and the straight build-up method. Of course, if these build-up method figures were presented in a formal valuation report, each of the numbers in the calculation would be footnoted as to its source, and each would be supported by a narrative explanation.
SUMMARY The build-up model for estimating the cost of equity capital has five components: A risk-free rate A general equity risk premium A small company premium A company-specific risk adjustment (which can be either positive or negative, depending on the risk comparisons between the subject company and others from which the size premium was derived) 5. Possibly, an industry adjustment factor 1. 2. 3. 4.
These factors are summarized schematically in Exhibit 7.2. In a sense, the build-up method is a version of the Capital Asset Pricing Model without specifically incorporating systematic risk.
Exhibit 7.2
Summary of Development of Equity Discount Rate Using Build-up Method
Risk-free rate* + Equity risk premium + Small company premium +/ Specific risk
20-year, 5-year, or 30-day Treasury yield as of valuation date Expected equity risk premium corresponding to risk-free rate Small stock premium or premium over return expected by CAPM Specific risk difference in subject company relative to companies from which above data are drawn.
*The ‘‘risk-free’’ rate actually has one element of risk: maturity risk (sometimes called interest rate or horizon risk), the risk that the value of the bond will fluctuate with changes in the general level of interest rates.
Chapter 8
Capital Asset Pricing Model
Concept of Market or Systematic Risk Background of the Capital Asset Pricing Model Market or Systematic and Unique or Unsystematic Risks Using Beta to Estimate Expected Rate of Return Expanding CAPM to Incorporate Size Premium and Specific Risk Firm Size Phenomenon Company-Specific Risk Factor Expanded CAPM Cost of Capital Formula Examples of the CAPM Example of CAPM Method Using Morningstar Data Example of CAPM method using Duff & Phelps Size Study Data Assumptions Underlying the Capital Asset Pricing Model Summary
CONCEPT OF MARKET OR SYSTEMATIC RISK For more than 30 years, financial theorists generally have favored the notion that using the Capital Asset Pricing Model (CAPM) as the preferred method to estimate the cost of equity capital. In spite of many criticisms, it is still one of the most widely used models for estimating the cost of equity capital, especially for larger companies.* The primary difference between the CAPM and the build-up model presented in Chapter 7 is the introduction of market or systematic risk for a specific stock as a modifier to the general equity risk premium. Market risk is measured by a factor called beta. Beta measures the sensitivity of excess total returns (total returns over the risk-free rate of returns) on any individual security or portfolio of securities to the total excess returns on some measure of the market, such as the Standard & Poor’s (S & P) 500 Index or the New York Stock Exchange (NYSE) Composite Index. Chapter 10 discusses methods for estimating beta. Note at this point, however, that beta is measured by reference to total stock returns, which have two components: 1. Dividends 2. Change in market price Because closely held companies divisions and reporting units have no market price, their betas cannot be measured directly. Thus, to use the CAPM to estimate the cost of capital for a closely held
* Chapter 8 draws heavily on Shannon P. Pratt, Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed. (New York: McGraw-Hill, 2008).
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Cost of Capital
company division or reporting unit, it is necessary to estimate a proxy beta for that business. This usually is accomplished by using an average or median beta for the industry group or by selecting specific guideline public companies and using some composite, such as the average or median, of their betas. CAPM is one of several mechanisms to estimate the cost of equity capital. All other things being equal, the cost of capital for any given company is the same whether you arrive at it by CAPM or by the build-up method. CAPM, however, generally requires public companies from which to develop betas. For some industries, especially those characterized by many small companies, public companies on which to base an estimate of beta simply do not exist.
BACKGROUND OF THE CAPITAL ASSET PRICING MODEL The Capital Asset Pricing Model is part of a larger body of economic theory known as capital market theory (CMT). CMT also includes security analysis and portfolio management theory, a normative theory that describes how investors should behave in selecting common stocks for their portfolios, under a given set of assumptions. In contrast, the CAPM is a positive theory, meaning it describes the market relationships that will result if investors behave in the manner prescribed by portfolio theory. The CAPM is a conceptual cornerstone of modern capital market theory. Its relevance to business valuations and capital budgeting is that businesses, business interests, and business investments are a subset of the investment opportunities available in the total capital market; thus, the determination of the prices of businesses theoretically should be subject to the same economic forces and relationships that determine the prices of other investment assets.
MARKET OR SYSTEMATIC AND UNIQUE OR UNSYSTEMATIC RISKS In Chapter 5 we defined risk conceptually as the degree of uncertainty regarding the realization of future economic income. Capital market theory divides risk into two components (other than maturity risk): market or systematic risk and unique or unsystematic risk. Stated in nontechnical terms, market risk or systematic risk (also known as undiversifiable risk) is the uncertainty of future returns owing to the sensitivity of the return on the subject investment to variability in the returns for a composite measure of marketable investments. Unique or unsystematic risk (also known as diversifiable risk, residual risk, or specific risk) is a function of the characteristics of the industry, the individual company, and the type of investment interest and is unrelated to variation of returns in the market as a whole. To the extent that the industry as a whole is sensitive to market movements, that portion of the industry’s risk would be captured in beta, the measure of market risk. Company-specific characteristics may include, for example, management’s ability to weather changing economic conditions, relations between labor and management, the possibility of strikes, the success or failure of a particular marketing program, or any other factor specific to the company. Total risk depends on both systematic and unsystematic factors. A fundamental assumption of the CAPM is that the risk premium portion of a security’s expected return is a function of that security’s market risk. That is because capital market theory assumes that investors hold, or have the ability to hold, common stocks in large, well-diversified portfolios. Under that assumption, investors will not require compensation (i.e., a higher return) for the unsystematic risk because they can easily diversify it away. Therefore, the only risk pertinent to a study of capital asset pricing theory is market risk. As one well-known corporate finance text puts it: ‘‘The crucial
Using Beta to Estimate Expected Rate of Return
81
distinction between diversifiable and nondiversifiable risks is the main idea underlying the capital asset pricing model.’’1
USING BETA TO ESTIMATE EXPECTED RATE OF RETURN The CAPM leads to the conclusion that a security’s equity risk premium (the required excess rate of return for a security over and above the risk-free rate) is a linear function of the security’s beta. This linear function is described in this univariate linear regression formula: (Formula 8.1) EðRi Þ ¼ R f þ BðRPm Þ where: E(Ri) ¼ Expected return (cost of capital) for an individual security Rf ¼ Rate of return available on a risk-free security (as of the valuation date) B ¼ Beta RPm ¼ Equity risk premium for the market as a whole (or, by definition, the equity risk premium for a security with a beta of 1.0) The preceding linear relationship is shown schematically in Exhibit 8.1, which presents the security market line (SML), a schematic portrayal of the expected return-beta relationship. According to CAPM theory, if the combination of an analyst’s expected rate of return on a given security and its risk, as measured by beta, places it below the security market line, such as security X in Exhibit 8.1, the analyst would consider that security (e.g., common stock) mispriced. It would be mispriced in the sense that the analyst’s expected return on that security is less than it would be if the security were correctly priced, assuming fully efficient capital markets. To put the security in equilibrium according to that analyst’s expectations, the price of the security must decline, allowing the rate of return to increase until it is just sufficient to compensate the investor for bearing the security’s risk. In theory, all common stocks in the market, in equilibrium, adjust in price until the consensus expected rate of return on each is sufficient to compensate investors for holding them. In that situation, the market risk/expected rate of return characteristics of all those securities will place them on the security market line. As Exhibit 8.1 shows, the beta for the market as a whole is 1.0. Therefore, from a numerical standpoint, beta has the following interpretations:
Beta > 1.0
Beta ¼ 1.0
1
When market rates of return move up or down, the rates of return for the subject tend to move in the same direction and with greater magnitude. For example, for a stock with no dividend, if the market is up 10%, the price of a stock with a beta of 1.2 would be expected to be up 12%. If the market is down 10%, the price of the same stock would be expected to be down 12%. Many hightech companies are good examples of stocks with high betas. Fluctuations in rates of return for the subject tend to equal fluctuations in rates of return for the market.
Richard A. Brealey, Stewart C. Myers, and Franklin Allen, Principles of Corporate Finance, 8th ed. (Boston: Irwin McGrawHill, 2006), 958.
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Cost of Capital
Beta < 1.0
Negative beta (rare)
When market rates of return move up or down, rates of return for the subject tend to move up or down, but to a lesser extent. For example, for a stock with no dividend, if the market is up 10%, the price of a stock with a beta of .8 would be expected to be up 8%. The classic example of a lowbeta stock would be a utility that has not diversified into riskier activities. Rates of return for the subject tend to move in the opposite direction from changes in rates of return for the market. Stocks with negative betas are rare. A few gold-mining companies have had negative betas. Another example would be an investment company whose investment policy was to take short positions. It would have a negative beta.
To illustrate, using Formula 8.1 as part of the process of estimating a company’s cost of equity capital, consider stocks of average size, publicly traded companies i, j, and k, with betas of 0.8, 1.0, and 1.2, respectively; a risk-free rate in the market (Rf) of 4.6% (0.046) at the valuation date; and a market equity risk premium (RPm) of 5% (0.05). For company i, which is less sensitive to market movements than the average company, we can substitute in Formula 8.1 in this way: (Formula 8.2) EðRi Þ ¼ 0:046 þ 0:8ð0:05Þ ¼ 0:046 þ 0:04 ¼ 0:086 Thus, the indicated cost of equity capital for company i is estimated to be 8.6% because it is less risky, in terms of market risk, than the average stock on the market.
Expected Rate of Return
E(Ri)
Security Market Line 0.166 0.15 E(Rm)
X
0.134 Rf
0.8
Exhibit 8.1
1.0
1.2 Beta
Security Market Line
Source: Shannon P. Pratt, Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed. (New York: The McGraw-Hill Companies, Inc., 2008). Reprinted with permission. All rights reserved. E(Ri) = Expected return for the individual security E(Rm) = Expected return on the market Rf = Risk-free rate available as of the valuation date In a market in perfect equilibrium, all securities would fall on the security market line. The security X is mispriced, with a return less than it would be on the security market line.
Expanding CAPM to Incorporate Size Premium and Specific Risk
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For company j, which has average sensitivity to market movements, we can substitute in (Formula 8.1) in this way: (Formula 8.3) EðRi Þ ¼ 0:046 þ 1:0ð0:05Þ ¼ 0:046 þ 0:05 ¼ 0:096 The indicated cost of equity capital for company j is estimated to be 9.6%, the estimated cost of capital for the average stock, because its market risk is equal to the average of the market as a whole. For company k, which has greater-than-average sensitivity to market movements, we can substitute in Formula 8.1 as shown: (Formula 8.4) EðRi Þ ¼ 0:046 þ 1:2ð0:05Þ ¼ 0:046 þ 0:06 ¼ 0:106 Thus, the indicated cost of equity capital for company k is estimated to be 10.6% because it is riskier, in terms of market risk, than the average stock on the market. Note that in the preceding pure formulation of the CAPM, the required rate of return for a given stock is composed of only three factors: 1. The risk-free rate 2. The market’s general equity risk premium of the subject security 3. The stock’s volatility to the market, the beta See Chapter 9 for a discussion of the market’s general equity risk premium.
EXPANDING CAPM TO INCORPORATE SIZE PREMIUM AND SPECIFIC RISK FIRM SIZE PHENOMENON Many empirical studies performed since CAPM was originally developed have indicated that realized total returns on smaller companies have been substantially greater over a long period of time than the original formulation of the CAPM (as given in Formula 8.1) would have predicted. Morningstar comments on this phenomenon: One of the most remarkable discoveries of modern finance is that of a relationship between firm size and return. The relationship cuts across the entire size spectrum but is most evident among smaller companies, which have higher returns on average than larger ones. . . . The firm size phenomenon is remarkable in several ways. First, the greater risk of small stocks does not, in the context of the capital asset pricing model (CAPM), fully account for their higher returns over the long term. In the CAPM, only systematic or beta risk is rewarded; small company stocks have had returns in excess of those implied by their betas. Second, the calendar annual return differences between small and large companies are serially correlated. This suggests that past annual returns may be of some value in predicting future annual returns. Such serial correlation, or autocorrelation, is practically unknown in the market for large stocks and in most other equity markets but is evident in the size premia.2 2
SBBI, Valuation Edition 2007 Yearbook (Chicago: Morningstar, 2007), 129, 134.
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Cost of Capital
There are currently two widely used sources of size premium data: SBBI Yearbook and the Duff & Phelps Size Study. The size effect and those sources are the subjects of Chapter 12. COMPANY-SPECIFIC RISK FACTOR The notion that the only component of risk that investors care about is market or systematic risk is based on the assumption that all unique or unsystematic risk can be eliminated by holding a perfectly diversified portfolio of risky assets that will, by definition, have a beta of 1.0. Without addressing the validity of that assumption for the public markets here, it is obviously not feasible for investors in closely held companies to hold such a perfectly diversified portfolio that would eliminate all unique risk. Therefore, for the cost of capital for closely held companies, even when using the CAPM, we have to consider whether there may be other risk elements that neither the beta factor (market risk factor) nor the size premium fully accounts for. If so, an adjustment to the discount rate for unique risk would be appropriate. Just as in the build-up model, the ‘‘specific risk’’ factor could be negative if the analyst concluded that the subject company was less risky than the average of the other companies from which the proxy estimates for the other elements of the cost of equity capital were drawn. For example, a company could have a well-protected, above-average price for its products as a result of a strong trademark, resulting in significantly less earnings volatility than experienced by its competitors.
EXPANDED CAPM COST OF CAPITAL FORMULA If we expand CAPM to also reflect the size effect and company specific risk, we can expand the cost of equity capital formula to add these two factors: (Formula 8.5) EðRi Þ ¼ R f þ BðRPm Þ þ RPs þ RPu where: E(Ri) ¼ Expected rate of return on security i Rf ¼ Rate of return available on a risk-free security as of the valuation date B ¼ Beta RPm ¼ General equity risk premium for the market RPs ¼ Risk premium for small size RPu ¼ Risk premium attributable to the specific company (u stands for unique or unsystematic risk)
EXAMPLES OF A CAPM MODEL The next examples use two sources of size premium data: Morningstar and the Duff & Phelps Study. EXAMPLE OF CAPM METHOD USING MORNINGSTAR DATA To put some numbers into Formula 8.5, we will make five assumptions about Unique Computer Systems (UCS), a fictional specialty manufacturer in the computer industry with publicly traded stock:
Examples of a CAPM Model
85
1. Risk-free rate. As of the valuation date, the yield to maturity on 20-year U.S. government bonds is 4.6%. 2. Beta. The UCS beta is 1.6. 3. Equity risk premium. We will use the results of the research on the expected equity risk premium discussed in Chapter 9 and use estimate of 5.0% for this example. 4. Size premium. The SBBI Valuation Edition 2006 Yearbook shows that the size premium for microcap stocks (the size premium for this size firm in excess of the risk captured in CAPM through beta) is 3.95%. (We will assume here that this is on the borderline between Morningstar’s ninth and tenth size deciles and use the micro-cap size premium.) 5. Company-specific risk factor. Because of special risk factors, the analyst has estimated that there should be an additional specific risk factor of 1.0%. Substituting this information in Formula 8.5, we have: (Formula 8.6) EðRi Þ ¼ 4:6 þ 1:6ð5:0Þ þ 3:95 þ 1:0 ¼ 4:6 þ 8:0 þ 3:95 þ 1:0 ¼ 17:55% Thus, the indicated cost of equity capital for UCS is estimated to be 18% (rounded). Some analysts prefer to present the preceding calculations in tabular form:
Risk-free Rate Equity risk premium: General equity risk premium Beta Size premium Company-specific risk premium UCS cost of equity capital
4.6% 5.01.6 8.0% 3.95 1.0 18% (rounded)
EXAMPLE OF A CAPM METHOD USING DUFF & PHELPS SIZE STUDY DATA The Size Study sorts companies by eight size measures, breaking the NYSE universe of companies into 25 size-ranked categories or portfolios and adding AMEX- and Nasdaq-listed companies to each category based upon their respective size measures. Again, using Formula 8.5, we assume: 1. Risk-free rate. As of the valuation date, the yield to maturity on 20-year U.S. government bonds is 4.6%. 2. Beta. The UCS beta is 1.6. 3. Equity risk premium. We will use the results of the research on the expected equity risk premium discussed in Chapter 9 and use an RPm estimate of 5.0% for this example. 4. Size premium. The Duff & Phelps Risk Premium Report Size Study (premium over CAPM) indicates that the size premia for UCS are:
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Cost of Capital
Size as Measured by
Size Premium
Market Value of Common Equity Book Value of Common Equity 5-year Average Net Income Market Value of Invested Capital Total Assets 5-year Average EBITDA Sales Number of Employees Median Size Premium
5.03% 4.34% 5.21% 4.17% 4.58% 4.75% 4.11% 5.63% 4.7% (rounded)
5. Company-specific risk factor. Because of special risk factors, the analyst has estimated that there should be an additional specific risk factor of 1.0%. Substituting this information in Formula 8.5, we have: (Formula 8.7) EðRi Þ ¼ 4:6 þ 1:6ð5:0Þ þ 4:7 þ 1:0 ¼ 4:6 þ 8:0 þ 4:7 þ 1:0 ¼ 18:30% Thus, the indicated cost of equity capital for UCS is estimated to be 18% (rounded). Some analysts prefer to present the preceding calculations in tabular form: Risk-free rate Equity risk premium: General equity risk premium Beta Small stock size premium Specific risk premium UCS cost of equity capital
4.6% 5.01.6 8.0% 4.7 1.0 18% (rounded)
Of course, if this information were presented in a formal valuation report, each of the numbers would be footnoted as to its source, and each would be supported by narrative explanation.
ASSUMPTIONS UNDERLYING THE CAPITAL ASSET PRICING MODEL Eight assumptions underlie the CAPM: Investors are risk averse. Rational investors seek to hold efficient portfolios (i.e., portfolios that are fully diversified). All investors have identical investment time horizons (i.e., expected holding periods). All investors have identical expectations about such variables as expected rates of return and how capitalization rates are generated. 5. There are no transaction costs. 1. 2. 3. 4.
Summary
87
6. There are no investment-related taxes. (However, there may be corporate income taxes.) 7. The rate received from lending money is the same as the cost of borrowing money. 8. The market has perfect divisibility and liquidity (i.e., investors can readily buy or sell any desired fractional interest). Obviously, the extent to which these assumptions are or are not met in the real world will have a bearing on the validity of the CAPM for the valuation of any company and particularly closely held businesses, business interests, or investment projects. For example, while the perfect divisibility and liquidity assumption approximates reality for publicly traded stocks, the same is not true for closely held companies. This is one reason why the company-specific, nonsystematic risk factor may be rewarded in expected returns for closely held companies, even if it is not for public companies. The CAPM, like most economic models, offers a theoretical framework for how certain relationships would exist subject to certain assumptions. Although not all assumptions are met in the real world, the CAPM provides a reasonable framework for estimation of the cost of capital. Other models are discussed in later chapters.
SUMMARY The Capital Asset Pricing Model expands on the build-up model by introducing the beta coefficient, an estimate of market risk or systematic risk, the sensitivity of returns for the subject company stock to returns for the market. The CAPM has several underlying assumptions, which may be met to a greater or lesser extent for the market as a whole or for any particular company or investment. While some question its usefulness given its underlying assumptions, CAPM is widely used today.3 But CAPM has been attacked because beta (discussed in Chapter 11) has not been found to be a very reliable measure of risk in practice and because its underlying assumptions may not in fact hold true in practice. Therefore, practitioners in all fields must understand its usefulness and its limitations. Exhibit 8.2 is a schematic summary of using the CAPM to estimate the cost of equity capital.
Exhibit 8.2
Capital Asset Pricing Model Method of Estimating Equity Discount Rate
Risk-free rate* + Equity risk premiumy + Size premium Specific risk *
y
3
20-year, 5-year, or 30-day Treasury yield as of valuation date Expected equity risk premium corresponding to risk-free rate. In CAPM, multiplied by beta. Premium over that predicted by beta Specific risk difference in subject company relative to companies from which above data are drawn
The ‘‘risk-free’’ rate actually has one element of risk: maturity risk (sometimes called interest risk or horizon risk)—the risk that the value of the bond will fluctuate with changes in the general level of interest rates. Short-term estimate matched to 30-day risk-free rate; mid-term estimate matched to 5-year risk-free rate; long-term estimate matched to 20-year risk-free rate. Such data available from Morningstar. The equity risk premium could also be estimated by other models, as discussed in Chapter 9, Equity Risk Premium.
John R. Graham, and Campbell R. Harvey, ‘‘The Theory and Practice of Corporate Finance,’’ Journal of Financial Economics (May 2001): 187–243, survey corporate executives and find that 75% of firms use the CAPM to estimate the cost of equity capital; 34% use CAPM with additional adjustment factors (such as premium for international operations), 39% use historical realized returns (combining market and unique risks), and 15% input cost of equity capital from a discounted cash flow model. Many firms use more than one method.
Chapter 9
Equity Risk Premium
Introduction Defining the Equity Risk Premium Estimating the ERP Nominal or Real? Which Risk-free Rate to Use in Estimating the ERP Matching Risk-free Rate with ERP Measuring the Average Period of the Expected Cash Flows Realized Risk Premium (ex Post) Approach Measuring Realized Risk Premiums Historical Stock and Bond Returns Summarizing Realized Risk Premium Data What Periodicity of Past Measurement? Selecting a Sample Period Is Bias Introduced by Using the Arithmetic Average in Estimating ERP? Comparing Investor Expectations to Realized Risk Premiums Changes in Economics that Caused Unexpectedly Large Realized Risk Premiums Forward-Looking (ex Ante) Approaches Bottom-up Approaches Top-down Approaches Surveys Other Sources of ERP Estimates Unconditional versus Conditional ERP Summary Appendix 9A
INTRODUCTION The equity risk premium (ERP) (often interchangeably referred to as the market risk premium) is defined as the extra return (over the expected yield on risk-free securities) that investors expect to receive from an investment in a diversified portfolio of common stocks.
The authors wish to acknowledge the contribution of David King, CFA, former colleague of Mr. Grabowski, to the discussion contained herein. This chapter is an update and expansion to prior work of these authors; see Roger Grabowski and David King, ‘‘Equity Risk Premium,’’ in The Handbook of Business Valuation and Intellectual Property Analysis (New York: McGraw-Hill, 2004), 3–29; ‘‘Equity Risk Premium: What Valuation Consultants Need to Know About Current Research—2005 Update,’’ Valuation Strategies (September/October 2005); and Roger Grabowski, ‘‘Equity Risk Premium: 2006 Update,’’ Business Valuation Review (Summer 2006). We also wish to thank David Turney and Aaron Reddington for the calculation assistance they provided.
89
90
Cost of Capital
Estimating the ERP is one of the most important decisions you must make in developing a discount rate. For example, the effect of a decision that the appropriate ERP is 4% instead of 8% in the Capital Asset Pricing Model (CAPM) will generally have a greater impact on the concluded discount rate than alternative theories of the proper measure of other components, for example, beta. One academic study looked at sources of error in estimating expected rates of return over time and concluded: We find that the great majority of the error in estimating the cost of capital is found in the risk premium estimate, and relatively small errors are due to the risk measure, or beta. This suggests that analysts should improve estimation procedures for market risk premiums, which are commonly based on historical averages.1
In ranking what matters and what does not matter in estimating the cost of equity capital, another author categorizes the choice of the ERP as a ‘‘high impact decision,’’ likely to make a difference of more than two percentage points and could make a difference of more than four points.2 Three driving forces behind the discussions that have evolved on ERP include: 1. What returns can be expected from investments by retirement plans in publicly traded common stocks by retirement plans? 2. What expected returns are being priced in the observed values of publicly traded common stocks? 3. What is the appropriate cost of capital to use in discounting future cash flows of a company or a project to their present value equivalent? Because of the importance of the ERP estimate and the fact that we find many practitioners confused about estimating ERP, we report on recent studies and report on ERP estimates at the beginning of 2007. We conclude with our recommended ERP.
DEFINING THE EQUITY RISK PREMIUM The ERP (or notational RPm) is defined as: where:
RPm ¼ Rm R f
RPm ¼ the equity risk premium Rm ¼ the expected return on a fully diversified portfolio of equity securities Rf ¼ the rate of return expected on a risk-free security What is referred to as the ERP means, in practice, a general equity risk premium using as a proxy for the ‘‘market’’ either the Standard & Poor’s (S&P) 500 or the New York Stock Exchange (NYSE) composite stock index. ERP is a forward-looking concept. It is an expectation as of the valuation date for which no market quotes are observable. In this chapter, we are addressing returns of publicly traded stocks. Those returns establish a beginning benchmark for closely held investments. 1
2
Wayne Ferson and Dennis Locke, ‘‘Estimating the Cost of Capital through Time: An Analysis of the Sources of Error,’’ Management Science (April 1998): 485–500. Seth Armitage, The Cost of Capital: Intermediate Theory (Cambridge: Cambridge University Press, 2005), 319–320.
Which Risk-free Rate to Use in Estimating the ERP
91
ESTIMATING THE ERP While you can observe premiums realized over time by referring to historical data (i.e., realized return approach or ex post approach), such realized premiums do not represent the ERP expected in prior periods, nor do they represent the current ERP. Rather, realized premiums may, at best, represent only a sample from prior periods of what may have been the expected ERP. To the extent that realized premiums on the average equate to expected premiums in prior periods, such samples may be representative of current expectations. But to the extent that events that are not expected to reoccur caused realized returns to differ from prior expectations, such samples should be adjusted to remove the effects of these nonrecurring events. Such adjustments are needed to improve the predictive power of the sample. Alternatively, you can directly derive implied forward-looking estimates for the ERP from data on the underlying expectations of growth in corporate earnings and dividends or from projections of specific analysts as to dividends and future stock prices (ex ante approach).3 The goal of either approach is to estimate the true expected ERP as of the valuation date. Even then the expected ERP can be thought of in terms of a normal or unconditional ERP and a conditional ERP based on current prospects.4 We address issues involving the conditional ERP later. There is no one universally accepted standard for estimating ERP. A wide variety of premiums are used in practice and recommended by academics and financial advisors. NOMINAL OR REAL? Both the expected return on a fully diversified portfolio of equity securities and the rate of return expected on a risk-free security can be stated in nominal (including expected inflation) or real terms (expected inflation removed). ERP should not be affected by inflation. If both returns are expressed in nominal terms, the difference in essence removes the expected inflation; if both returns are expressed in real terms, inflation has been removed, but the difference remains the same. But ex post realized returns will be affected by differences between expected inflation and realized inflation.
WHICH RISK-FREE RATE TO USE IN ESTIMATING THE ERP Any estimate of ERP must be made in relation to a risk-free security. That is, the expected return on a fully diversified portfolio of equity securities must be measured in its relationship to the rate of return expected on a risk-free security. The selection of an appropriate risk-free security with which to base the ERP estimate is a function of the expected holding period for the investment to which the discount rate (rate of return) is to apply. For example, if you were estimating the equity return on a highly liquid investment and the expected holding period were potentially short-term, a U.S. government short-term bond (e.g., Treasury or T-bill) may be an appropriate instrument to use in benchmarking the ERP estimate. Alternatively, if you were estimating the equity return on a long-term investment, such as the valuation of a business where the value can be equated to the present value of a series of future cash flows over many years, then the yield on a long-term U.S. government bond may be the more appropriate instrument in benchmarking the ERP estimate.
3 4
See, for example, Eugene F. Fama and Kenneth R. French, ‘‘The Equity Premium.’’ Journal of Finance (April 2002): 637–659. Robert Arnott, ‘‘Historical Results,’’ Equity Risk Premium Forum, AIMR (November 8, 2001): 27.
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Cost of Capital
Common academic practice in empirical studies of rates of return realized on portfolios of stocks in excess of a risk-free rate is to benchmark stock returns against realized monthly returns of ‘‘riskfree’’ 90-day T-bills or one-year government bonds. A T-bill rate is the purest risk-free base rate because it contains essentially no maturity risk. If inflation is high, it does reflect the inflation component, but it contains little compensation for inflation uncertainty. Problems in using such a risk-free security as a benchmark are that (1) T-bill rates may not reflect market-determined investor return requirements on long-term investments due to central bank actions affecting the short-term interest rates, and (2) rates on short-term securities tend to be more volatile than yields on longer maturities. Long-term government bonds are free of default risk but are not ‘‘risk-free.’’ Long-term government bonds are sensitive to future interest fluctuations. Investors are not sure of the purchasing power of the dollars they will receive upon maturity or the reinvestment rate that will be available to them to reinvest the interest payments received over the life of the bond. As a result, the long-term empirical evidence is that returns on long-term government bonds on the average exceed the returns on T-bills.5 The long-term premium of government bond returns in excess of the average expected interest rates on T-bills (average of future forward rates) is commonly referred to as the horizon premium. The horizon premium compensates the investor for the maturity risk of the bond. The horizon premium equals the added return expected on the average on long-term bonds due to inflation and interest rate risk. As interest rates change unexpectedly in the future, the bond price will vary. That is, bonds are subject to market risk due to unexpected changes in interest rates. The horizon premium compensates investors for that market risk. MATCHING RISK-FREE RATE WITH ERP In theory, when determining the risk-free rate and the matching ERP you should be matching the risk-free security and the ERP with the period in which the investment cash flows are expected. For example (where b is a risk measure for the investment): Short-term cash flows: Current T-bill rate þ b ðRPm over T-billsÞ Cash flows expected in: Year 1 : 1-year government bond rate þ b ðRPm over1-year bondsÞ Year 2 : 2-year forward rate on government bonds þ b ðRPm over 2-year bondsÞ Year 3 : 3-year forward rate on government bonds þ b ðRPmÞ over3-year bondsÞ; and so on Cash flows expected in the long-term : Current long-term government bond rate þ b ðRPm over long-term government bondsÞ MEASURING THE AVERAGE PERIOD OF THE EXPECTED CASH FLOWS Can one measure the ‘‘average’’ period of expected cash flows and use an average maturity period for the risk-free security and the ERP? One measure of the length of planning horizon over which cash flows are expected is the duration of cash flows. We introduced the concept of duration in Chapter 6 as a measure of the effective time period over which you receive cash flows from bonds. In a similar manner, you can calculate the expected duration of any stream of expected cash flows for any project. For valuation of a ‘‘going-concern’’ business, for example, assume you expect the cash flow in the first year following the valuation date of $1 million to increase at an average 5
When short-term interest rates exceed long-term rates, the yield curve is ‘‘inverted.’’
Realized Risk Premium (ex Post ) Approach
93
compound rate of 4% per annum. Assume a discount rate of 15%. If you project cash flows each year for 100 years, the calculated duration of the cash flows is approximately 10.5 years.6 In practice, few discount each cash flow using a matched maturity risk-free rate and ERP estimate. In valuing going-concern businesses and long-term investments made by businesses, practitioners generally use long-term government bonds as the risk-free security and estimate the ERP in relation to long-term government bonds. This convention both represents a realistic, simplifying assumption and is consistent with the CAPM.7 If the expected cash flows are risky and follow a random walk, but the risk-free rate and the ERP are expected to be constant over time, then the risk-adjusted discount rate for discounting the risky cash flows is constant as well. Most business investments have long durations and suffer from a reinvestment risk comparable to that of long-term government bonds. As such, the use of long-term government bonds and an ERP estimated relative to long-term bonds more closely matches the investment horizon and risks confronting business managers in capital budgeting decisions and valuators in valuation problems than reference to T-bills. Therefore, in the remainder of this chapter we have translated all estimates of ERP to estimates relative to long-term government bonds.
REALIZED RISK PREMIUM (ex POST ) APPROACH While academics and practitioners agree that ERP is a forward-looking concept, many practitioners use historical data only to estimate the ERP under the assumption that historical data are a valid proxy for current investor expectations. In the realized risk premium approach, the estimate of the ERP is the risk premium (realized return on stocks in excess of the risk-less rate) that investors have, on the average, realized over some historical holding period (realized risk premium). The underlying theory is that the past provides a reasonable indicator of how the market will behave in the future and investors’ expectations are influenced by the historical performance of the market. If period returns on stocks (e.g., monthly stock returns) are not correlated (e.g., this month’s stock returns are not predictable based on last month’s returns) and if expected stock returns are stable through time, then the arithmetic average of historical stock returns provides an unbiased estimate of expected future stock returns. Similarly, the arithmetic average of realized risk premiums provides an unbiased estimate of expected future risk premiums (the ERP). A more indirect justification for use of the realized risk premium approach is the contention that, for whatever reason, securities in the past have been priced in such a way as to earn the returns observed. By using an estimated cost of equity capital incorporating the average of realized risk premiums in applying the income approach to valuation, you may to some extent replicate this level of pricing.
MEASURING REALIZED RISK PREMIUMS The measure of the risk-free rate is not controversial once the proper duration (long term versus short term) of the investment has been estimated since the expected yield to maturity on appropriate
6
½ð1;000;000 1Þ=ð1:15Þ þ ð1;000;000 1:04 2Þ=ð1:15Þ2 þ ð1;000;000 1:042 3Þ=ð1:15Þ3 . . . ½ð1;000;000 1Þ=ð1:15Þ þ ð1;000;000 1:04Þ=ð1:15Þ2 þ ð1;000;000 1:042 Þ=ð1:15Þ3 . . .
7
¼ 10:5ðroundedÞ
Carmelo Giaccotto, ‘‘Discounting Mean Reverting Cash Flows with the Capital Asset Pricing Model,’’ The Financial Review (May 2007): 247–265. This is true for both the textbook CAPM of Sharpe and Linter and the extension of the textbook CAPM, the intertermporal CAPM of Merton.
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Cost of Capital
government securities is directly observable in the marketplace. Differences in approach to estimating the ERP then hinge on the measure of expected return on equity securities. In applying the realized risk premium approach, the analyst selects the number of years of historical return data to include in the average. One school of thought holds that the future is best estimated using a very long horizon of past returns. Another school of thought holds that the future is best measured by the (relatively) recent past. These differences in opinion result in disagreement as to the number of years to include in the average. HISTORICAL STOCK AND BOND RETURNS The highest-quality data are available for periods beginning in 1926 (the year that the forerunner of the current S&P 500 was first published) from the Center of Research in Security Prices (CRSP) at the University of Chicago. The SBBI Yearbook contains summaries of returns on United States stocks and bonds derived from that data.8 The reported returns include the effects from the reinvestment of dividends. Returns on common stocks have been assembled by various sources and with various qualities for earlier periods. Good stock market data are available back to 1872, and less reliable data are available from various sources back to the end of the eighteenth century. (In the earliest period, the market consisted almost entirely of bank stocks, and by the mid-nineteenth century, the market was dominated by railroad stocks.9) Data for government bond yield data have also been assembled for these periods. Exhibit 9.1 presents the realized average annual risk premium for stocks assembled from various sources for alternative periods through 2006. We measure the realized risk premium by comparing the stock market returns realized during the period to the income return on long-term government bonds (or yield to maturity for the years before 1926). While some may question looking at averages including early periods for estimating today’s ERP, what is striking is that the largest arithmetic average of one-year returns is the 81 years from 1926 to 2006. Why use the income return on long term government bonds? The income return in each period represented the expected yield on the bonds at the time of the investment. An investor makes a decision to invest in the stock market today by comparing the expected return from that investment to the rate of return today on a benchmark security (in this case the long-term government bond). While the investor did not know the stock market return when one invested at the beginning of each year, he or she did know the rate of interest promised on long-term government bonds. To try to match the expectations at the beginning of each year, we measure historical stock market returns on an expectation that history will repeat itself over the expected return on bonds in each year. 8 9
Stocks, Bonds, Bills and Inflation (SBBI) Valuation Edition 2007 Yearbook (Chicago: Morningstar, 2007). See Lawrence Fisher and James Lorie, ‘‘Rates of Return on Investments in Common Stocks,’’ Journal of Business 37, no. 1 (1964); J. W. Wilson and C. P. Jones, ‘‘A Comparison of Annual Stock Market Returns: 1871–1925 with 1926–1985,’’ Journal of Business 60, no. 2 (1987): 239–258; G. W. Schwert, ‘‘Indexes of Common Stock Returns from 1802 to 1987,’’ Journal of Business 63, no. 3 (1990): 399–425; Roger G. Ibbotson and Gary P. Brinson, Global Investing: The Professional’s Guide to the World Capital Markets (New York: McGraw-Hill, 1993); J. W. Wilson and C. P. Jones, ‘‘An Analysis of the S&P 500 Index and Cowles’s Extensions: Price Indexes and Stock Returns, 1870–1999,’’ Journal of Business 75, no. 3 (2002): 505–533; S. H. Wright, ‘‘Measures of Stock Market Value and Returns for the US Nonfinancial Corporate Sector, 1900–2000,’’ Working paper, February 1, 2002; W. Goetzmann, R. Ibbotson, and L. Peng, ‘‘A New Historical Database for NYSE 1915 to 1925: Performance and Predictability,’’ Journal of Financial Markets 4 (2001): 1–32; E. Dimson, P. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns (Princeton, NJ: Princeton University Press, 2002) with annual updates of their Global Returns database available at http://corporate.morningstar.com/ib; W. Goetzmann and R. Ibbotson, ‘‘History and the Equity Risk Premium,’’ Yale ICF Working Paper No. 05-04, April 6, 2005.
Realized Risk Premium (ex Post ) Approach Exhibit 9.1
95
Historical Realized Premiums: Stock Market Returns Treasury Bonds
Period 20 years (1987–2006) 30 years (1977–2006) 40 years (1967–2006) 50 years (1957–2006) 81 years (1926–2006)** 107 years (1900–2006) 135 years (1872–2006) 209 years (1798–2006)
Arithmetic Average
Standard Error*
Geometric Average
6.4% 5.8% 4.8% 5.2% 7.1% 6.8% 5.9% 5.1%
3.7% 2.8% 2.6% 2.3% 2.2% 1.9% 1.6% 1.2%
5.2% 4.7% 3.6% 3.9% 5.2% 4.9% 4.3% 3.6%
*
Calculated as standard deviation of realized excess returns divided by square root N, number of years in sample. SBBI Valuation Edition 2007 Yearbook. Source: Data compiled from R. Ibbotson and G. Brinson, Global Investing (New York: McGraw-Hill, 1993); W. Schwert, ‘‘Indexes of U.S. Stock Prices from 1802 to 1987,’’ Journal of Business, 1990; S. Homer and R. Sylla, A History of Interest Rates, 3rd ed. (Piscataway, NJ: Rutgers University Press, 1991); and SBBI, 2007 Yearbook (Chicago: Morningstar, 2007). **
The realized risk premiums vary year to year, and the estimate of the true ERP resulting from this sampling is subject to a degree of error. We display the standard errors of estimate for each period in Exhibit 9.1. The standard error of estimate allows you to measure the likely accuracy of using the realized risk premium as the estimate of ERP. That statistic indicates the estimated range within which the true ERP falls (i.e., assuming normality, the true ERP can be expected to fall within two standard errors with a 95% level of confidence).
SUMMARIZING REALIZED RISK PREMIUM DATA The summarized data in Exhibit 9.1 represent the arithmetic and geometric averages of realized risk premiums for one-year returns. That is, the dollars invested including reinvested dividends are reallocated to available investments annually and the return is calculated for each year. The arithmetic average is the mean of the annual returns. The geometric average is the single compound return that equates the initial investment with the ending investment assuming annual reallocation of investment dollars and reinvestment of dividends. For example, assume this series of stock prices (assuming no dividends): Period 1 2 3
Stock price
Period Return
$10 $20 $10
100% 50%
The arithmetic average of period returns equals (100% þ 50%)/2 ¼ 25% while the geometric average equals (1 þ r1)(1 þ r2)1/2 1 ¼ (1 ¼ 1.00 1 .5)1/2 1 ¼ 0. Realized return premiums measured using the geometric (compound) averages are always less than those using the arithmetic average. The geometric mean is the lower boundary of the arithmetic mean, and the two are equal in the unique situation that every observation is identical to every other observation. Further, the more variable the period returns, the greater the difference between the arithmetic and geometric averages of those returns. This is simply the result of the mathematics of a series that has experienced deviations.
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Cost of Capital
The choice between which average to use is a matter of disagreement among practitioners. The arithmetic average receives the most support in the literature,10 though other authors recommend a geometric average.11 The use of the arithmetic average relies on the assumption that (1) market returns are serially independent (not correlated) and (2) the distribution of market returns is stable (not time-varying). Under these assumptions, an arithmetic average gives an unbiased estimate of expected future returns assuming expected conditions in the future are similar to conditions during the observation period. Moreover, the more observations available, the more accurate will be the estimate. . . .the arithmetic mean equates the expected future value of investment with its present value . This property makes the arithmetic mean the correct return to use as the discount rate or cost of capital.12 . . .the geometric mean measures changes in wealth over more than one period on a buy and hold (with dividends reinvested) strategy. . . . The arithmetic mean would provide a better measure of typical performance over a single historical period.13
WHAT PERIODICITY OF PAST MEASUREMENT? But even if we agree that stock returns are serially independent, the arithmetic average of realized risk premiums based on one-year returns may not be the best estimate of future returns. Textbook models of stock returns (e.g., CAPM) are generally single-period models that estimate returns over unspecified investment horizons. For example, assume that the investment horizon equals two years. Then in using realized returns to estimate expected returns, you need to calculate realized returns over two-year periods (i.e., the geometric average over consecutive two-year periods) and then calculate the arithmetic average of the two-year geometric averages to arrive at the unbiased estimate of future returns. For example, assume that the realized one-year returns are: Year 1 ¼ 10% Year 2 ¼ 25% Year 3 ¼ 15% The geometric averages of the two-year holding periods are: ð1:10 1:25Þ1=2 1 ¼ 17:3% ð1:25 0:85Þ1=2 1 ¼ 3:1% The arithmetic average of typical two-year periods is therefore: ð17:3 þ 3:1Þ ¼ 10:2% 2
10
11
12 13
See, e.g., Paul Kaplan, ‘‘Why the Expected Rate of Return Is an Arithmetic Mean,’’ Business Valuation Review (September 1995); SBBI Valuation Edition 2002 Yearbook, 71–73; Mark Kritzman, ‘‘What Practitioners Need to Know about Future Value,’’ Financial Analysts Journal (May/June 1994): 12–15; Zvi Bodie, Alex Kane, and Alan J. Marcus, Investments (1989): 720–723. See, for example, Aswath Damodaran, Investment Valuation:Tools and Techniques for Determining the Value of Any Asset, 2nd ed. (Hoboken, N.J.: John Wiley & Sons, 2002), 161–162. Roger Ibbotson and Rex Sinquefeld, Stocks, Bonds, Bills and Inflation: Historical Returns (1926–1987) (1989), 127. Willard T. Carleton and Josef Lakonishok ‘‘Risk and Returns on Equity: the Use and Misuse of Historical Estimates,’’ Financial Analysts Journal 41, no. 1 (1985): 39.
Realized Risk Premium (ex Post ) Approach
97
The issue then becomes what is the appropriate interval over which average realized returns should be measured (1-year periods as in the case of the returns reported in the SBBI Yearbook; 2-year periods; 20-year periods)? When you are valuing businesses, should you compare returns over periods greater than one year? The most likely answer is yes. Practitioners have adopted the use of interest rates on long-term government bonds, typically 20-year bonds, as the appropriate long-term benchmark risk-free rate when valuing businesses. It follows then that a longer investment horizon of, say, 20 years is the appropriate period over which you should calculate realized returns. As the investment horizon increases, the arithmetic average of realized investment returns decreases asymptotically to the geometric average of the entire series. While Morningstar only reports on the arithmetic average of one-year returns, we calculated the realized risk premiums for various investment horizons using the data from 1926 to 2006 as shown in the next table.14 Arithmetic Average of 1
1-year returns 2-year returns2 3-year returns3 4-year returns4 5-year returns5 81-year returns (geometric average)1
Realized Risk Premium 7.1% 6.1% 5.8% 5.5% 5.3% 5.2%
1
SBBI Valuation Edition 2007 Yearbook. Excluding investment period beginning 2006. 3 Excluding investment periods beginning 2005 and 2006. 4 Excluding investment periods beginning 2004, 2005, and 2006. 5 Excluding investment periods beginning 2003, 2004, 2005, and 2006. Source: Compiled from data in Stocks, Bonds, Bills, and Inflation 2007 Yearbook. Copyright # 2007 Morningstar, Inc. All rights reserved. Used with permission. 2
Assuming that you have an investment horizon longer than one year, you can conclude that the realized risk premium that provides the ‘‘best estimate’’ of the ERP is likely between the arithmetic average of one-year returns and the geometric average of the entire series. In one recent study, the authors show that compounding the arithmetic average of historical oneyear returns as a forecaster of cumulative future returns results in estimates of cumulative returns that overstate the future cumulative returns that investors are likely to realize. This is due to the fact that distributions of stock market returns are skewed. The authors show that use of the geometric mean of historical one-year returns result in estimates of cumulative returns that more approximate the median of cumulative returns (50% if investors will realize more than the median cumulative return and 50% will realize less than the median return). They demonstrate that the difference between the median of forecasted cumulative returns obtained from compounding the arithmetic average versus the geometric average of one-year historical returns increases as the expected investment horizon increases.15 14
15
The equity risk premium of each investment horizon was calculated by taking equity returns (S&P 500) less the bond returns (U.S. Long-term Government Bond Income Return) for the respective periods. We calculated a series of rolling returns, one for stocks and another for bonds, for each investment horizon. We then took the arithmetic average of each series of rolling returns for the respective investment horizon. For example, the 2-year return, for equities and bonds, is the arithmetic average of a series of 2-year rolling returns from 1926 to 2006. We performed the same calculation for each investment horizon. We then subtract the bond return from the equity return to estimate the equity risk premium for each investment horizon. Eric Hughson, Michael Stutzer, and Chris Yung, ‘‘The Misuse of Expected Returns,’’ Financial Analysts Journal (November/ December 2006): 88–96.
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Cost of Capital
SELECTING A SAMPLE PERIOD The average realized risk premium is sensitive to the period chosen for the average. While the selection of 1926 as a starting point corresponds to the initial publishing of the forerunner to the current S&P 500, that date is arbitrary. Regarding the historical time period over which equity risk should be calculated, Morningstar offers two observations16: 1. Reasons to focus on recent history: The recent past may be most relevant to an investor. Return patterns may change over time. The longer period includes ‘‘major events’’ (e.g., World War II, the Depression) that have not repeated for over 50 years. 2. Reasons to focus on long-term history:
Long-term historical returns have shown surprising stability. Short-term observations may lead to illogical forecasts. Focusing on the recent past ignores dramatic historical events and their impact on market returns. We do not know what major events lie ahead. Law of large numbers: More observations lead to a more accurate estimate.
But the average calculated using 1926 return data as a beginning point may be too heavily influenced by the unusually low interest rates during the 1930s to mid-1950s. For example, the average yield on long-term government bonds was only 2.3% during the 1940s (the lowest decade on record) and under 3% in each year from 1934 through 1955. Yields on government bonds exceeded 4% for most of the nineteenth century and have been consistently higher since the 1960s. The years 1942 through 1951 were a period of artificial stability in U.S. government bond interest rates. In April 1942, the Federal Reserve publicly committed itself to maintaining an interest rate ceiling on government debt, both long term and short term, to support the financing of World War II. After World War II, the Fed continued maintaining an interest rate ceiling fearing return to the high unemployment of the Great Depression. But postwar inflationary pressures caused the Treasury and the Fed to reach an accord announced March 4, 1951, freeing the Fed of its obligation of pegging interest rates. Including this period in calculating realized returns is analogous to valuing airline stocks today by looking at prices of airline stocks before deregulation. Some observers have suggested that the period, which includes the 1930s, 1940s, and the immediate post–World War II boom years, may have exhibited an unusually high average realized return premium. The 1930s exhibited extreme volatility while the 1940s and early 1950s saw a combination of record low interest rates and rapid economic growth that led the stock market to outperform Treasury bonds by a wide margin. The low real rates on bonds may have contributed to higher equity returns in the immediate postwar period. Since firms finance a large part of their capital investment with bonds, the real cost of obtaining such funds increased returns to shareholders. It may not be a coincidence that the highest 30-year average equity return occurred in a period marked by very low real returns on bonds. As real returns on fixedincome assets have risen in the last decade, the equity premium appears to be returning to the 2% to 3% norm that existed before the postwar surge.17
16 17
SBBI Valuation Edition 2007 Yearbook (Chicago: Morningstar, 2007), 129, 134. Jeremy Siegel, Stocks for the Long Run (New York: McGraw-Hill, 1994), 20.
Realized Risk Premium (ex Post ) Approach Exhibit 9.2
99
Realized Equity Risk Premiums over Treasury Bond Income Returns
Nominal (i.e., without inflation removed) Arithmetic Average Geometric Average Standard Deviations Stock Market Annual Returns Long-term Treasury Income Returns Long-term Treasury Total Returns Ratio of Equity to Bond Total Return Volatility
1926–1955 10.5% 7.5%
1956–2006 5.1% 3.9%
25.3% 0.5% 4.7% 5.4
16.5% 2.4% 10.9% 1.5
Source: Compiled from data in Stocks, Bonds, Bills and Inflation 2007 Yearbook. Copyright # 2007 Morningstar, Inc. All rights reserved. Used with permission. For more information on other Morningstar publications, please visit global.morningstar.com/ DataPublications. Calculated (or Derived) based on CRSP1 data, #2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago.
If we disaggregate the 81 years reported in the SBBI Yearbook into two subperiods, the first covering the periods before and after the mid-1950s, we get the comparative figures for stock and bond returns shown in Exhibit 9.2. The period since the mid-1950s has been characterized by a more stable stock market and a more volatile bond market compared to the earlier period. Interest rates, as reflected in Long-term Government Bond Income Return statistics as summarized in the SBBI Yearbook, have become more volatile in the later period. The effect is amplified in the volatility of Long-term Government Bond Total Returns as summarized in the SBBI Yearbook, which include the capital gains and losses associated with interest rate fluctuations. From these data, we can conclude that the relative risk of stocks versus bonds has narrowed; based on this reduced relative risk, we would conclude that the ERP is likely lower today. As a result, we question the validity of using the arithmetic average of one-year returns since 1926 as the basis for estimating today’s ERP. Evidence since 1871 clearly supports the premise that the difference between stock yields and bond yields is a function of the long-run difference in volatility between these two securities.18 And if you examine the volatility in stock returns (as measured by rolling 10-year average standard deviation of real stock returns), you find that the volatility beginning in 1929 dramatically increased and that the volatility since the mid-1950s has returned to prior levels.19 This also suggests that the arithmetic average realized risk premiums reported for the entire data series since 1926 as reported in the SBBI Yearbook likely overstate expected returns. Using historical data may also tend to overstate expected returns given the increasing opportunities for international diversification. International diversification lowers the volatility of investors’ portfolios, which in theory should lower the required return on the average asset in the portfolio. This would lower the expected return on U.S. government securities generally and hence would suggest a lower ERP on a forward-looking basis than indicated by historical data. Several authors have studied the influence of increased globalization, and their results suggest that costs of capital for companies operating in the international markets have decreased.20
18
19
20
Clifford S. Asness, ‘‘Stocks versus Bonds: Explaining the Equity Risk Premium,’’ Financial Analysts Journal (March/April 2000): 96–113. Laurence Booth, ‘‘Estimating the Equity Risk Premium and Equity Costs: New Ways of Looking at Old Data,’’ Journal of Applied Corporate Finance (Spring 1999):100–112 and ‘‘The Capital Asset Pricing Model þ Equity Risk Premiums and the Privately-Held Business,’’ 1998 CICBV/ASA Joint Business Valuation Conference (September 1998): 23. See, e.g., Kate Phylaktis and Lichuan Xia, ‘‘Sources of Firm’s Industry and Country Effects in Emerging Markets,’’ Journal of International Money and Finance (2005): 459–475; and Gikas Hardouvelis, Dimitrious Malliartopulos, and Richard Priestly, ‘‘The Impact of Globalization on the Equity Cost of Capital,’’ Working paper, May 9, 2004.
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Cost of Capital
If the average expected risk premium has changed through time, then averages of realized risk premiums using the longest available data become questionable. A shorter-run horizon may give a better estimate if changes in economic conditions have created a different expected return environment than that of more remote past periods. Why not use the average realized return over the past 20year period? A drawback of using averages over shorter periods is that they are susceptible to large errors in estimating the true ERP due to high volatility of annual stock returns. Also, the average of the realized premiums over the past 20 years may be biased high due to the general downward movement of interest rates since 1981. While we can only observe historical realized returns in the stock market, we can observe both expected returns (yield to maturity) and realized returns in the bond market. Prior to the mid-1950s, the difference between the yield at issue and the realized returns was small since bond yields and therefore bond prices did not fluctuate very much. Beginning in the mid-1950s until 1981, bond yields trended upward, causing bond prices to generally decrease. Realized bond returns were generally lower than returns expected when the bonds were issued (as the holder experienced a capital loss if sold before maturity). Beginning in 1981, bond yields trended downward, causing bond prices to generally increase. Realized bond returns were generally higher than returns expected when the bonds were issued (as the holder experienced a capital gain if sold before maturity). If we choose the period during which to measure realized premiums beginning from the late 1950s/early 1960s to today, we will be including a complete interest rate cycle.21 Even if we use long-term observations, the volatility of annual stock returns will be high. Assuming that the 81-year average gives an unbiased estimate, still a 95% confidence interval for the unobserved true ERP spans a range of approximately 3.0% to 11.5%.22 IS BIAS INTRODUCED BY USING THE ARITHMETIC AVERAGE IN ESTIMATING ERP? The issue of bias is important from two different vantage points when using an ERP estimate derived from the arithmetic average of realized risk premium data: 1. In predicting the compound return you might expect for an investment in stocks, will you get an answer that is biased? (i.e., will measurement error be introduced simply due to the mathematics?) 2. In discounting expected cash flows where you develop a cost of equity capital estimate using that ERP estimate, will you get an answer that is biased? Even if you accept the arithmetic average of annual realized risk premiums as an unbiased estimate of expected annual risk premium (i.e., investment horizon equals one year), it is a somewhat stronger assumption to compound this annual average over multiple periods (i.e., investment horizon equals n years); you are assuming that the estimate of the expected single-period return is accurate (in other words, that the estimate has no allowance for error). If you introduce measurement error and compound the estimated annual return over multiple periods, you will get a biased estimate of the true expected future value. This upward bias occurs even if the single-period arithmetic average itself is an unbiased estimate. The fact that you get an expected upward bias in future investment results if you project future returns using an arithmetic average is important if you are estimating the returns 21 22
Booth, ‘‘Estimating the Equity Risk Premium and Equity Costs.’’ Calculated as two standard errors around the average; 7.1% Aþ/ (2 2.2%).
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101
you might expect to realize when investing funds for future retirement. This is the subject of much discussion in the pension investment literature. The statistical properties of this problem are such that you get a different answer if, instead of focusing on unbiased expected future values, you seek instead an unbiased estimate of the present value discount factor. One proposed correction that focuses on present value factors finds that the adjustment from the arithmetic average is small even when discounting over fairly long periods.23 Moreover, the bias is toward discount rates that are too high rather than too low. Most of the value in a discounted cash flow analysis typically is derived from cash flows over the first 10 years, which limits potential bias in an overall present value calculation.24 Is bias introduced by using the arithmetic average in compounding expected cash flows? If we reverse the discounting process and compound the expected cash flows, do we get an unbiased estimate of an investor’s expected cumulative wealth? If the expected returns are not correlated, then the arithmetic average of realized risk premiums is an unbiased estimator of the mathematical expected return per period. If we compound those returns will the result equal the amount a typical investor would expect (i.e., the median—50% of the time the investor’s wealth will be less than the amount and 50% of the time the investor’s wealth will be greater than the amount)? Compounding rates of returns estimated using the arithmetic average of realized risk premiums will in fact result in an expected cumulative wealth that exceeds the median. The result is biased high and the difference grows larger as the investment horizon increases.25 A number of academic studies have suggested that U.S. stock returns are not serially independent but rather have exhibited negative serial correlation.26 One recent study suggests that if stock returns have negative serial correlation, then the best estimate of expected returns would lie somewhere between the arithmetic and geometric averages, moving closer to the geometric average as the degree of negative correlation increases and the projection period lengthens.27 But another study has shown that if the rates of return are not independent but display even a small amount of negative serial correlation, then the degree of bias in cumulative wealth is reduced substantially. This also is the case if the rates of return are independent but the risky expected cash flows are mean reverting. The result is that the cumulative wealth will be slightly greater than that expected by the typical investor (i.e., the median) even over a long investment horizon.28 All in all, using the arithmetic average of realized risk premiums as an estimate of ERP does not appear to introduce serious bias in estimating expected cumulative wealth. COMPARING INVESTOR EXPECTATIONS TO REALIZED RISK PREMIUMS Much has recently been written comparing the realized returns as reported in sources such as the SBBI Yearbook and the ERP that must have been expected by investors, given the underlying economics of publicly traded companies (e.g., expected growth in earnings or expected growth in 23
24 25
26
27
28
Ian Cooper, ‘‘Arithmetic versus Geometric Mean Estimators: Setting Discount Rates for Capital Budgeting,’’ European Financial Management (July 2001): 157–167. See Appendix 9A for a more complete explanation of the bias issue. Eric Hughson, Michael Stutzer, and Chris Yung, ‘‘The Misuse of Expected Returns,’’ Financial Analyst Journal (November/ December 2006): 88–96. Eugene F. Fama and Kenneth R. French, ‘‘Dividend Yields and Expected Stock Returns,’’ Journal of Financial Economics (October 1988): 3–25; Andrew Lo and Craig McKinlay, ‘‘Stock Market Prices Do Not Follow Random Walks,’’ Review of Financial Studies 1 (1988): 41–46; James Poterba and Lawrence Summers, ‘‘Mean Reversion in Stock Prices: Evidence and Implications,’’ Journal of Financial Economics (October 1988): 27–59. Daniel C. Indro and Wayne Y. Lee, ‘‘Biases in Arithmetic and Geometric Averages as Estimates of Long-Run Expected Returns and Risk Premia,’’ Financial Management (Winter 1997): 81–90. Giaccotto, The Financial Review (2007).
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Cost of Capital
dividends) and the underlying economics of the economy (e.g., expected growth in gross domestic product [GDP]). Such studies conclude that investors could not have expected as large an ERP as the equity risk premiums actually realized. A sampling of those studies follows.
Robert Arnott and Peter Bernstein conclude that the long-run normal ERP is approximately 4.5% on an arithmetic average basis (for the period studied, 1926 to 2001).29 They believe that the historical realized premium exceeded the expected premium because (1) the expected ERP in 1926 was above the long-term average, making 1926 a better-than-average starting point for the realized returns, and (2) important nonrecurring developments occurred that were not anticipated by investors (such as rising valuation multiples, survivor bias of the U.S. economy, and regulatory reform).30 Eugene Fama and Kenneth French examine the unconditional expected stock returns from fundamentals, estimated as the sum of the average dividend yield and the average growth rate of dividends or earnings derived from studying historical observed relationships for 1872 to 2000. They conclude that investors (during the period they studied, 1951 to 2000) should have expected an ERP lower than the actual realized risk premium. Their calculations indicate expected ERP of 2.6% (based on dividend growth rate fundamentals) or 3.6% (based on earnings growth rate fundamentals).31 Fama and French believe that the greater premium actually realized during those years was due to an unanticipated decline in the discount rate: [T]he bias-adjusted expected return estimates for 1951 to 2000 from fundamentals are a lot lower (more than 2.6% per year) than bias-adjusted estimates from realized returns. Based on this and other evidence, our message is that the unconditional expected equity premium of the last 50 years is probably far below the realized premium.32
Elroy Dimson, Paul Marsh, and Mike Staunton studied the realized equity returns and equity premiums for 17 countries (including the United States) from 1900 to the end of 2006.33 These authors report that the realized risk premiums have been 6.6% on an arithmetic basis (4.6% on a geometric basis) for the United States (in excess of the total return on government bonds). Dimson, Marsh, and Staunton observe larger equity returns earned in the second half of the twentieth century compared to the first half due to (1) corporate cash flows growing faster than
29
30 31
32 33
Robert D. Arnott and Peter L. Bernstein, ‘‘What Risk Premium is Normal?’’ Financial Analysts Journal (March/April 2002): 64–85. Arnott and Bernstein estimate that a ‘‘normal’’ equity risk premium equals 2.4% (geometric average). One method of converting to the geometric average from an arithmetic average is to assume the returns are independently log-normally distributed over time. Then the arithmetic and geometric averages approximately follow the relationship: Arithmetic average of returns for the period ¼ Geometric average of returns for the period plus (variance of returns for the period/2). In this case we get: 2.4% þ (.0412/2) ¼ 4.5% approximately. During the period 1926 to 2001, the arithmetic average realized premium (relative to Treasury bonds) was 7.4%. The difference is therefore 7.4% minus 4.5%, or approximately 3%. Ibid. Eugene F. Fama and Kenneth R. French, ‘‘The Equity Premium,’’ Journal of Finance (April 2002): 637–659. Fama and French estimate that the expected ERP using dividend growth rates was approximately 3.83% (after correcting for bias in the observed data) and using earnings growth rates was approximately 4.78% (after correcting for bias in the observed data) (arithmetic averages compared to six-month commercial paper rates). Subtracting a difference between the return on government bonds versus bills of 1.19% for the period of the study gives indicated premiums over long-term government bonds of approximately 2.6% and 3.6% (arithmetic average). Ibid, 658. Elroy Dimson, Paul Marsh, and Mike Staunton, ‘‘Global Evidence on the Equity Premium,’’ Journal of Applied Corporate Finance (Summer 2003): 27–38; ‘‘The Worldwide Equity Premium: A Smaller Puzzle’’ EFA 2006 Zurich Meetings Paper, April 7, 2006; Global Investment Returns Yearbook 2007 (London: ABN-AMRO/London Business School, February 2007).
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investors anticipated (fueled by rapid technological change and unprecedented growth in productivity and efficiency), (2) transaction and monitoring costs falling over the course of the century, (3) inflation rates generally declining over the final two decades of the century and the resulting increase in real interest rates, and (4) required rates of return on equity declining due to diminished business and investment risks. They conclude that the observed increase in the overall price-to-dividend ratio during the century is attributable to the long-term decrease in the required risk premium and that the decrease will most likely not continue into the future. They also conclude that a downward adjustment in the ERP compared to the realized risk premiums due to the increase in price/dividend ratio is reasonable. Removing the historical increase in the price/dividend ratio results in an adjusted realized risk premium (relative to bonds) of approximately 5.9% on an arithmetic basis (3.9% on a geometric basis) for the United States.34 This is before converting the adjusted realized risk premium to their estimate of a forward ERP (by adjusting the historical average dividend yield to today’s dividend yield).
Roger Ibbotson and Peng Chen report on a study in which they estimated forward-looking longterm sustainable equity returns and expected ERPs since 1926. They first analyzed historical equity returns by decomposing returns into factors including inflation, earnings, dividends, priceto-earnings ratio, dividend-payout ratio, book values, return on equity, and GDP per capita (the fundamental building blocks of ‘‘supply side’’ equity returns). They forecast the ERP through supply side models built from historical data. These authors determine that the long-term ERP that could have been expected given the underlying economics was less than the realized premium.35 In the most recent update to this study reported in the SBBI Yearbook, the long-term ERP since 1926 that could have been expected given the underlying economics (the supply side model estimate) was approximately 6.3% on an arithmetic basis (4.3% on a geometric basis) compared to the realized risk premium of 7.1% on an arithmetic basis (5.0% on a geometric basis). The greater-than-expected realized risk premiums were caused by an unexpected increase in market multiples relative to economic fundamentals (i.e., decline in the discount rates) for the market as a whole. This resulted in an extra return of 0.63% per annum (due to the price to earnings multiple in 1926 of 10.2 increasing to a price to earnings multiple of 17.4 in 2006). They do not anticipate that market multiples will continue to increase in future periods.36
William Goetzmann and Roger Ibbotson, commenting on the supply side approach of estimating expected risk premiums, note: These forecasts tend to give somewhat lower forecasts than historical risk premiums, primarily because part of the total returns of the stock market have come from price-earnings ratio expansion. This expansion is not predicted to continue indefinitely, and should logically be removed from the expected risk premium.’’37
34
35
36 37
Based on Grabowski’s converting premium over total returns on bonds as reported by Dimson, Marsh, and Staunton, removing the impact of the growth in price-dividend ratios from the geometric average historical premium and converting to an approximate arithmetic average. Roger G. Ibbotson and Peng Chen, ‘‘Long-Run Stock Market Returns: Participating in the Real Economy,’’ Yale ICF Working Paper No. 00-44, March 2002, Financial Analysts Journal (January/February 2003): 88–98; Charles P. Jones and Jack W. Wilson, ‘‘Using the Supply Side Approach to Understand and Estimate Stock Returns,’’ Working paper, June 6, 2006. SBBI Valuation Edition 2007. Goetzmann and Ibbotson, ‘‘History and the Equity Risk Premium,’’ 8.
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Cost of Capital
The greater than expected historical realized equity returns were caused by an unexpected increase in market multiples and a decline in discount rates relative to economic fundamentals. Each of these studies attempts to improve the estimate of the true ERP by removing the effects of changes in underlying economics that caused the realized risk premiums to differ from the ERP investors expected. However, even after adjusting for such unexpected changes, the realized risk premiums still are only estimates subject to statistical error. This potential for error reduces the reliability of claiming the resulting estimate is the true ERP. For example, in the study performed by Fama and French already discussed, those authors provide estimates of the ERP investors should have expected for the period 1951 to 2000 with confidence intervals. As is common, their study considers one variable at a time. They studied the relationship of underlying economic factors (growth in earnings and dividends) to realized risk premiums in years before 1951 and then asked what risk premium should have been expected given the underlying economic fundamentals in the years 1951 to 2000, if the relationships observed in prior years are assumed to continue. That is, based on the average observed relationship of dividend growth to return on equity capital during the periods 1872 through 1951 and then updated annually through 2000, they estimated the average return on equity (and volatility of the estimates) that should have been expected during 1951 through 2000 and subtracted the average risk-free rate. The Fama and French mean estimate of the equity risk premium that could have been expected based on dividend growth rate fundamentals is approximately 2.6% with a confidence interval (based on two standard errors), indicating that the average true ERP was between 0.1% and 3.8%.38 Similarly, their mean estimate of the equity risk premium that could have been expected based on earnings growth rate fundamentals is approximately 3.6% with a confidence interval (based on two standard errors) indicating that the average true ERP was between (effectively) zero and 7.4%. It is possible to consider multiple variables simultaneously and simulate an expected ERP that must have been expected to result in the realized return. For example, if you consider such variables as dividend yield, equity returns, volatility of equity returns, and average realized equity premium, what ERP might have been anticipated by investors that resulted in the realized returns observed? It is possible that such a joint simulation may result in a more accurate estimate of the true ERP during a period.
38
R. Glen Donaldson, Mark J. Kamstra, and Lisa A. Kramer have conducted such a joint simulation covering the period 1952 through 2004 using Monte Carlo simulation techniques with the parameters of the probability distributions of the variables derived from actual data observed during the period. They incorporate numerous variables but find average dividend yield, average equity return, and equity return volatility particularly informative in determining the ERP that must have been anticipated. They compare joint multivariate distributions of their simulated data with observed data and find that there was only a small range of anticipated ERP that could have yielded the outcomes during their study period: high average observed equity returns; the observed standard deviation of equity returns; the observed low dividend yield (which in part results due to the fact that firms increasingly distributed cash to shareholders via share repurchases instead of via dividends); high realized risk premium. Their results indicate that the average ERP that must have been expected during 1952 through 2004 is centered very close to 3.1% (arithmetic average premium over long-term government bonds) with a confidence interval (two standard errors) of 50 basis points. That is, they estimate
Based on Grabowski’s adjustment for bias reported in the Fama and French study and conversion of their results into the equivalent premium over long-term government bonds.
Realized Risk Premium (ex Post ) Approach
105
that the average true ERP was between 2.6% and 3.6%.39 Obviously their estimates are based on the assumed growth rates and the data-generating processes they hypothesize. We asked Morningstar to provide us with their supply side ERP estimates for the same period as used by Donaldson et al. (1952–2004) to compare the results. The supply side ERP estimates for 1952 to 2004 that could have been expected given the underlying economics were approximately 4.9% on an arithmetic basis (3.4% on a geometric basis) compared to the realized risk premium of 6.4% on an arithmetic basis (4.8% on a geometric basis).
CHANGES IN ECONOMICS THAT CAUSED UNEXPECTEDLY LARGE REALIZED RISK PREMIUMS Has there been a change in the relative volatility of market returns? Scott Mayfield found evidence of a structural shift in the relative volatility of market returns in 1940. His premise is that if the decrease in market risk was not fully anticipated, then stock prices during the subsequent period would be bid up and realized returns will not be representative of the ERP. He estimates that when looking at expectations following the structural shift in market volatility, the ERP (the risk premium over longterm government bonds that could have been expected for the period he studied, 1940 to 1997) was approximately 2.7%.40 McGrattan and Prescott find that the value of the stock market relative to the GDP in 2000 was nearly twice as large as in 1962.41 They determined that the marginal income tax rate declined (the marginal tax rate on corporate distributions averaged 43% in the 1955 to 1962 period and averaged only 17% in the 1987 to 2000 period). The regulatory environment also changed. Equity investments could not be held ‘‘tax free’’ in 1962. But by 2000, equity investments could be held ‘‘tax deferred’’ in defined benefit and contribution pension plans and in individual retirement accounts. The decrease in income tax rates on corporate distributions and the inflow of retirement plan investment capital into equity investments combined to lower discount rates and increase market multiples (i.e., lower capitalization rate) relative to economic fundamentals. Assuming that investors did not expect such changes, the true ERP during this period has been less than the realized risk premiums calculated as the arithmetic average of excess returns realized since 1926. Further, assuming that the likelihood of changes in such factors being repeated are remote and investors do not expect another such decline in discount rates, the true ERP as of today can also be expected to be less than the average realized risk premium.
39
40
41
R. Glen Donaldson, Mark J. Kamstra and Lisa A. Kramer, ‘‘Estimating the Ex Ante Equity Premium,’’ Working paper, November 2006, and ‘‘Stare Down the Barrel and Center the Crosshairs: Targeting the Ex Ante Equity Premium,’’ Working paper 2003-4, Federal Reserve Bank of Atlanta, January 2003. E. Scott Mayfield, ‘‘Estimating the Market Risk Premium,’’ Working paper, October 1999. See also: Chang-Jin Kim, James C. Morley, and Charles R. Nelson, ‘‘The Structural Break in the Equity Premium,’’ Journal of Business & Economic Statistics (April 2005): 181–191, in which they find evidence of a structural break that likely occurred in the early 1940s and appears to be driven by a reduction in the general level and persistence of market volatility; Lubos Pastor and Robert F. Stambaugh, ‘‘The Equity Premium and Structural Breaks,’’ Journal of Finance (August 2001): 1207–1239, study the equity risk premium from 1834 through 1999 and find several ‘‘structural breaks’’ (changes in volatility) in 1929 (increase compared to historic), 1941 (returning to historic levels), and 1992 (further reduced volatility). They find that the ERP compared to T bills (or equivalent) fluctuated between 3.9% to 6.0% over the period from January 1834 through June 1999. Ellen R. McGrattan and Edward C. Prescott, ‘‘Is the Market Overvalued?’’ Federal Reserve Bank of Minneapolis Quarterly Review 24 (2000): 20–24; ‘‘Taxes, Regulations and Asset Prices,’’ Working paper, Federal Reserve Bank of Minneapolis, July 2001.
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Cost of Capital
FORWARD-LOOKING (ex Ante) APPROACHES Forward-looking approaches estimate the ERP by subtracting the current risk-free rate from the implied expected return for the stock market. Forward-looking approaches can be categorized into three groups based on the approach taken: 1. Fundamental information. This approach uses information such as earnings or dividends to estimate a bottom-up rate of return for a number of companies. An expected rate of return for an individual company can be implied by solving for the present value discount rate that equates the current market price of a stock with the present value of expected future dividends, for example. A bottom-up implied ERP begins with the averaging of the implied rates of return (weighted by market value) for a large number of individual companies and then subtracting the government bond rate. The bottom-up approach attempts to directly measure investor’s expectations concerning the overall market by using forecasts of the rate of return on publicly traded companies. 2. Top-down. This approach uses relationships across publicly traded companies over time between real stock returns, price/earnings ratios, earnings growth, and dividend yields. An estimate of the real rate of equity returns is developed from current economic observations applied to the historical relationships. Subtracting the current rate of interest provides an estimate of the expected ERP implied by the historical relationships. 3. Opinions. This approach relies on opinions of investors and financial professionals through surveys of their views on the prospects of the overall market. BOTTOM-UP APPROACHES This section presents estimates of ERP from three sources of bottom-up data. Merrill Lynch publishes bottom-up expected return estimates for the S&P 500 Stock Index derived from averaging return estimates for stocks in the S&P 500. While Merrill Lynch does not cover every company in the S&P 500 index, it does cover a high percentage of the companies as measured in market value terms. Merrill Lynch uses a multistage dividend discount model (DDM) to calculate expected returns for several hundred companies using projections from its own securities analysts. The resulting data are published monthly in the Merrill Lynch publication Quantitative Profiles. The Merrill Lynch expected return estimates have indicated an implied ERP ranging from 3% to 6.7% in recent years, with an average over the last 15 years of approximately 4.9%. The expected premium was approximately 5.1% at the end of 2006. In a DDM, the analyst first projects future company dividends. Merrill Lynch then calculates the internal rate of return that sets the current market price equal to the present value of the expected future dividends. If the projections correspond to the expectations of the market, then Merrill Lynch has estimated the rate at which the market is discounting these dividends in pricing the stock. The DDM is a standard method for calculating the expected return on a security.42 The theory assumes that the value of a stock is the present value of all future dividends. If a company is not currently paying dividends, the theory holds that it must be investing in projects today that will lead to dividends in the future. A number of consulting firms reportedly are using Merrill Lynch DDM estimates to develop discount rates. One author comments on the Merrill Lynch data:
42
See, for example, Sidney Cottle, Roger F. Murray, and Frank E. Block, Graham & Dodd’s Security Analysis, 5th ed. (New York: McGraw-Hill, 1988), 565–568.
Forward-Looking (ex Ante) Approaches
107
Two potential problems arise when using data from organizations like Merrill Lynch. First, what we really want is investor’s expectations, and not those of security analysts. However. . .several studies have proved beyond much doubt that investors, on the average, form their own expectations on the basis of professional analysts’ forecasts . The second problem is that there are many professional forecasters besides Merrill Lynch, and, at any given time, their forecasts of future market returns are generally somewhat different. . . .However, we have followed the forecasts of several of the larger organizations over a period of years, and we have rarely found them to differ by more than [plus or minus] 0.3 percentage points from one another.43
Although expected rates of return would be underestimated if the effects of share repurchases are not adequately considered, personnel from Merrill Lynch have indicated that their analysts take share repurchases into account by increasing long-term growth rates in earnings per share. If the effect is not completely modeled, the Merrill Lynch estimates may be biased downward. It is also possible that the DDM may understate expected returns to the extent that expected dividends are measured based on earnings from assets in place and understate future growth opportunities. But this is most likely a larger problem for the analysis of smaller companies than for the large companies that predominate the S&P 500 Index in market value terms. Value Line projections can be used to produce estimates of expected returns on the market. Value Line routinely makes ‘‘high’’ and ‘‘low’’ projections of price appreciation over a three- to five-year horizon for over 1,500 companies. Value Line uses these price projections to calculate estimates of total returns, making adjustments for expected dividend income. The high and low total return estimates are published each week in the Value Line Investment Survey. Midpoint total return estimates are published in Value Line Investment Survey for Windows CD database. There is some evidence that the Value Line analysts’ projections, at least for earnings growth, tend to be biased high.44 Implied ERP estimates developed from Value Line data have been more volatile than the Merrill Lynch DDM models. Recent implied ERP estimates have ranged from slightly below zero at the end of 1999 to more than 12% at the end of 2002, with the average implied ERP over the past 15 years being 5.3%. The most recent implied ERP was 5.0% as of the end of 2006. We believe that Value Line’s estimates of future prices are ‘‘sticky’’ (i.e., they tend to change slowly), with the result that the expected premium appears to rise after a bear market and fall after a bull market. The Cost of Capital Yearbook published by Morningstar annually reports the implied rates of return for a large number of companies derived from both a single-stage DDM and a three-stage DDM (with quarterly updates reported in their Cost of Capital Quarterly).45 Expected growth rates in dividends are derived from analysts’ estimates as reported in the Institutional Broker’s Estimate System (I/B/E/S) Consensus Estimates database. The Cost of Capital Yearbook reports statistics for large composite groups of companies, and from these statistics you can derive an ERP for the overall market. Implied ERP estimates derived from the reported three-stage DDM rates of return have ranged from 4.9% to 8.0% since publication commenced in 1994, with the implied ERP at the beginning of 2007 being 7.5%. Several academic studies have employed consensus forecasts of long-run earnings per share growth as a proxy for projected dividends in a DDM. One study extracted ex ante estimates of the ERP from several versions of the CAPM.46 The results suggest that the ERP varies over the business cycle; it is lowest in periods of business expansion and greatest in periods of recession. The ERP 43
44
45 46
Eugene Brigham and Louis Gapenski, Financial Management: Theory and Practice, 5th ed. (Fortworth, TX: Dryden Press 1988), 227. David T. Doran, ‘‘Forecasting Error of Value Line Weekly Forecasts,’’ Journal of Business Forecasting (Winter 1993–94): 22–26. See, for example, Cost of Capital Yearbook 2007 (Chicago: Morningstar, 2007). Fabio Fornari, ‘‘The Size of the Equity Premium,’’ Working paper, January 2002.
108 Exhibit 9.3
Cost of Capital Implied ERP Estimates
Merrill Lynch Value Line: 3- to 5-year horizon Cost of Capital Yearbook
Range
Period
Mean
As of Early 2007
3.0% to 6.7% 1.0% to 12.3% 4.9% to 8.0%
1988–2006 1988–2006 1994–2006
4.9% 5.7% 6.4%
5.1%* 5.0% 7.5%
*
As of the end of January 2007.
appears to be positively correlated with long-term bond yields (increasing as bond yields increase) and with the default premium (increasing as the differential between Aaa- and Baa-rated bond yields increases). Studies have indicated that analysts’ earnings forecasts (such as those reported by I/B/E/S and First Call) are biased high.47 These biases lead to high implied estimates of ERP. Exhibit 9.3 summarizes three forward-looking implied ERP estimates published over the past several years. TOP-DOWN APPROACHES Various researchers have published estimates of the expected ERP based on their analyses of the historical relationship of such variables as earnings growth, stock market levels in terms of price to earnings ratios and dividend yields, changes in interest rates, and real stock returns. They apply the observed relationships to the state of the current economic variables and stock market levels and project future real returns on stocks. By subtracting the current interest rates, you obtain an estimate of the expected ERP. A sampling of those studies follows.
Jeremy Siegel studied the link between real equity returns, price/earnings ratio, real growth, replacement cost of capital invested, and market value of capital. He estimates that the long-run price/earnings ratio will settle between 20 and 25 and that the real (before inflation) average compound future total equity return will be approximately 5%. This converts to an expected geometric ERP of 2% (equivalent to approximately 4% arithmetic average).48
Bradford Cornell studied the relationship between growth in real domestic product and earnings and dividends. He estimates that under any reasonable underlying assumptions about inflation, equity risk premiums cannot be more than 3% (geometric average) because the earnings growth rate is constrained unconditionally in the long run by the real growth rate in the economy, which has been in the range of 1.5% to 3.0%.49
47
48 49
James Claus and Jacob Thomas, ‘‘The Equity Premia as Low as Three Percent? Evidence from Analysts’ Earnings Forecasts for Domestic and International Stock Markets,’’ Journal of Finance (October 2001): 1629–1666; Alon Brav, Reuven Lehavy, and Roni Michaely, ‘‘Using Expectations to Test Asset Pricing Models,’’ Financial Management (Autumn 2005): 5–37; Sundaresh Ramnath, Steve Rock, and Philip Stone, ‘‘Value Line and I/B/E/S Earnings Forecast,’’ International Journal of Forecasting (January 2005): 185–198. Those authors report the results of projected earnings amounts rather than growth rates (they use the I/ B/E/S long-term growth rate to project the EPS four years into the future), and compare this with the actual EPS four years in the future. The results indicate that I/B/E/S mean forecast error in year 4 EPS is negative. This can be translated into a preliminary typical growth rate adjustment for, say, a projected 15% growth rate as follows: ((1.15^4)(1 .0545))^.25 1 ¼ 13.4%, implying a ratio of actual to forecast of .134/.15 ¼ .89. This would imply that equity risk premium forecasts using analyst forecasts are biased high; Roberto Bianchini, Stefano Bonini, and Laura Zanetti, ‘‘Target Price Accuracy in Equity Research,’’ Working paper, January 2006. Jeremy Siegel, ‘‘Historical Results: Discussion,’’ Equity Risk Premium Forum, AIMR (November 8, 2001): 30–34. Bradford Cornell, ‘‘Historical Results: Discussion,’’ Equity Risk Premium Forum, AIMR (November 8, 2001): 38–41.
Forward-Looking (ex Ante) Approaches
109
Given the level of the S&P 500 in early 2001 (the time of his study), his analysis indicates a current conditional estimate of the ERP of at most 3.5% on a geometric basis (equivalent to approximately a 5.5% arithmetic average).
Elroy Dimson, Paul Marsh, and Mike Staunton studied the realized equity returns and historical equity premiums for 17 countries (including the United States) from 1900 to the end of 2006.50 Assuming that the standard deviation of annual returns on equity will approximately equal the historical standard deviation, their analysis indicates an estimate of ERP in early 2007 of 3.9% on a geometric basis (equivalent to approximately a 5.9% arithmetic average) versus U.S. government bonds. The authors note that: Further adjustments should almost certainly be made to historical risk premiums to reflect long-term changes in capital market conditions. Since, in most countries corporate cash flows historically exceeded investors’ expectations, a further downward adjustment is in order.
They conclude that a further downward adjustment of approximately 50 to 100 basis points in the expected ERP at the beginning of 2007 is plausible. Adjusting the realized risk premium for the increase in price-to-dividend ratio which resulted from a decrease in the discount rate and dividend yield to current levels, the resulting estimated ERP at the beginning of 2007 for the United States is in the range of 4.9% to 5.4% (arithmetic average over U.S. government bonds; 2.9% to 3.4% geometric average over U.S. government bonds).51
Roger Ibbotson and Peng Chen prepared a forecast of ERP based on the contribution of earnings growth to price/earnings ratio growth and on growth in per capita GDP. Their supply side estimate of ERP at the beginning of 2007 is about 6.3% (arithmetic average relative to government bonds; 4.3% on a geometric basis).52 These forecasts tend to give somewhat lower forecasts than historical risk premiums, primarily because part of the total returns of the stock market have come from price-earnings ratio expansion. This expansion is not predicted to continue indefinitely, and should logically be removed from the expected risk premium.53
SURVEYS
50
51
52 53
54
Ivo Welch surveyed over 500 finance and economics professors at leading universities and found that, for long-term investments, the median forecast ERP (premium over T-bills) was 5%, with the interquartile range of 4% to 7%.54 Adjusting for the horizon premium embedded in government bonds versus T-bills, these results translate to a median forecast ERP (premium over government bonds) of 3.6%, with an interquartile range of 2.6% to 5.6%. Dimson, Marsh, and Staunton, ‘‘Global Evidence on the Equity Premium’’; ‘‘The Worldwide Equity Premium: A Smaller Puzzle’’ EFA 2006 Zurich Meetings Paper, April 7, 2006; Global Investment Returns Yearbook 2007. Based on converting the premium over total returns on bonds as reported by Dimson, Marsh, and Staunton, removing the impact of the growth in price-dividend ratios from the geometric average historical premium, reducing the historical average dividend yield to a current dividend yield, and converting to an approximate arithmetic average. SBBI Valuation Edition 2007 Yearbook. Goetzmann and Ibbotson, ‘‘History and the Equity Risk Premium,’’ 8. Also note that the supply side estimate of ERP for the period 1952 to 2004 discussed earlier is 4.9% arithmetic average (4.8% geometric average). Ivo Welch, ‘‘The Equity Premium Consensus Forecast Revisited,’’ Cowles Foundation Discussion Paper no. 1325, September 2001.
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Cost of Capital
John Graham and Campbell Harvey report the results from quarterly surveys of chief financial officers of U.S. corporations conducted from mid-2000 to the end of 2006. The current survey attracts about 400 respondents (10% from companies with less than $10 million in revenue; 50% from companies with less than $500 million in revenue; 40% are private companies). That study reports that the range of ERP given a 10-year investment horizon was 2.5% to 4.7% (premium over 10-year government bonds), with the most recent survey concluding 3.3%.55
Greenwich Associates publishes an annual survey of several hundred pension plan officers concerning their expected returns for the S&P 500 Index for a five-year holding period. Using the survey and converting the results to an ERP estimate, it generally indicated an expected premium over long-term U.S. government bonds of between 2% and 4%. Their most recent survey indicated an expected premium over long-term U.S. government bonds of 3.4%.56
OTHER SOURCES OF ERP ESTIMATES A list of published opinions and guidelines on ERP. These are not the only sources but represent a cross section of opinion on the subject.
Principals of Corporate Finance, 8th ed., takes no official position on the exact ERP. But the authors believe a range of 5% to 8% premium over T-bills is reasonable for the United States (equivalent to a premium over government bonds of approximately 3.5% to 6.5%). They warn that ‘‘out of this debate only one firm conclusion emerges: Do not trust anyone who claims to know what returns investors expect.’’57
Valuation: Measuring and Managing the Value of Companies, 4th ed., recommends an ERP of 4.5% to 5.5%.58 The authors use a forward-looking model to estimate real expected market returns for 1962 through 2002 averaging 7.0%. Subtracting the real return on U.S. government inflation-protected bonds (TIPS), they estimate the risk premium. The authors conclude on their assessment of the research and evidence: Although many in the finance profession disagree about how to measure the (ERP), we believe 4.5 to 5.5% is the appropriate range. Historical estimates found in most textbooks (and locked in the minds of many), which often report numbers near 8%, are too high for valuation purposes because they compare the market risk premium versus short-term bonds, use only 75 years of data, and are biased by the historical strength of the U.S. market.59
55
56 57
58
59
John R. Graham and Campbell R. Harvey, ‘‘Expectations of Equity Risk Premia, Volatility and Asymmetry from a Corporate Finance Perspective,’’ Working paper, National Bureau of Economic Research, July 2003, updated quarterly by Duke CFO Outlook Survey, www.cfosurvey.org; ‘‘The Equity Risk Premium in January 2007: Evidence from the Global CFO Outlook Survey,’’ working paper reporting on the autumn 2006 survey, January 2007. Graham and Harvey believe the results represent a geometric average expected return. Grabowski estimated the arithmetic average equivalent ¼ geometric average risk premium estimate ¼ (standard deviation of risk premium estimates)2/2. The survey question answered is ‘‘On November 10, 2006 the annual yield on 10-year treasury bonds was 4.6%. Over the next 10 years, I expect the average annual S&P 500 return will be:___%.’’ This question leads us to question whether the replies represent the expected compound return over the next 10 years (geometric average) or the annual average return (arithmetic average). Greenwich Associates, ‘‘Market Trends, Actuarial Assumptions, Funding, and Solvency Ratios’’ (Fall 2006). Richard Brealey, Stuart Myers, and Franklin Allen, Principals of Corporate Finance, 8th ed. (Boston: Irwin McGraw-Hill, 2006), 154. Tim Koller, Marc Goedhart and David Wessels, Valuation: Measuring and Managing the Value of Companies, 4th ed. (New York: John Wiley & Sons, 2005), 305–306. Ibid., 306.
Other Sources of ERP Estimates
111
Damodaran on Valuation, 2nd ed., concludes that the most relevant realized return is the geometric average realized return versus government bonds 4.84% (geometric average realized premium 1926 through 2004 over government bonds) while the average implied (forwardlooking approach using expected dividends and expected dividend growth) EPR is only about 4% as of January 2006 (premium over government bonds).60 The author notes that the average implied ERP has been about 4% over the past 40 years.61 He uses 4% in most of his valuation examples.
The Equity Risk Premium concludes that ‘‘reasonable forward-looking ranges for the future equity risk premiums in the long run are 3.5% to 5.5% over treasury bonds. . . .’’62
Creating Shareholder Value, revised and updated, recommends that the premium should be based on expected rates of return rather than average historical rates. This approach is crucial because with the increased volatility of interest rates over the past two decades the relative risk of bonds increased, thereby lowering risk premiums to a range of 3 to 5%.63
60
61 62 63 64 65 66 67
68 69
Graham and Dodd’s Security Analysis uses an ‘‘equity risk premium’’ of 2.75% over the yield on Aaa industrial bonds for valuing the aggregate S&P 400 Index that approximates a 10-year historical average.64 This translates to a premium of approximately 3% over long-term government bonds. The authors reproduce the opinion of one security analyst who recommended a premium over the S&P Composite Bond yield of 3.5% to 5.5% in 1978 and 3.0% to 3.5% in 1983;65 this translates to premiums of approximately 4.5% to 7% in 1978 and 4% to 6% in 1983 over longterm government bonds. Stocks for the Long Run, concludes that ‘‘as real returns on fixed-income assets have risen in the last decade, the equity premium appears to be returning to the 2% to 3% norm that existed before the postwar surge.’’66 The author updates his views to the beginning of 2006 and concludes that projected equity returns of 3.5% to 4.5% (equivalent arithmetic average return) over government bonds ‘‘will still give ample rewards for investors willing to tolerate the short-term risks of stocks.’’67 The Quest for Value recommends a 6% premium based on a long-run geometric average difference between the total returns on stocks and bonds.68 Financial Statement Analysis and Security Valuation notes that ‘‘the truth is that the equity risk premium is a speculative number.’’ The author uses 5% in his examples but notes the wide range of estimates.69
Aswath Damodaran, Damodaran on Valuation: Security Analysis for Investment and Corporate Finance, 2nd ed. (New York: John Wiley & Sons, 2006), 41 and 48. Ibid., 47. Bradford Cornell, Equity Risk Premium: The Long-Run Future of the Stock Market (New York: John Wiley & Sons, 1999), 201. Alfred Rappaport, Creating Shareholder Value, rev. and updated (New York: The Free Press, 1997), 39. See Cottle, Murray, and Block, Graham & Dodd’s Security Analysis, 573. Ibid., 83–85. Siegel, Stocks for the Long Run, 20. Siegel, ‘‘Perspectives on the Equity Risk Premium.’’ Grabowski converted Siegel’s conclusion in terms of geometric average return (p. 70) compared to government bonds. G. Bennett Stewart, The Quest for Value (New York: HarperCollins, 1991), 436–438. Stephen H. Penman, Financial Statement Analysis and Security Valuation, 3rd ed. (New York: McGraw-Hill, 2007), 476.
112
Cost of Capital
Equity Premium: Historical, Expected, Required and Implied recommends that ‘‘an additional 4% (over government bonds) compensates the additional risk of a diversified portfolio.’’70 In the Duff & Phelps Risk Premium Report 2007, the historical realized equity premium for the period of 1963 through 2006 was 4.9%.71
UNCONDITIONAL VERSUS CONDITIONAL ERP The evidence presented represents a long-term average or unconditional estimate of the ERP. That is, what is a reasonable range of ERP that can be expected over an entire business cycle? Where in this range is the current ERP? Research has shown that ERP is cyclical during the business cycle. We use the term conditional ERP to mean the ERP that reflects current market conditions. For example, when the economy is near or in recession (and reflected in recent relatively low returns on stocks), the conditional ERP is more likely at the higher end of the range. When the economy improves (with expectations of improvements reflected in recent increasing stock returns), the conditional ERP moves toward the midpoint of the range. When the economy is near its peak (and reflected in recent relatively high stock returns), the conditional ERP is more likely at the lower end of the range. The issue of predicting future returns on the S&P 500 is the subject of much research, which generally has centered on the power of various models to predict future returns on the S&P 500 and the resultant equity premium given current prospects as measured by observed relationships. For example, Amit Goyal and Ivo Welch test a range of variables that have been held to predict ERP: dividend-to-price ratios, dividend yields, price/earnings ratios, interest rates, inflation rates, and consumption-based macroeconomic ratios. They find that the models are unstable when used to predict the resulting equity risk premium in periods not included in the sample periods. They find that ‘‘most models not only cannot beat the unconditional benchmark, but also outright underperform it.’’72 Others have disputed their results, finding that predictive power is small, but economically meaningful, or their results are really the result of poor predictability of, say, dividend growth.73 But research suggests that only models allowing explicitly for time varying factors succeed in maintaining their predictive power across periods of time.74 But the predictability of the ERP most impacts short-term investment. As the focus of this book is valuation of businesses and investments by businesses, the conditional ERP is of less importance, and we can fall back on using the long-term, unconditional ERP in developing discount rates.
SUMMARY The results presented in this chapter do not point to a single estimate of ERP. They point to a conclusion that the current ERP is in a range that is consistent with the principle that investor’s 70 71
72
73
74
Pablo Fernandez, ‘‘Equity Premium: Historical, Expected, Required and Implied,’’ Working paper, February 18, 2007, 28. See Chapter 12 for a discussion of the realized risk premiums observed for the period covered by that study. Duff & Phelps Risk Premium Report 2007. Available at www.corporate.morningstar.com/ib or www.bvresources.com. Amit Goyal and Ivo Welch, ‘‘A Comprehensive Look at the Empirical Performance of Equity Premium Prediction,’’ Working paper, January 11, 2006. John Y. Campbell and Samuel B. Thompson, ‘‘Predicting the Equity Premium Out of Sample: Can Anything Beat the Historical Average?’’ HIER Discussion Paper No. 2084 (July 2005); John H. Cochrane, ‘‘The Dog That Did Not Bark: A Defense of Return Predictability,’’ Working paper, January 30, 2006. Thomas Dangl, Michael Halling, and Otto Randl, ‘‘Equity Return Prediction: Are Coefficients Time Varying?’’ Working paper, April 2006.
Summary
113
expectations are not homogeneous. Different investors have different cash flow expectations and future assessments of the risk that those cash flows will be realized. You can think of this in terms of the dividend discount model; numerous combinations of expected future cash flows and discount rates equate to the existing price.75 Estimating the ERP is one of the most important issues when you estimate the cost of capital of a subject business or project. You need to consider a variety of alternative sources, including examining realized returns over various periods and employing forward-looking estimates such as those implied from projections of future prices, dividends, and earnings. What is a reasonable estimate of ERP in 2007? While giving consideration to long-run historical arithmetic average of realized risk premiums, these authors conclude that the post-1925 historical arithmetic average of one-year realized premiums as reported in the SBBI Yearbook results in an expected ERP estimate that is too high. We come to that conclusion based on the works of various researchers (e.g., Dimson, Marsh, and Staunton; Goetzmann and Ibbotson) and current market expectations (e.g., survey of chief financial officers). Some practitioners express dismay over the necessity of considering a forward ERP since that would require changing their current ‘‘cookbook’’ practice of relying exclusively on the post-1925 historical arithmetic average of one-year realized premiums reported in the SBBI Yearbook as their estimate of the ERP. Our reply is that valuation is a forward-looking concept, not an exercise in mechanical application of formulas. Correct valuation requires applying value drivers reflected in today’s market pricing. You need to mimic the market. In our experience, you often cannot match current market pricing for equities using the post-1925 historical arithmetic average of one-year realized premiums as the basis for developing discount rates. The entire valuation process is based on applying reasoned judgment to the evidence derived from economic, financial, and other information and arriving at a well-reasoned opinion of value. Estimating the ERP is no different. After considering the evidence, a reasonable long-term estimate of the normal or unconditional ERP as of the beginning of 2007 should be in the range of 3.5% to 6%. For examples in this book, the authors have concluded that an estimate of ERP of 5% is consistent with the research presented here and we use 5% in the examples. While we present data and calculations elsewhere in this book using data through the end of 2005 and earlier, we do that to help the reader understand the methodology. Since the choice of ERP is so important, in this chapter we present data that are as up to date as possible as we were preparing the text.
75
Fernandez, ‘‘Equity Premium: Historical, Expected, Required and Implied.’’
Appendix 9A
Bias Issues in Compounding and Discounting
Bias in Compounding Bias in Discounting
BIAS IN COMPOUNDING In predicting the compound return, you might expect for an investment in stocks using an ERP estimate derived from the arithmetic average of realized risk premium data that you will get an answer that is biased (i.e., will measurement error be introduced simply due to the mathematics). Comparing future values that result from compounding an investment at an erroneous ‘‘too high’’ rate of return with results from compounding an investment at an equally erroneous ‘‘too low’’ estimated rate of return, the estimated future value in the too-high case will be further from the true expected future value than the estimate in the too-low case. This is simply a function of the mathematics of compounding. Averaging across these possibilities, the compounded future values derived from arithmetic averages will be too high in general. For example, assume that the true expected annual return on stocks for the next 10-year holding period equals 10%. The true expected future value in 10 years will then equal (1.10)10 ¼ 2.5937. The true expected return is not observable; historical data are compiled in an attempt to estimate the true expected return. While the estimation process of compiling an arithmetic average of historical returns results in an unbiased estimate, the estimate will be either too high or too low. Assume that there is a 50/50 chance of choosing an estimated future return that is either too high or too low. If the estimate is too high (e.g., the estimate is that the future return will be 12%), the estimated future value will equal (1.12)10 ¼ 3.1058. Alternatively if the estimate is too low (e.g., the estimate is that the future return will be 8%), the estimated future value will equal (1.08)10 ¼ 2.1589. The average of these two estimates equals 2.6324, which is greater than the true expected return of 2.5937. Using the arithmetic average of historical returns or realized risk premiums with error (and we know there will always be error) as the estimate of the true expected return results in too high a compounded future return on average. Several authors have studied biases that may arise in multiperiod compounding when the single-period estimate of expected return is subject to measurement error.1 Proposals in the academic literature for a correction of this bias (for predicting future values) involve downward adjustments in the arithmetic average of single-period realized returns. These 1
Michael E. Blume, ‘‘Unbiased Estimators of Long-Run Expected Growth Rates,’’ Journal of the American Statistical Association (September 1974): 634–638; Ian Cooper, ‘‘Arithmetic Versus Geometric Mean Estimators: Setting Discount Rates for Capital Budgeting,’’ European Financial Management (July 2001): 157–167; Eric Jacquier, Alex Kane, and Alan J. Marcus, ‘‘Optimal Forecasts of Long-Term Returns and Asset Allocation: Geometric, Arithmetic, or Other Means?’’ Working paper, October 31, 2002.
114
Bias in Discounting
115
adjustments increase as the length of the investment horizon increases. One proposed correction has the expected rate of return falling to the geometric average rate of return if the investment horizon is as long as the time horizon over which the historical averages are measured.2 While corrections for the measurement error problem in the arithmetic average of annual realized returns may be material for compounding over several decades, the proposed corrections for near-term compounding are minor. You should always use the geometric average of historical data (i.e., stock returns, earnings before interest, taxes, depreciation, and amortization [EBITDA], etc.) for projections. For example, you should use the geometric average of realized risk premiums in projecting future value of a portfolio of stocks, not the arithmetic average. You should use the geometric average of historical growth in EBITDA to project future EBITDA, not the arithmetic average.3
BIAS IN DISCOUNTING In discounting expected cash flows where you develop a cost of equity capital estimate using an ERP estimate derived from the arithmetic average of realized risk premium data, will you get an answer that is biased? The statistical properties of this problem are such that you get a different answer if, instead of focusing on unbiased expected future values, you seek instead an unbiased estimate of the present value discount factor.4 A proposed correction that focuses on present value factors finds that the adjustment from the arithmetic average is small even when discounting over fairly long periods.5 Moreover, the bias is towards discount rates that are too low rather than too high. For example, assume that the true expected annual return on stocks for the next 10-year holding period equals 10% and that rate of return represents the correct risk-adjusted return to use in discounting a stream of future cash flows. The correct discount factor to use in determining the present value of cash flows expected 10 years in the future will then equal (1.10)10 ¼ 0.3855. Again the true expected return is not observable, and historical data are compiled in an attempt to estimate the true expected return. While the estimation process of compiling an arithmetic average of historical returns results in an unbiased estimate, the estimate will be either too high or too low. Assume that there is a 50/50 chance of choosing an estimated future return that is either too high or too low. If the estimate is too high (e.g., the estimate is that the future return will be 12%), the discount factor will equal (1.12)10 ¼ 0.3220. Alternatively, if the estimate is too low (e.g., the estimate is that the future return will be 8%), the discount factor will equal (1.08)10 ¼ 0.4632. The average of these two estimates equals 0.3926 (the arithmetic average results in an equivalent of a 9.8% rate of return), which results in a larger present value than had you used the correct discount factor of 0.3855 (i.e., the equivalent rate of return of 9.8% is too low compared to the true rate of return of 10%). Using the arithmetic average of historical realized premiums with error as the estimate of the true ERP results in an estimated rate of return that is too low. But the error in most practical valuations is minimal. The arithmetic average of historical realized premiums can be used as one estimate of the ERP without introducing mathematical bias.
2 3 4
5
Jacquier, Kane, and Marcus, ‘‘Optimal Forecasts of Long-Term Returns and Asset Allocations.’’ Pablo Fernandez, ‘‘80 Common Errors in Company Valuation,’’ Working paper, May 12, 2004: 12. When there is measurement error in expected returns, the unbiased estimate of the present value discount factor is not equal to the inverse of the unbiased estimate of future value. The bias in the arithmetic average for discounting runs in the direction opposite that of the bias for future values (i.e., the bias causes an underestimate of the true compounded discount rate rather than an overestimate). Cooper, ‘‘Arithmetic Versus Geometric Mean Estimators.’’
Chapter 10
Beta: Differing Definitions and Estimates
Introduction Estimation of Equity Beta Differences in Estimation of Equity Beta Length of the Sample or Look-Back Period Frequency of Return Measurement Choice of Market Index Choice of Risk-free Rate Levered and Unlevered Equity Betas Formulas for Unlevering and Levering Equity Betas Choosing Among Unlevering or Levering Formulas Adjusting Asset Beta Estimates for Differences in Operating Leverage Adjusting Asset Beta Estimates for Excess Cash and Investments Modified Betas: Adjusted, Smoothed, and Lagged Adjusted Beta Incorporates Industry Norm Smoothed beta ‘‘Sum Beta’’ Incorporates Lag Effect ‘‘Full-Information’’ Equity Beta Peer Group Equity Beta Fundamental Equity Beta Equity Beta Estimation Research Estimation of Debt Beta Other Beta Considerations Summary Appendix 10A Appendix 10B
INTRODUCTION Betas for equity capital are used as a modifier to the equity risk premium in the context of the Capital Asset Pricing Model (CAPM). Beta is the sole risk measure of equity capital of the textbook CAPM. The combination of equity beta times the ERP equals the estimated market risk premium. The concept of beta as a risk measure can be extended to debt capital. If equity capital is bearing all of the risk of the variability of operating income, then the debt capital is bearing no market risk and its beta is zero. But as the level of debt financing of the firm increases and the credit rating decreases, debt capital is also bearing market risk. That market risk can likewise be measured in terms of a beta.
117
118
Cost of Capital
This chapter explores some widely used methods in the estimation and applications of betas for equity capital and debt capital. Beta estimates are derived from data on publicly traded securities. If one is valuing a closely held company or a non-public, division or reporting unit, for example, one is using the beta estimate of publicly traded securities as a proxy for the non-public business.
ESTIMATION OF EQUITY BETA Market or systematic risk is measured in CAPM by a factor called beta. Beta is a function of the expected relationship between the return on an individual security (or portfolio of securities) and the return on the market. The market is generally measured by a broad market index, such as the Standard & Poor’s (S&P) 500 Index. The broad market index is a proxy for the broad economy. The beta is theoretically the expected sensitivity of the individual security to changes in the economy and, similar to the equity risk premium (ERP), beta is a forward-looking concept. The sensitivity of individual security returns is the sensitivity of the company to cash flow risks and discount rate risk. It represents the sensitivity of changing expectation about expected cash flows of the company relative to changing expectations about expected cash flows of the economy as a whole (i.e., the market), changing expectations for the ERP.1 Existing techniques for estimating beta generally use historical data over a sample or ‘‘look-back’’ period and assume that the future will be sufficiently similar to this past period to justify extrapolation of betas calculated using historical data. Research shows betas are time-varying (i.e., sensitive to market changes as the economy changes; beta differs during improving economic conditions compared to during declining economic conditions). Using a historical method based on a sample period may not perform well when economic conditions are changing. The current and expected future economic conditions may differ from the economic conditions during the look-back period. Therefore, the beta estimated using the data for the look-back period will not reflect the future. Theorists prefer to estimate beta by comparing the excess returns on an individual security relative to the excess returns on the market index. By excess return, we mean the total return (which includes both dividends and capital gains and losses) over and above the return available on a risk-free investment (e.g., U.S. government securities). For a publicly traded stock, you can estimate beta via regression (ordinary least squares [OLS] regression), regressing the (excess) returns on the individual security ðR R f Þ against the (excess) returns on the market ðRm R f Þ during the look-back period. The resulting slope of the best-fit line is the beta estimate. Formula 10.1 shows the regression formula. (Formula 10.1) ðR R f Þ ¼ a þ B ðRm R f Þ þ e where: R ¼ Historical return for publicly traded stock Rf ¼ Risk-free rate a ¼ Regression constant B ¼ Estimated beta based on historical data Rm ¼ Historical return on market portfolio e ¼ Regression error term 1
John Y. Campbell and Jianping Mei, ‘‘Where Do Betas Come From? Asset Price Dynamics and the Sources of Systematic Risk,’’ The Review of Financial Studies 6 No. 3 (1993): 567–592.
Estimation of Equity Beta
119
Morningstar uses excess returns in all its computations. Practitioners and some financial data services calculate betas using total returns instead of excess returns. The OLS regression using total return is: (Formula 10.2) R ¼ a þ B Rm þ e where variables are defined as above. However, comparisons of measurements using excess returns or total returns show that, as a practical matter, it makes little difference. Beta equals the covariance of the returns for subject security to the returns for the market (the S&P Index) relative to the variance in the returns for the market during the sampling or look-back period. An example of calculating betas using total returns is shown in Exhibit 10.1. The look-back period in this example is 120 months. An example of a beta estimate using the OLS regression method for a look-back period of 60 months of total returns for J.B. Hunt Transport Services, Inc. (as of December 2005) is displayed in Exhibit 10.2. Because beta is an expected sensitivity, any estimation using historical methods is subject to error. How useful are the results of the regression in estimating the relationship between the returns on a stock and the returns on the market? Or, how close to the true beta is the estimated beta? Exhibit 10.1 Month End, t [a] 1/89 2/89 3/89 10/98 11/98 12/98 Sum Average Beta ¼
Illustrative Example of One Common Method for the Calculation of Beta Return on Security A [b]
Return on S&P Index [c]
Calculated Covariance [d]
0.041 (0.007) 0.052
0.069 (0.029) 0.021
0.00211 0.00045 0.00043
0.00325 0.00168 0.00008
0.113 0.033 (0.016)
0.077 0.057 0.055
0.00709 0.00131 (0.00086)
0.00423 0.00203 0.00185
0.500 0.004
1.488 0.012
0.21060 0.00176 [f]
Calculated Variance [e]
0.26240 0.00219 [g]
CovarianceðSecurity A; S&P IndexÞ 0:00176 ¼ ¼ 0:80 Variance of S&P Index 0:00219
a. 10 years or 120 months. b. Returns based on end-of-month prices and dividend payments (versus quarterly or annually). c. Returns based on end-of-month S&P Index. d. Values in this column are calculated as: (Observed return on Security A Average return on Security A) (Observed return on S&P Index Average return on S&P Index) 0:00211 ¼ ½ð0:041 0:004Þ ð0:069 0:012Þ e. Values in this column are calculated as: (Observed return on S&P Index Average return on S&P Index) 0:00325 ¼ ð0:069 0:012Þ f. The average of this column is the covariance between Security A and the S&P Index. g. The average of this column is the variance of return on the S&P Index. Source: Shannon P. Pratt, Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed. (New York: McGraw-Hill Companies, 2008), Chap. 9. Reprinted with permission. All rights reserved.
120
Cost of Capital
Exhibit 10.2
Example of Beta Estimation for J.B. Hunt Transport Service, Inc.
Ticker Symbol: JBHT SIC 4213: Trucking, Except Local Date: December, 2005 Company: J.B. Hunt Transport Services, Inc., together with its subsidiaries, provides full-load freight transportation services in the United States, Canada, and Mexico. Calculated OLS Beta Number of Months of Data Regression Coefficients R-Squared Intercept Beta T-Statistic Summary Statistics Average Return Standard Deviation Correlation Matrix Company Market
1.62 60 OLS 0.30 3.49% 1.624 4.95 Company 3.716% 12.742% Company 1.000 0.545
Average Monthly Volume (millions) Average Volume/Total Outstanding
Market 0.138% 4.275% Market 1.000
34.978 22.74%
Monthly Returns versus Market Index
40%
Company Returns
30% 20% 10% 0%
++ + ++ +
+
–10% +
–20%
++ + + + + + + ++ + +++ +++ + + + + + +++ ++ + + + ++ +++ + + + ++ ++ +
–30% –40% –50% –25%
+ –20%
–15%
–10%
0% 5% –5% S&P 500 Returns
+ Observed returns
10%
15%
20%
25%
Y = 3.49% + 1.62 X
Source: Calculated (or derived) based on Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
Accuracy of the beta estimate can be described in statistical terms. Important statistics are:
T-statistic: Only indicates if the beta coefficient is different from zero (i.e., if t-statistic > x, beta differs from zero).
Standard error of estimate: Measures likelihood that true beta is measured by estimate of the beta made by regression.
See Appendix F for a discussion of the relationship between two sets of measures (the return on the subject security and the return on the market).
Differences in Estimation of Equity Betas
121
The beta estimate for the example in Exhibit 10.2 equals 1.624. The t-statistic in the example equals 4.95, indicating that the data provide a beta estimate that is statistically significant (i.e., different from zero). R2 equals 0.30. The standard error of estimate equals 0.328.2 That is, we have 95% confidence that the true beta is between 1.62 þ= (2)(0.328) or between .96 and 2.28. Because we cannot compute a beta directly for a division, reporting unit, or closely held company, we need to estimate a proxy beta for these businesses. We can either calculate beta estimates or go to reference sources to obtain beta estimates for guideline public companies or industries to use as a proxy beta for our subject business. In developing a proxy beta, you must consider the differences between the subject company and the possible guideline public companies. Also, you must be cautious of beta estimates using smaller public companies without an active market, as their betas tend to be underestimated using OLS beta estimates and by reference sources. Further, the more beta estimates drawn from guideline public companies you use as the basis for the beta estimate of the subject business, the better the accuracy because the standard error of estimation is reduced. Details on sources of beta estimates can be found in Appendix B.
DIFFERENCES IN ESTIMATION OF EQUITY BETAS Be aware that significant differences exist between betas for the same stock published by different financial reporting services. One of the implications of this fact is that betas for guideline companies used in a valuation should all come from the same source. If all betas for guideline companies are not available from a single source, the best solution probably is to use the source providing betas for the greatest number of guideline companies and not use betas given for the others. Otherwise an applesand-oranges mixture will result. Differences in the beta measurement derive from choices within four variables: 1. The length of the time period over which the historical returns are measured (i.e., the length of the look-back period) 2. The periodicity (frequency) of return measurement within that time period 3. The choice of an index to use as a market proxy 4. The risk-free rate above which the excess returns should be measured In addition to how these four variables are treated, adjustments can be made to recognize the beta’s tendency to adjust toward either the industry average beta or the market portfolio beta (1.0). These adjustments are discussed later in this chapter. LENGTH OF THE SAMPLE OR LOOK-BACK PERIOD Most services that calculate beta use a two- to five-year sample measurement or look-back period. Five years is the most common historical period on which the forward estimate is based. This balances the use of a long history with the likelihood that betas are changing and betas estimated with ‘‘older’’ data may not be representative of future betas. The Morningstar Beta Book uses a 60-month look-back period for most stocks but includes a beta based on as few as 36 months if data are available for only this length of time. The Beta Book is published semiannually in hard copy and contains beta information on public companies. You can also get beta information by company on the Morningstar Web site (www.Morningstar.com). The example in Exhibit 10.1 uses a look-back period of 120 months. The beta estimate for J.B. Hunt displayed in Exhibit 10.2 uses a look-back period of 60 months. 2
Standard error of estimate of the beta coefficient ¼ beta=t-statistic.
122
Cost of Capital
But if the company characteristics change during the sampling period (e.g., major divestiture or acquisition), it may be more appropriate to use a shorter period. However, as the sampling period used is reduced, the accuracy of the estimate is generally reduced. FREQUENCY OF RETURN MEASUREMENT Returns for the publicly traded stock and the market returns may be measured on a daily, weekly, monthly, quarterly, or annual basis. Monthly is the most common frequency, although Value Line uses five years of weekly data. CHOICE OF MARKET INDEX The market index used in calculating beta could be any of these or, in some cases, another index:
Standard & Poor’s (S&P) 500 Index
New York Stock Exchange (NYSE) Composite Index NYSE and American Stock Exchange (AMEX) Index
NYSE, AMEX, and over-the-counter (OTC) Index Value Line Index
For an index to be representative of the market, it must be market-capitalization weighted. That is, the weight for each company in the index is determined by the market value of its equity. The sizes of the companies in the S&P 500 Index are so great that the index comprises about 70% of the total capitalization of all of the stocks constituting the combined indexes listed here. Furthermore, the broader market indexes listed correlate almost perfectly with the S&P 500 Index. As a result, it generally does not make a great deal of difference which index is used. Morningstar uses the S&P 500 in its calculations for the Cost of Capital Yearbook and the Beta Book. But the beta estimate for a specific company may underestimate that company’s true beta if the market index used during the look-back period is overweighted by a specific industry. The theory is that the market index should reflect the overall economy. But at times the market value for a particular segment of the economy will ‘‘take over’’ the market index (e.g., technology stocks in the late 1990s). For example, the risks for basic manufacturing companies appeared to have gone down in the late 1990s. Prior to the run-up in prices of technology stocks, basic manufacturing companies represented significant weight in the stock indices. Changes in the returns on basic manufacturing stocks were highly correlated to the changes in the stock indices. As technology stocks began to dominate the indices, the returns on the stocks of basic manufacturing companies were significantly less correlated with returns in the market indices, making it appear that their risks had been reduced. The underlying risks of basic manufacturing companies had not changed. But their observed betas then looked low compared to their long-term average betas. At times when one segment takes over the market index, alternative, longer look-back periods or alternative beta measurements, such as fundamental betas (discussed later in this chapter), may be more representative of the risks of the companies in other segments. CHOICE OF RISK-FREE RATE To avoid the maturity risk (interest rate risk) inherent in long-term bonds, the risk-free rate used to compute excess returns generally is either the Treasury bill (T-bill) rate or the interest yield from U.S. government bonds. Morningstar uses the 30-day T-bill rate in its calculations for the Cost of Capital Yearbook and the Beta Book. Differences in the choice of risk-free rate will cause differences in the beta estimates.
Levered and Unlevered Equity Betas
123
LEVERED AND UNLEVERED EQUITY BETAS Published and calculated betas for public stocks typically reflect the capital structure of each respective company at market values. These betas sometimes are referred to as levered betas, betas reflecting the leverage in the company’s capital structure. Levered betas incorporate two risk factors that bear on systematic risk: business (or operating) risk and financial (or capital structure) risk. Removing the effect of financial leverage leaves the effect of business risk only. The unlevered beta is often called an asset beta. Asset beta is the beta that would be expected were the company financed only with equity capital. When a firm’s beta estimate is measured based on observed historical total returns (as most beta estimates are), its measurement necessarily includes volatility related to the company’s financial risk. In particular, the equity of companies with higher levels of debt is riskier than the equity of companies with less leverage (all else being equal). If the leverage of the division, reporting unit, or closely held company subject to valuation differs significantly from the leverage of the guideline public companies selected for analysis, or if the debt levels of the guideline public companies differ significantly from one another, it typically is desirable to remove the effect that leverage has on the betas before using them as a proxy to estimate the beta of the subject company. This adjustment for leverage differences is performed in three steps: Step 1. Compute an unlevered beta for each of the guideline public companies. An unlevered beta is the beta a company would have if it had no debt. Step 2. Decide where the risk would fall for the subject company relative to the guideline companies, assuming all had 100% equity capital structures. Step 3. Lever the beta for the subject company based on one or more assumed capital structures (i.e., relever the beta). The result will be a market-derived beta specifically adjusted for the degree of financial leverage of the subject company. If the relevered beta is used to estimate the market value of a company on a controlling basis, and if it is anticipated that the actual capital structure will be adjusted to the proportions of debt and equity in the assumed capital structure, then only one assumed capital structure is necessary. However, if the amount of debt in the subject capital structure will not be adjusted, an iterative process may be required. The initial assumed capital structure for the subject will influence the cost of equity, which will, in turn, influence the relative proportions of debt and equity at market value. It may be necessary to try several assumed capital structures until one of them produces an estimate of equity value that actually results in the assumed capital structure. We discuss the iterative process in Chapter 17. This process of unlevering and relevering betas to an assumed capital structure is based on the assumption that the subject business interest has the ability to change the capital structure of the subject company. In the case of the valuation of a minority ownership interest, for example, the subject business interest may not have that ability and the existing capital structure should likely be the one assumed. FORMULAS FOR UNLEVERING AND LEVERING EQUITY BETAS The general relationship of the various formulas for unlevering and levering betas can be defined in terms of the next equations: Value of Levered Firm ¼ Value of Levered Assets or alternatively; Value of the Levered Firm ¼ Value of the Unlevered Assets þ Present Value of Tax Shield
124
Cost of Capital
Value of Levered Firm = Value of Levered Assets Capital Assets Value of Levered Assets
Value of Debt Capital minus Value of Tax Shield plus Value of Equity Capital
In this formulation, cost of debt capital is measured after the tax affect (kd) as the value of the tax deduction on interest payment reduces the cost of debt capital. Value of the Levered Firm = Value of the Unlevered Assets + Present Value of Tax Shield Assets
Capital
Value of Unlevered Assets
Value of Debt Capital
plus
plus
Value of Tax Shield
Value of Equity Capital
In this formulation, the cost of debt capital is measured prior to the tax effect (kd(pt)) as the value of the tax deduction on the interest payments equals the value of the tax shield.
Exhibit 10.3
Value of a Levered Firm
The value of the tax shield equals the present value of the expected tax deductions on interest payments for the debt capital financing. Graphically the relationship is shown in Exhibit 10.3. The values of debt capital and equity capital are expressed as market values. Various authors have proposed alternative formulas for unlevering and relevering betas. These formulas are generally functions of the risk of realizing the tax savings resulting from the tax deductions from the interest expense of the debt component of the capital structure. For example, if the guideline public company is losing money, has tax-loss carryforwards from prior-period losses, or is marginally profitable, the tax savings from current interest payments will not be recognized in the current period; in essence the cost of debt is greater by the loss or deferral of the income tax savings. In Appendix 10A we present a discussion and examples for these formulas:
Hamada formulas
Miles-Ezzell formulas Harris-Pringle formulas
Levered and Unlevered Equity Betas
Exhibit 10.4
125
Summary of Examples
Hamada Miles-Ezzell Harris-Pringle Practitioners’
Practitioners’ method formulas
Fernandez formulas
BU
BL
0.95 0.876 0.87 0.84
1.85 1.92 1.95 2.25
These formulas can be modified for the effects of warrants, employee stock options, and convertible debt.3 CHOOSING AMONG UNLEVERING OR LEVERING FORMULAS Each of these formulas assumes that there are no cost-negative effects to leverage (other than interest expense). That is, they assume that there are no negative impacts on the operations of the business from the amount of debt in the capital structure. We discuss such costs in Chapter 15. Exhibit 10.4 summarizes the beta estimates from applying the various formulas as shown in Exhibits 10A.1–10A.4. The guideline public company in each example had a published (levered) beta of 1.2. The Hamada formula, compared to the other formulas, assumes that more of the total risk was business risk rather than financial risk. That is, the Hamada formula understates the benefit from the tax shield for the example guideline public company with highly rated debt because it assumes that debt is constant. Upon relevering the concluded asset beta of the subject company of 0.90, the practitioners’ method formula results in the greatest increase in total risk due to the increased financial risk of the subject company compared to the guideline public company as it assumes the least benefit from the tax shield. Exhibit 10.5 shows an example of the different relevered betas and discount rates of common equity capital you get when applying Formulas 10A.2, 10A.4, 10A.6, 10A.8, and 10A.10. The choice of unlevering and relevering formula is important. The examples in Exhibit 10.5 indicate the impact on the resulting cost of equity capital estimates based on the underlying risk of realizing the tax shield. The less likely that tax deductions from interest payments will be realized in the periods in which interest is paid, the more risky is the leverage and the greater will be the resulting cost of equity capital. For example, if you are deriving a beta estimate for a subject business using guideline public company beta estimates and one or more of the guideline public companies carry a large amount of debt financing, the unlevered beta estimate will be overestimated if you use the Hamada formula Formula 10A.1. Assume that the higher-leveraged guideline public company likely cannot currently benefit from tax deductions on its interest expense. Its levered (observed) beta estimate equals 2.8 and its debt to capital ratio (at market value weights) equals 75%. Unlevering this beta estimate using Formula 10A.1, the Hamada formula, we get: BU ¼
3
2:8 ¼ 1:0 1 þ ð1 0:40Þð0:75=0:25Þ
Phillip R. Daves and Michael C. Ehrhardt, ‘‘Convertible Securities, Employee Stock Options, and the Cost of Equity,’’ Working paper, June 7, 2004.
126
Cost of Capital
Exhibit 10.5 Example of Applying Formulas for Relevering Beta Assume that for the subject company: Concluded asset beta for subject firm: 1.15 Tax rate: 0.30 Capital structure: 50% debt (market value of debt equity $25 million), 50% equity (market value of equity $25 million) Interest rate on debt: 8% Beta of debt capital: 0.20 Risk-free rate: 6% ERP: 5%
Using the Hamada formula (10A.2) we get: BL ¼ 1:15ð1 þ ð1 0:30Þ0:50=0:50Þ ¼ 1:15ð1 þ 0:70ð1ÞÞ ¼ 1:15ð1:7Þ ¼ 1:955 Discount rate for common equity: ke ¼ 0:06 þ 1:955 0:05 ¼ 15:78%
Using the Miles-Ezzell Formula (10A.4) we get: BL ¼ 1:15 þ
0:50 ð0:30 0:08Þ ð1:15 0:20Þ 1 0:50 ð1 þ 0:08Þ
¼ 1:15 þ 1 0:95 ð1 :022Þ ¼ 2:079 Discount rate for common equity: ke ¼ 0:06 þ 2:079 0:05 ¼ 16:40%
Using the Harris-Pringle Formula (10A.6) we get: BL ¼ 1:15 þ ð0:50=0:50Þð1:15 0:20Þ ¼ 1:15 þ 0:95 ¼ 2:10 Discount rate for common equity: ke ¼ 0:06 þ 2:10 0:05 ¼ 16:50%
Using the practitioners’ method formula (10A.8) we get: BL ¼ 1:15ð1 þ ð0:50=0:50ÞÞ
Discount rate for common equity:
¼ 1:15 þ 2 ¼ 3:15 ke ¼ 0:06 þ 3:15 0:05 ¼ 21:75%
Levered and Unlevered Equity Betas
127
Using the Fernandez formula (10A.10) we get: BL ¼ 1:15 þ ð0:50=0:50Þð1 0:30Þð1:15 0:20Þ ¼ 1:15 þ 1 0:70 0:95 ¼ 1:15 þ 0:665 ¼ 1:815 Discount rate for common equity:
ke ¼ 0:06 þ 1:815 0:05 ¼ 15:08% ke estimated using CAPM without regard to any size premium or company-specific risk premiums.
But if we use Formula 10A.7, the practitioners’ method formula, we get: BU ¼ :25 2:8 ¼ 0:70 Using the Hamada formula, 10A.1 results in an estimated asset beta that is too high because the formula implies that the value of the tax shield on the observed beta is too great. With respect to levered versus unlevered betas, the capital structure of companies often can change significantly over the measurement period of the beta. For example, a beta often is estimated using five years of returns in which, for the majority of time, a company was unleveraged. If at the end of the five-year period the company has become highly leveraged, the levered betas computed would incorporate very little leverage. Yet in unlevering the beta, the analyst would incorporate the current level of high leverage. Thus the unlevered beta could be highly underestimated. The reverse effect applies for a company that reduces its outstanding debt during the beta estimation period. There is no specific method of correcting for this other than accounting for capital structure changes when unlevering the beta. A reasonable approach might be to determine the average leverage for the company during the beta measurement period rather than the leverage at the end of the estimation period. The practitioner must apply judgment in unlevering guideline public company betas and relevering betas for subject businesses. Authors have concluded that of the formulas presented, the Miles-Ezzell and Harris-Pringle formulas are the most consistent if the assumption is that the firm will maintain a constant debt-to-equity ratio based on market value weights.4 The Fernandez formulas are the most consistent if the assumption is that the firm will maintain a fixed book value leverage ratio.5 Exhibit 10.6 outlines our guidance as to the formulas to apply if the assumption is that the firm will maintain a constant debt-to-equity ratio based on market value weights. ADJUSTING ASSET BETA ESTIMATES FOR DIFFERENCES IN OPERATING LEVERAGE Applying the unlevering formula to levered betas of guideline public companies adjusts for the effect of financial risk only and provides an estimate of business risk. (See Chapter 5 for a discussion of business risk.) But the operating leverage of the guideline companies may differ from that of the 4
5
Andre Farber, Roland Gillet, and Ariane Szafarz, ‘‘A General Formula for the WACC,’’ International Journal of Business (Spring 2006): 211–218; Enrique R. Arzac and Lawrence R. Glosten, ‘‘A Reconsideration of Tax Shield Valuation,’’ European Financial Management (2005): 458. Pablo Fernandez, ‘‘Levered and Unlevered Beta,’’ Working paper, April 20, 2006, 1.
128
Cost of Capital
Exhibit 10.6
Guidance for Applying Levering and Relevering Formulas
Formulas for Unlevering Returns of Guideline Public Companies: o Public debt (1) o
Debt not public Credit rated AAA to A-(2)
o
Debt not public Credit rated BBB+ to BBB-(3)
o
Debt not public Credit rated lower than BBB-(4) Formulas for Relevering Betas of Subject Company: Public debt (1)
o o
Debt not public Credit rated AAA to A-
o
Debt not public Credit rated BBB þ to BBB-
o
Debt not public Credit rated lower than BBB-
Formula 10A.3 or Formula 10A.5 Formula 10A.3 Assume Bd ¼ 0 Formula 10A.3 or Assume Bd ¼ 020 Formula 10A.7
Formula 10A.4 or Formula 10A.6 Formula 10A.4 Assume Bd ¼ 0 Formula 10A.4 or 10A.6 Assume Bd ¼ 030 Formula 10A.8
(1) Can calculate beta of debt. (2) AAA is the highest investment-grade S&P debt rating; Aaa is the equivalent Moody’s rating. The A-S&P debt rating is equivalent to the A3 Moody’s rating. (3) BBB- is the lowest investment-grade S&P debt rating; Baa3 is the equivalent Moody’s rating. It indicates adequate-payment capacity. (4) Ratings below the S&P debt rating BBB- and equivalent Moody’s rating Baa3 are speculative grade.
subject division, reporting unit, or closely held company. We can think of fixed operating costs in much the same way as interest expense of debt capital and apply the unlevering formulas to remove the effects of fixed expenses from the asset beta estimates. This ‘‘unlevered’’ asset beta can be thought of as an operating beta. We can then adapt the operating beta for the operating leverage of the subject company. We can use a variation of the Harris-Pringle formula to remove the effects of operating leverage, where the weight in the operating expense structure of fixed costs is equivalent to the weight of debt in the capital structure and the weight in the operating expense structure of variable costs is equivalent to the weight of equity in the capital structure. (Formula 10.3) Bop ¼
Bu ð1 þ F=VÞ
where: Bop ¼ Operating beta or beta with effects of fixed operating expense’s removed F ¼ Fixed operating costs (without regard to costs of financing) V ¼ Variable operating costs Once the operating leverage of the subject business is analyzed, then we can relever the operating beta to arrive at an estimated asset beta for the subject business. Formula 10.4 can be used for estimating the asset beta from the operating beta.
Levered and Unlevered Equity Betas Exhibit 10.7
129
Example of Computing Operating Beta and Recomputing Asset Betas
Example 1 Assume that for guideline public company A: Levered (published) beta: 1.2 Capital structure: 30% debt, 70% equity Operating cost structure: 75% fixed, 25% variable Beta of debt capital: Zero Using Formula 10A.5 we get: Using Formula 10.3 we get:
Bu ¼ 0:84 0:84 ð1 þ 0:75=0:25Þ 0:84 ¼ ð1 þ 3Þ 0:84 ¼ 4 ¼ 0:21
Bop ¼
Assume that you make the previous calculation for all guideline companies, the median operating beta was 0.40, and you believe the riskiness of the subject company is about equal to the median of the guideline companies. The next step is to estimate the asset beta for your subject company. Example 2 Assume for the subject company: Operating beta: 0.40 Operating cost structure: 25% fixed, 75% variable Using Formula 10.4 we get:
0:25 BU ¼ 0:40 þ 1 þ 0:75 ¼ 0:53
You can then relever the asset beta given the appropriate debt to equity structure, tax rate, and beta of debt capital for the subject business.
(Formula 10.4) BU ¼ Bop ð1 þ F=VÞ An example of the adjustment is shown in Exhibit 10.7.
ADJUSTING ASSET BETA ESTIMATES FOR EXCESS CASH AND INVESTMENTS The assets of the guideline public companies used in estimating beta often include excess cash and marketable securities. If you do not take into account the excess cash and marketable securities, you can arrive at an incorrect estimate of the asset beta for the operating business, which often is a guideline public company. This will lead to an incorrect estimate of the beta for the subject company. After unlevering the beta for the guideline public companies, you adjust the unlevered beta estimates for any excess cash or marketable securities held by each guideline public company. This adjustment is
130
Cost of Capital
Exhibit 10.8
Examples of Adjusting Asset Beta Estimates for Excess Cash and Investments
Assume that for guideline public company A: Levered (published) beta: 1.2 Tax rate: 0.40 Capital structure: market value of debt $500, market value of equity $1,000 Interest rate on debt: 10% Beta of debt capital: Zero Excess cash and investments: $300 Using Formula 10A.3 we get: $1;000 1:2 þ $500 0½1 ð0:4 0:1Þ=ð1 þ 0:1Þ $1;000 þ $500½1 ð0:4 0:1Þ=ð1 þ 0:1Þ $1;200 ¼ $1;000 þ $500½0:9721 $1;200 ¼ $1;000 þ $486:05 $1;200 ¼ $1;486:05 ¼ 0:808
BU ¼
Overall asset beta ¼ ½Asset beta for operations ðoperating assets=total assetsÞ
þ ½Asset beta for surplus assets ðsurplus assets=total assetsÞ Since the market value of invested capital equals $1,500 and excess cash and investments equals $300, operating assets equals $1,200. Assuming the excess investments are held in low-risk securities (i.e., shorter-term U.S. government bonds), the beta for surplus cash and investments will generally near zero and the second part of the equation equals zero. For guideline public company A, therefore, we have:
0:808 ¼ ½Asset beta of operations ð$1;200=$1;500Þ þ ½Zero Solving for the asset beta of operations, we have:
Asset beta for operations ¼ 0:808=ð$1;200=$1;500Þ ¼ 1:01 The adjusted asset beta of the operating business is 1.01.
based on the principle that the beta of the overall company is the market-value weighted average of the businesses or assets (including excess cash) comprising the overall firm. An example of the adjustment is shown in Exhibit 10.8.
MODIFIED BETAS: ADJUSTED, SMOOTHED, AND LAGGED Several research studies have provided significant support for two interesting hypotheses regarding betas: 1. Tendency toward industry or market average. Over time, a company’s beta tends toward its industry’s average beta. The higher the standard error in the regression used to calculate the beta, the greater the tendency to move toward the industry average.
Modified Betas: Adjusted, Smoothed, and Lagged
131
2. Lag effect. For all but the largest companies, the prices of individual stocks tend to react in part to movements in the overall market with a lag. The smaller the company, the greater the lag in the price reaction. Recognizing these phenomena, Paul D. Kaplan, himself a participant in some of the relevant studies, introduced new methodologies in the first 1997 Beta Book to reflect this latest research. He called it the ‘‘sum beta’’ because it averaged more than one month’s beta.6 But Morningstar stopped presenting the sum beta starting with the second 2001 edition because they did not know whether anyone was using it. ADJUSTED BETA INCORPORATES INDUSTRY NORM The adjusted beta is computed by a rather sophisticated technique called Vasicek shrinkage.7 The general idea is that betas with the highest statistical standard errors are adjusted toward the industry average more than are betas with lower standard errors. Because high-beta stocks also tend to have the highest standard errors in their betas, they tend to be subject to the most adjustment toward their industry average. This is the adjustment used in the Morningstar Beta Book. This adjusted beta is labeled Morningstar Beta in the Beta Book. SMOOTHED BETA An alternative adjustment that is used by Bloomberg and Value Line adjusts the historical beta to a ‘‘forward’’ estimated beta by averaging the historical beta estimate by two-thirds and the market beta of 1.0 by one-third. This adjustment is based on the assumption that over time, betas gravitate toward the market beta of 1.0. This is a mechanical adjustment and does not indicate that any adjustment to the data used in calculating the historical beta estimate was made. ‘‘SUM BETA’’ INCORPORATES LAG EFFECT A sum beta consists of a multiple regression of a stock’s current month’s excess returns over the 30day T-bill rate on the market’s current month’s excess returns and on the market’s previous month’s excess returns, and then a summing of the coefficients. This helps to capture more fully the lagged effect of comovement in a company’s returns with returns on the market (systematic risk).8 Because of the lag in all but the largest companies’ sensitivity to movements in the overall market, traditional betas tend to understate systematic risk. As the first 2006 edition of the Beta Book explains it, ‘‘Because of non-synchronous price reactions, the traditional betas estimated by ordinary least squares are biased down for all but the largest companies.’’9 Exhibit 10.9 shows the differences between OLS betas and sum betas for the companies comprising the Center for Research in Security Prices (CRSP) deciles. Exhibit 10.10 displays the differences in beta estimates by size of company for a sampling of industries.
6 7
8
9
Former Ibbotson Associates vice president and economist, now vice president, Quantitative Research, Morningstar, Inc. The formula, used in the Morningstar Beta Book, was first suggested by Oldrich A. Vasicek, ‘‘A Note on Using Cross-Sectional Information in Bayesian Estimation of Security Prices,’’ Journal of Finance (1973). The company beta and the peer group (industry) beta are weighted. The greater the statistical confidence in the company beta, the greater the weight on the company beta relative to the peer group beta. The sum beta estimates conform to the expectation that betas are higher for lower capitalization stocks. Research also shows that sum betas are positively related to subsequent realized returns over a long period of time; see Roger G. Ibbotson, Paul D. Kaplan, and James D. Peterson, ‘‘Estimates of Small-Stock Betas Are Much Too Low,’’ Journal of Portfolio Management (Summer 1997): 104–111. Morningstar, Beta Book, 2006 ed. (Chicago: Morningstar, 2006). The second 2001 edition discontinued presenting sum betas.
132
Cost of Capital
Exhibit 10.9
Comparison of OLS Betas and Sum Betas by Company Size
CRSP Market Value-Based Deciles Decile 1 2 3 4 5 6 7 8 9 10 Mid-Cap 3–5 Low-Cap 6–8 Micro-Cap 9–10
60 Months Ending December 2006
Largest
OLS Beta
Sum Beta
Difference
$ 398,907 17,292 7,913 4,221 2,812 1,985 1,343 956 639 321
0.96 0.96 1.09 1.08 1.08 1.15 1.23 1.26 1.29 1.17
0.95 1.11 1.31 1.40 1.39 1.46 1.64 1.75 1.84 1.70
0.01 0.15 0.22 0.32 0.31 0.31 0.41 0.48 0.54 0.53
7,913 1,985 639
1.08 1.21 1.24
1.36 1.59 1.79
0.27 0.39 0.54
}
Not much difference for larger companies
}
Difference is material for smaller companies
Source: Calculated (or derived) based on CRSP1 data, # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago, and Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
The research suggests that this understatement of systematic risk by the traditional beta measurements accounts in part, but certainly not wholly, for the fact that small stocks achieve excess returns over their apparent CAPM required returns (where the market equity risk premium is adjusted for beta). The formula for the sum beta is: ðRn R f ;n Þ ¼ a þ Bn ðRm;n R f ;n Þ þ Bn1 ðRm;n1 R f ;n1 Þ þ e (Formula 10.5) Sum beta ¼ Bn þ Bn1 where: Rn ¼ Return on individual security subject stock in current month Rf,n ¼ Risk-free rate in current month a ¼ Regression constant Bn ¼ Estimated market coefficient based on sensitivity to excess returns on market portfolio in current month Rm ¼ Historical return on market portfolio ðRm;n R f ;n Þ ¼ Excess return on the market portfolio in the current month Bn1 ¼ Estimated lagged market coefficient based on sensitivity to excess returns on market portfolio last month ðRm;n1 R f ;n1 Þ ¼ Excess return on market portfolio last month e ¼ Regression error term The 2006 SBBI Valuation Edition has a table (Table 7–10) titled ‘‘Long-term Return in Excess of CAPM for Decile Portfolios of the NYSE/AMEX/NASDAQ, with Sum Beta,’’10 which is included as Exhibit 13.1 in Chapter 13 in this book. The table shows that the returns in excess of CAPM are much lower than for the OLS betas, reflecting the superiority of sum betas over OLS betas. Graph 7–5 in the 2006 SBBI Valuation Edition on the same page shows how much closer the portfolios track the 10
SBBI Valuation Edition 2006 Yearbook (Chicago: Morningstar, 2006), 143.
Modified Betas: Adjusted, Smoothed, and Lagged Exhibit 10.10
133
Comparison of OLS Betas and Sum Betas for Different Industries
Data as of December 2006 Median Count
OLS Beta
Sum Beta
Healthcare (SIC 80) All Companies Over $1 Billion* Under $200 Million*
117 23 48
0.69 0.30 0.74
1.19 0.70 1.29
Publishing (SIC 27) All Companies Over $1 Billion Under $200 Million
82 20 58
0.74 0.62 0.71
0.91 0.62 0.90
Petroleum & Natural Gas (SIC 1311) All Companies 84 Over $1 Billion 35 Under $200 Million 15
0.70 0.61 1.03
0.80 0.74 0.78
Computer Software (SIC 7372) All Companies Over $1 Billion Under $200 Million
360 47 217
1.85 1.87 1.66
2.32 1.99 2.40
Auto Parts (SIC 3714) All Companies Over $1 Billion Under $200 Million
60 12 26
0.90 1.02 0.55
1.40 1.35 1.18
Pharmaceutical (SIC 2834) All Companies Over $1 Billion Under $200 Million
278 54 119
1.27 0.85 1.31
1.68 0.94 1.87
*Market value of equity as of December, 2006.
Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
Security Market Line, except for the tenth decile.11 If sum betas are used, the size effect (realized returns in excess of those predicted by CAPM) is greatly reduced. Sum betas for individual stocks can be calculated using Microsoft Excel and 61 months of return data, which is available from several sources, such as Compustat. Thus, even though the sum betas have been removed from the Beta Book, some analysts prefer to calculate their own sum betas for a peer group of public companies (which they use as a proxy for the beta of their subject private company in the context of CAPM), and thus make a smaller adjustment for the size effect. The theory is that this corrects for the larger size effect that is principally due to a misspecification of beta when using traditional OLS betas for the smaller companies. Exhibit 10.11 shows the sum beta estimate for J.B. Hunt. The sum beta estimate equals 1.979 (21.8% over the OLS beta estimate). While some may consider J.B. Hunt a large company, its market value of equity ($3,482 million) plus debt capital ($124 million) only ranks the company as a ‘‘midcap’’ firm (as of December 31, 2005). For smaller firms the difference can be even greater. Exhibit 10.12 shows the OLS and sum beta calculation for Martin Transport, Ltd. It had $393 million (as of December 31, 2005) market value of 11
Ibid.
134 Exhibit 10.11
Cost of Capital Example of Beta Estimation for J.B. Hunt Transport Services, Inc.
Ticker Symbol: JBHT SIC 4213: Trucking, Except Local Date: December 2005 Company: J.B. Hunt Transport Services, Inc., together with its subsidiaries, provides full-load freight transportation services in the United States, Canada, and Mexico. Calculate OLS Beta Calculate Sum Beta Number of Months of Data Regression Coefficients R-Squared Intercept Market Coefficient Market Lag Coefficient Beta T-Statistic Summary Statistics Average Return Standard Deviation
1.62 1.98 60 OLS 0.30 3.49%
1.624 4.95 Company 3.716% 12.742%
Correlation Matrix Company Market Market Lag
Company 1.000 0.545 0.162
Sum Beta 0.31 3.44% 1.599 0.380 1.979 Market 0.138% 4.275%
Market Lag 0.145% 4.275%
Market
Market Lag
1.000 0.065
1.00
Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
Exhibit 10.12
Example of Beta Estimation for Marten Transport. Ltd.
Ticker Symbol: MRT SIC 4213: Trucking, Except Local Date: December 2005 Company: Marten Transport, Ltd., operates as a temperature-sensitive truckload carrier in the United States and Canada. Calculated OLS Beta Calculated Sum Beta Number of Months of Data Regression Coefficients R-Squared Intercept Market Market Lag Beta T-Statistic Summary Statistics Average Return Standard Deviation Correlation Matrix Company Market Market Lag
0.23 1.00 60 OLS 0.01 3.13% 0.230 0.230 0.89 Company 3.161% 8.991% Company 1.000 0.109 0.395
Sum Beta 0.16 3.02% 0.177 0.819 0.996 Market 0.138% 4.275% Market 1.000 0.065
Market Lag 0.145% 4.275% Market Lag
1.00
Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
Peer Group Equity Beta
135
equity plus $50 million debt capital. Its OLS beta estimate is equal to 0.230 and its sum beta estimate is equal to 0.996 (a 333% difference). Appendix 10.B provides an example of estimating beta using the OLS beta and sum beta methods.
‘‘FULL INFORMATION’’ EQUITY BETA Betas for individual companies can be unreliable. There may be many divisions of the largest companies in the industry, making ‘‘pure play’’ (e.g., 75% of revenue from single Standard Industrial Classification [SIC] code) beta estimation difficult. Morningstar’s Beta Book includes industry betas calculated using full-information methodology (the full-information beta is seen as RIi in Appendix 10B and Chapter 19).12 After identifying all companies with segment sales in an industry, Morningstar calculates the beta. They then run a multiple regression with betas as the dependent variables (applying a weight to each beta based on its relative market capitalization to the industry market capitalization) and sales of the segments of each of the companies in the industry as the independent variable. That is, they are measuring the relative impact on the betas of companies in an industry based on the relative sales each company has within the industry. Measuring the impact on betas using segment sales data may present a problem in that the market weights profits, not sales. This procedure can overweight the relative importance of business segments with high sales and low profits. Appendix 10.B provides an example of estimating beta using the full-information methodology.
PEER GROUP EQUITY BETA Morningstar’s Beta Book also includes a peer group beta by industry. The peer group beta is calculated using the full-information betas by industry and weighting them for the subject company based on the sales by segments of the subject company. Exhibit 10.13 shows an example of calculating a peer group beta. Exhibit 10.14 is an excerpt from Morningstar’s second 2006 edition Beta Book (which is published twice annually). Note that it includes (1) traditional least squares regression beta (labeled raw beta, both levered and unlevered); (2) peer group beta; (3) adjusted beta (labeled Morningstar Beta, both levered and unlevered); and (4) the Fama-French 3-factor models. Chapter 19 on using Morningstar data shows an entire sample page from the 2006 edition Beta Book.
Exhibit 10.13
Example of Calculating the Peer Group Beta
Segment reporting lists ‘‘sales’’ in three different two-digit SIC codes.
SIC Code 1221 6794 4953
12
Industry Composite Beta
Company Sales in Industry ($ millions)
% of Company Sales in Industry
Sales-Weighted Beta Component
1.10 1.16 1.56
113.80 1.30 36.10
75.30% 0.84% 23.86%
.83 .01 .37
Totals
151.20
100.00%
1.21
Paul D. Kaplan and James D. Peterson, ‘‘Full Information Betas,’’ Financial Management (Summer 1998): 85–93.
136 Exhibit 10.14
Cost of Capital Excerpt from Second 2006 Edition Beta Book CAPM: Ordinary Least Squares Fama-French Three-Factor Model Levered Raw
Unlevered Pr Grp Ibbotson Raw Ibbotson FF
FF SMB SMB HML HML
FF
Beta t-Stat R-Sqr Beta APPA AP PHARMA INC 1.13 1.94 0.06 0.67
Beta 1.04
Beta 1.13
Beta 1.04
Beta t-Stat Prem t-Stat Prem t-Stat R-Sqr 1.01 1.64 3.02 3.65 2.24 2.46 0.08
APAT APA ENTERPRISES 2.46 3.98 0.21 0.63 INC
2.07
2.26
1.88
1.73 3.09 11.89 15.72 0.62 0.75 0.44
APAC APAC CUSTOMER 0.72 1.19 0.02 1.67 SERVICES INC
0.92
0.72
0.92
0.35 0.56 1.72 2.04 8.54
APA APACHE CORP
0.18 0.71 0.01 0.63
0.20
0.16
0.18
0.15 0.57 1.65 4.62 2.39 6.11 0.06
AIV APARTMENT INVT & MGMT-CLA
0.34 1.94 0.06 0.40
0.34
0.20
0.12
0.28 1.49 1.04 4.16 0.07 0.27 0.09
9.28 0.11
Source: Ibbotson Associates’ Beta Book, First 2006 Edition. Copyright # 2006 Ibbotson Associates, Used with permission. All rights reserved. (Morningstar, Inc. acquired Ibbotson in 2006.) To purchase copies of The Beta Book, or for more information on other Morningstar publications, please visit Global.Morningstar.com/DataPublications. Calculated (or derived) based on CRSP1 data, # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago.
FUNDAMENTAL EQUITY BETA As an alternative to using betas estimated from market information, you can estimate a fundamental beta, the sensitivity of subject company’s operating characteristics to changes in operating characteristics of the industry or market (segment or whole). Various studies have measured fundamental betas for publicly traded companies.13 For example, you can calculate a fundamental beta for a division, reporting unit, or closely held company by regressing quarterly changes in subject company operating profit to quarterly changes in the S&P 500 operating profit or to the appropriate S&P industry operating profit. Using operating profit for both the subject company and the S&P 500 should yield beta estimate equivalent to unleveled asset betas. Exhibit 10.15 displays fundamental betas for the sectors of the S&P 500 Index. The fundamental beta estimates can be useful during periods of large downward stock price adjustments when reliable beta estimates are difficult to derive. A source of fundamental beta estimates is Barra (www.mscibarra.com). Barra ‘‘predicted’’ betas are, in essence, historical OLS betas (calculated by regressing the log of 60 months of excess returns to log of excess returns of S&P 500) adjusted to be forward estimates. Barra actively cleans stock return data to ensure that stock splits, time gaps between trades, and other price inconsistencies are correctly accounted for. But historical betas do not recognize fundamental changes in a company’s operations during the prior 60 months and may be influenced by specific events that are unlikely to be repeated. Barra predicted betas are derived from a fundamental risk model. Risk factors are reestimated monthly and reflect changes in companies’ underlying risk structures in a timely manner. Barra uses 13
See, for example, Carolyn M. Callahan and Roseanne M. Mohr, ‘‘The Determinants of Systematic Risk: A Synthesis,’’ Financial Review (May 1989); Kee H. Chung, ‘‘The Impact of Demand Volatility and Leverage on the Systematic Risk of Common Stocks,’’ Journal of Business Finance and Accounting (1989); Aswath Damodaran, Investment Valuation, 2nd ed. (New York: John Wiley & Sons, 2002), 58–59.
Fundamental Equity Beta Exhibit 10.15
137
Fundamental Betas and OLS Betas by Sector Fundamental Beta
Consumer Discretionary Consumer Staples Energy Financials Healthcare Industrials Information Technology Materials Telecom Services Utilities
2.3 0.3 0.6 0.4 0.1 0.5 1.6* 0.8 2.2 1.5
Betas shown were calculated based on the relative quarterly change for the given sector compared to the change in the S&P 500 as a whole. The quarterly data used were from the time period from March 31, 1997 to December 31, 2006. The fundamental betas were calculated based on the operating earnings for each sector and the operating earnings of the S&P 500 as a whole. These are unlevered asset betas. *Excludes fourth quarter of 2001 with negative operating earnings considered abnormal.
Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
company risk factors (company characteristics) plus industry risk exposures in developing their predicted betas. These risk factors are: Company Risk Factors Variability in markets—predictor of volatility of stock based on behavior of stock’s options; measures stocks’ overall volatility and response to market
Success compared to historical earnings growth information (i.e., analysts’ earnings estimates) ‘‘Size’’ based on log of market capitalization and log of total assets
Trading activity and number of analysts following stock Growth: Historical and expected future
Earnings-to-price ratio
Book-to-price ratio Earnings variability
Financial leverage Foreign income: Sensitivity to currency exchange rate changes
Labor intensity: Labor costs versus capital costs
Dividend yield ‘‘Low-cap’’ characteristics (extension of size model based on market capitalization)
Industry Risk Exposure Company categorized into up to 6 of 55 industry groups
Historical stock returns correlated with company risk factors, and these relationships are used to estimate company betas conditional on company characteristics Industry seems to be a dominant factor
138
Cost of Capital
Exhibit 10.16
Comparison of Barra Historical (OLS) Predicted Betas to Sum Betas Market Weighted Averages
Equal Weighted Averages
Medians
Largest Company Barra Barra Sum Barra Barra Sum Barra Barra Sum Decile Mkt Cap Count Historical Predicted Beta Historical Predicted Beta Historical Predicted Beta 1 2 3 4 5 6 7 8 9 10
$398,907 17,292 7,913 4,215 2,812 1,975 1,343 953 639 321
176 189 197 198 203 275 487 331 662 1,696
0.99 1.14 1.16 1.11 1.20 1.22 1.19 1.34 1.27 1.27
0.98 1.10 1.11 1.14 1.16 1.17 1.15 1.18 1.14 1.10
0.98 1.29 1.38 1.37 1.46 1.47 1.59 1.75 1.71 1.76
0.99 1.14 1.15 1.12 1.21 1.21 1.19 1.33 1.28 1.21
1.01 1.10 1.10 1.13 1.16 1.17 1.15 1.18 1.14 1.12
1.04 1.27 1.39 1.37 1.46 1.46 1.59 1.75 1.72 1.72
0.84 0.93 0.93 0.94 1.02 1.05 0.95 1.05 1.02 0.95
0.97 1.06 1.07 1.11 1.14 1.17 1.11 1.14 1.13 1.09
0.86 1.07 1.11 1.10 1.18 1.24 1.31 1.39 1.46 1.36
Source: Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
The predicted betas are based on Barra’s proprietary model. How do Barra predicted betas fare with small companies? Barra tends to report small predicted betas for small companies. Exhibit 10.16 shows a comparison of market capitalization data as of September 30, 2006, and Barra predicted betas as of December 2006 to historical beta estimates. We believe that since Barra bases its predicted beta estimate on OLS beta estimates, it may miss the lag effect on returns for smaller-company stocks captured by the sum beta. This is likely due to Barra’s focus on larger-company stocks.
EQUITY BETA ESTIMATION RESEARCH There continues to be much research on improving beta estimation techniques. For example, in one study the authors found that OLS beta estimates are subject to misestimation due to the small fraction of exceptionally large or small returns, called outliers, that are not predictable.14 They found that outliers occur more frequently with small companies. They recommend using weighted least squares estimation where outliers are discarded based on their impact on residual (error in the fit). Using a computational algorithm in a statistical modeling system S-Plus (MathSoft, 1999), they test the difference in predicting future or true beta. The authors found that when data do not contain influential outliers, OLS beta is the most precise estimate of true beta. But when influential outliers are present, OLS beta is an exceedingly poor estimate of true beta and the beta estimate is improved by removing outliers from the sample period. In another study, the authors extract ‘‘forward-looking’’ beta estimates from option pricing data on the Dow Jones 30.15 They use option models to estimate the implied volatility of the stocks and the covariance of the individual stocks with the market. They find that forward-looking betas extracted from data on liquid options often outperform historical market beta in following periods. They find that 180 days of historical excess returns provides the ‘‘best’’ estimate of forward-looking betas.
14
15
R.D. Martin and T.T. Simin, ‘‘Outlier-Resistant Estimates of Beta,’’ Financial Analysts Journal (September/October 2003): 56–69. Peter F. Christoffersen, Kris Jacobs, and Gregory Vainberg, ‘‘Forward-Looking Betas,’’ Working paper, February 27, 2007.
Estimation of Debt Beta
139
ESTIMATION OF DEBT BETA The risk of debt capital can be measured by the beta of the debt capital (in cases where the debt capital is publicly traded). The Bd can be measured in a manner identical to measuring the BL of equity. For a public company, a regression of returns provides an estimate of Bd. That estimate indicates how the market views the riskiness of the debt capital as the stock market changes (or a proxy for the economy). That risk is a function of the amount of debt capital in the capital structure, the variability of earnings before interest, taxes, depreciation, and amortization (EBITDA), the level of and variability of EBITDA/Sales, and so on. These are fundamental risks that the interest (and principal) will or can be paid when due. Research has found that long-run betas on debt capital have been in the range of 0.30 to 0.40.16 Betas of debt generally correlate with credit ratings. Exhibit 10.17 shows an example of the relationship between bond ratings and estimated betas of debt. The general formula for estimating the beta for debt (e.g., traded bonds) is:17 (Formula 10.6) Rd ¼ a þ Bd ðRm R f ð1 tÞÞ þ e
Exhibit 10.17 [A] Rating AAA AA A+ A A BBB BB B+ B B CCC
Estimated Beta of Debt Based on Credit Ratings [B] Default Spread (Over RFR) 0.53% 0.73 0.81 0.88 0.95 1.36 2.80 3.15 3.95 4.55 9.90
[C] Cost of Debt
[D] Beta of Debt
5.44% 5.64 5.72 5.79 5.86 6.27 7.71 8.06 8.86 9.46 14.81
0.05 0.07 0.08 0.09 0.10 0.14 0.28 0.32 0.40 0.46 0.99
½C ¼ ½B þ R f of 4.91% To estimate the beta of debt, we used the default spread at each level of debt, and assumed that half the risk is market risk ½D ¼ ð½B=5:0%Þ 0:5; where ERP ¼ 5:0% Note: This is an update of beta estimates that appear in Aswath Damodaran, Investment Valuation: Tools and Techniques for Determining the Value of Any Asset, 2nd ed. (Hoboken, NJ: John Wiley & Sons, 2002), 413. Source: BondsOnline; FT Interactive Data; Bloomberg; calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
16
17
See, for example, Tim Koller, Marc Goedhart, and David Wessels, Valuation: Measuring and Managing the Value of Companies, 4th ed. (Hoboken, NJ: John Wiley & Sons, 2005), 32. Simon Benninga, Financial Modeling, 2nd ed. (Cambridge: MIT Press, 2000), 414.
140
Cost of Capital
where: Rd ¼ Rate of return on subject debt (e.g., bond) capital a ¼ Regression constant Bd ¼ Estimated beta for debt capital based on historical data Rm ¼ Historical rate of return on the ‘‘market’’ t ¼ Marginal corporate tax rate e ¼ Regression error term Research has shown that longer-maturity bonds appear to have greater market risk and often have betas more closely resembling those of small-capitalization stocks compared to shorter-maturity bonds.18
OTHER BETA CONSIDERATIONS ‘‘Top-down’’ beta estimate for a publicly traded company comes from a regression of excess returns of the company’s stock to the excess returns of a market portfolio. Alternatively, a ‘‘bottom-up’’ beta can be estimated by:
Identifying the businesses in which the company operates
Identifying the unlevered (asset) betas of other companies in these businesses
Taking a weighted average of these unlevered betas, where the weights are based on the relative operating income Re-levering using the subject company’s debt/equity ratio
Bottom-up beta will give you a better estimate of the true beta when:
The standard error of the beta from the regression is high and the top-down beta for the subject company is very different from the average of the bottom-up betas for the businesses. Averaging across regression betas reduces standard error. Standard error pffiffiffi of average beta ¼ average standard deviation of individual company beta estimates= n. The subject company has reorganized or restructured itself substantially during the period of the regression.
And of course, you need to use bottom-up beta when the subject company is a division, reporting unit, or closely held business. The beta of a company after a merger is the market-value weighted average of the betas of the companies involved in the merger. The beta of an overall company is the market-value weighted average of the businesses (i.e., divisions and/or projects) or assets (operating assets and excess cash and investments) comprising the overall firm.
18
Tao-Hsien Dolly King and Kenneth Khang, ‘‘On the Importance of Systematic Risk Factors in Explaining the Cross-Section of Corporate Bond Yield Spreads,’’ Journal of Banking & Finance (2005): 3149.
Summary
141
SUMMARY An equity beta is a measure of the sensitivity of the movement in returns on a particular stock to movements in returns on some measure of the market. As such, beta measures market or systematic risk. In cost of capital estimation, beta is used as a modifier to the general equity risk premium in using the Capital Asset Pricing Model. There are many variations on the way betas are estimated by different sources of published betas. Thus, a beta for a stock estimated by one source may be very different from a beta estimated for the same stock by another source. Modern research is attempting to improve betas. Two such improvements implemented are the adjusted beta, which blends the individual stock beta with the industry beta, and the lagged beta, also called the sum beta, which blends the beta for the stock and the market during a concurrent time period with a beta regressed on the market’s previous period returns. These two adjustments both help to reduce outliers, thus perhaps making the betas based on observed historical data a little more representative of future expectations. The size premium in excess of CAPM is much lower using sum betas. However, betas are not very stable over time, especially for individual securities. Here are some recommendations from the authors. First we recommend graphing the returns over the sample or look-back period for any guideline public company you will be using in developing a beta estimate (time along the x-axis, returns or excess return along the y-axis). Similarly, graph the returns for the S&P 500 Index. You can then examine any changes in the relative pattern of returns over time. This will alert you to investigate if an underlying change has occurred in the public company (e.g., a merger, change in relative expectations about the company, etc.). Then you should investigate any changes. If the underlying fundamentals of the company have changed, that will indicate that a more recent period should be used in developing a beta estimate. This will often require calculating your own beta estimate. We recommend using sum beta calculations (whether you are using a pure-play or full-information beta methodology) for smaller public companies. We calculate OLS and sum beta estimates for all comparable public companies we are investigating for use in developing a better estimate. If the estimates differ, we gravitate to using the sum beta estimate. We recommend initially unlevering all the calculated beta estimates for the guideline public companies. Differences in leverage (both financial and operating leverage) are important differences in risk. For example, empirical evidence indicates that stock return volatility generally rises when stock prices decrease and stock return volatility generally falls when stock prices rise. One study found that approximately 85% of this change in stock return volatility is due to financial leverage and 15% is due to operating leverage.19 Care needs to be exercised in choosing the formula for unlevering betas. Generally use either the Miles-Ezzell, Harris-Pringle, or Fernandez formulas for unlevering public guideline company betas. The widely used Hamada formulas are generally inconsistent with capital structure theory and practice. The practitioners’ method formulas should be used only for companies with low debt ratings. Examine the differences in operating leverage (ratio of fixed operating costs to variable operating costs) among the guideline public companies and compare to the subject company. If significantly different, calculate the operating betas for each and adjust the unlevered beta for the subject company accordingly. Rank the companies by size characteristics (e.g., sales) other than market capitalization. Generally, do large companies have lower unlevered betas than smaller companies? If the unlevered betas for the smallest companies (even derived from sum beta methodology) are greater than the unlevered 19
Hazem Daouk and David Ng, ‘‘Is Unlevered Firm Volatility Asymmetric?’’ AFA 2007 Chicago meetings, January 11, 2007.
142
Cost of Capital
betas for larger companies, examine the reasons why the business risk of these smallest companies appears to be less than that of larger companies. They may be thinly traded, and conventional beta estimation methods may not be providing reliable beta estimates. Estimate the appropriate unlevered beta for the subject business (company, division, reporting unit, function within the firm) and relever that estimate based on the characteristics of the subject business (e.g., using its debt capacity, etc.). Finally, compare your estimated relevered beta with industry betas (e.g., Morningstar Cost of Capital Yearbook). Are differences sensible, given the differences between the subject business and the typical company comprising the industry statistics? Betas are an important element in estimating the cost of equity capital. The process of estimating beta requires considerable diligence, effort, and judgment on the part of the analyst.
Appendix 10A
Formulas and Examples for Unlevering and Levering Equity Betas
Hamada Formulas Miles-Ezzell Formulas Harris-Pringle Formulas Practitioners’ Method Formulas Capital Structure Weights Fernandez Formulas
HAMADA FORMULAS The Hamada formulas are commonly cited formulas for unlevering and levering equity beta estimates.1 The Hamada formula for unlevering beta is shown as Formula 10A.1. This is the formula used by Morningstar to unlever betas in its Beta Book. (Formula 10A.1) Bu ¼
BL 1 þ ð1 tÞWd =We
where: Bu ¼ Beta unlevered BL ¼ Beta levered t ¼ Tax rate for the company Wd ¼ Percent debt in the capital structure We ¼ Percent equity in the capital structure The companion Hamada formula for relevering beta is Formula 10A.2. (Formula 10A.2) BL ¼ Bu ð1 þ ð1 tÞWd =We Þ where the definitions of the variables are the same as in Formula 10A.1. 1
Robert S. Hamada, ‘‘The Effect of the Firm’s Capital Structure on the Systematic Risk of Common Stocks,’’ Journal of Finance (May 1972): 435–452.
143
144
Cost of Capital
The Hamada formulas are consistent with the theory that:
The discount rate used to calculate the tax shield equals the cost of debt capital (i.e., the tax shield has the same risk as debt).
Debt capital has negligible risk that interest payments and principal repayments will not be made when owed, which implies that tax deductions on the interest expense will be realized in the period in which the interest is paid (i.e., beta of debt capital equals zero). Value of the tax shield is proportionate to the value of the market value of debt capital (i.e., value of tax shield ¼ t Wd).
But the Hamada formulas are based on Modigliani and Miller’s formulation of the tax shield values for constant debt. The formulas are not correct if the assumption is that debt capital remains at a constant percentage of equity capital (equivalent to debt increasing in proportion to net cash flow to the firm in every period).2 The formulas are equivalent to assuming a steadily decreasing ratio of debt to equity value if the company’s cash flows are increasing. The formulas are often wrongly assumed to hold in general. An example of applying the Hamada formula is shown in Exhibit 10A.1.
MILES-EZZELL FORMULAS The Miles-Ezzell formulas are alternative formulas for unlevering and levering equity betas which assume that there is risk in the timely realization of the tax deductions for interest payments on debt capital.3 The Miles-Ezzell formula for unlevering beta is shown in Formula 10A.3. (Formula 10A.3) BU ¼
Me BL þ Md Bd ½1 ðt kdð ptÞ Þ=ð1 þ kdð ptÞ Þ Me þ Md ½1 ðt kdð ptÞ Þ=ð1 þ kdð ptÞ Þ
where: BU ¼ Unlevered beta of equity capital BL ¼ Levered beta of equity capital Me ¼ Market value of equity capital (stock) Md ¼ Market value of debt capital Bd ¼ Beta of debt capital t ¼ Tax rate for the company kd(pt) ¼ Cost of debt prior to tax affect We discuss the beta of debt capital in Chapter 10. The companion Miles-Ezzel formula for relevering beta is Formula 10A.4. (Formula 10A.4) " # ðt kdð ptÞ Þ Wd B L ¼ BU þ ðBU Bd Þ 1 We ð1 þ kdð ptÞ Þ where the definitions of the variables are the same as in Formulas 10A.1 and 10A.3. 2
3
Enrique R. Arzac and Lawrence R. Glosten, ‘‘A Reconsideration of Tax Shield Valuation,’’ European Financial Management (2005): 453–461. James A. Miles and John R. Ezzell, ‘‘The Weighted Average Cost of Capital, Perfect Capital Markets and Project Life: A Clarification,’’ Journal of Financial and Quantitative Analysis (1980): 719–730
Miles-Ezzell Formulas
Exhibit 10A.1
145
Computing Unlevered and Relevered Betas Using Hamada Formulas
Example 1 Assume that for guideline public company A: Levered (published) beta: 1.2 Tax rate: 0.40 Capital structure: 30% debt, 70% equity Using Formula 10A.1 we get: Bu ¼ ¼
1:2 1 þ ð1 0:40Þ0:30=0:70 1:2 1 þ 0:60ð0:429Þ
1:2 1:257 ¼ 0:95 ¼
Assume you made the previous calculation for all the guideline public companies, the median unlevered beta was 0.90, and you believe the riskiness of your subject company, on an unlevered basis, is about equal to the median for the guideline public companies. The next step is to relever the beta for your subject company based on its tax rate and one or more assumed capital structures. Example 2 Assume for the subject company: Unlevered beta: 0.90 Tax rate: 0.30 Capital structure: 60% debt, 40% equity Using Formula 10A.2 we get: BL ¼ 0:90ð1 þ ð1 0:30Þ0:60=0:40Þ ¼ 0:90ð1 þ 0:70ð1:5ÞÞ ¼ 0:90ð2:05Þ ¼ 1:85 Source: Shannon P. Pratt, Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed. (New York: McGraw-Hill, 2007), Chapter 9. All rights reserved. Used with permission.
The Miles-Ezzell formulas are consistent with the theory that:
The discount rate used to calculate the tax shield equals the cost of debt capital (i.e., the tax shield has the same risk as debt) during the first year and the discount rate used to calculate the tax shield thereafter equals the cost of equity calculated using the asset beta of the firm (i.e., the risk of the tax shield after the first year is comparable to the risk of the operating cash flows). That is, the risk of realizing the tax deductions is greater than assumed in the Hamada formulas.
Debt capital bears the risk of variability of operating net cash flow in that interest payments and principal repayments may not be made when owed, which implies that tax deductions on the interest expense may not be realized in the period in which the interest is paid (i.e., beta of debt capital may be greater than zero).
146
Cost of Capital
Exhibit 10A.2 Computing Unlevered and Relevered Betas Using Miles-Ezzell Formulas Example 1 Assume that for guideline public company A: Levered (published) beta: 1.2 Tax rate: 0.40 Capital structure: 30% debt (market value of $15 million), 70% equity (market value of $35 million) Interest rate on debt: 7.5% Beta of debt capital: 0.10 Using Formula 10A.3 we get: BU ¼ ¼
$35m 1:2 þ $15m 0:10½1 ð0:4 0:075Þ=ð1 þ 0:075Þ $35m þ $15m½1 ð0:4 0:075Þ=ð1 þ 0:075Þ $42m þ $15m 0:10½0:972 $35m þ $15m½1 0:0279
$42m þ $1:458m $35m þ $14:5815 $43:458m ¼ $49:5815m ¼
¼ 0:876 Assume that you make the previous calculations for all guideline companies, the median unlevered beta was 0.90, and you believe the riskiness of your subject company, on an unlevered basis, is about equal to the median of the guideline companies. The next step is to relever the beta for your subject company tax rate and one or more assumed capital structures. Example 2 Assume for the subject company: Unlevered beta: 0.90 Tax rate: 0.30 Capital structure: 60% debt, 40% equity Interest rate on debt: 9.0% Beta of debt capital: 0.20 Using Formula 10A.4 we get: BL ¼ 0:90 þ
0:60 ð0:40 0:090Þ ð0:90 0:20Þ 1 0:40 ð1 þ 0:090Þ
¼ 0:90 þ 1:5 0:70 ð1 :033Þ ¼ 1:92
Market value of debt capital remains at a constant percentage of equity capital, which is equivalent to saying that debt increases in proportion to the net cash flow of the firm (net cash flow to invested capital) in every period.
An example of applying the Miles-Ezzell formulas is shown in Exhibit 10A.2. We begin with Example 1, where Bd, the beta of debt capital, equals 0.10 (i.e., the debt is highly rated and there is little risk to the debt capital that interest and principal will not be repaid when due for the guideline public company). But there is risk to the company that tax deductions on interest expense will not result in tax savings in the same period as the interest is paid in future years.
Harris-Pringle Formulas
147
In Example 2 we relever the beta, taking into account that the risk of debt capital is not negligible because the ratio of debt capital to equity capital is greater than that of the guideline public company in Example 1. We assume beta of debt capital Bd ¼ 0.20 (i.e., the debt is lower-rated than the debt of the guideline public company in Example 1).
HARRIS-PRINGLE FORMULAS The Harris-Pringle formulas are alternative formulas for unlevering and levering equity beta estimates that assume the tax shield is even more risky.4 Formula 10A.5 shows the Harris-Pringle formula for unlevering beta. (Formula 10A.5) Wd B L þ Bd We BU ¼ Wd 1þ We where the definitions of the variables are the same as in Formula 10A.6. The companion Harris-Pringle formula for relevering beta is Formula 10A.6. (Formula 10A.6) Wd BL ¼ BU þ ðBU Bd Þ We where the definitions of the variables are the same as in Formulas 10A.1 and 10A.3. The Harris-Pringle formulas are consistent with the theory that:
The discount rate used to calculate the tax shield equals the cost of equity calculated using the asset beta of the firm (i.e., the risk of the tax shield is comparable to the risk of the operating cash flows). That is, the risk of realizing the tax deductions is greater than assumed in the Hamada and Miles-Ezzell formulas. Debt capital bears the risk of variability of operating net cash flow in that interest payments and principal repayments may not be made when owed, which implies that tax deductions on the interest expense may not be realized in the period in which the interest is paid (i.e., beta of debt capital may be greater than zero) Market value of debt capital remains at a constant percentage of equity capital, which is equivalent to saying that debt increases in proportion to the net cash flow of the firm (net cash flow to invested capital) in every period.
An example of applying the Harris-Pringle formulas is shown in Exhibit 10A.3. We begin with Example 1, where Bd, the beta of debt capital, equals 0.10 (i.e., the debt is highly rated and there is little risk that interest and principal will not be repaid when due for the guideline public company). But there is risk to the company that tax deductions on interest expense will not result in tax savings in the same period as the interest is paid in future years. In Example 2, we relever the beta, taking into account that the risk of debt capital is not negligible because the ratio of debt capital to equity capital is greater than that of the guideline public company in Example 1. The debt is lower rated than the debt of the guideline public company in Example 1. 4
R. S. Harris and J. J. Pringle, ‘‘Risk-Adjusted Discount Rates—Extensions from the Average Risk Case,’’ Journal of Financial Research (Fall 1985): 237–244.
148
Cost of Capital
Exhibit 10A.3 Computing Unlevered and Relevered Betas Using Harris-Pringle Formulas Example 1 Assume that for guideline public company A: Levered (published) beta: 1.2 Tax rate: 0.40 Capital structure: 30% debt (market value of $15 million), 70% equity (market value of $35 million) Beta of debt capital: 0.10 Using Formula 10A.5 we get:
0:30 1:2 þ 0:10 0:70 BU ¼ 0:30 1þ 0:70 ¼ 0:87
Assume that you make the previous calculations for all guideline companies, the median unlevered beta was 0.90, and you believe the riskiness of your subject company, on an unlevered basis, is about equal to the median of the guideline companies. The next step is to relever the beta for your subject company tax rate and one or more assumed capital structures. Example 2 Assume for the subject company: Unlevered beta: 0.90 Tax rate: 0.30 Capital structure: 60% debt, 40% equity Beta of debt capital: 0.20 Using Formula 10A.6 we get: BL ¼ 0:90 þ
0:60 ð0:90 0:20Þ 0:40
¼ 1:95
PRACTITIONERS’ METHOD An alternative formulation often used by consultants and investment banks is referred to as the practitioners’ method. In this formula, no certainty for the tax deduction of interest payments is assumed. It has also been called the conventional relationship.5 The practitioners’ method formula for unlevering beta is shown in Formula 10A.7 (Formula 10A.7) BL Bu ¼ Wd 1þ We where the definitions of the variables are the same as in Formula 10A.1. The companion practitioners’ method formula for relevering beta is Formula 10A.8. 5
Tim Ogier, John Rugman, and Lucinda Spicer, The Real Cost of Capital (New York: Financial Times Prentice-Hall, 2004), 49.
Practitioners’ Method
149
(Formula 10A.8)
BL ¼ BU
Wd 1þ We
where the definitions of the variables are the same as in Formula 10A.1. The practitioners’ method formulas are consistent with the theory that:
The discount rate used to calculate the tax shield equals the cost of equity calculated using the asset beta of the firm (i.e., the risk of the tax shield is comparable to the risk of the operating cash flows). That is, the risk of realizing the tax deductions is greater than assumed in the Hamada and Miles-Ezzell. Market value of debt capital remains at a constant percentage of equity capital, which is equivalent to saying that debt increases in proportion to the net cash flow of the firm (net cash flow to invested capital) in every period.
This formula assumes the least benefit from tax deductions on interest payments and may be looked on as indirectly introducing costs of leverage beyond interest expense. An example of applying the practitioners’ method formulas is shown in Exhibit 10A.4. In Example 2, we relever the beta.
Exhibit 10A.4
Computing Unlevered and Relevered Betas Using Practitioners’ Method Formulas
Example 1 Assume that for guideline public company A: Levered (published) beta: 1.2 Capital structure: 30% debt (market value of $15 million), 70% equity (market value of $35 million) Using Formula 10A.7 we get: 1:2 BU ¼ 0:30 1þ 0:70 ¼ 0:84 Assume that you make the previous calculations for all guideline companies, the median unlevered beta was 0.90, and you believe the riskiness of your subject company, on an unlevered basis, is about equal to the median of the guideline companies. The next step is to relever the beta for your subject company tax rate and one or more assumed capital structures. Example 2 Assume for the subject company: Unlevered beta: 0.90 Capital structure: 60% debt, 40% equity Using Formula 10A.8 we get:
0:60 BL ¼ 0:90 1 þ 0:40 ¼ 2:25
150
Cost of Capital
CAPITAL STRUCTURE WEIGHTS Each of the formulas discussed—Hamada, Miles-Ezzell, Harris-Pringle, and practitioners’ method— are based on measuring debt capital and equity capital at market values. But in relevering the beta for a division, reporting unit, or closely held business, we do not know the market value of equity capital until we are completed with the valuation. Appendix 17A discusses the use of the iterative process using the Capital Asset Pricing Method (CAPM) for estimating the cost of equity capital, including the calculation of a relevered beta, assuming a constant capital structure in future years (i.e., debt capital changes in proportion to changes in the net cash flows to the firm). Appendix 17B discusses the use of the iterative process using CAPM for estimating the cost of equity capital, including the calculation of a relevered beta, assuming a varying capital structure in future years.
FERNANDEZ FORMULAS The levering and unlevering Fernandez formulas are useful in cases when it is assumed that the company maintains a fixed book value leverage ratio (ratio of debt to book value of equity remains constant).6 Chapter 17 discusses the use of market value versus book value weights. Formula 10.A.9 is the Fernandez formula for unlevering beta. (Formula 10A.9) Wd ð1 tÞBd BL þ W e Bu ¼ Wd ð1 tÞ 1þ We where the definitions of the variables are the same as in Formulas 10A.1 and 10A.3. The companion Fernandez formula for relevering beta is Formula 10A.10. (Formula 10A.10) Wd ð1 tÞðBU Bd Þ BL ¼ BU þ We where the definitions of the variables are the same as in Formulas 10A.1 and 10A.3. The Fernandez formula is consistent with the theory that:
Debt capital is proportionate to equity book value, and the increase in assets is proportionate to increases in net cash flow. Debt capital bears the risk of variability of operating net cash flow in that interest payments and principal repayments may not be made when owed, which implies that tax deductions on the interest expense may not be realized in the period in which the interest is paid (i.e., beta of debt capital may be greater then zero).
Formulas 10A.9 and 10A.10 are identical to Formulas 10A.1 and Formulas 10A.2 when Bd equals zero (i.e., equity capital is bearing all of the risk of the firm). de Bodt and Levasseur offer an alternative formula to the Fernandez formulas, consistent with the theory that debt capital is proportionate to equity book value, and the increase in assets is proportionate to increases in net cash flow.7 6 7
Pablo Fernandez, ‘‘Levered and Unlevered Beta,’’ Working paper, April 20, 2006. Eric de Bodt, and Michel Levasseur, ‘‘A Short Note on the Hamada Formula,’’ Working paper, March 26, 2007.
Appendix 10B
Examples of Computing OLS Beta, Sum Beta, and Full-Information Beta Estimates David Ptashne, CFA Introduction Computing OLS and Sum Beta Estimates—An Example Computing Historical Return Data Computing OLS Beta Estimate Computing Sum Beta Estimate Computing Full-Information Beta Estimate— An Example
INTRODUCTION Two common methods of calculating beta estimates for a subject public company involve regressing returns for the subject public company against the returns of a benchmark market index over the same periods (also known as ordinary least squares regression or OLS estimate of beta) or lagged returns (sum beta estimate of beta). These public company beta estimates can also be used as proxy beta estimates for a particular division, reporting unit, or comparable closely held company. An alternative method for estimating a beta for a subject company involves selecting and analyzing many guideline public companies that report segment data for businesses that are comparable to all or part of the business operations of the subject company. This ‘‘full-information’’ methodology takes into account the influence on beta of each of the business segments.
COMPUTING OLS AND SUM BETA ESTIMATES—AN EXAMPLE Estimating OLS beta and sum beta for a public company (subject company) as of a specific date (subject date) can be performed in the general steps shown using Microsoft Excel and common market data that can be obtained from a variety of industry data sources, such as Bloomberg or Standard & Poor’s (S&P) Compustat or Capital IQ. For purposes of these examples only, the beta estimates are based on a 12-month ‘‘look-back’’ period and are computed using 13 observations of historical monthly data for OLS beta and 14 observations of historical monthly data for sum beta. Note that a 12-month look-back period was chosen for purposes of this example for simplicity. Ordinarily, we recommend computing OLS and sum beta estimates using a longer look-back period, such as 60 months, which would require 62 months of historical data to compute both estimates accurately. We wish to thank Nick Arens and Brendan Achariyakosol for their assistance in preparing these examples.
151
152
Cost of Capital
Exhibit 10B.1
Example of Return Data for J.B. Hunt Transport Service, Inc. and S&P 500 Subject Company Return Data A Closing Price
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Dec05 Nov05 Oct05 Sep05 Aug05 Jul05 Jun05 May05 Apr05 Mar05 Feb05 Jan05 Dec04 Nov04 Oct04
22.640 22.390 19.410 19.010 18.070 19.630 19.230 20.080 19.545 21.885 23.595 22.060 22.425 20.100 20.430
B Dividends/ Share 0.060
0.060
0.060
0.060 0.015
Market Index Return Data
C Total Return
D S&P500 Index
E S&P500 Dividends
F Index Return
G Lagged Return
H Lead Return I
1.12% 15.66% 2.10% 5.20% 7.95% 2.39% 4.23% 2.74% 10.42% 7.25% 6.96% 1.36% 11.57% 1.54% 10.02%
1248.29 1249.48 1207.01 1228.81 1220.33 1234.18 1191.33 1191.50 1156.85 1180.59 1203.60 1181.27 1211.92 1173.82 1130.20
1.64 3.14 1.30 1.40 2.60 1.43 1.88 2.13 1.36 1.72 2.52 1.11 1.83 2.10 1.41
0.04% 3.78% 1.67% 0.81% 0.91% 3.72% 0.14% 3.18% 1.90% 1.77% 2.10% 2.44% 3.40% 4.04% 1.53%
3.78% 1.67% 0.81% 0.91% 3.72% 0.14% 3.18% 1.90% 1.77% 2.10% 2.44% 3.40% 4.04% 1.53% 1.08%
0.04% 3.78% 1.67% 0.81% 0.91% 3.72% 0.14% 3.18% 1.90% 1.77% 2.10% 2.44% 3.40% 4.04%
Note: Total return ¼ (this month’s price þ current dividend)=(last month’s price) 1; use price only if no dividend information available. Index return ¼ (this month’s price þ current dividend)=(last month’s price) 1. Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
COMPUTING HISTORICAL RETURN DATA Exhibit 10B.1 presents the basic return data that must be calculated for the subject company and market index prior to computing the OLS and sum beta estimates. In this example, the subject company is J.B. Hunt Transport Services, Inc. (J.B. Hunt) and the subject market benchmark is the S&P 500 Index. This is the same company used in Exhibits 10.2 and 10.11 in Chapter 10. For simplicity, this example assumes that each beta estimate is to be computed based on a 12-month look-back period. The steps to obtain the required historical total return data for the subject company and benchmark index are:1 1. Column A. Obtain historical month-end closing prices (adjusted for splits, etc.) for your subject company for N þ 2 months, where N is the number of months in your look-back period. In this example, since our look-back period (N) is 12 months, we have obtained N þ 2, or 14 months, of historical data. 2. Column B. Obtain historical monthly cash dividends for your subject company for N þ 1 months. 3. Column C. Compute total monthly return for your subject company, which is defined as (current month’s price þ current month’s dividend)=(last month’s price) less 1. 4. Column D. Obtain historical month-end closing prices for your selected benchmark index for N þ 2 months. 5. Column E. Obtain historical monthly cash dividends for your benchmark index for N þ 1 months. 1
These steps assume the use of Microsoft Excel. Note that specific formulas entered into Excel to re-create this example might be slightly different, depending on placement of historical return data on your worksheet.
Computing OLS and Sum Beta Estimates—An Example
153
6. Column F. Compute total monthly returns for your benchmark index, which is defined as (current month’s price þ current month’s dividend)=(last month’s price) less 1. 7. Column G. Compute the lagged return of the selected benchmark index. The lagged return is defined as (previous month’s price þ previous month’s dividend)=(price from 2 months ago). Compare columns F and G. Note that the lagged return G for the current month is simply the index return F from the previous month. This computation of lagged return will be used in the calculation of sum beta. COMPUTING OLS BETA ESTIMATE OLS beta can be computed in Excel in a single cell using this formula: OLS beta ¼ CovarðCompany; MarketÞ=VarpðMarketÞ where: Covar ¼ Covariance function in Excel, which returns the covariance (the average of the products of deviations for each data point pair) of two arrays. Company ¼ Array of the subject company’s total returns for months 0 to –11 for a 12-month look-back period. In Excel, it would be the range of cells that includes (C0:C-11). Market ¼ Array of benchmark index total returns for months 0 to –11 for a 12–month lookback period. In Excel, it would be the range of cells that includes (F0:F-11). Varp ¼ Variance function in Excel, which returns the variance of a user-defined population. If you were to follow the example exactly, the resulting OLS beta estimate would equal 2.309 for the 12–month look-back period. By following the same procedures, an OLS beta estimate for J.B. Hunt as of the subject date using the recommended 60-month look-back period was computed to be 1.624 (Exhibit 10.11). COMPUTING SUM BETA ESTIMATE Sum beta can be computed in Excel in three steps. Step 1. Compute the market coefficient in Excel in a separate cell using this formula: Market coefficient ¼ þ ðVarpðLaggedÞ CovarðMarket; CompanyÞCovarðMarket; LaggedÞ CovarðCompany; LaggedÞÞ=ðVarpðMarketÞ VarpðLaggedÞ CovarðMarket; LaggedÞ^ 2Þ where: Varp ¼ Variance function in Excel, which returns the variance of a user-defined population. Lagged ¼ Array of lagged total returns for months 0 to –11 for a 12-month look-back period. In Excel, it would be the range of cells that includes (G0:G-11). Covar ¼ Covariance function in Excel, which returns the covariance (the average of the products of deviations for each data point pair) of two arrays. Market ¼ Array of benchmark index total returns for months 0 to –11 for a 12-month lookback period. In Excel, it would be the range of cells that includes (F0:F-11).
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Cost of Capital
Company ¼ Array of subject company total returns for months 0 to –11 for a 12-month lookback period. In Excel, it would be the range of cells that includes (C0:C-11). Step 2. Compute the market lagged coefficient in Excel in a separate cell using this formula: Market lagged coefficient ¼ þ VarpðMarketÞ CovarðCompany; LaggedÞ CovarðMarket; LaggedÞ CovarðCompany; MarketÞ=ðVarpðMarketÞ
VarpðLaggedÞ CovarðMarket; LaggedÞ^ 2Þ
where: Varp ¼ Variance function in Excel, which returns the variance of a user-defined population. Market ¼ Array of benchmark index total returns for months 0 to –11 for a 12-month lookback period. In Excel, it would be the range of cells that includes (F0:F-11). Covar ¼ Covariance function in Excel, which returns the covariance (the average of the products of deviations for each data point pair) of two arrays. Company ¼ Array of subject company total returns for months 0 to –11 for a 12-month lookback period. In Excel, it would be the range of cells that includes (C0:C-11). Lagged ¼ Array of lagged total returns for months 0 to –11 for a 12-month look-back period. In Excel, it would be the range of cells that includes (G0:G-11). Step 3. Add the value computed in Step 1 to the value computed in Step 2. This is the sum beta estimate. If you were to follow the example exactly, the resulting sum beta estimate would equal 1.739 for the 12-month look-back period. By following the same procedures, a sum beta estimate for J.B. Hunt as of the subject date using the recommended 60-month look-back period was computed to be 1.979 (Exhibit 10.11).
COMPUTING FULL-INFORMATION BETA ESTIMATE—AN EXAMPLE A full-information beta estimate as of a specific date can be calculated in the general steps described using Excel and market data of guideline public companies obtained from industry data sources, such as Standard & Poor’s Compustat or Capital IQ or from the public filings of the selected guideline companies. For purposes of this example, we are attempting to estimate a full-information beta for Exxon Mobil Corp. (Exxon), which operates in the Oil and Gas industry. We further distinguished the businesses of Exxon for this example as upstream operations such as exploration (Upstream), downstream operations such as refining (Downstream), Chemicals, and Other. The Other segment was used as a reservoir for all sales and operating income that were not attributable to the Upstream, Downstream, or Chemical segments, such as corporate headquarters, pipelines, and finance; a wellselected group of guideline public yet non–pure play companies should represent businesses accounting for the bulk of the business of the subject company. We have gathered selected segment-level data for 19 guideline companies, including sales and operating income information for FY2006. Our guideline companies were selected because each report segment-level results for a segment of its operations that is comparable to one or more of the main business segments of Exxon excluding
Computing Full-Information Beta Estimate—An Example Exhibit 10B.2
155
Business Segment Data for Exxon
EXXON MOBIL CORP TICKER: XOM SIC: 2911 GICS: 10102010 FISCAL YEAR ENDED: December 2006 Segment Business Segments SIC Codes U.S. Upstream Non-U.S. Upstream U.S. Downstream Non-U.S. Downstream U.S. Chemicals Non-U.S. Chemicals Corporate & Financing
Segment % of Segment % of Segment % of Segment % of Segment % of Sales Total Oper Inc Total Depr Total Car Exp Total Assets Total
1,311 1,311 2,911 2,911
1,321 1,321 NA NA
6,054 26,821 93,437 205,020
2,911 2,911 NA
2,824 13,273 2,824 NA 37
1.66 5,168 13.08 1,263 11.06 1,942 12.56 21,119 9.64 7.34 21,062 53.32 6,482 56.78 9,735 62.96 75,090 34.29 25.57 4,250 10.76 632 5.54 718 4.64 16,740 7.64 56.10 4,204 10.64 1,605 14.06 1,757 I1.36 47,694 21.78 3.63 5.70 0.01
1,360 3,022 434
3.44 7.65 1.10
427 473 534
3.74 4.14 4.68
257 384 669
1.66 7,652 3.49 2.48 11,885 5.43 4.33 38,835 17.73
Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
Other (i.e., Upstream, Downstream, or Chemicals). Note that in our example, the Other segment only accounted for 5.5% of sales and 6.16% of operating income for the group and 0.01% of sales and 1.1% of operating income for Exxon. Our list of guideline companies is not intended to be an exhaustive list of guideline companies for Exxon but rather was selected for demonstrative purposes. We are using data for the 19 guideline companies to estimate the beta for Exxon. We will then compare the full-information beta estimate with the OLS beta estimate for Exxon. In order to estimate a full-information beta, you must first aggregate the reported segment data for the subject company into the four identified segments. This is accomplished by the analyst with the assistance of the Standard Industrial Classification (SIC) codes assigned to each of the companies’ segments as provided by compustat. An example of this raw data for Exxon is shown in Exhibit 10B.2. Note that this information provides segment data for sales, operating income, depreciation, capital expenditures, and assets. For purposes of calculating this example’s full-information beta estimate, we will compare the estimate using sales and operating income as the weighting factors. That is, we will weight the influence of differences in segment sales and segment operating income in the betas of the 19 guideline public companies. The SIC codes and corresponding segments that were applicable in our example were identified to be: SIC Code (starting with):
Segment
131 & 132 291 282
Upstream Operations Downstream Operations Chemicals
Notice in Exhibit 10B.2 that two SIC codes are provided for some of the segments and none is provided for other segments. Compustat often assigns two SIC codes to a single segment;
156 Exhibit 10B.3
Cost of Capital Segment Operating Income Segment Operating Income
EXXON MOBIL CORP ANADARKO PETROLEUM CORP CANADIAN NATURAL RESOURCES CHESAPEAKE ENERGY CORP CHEVRON CORP CONOCOPHILLIPS DEVON ENERGY CORP DOW CHEMICAL DU PONT (E I) DE NEMOURS DUKE ENERGY CORP EL PASO CORP HESS CORP IMPERIAL OIL LTD MARATHON OIL CORP MURPHY OIL CORP OCCIDENTAL PETROLEUM CORP ROHM AND HAAS CO SUNCOR ENERGY INC TESORO CORP WILLIAMS COS INC
Upstream
Downstream
Chemicals
Other
Total Segments
26,230 5,370 2,745 3,192 13,142 10,324 4,496 – – 569 640 1,763 2,661 2,019 616 7,239 – 3,114 – 530
8,454 – – – 3,973 4,481 – – – – – 390 784 2,795 105 – – 328 1,476 –
4,382 – – – 539 – – 4,893 2,296 – – – 188 – – 901 649 – – –
434 (483) 35 147 – 745 – 510 1,987 3,360 1,110 (237) (114) – (83) (239) 106 – (159) 840
4 1 2 2 3 3 1 2 2 2 2 2 3 2 2 2 2 2 1 2
Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
therefore, in some instances it is necessary to determine which SIC code and thus which segment label ‘‘best’’ defines the sales and operating income for that segment. In instances where two SIC codes fell into the same segment label—for example, US Upstream—since both 131 and 132 correspond with upstream operations, that segment is clearly labeled as an Upstream segment. However, in some segments, such as US Chemicals, the two SIC codes listed are 291 and 282, which correspond to Downstream Operations and Chemicals, respectively. In these instances, it is necessary to determine a single segment in which to classify the revenue and operating income. Based on the segment name, this is clearly more closely aligned to the Chemicals segment, and so we assigned it to Chemicals. Finally, notice that the business segment named Corporate & Financing has no SIC code assigned to it; in this instance, we determined that this should be categorized into the Other segment. Once all of the companies’ business segments were appropriately assigned into our four segment categories, we organized these data into a chart as shown in Exhibit 10B.3. (While this analysis was completed separately with sales and operating income data, for brevity we show only operating income results in the exhibit.) Using these amounts, we then created a segment weighting for each company. The segment weighting and the OLS beta estimates for each guideline public company (using a look-back period of 60 months) are displayed in Exhibit 10B.4. Although we are estimating the beta for Exxon using the other 19 guideline public companies, we display Exxon’s beta estimate in this exhibit for comparison purposes. The data in Exhibit 10B.4 are then used to run the regression necessary to estimate the fullinformation beta for the subject company (i.e., Exxon) with operating income weights.
Computing Full-Information Beta Estimate—An Example
157
Segment Operating Income Weights and OLS Beta Estimates
Exhibit 10B.4
Segment Operating Income Weights
EXXON MOBIL CORP ANADARKO PETROLEUM CORP CANADIAN NATURAL RESOURCES CHESAPEAKE ENERGY CORP CHEVRON CORP CONOCOPH1LLIPS DEVON ENERGY CORP DOW CHEMICAL DU PONT (E I) DE NEMOURS DUKE ENERGY CORP EL PASO CORP HESS CORP IMPERIAL OIL LTD MARATHON OIL CORP MURPHY OIL CORP OCCIDENTAL PETROLEUM CORP ROHM AND HAAS CO SUNCOR ENERGY INC TESORO CORP WILLIAMS COS INC
OLS Beta
Upstream
Downstream
Chemicals
Other
0.763 0.623 0.316 0.596 0.743 0.642 0.562 1.066 1.072 1.185 2.219 0.458 0.291 0.560 0.418 0.498 0.992 0.371 1.723 2.726
66.4% 109.9% 98.7% 95.6% 74.4% 66.4% 100.0% 0.0% 0.0% 14.5% 36.6% 92.0% 75.6% 41.9% 96.5% 91.6% 0.0% 90.5% 0.0% 38.7%
21.4% 0.0% 0.0% 0.0% 22.5% 28.8% 0.0% 0.0% 0.0% 0.0% 0.0% 20.4% 22.3% 58.1% 16.5% 0.0% 0.0% 9.5% 112.1% 0.0%
11.1% 0.0% 0.0% 0.0% 3.1% 0.0% 0.0% 90.6% 53.6% 0.0% 0.0% 0.0% 5.3% 0.0% 0.0% 11.4% 86.0% 0.0% 0.0% 0.0%
1.1% 9.9% 1.3% 4.4% 0.0% 4.8% 0.0% 9.4% 46.4% 85.5% 63.4% 12.4% 3.2% 0.0% 13.0% 3.0% 14.0% 0.0% 12.1% 61.3%
Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
Full-Information Regression Results Using Operating Income Weights
Exhibit 10B.5 Summary Output
Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations
0.927 0.860 0.765 0.466 19
Anova
Regression Residual Total
df
SS
MS
F
Significance F
4 15 19
20.030 3.259 23.290
5.008 0.217
23.047
0.000
Coefficients Standard Error t Stat P-Value Lower 95% Upper 95% Intercept Upstream Downstream Chemicals Other
0 0.491 1.446 0.707 2.359
0.158 0.360 0.352 0.360
3.106 4.016 2.007 6.551
0.007 0.001 0.063 0.000
0.154 0.678 0.044 1.591
0.827 2.213 1.459 3.126
Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
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Cost of Capital
In order to run the regression in Excel, we utilized the Regression function found under Tools ! Data Analysis. The Y Variable Range is the column of OLS beta estimates for the 19 guideline public companies, and the X Variable Range is the four columns of segment weights. In the regression tool, we then select ‘‘Labels’’ (to show the labels in the output), ‘‘Constant is Zero’’ (to force the intercept of the regression line through the origin), and a 95% confidence level. The regression output for operating income weights is shown in Exhibit 10B.5. According to these results, the divisional beta for the segment Upstream, for example, is 0.491 with a 95% confidence interval of 0.154 to 0.827. These results also show that the R-square value of the regression is 0.860. Using Formula 10B.1, the formula for full-information beta: (Formula 10B.1) RIiL ¼
n X ðWs BLs Þ 1
where: RIiL ¼ Full-information levered beta estimate of the subject company Ws ¼ Weight of each segment of the subject company BLs ¼ Levered beta estimate of each segment from the regression n ¼ Number of segments
Exhibit 10B.6
Full-Information Regression Results Using Sales Weights
Summary Output Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations
0.941 0.885 0.795 0.422 19
Anova
Regression Residual Total
df
SS
MS
F
Significance F
4 15 19
20.614 2.676 23.290
5.153 0.178
28.890
0.000
Coefficients Standard Error t Stat P-Value Lower 95% Upper 95% Intercept Upstream Downstream Chemicals Other
0 0.384 0.739 0.625 2.087
0.205 0.195 0.348 0.249
1.874 3.794 1.796 8.378
0.081 0.002 0.093 0.000
0.053 0.324 0.177 1.556
0.821 1.154 1.367 2.618
Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
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159
we then calculate the full-information beta estimate for Exxon to be: BExxon ¼ ð0:491 0:664Þ þ ð1:446 0:214Þ þ ð0:707 0:111Þ þ ð2:359 0:011Þ ¼ 0:740 This full-information beta estimate of 0.740 closely approximates the OLS beta estimate for Exxon of 0.763 (difference of 3.1%). Similarly, we calculated the full-information beta estimate using sales weights. The regression results are displayed in Exhibit 10B.6. We then calculate the full-information beta estimate for Exxon to be: BExxon ¼ ð0:384 0:090Þ þ ð0:739 0:817Þ þ ð0:625 0:093Þ þ ð2:087 0:000Þ ¼ 0:696 This yields a full-information beta estimate of 0.696. This estimate compares with the OLS beta estimate for Exxon of 0.763 (difference of 8.8%). Why is the full-information beta estimate using operating income weights more accurate than using sales weights? Stock returns are driven by profits, not revenues. In the case of Exxon, the segment operating margin (operating income/sales) differed across segments. The Upstream segment represented 9% of the sales but 66.4% of the operating income (operating margin of 79.8%) while the Downstream segment represented 81.7% of the sales but only 21.4% of the operating income (operating margin of 2.8%).
Chapter 11
Criticism of CAPM and Beta versus Other Risk Measures
Introduction CAPM Assumptions and Beta as a Risk Measure Problems with CAPM Assumptions Is Beta a Reliable Risk Measure? Variations of CAPM Risk Measures Unique or Unsystematic Risk Total Risk Adjusting the Textbook CAPM Downside Risk Value at Risk Adjusting Beta for Risk of Company Size and Company-Specific Risk Duration Yield Spreads Fundamental Risk Summary Appendix 11A
INTRODUCTION Even though the Capital Asset Pricing Model (CAPM) is the most widely used method of estimating cost of equity capital, the accuracy and predictive power of beta as the sole measure of risk has increasingly come under attack. As a result, alternative measures of risk have been suggested. That is, despite its wide adoption, academics and practitioners alike have questioned the usefulness of CAPM in accurately estimating the cost of equity capital and beta as a reliable measure of risk. This chapter explores the criticisms and alternative measures of risk, and the resulting methods used to estimate the cost of equity capital.
CAPM ASSUMPTIONS AND BETA AS A RISK MEASURE Harry Markowitz, father of modern portfolio theory, organized the concepts and methodology of portfolio selection using statistical techniques.1 His goal was to help investors choose portfolios that were mean-variance efficient; that is, to choose stocks that minimize expected portfolio variance
1
Harry M. Markowitz, ‘‘Portfolio Selection,’’ Journal of Finance (March 1952): 77–91.
161
162
Cost of Capital
given an expected return, or alternatively, choose stocks that maximize an expected return given expected portfolio variance. Markowitz decided on variance as a risk measure because variance was ‘‘cheaper’’ to calculate, given the computing power at the time, application of the formula for portfolio was straightforward, and variance was a familiar concept. But Markowitz found that other measures of portfolio risk resulted in ‘‘better’’ portfolios; that is, portfolios with lower risk given an expected return. William Sharpe2 and John Lintner3 extended the Markowitz model by introducing assumptions of (1) complete agreement among investors on the joint probability distribution of asset returns from time ‘‘t–1’’ to time ‘‘t’’ (and its true probability distribution) (2) and unrestricted risk-free borrowing and lending. The results were that the only risk measure that mattered was beta. Beta measures expected market or systematic risk in the CAPM. The eight assumptions underlying the CAPM are: 1. Investors are risk averse. 2. Rational investors seek to hold efficient portfolios and, as a result, the portfolios they hold are fully diversified. 3. All investors have identical investment time horizons (i.e., expected holding periods). 4. All investors have identical expectations about such variables as expected rates of return and how capitalization rates are generated. 5. There are no transaction costs. 6. There are no investment-related taxes. (However, there may be corporate income taxes.) 7. The rate received from lending money is the same as the cost of borrowing money. 8. The market has perfect divisibility and liquidity (i.e., investors can readily buy or sell any desired fractional interest). These assumptions, combined with the assumption that security returns are normally distributed, result in beta being the correct risk measure. Because risk of an individual security is considered only in relation to other securities in the portfolio, all investors will choose to hold the market portfolio, M. Obviously, the extent to which these assumptions are not met in the real world will have a bearing on the validity of the CAPM. Traditional CAPM theory predicts that only market (or systematic) risk should be priced in equilibrium. But the inability to hold a market portfolio or choose not to hold a market portfolio will force investors to consider more than market risk.
PROBLEMS WITH CAPM ASSUMPTIONS A central conclusion of the textbook CAPM is that every investor holds the identical market portfolio stemming from two assumptions: homogenous expectations and no transaction costs. But many investors hold small portfolios.
2
3
William F. Sharpe, ‘‘Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk,’’ Journal of Finance (September 1964): 425–442. John Lintner, ‘‘The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets,’’ Review of Economics and Statistics (February 1965): 13–37.
Is Beta a Reliable Risk Measure?
163
Market evidence indicates that individual investors do not wish to hold the market portfolio. Investors are willing to pay fees and expenses to hold nonindexed mutual funds.4 And holding a diversified portfolio is more difficult today than in the past. For example, the number of stocks needed to have a well diversified portfolio has increased due to the increase in unique risk (idiosyncratic risk or residual volatility of the portfolio).5 How diversifiable is unique or unsystematic risk? In one study, researchers compared the number of securities in a portfolio and the remaining idiosyncratic risk. Their empirical results demonstrate that even very large portfolios have substantial firm-specific risk. Failure to hold any portfolio except the market portfolio exposes an investor to the risk of experiencing firm-specific shocks. They conclude that since firm-specific risk is not easily diversifiable, then firm-specific risk may be ‘‘priced’’ (i.e., drive returns). Arguments that claim little added diversification is gained beyond, say, 30 or 50 stocks are erroneous.6 Another study concludes that investors need many more stocks to diversify and reduce their risk. In fact, investors need at least 164 stocks to have at most a 1% chance of underperforming U.S. government bonds.7 If there is no unrestricted risk-free borrowing and unrestricted short sales of risky assets are not allowed, then the market portfolio almost surely is not efficient, so the CAPM risk-return relationship does not hold. Further, research has shown that the unconditional security return distribution is not normal. Therefore, mean and variance of returns alone are insufficient to characterize return distributions completely. But despite its drawbacks, CAPM, when properly applied, may be a useful benchmark discount rate, even for investments in closely held businesses. It provides a benchmark measure of expected risk versus expected return. Given the problems with the underlying assumptions of CAPM, you must understand problems and benefits/issues of using alternative cost of capital methodologies and alternative risk measures. In fact, multiple methods of estimating the cost of equity capital with the conclusion drawn from the range of methods may be better than relying on a single methodology.
IS BETA A RELIABLE RISK MEASURE? Beta is a forward-looking concept similar to equity risk premium (ERP). The true beta must be estimated. Existing techniques for estimating beta generally use historical data and assume that the future will be sufficiently similar to the past to justify extrapolation of betas calculated using historical data. A series of studies have studied the predictive power of beta. That is, do ‘‘high-beta’’ stocks earn higher returns in future periods? (The theory implies that with a high beta, the market perceives the
4
5
6 7
See, for example, William N. Goetzmann and Alok Kumar, ‘‘Why Do Individual Investors Hold Underdiversified Portfolios?’’ Working paper, November 2004. The authors study diversification decisions of 60,000 individual investors during 1991 to 1996 and find that the majority are underdiversified with greatest underdiversification in retirement accounts; and Theodore Day, Yi Wang, and Yexiao Xu, ‘‘Investigating Underperformance by Mutual Fund Portfolios,’’ Working paper, May 2001; the authors demonstrate that the portfolios of equity mutual funds are not mean-variance efficient with respect to their holdings. John Y. Campbell, Martin Lettau, Burton G. Malkiel, and Yexiao Xu, ‘‘Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk,’’ Journal of Finance (February 2001): 1–43; the authors demonstrate that a welldiversified portfolio needs at least 40 stocks in recent decades due to increasing trends in idiosyncratic volatility. James A. Bennett and Richard W. Sias, ‘‘How Diversifiable Is Firm-Specific Risk?’’ Working paper, February 2007. Dale L. Domian, David A. Louton, and Marie D. Racine, ‘‘Diversification in Portfolios of Individual Stocks: 100 Stocks Are Not Enough,’’ Working paper, April 4, 2006; In press The Financial Review.
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Cost of Capital
investment to be more risky). Similarly, do ‘‘low-beta’’ stocks earn lower returns in future periods? (The theory implies that the lower the beta, the market perceives the investment to be less risky.) For example, in one study, the author found that realized returns on stocks with high earnings-tomarket price were greater than predicted by beta and the realized returns on stocks with low earningsto-market price were lower than predicted.8 In another study, that author documents that the average realized returns on small stocks are greater than predicted by CAPM (i.e., the size effect).9 In another study, the author found that companies with high debt-to-market value of equity ratio earn too high a return relative to their betas.10 In two studies the respective authors investigated the relationship between average return and ratio of book-value-to-market-value of stocks. They found that returns on stocks with high book-value-to-market-value ratios had greater average realized returns than implied by their betas and returns on stocks with low book-value-to-market-value ratios realized lower average realized returns than implied by their betas. These studies imply that ratios involving stock prices have information about expected returns missed by betas. A stock’s price depends on expected cash flows and on expected returns that discount expected cash flows to present value.11 Eugene Fama and Kenneth French (FF) published two studies critical of beta. In one study they state: The efficiency of the market portfolio implies that (a) expected returns on securities are a positive linear function of their market betas (the slope in the regression of a security’s return on the market’s return), and (b) market betas suffice to describe the cross-section of expected returns.
They observed that the relation between market beta and average return is flat.12 In a follow-on study, they find that problems with CAPM using U.S. data show up in the same way in the stock returns of 12 non-U.S. major markets.13,14 Further, the CAPM cost of equity estimates for high-beta stocks are too high and estimates for low-beta stocks are too low relative to historical returns. And finally, CAPM cost of equity estimates for high book-value-to-market-value stocks (so-called value stocks) are too low and estimates for low book-value-to-market-value stocks (so-called growth stocks) are too high (relative to historical returns). The implications of their work are if market betas do not suffice to explain expected returns, the market portfolio is not efficient then CAPM has potentially fatal problems. They believe that their results point to the need for an asset pricing model not dependent on beta alone because beta as traditionally measured is not a complete description of an asset’s risk.15 FF go on to introduce another cost of equity capital model, the Fama-French 3-factor model based on an empirical study confirming 8
Sanjay Basu, ‘‘Investment Performance of Common Stocks in Relation to Their Price-Earnings Ratios,’’ Journal of Finance (1977): 129–156. 9 Rolf W. Banz, ‘‘The Relationship between Return and Market Value of Common Stocks,’’ Journal of Financial Economics (March 1981): 3–18. 10 Laxmi Chad Bhandari, ‘‘Debt/Equity Ratio and Expected Common Stock Returns: Empirical Evidence,’’ Journal of Finance (June 1988): 507–528. 11 See Dennis W. Stattman, ‘‘Book Value and Stock Returns,’’ The Chicago MBA: A Journal of Selected Papers 4 (1980): 25–45; and Ronald Lanstein, Kenneth Reid, and Barr Rosenburg, ‘‘Persuasive Evidence of Market Inefficiency,’’ Journal of Portfolio Management 11, no. 3 (1985): 9–17. 12 Eugene Fama and Kenneth French, ‘‘The Cross-Section of Expected Stock Returns,’’ Journal of Finance (June 1992): 427–486. 13 Eugene Fama and Kenneth French, ‘‘Value versus Growth: The International Evidence,’’ Journal of Finance (December 1998): 427–465. 14 One author has determined that a basic problem with these and other studies about beta is the result of using periodic returns, rather than continuously compounded returns. See Carl R. Schwinn, ‘‘The Predictable and Misleading Consequences When Using Periodic Returns in Traditional Tests of the Capital Asset Pricing Model,’’ Working paper, December 2006. 15 See Fama and French note 12 above.
Is Beta a Reliable Risk Measure?
165
that size, earnings-to-price, debt-to-equity, and book-value-to-market-value ratios all add to an explanation of realized returns provided by market betas. We discuss the FF 3-factor model in Chapter 16. After the FF 3-factor model was introduced, researchers discovered that this empirically based model was not very reliable either. In several studies researchers show that within portfolios formed on price ratios (e.g., book-value-to-market-value of stocks), stocks with higher expected cash flows have higher expected return, a measure not captured by FF 3-factor model or by CAPM.16 Still other studies found additional problems with the FF 3-factor model. A stock’s price is the present value of future cash flows discounted at the required return on the stock; therefore, given the same book-value-to-market-value ratio, expected return is positively related to cash flows. If two stocks have the same price, the one with higher expected cash flows must also have higher expected return. Given a particular book-value-to-market-value ratio, positive relation between expected profitability and expected return is a direct prediction of valuation theory. But the FF 3-factor model does not indicate which stocks with the same book-value-to-market-value ratio are expected to have higher returns.17 Other researchers found that traditional CAPM works over the long run, but not after 1963 (i.e., on the average, stocks with higher betas realized higher returns and stocks with lower betas realized lower returns). The book-value-to-market-value relationship better explains differences in returns after 1963 (though after 1980 its explanatory power is almost zero). They estimate CAPM with timevarying betas (dependent on economic conditions), constant market risk premium, and constant market volatility. They find that time-varying betas explain the book-value-to-market-value effect except for medium-size stocks. They question if the post-1963 problem with beta is just a small-samplesize’’ issue.18 Alternatively, could it be that the problem with CAPM and beta is the use of historical excess returns? Could it be that expectations can change so quickly that standard statistical methods for estimating beta using historical excess returns are just not sensitive enough to measure those expectations? In another study of CAPM and beta, the authors use expected returns from two sources (Value Line data for the period 1975 to 2001 and expected returns based on sell-side analysts as reported by First Call for the period 1997 to 2001) rather than historic realized returns to compare to beta estimates. They find that stocks’ expected returns for the periods using both sources were positively related to their estimated betas. Further they found that investors expected higher rates of return on small-cap stocks and on average received higher returns. That is, they found that the expected return on small (market value) stocks was greater than for large (market value) stocks after taking into account differences in beta estimates, consistent with the size effect.19 In still another study, researchers used information embedded in the prices of individual stock options and index options to compute forward-looking, or option implied, beta estimates. They 16
17
18 19
Richard Frankel and Charles M.C. Lee, ‘‘Accounting Valuation, Market Expectation, and Cross-Sectional Stock Returns,’’ Journal of Accounting and Economics (June 1998): 283–319; Patricia M. Dechow, Amy P. Hutton, and Richard G. Sloan, ‘‘An Empirical Assessment of the Residual Income Valuation Model,’’ Journal of Accounting and Economics (January 1999): 1–34; Joseph D. Piotroski, ‘‘Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers,’’ Journal of Accounting Research 38 (Supplement 2000): 1–41. John Y. Campbell and Robert J. Shiller, ‘‘The Dividend—Price Ratio and Expectations of Future Dividends and Discount Factors,’’ Review of Financial Studies (May 1989): 195–228; Tuomo Vuolteenaho, ‘‘What Drives Firm Level Stock Returns,’’ Journal of Finance (February 2002): 233–264. Andrew Ang and Joseph Chen, ‘‘CAPM over the Long-Run: 1926–2001,’’ Working paper, October 2002. Brav, Lehavy, and Michaely, ‘‘Using Expectations to Test Asset Pricing Models,’’ Financial Management (Autumn 2005): 5–37.
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Cost of Capital
compared their forward-looking beta estimates to historical-based beta estimates. They determined that the forward-looking beta estimates have better predictive power (i.e., high-beta stocks earn greater returns in future periods, etc.) than the best performing historical-based beta estimates in about half the cases. In total, the forward-looking beta estimates explain about 22% of the variation in the returns across the securities studied.20 Other researchers have shown that stock returns are not normally distributed; that problem alone creates the situation where beta is not the sole measure of risk.21 In summary, these studies show that beta alone is not a reliable measure of risk and realized future returns (at least not using betas drawn from historical excess returns). Yet CAPM and beta persist even today as the most widely used method of estimating the cost of equity capital. As one commentator said: In spite of the lack of empirical support, the CAPM is still the preferred model for classroom use in MBA and other managerial finance courses. In a way it reminds us of cartoon characters like Wile E. Coyote who have the ability to come back to original shape after being blown to pieces or hammered out of shape.22
VARIATIONS OF CAPM RISK MEASURES Could the market be measuring risk using a risk measure other than or in addition to beta? Could the market be measuring risk using some combination of total risk (market or systematic plus unique or unsystematic risk)? UNIQUE OR UNSYSTEMATIC RISK Unsystematic volatility of returns on stocks has increased over the past forty years. This increase has been linked to an increase in the fundamental volatility of firms’ earnings, cash flows, and sales.23 But is unsystematic risk priced by the market? That is, do firms with higher unsystematic risk earn higher returns (possibly the theory of higher-beta stocks earning higher returns)? One set of researchers confirm FF’s findings for a later time period, finding that the relationship of realized returns and beta measured using historical excess returns is essentially flat for the period 1963 to 1994. They confirm FF’s finding that size (as measured by market value) is a better proxy for risk than beta. While the volatility of the market as a whole during the 1980s and early 1990s was lower than earlier decades, volatility of individual stocks has been rising over time. The residual
20
21
22
23
Peter Christoffersen, Kris Jacobs, and Gregory Vainberg, ‘‘Forward-Looking Betas,’’ Working paper, August 4, 2006, rev. March 16, 2007. Fang and Lai in ‘‘Co-Kurtosis and Capital Asset Pricing,’’ Financial Review (May 1997): 293–307, derive a four-moment CAPM and show that systematic variance, systematic skewness, and systematic kurtosis contribute to the risk premium, not just beta; Arditti in ‘‘Risk and the Required Return on Equity,’’ Journal of Finance (March 1967): 19–36, demonstrates that skewness and kurtosis cannot be diversified away by increasing the size of the portfolios. Jagannathan and Wang, ‘‘The Conditional CAPM and the Cross-Section of Expected Returns,’’ Journal of Finance (August 1996): 3–53. Paul J. Irvine and Jeffrey Pontiff, ‘‘Idiosyncratic Return, Cash Flows, and Product Market Competition,’’ Working paper, April 2005.
Variations of CAPM Risk Measures
167
risk or idiosyncratic volatility of individual stocks is strongly related to size of company. They hypothesize that the size effect found by FF may be reflecting idiosyncratic volatility.24 In a later study, these same researchers study the impact on returns if some investors cannot hold the market portfolio. In those circumstances, idiosyncratic volatility (unsystematic risk) is useful in explaining expected returns across stocks. They find that stock returns directly covary with idiosyncratic risk. They find that the intercept (a) and beta estimated from CAPM are highly negatively correlated, reducing the explanatory power of beta. Idiosyncratic volatility is greater for small-size (small-market-value stocks) portfolios of stocks than for large-size (large-market-value stocks) portfolios. They do find that stocks with high betas tend to have high idiosyncratic risk. They recommend including an idiosyncratic risk measure.25 And in a subsequent study these same researchers use two methods to estimate idiosyncratic risk. Large stocks (as measured by market value) rather than small stocks appear to play an important role in the increasing idiosyncratic volatility of individual stocks because of increases in holdings by institutions that do not hold diversified portfolios. Stocks with greater expected growth have greater idiosyncratic volatility.26 What could be the tie between idiosyncratic volatility and small firms? Two other researchers examine averages of idiosyncratic risk in portfolios of firms grouped by market value and length of listing (proxy for age) using data from August 1963 to December 2001. They find that idiosyncratic volatilities of small firms (market capitalization below the median market capitalization of all issues: approximately 3% of total market capitalization in 1962–1969 and 1% in 2000–2001) are positive predictors of stock returns (and are unlike volatilities of bigger, older, and newer firms). They find that ‘‘size’’ is a significant predictor of returns primarily because it is a proxy for entrepreneurial risk. Entrepreneurial risk exists because investors with proprietary business income are significant stockholders and appear to invest in smaller, entrepreneurial companies. The authors find that entrepreneurial risk (measured by covariance with proprietary business income) is correlated with the positive effect of size on expected future returns. Entrepreneurial risk is an economically important determinant of variations in expected equity returns.27 In a further study using data from the London Stock Exchange from 1979 through 2003, researchers found that valuing idiosyncratic volatility of small companies (measured by market capitalization) is a predictor of returns for small-capitalization stocks (and insignificant as a predictor of returns for larger-capitalization stocks).28 In another study, the authors found no statistical significance of idiosyncratic volatility in predicting stock prices across both small and large company (by market capitalization) stocks.29 TOTAL RISK Shannon Pratt called his doctoral dissertation ‘‘The Relationship between Risk and the Rate of Return for Common Stocks.’’ He used the standard deviation of 12 quarters of past returns as his measure of risk. He divided the stocks into quintiles based on the values of the risk measures. It turned out 24 25 26
27
28
29
Burton G. Malkiel and Yexiao Xu, ‘‘Risk and Return Revisited,’’ Journal of Portfolio Management (Spring 1997): 9–14. Burton G. Malkiel and Yexiao Xu, ‘‘Idiosyncratic Risk and Security Returns,’’ Working paper (July 2000). Burton G. Malkiel and Yexiao Xu, ‘‘Investigating the Behavior of Idiosyncratic Volatility,’’ Journal of Business (October 2003): 613–644. David P. Brown and Miguel A. Ferreira, ‘‘Information in the Idiosyncratic Volatility of Small Firms and Entrepreneurial Risk,’’ Working paper (December 2005). Timotheos Angelidis and Nikolaos Tessaromatis, ‘‘Equity Returns and Idiosyncratic Volatility: UK Evidence,’’ Working paper, June 2, 2005. Note: idiosyncratic risk measured a residual from FF 3-factor model. Turan G. Bali and Nusret Cakici, ‘‘Idiosyncratic Volatility and the Cross-Section of Expected Returns,’’ Working paper, July 2006. Note: idiosyncratic risk measured a residual from FF 3-factor model.
168
Cost of Capital
Annual Rates of Return
Figure 1 Average Annual Rates of Return for Stock Portfolios of Different Risk Grades (Annual Rates Derived from Geometric Mean IPRs) .175 .170 .165 .160 .155 .150 .145 .140 .135 .130 .125 .120 .115 .110 .105 .100 0.95
1929–1960
A
1-Year Holding Periods 3-Year Holding Periods 5-Year Holding Periods 7-Year Holding Periods
B
C
D
E
Annual Rates of Return
Figure 2 Average Annual Rates of Return for Stock Portfolios of Different Risk Grades (Annual Rates Derived from Geometric Mean IPRs)
Exhibit 11.1
.175 .170 .165 .160 .155 .150 .145 .140 .135 .130 .125 .120 .115 .110 .105 .100 0.95
1931–1960
1-Year Holding Periods 3-Year Holding Periods 5-Year Holding Periods 7-Year Holding Periods A
B
C
D
E
Relationship between Risk and the Rate of Return for Common Stocks
Source: E. Bruce Fredrikson, Frontiers of Investment Analysis, 2nd ed. (Scranton, PA: Intext Educational Publishers, 1971), 345. Used with permission. All rights reserved.
to be a very good risk measure in the sense that the cross-sectional standard deviations of future oneyear returns rose dramatically with each quintile. The returns rose through the fourth quintile and dropped off a little for the fifth quintile. The results are shown schematically in Exhibit 11.1
Variations of CAPM Risk Measures
169
Other researchers have also found that total risk matters, not just market risk.30 To the extent that undiversified investors have an impact in the market, this should be reflected in pricing of the overall stock market. They cite another study in which those researchers found that over 45% of the net worth of investors with closely held businesses consists of private equity, with more than 70% concentrated in a single firm; these investors are not diversified.31 They then study the relation between average stock total risk and market return over time and find a significant positive relation between average stock variance and return on the market. If you view equity and debt as contingent claims on assets of a company, as the volatility of the assets increases, the value of the equity goes up at the expense of the debt holders. They conclude that total risk, including unique or idiosyncratic risk (volatility of returns), drives forecastability of the stock market. ADJUSTING THE TEXTBOOK CAPM Some authors acknowledge that it is appropriate to adjust textbook CAPM but only when considering the rate of return appropriate for an undiversified investor. This will result in a set of rates of return for diversified investors (those for whom in theory only beta risk matters) and another set of rates of return for undiversified investors (those for whom idiosyncratic risk matters). But the theory of cost of capital is that it should be a function of beta or market risk. The studies are mixed as to whether unsystematic risk is priced by the market. One study finding no statistical relationship between unsystematic risk and expected returns measured idiosyncratic risk in terms of residuals from the FF 3-factor model, not the textbook CAPM.32 The FF 3-factor model controls for size and other differences among the firms. Another study though finds a strong X link between implied idiosyncratic volatility derived from options and future returns.33 We, therefore, believe that it is appropriate to adjust cost of capital for smaller companies when using CAPM to estimate the cost of equity capital. One method of adjusting is adding a size premium (we discuss this adjustment in Chapter 12). An alternative method would be to adjust the beta estimate to account for risks not measured by the risk of the investment rather than to adjust for the characteristics of particular investors. How can a company estimate its cost of capital if it needs to ‘‘guess’’ if its investors are diversified? The studies we have just cited suggest that investors in general are much less diversified than predicted by the textbook CAPM. Other studies suggest that at least for small companies (measured by market capitalization), returns are a function of more than beta. One such method of adjusting beta is called total beta, beta adjusted for the total risk of the firm. The R2 of the regression of excess returns used to estimate beta regression measures proportion of risk that is market risk and can be used to adjust beta.34 For example, assume the average guideline public company beta ¼ 1.10, the correlation of the regression used to estimate beta ¼ .33 (i.e., R not R2; risk-free rate ¼ 6%; RPm equal 5%). We can calculate total beta as: Total beta ¼ 1:10=0:33 ¼ 3:30
30 31 32
33
34
Amit Goyal and Pedro Santa-Clara, ‘‘Idiosyncratic Risk Matters!’’ Journal of Finance (June 2003): 975–1008. Tobias J. Moskowitz and Annette Vissing-Jorgensen, ‘‘The Private Equity Premium Puzzle,’’ Working paper, November 2000. Turan G. Bali and Nusret Cakici, ‘‘Idiosyncratic Volatility and the Cross-Section of Expected Returns,’’ Working paper, July 2006. Dean Diavatopoulos, James S. Doran, and David R. Peterson, ‘‘Implied Idiosyncratic Volatility and the Cross-Section of Stock Returns,’’ Working paper, April 8, 2007. Aswath Damodaran, Damodaran on Valuation, 2nd ed. (New York: John Wiley & Sons, 2006): 58–59.
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Cost of Capital
Total Cost of Equity ¼ 6% þ 3:30 ð5:0%Þ ¼ 22:5% ðnot CAPM 11:5%Þ: Total beta includes any risk premium for company size and company-specific risk premium inherent in the guideline public companies used in the analysis. DOWNSIDE RISK Conduct a survey of the ‘‘man on the street’’ and the common concept of risk is loss below some threshold. Several concepts of risk emerge:
Downside frequency. How often investment is likely to fall below threshold over specified time horizon
Average downside. Average shortfall when returns fall below threshold Semivariance. Variance on downside—combination of downside frequency and average downside35
If the distribution of security returns is not normally distributed, is the market measuring downside risk instead of equally weighting upside and downside risk? Two researchers compared the mean-variance (MV) CAPM with regular beta as risk measure to mean-semivariance (MS) CAPM with downside beta as risk measure. Downside beta measures comovement of returns with the market portfolio in falling markets. They found that return distributions are not normal and, as a result, MV CAPM and MS CAPM give different results. They found that:
Downside betas for low-beta portfolios are greater than regular beta; regular beta understates risk of low-beta stocks.
Downside betas for high-beta portfolios are smaller than the regular beta; regular beta overstates risk of high-beta stocks.
They found that combining downside risk and time variation works best in explaining stock returns. Further they found:
The role of downside betas is more pronounced during ‘‘bad times’’ (periods of low stock prices and resulting high dividend yield for the market).
Investors fear negative stock returns during ‘‘bad times’’ most. Downside beta better explains observed returns during those times.
Even then they found a residual size effect not fully explained by MS CAPM. That is, returns on small-cap companies are not fully explained by MS CAPM downside beta. MS CAPM assumes perfect capital markets and ignores transaction costs and market liquidity—issues that affect returns of small-cap companies the most.36 More researchers are now finding empirical results implying that the market prices stocks based on their downside risk. For example, in another study, the authors found that stocks that covary with the market when the market declines have high average return, which is consistent with investors 35
36
Philip S. Fortuna ‘‘Old and New Perspectives on Equity Risk,’’ Practical Issues in Equity Analysis (CFA Institute AIMR) (February 2000): 37–45. Thierry Post and Pim vanVliet, ‘‘Conditional Downside Risk and the CAPM,’’ Working paper, June 2004.
Variations of CAPM Risk Measures Exhibit 11.2
171
Comparison of OLS Betas, Sum Betas, and Downside Betas Different for Industries Median Count
OLS Beta
Sum Beta
Downside Beta
Healthcare (SIC 80) All Companies Over $1 Billion* Under $200 Million*
117 23 48
0.69 0.30 0.74
1.19 0.70 1.29
1.14 0.77 1.33
Publishing (SIC 27) All Companies Over $1 Billion Under $200 Million
82 20 58
0.74 0.62 0.71
0.91 0.62 0.90
0.75 0.64 1.42
Petroleum & Natural Gas (SIC 1311) All Companies Over $1 Billion Under $200 Million
84 35 15
0.70 0.61 1.03
0.80 0.74 0.78
1.00 0.64 1.42
360 47 217
1.85 1.87 1.66
2.32 1.99 2.40
2.20 1.91 2.23
60 12 26
0.90 1.02 0.55
1.40 1.35 1.18
1.22 1.03 1.22
278 54 119
1.27 0.85 1.31
1.68 0.94 1.87
1.76 1.11 1.87
Computer Software (SIC 7372) All Companies Over $1 Billion Under $200 Million Auto Parts (SIC 3714) All Companies Over $1 Billion Under $200 Million Pharmaceutical (SIC 2834) All Companies Over $1 Billion Under $200 Million
*Market value of equity as of December, 2006. Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
placing greater weight on downside risk than on upside gains. Downside risk not simply measured by market beta. They found that pricing of downside risk is not subsumed by coskewness or liquidity risk either. They found that past downside beta is a good predictor of future covariation with down market movements.37 Exhibit 11.2 repeats the data from ordinary least squares (OLS) beta and sum beta from Exhibit 10.9 and adds downside beta estimates. Exhibit 11.2 compares OLS betas, sum betas, and downside betas for different industries. We show an example of calculating downside beta in Appendix 11A. Semi-variance is an alternative downside risk measure. It’s the ratio of semivariance of the individual security (variance on downside) to the semivariance of the market.38 VALUE AT RISK Value at risk (VaR) is a statistical measure of downside risk. VaR measures the largest percentage of the portfolio value that you might lose over a given time period, to a given degree of certainty, based 37 38
Andrew Ang, Joseph Chen, and Yuhang Xing, ‘‘Downside Risk,’’ Review of Economic Studies 19, no. 4 (2006): 1191–1139. Javier Estrada, ‘‘Downside Risk in Practice,’’ Journal of Applied Corporate Finance (Winter 2006): 117–125.
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Cost of Capital
on historical average return and variability. For example, for a given asset held over the next six months, you might be 95% sure that the asset value will fall by no more than 15%. Value at risk has become widely used since the 1994 introduction of the J.P. Morgan RiskMetrics1 system, which provides the data required to compute VaR for a variety of financial instruments. New Federal Reserve Board rules require banks to compute the VaR of all their assets, and this total firm-wide VaR determines the bank’s capital requirements. ADJUSTING BETA FOR RISK OF COMPANY SIZE AND COMPANY-SPECIFIC RISK Assume that you use the expanded CAPM (Formula 8.5) to estimate the cost of equity capital. You now need to estimate the effect of expanding the CAPM model in, say, an option pricing model. The effect of adding risk premiums for company size and specific company risk is equivalent to increasing the variability of returns, as risk is no longer measured by beta alone. We can adjust beta in this way to get an expanded beta or Be (beta adjusted from the expanded CAPM): (Formula 11.1) EðRÞ ¼ R f þ ðBL RPM Þ þ RPs þ RPu EðRÞ R f ¼ ðBL RPM Þ þ RPs þ RPu Be ¼
ðEðRÞ R f Þ RPs RPu RPM RPM RPM
where: E(R) ¼ Expected rate of return Rf ¼ Rate of return on a risk-free security BL ¼ Levered beta for (equity) capital RPm ¼ Risk premium for the ‘‘market’’ RPs ¼ Risk premium for ‘‘small’’ stocks RPu ¼ Risk premium for company-specific or unsystematic risk attributable to the specific company Be ¼ Expanded beta (equity) Expanded beta incorporates both the small-company risk and company-specific risk. Assuming that any further traditional nondiversified risk is small, we can then derive variance of returns for use in option pricing models as follows: s 2 ¼ B2L s 2M þ s 2e Substituting expanded beta Be for B and assuming s 2e is close to zero, we get: s 2 ¼ Be s 2M where: s2 ¼ Variance of returns for subject company stock BL ¼ Levered beta (equity) s 2M ¼ Variance of the returns on the market portfolio (e.g., S&P 500) s 2e ¼ Variance of error terms Be ¼ Expanded beta (equity) s2 takes into account the entirety of the effect of all risk factors used in the expanded CAPM.
Duration
173
DURATION Is the length of time one expects to receive cash flows a good risk measure? That is, if one expects cash flows in early years, is that a less risky company or project than one where expected cash flows do not develop until years later? Researches have developed a measure of implied duration based on traditional measure of bond duration (see Chapter 6). They project future cash distributions for common equity using simple forecasting models based on historical financial data for 10 years and spreading the remaining market value implicit in observed stock price as a level perpetuity thereafter. They find:
Stock return volatility and betas are both increasing as equity duration increases. Book value-to-market value factor may be interpreted as a noisy duration factor. Stocks categorized as value stocks generally have shorter equity duration than stocks categorized as value stocks.39
But duration can be combined with the more commonly used risk measure variability to better quantify uncertainty as to both the amounts and the timing of expected economic income. Further, investors may not have the same risk tolerance. This does not mean that one should not measure the risk of the investment in determining the cost of equity capital. It simply means that there are different pools of investors with different risk tolerances; one pool may prefer longer term investments with greater absolute risk and another pool may prefer shorter term investments with lesser absolute risk. This is consistent with the so-called ‘‘clientele’’ explanation of investing; investments with different risks attract a different clientele of investors. It may be appropriate to think in terms of measuring the cost of equity capital in terms of the clientele attracted to investments with certain risk characteristics. Assuming that investment returns each future year are approximately normally distributed, the standard deviation of the expected value of the investment increases as the duration of the net cash flows increase, but the per-annum risk of the investment decreases because the marginal risk of an investment declines as a function of the square root of time. Risk, as measured by standard deviation, increases at a declining rate over time. For example, assume that a project with an initial investment of $100 (time ¼ zero to N). Assume that the present value of future net cash flows increase over time such that measuring the net present value of cash flows at the end of the first year (time ¼ 1 to N) equals $120. That is, the value of the investment increased $20. Assume that the standard deviation of the present value equals $10. That is, there is an approximate 2/3 chance that the present value of net cash flows from time ¼ 1 to N will be between $110 and $130. Assume that the value is expected to increase by $20 measured each year in the future (e.g., the value of net cash flows measured from the end of year 2 ¼ $140) and the standard deviation of that expected present value is $10. At the end of 5 years, the expected value is $200 (¼ $100 þ 5 years $20) with a standard deviation of $22.36 (¼ $10 H5). The normalized per-annum risk of the investment equals $4.47 (¼ $22.36/5 years). At the end of 25 years, the expected value of the investment is $600 (¼ $100 ¼ 25 years $20) with a standard deviation of $50 (¼ $10 H25). But the normalized per annum risk of the investment has decreased to $2 (¼ $50/25 years). The risk premium (i.e., cost of equity capital measured as the rate of return per annum) should be less for the longer-term investment compared to the shorter-term investment. 39
Patricia M. Dechow, Richard G. Sloan, and Mark T. Soliman, ‘‘Implied Equity Duration: A New Measure of Equity Risk,’’ Review of Accounting Studies (June 2004): 197–228.
174
Cost of Capital
If one assumes that there is a pool of investors with short-term investment horizons, those investors will likely invest in short-term investments (short duration) with low absolute risk. On the other hand, the pool of investors with long-term investment horizons may be attracted to longer-term investments with greater absolute risk but lower per annum risk; investors with longer-term investment horizons have an increased appetite for risk (as measured only by variance) knowing that over time the annualized variance is less. One study looks at the types of industries that are populated by companies owned by investors with generally shorter-term investment horizons (firms controlled by short-term institutional investors with ‘‘professional’’ management) and compares industry characteristics with the types of industries that are populated by companies controlled and managed by founding families (so-called ‘‘family firms) that attract long-term institutional investors.40 The authors find that as the cyclical nature of industries increases, the greater percentage of companies in the industry that are family firms also increases. Such firms can invest in (and create value from investing in) longer-term projects with lower per-annum returns because the appropriate cost of capital (measured as return per annum) is less. On the other hand, firms with short-term oriented investors and management can only invest in projects with higher per annum returns because the appropriate cost of capital (measured as return per annum) is greater.
YIELD SPREADS Can you use a company’s bond rating and the yield spread among bond ratings to directly estimate a company’s cost of equity capital? A company’s bond rating reflects its size and company-specific risk. In one study, the authors constructed an ex ante measure of expected equity return based on data from bond yield spreads (after adjusting bond yields for default risk, ratings transition risk, and tax spreads [differences in yields due to taxation of interest] between corporate bonds and U.S. government bonds). Their approach is based on the premise that providers of both debt capital and equity capital have contingent claims on the same set of assets; therefore, they must share the same risk factors that govern covariance between the underlying firm’s business risk (asset risk) and the economy. They found that beta plays a significant role in explaining variation in expected returns among firms (even after controlling for size and book-value-to-market-value ratio) and that the yield spread is highly correlated with systematic risk. They also found the company size premium statistically significant.41
FUNDAMENTAL RISK The Duff & Phelps Risk Study is discussed in Chapter 14. That research correlates realized equity returns (and historical realized risk premiums) directly with measures of company risk derived from accounting information. The measures of company risk derived from accounting information may also be called ‘‘fundamental’’ or ‘‘accounting’’ measures of company risk to distinguish these risk measures from a stock market-based measure of equity risk such as beta. 40
41
Thomas Zellweger, ‘‘Time Horizon, Costs of Equity Capital, and Generic Investment Strategies of Firms,’’ Family Business Review 20 No.1 (March 2007): 1–15. Murillo Campello, Long Chen, and Lu Zhang, ‘‘Expected Returns, Yield Spreads, and Asset Pricing Tests,’’ Working paper, January 2004.
Summary
175
The Risk Study examines three separate measures of risk: 1. Operating margin (the lower the operating margin, the greater the risk) 2. Coefficient of variation in operating margin (the greater the coefficient of variation, the greater the risk) 3. Coefficient of variation in return on equity (the greater the coefficient of variation, the greater the risk) Other authors also study fundamental risk. For example, in one recent study, the authors identified four cash-flow-related factors for explaining returns: earnings yield, capital investment, changes in profitability, and growth opportunities. The cash-flow-related factors plus any change in the discount rate form a full set of information associated with returns. Their model explains approximately 17% of variation in annual stock returns with earnings yield and changes in profitability being the most important factors and the change in the discount rate over time the least important factor.42 In another study, the authors derived a simplified covariance risk adjustment based on accounting variables. They use covariance of excess firm return on equity (ROE) (residual or abnormal earnings is equal to income minus a charge for the use of capital measured by the beginning book value times the cost of capital) with market excess ROE (developing a fundamental or accounting beta) and ROE of company size as measured by market capitalization and book-value-to-market-value factors as accounting-based risk measures to estimate the covariance risk of the firm. They find that valuation errors are reduced (i.e., expected returns are more accurately measured) compared to CAPM and FF 3-factor models.43
SUMMARY The conclusion that can be reached by studying the research reviewed in this chapter is that textbook CAPM and its sole risk measure, beta, while theoretically appealing and useful tools for understanding risk, are not reliable measures alone for measuring the cost of equity capital for many firms. This fact has caused academics and practitioners alike to look beyond the textbook CAPM. As the authors of one paper stated: While the CAPM ‘‘has been the model on which most finance theory and practice was built . . . tests of CAPM by F-F (1992) revealed that the model is no longer able to explain the cross-section of asset returns.’’44
Accurately measuring risk is the subject of continued research. We conclude that beta does not fully measure the risk of most securities, especially securities of smaller companies. We recommend that analysts use other risk measures beyond just beta, particularly for smaller companies. We recommend that the analyst use multiple estimates of risk (for example, OLS beta, sum beta, downside beta), compare the results and use judgment to decide on which estimate best represents the risk of the subject company. Mechanical use of beta estimates from a published service often leads to erroneous estimates of the cost of equity capital. 42
43
44
Peter F. Chen and Guochang Zhang, ‘‘How Do Accounting Variables Explain Stock Price Movements? Theory and Evidence,’’ Working paper, June 2006. Alexander Nekrasov and Pervin K. Shroff, ‘‘Fundamentals-Based Risk Measurements in Valuation,’’ Working paper, January 2007. Qing Li, Maria Vassalou, and Yuhang Xing, ‘‘An Investment-Growth Asset Pricing Model,’’ AFA 2002 Atlanta Meetings, March 7, 2001.
Appendix 11A
Example of Computing Downside Beta Estimates David Ptashne, CFA Introduction Computing Downside Beta Estimates
INTRODUCTION This appendix is a continuation of Appendix 10B, which presents examples of how to calculate historical returns, ordinary least squares (OLS) beta, and sum beta. Here we present an example of how to compute downside beta for a guideline public company. Similar to OLS beta and sum beta, this guideline public company downside beta estimate can be used as a proxy beta estimate for a division, reporting unit, or closely held company.
COMPUTING DOWNSIDE BETA ESTIMATES Estimating downside beta for a public company (subject company) as of a specific date (subject date) can be performed in the general steps shown using Microsoft Excel and common market data that can be obtained from industry data providers, such as Standard and Poor’s (S&P) Compustat or Capital IQ. For purposes of this example, we have assumed that the downside beta estimate will be based on 12 months of observed returns, which is computed using 13 observations of historical monthly data (as discussed in Appendix 10B). Note that a 12-month look-back period was chosen for purposes of this example only. Ordinarily, we recommend computing this risk measure using a longer period, such as a 60-month look-back period, which would require 61 months of historical data. In this example, the subject company is J.B. Hunt Transport Services, Inc. (J.B. Hunt) and the subject market benchmark is the S&P 500 Index. Exhibit 11A.1 presents historical returns for our subject company over the look-back period. For more detail regarding the computation of historical returns, see Appendix 10B.2. The next example presents the computation of the downside beta with respect to the average total return over the look-back period. This downside beta can be computed as shown:1
We wish to thank Nick Arens for his assistance in preparing these examples. These steps assume the use of Microsoft Excel. Also note that specific formulas entered into Excel to recreate this example might be slightly different depending on where on your worksheet you place historical return data.
1
176
Computing Downside Beta Estimates Exhibit 11A.1
177
Example of Return Data for J.B. Hunt Transport Service Inc. and S&P 500 Subject Company Return Data A Closing Price
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Dec05 Nov05 Oct05 Sep05 Aug05 Jul05 Jun05 May05 Apr05 Mar05 Feb05 Jan05 Dec04 Nov04 Oct04
22.640 22.390 19.410 19.010 18.070 19.630 19.230 20.080 19.545 21.885 23.595 22.060 22.425 20.100 20.430
B Dividends/ Share 0.060
0.060
0.060
0.060 0.015
Market Index Return Data
C Total Return
D S&P500 Index
E S&P500 Dividends
1.12% 15.66% 2.10% 5.20% 7.95% 2.39% 4.23% 2.74% 10.42% 7.25% 6.96% 1.36% 11.57% 1.54% 10.02%
1,248.29 1,249.48 1,207.01 1,228.81 1,220.33 1,234.18 1,191.33 1,191.50 1,156.85 1,180.59 1,203.60 1,181.27 1,211.92 1,173.82 1,130.20
1.64 3.14 1.30 1.40 2.60 1.43 1.88 2.13 1.36 1.72 2.52 1.11 1.83 2.10 1.41
F Index Return
G Lagged Return
H Lead Return
0.04% 3.78% 1.67% 0.81% 0.91% 3.72% 0.14% 3.18% 1.90% 1.77% 2.10% 2.44% 3.40% 4.04% 1.53%
3.78% 1.67% 0.81% 0.91% 3.72% 0.14% 3.18% 1.90% 1.77% 2.10% 2.44% 3.40% 4.04% 1.53% 1.08%
0.04% 3.78% 1.67% 0.81% 0.91% 3.72% 0.14% 3.18% 1.90% 1.77% 2.10% 2.44% 3.40% 4.04%
Note: Total return ¼ (this month’s price þ current dividend)/(last month’s price)1; use price only if no dividend information available. Index return ¼ (this month’s price þ current dividend)/(last month’s price)1. Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
Step 1. Compute the average return for the subject company over the look-back period. In this case, the formula is ‘¼Average(C0:C-11)’. Let us call the cell that contains the subject company’s average return value ‘‘XX’’ for purposes of this example. Step 2. Compute the average return for the benchmark index over the look-back period. In this case, the formula is ‘¼Average(F0:F-11)’. Let us call the cell that contains the benchmark index’s average return value ‘‘YY’’ for purposes of this example. Step 3. In a separate cell in Excel, input ‘¼Linest(If(C0:C-11<XX, C0:C-11-XX,0),If(F0:F11
Chapter 12
Size Effect
Introduction Morningstar Studies Using Morningstar Data in the Build-up Method Using Morningstar Data in the CAPM Method Duff & Phelps Studies What Is Size? Description of the Data Using the Duff & Phelps Size Study in the Build-up Method Using the Duff & Phelps Size Study in the CAPM Method Summary
INTRODUCTION In the chapters on the build-up and the Capital Asset Pricing Model (CAPM) cost of equity capital models we have made reference to the ‘‘size effect,’’ based on the empirical observations that smaller size is associated with greater risk and, therefore, higher cost of capital. While the size effect is a factor in other cost of capital methods—for example, the Fama-French 3-factor method (see Chapter 15)—in this chapter we discuss evidence of the size effect and its measurement in the context of the build-up and CAPM methods. The size effect is not without controversy. Here we first examine studies that quantify the existence of the size effect. In Chapter 13 we examine the criticisms of the size effect. The evidence that the size effect is a correction to the cost of capital models is mostly applicable for smaller companies. To help measure the size effect in terms of its impact on cost of equity capital, this chapter presents empirical data from two independent sets of studies: Morningstar studies and Duff & Phelps studies. Both of these sets of studies use rate of return data developed at the University of Chicago Center for Research in Security Prices (CRSP) and document the empirical evidence that smaller firms have greater risk-adjusted equity returns than large firms.1
MORNINGSTAR STUDIES Morningstar, Inc., breaks down New York Stock Exchange (NYSE) stock returns into deciles by size, as measured by the aggregate market value of common equity, and adds the returns on American Stock Exchange (AMEX) stocks and returns of NASDAQ stocks that fall into the respective size 1
We have included in this chapter exhibits drawn from the SBBI Valuation Edition 2006 Yearbook and the Duff & Phelps Risk Premium Report 2006, both of which report data through 2005. Other data presented herein also is displayed through 2005 for comparison purposes.
179
180 Exhibit 12.1
Cost of Capital Returns in Excess of CAPM with S&P 500 Benchmark
Term Returns in Excess of CAPM Estimation for Decile Portfolios of the NYSE/AMEX/NASDAQ, 1926–2005
Decile
Beta*
1-Largest 2 3 4 5 6 7 8 9 10-Smallest Mid-Cap, 3–5 Low-Cap, 6–8 Micro-Cap, 9–10
0.91 1.04 1.10 1.13 1.16 1.18 1.23 1.28 1.34 1.41 1.12 1.22 1.36
Arithmetic Mean Return 11.29% 13.22% 13.84% 14.31% 14.91% 15.33% 15.62% 16.60% 17.48% 21.59% 14.15% 15.66% 18.77%
Realized Return in Excess of Riskless Ratey
Estimated Return in Excess of Riskless Ratez
Size Premium (Return in Excess of CAPM)
6.07% 8.00% 8.62% 9.09% 9.69% 10.11% 10.40% 11.38% 12.26% 16.37% 8.94% 10.44% 13.55%
6.45% 7.33% 7.77% 7.98% 8.20% 8.38% 8.73% 9.05% 9.50% 10.01% 7.91% 8.63% 9.61%
0.37% 0.67% 0.85% 1.10% 1.49% 1.73% 1.67% 2.33% 2.76% 6.36% 1.02% 1.81% 3.95%
*Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 total returns in excess of the 30-day U.S. Treasury bill, January 1926-December 2005. y Historical riskless rate is measured by the 80-year arithmetic mean income return component of 20-year government bonds (5.22 percent). z Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 (12.30 percent) minus the arithmetic mean income return component of 20-year government bonds (5.22 percent) from 1926–2005. Source: Stocks, Bonds, Bills, and Inflation1 Valuation Edition 2006 Yearbook. Copyright # 2006 Morningstar, Inc. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) To purchase copies of the Valuation Edition Yearbook, or for more information on other Morningstar publications, please visit global.morningstar.com/DataPublications. Calculated (or derived) based on CRSP1 data, #2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago.
deciles as computed based on the NYSE. The excess returns over the basic realized return for the market increase dramatically with decreasing size, as shown in Exhibit 12.1. This excess return is especially noticeable for the smallest 10% of the companies. Exhibit 12.2 shows the market capitalization by value of company equity of the largest company in each of the respective decile groups as of September 30, 2005. Morningstar also reports the results of changing the benchmark used to calculate the market portfolio from the Standard & Poor’s (S&P) 500 stock index to the NYSE total value weighted index. Those results also support the relationship between size and realized return. Morningstar examined alternative methods of calculating beta. For example, Morningstar calculates betas based on excess annual returns. This method helps correct for certain problems associated with monthly data for smaller companies when using more common methods of estimating beta. The ‘‘annual’’ betas are greater for smaller companies than the betas derived using a monthly frequency of data. Exhibit 12.3 displays the same analysis as Exhibit 12.1 except that annual betas are used. The annual betas are similar to betas calculated by Morningstar using the ‘‘sum beta’’ method. The sum beta method is an alternative way of handling monthly data. This method can provide a better measure of beta for small stocks by taking into account the lagged price reaction of stocks of small companies to movements in the stock market. The data indicates that even using the sum beta method, when applied to the CAPM, does not account for the returns in excess of the risk-free rate historically found in small stocks. Notice that the size premium is smaller using annual betas (4.69%)
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181
Exhibit 12.2 Size-Decile Portfolios of the NYSE/AMEX/NASDAQ, Largest Company and Its Market Capitalization by Decile Decile
Market Capitalization of Largest Company (in thousands)
Company Name
$367,495,144 16,016,450 7,187,244 3,961,425 2,519,280 1,728,888 1,280,966 872,103 596,393 264,981
General Electric Co. Entergy Corp. Chesapeake Energy Ball Corp. Celenese Corp. AGCO Corp. ESCO Technologies inc. West Pharmaceutical Services, Inc. General Cable Corp. 4 Kids Entertainment
1-Largest 2 3 4 5 6 7 8 9 10-Smallest
Source: Stocks, Bonds, Bills, and Inflation1 Valuation Edition 2006 Yearbook. Copyright # 2006 Morningstar, Inc. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) To purchase copies of the Valuation Edition Yearbook, or for more information on other Morningstar publications, please visit global.morningstar.com/DataPublications. Calculated (or derived) based on CRSP1 data, # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago.
Exhibit 12.3 Returns in Excess of CAPM with S&P 500 Benchmark Long-Term Returns in Excess of CAPM Estimation for Decile Portfolios of the NYSE/AMEX/NASDAQ, with Annual Beta, 1926–2005
Decile 1-Largest 2 3 4 5 6 7 8 9 10-Smallest Mid-Cap, 3–5 Low-Cap, 6–8 Micro-Cap, 9–10
Annual Beta*
Arithmetic Mean Return
Realized Return in Excess of Riskless Ratey
0.94 1.04 1.08 1.17 1.20 1.20 1.30 1.37 1.46 1.65 1.13 1.27 1.51
11.29% 13.22% 13.84% 14.31% 14.91% 15.33% 15.62% 16.60% 17.48% 21.59% 14.15% 15.66% 18.77%
6.07% 8.00% 8.62% 9.09% 9.69% 10.11% 10.40% 11.38% 12.26% 16.37% 8.94% 10.44% 13.55%
Estimated Return in Excess of Riskless Ratez
Size Premium (Return in Excess of CAPM)
6.65% 7.38% 7.68% 8.27% 8.51% 8.51% 9.21% 9.67% 10.31% 11.69% 8.01% 8.98% 10.72%
0.58% 0.62% 0.94% 0.82% 1.19% 1.60% 1.19% 1.71% 1.95% 4.69% 0.93% 1.46% 2.83%
*Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 total returns in excess of the 30-day U.S. Treasury bill, January 1926–December 2005. y Historical riskless rate is measured by the 80-year arithmetic mean income return component of 20-year government bonds (5.22 %). z Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 (12.30 %) minus the arithmetic mean income return component of 20-year government bonds (5.22 %) from 1926 to 2005. Source: Stocks, Bonds, Bills, and Inflation1 Valuation Edition 2006 Yearbook. Copyright # 2006 Morningstar, Inc. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) To purchase copies of the Valuation Edition Yearbook, or for more information on other Morningstar publications, please visit global.morningstar.com/DataPublications. Calculated (or derived) based on CRSP1 data, # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago.
182
Cost of Capital
than monthly betas (6.36%); we discuss this more fully later when we explore controversies surrounding the size premium. More recently, Morningstar has divided the tenth decile into 10a and 10b, with 10a being the top half of the decile and 10b being the bottom half of the decile (measured by market capitalization). We present and discuss that data and explore the difficulties of using market value to measure size and the problems with 10b later in this chapter. From 1926 through 1981, Morningstar’s ‘‘small-stock’’ group was composed of stocks making up the fifth quintile (i.e., ninth and tenth deciles) of the NYSE, ranked by capitalization (price times number of shares outstanding). From 1982 forward, the small-stock return series has been the total return achieved by the Dimensional Fund Advisors (DFA) Small Company 9/10 (for ninth and tenth deciles) Fund. The fund is a market-value-weighted index of the ninth and tenth deciles of the NYSE, plus stocks listed on the AMEX and NASDAQ with the same or less capitalization than the upper bound of the NYSE ninth decile. The Morningstar data in the Stocks, Bonds, Bills, and Inflation (SBBI) Valuation Edition Yearbook show, for all size categories, both total realized returns in excess of the risk-free rate and the size effect over and above CAPM (the latter having already accounted for beta, which tends to be higher for smaller stocks), so the data can be used either with a build-up method or with a CAPM method. They also show the average arithmetic mean return for each size category and the arithmetic average return on the S&P 500 Index. USING MORNINGSTAR DATA IN THE BUILD-UP METHOD You can use the data to derive a ‘‘small-company premium’’ by subtracting the difference between the realized returns on small-company stocks and large-company stocks for use in the build-up method (a procedure that Morningstar use to suggest). This small-company premium is not beta adjusted. Exhibit 12.4 displays the small stock premium, RPs, using data from 1926 to 2005 for the 10 deciles. The data can be used to estimate RPs in the build-up model, Formula 12.1, which is the same as Formula 7.1. Exhibit 12.4 Small-Company Premium Based on CRSP Decile Long-term Total Returns for Decile Portfolios at NYSE/AMEX/NASDAQ, 12/1926–12/2005 Decile Total Returns for 80 Periods 1-Largest 2 3 4 5 6 7 8 9 10-Smallest S&P 500 CRSP NYSE Deciles 1–10
Geometric Mean (%)
Arithmetic Mean (%)
Standard Deviation (%)
9.52 10.95 11.31 11.31 11.65 11.75 11.62 11.80 12.03 13.96 10.36 10.19
11.29 13.22 13.84 14.31 14.91 15.33 15.63 16.59 17.49 21.60 12.30 12.05
19.17 21.86 23.66 25.95 26.78 27.84 29.98 33.48 36.54 45.44 20.20 19.71
SmallCompany Premium
Arithmetic Mean/ Standard Dev.
1.01 0.92 1.54 2.01 2.61 3.03 3.32 4.29 5.19 9.30
0.589 0.605 0.585 0.552 0.557 0.551 0.521 0.496 0.479 0.475
Source: Compiled from CRSP1 data. Copyright # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
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183
(Formula 12.1) EðRi Þ ¼ R f þ RPm þ RPs þ RPu For example, if the subject company had a market capitalization that ranked it in the eighth decile, RPs ¼ 4.3% (rounded). In the build-up method, Morningstar now recommends starting with the return in excess of the return predicted by CAPM (‘‘size premium’’) and then adding (or subtracting) an industry adjustment (which Morningstar’s SBBI Valuation Edition Yearbook presents for about 450 Standard Industrial Classification [SIC] codes) instead of using a small-company premium (non–beta adjusted). However, not all practitioners have endorsed this procedure. This quote from Michael Mattson is typical of the dissenting opinions: I am not in total agreement with [Morningstar]’s contention that the only size premium to use is the one that is ‘‘beta adjusted.’’ The problem in the build-up approach is that we have no place for a beta, so the aspect of size that is captured by a higher beta—an additional 0.4 over the market beta of 1.0 for 10th decile stocks—is not captured anywhere. Using the full size premium, as opposed to the beta-adjusted one, assumes that the small company being valued has similar risk characteristics to the average 10th decile company—this may not be such a bad assumption for many of the smallest companies we value. Assuming that 10th decile companies are not in riskier industries than companies in the other size groupings, then their higher beta is due primarily to their size and the size effect is in both the beta and the premium over the CAPM line.2
Further, consistent with the discussion on the equity risk premium (Chapter 9), the arithmetic average realized small-company premium is simply an estimate of what might be expected in the future. Again, as in the discussion of the equity risk premium, you must choose the appropriate period to include in the sample years, and the sample years should represent current expectations of investors. If we examine the data in Exhibit 12.4 for the tenth decile, we see that the standard deviation of returns is (approximately) 45% and the small-company premium is 9.3% (for period 1926 to 2005). But looking at a shorter period, say the last 50 years in Exhibit 12.5 (1956 to 2005), we see that the standard deviation of returns for the tenth decile is (approximately) 32% and the small-company premium is only 5.4%. The arithmetic average realized return and the standard deviation of realized returns for the tenth decile and the derived small-company premiums for varying periods are displayed in Exhibit 12.6. As in the case of the discussion on the equity risk premium, the realized returns from periods before the mid-1950s appear to bias upward the results of using any average for the entire post1925 period. The standard deviations of small-stock returns in recent periods are consistently smaller than they were in the earlier period. These results point to the conclusion that a realistic, current small-company premium is in the range of 2% to 6%, and not 9%, for companies that would fall in the tenth decile where size is measured by market capitalization. This conclusion parallels the earlier conclusion that using realized risk premiums for the entire post-1925 period as an estimate of the current equity risk premium results in an unrealistically high result relative to current expectations.
2
Shannon P. Pratt, Cost of Capital: Estimation and Applications, 2nd ed. (New York: John Wiley & Sons, 2002), 93.
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Cost of Capital
Exhibit 12.5 Small-Company Premium Based on CRSP Decile Long-term Total Returns for Decile Portfolios at NYSE/AMEX/Nasdaq: 12/1956–12/2005 Decile Total Returns For 50 Periods 1-Largest 2 3 4 5 6 7 8 9 10-Smallest S&P 500 CRSP NYSE Deciles 1–10
Geometric Mean (%)
Arithmetic Mean (%)
Standard Deviation (%)
Small-Company Premium
Arithmetic Mean/Standard Dev.
9.80 11.46 12.43 12.34 12.18 12.84 12.46 13.18 12.42 12.96 10.44
11.12 12.81 13.89 14.19 14.18 15.14 15.07 16.16 15.72 17.15 11.72
16.91 17.28 18.70 20.45 21.24 22.75 24.30 26.42 27.83 32.11 16.70
0.60 1.09 2.26 2.47 2.46 3.42 3.35 4.44 4.00 5.43
0.658 0.741 0.748 0.694 0.667 0.666 0.620 0.612 0.565 0.534
10.76
11.97
16.23
Source: Compiled from CRSP1 data. Copyright # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
USING MORNINGSTAR DATA IN THE CAPM METHOD In using the data with a CAPM model, you would use the size premium over the CAPM-indicated equity risk premium, recognizing that the beta has captured some of the size effect. The size premium is also called the beta-adjusted size premium. The size premium is an empirically observed correction to the CAPM. For the CAPM, there would be no further adjustment (except for a possible company-specific adjustment), because beta presumably would reflect any industry effects. We get Formula 12.2, which is the same as Formula 8.5: (Formula 12.2) EðRi Þ ¼ R f þ BðRPm Þ þ RPs þ RPu
Exhibit 12.6 Small-Company Premium Based on CRSP Decile Long-term Total Returns for the TenthDecile Portfolios at NYSE/AMEX/NASDAQ for Various Time Periods Period 1986–2005 1976–2005 1966–2005 1956–2005 1926–2005
Years
Arithmetic Mean(%)
Standard Deviation (%)
Small Stock Premium
Arithmetic Mean/Standard Dev.
20 30 40 50 80
15.32 18.85 17.61 17.15 21.60
27.30 25.28 33.46 32.11 45.44
2.16 5.02 6.00 5.43 9.30
0.561 0.745 0.526 0.534 0.475
Source: Compiled from CRSP1 data. Copyright # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
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185
Using the data in Exhibit 12.1 or Exhibit 12.3, and assuming that the subject company was ranked in the eighth decile by market capitalization, we would get: RPs ¼ 2:3% ðfrom Exhibit 12:1; roundedÞ or RPs ¼ 1:7% ðfrom Exhibit 12:3; roundedÞ As we discussed, in the build-up method the applicable procedure is less clear-cut. But Morningstar now recommends starting with the return in excess of CAPM for both the build-up and CAPM methods. Do you adjust the Morningstar size premium data if you estimate the equity risk premium to be smaller than the realized risk premium using data from 1926 through the most recent year? For example, assume your valuation date is December 31, 2005, and you conclude that the most reasonable estimate of the ERP is less than the arithmetic average of the realized risk premiums for the period 1926 to 2005; 7.08% (total return on the S&P 500 (12.30%) minus income return component on long-term government bonds (5.22%)).3 You conclude that those realized risk premiums were influenced by economic factors not expected to reoccur (e.g., decrease in the cost of equity over time as income tax rates decreased) and the arithmetic average is too high an estimate of the current ERP. Based on that analysis, you decide to use the estimate of the ERP equal to Morningstar’s ‘‘supplyside’’ estimate (6.28% arithmetic average for the period 1926 to 2005) as your estimated ERP.4 You multiply the ERP by beta and then add the size premium. One commentator has suggested that in such an example, the Morningstar size premiums (premiums in excess of that predicted by the CAPM) should be increased by the difference between the historical realized risk premium and the supply-side risk premium (7.08% minus 6.28% in this example). This is not correct. If you believe that economic factors not expected to reoccur caused the returns on the broad market to be higher than you would have expected, then the returns of stocks comprising all deciles were likely influenced by the same factors. Further discussion of the use of the Morningstar small-stock data is included in Chapter 19.
DUFF & PHELPS STUDIES Beginning in 1990, Roger Grabowski began closely studying the returns by size of companies as reported in the SBBI Yearbooks. He was interested in understanding whether the stock market recognized the differences in risk of different size companies where size was measured by alternative accounting or fundamental measures instead of only by market price of the company stock (as it is in the SBBI Yearbooks for the 10 deciles). Grabowski, working with his then colleague, David King, engaged CRSP to build a database combining stock prices, number of shares, and dividend data by company from the CRSP database with accounting and other data from the Standard & Poor’s Compustat database and designed software to analyze the data. Thereafter, they published a series of articles reporting their findings.5 The Duff & Phelps Risk Premium Report Size Study annually updates this research.6 3
4 5
6
Arithmetic average of realized risk premiums for 80 years (1926–2005). SBBI Valuation Edition 2006 Yearbook (Chicago: Morningstar, 2006), 98. ‘‘Supply-side’’ equity risk premium (arithmetic average) (1926–2005), Table 5–6, ibid. Mr. King, CFA, is National Technical Director of Valuation Services at Mesirow Financial Consulting, LLC. The research began when both Mr. Grabowski and Mr. King were at Price Waterhouse, predecessor firm to PricewaterhouseCoopers. This section is adapted from the Duff & Phelps Risk Premium Report 2006. Used with permission. The Risk Premium Report was published as the Standard & Poor’s Corporate Value Consulting Risk Premium Report for reports from 2002 to 2004 and as the PricewaterhouseCoopers Risk Premium Reports and Price Waterhouse Risk Premium Reports for years before 2002.
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Cost of Capital
WHAT IS SIZE? Traditionally, researchers have used market value of equity as a measure of ‘‘size’’ in conducting historical rate of return research. For instance, this is the basis of the ‘‘small-company’’ return series published in the SBBI Yearbooks. But there are various reasons for seeking alternative measures of size. First, it has been pointed out in the financial literature that researchers may unwittingly introduce a bias when ranking companies by ‘‘market value.’’7 Market value of a company’s equity is not just a function of ‘‘size’’; it is also a function of the discount rate. Therefore, some companies will not be risky (high discount rate) because they are small, but instead will be ‘‘small’’ (low market value) because they are risky. Choosing a measure of size other than market value of equity helps isolate the effects that are purely due to small size. Also, the market value of equity is an imperfect measure of the size of a company’s operations. Companies with large sales or operating income may have a small market value of equity if they are highly leveraged. The use of fundamental accounting measures (such as assets or net income) may have the practical applied benefit of removing the need to make a guesstimate of size when determining a discount rate. For example, such data might eliminate certain circularities that may arise in applying size-based adjustments (where size is measured by market value of equity and you need to know size to choose the adjustment) to a discount rate for determining the market value of a nonpublic business. Because Grabowski and King were interested in understanding how the stock market prices the risk of established companies based on their size, the Duff & Phelps studies are limited to companies with a track record of profitable performance. They use eight alternate measures of company size, including fundamental accounting characteristics such as sales and book value. The data show a clear inverse relationship between size and historical rates of return and realized premiums.
DESCRIPTION OF THE DATA The Duff & Phelps studies make use of the CRSP database together with Standard & Poor’s Compustat database. This causes the population of companies considered to be limited to firms that are covered by both databases. The Duff & Phelps studies exclude American Depository Receipts (ADRs), nonoperating holding companies, and financial services companies (Standard Industrial Classification [SIC] code ¼ 6).8 The Compustat database was established in 1963. The Duff & Phelps studies report historical returns for the period 1963 through the current year-end.9 For each year covered, Grabowski and King consider only financial data for the fiscal year ending no later than September of the previous year. For example, in allocating a company to a portfolio to calculate realized returns for calendar year 1995, they consider financial data through the latest fiscal year ending September 1994 or earlier (depending on when the company’s fiscal year ended). In this way they ensure that returns in any year are calculated for companies for which all information was 7 8
9
Jonathan B. Berk, ‘‘A Critique of Size Related Anomalies,’’ Review of Financial Studies 8, no. 2 (1995): 275–286. Some of the financial data used in the Duff & Phelps studies are difficult to apply to many companies in the financial sector (e.g., ‘‘sales’’ at a commercial bank), and financial institutions support a much higher ratio of debt to equity than is normal in other industries. Also, companies in the financial services sector were poorly represented during the early years of the Compustat database. Compustat data are available for some companies going back into the 1950s, but these earlier data consist only of back histories for companies that were added to Compustat in 1963 or later. Grabowski and King begin with 1963 data to avoid the obvious selection bias that would otherwise result.
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known before the year 1995 began. For example, companies included in 1963 are screened by looking at data for the latest fiscal year ending September 1962 (or earlier) and the prior four fiscal years; companies included for 1964 are screened looking at data for the latest fiscal year ending September 1963 (or earlier) and the prior four fiscal years; and so on. For each year since 1963, their universe of companies excludes companies lacking five years of publicly traded price history (i.e., companies with recent initial public offerings); companies with sales below $1 million in any of the previous five fiscal years (i.e., start-up companies); and companies with a negative five-year-average EBITDA (earnings before interest, taxes, depreciation, and amortization) for the previous five fiscal years (unprofitable companies). Companies that pass this test have been traded for several years, have been selling at least a minimal quantity of product, and have been able to achieve some degree of positive cash flow from operations. This screening was a response to the argument that the small-cap universe may consist of a disproportionate number of recent initial public offerings, high-technology companies, and start-up companies, and that these unseasoned companies may be inherently riskier than companies with a track record of viable performance. The number of companies eliminated by these criteria varies from year to year. Once the companies just described were eliminated, a separate portfolio for companies with any one of these characteristics was created for companies:
Identified by Compustat as in bankruptcy or in liquidation
With five-year-average net income available to common equity for the previous five years less than zero (either in absolute terms or as a percentage of the book value of common equity) With five-year-average operating income for the previous five years (defined as sales minus [cost of goods sold plus selling, general, and administrative expenses plus depreciation expense]) less than zero (either in absolute terms or as a percentage of net sales)
With negative book value of equity at any of the previous five fiscal year-ends With debt to total capital of more than 80% (with ‘‘debt’’ measured as preferred stock at carrying value plus long-term debt (including current portion) and notes payable in book value terms and total capital measured as book value of debt plus market value of equity
These companies were excluded from the base set of companies and placed in a separate portfolio called the high-financial-risk portfolio. Segregating such companies into a separate portfolio isolates the effects of high financial risk. Otherwise, the results might be biased for smaller companies to the extent that highly leveraged and financially distressed companies tend to have both high returns and low market values. It is possible to imagine financially distressed (or highly risky) companies that lack any of the listed characteristics. It is also easy to imagine companies that have one of these characteristics but that would not be considered financially distressed. The resulting high-financial-risk portfolio is composed largely of companies whose financial condition is significantly inferior to the average, financially ‘‘healthy’’ public company. We discuss using the high-financial-risk portfolio in Chapter 14. The exclusion of companies based on historical financial performance does not imply any unusual foresight on the part of investors in these portfolios. In forming portfolios to calculate returns for a given year, companies are excluded on the basis of performance during previous years (e.g., average net income for the five prior fiscal years) rather than current or future years. Grabowski/King chose to exclude or segregate certain types of companies on the basis of past financial performance in response to arguments that the inclusion of such companies might introduce
188
Cost of Capital
a bias in favor of the size effect to the extent that such companies tend to have low market values. A critic unfamiliar with this history might question whether we are introducing a bias by excluding such companies.10 Their procedures parallel procedures used in applying the guideline publicly traded company method of valuation. Assume you are valuing a profitable company. First you do a screen of all potential guideline companies, say by SIC code. Then you review the financial and operating data of the potential guideline companies and exclude those companies that may be unprofitable and so on. The financial data used in this screening include only the data that were known or knowable as of the valuation date (equivalent in this case to the beginning of the year for which the return is calculated). You then develop multiples for companies that best compare to the financial and operating data of the subject company. The screens used in the Duff & Phelps studies are similar to the screening you use in determining appropriate guideline companies. Ranking Companies by Size For the companies remaining in the data set, Grabowski and King form portfolios of securities based on relative size. Since NASDAQ and AMEX companies are generally small relative to NYSE companies, their addition to the data set produces portfolios that are more heavily populated by small-cap stocks. The portfolios are rebalanced annually; that is, the companies are reranked and sorted at the beginning of each year. Portfolio rates of return were calculated using an equal-weighted average of the companies in the portfolio (to understand the returns of the median company included in each portfolio). Correcting for ‘‘Delisting Bias’’ An article by Tyler Shumway provided evidence that the CRSP database omits delisting returns for a large number of companies.11 These returns are missing for the month in which a company is delisted from an exchange. Shumway collected data for a large number of companies that had been delisted for performance reasons (such as bankruptcy or insufficient capital). He found that investors incurred an average loss of about 30% after delisting. He further showed that delisting for nonperformance reasons (such as mergers or changes of exchange) tended to have a neutral impact in the month that the delisting occurred. Skeptics of the small-stock phenomenon often dismiss these results, holding that the returns of the small companies are biased high because that group of companies is most influenced by this overestimate of the realized returns. Grabowski and King incorporate the Shumway evidence into their rate of return calculations. In calculating rates of return, they impute a 30% loss in the month of delisting in all cases in which CRSP identified the reason for delisting as performance related and in all cases in which the reason for delisting was unknown. Eight Measures of Size, Twenty-Five Size Categories The Size Study presents average realized risk premiums for the period 1963 through the most recent year-end. As discussed in Chapter 9, a longer-run average realized risk premium often is used as an indicator of the expected equity risk premium of a typical investor. 10
11
Grabowski and King report that they ran alternative analyses in which no company was excluded or segregated on the basis of past history (i.e., using all available nonfinancial companies), and the results are similar to those reported in the Risk Premium Report. Tyler Shumway, ‘‘The Delisting Bias in CRSP Data,’’ Journal of Finance (March 1997): 327–340.
Duff & Phelps Studies
189
To calculate realized risk premiums, Grabowski and King first calculate an average rate of return for each portfolio over our sample period. Returns are based on dividend income plus capital appreciation and represent returns after corporate-level income taxes (but before owner-level taxes). Then they subtract the average income return earned on long-term U.S. government bonds over the same period (using SBBI data) to arrive at an average realized risk premium. The eight Size Study exhibits for use in the build-up model are: Measures of Equity Size 1. Market value of common equity 2. Book value of common equity 3. Five-year average net income before extraordinary items for previous five fiscal years Measures of Company Size 4. Market value of invested capital (MVIC) 5. Total assets (as reported on the balance sheet) 6. Five-year average EBITDA for the previous five fiscal years 7. Sales 8. Number of employees The exhibits of the Size Study include these statistics for each of 25 size categories:
Average of the size measure (e.g., average number of employees) for the latest year
Log (base-10) of the median of the size measure Number of companies in each portfolio in the latest year
Beta relative to the S&P 500 calculated using the sum beta method applied to monthly returns for 1963 through the latest year
Standard deviation of annual realized equity returns for each portfolio since 1963 Geometric average realized equity return for each portfolio since 1963
Arithmetic average realized equity return for each portfolio since 1963 Arithmetic average realized risk premium (realized equity return over long-term government bonds) since 1963 (labeled ‘‘arithmetic risk premium’’) ‘‘Smoothed’’ average realized risk premium (i.e., the fitted premium from a regression with the average realized risk premium as the dependent variable and the logarithm of the size measure as the independent variable) (labeled ‘‘smoothed average risk premium’’). Average carrying value of the sum of preferred stock plus long-term debt (including current portion) plus notes payable (‘‘debt’’) as a percent of MVIC since 1963 (labeled ‘‘average debt/MVIC’’)
The study presents the coefficients and other statistics from the regression analysis of the average realized risk premiums (the regression results in the smoothed average realized risk premiums). We have included two of their Size Study exhibits for use in the build-up method: Exhibit 12.7, in which size is measured by market value of common equity, and Exhibit 12.8, in which size is measured by book value of common equity (exhibits reproduced herein are for years ending 2005). Each of eight Size Study exhibits for use in the build-up method displays one line of data for each of the 25 size-ranked categories or portfolios, plus a separate line for the high-financial-risk portfolio.
96,796 26,818 14,912 10,930 8,014 5,996 4,872 3,745 3,185 2,758 2,441 2,121 1,845 1,588 1,382 1,117 1,025 870 736 626 541 436 326 225 76
Average Mkt Value ($mils.)
7.20%
17.67%
12.01%
21.73%
11.87% 12.13% 10.83% 12.84% 13.28% 14.19% 14.93% 14.34% 15.28% 14.52% 15.33% 15.07% 13.84% 16.08% 15.65% 17.56% 17.47% 16.88% 16.81% 17.80% 18.03% 17.64% 18.04% 19.37% 23.32%
Arithmetic Average Return
10.47%
4.81%
14.53%
4.67% 4.93% 3.63% 5.64% 6.08% 6.99% 7.73% 7.14% 8.08% 7.32% 8.13% 7.87% 6.64% 8.88% 8.45% 10.36% 10.27% 9.68% 9.61% 10.60% 10.83% 10.44% 10.84% 12.17% 16.12%
Arithmetic Risk Premium 2.35% 4.40% 5.33% 5.83% 6.32% 6.79% 7.12% 7.54% 7.80% 8.02% 8.22% 8.44% 8.67% 8.90% 9.13% 9.47% 9.60% 9.86% 10.13% 10.39% 10.62% 10.97% 11.43% 12.02% 13.74%
Smoothed Average Risk Premium
47.51%
16.24% 22.74% 24.97% 25.96% 26.92% 26.86% 27.51% 26.00% 25.31% 24.96% 24.98% 25.48% 26.50% 26.98% 26.56% 26.82% 26.46% 26.97% 26.36% 27.19% 27.29% 27.67% 28.04% 28.74% 30.99%
Average Debt/MVIC
Source: Compiled from data from the Center for Research in Security Prices. Source: # CRSP1, Center for Research in Security Prices. Graduate School of Business, The University of Chicago. Used with permission. All rights reserved. wwwcrsp.chicagogsb.edu. Calculations by Duff & Phelps LLC.
7.18%
16.49%
10.58% 10.87% 9.61% 11.66% 12.12% 12.94% 13.52% 12.65% 13.79% 12.96% 13.82% 13.51% 11.92% 14.42% 13.77% 15.47% 15.19% 14.62% 14.34% 15.32% 15.74% 15.11% 15.48% 16.80% 19.53%
Geometric Average Return
Long-term Treasury Income (SBBI data)
38.05%
16.73% 16.65% 16.36% 16.32% 16.13% 16.81% 18.19% 19.53% 18.50% 18.89% 18.40% 19.14% 20.90% 19.45% 20.45% 22.00% 23.53% 22.77% 24.33% 23.93% 23.68% 24.23% 24.61% 25.01% 31.28%
Standard Deviation of Returns
15.01%
1.62
0.90 0.93 0.97 0.98 0.96 1.03 1.02 1.09 1.09 1.10 1.09 1.11 1.09 1.14 1.14 1.14 1.21 1.20 1.24 1.27 1.26 1.27 1.24 1.28 1.30
Beta (Sum Beta) Since ‘63
Small Stocks (SBBI data)
680
46 36 40 39 45 41 44 45 48 41 42 41 47 51 58 52 53 61 57 77 64 80 90 162 332
Number as of 2005
10.75%
4.99 4.43 4.17 4.04 3.90 3.78 3.69 3.57 3.50 3.44 3.39 3.33 3.27 3.20 3.14 3.05 3.01 2.94 2.87 2.80 2.73 2.64 2.51 2.35 1.88
Log of Average Mkt Value
Large Stocks (SBBI data)
High financial risk
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Portfolio Rank by Size
Historical Equity Risk Premium: Averages Since 1963 Data for Year Ending December 31, 2005
Exhibit 12.7 Duff & Phelps Size Study: Risk Premiums for Use in Build-up Method: Companies Ranked by Market Value Equity
3.670% 0.294% 12.46
Regression Output:
0% 1.0
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
1.5
4.0 4.5 5.0 2.0 2.5 3.0 3.5 Log of Average Market Value of Equity
Smoothed Premium vs. Unadjusted Average
5.5
20.653% 0.992% 87% 25 23
Smoothed Premium = 20.653% 3.670% * Log(Market Value)
X Coefficient(s) Std Err of Coef. t-Statistic
Constant Std Err of Y Est R Squared No. of Observations Degrees of Freedom
Risk Premium Study: Data through December 31, 2005 Data Smoothing with Regression Analysis Dependent Variable: Average Premium Independent Variable: Log of Average Market Value of Equity
Equity Premium
190
191
7.20%
17.67%
12.01%
21.87%
12.32% 12.34% 14.50% 13.21% 13.67% 13.90% 13.92% 14.44% 15.54% 15.05% 14.58% 16.49% 15.25% 15.59% 16.39% 16.57% 16.96% 15.73% 16.65% 17.63% 16.66% 18.92% 17.76% 18.02% 20.98%
Arithmetic Average Return
10.47%
4.81%
14.67%
5.12% 5.14% 7.30% 6.01% 6.47% 6.70% 6.72% 7.24% 8.34% 7.85% 7.38% 9.29% 8.05% 8.39% 9.19% 9.37% 9.76% 8.53% 9.45% 10.43% 9.46% 11.72% 10.56% 10.82% 13.78%
Arithmetic Risk Premium 3.85% 5.38% 5.95% 5.42% 6.90% 7.25% 7.47% 7.73% 8.02% 8.15% 8.31% 8.46% 8.68% 8.81% 9.09% 9.17% 9.41% 9.54% 9.74% 9.93% 10.19% 10.45% 10.71% 11.14% 12.34%
Smoothed Average Risk Premium
48.32%
27.19% 31.63% 33.59% 31.61% 30.17% 30.64% 28.90% 27.47% 27.74% 29.28% 28.20% 30.29% 27.54% 27.67% 27.74% 27.80% 28.06% 27.61% 28.19% 26.75% 27.54% 26.86% 27.62% 27.28% 26.65%
Average Debt/MVIC
Source: Compiled from data from the Center for Research in Security Prices. Source: # CRSP1, Center for Research in Security Prices. Graduate School of Business, The University of Chicago. Used with permission. All rights reserved. wwwcrsp.chicagogsb.edu. Calculations by Duff & Phelps LLC.
7.18%
16.75%
11.11% 11.15% 13.31% 11.99% 12.47% 12.36% 12.70% 13.29% 13.97% 13.51% 13.04% 14.88% 13.72% 13.92% 14.71% 14.62% 14.88% 13.79% 14.72% 15.50% 14.55% 16.39% 15.28% 15.29% 17.20%
Geometric Average Return
Long-term Treasury Income (SBBI data)
37.64%
16.22% 16.47% 16.57% 16.76% 16.74% 18.87% 16.57% 16.36% 19.23% 18.93% 18.78% 19.17% 18.71% 19.66% 19.59% 20.90% 21.87% 21.11% 21.48% 22.57% 22.04% 24.48% 24.11% 25.19% 31.59%
Standard Deviation of Returns
15.01%
1.62
0.84 0.84 0.89 0.91 0.99 1.00 1.00 1.05 1.08 1.03 1.09 1.05 1.12 1.12 1.11 1.17 1.19 1.24 1.19 1.22 1.22 1.25 1.26 1.29 1.33
Beta (Sum Beta) Since ‘63
10.75%
680
41 36 37 36 40 48 39 44 37 40 44 42 47 49 53 47 56 62 59 63 77 75 102 122 391
Number as of 2005
Small Stocks (SBBI data)
4.43 3.94 3.76 3.60 3.45 3.34 3.27 3.19 3.09 3.05 3.00 2.95 2.88 2.84 2.75 2.72 2.64 2.60 2.54 2.48 2.39 2.31 2.23 2.09 1.71
Log of Average Book Val.
Large Stocks (SBBI data)
26,924 8,688 5,700 4,019 2,828 2,177 1,854 1,533 1,236 1,123 995 890 760 687 562 529 441 402 347 302 248 206 169 123 51
Average Book Val. ($mils.)
High financial risk
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Portfolio Rank by Size
Historical Equity Risk Premium: Average Since 1963 Data for Year Ending December 31, 2005
Exhibit 12.8 Duff & Phelps Size Study: Risk Premiums for Use in Build-up Method: Companies Ranked by Book Value Equity
3.118% 0.251% 12.40
17.660% 0.757% 87% 25 23
20% 18% 16% 14% 12% 10% 8% 6% 4% 2% 0% 1.0
1.5
2.0 2.5 3.0 3.5 4.0 Log of Average Book Value of Equity
Smoothed Premium vs. Unadjusted Average
4.5
Smoothed Premium = 17.660% 3.118% * Log(Book Value)
Constant Std Err of Y Est R Squared No. of Observations Degrees of Freedom X Coefficient(s) Std Err of Coef. t-Statistic
Regression Output:
Risk Premium Study: Data through December 31, 2005 Data Smoothing with Regression Analysis Dependent Variable: Average Premium Independent Variable: Log of Average Market Value of Equity
Equity Premium
Equity Premium
Equity Premium
2.5 3.0 3.5 4.0 4.5 Log of Average Market Value of Equity
4.0
0% 1.0 3.5
6%
8%
10%
12%
14%
16%
18%
20%
0% 1.0
2% 3.0
5.5
0% 0.0 1.5 2.0 2.5 Log of Average Net Income
5.0
4%
1.0
Smoothed Premium vs. Unadjusted Average
Companies Ranked by 5-Year Average Net Income
2.0
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
2%
0.5
1.5
Smoothed Premium vs. Unadjusted Average
Companies Ranked by Market Value of Equity
4%
6%
8%
10%
12%
14%
16%
18%
20%
0% 1.0
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
Equity Premium Equity Premium
192 1.5
2.0 2.5 3.0 3.5 Log of Average Book Value of Equity
2.0
3.0
3.5
4.0 Log of Average Market Invested Capital
2.5
Smoothed Premium vs. Unadjusted Average
4.5
5.0
4.0
Companies Ranked by Market Value of Invested Capital
1.5
Smoothed Premium vs. Unadjusted Average
Companies Ranked by Book Value of Equity
5.5
4.5
193
Equity Premium
3.5
Log of Total Assets
3.0
4.0
Companies Ranked by Sales
2.5
4.5
4.0
4.5
5.0
2.5
0.50
2.00
2.50
3.00
Log of Average EBITDA
1.50
3.50
3.0
4.0
4.5 Log of Number of Employees
3.5
5.0
Smoothed Premium vs. Unadjusted Average
Companies Ranked by Number of Employees
1.00
Smoothed Premium vs. Unadjusted Average
Companies Ranked by 5-Year Average EBITDA
Source: Compiled from data from the Center for Research in Security Prices. Source: # CRSP1, Center for Research in Security Prices. Graduate School of Business, The University of Chicago. Used with permission. All rights reserved. wwwcrsp.chicagogsb.edu. Calculations by Duff & Phelps LLC.
Duff & Phelps Size Study: Risk Premiums for Use in Build-up Method
Log of Sales
0% 2.0
3.5
6%
8%
10%
12%
14%
16%
18%
20%
0% 0.00
2% 3.0
5.5
0% 1.0 2.5
5.0
4%
2.0
Smoothed Premium vs. Unadjusted Average
2.0
2%
4%
6%
8%
10%
12%
14%
16%
2%
1.5
1.5
Smoothed Premium vs. Unadjusted Average
Companies Ranked by Total Assets
4%
6%
8%
10%
12%
14%
16%
18%
20%
0% 1.0
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
Exhibit 12.9
Equity Premium
Equity Premium Equity Premium
5.5
4.00
6.0
4.50
194
Cost of Capital
Observations on the Data By whatever measure of size they use, the result is a clear inverse relationship between size and historical risk premiums. Exhibit 12.9 displays the relationships among four of the eight size measures and the historical risk premiums. However, when you sort by a size measure other than market value, the relationship is slightly flattened. The average realized risk premiums for the smallest companies are generally lower when you sort by criteria other than market value. For the 25 size-ranked portfolios with an arithmetic equity risk premium in excess of the average realized market premium (4.81% for 1963 through 2005 from the SBBI series for large companies), the premium incorporates a non–beta-adjusted size premium. The general market realized risk premium for the period 1963 through 2005, 4.81%, is consistent with the range for the general market equity risk premium we found in Chapter 9. The historical average Debt to MVIC ratio is approximately 30% for most size categories for all of the sorting criteria. This suggests that differences in leverage do not explain the small-company effect in the data for these years. The leverage in the high-financial-risk portfolio is significantly higher than that of any of the other portfolios. USING THE DUFF & PHELPS RISK PREMIUM REPORT SIZE STUDY IN THE BUILD-UP METHOD As an alternative to the Formula 12.1 for the build-up method, EðRi Þ ¼ R f þ RPm þ RPs þ RPu , where you add a general equity risk premium for the ‘‘market’’ (equity risk premium) and a risk premium for small size to the risk-free rate, you can use the Size Study to develop a risk premium for the subject company that measures risk in terms of the total effect of market risk and size. The formula then is modified to be: (Formula 12.3) EðRi Þ ¼ R f þ RPmþs þ RPu where: E(Ri) ¼ Expected (market required) rate of return on security i Rf ¼ Rate of return available on a risk-free security as of the valuation date RPmþs ¼ Risk premium for the ‘‘market’’ plus risk premium for size RPu ¼ Risk premium attributable to the specific company or to the industry The Size Study sorts companies by size, breaking the NYSE universe of companies into 25 sizeranked categories or portfolios and adding AMEX and NASDAQ listed companies to each category based on their respective size measures. Examples These data can be used as an aid in formulating estimated required rates of return using objective measures of the ‘‘size’’ for a subject company. The realized risk premiums reported in the eight exhibits have not been adjusted to remove beta risk. Therefore, they should not be multiplied by a CAPM beta or otherwise included in a CAPM analysis. If you are estimating the cost of equity capital for a publicly traded company, you can determine all eight measures of size and estimate an appropriate risk premium based on all eight. If you are estimating the cost of equity for a closely held
Duff & Phelps Studies
195
entity, you can use six measures of size (ignoring the measures of size based on the market value of common equity and the MVIC) and estimate an appropriate risk measure based on the six fundamental accounting measures of size. A straightforward method of arriving at a discount rate using the build-up method with the data presented in eight exhibits is to derive RPmþs for use in Formula 12.3. The premiums, RPmþs , incorporate the small-company. You could match the sales or total assets of the subject company with the portfolios composed of companies of similar size. The smoothed historical realized premiums of these portfolios can then be added to the yield on long-term U.S. government bonds as of the valuation date to obtain benchmarks for the cost of equity capital. Assume the subject public company has these characteristics:
Market value of common equity Book value of common equity 5-year average net income Debt Market value of invested capital Total assets 5-year average EBITDA Sales Number of employees
$120 $100 $10 $60 $180 $300 $30 $250 200
million million million million million million million million
The simplest approach is to use the eight exhibits (such as in Exhibit 12.7), and, for each of the eight size categories, locate the portfolio whose size is most similar to the subject company. For each guideline portfolio, the column labeled ‘‘Smoothed Average Equity Risk Premium’’ gives an indicated historical realized premium over the risk-free rate, RPmþs . Exhibit 12.10 shows the premiums indicated for our subject company. In deriving the average realized risk premiums reported in their exhibits, Grabowski and King use the SBBI income return on long-term U.S. government bonds as their measure of the historical riskfree rate; therefore, a 20-year U.S. government bond yield is the most appropriate measure of the risk-free rate for use with the reported premiums in developing an indicated cost of equity capital.
Exhibit 12.10
Size-Adjusted Risk Premiums over Risk-free Rate: Using Guideline Portfolios Company Size
Market Value of Equity Book Value of Equity 5-year Average Net Income Market Value of Invested Capital Total Assets 5-year Average EBITDA Sales Number of Employees Mean premium over risk-free rate, RPmþs Median premium over risk-free rate, RPmþs
$120 $100 $10 $180 $300 $30 $250 200
mil. mil. mil. mil. mil. mil. mil.
Exh
Guideline Portfolio
12.7 12.8 (1) (1) (1) (1) (1) (1)
24 24 23 24 23 24 23 25
(1) From additional exhibits provided in the Risk Premium Report. Source: Duff & Phelps LLC Risk Premium Report 2006, Copyright # 2006. Used with permission. All rights reserved.
RPm þ s 12.0% 11.1% 11.3% 11.9% 11.1% 11.7% 11.0% 12.6% 11.6% 11.5%
196 Exhibit 12.11
Cost of Capital Size-Adjusted Risk Premiums over Risk-free Rate: Using Regression Equations
Market Value of Equity Book Value of Equity 5-year Average Net Income Market Value of Invested Capital Total Assets 5-year Average EBITDA Sales Number of Employees Mean premium over risk-free rate, RPmþs Median premium over risk-free rate, RPmþs
Company Size
Exh
Constant Term
Slope Term
log(Size)
$120 $100 $10 $180 $300 $30 $250 200
12.7 12.8 (1) (1) (1) (1) (1) (1)
20.653% 17.660% (1) (1) (1) (1) (1) (1)
3.670% 3.118% (1) (1) (1) (1) (1) (1)
2.079 2.000 1.000 2.2255 2.477 1.477 2.398 2.301
mil. mil. mil. mil. mil. mil. mil.
RPmþs 13.0% 11.4% 11.5% 12.5% 11.2% 11.7% 11.1% 12.4% 11.9% 11.6%
(1) From additional exhibits provided in the Risk Premium Report. Source: Duff & Phelps LLC Risk Premium Report 2006, Copyright # 2006. Used with permission. All rights reserved.
With a risk-free rate as of the valuation date of 5.5%, for example, the premiums would indicate the cost of equity capital ranging from 16.5% to 18.1%, with an average of 17.1% before consideration of RPu, the risk premium attributable to the specific company or to the industry. As an alternative, you can estimate premiums using the regression equations that underlie the smoothed premium calculations. To estimate a premium, you multiply the logarithm (log base-10) of the ‘‘size’’ measure by the slope coefficient and add the constant term, as described. In practice, this approach generally produces results that are very similar to those of the guideline portfolio approach presented earlier (unless you are extrapolating to a company that is much smaller than the average size for the twenty-fifth portfolio). Exhibit 12.11 illustrates use of the regression equations from Exhibits 12.7 and 12.8 for our example subject company. Practical Application of the Data The ‘‘smoothed’’ average realized risk premium is the most appropriate indicator for most of the portfolio groups. At the largest-size and smallest-size ends of the range, the average realized risk premiums tend to jump off of the smoothed line, particularly for the portfolios ranked by size as measured by market value (market value of equity and market value of invested capital). For the largest companies (the first portfolio), the observed historical relationship flattens out, and the smoothed premium may be an inappropriate indicator. Note, however, that a pronounced jump exists in the premium in the smallest 4% of companies.12 Sometimes you must estimate the required rate of return for a company that is significantly smaller than the average size of even the smallest of the 25 portfolios. In such cases, it may be appropriate to extrapolate the smoothed average premium to smaller sizes using the slope and constant terms from the regression relationships that we use in deriving the smoothed premiums. In so doing, you must be careful to remember that the logarithmic relationship is base-10 and that the financial size
12
This fact is of interest to many business valuators, since this jump occurs in a size category in which, as a practical matter, many more valuation assignments are performed. For seven of the eight size measures, the actual premium for the smallest group was greater than the smoothed premium, generally by a considerable margin. For the smallest companies (portfolio 25), the smoothed average premium is likely the more appropriate and conservative indicator of the size premium.
Duff & Phelps Studies
197
data are in millions of dollars, such that the log of $10 million is log(10), not log(10,000,000). Also, as a general rule, you should be cautious about extrapolating a statistical relationship far beyond the range of the data used in the statistical analysis. The next example illustrates the use of the regression equations in estimating a risk premium. Assume the subject a company has a book value of $50 million. If we insert this figure into the regression relationship reported in Exhibit 12.8 (‘‘Companies Ranked by Book Value of Equity’’), we obtain this estimate of RPmþs : Smoothed Premium ¼ 17:660% 3:118% logð50Þ ¼ 17:660% 3:118% ð1:699Þ ¼ 12:36% Use of a portfolio’s average realized rate of return to calculate a cost of equity capital is based (in part) on the implicit assumption that the risks of the subject company are quantitatively similar to the risks of the average company in the subject portfolio. If the risks of the subject company differ materially from the average company in the subject portfolio, then an appropriate discount rate may be lower (or higher) than a return derived from the average realized risk premium for a given portfolio. We have included two of the exhibits displaying various risk measures for each portfolio. Exhibit 12.12 displays various risk measures for portfolios where companies were ranked by size by market value of equity, and Exhibit 12.13 displays various risk measures for portfolios where companies were ranked by size by book value of equity. These exhibits can be useful in identifying material differences between the expected returns of a subject company of a given size and the characteristics of the companies comprising the portfolio. Material differences between the expected returns for a subject company of a given size and the stocks comprising the portfolio may arise due to differences in:
Leverage (the average debt/MVIC and the average levered portfolio beta (the CAPM risk measure) of the portfolios are displayed)13 Operating risks (the average unlevered portfolio sum betas, the average operating margin, and the average coefficient of variation of operating margin14 for the portfolios are displayed) Other fundamental risk factors
For example, were the subject company ranked in the twenty-fourth portfolio based on its market value of equity, you can compare the operating margin of the subject company to the average operating margin of companies included in the twenty-fourth portfolio. Looking at Exhibit 12.12, you see that the average operating margin of the companies in the twenty-fourth portfolio is 7.6%. Were the average operating margin of the subject company less than the average of the portfolio companies, you can conclude that the subject company is likely more risky than the average company of its size. Further, you can compare the coefficient of variation of operating margin of the subject company to the average coefficient of variation of operating margin of companies included in the twenty-fourth portfolio. Looking at Exhibit 12.12, you see that the average coefficient of variation of operating margin of the companies in the twenty-fourth portfolio is 28.7%. Were the average coefficient of operating margin of the subject company greater than the average of the
13
14
Operating margin ¼ [sales minus (cost of goods sold plus selling, general and administrative expenses plus depreciation expense)] divided by sales. Coefficient of operating margin ¼ Standard deviation of operating margin over five years divided by the mean operating margin over those same five years.
198
Duff & Phelps Study: Comparative Risk Statistics
96,796 26,818 14,912 10,930 8,014 5,996 4,872 3,745 3,185 2,758 2,441 2,121 1,845 1,588 1,382 1,117 1,025 870 736 626 541 436 326 225 76
Average Mkt Value ($mils.)
4.99 4.43 4.17 4.04 3.90 3.78 3.69 3.57 3.50 3.44 3.39 3.33 3.27 3.20 3.14 3.05 3.01 2.94 2.87 2.80 2.73 2.64 2.51 2.35 1.88
Log of Size 46 36 40 39 45 41 44 45 48 41 42 41 47 51 58 52 53 61 57 77 64 80 90 162 332
Number of Firms 4.7% 4.9% 3.6% 5.6% 6.1% 7.0% 7.7% 7.1% 8.1% 7.3% 8.1% 7.9% 6.6% 8.9% 8.5% 10.4% 10.3% 9.7% 9.6% 10.6% 10.8% 10.4% 10.8% 12.2% 16.1%
Average Risk Premium 16.24% 22.74% 24.97% 25.96% 26.92% 26.86% 27.51% 26.00% 25.31% 24.96% 24.98% 25.48% 26.50% 26.98% 26.56% 25.82% 26.46% 26.97% 26.36% 27.19% 27.29% 27.67% 28.04% 28.74% 30.99%
Average Debt to MVIC 19.4% 29.4% 33.3% 35.1% 36.8% 36.7% 38.0% 35.1% 33.9% 33.3% 33.3% 34.2% 36.1% 36.9% 36.2% 34.8% 36.0% 36.9% 35.8% 37.3% 37.5% 38.3% 39.0% 40.3% 44.9%
Average Debt to Market Value of Equity 4.2% 4.3% 3.1% 4.7% 5.1% 5.8% 6.4% 6.0% 6.8% 6.2% 6.9% 6.6% 5.6% 7.4% 7.1% 8.7% 8.6% 8.1% 8.1% 8.8% 9.0% 8.7% 9.0% 10.0% 13.0%
0.90 0.93 0.97 0.98 0.96 1.03 1.02 1.09 1.09 1.10 1.09 1.11 1.09 1.14 1.14 1.14 1.21 1.20 1.24 1.27 1.26 1.27 1.24 1.28 1.30
Beta (Sum Beta) Since ‘63 0.81 0.80 0.82 0.82 0.80 0.86 0.85 0.91 0.92 0.93 0.93 0.94 0.91 0.95 0.96 0.96 1.01 1.00 1.04 1.06 1.05 1.05 1.03 1.05 1.05
Average Unlevered Beta
Portfolio Statistics for 1963–2005 Average Unlevered Risk Premium 15.4% 13.1% 13.3% 12.7% 12.7% 13.3% 12.6% 12.3% 12.2% 12.0% 11.8% 11.6% 11.0% 11.2% 10.9% 10.3% 10.0% 9.7% 9.4% 9.0% 8.5% 8.2% 7.9% 7.6% 6.2%
Average Operating Margin 9.6% 10.6% 11.3% 12.2% 13.1% 12.7% 13.9% 13.5% 14.1% 13.8% 14.8% 14.8% 14.7% 15.2% 17.1% 17.8% 18.2% 20.6% 20.8% 23.7% 23.1% 25.2% 27.0% 28.7% 42.2%
Average CV(Operating Margin)
14.4% 17.9% 18.1% 19.0% 20.1% 18.9% 21.2% 20.4% 21.6% 21.6% 21.0% 20.2% 20.7% 21.9% 23.2% 24.5% 25.8% 28.2% 27.1% 30.8% 30.9% 35.0% 34.8% 38.8% 56.0%
Average CV(ROE)
Note: CV(X) ¼ Standard deviation of X divided by mean of X, calculated over 5 fiscal years. For Portfolios 1–25, calculation uses statutory federal tax rates plus weighted average effective state tax rates. The average blended income tax rate used is 45.9%. Source: Compiled from data from the Center for Research in Security Prices. Source: # CRSP1, Center for Research in Security Prices. Graduate School of Business, The University of Chicago. Used with permission. All rights reserved. wwwcrsp.chicagogsb.edu. Calculations by Duff & Phelps LLC.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Portfolio Rank by Size
Portfolio Statistics for 2005
Companies Ranked by Market Value of Equity: Comparative Risk Characteristics Data for Year Ending December 31, 2005
Exhibit 12.12
199
Duff & Phelps Study: Comparative Risk Statistics
26,924 8,688 5,700 4,019 2,828 2,177 1,854 1,533 1,236 1,123 995 890 760 687 562 529 441 402 347 302 248 206 169 123 51
Average Book Value ($mils.) 4.43 3.94 3.76 3.60 3.45 3.34 3.27 3.19 3.09 3.05 3.00 2.95 2.88 2.84 2.75 2.72 2.64 2.60 2.54 2.48 2.39 2.31 2.23 2.09 1.71
Log of Size 41 36 37 36 40 48 39 44 37 40 44 42 47 49 53 47 56 62 59 68 77 75 102 122 391
Number of Firms 5.1% 5.1% 7.3% 6.0% 6.5% 6.7% 6.7% 7.2% 8.3% 7.9% 7.4% 9.3% 8.1% 8.4% 9.2% 9.4% 9.8% 8.5% 9.5% 10.4% 9.5% 11.7% 10.6% 10.8% 13.8%
Average Risk Premium 27.19% 31.63% 33.59% 31.61% 30.17% 30.64% 28.90% 27.47% 27.74% 29.28% 28.20% 30.29% 27.54% 27.67% 27.74% 27.80% 26.06% 27.61% 28.19% 26.75% 27.54% 26.86% 27.62% 27.28% 26.65%
Average Debt to MVIC 37.3% 46.3% 50.6% 46.2% 43.2% 44.2% 40.7% 37.9% 38.4% 41.4% 39.3% 43.4% 38.0% 38.3% 38.4% 38.5% 35.2% 38.1% 39.2% 36.5% 38:0% 36.7% 38.2% 37.5% 36.3%
Average Debt to Market Value of Equity 4.3% 4.1% 5.7% 4.8% 5.2% 5.4% 5.5% 6.0% 6.9% 6.4% 6.1% 7.5% 6.7% 7.0% 7.6% 7.8% 8.2% 7.1% 7.8% 8.7% 7.9% 9.8% 8.8% 9.0% 11.5%
0.84 0.84 0.89 0.91 0.99 1.00 1.00 1.05 1.08 1.03 1.09 1.05 1.12 1.12 1.11 1.17 1.19 1.24 1.19 1.22 1.22 1.25 1.26 1.29 1.33
Beta (Sum Beta) Since ‘63 0.69 0.67 0.70 0.72 0.80 0.81 0.82 0.87 0.90 0.84 0.90 0.85 0.93 0.93 0.92 0.97 1.00 1.03 0.98 1.02 1.01 1.04 1.04 1.07 1.11
Average Unlevered Beta
Portfolio Statistics for 1963–2005 Average Unlevered Risk Premium 13.1% 14.1% 12.2% 12.5% 13.0% 12.4% 13.0% 12.7% 12.3% 11.7% 11.8% 12.2% 11.4% 10.9% 10.6% 10.1% 10.7% 10.1% 9.9% 9.3% 9.3% 8.5% 8.7% 8.1% 7.2%
Average Operating Margin 12.8% 11.9% 11.9% 12.5% 12.9% 13.5% 13.4% 14.0% 14.3% 14.8% 15.1% 14.5% 16.4% 15.6% 15.8% 17.8% 16.8% 19.4% 19.4% 20.8% 22.4% 24.2% 23.9% 26.2% 37.6%
Average CV(Operating Margin)
19.2% 17.0% 19.4% 21.9% 21.5% 22.4% 22.1% 22.0% 21.2% 20.2% 23.9% 20.9% 22.7% 22.0% 22.8% 25.4% 24.5% 26.1% 28.2% 30.0% 31.7% 30.5% 33.8% 36.5% 50.6%
Average CV(ROE)
Note: CV(X) = Standard deviation of X divided by mean of X, calculated over 5 fiscal years. For Portfolios 1–25, calculation uses statutory federal tax rates plus weighted average effective state tax rates. The average blended income tax rate used is 45.9 %. Source: Compiled from data from the Center for Research in Security Prices. Source: # CRSP1, Center for Research in Security Prices. Graduate School of Business, The University of Chicago. Used with permission. All rights reserved. wwwcrsp.chicagogsb.edu. Calculations by Duff & Phelps LLC.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Portfolio Rank by Size
Portfolio Statistics for 2005
Companies Ranked by Market Value of Equity: Comparative Risk Characteristics Data for Year Ending December 31, 2005
Exhibit 12.13
200
Cost of Capital
portfolio companies, you can conclude the subject company is likely more risky than the average company of its size. If your estimate of the ERP for the S&P 500 on a forward-looking basis were materially different from the average historical realized premium since 1963, it may be reasonable to assume that the other historical portfolio returns reported here would differ on a forward-looking basis by approximately a similar differential. For example, at the end of 2005, the average historical realized premium since 1963 for Large Company stocks equaled 4.81% (see the bottom of Exhibit 12.7). This is the market risk premium, RPm, inherent in the Size Study exhibits for use in the build-up method as of that date. The risk premiums displayed in the Size Study exhibits for the build-up method equals RPmþs , as shown in Formula 12.3 (RPm plus RPs). Assume that your estimate of the expected equity risk premium at the end of 2005 is equal to 4%. That difference (4.81% minus 4%) can be subtracted from the average risk premium, RPmþs , for the portfolio (observed or ‘‘smoothed’’) that matches to the size of the subject company to arrive at an adjusted ‘‘forward-looking’’ risk premium for the subject company (matching your forward-looking ERP estimate). Then this forward-looking risk premium can be added to the risk-free rate as of the valuation date to estimate an appropriate cost of equity capital for the subject company. You can adjust the observed premiums over the risk-free rate for differences in financial leverage between the average companies comprising the portfolio and the subject company. The subject company above has a debt/MVIC ¼ $60/$180 ¼ 33%, which is slightly more leverage than the average of the companies comprising portfolio 24 of Exhibit 12.7 (28.74%). But assume that the subject company had no debt in its capital structure. Duff & Phelps displays unlevered average levered risk premium where the average debt to equity (D/E) ratio of the portfolio is based on the average debt to MVIC for the portfolio since 1963 and the income tax rate is the estimated federal income tax rate plus effective state income tax rate for the companies comprising the portfolio companies. The Duff & Phelps study presents unlevered average realized risk premiums for each of the eight size measures in exhibits displaying various risk measures for each size category (see, e.g., Exhibits 12.12 and 12.13). The unlevered average realized risk premium for portfolio 24 equals 10.0%. This compares to the average levered realized risk premium of 12.2% (rounded, but not smoothed) reported in Exhibit 12.7. These unlevered realized risk premiums represent the rates of return on a debt-free basis; the unlevered realized risk premiums can be used for estimating required rates of return for companies with no debt. The unlevered realized risk premiums displayed in Exhibits 12.12 and 12.13 are informative in that they generally indicate that the market views operations of smaller companies to be more risky than the operations of larger companies (i.e., unlevered risk premiums increase as size decreases). The unlevered realized risk premium can also be used as the first step in a relevering calculation where the subject company’s debt level differs from the average debt level of the portfolio companies. USING THE DUFF & PHELPS SIZE STUDY IN THE CAPM METHOD Using similar methodology, Grabowski and King computed premiums over CAPM. (Recall that beta captures some, but not all, of the size premium.) These can be used with the Capital Asset Pricing Model. We have included two exhibits: Exhibit 12.14, where size is measured by market value of common equity, and Exhibit 12.15, where size is measured by book value of common equity (exhibits reproduced herein are for years ending 2005).
201
96,796 26,818 14,912 10,930 8,014 5,996 4,872 3,745 3,185 2,758 2,441 2,121 1,845 1,588 1,382 1,117 1,025 870 736 626 541 436 326 225 76
Average Mkt Value ($mils.)
4.99 4.43 4.17 4.04 3.90 3.78 3.69 3.57 3.50 3.44 3.39 3.33 3.27 3.20 3.14 3.05 3.01 2.94 2.87 2.80 2.73 2.64 2.51 2.35 1.88
Log of Size
12.01% 17.67% 7.20%
21.73%
11.87% 12.13% 10.83% 12.84% 13.28% 14.19% 14.93% 14.34% 15.28% 14.52% 15.33% 15.07% 13.84% 16.08% 15.65% 17.56% 17.47% 16.88% 16.81% 17.80% 18.03% 17.64% 18.04% 19.37% 23.32%
Arithmetic Average Return
4.81% 10.47%
14.53%
4.67% 4.93% 3.63% 5.64% 6.08% 6.99% 7.73% 7.14% 8.08% 7.32% 8.13% 7.87% 6.64% 8.88% 8.45% 10.36% 10.27% 9.68% 9.61% 10.60% 10.83% 10.44% 10.84% 12.17% 16.12%
Arithmetic Risk Premium
7.81%
4.33% 4.46% 4.67% 4.69% 4.64% 4.94% 4.91% 5.23% 5.23% 5.28% 5.26% 5.33% 5.26% 5.46% 5.50% 5.46% 5.82% 5.78% 5.98% 6.12% 6.08% 6.12% 5.97% 6.15% 6.25%
Indicated CAPM Premium
6.73%
0.34% 0.46% 1.04% 0.94% 1.45% 2.05% 2.83% 1.90% 2.85% 2.04% 2.87% 2.54% 1.39% 3.41% 2.95% 4.90% 4.45% 3.90% 3.63% 4.48% 4.75% 4.32% 4.86% 6.02% 9.87%
Premium over CAPM 1.69% 0.09% 0.64% 1.02% 1.41% 1.77% 2.03% 2.36% 2.56% 2.74% 2.89% 3.06% 3.24% 3.42% 3.60% 3.86% 3.97% 4.17% 4.38% 4.58% 4.76% 5.03% 5.39% 5.86% 7.20%
Smoothed Premium over CAPM
Source: Compiled from data from the Center for Research in Security Prices. Source: # CRSP1, Center for Research in Security Prices. Graduate School of Business, The University of Chicago. Used with permission. All rights reserved. wwwcrsp.chicagogsb.edu. Calculations by Duff & Phelps LLC.
1.62
0.90 0.93 0.97 0.98 0.96 1.03 1.02 1.09 1.09 1.10 1.09 1.11 1.09 1.14 1.14 1.14 1.21 1.20 1.24 1.27 1.26 1.27 1.24 1.28 1.30
Beta (Sum Beta) Since ‘63
Large Stocks (SBBI data) Small Stocks (SBBI data) Long-term Treasury Income (SBBI data)
High financial risk
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Portfolio Rank by Size
Historical Equity Risk Premium: Averages Since 1963 Data for Year Ending December 31, 2005
Exhibit 12.14 Duff & Phelps Size Study for Use in CAPM: Companies Ranked by Market Value of Equity: Premium over CAPM
2.865% 0.295% 9.70
0.994% 80% 25 23
12.594%
–4% 1.0
–2%
0%
2%
4%
6%
8%
10%
12%
2.0 3.0 4.0 5.0 Log of Average Market Value of Equity
Smoothed Premium vs. Unadjusted Average
6.0
Smoothed Premium = 12.594% 2.865% * Log(Market Value)
X Coefficient(s) Std Err of Coef. t-Statistic
Constant Std Err of Y Est R Squared No. of Observations Degrees of Freedom
Regression Output:
Risk Premium Study: Data through December 31, 2005 Data Smoothing with Regression Analysis Dependent Variable: Premium over CAPM Independent Variable: Log of Average Market Value of Equity
Premium over CAPM
4.43 3.94 3.76 3.60 3.45 3.34 3.27 3.19 3.09 3.05 3.00 2.95 2.88 2.84 2.75 2.72 2.64 2.60 2.54 2.48 2.39 2.31 2.23 2.09 1.71
Log of Size
1.62
0.84 0.84 0.89 0.91 0.99 1.00 1.00 1.05 1.08 1.03 1.09 1.05 1.12 1.12 1.11 1.17 1.19 1.24 1.19 1.22 1.22 1.25 1.26 1.29 1.33
Beta (Sum Beta) Since ‘63
12.01% 17.67% 7.20%
21.87%
12.32% 12.34% 14.50% 13.21% 13.67% 13.90% 13.92% 14.44% 15.54% 15.05% 14.58% 16.49% 15.25% 15.59% 16.39% 16.57% 16.96% 15.73% 16.65% 17.63% 16.66% 18.92% 17.76% 18.02% 20.98%
Arithmetic Average Return
4.81% 10.47%
14.67%
5.12% 5.14% 7.30% 6.01% 6.47% 6.70% 6.72% 7.24% 8.34% 7.85% 7.38% 9.29% 8.05% 8.39% 9.19% 9.37% 9.76% 8.53% 9.45% 10.43% 9.46% 11.72% 10.56% 10.82% 13.78%
Arithmetic Risk Premium
7.79%
4.02% 4.05% 4.27% 4.36% 4.77% 4.82% 4.79% 5.04% 5.20% 4.94% 5.24% 5.04% 5.37% 5.39% 5.34% 5.64% 5.70% 5.95% 5.73% 5.89% 5.86% 6.01% 6.04% 6.21% 6.40%
Indicated CAPM Premium
6.88%
1.11% 1.09% 3.03% 1.65% 1.71% 1.87% 1.93% 2.20% 3.14% 2.91% 2.13% 4.25% 2.69% 3.01% 3.85% 3.73% 4.06% 2.58% 3.73% 4.55% 3.60% 5.72% 4.52% 4.61% 7.38%
Premium over CAPM 0.16% 1.17% 1.55% 1.86% 2.17% 2.40% 2.55% 2.72% 2.91% 2.99% 3.10% 3.20% 3.34% 3.43% 3.61% 3.67% 3.83% 3.91% 4.04% 4.17% 4.34% 4.51% 4.68% 4.96% 5.75%
Smoothed Premium over CAPM
Source: Compiled from data from the Center for Research in Security Prices. Source: # CRSP1, Center for Research in Security Prices. Graduate School of Business, The University of Chicago. Used with permission. All rights reserved. wwwcrsp.chicagogsb.edu. Calculations by Duff & Phelps LLC.
Large Stocks (SBBI data) Small Stocks (SBBI data) Long-term Treasury Income (SBBI data)
26,924 8,688 5,700 4,019 2,828 2,177 1,854 1,533 1,236 1,123 995 890 760 687 562 529 441 402 347 302 248 206 169 123 51
Average Book Val. ($mils.)
High financial risk
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Portfolio Rank by Size
Data for Year Ending December 31, 2005
Exhibit 12.15 Duff & Phelps Size Study for Use in CAPM: Companies Ranked by Book Value of Equity: Premium over CAPM Historical Equity Risk Premium: Average Since 1963
2.052% 0.259% 7.93
9.253% 0.778% 73% 25 23
–4% 1.0
–2%
0%
2%
4%
6%
8%
10%
12%
1.5
2.0 2.5 3.0 3.5 4.0 4.5 Log of Average Book Value of Equity
Smoothed Premium versus Unadjusted Average
5.0
Smoothed Premium = 9.253% 2.052% * Log(Book Value)
X Coefficient(s) Std Err of Coef. t-Statistic
Constant Std Err of Y Est R Squared No. of Observations Degrees of Freedom
Regression Output:
Risk Premium Study: Data through December 31, 2005 Data Smoothing with Regression Analysis Dependent Variable: Premium over CAPM Independent Variable: Log of Average Market Value of Equity
Premium over CAPM
202
Duff & Phelps Studies
203
In the context of the CAPM, the greater betas of the smaller companies explain some but not all of the higher average returns in these size-ranked portfolios. An example of the calculation of ‘‘Return in Excess of CAPM’’ will illustrate the method. The next example uses data for portfolio 19 of companies ranked by book value of equity from Exhibit 12.15: Portfolio beta ¼ 1.19 (column 4, portfolio 19) Arithmetic average realized risk premium ¼ 4.81% (SBBI series for Large Companies) Indicated CAPM premium (A B) 5 ¼ .72% Arithmetic average U.S. government bond income return ¼ 7.20% (SBBI Long-term Government Bond Income Returns) 5. Indicated CAPM return (C + D) ¼ 12.92% 6. Arithmetic average historical return ¼ 16.65% 7. RPs ¼ Return in excess of CAPM (F E) ¼ 3.73% (column 8, portfolio 19)
1. 2. 3. 4.
The return in excess of CAPM is often called the size premium or beta-adjusted size premium. The size premium is an empirically observed correction to the CAPM. This return in excess of CAPM of 3.73% compares to a premium over the overall market of 4.64% (F minus D minus B). The Size Study exhibits report betas calculated using the sum beta method applied to monthly portfolio return data. This method yields higher betas for smaller companies (and smaller size premiums) than would be obtained using ordinary least squares. Eight Measures of Size, Twenty-Five Size Categories The eight Size Study size measures for use in the CAPM method are the same as those presented earlier for use in the build-up method. The eight exhibits for use in CAPM report these statistics for each of 25 size categories:
Average of the size criteria (e.g., average number of employees) for the latest year Log (base-10) of the median of the size measure
Beta relative to the S&P 500 calculated using the sum beta method applied to monthly returns for 1963 through the latest year
Arithmetic average realized equity return since 1963 Arithmetic average realized risk premium (realized equity return over long-term U.S. government bonds) since 1963 (labeled ‘‘arithmetic risk premium’’)
Indicated CAPM premium calculated as the beta of the portfolio multiplied by the arithmetic average realized market risk premium since 1963
Premium over CAPM calculated by subtracting the indicated CAPM premium from the arithmetic risk premium
‘‘Smoothed’’ premium over CAPM: the fitted premium from a regression with the historical ‘‘premium over CAPM’’ as the dependent variable and the logarithm (base-10) of the size measure as the independent variable
The premium over CAPM data should not be multiplied by beta. Rather it is the basis for RPs (in Formula 12.2) and is added to CAPM (Formula 8.1).
Premium over CAPM
Premium over CAPM
3.0 4.0 Log of Average Market Value of Equity
3.0
3.5
4.0
0%
2%
4%
6%
8%
10%
12%
–4% 1.0
1.5 2.0 2.5 Log of Average Net Income
6.0
–4% 0.0
1.0
5.0
–2%
0.5
Smoothed Premium vs. Unadjusted Average
Companies Ranked by 5-Year Average Net Income
2.0
Smoothed Premium vs. Unadjusted Average
Companies Ranked by Market Value of Equity
Premium over CAPM
–2%
0%
2%
4%
6%
8%
10%
12%
–4% 1.0
–2%
0%
2%
4%
6%
8%
10%
12%
Premium over CAPM
204 –4% 1.0
–2%
0%
2%
4%
6%
8%
10%
12%
2.0 2.5 3.0 3.5 4.0 Log of Average Book Value of Equity
2.0 3.0 4.0 5.0 Log of Average Market Value of Invested Capital
Smoothed Premium vs. Unadjusted Average
Companies Ranked by Market Value of Invested Capital
1.5
Smoothed Premium vs. Unadjusted Average
Companies Ranked by Book Value of Equity
4.5
6.0
5.0
205
Premium over CAPM
4.0
4.5
5.0
0%
2%
4%
6%
8%
10%
12%
–4% 0.0
–4% 2.0
2.5 3.0 3.5 Log of Average Sales
6.0
–4% 1.0
2.0
5.0
–2%
1.5
Companies Ranked by Sales
3.0 4.0 Log of Average Total Assets
Smoothed Premium vs. Unadjusted Average
2.0
–2%
0%
2%
4%
6%
8%
10%
12%
–2%
0%
2%
4%
6%
8%
10%
12%
–4% 1.0
–2%
0%
2%
4%
6%
8%
10%
12%
Companies Ranked by Total Assets
Premium over CAPM
2.5
2.0 3.0 Log of Average EBITDA
4.0
3.0 3.5 4.0 4.5 5.0 Log of Average Number of Employees
Smoothed Premium vs. Unadjusted Average
Companies Ranked by Number of Employees
1.0
Smoothed Premium vs. Unadjusted Average
Companies Ranked by 5-year Average EBITDA
5.5
6.0
5.0
Source: Compiled from data from the Center for Research in Security Prices. Source: # CRSP1, Center for Research in Security Prices. Graduate School of Business, The University of Chicago. Used with permission. All rights reserved. wwwcrsp.chicagogsb.edu. Calculations by Duff & Phelps LLC.
Exhibit 12.16 Duff & Phelps Size Study for Use in CAPM: Premium over CAPM
Premium over CAPM
Smoothed Premium vs. Unadjusted Average
Premium over CAPM
206 Exhibit 12.17
Cost of Capital Premiums over CAPM: Using Guideline Portfolios Company Size
Market Value of Equity Book Value of Equity 5-year Average Net Income Market Value of Invested Capital Total Assets 5-year Average EBITDA Sales Number of Employees Mean premium over CAPM, RPs Median premium over CAPM, RPs
$120 $100 $10 $180 $300 $30 $250 200
mil. mil. mil. mil. mil. mil. mil.
Exh
Guideline Portfolio
Premium over CAPM
12.14 12.15 (1) (1) (1) (1) (1) (1)
24 24 23 24 23 24 23 25
5.9% 5.0% 5.2% 5.6% 5.0% 5.5% 5.0% 6.4% 5.5% 5.4%
(1) From additional exhibits provided in the Risk Premium Report. Source: Duff & Phelps LLC Risk Premium Report 2006, Copyright # 2006. Used with permission. All rights reserved
By whatever measure of size they use, the result is a clear inverse relationship between the size and the size premium. Exhibit 12.16 displays the relationship between the eight size measures and the size premiums. Examples Continuing with the same subject company used in Exhibits 12.10 and 12.11, the simplest approach is to find the smoothed premium over CAPM of the guideline portfolios in a manner similar to that described for the Size Study data in the build-up method. Exhibit 12.17 illustrates this approach for the subject company. If the indicated CAPM estimate before the size adjustment, EðRi Þ ¼ R f þ BðRPm Þ, is, for example, 11.0%, then the size premiums, RPs, indicate a cost of equity capital ranging from 16.0% to 17.4%, with an average of 16.5% before consideration of RPu, risk premium attributable to the specific company. As an alternative, you can use the regression equations reported in exhibits to estimate premiums over CAPM. Exhibit 12.18 illustrates the results for the subject company. Exhibit 12.18
Premiums over CAPM: Using Regression Equations Company Size
Market Value of Equity Book Value of Equity 5-year Average Net Income Market Value of Invested Capital Total Assets 5-year Average EBITDA Sales Number of Employees Mean premium over CAPM, RPs Median premium over CAPM, RPs
$120 $100 $10 $180 $300 $30 $250 200
mil. mil. mil. mil. mil. mil. mil.
Exh
Constant Term
Slope Term
log(Size)
12.14 12.15 (1) (1) (1) (1) (1) (1)
12.594% 9.253% (1) (1) (1) (1) (1) (1)
2.865% 2.052% (1) (1) (1) (1) (1) (1)
2.079 2.000 1.000 2.255 2.477 1.477 2.398 2.301
Premium over CAPM
(1) From additional exhibits provided in the Risk Premium Report. Source: Duff & Phelps LLC Risk Premium Report 2006, Copyright # 2006. Used with permission. All rights reserved.
6.6% 5.1% 5.3% 6.0% 5.0% 5.5% 5.1% 6.3% 5.6% 5.4%
Summary
207
Practical Application of the Data The exhibits report levered and unlevered portfolio betas (for example see Exhibits 12.12 and 12.13) where the average debt to equity (D/E) ratio of the portfolio is based on the average debt to MVIC for the portfolio since 1963, and the income tax rate is the estimated federal income tax rate plus effective state income tax rate for the companies comprising the portfolio companies. The exhibits display unlevered portfolio betas for each of the eight size measures. For example, in Exhibits 12.12 and 12.13, the unlevered portfolio beta for portfolio 24 equals 1.05 (Exhibit 12.12). This compares to the levered portfolio beta of 1.28 reported in Exhibit 12.14. Unlevered betas are often called asset betas in the literature as they are intended to represent the risk of the operations of the business with the risk of financial leverage removed. The unlevered betas displayed in Exhibits 12.12 and 12.13 are informative in that they generally indicate that the market views the operations of smaller companies to be more risky than the operations of larger companies (i.e., unlevered betas increase as size decreases). While the unlevered portfolio betas are informative, they would not generally be appropriate to use in estimating the beta of a subject company as they represent betas calculated since 1963. The convention for estimating the beta appropriate for a subject company is generally to use data for a more recent look-back period (e.g., last 60 months excess returns). The unlevering formulas used in the exhibits for unlevering the average realized risk premiums and portfolio betas for size categories 1 through 25 assume that the business risk is fully borne by the equity capital; that is, the variability of operating cash flows has a negligible effect on the risk of the debt capital. As a first approximation, this assumption appears reasonable for most of the companies comprising size categories 1 through 25 because of the modest debt to equity levels.
SUMMARY The Duff & Phelps data cover the years 1963 through the present, as compared with 1926 through the present for the Morningstar data. Two results of the Size Study seem strikingly significant: 1. In spite of the different time period, the size effect results corroborate the Morningstar results that the size effect is empirically observed. 2. The results are significantly similar for all eight measures of company size. Although the market value of common equity has both the highest degree of statistical significance and the steepest slope when regressing average returns against size, all size measures show a high degree of statistical significance. This is quite convenient in the context of valuing private companies, since it enables the analyst to start with a known size measure rather than an estimated market value of equity, which is the value being sought.
Chapter 13
Criticisms of the Size Effect Introduction Is the Size Effect the Result of Incorrectly Measuring Betas? Composition of the Smallest Decile Data Issues Risks of Small Companies Relationship of Size and Measures of Risk Summary Appendix 13A
INTRODUCTION In Chapter 12, we discussed two sets of independent studies that document and quantify the size effect: Morningstar studies and Duff & Phelps studies. The size effect, though, is not without controversy, and various commentators question the validity of the small-stock effect. In fact, some commentators contend that the historical data are so flawed that practitioners can dismiss all research results that support the size effect. For example, is it simply the result of not measuring beta correctly? Are there simply market anomalies that cause the size effect to appear? Is size just a proxy for one or more factors correlated with size and one should directly use those factors to measure risk rather than size?
IS THE SIZE EFFECT THE RESULT OF INCORRECTLY MEASURING BETAS? Authors have investigated problems with measuring beta. If beta is underestimated, the size premium will be observed and the equity discount rate estimated using Formula 8.1 will be underestimated. The size premium can correct for this underestimation. For example, two papers investigated the problem with underestimating betas for troubled firms (which would populate the smaller deciles where size is measured by the market value of equity).1 The market value of equity gets bid down for a troubled company and the troubled company’s stock trades like a call option. In the 2004 study, the author estimates that the betas (measured by the ordinary least squares [OLS] method) for troubled companies are underestimated by more than 20% when the bankruptcy risk is 20%. This would cause the size premium to be overestimated in, for example, Exhibit 12.1 for the tenth decile where betas are estimated using the OLS method of monthly excess returns. 1
We would like to thank David Turney and Nick Arens of Duff & Phelps LLC for helping prepare material for this chapter. Carlos A. Mello-e-Souza, ‘‘Bankruptcy Happens: A Study of the Mechanics of Distressed Driven CAPM Anomalies,’’ Working paper, January 25, 2002, and ‘‘Limited Liability, the CAPM and Speculative Grade Firms: A Monte Carlo Experiment,’’ Working paper, August 18, 2004.
209
210
Cost of Capital
Exhibit 13.1 Size Premium Using Sum Betas Long-term Returns in Excess of CAPM for Decile Portfolios of the NYSE/AMEX/NASDAQ, with Sum Beta 1926–2005
Decile
Sum Beta*
Arithmetic Mean Return
Estimated Return in Excess of Riskless Ratey
1-Largest 2 3 4 5 6 7 8 9 10-Smallest Mid-Cap, 3–5 Low-Cap, 6–8 Micro-Cap, 9–10
0.91 1.06 1.13 1.20 1.24 1.30 1.38 1.48 1.55 1.71 1.17 1.36 1.60
11.29% 13.22% 13.84% 14.31% 14.91% 15.33% 15.62% 16.60% 17.48% 21.59% 14.15% 15.66% 18.77%
6.07% 8.00% 8.62% 9.09% 9.69% 10.11% 10.40% 11.38% 12.26% 16.37% 8.94% 10.44% 13.55%
Size Premium Return in Excess of Riskless Ratez 6.45% 7.50% 8.00% 8.49% 8.77% 9.24% 9.76% 10.50% 11.00% 12.12% 8.28% 9.66% 11.31%
(Return in Excess of CAPM) 0.38% 0.51% 0.62% 0.60% 0.92% 0.87% 0.64% 0.88% 1.26% 4.26% 0.65% 0.78% 2.24%
*Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 Index total returns in excess of the 30-day U.S. Treasury bill, January 1926–December 2005. y
Historical riskless rate is measured by the 80-year arithmetic mean income return component of 20-year government bonds (5.22%).
z
Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 (12.30%) minus the arithmetic mean income return component of 20-year government bonds (5.22%) from 1926 to 2005. Source: Stocks, Bonds, Bills, and Inflation1 Valuation Edition 2006 Yearbook. Copyright # 2006 Morningstar, Inc. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) To purchase copies of the Valuation Edition Yearbook, or for more information on other Morningstar publications, please visit global.morningstar.com/DataPublications. Calculated (or derived) based on CRSP1 data, Copyright # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago.
Morningstar publishes size premium statistics where betas are estimated using the sum beta method. The sum beta method is an alternative way of handling monthly data, essentially averaging betas for two or more months. This method can provide a better measure of beta for small stocks by taking into account the lagged price reaction of stocks of small companies to movements in the stock market. The data indicate that even using the sum beta method, when applied to the Capital Asset Pricing Method (CAPM), beta does not account for the returns in excess of the risk-free rate historically found in small stocks. Exhibit 13.1 displays the Morningstar size premium data using the sum beta method. Morningstar also calculates size premium data using annual betas (see Exhibit 12.3). Size premium calculated using annual betas (as displayed in Exhibit 12.3) or sum beta (as displayed in Exhibit 13.1) should be less plagued by the overestimation problem due to incorrectly measuring beta (see Chapter 10 section on sum beta). But the troubled company issue still plagues the tenth decile. Some commentators have stated that you should use the Morningstar size premiums derived using the OLS method (Exhibit 12.1) when estimating the subject company beta using the OLS method and sum beta method (Exhibit 13.1) when estimating the subject beta using the sum beta method, and this eliminates problems. This is not accurate. You should be using the most accurate estimate of the size premium and the most accurate method of estimating the beta for the subject company. Using two inaccurate estimates (size premium and subject company beta) does not make for an accurate estimate of anything.
Composition of the Smallest Decile
211
COMPOSITION OF THE SMALLEST DECILE Morningstar also divides the tenth decile into 10a and 10b, 10a being the top half of the tenth decile and 10b being the bottom half of the tenth decile (measured by market capitalization; see Exhibit 13.2). Comparing Exhibits 12.1 and 13.2 (both calculated using OLS beta estimates) shows the dramatic difference between the smallest 5% of companies and the next smallest 5%. The size premium for the tenth decile from Exhibit 12.1 equals 6.36% while the size premiums for deciles 10a and 10b from Exhibit 13.2 equal 4.39% and 9.83% respectively. What kind of companies populate decile 10b? Morningstar includes all companies with no exclusion of speculative grade or distressed companies whose market capitalization is small because they are speculative or distressed. Exhibit 13.3 displays information on the type of companies that are included in decile 10b (New York Stock Exchange [NYSE], American Stock Exchange [AMEX], and NASDAQ companies). From these data we can conclude:
Betas used for calculating the size premium for decile 10b (OLS method) understate the beta estimates and overstate the size premium. (See comparison of OLS betas and sum betas in ‘‘Measures of Risk’’ section of Exhibit 13.3).
Exhibit 13.2 Returns in Excess of CAPM with Tenth-Decile Split Long-Term Returns in Excess of CAPM Estimation for Decile Portfolios of the NYSE/AMEX/NASDAQ, with 10th Decile Split, 1926–2005
Decile
Beta*
Arithmetic Mean Return
1-Largest 2 3 4 5 6 7 8 9 10a 10b-Smallest Mid-Cap, 3–5 Low-Cap, 6–8 Micro-Cap, 9–10
0.91 1.04 1.10 1.13 1.16 1.18 1.23 1.28 1.34 1.43 1.39 1.12 1.22 1.36
11.29% 13.22% 13.84% 14.31% 14.91% 15.33% 15.62% 16.60% 17.48% 19.71% 24.87% 14.15% 15.66% 18.77%
Realized Return in Excess of Riskless Ratey
Estimated Return in Excess of Riskless Ratez
6.07% 8.00% 8.62% 9.09% 9.69% 10.11% 10.40% 11.38% 12.26% 14.49% 19.65% 8.94% 10.44% 13.55%
6.45% 7.33% 7.77% 7.98% 8.20% 8.38% 8.73% 9.05% 9.50% 10.10% 9.82% 7.91% 8.63% 9.61%
Size Premium (Return in Excess of CAPM) 0.37% 0.67% 0.85% 1.10% 1.49% 1.73% 1.67% 2.33% 2.76% 4.39% 9.83% 1.02% 1.81% 3.95%
*Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 total returns in excess of the 30-day U.S. Treasury bill, January 1926–December 2005. y Historical riskless rate is measured by the 80-year arithmetic mean income return component of 20-year government bonds (5.22%). z Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 (12.30%) minus the arithmetic mean income return component of 20-year government bonds (5.22%) from 1926 to 2005. Source: Stocks, Bonds, Bills, and Inflation1 Valuation Edition 2006 Yearbook. Copyright # 2006 Morningstar, Inc. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) To purchase copies of the Valuation Edition Yearbook, or for more information on other Morningstar publications, please visit global.morningstar.com/DataPublications. Calculated (or derived) based on CRSP1 data, Copyright # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago.
212 Exhibit 13.3 Million ($ millions) Size:
Cost of Capital Breakdown of Decile 10b Companies as of September 30, 2005: Market Value under $169
Mkt Value Equity
99th percentile 75th percentile Median 25th percentile 1st percentile
Book Equity
$161 $89 $54 $28 $5
MVIC*
Total Assets
$460 $120 $69 $35 $7
$1,078 $162 $53 $21 $4
$147 $48 $25 $11 $6
*MVIC ¼ Market Value of Equity þ Book Value of Preferred Stock þ Debt
Profitability:
Sales
5-yr avg Net Income before Ex.
99th percentile 75th percentile Median 25th percentile 1st percentile
$662 $61 $28 $12 $
$10 $2 $0 $5 $50
5-yr avg EBITDA
Latest Fiscal Year Return on Book Equity
$46 $5 $1 $2 $28
58% 10% 2% 21% 349%
Largest companies as measured by Total Assets ($ millions):
United Western Bancorp, Inc. ESB Financial Corp. First Mariner Bancorp First United Corporation CFS Bancorp, Inc. American Realty Investors, Inc. First M&F Corp. Exchange National Bancshares, Inc. Franklin Credit Management Corp. Ion Media Networks, Inc.
Assets
Mkt Value Equity
1-yr Price Change
$2,028 $1,832 $1,385 $1,300 $1,260 $1,257 $1,247 $1,180 $1,163 $1,151
$88 $158 $105 $122 $165 $96 $158 $118 $75 $35
þ2.7% 13.9% 1.9% 1.8% 3.4% þ11.4% þ5.7% 3.1% þ54.6% 66.7%
Mkt Value Equity
1-yr Price Change
$92 $155 $166 $68 $25 $82 $134 $167 $89 $81
þ65.3% þ22.8% þ61.4% 16.4% 59.2% 53.5% þ32.2% 42.0% 42.9% 41.8%
Largest companies as measured by Sales ($ millions): Sales Adams Resources & Energy, Inc. Bally Total Fitness Holding Corp. Village Super Market, Inc. GTSI Corp. Constar International, Inc. Finlay Enterprises, Inc. National Medical Health Card Systems, Inc. Pope & Talbot, Inc. Milacron, Inc. Tweeter Home Entertainment Group, Inc.
$2,269 $1,020 $984 $930 $928 $838 $830 $815 $805 $795
Composition of the Smallest Decile
213
Exhibit 13.3 (Continued) Largest companies as measured by Book Value ($ millions):
Pomeroy IT Solutions, Inc. Dominion Homes, Inc. Delta Galil Industries, Ltd. California First National Bancorp International Shipholding Corp. Zapata Corp. MAIR Holdings, Inc. InFocus Corp. Johnson Outdoors, Inc. Bombay Company, Inc.
Book Value
Mkt Value Equity
1-yr Price Change
$218 $194 $192 $188 $179 $173 $167 $167 $166 $166
$143 $131 $128 $144 $104 $137 $120 $137 $149 $160
10.3% 33.1% 43.7% 2.0% þ19.6% 3.6% 28.9% 62.3% 14.7% 39.8%
Largest companies as measured by 5-yr Average Net Income (before extraordinary items) ($ millions): 5-yr avg Net Income
Mkt Value Equity
1-yr Price Change
$20 $16 $16 $12 $12 $12 $12 $12 $11 $11
$131 $97 $149 $166 $143 $110 $161 $144 $136 $129
33.1% 23.8% 14.7% þ61.4% 10.3% þ24.5% 10.9% 2.0% 6.3% 43.8%
Dominion Homes, Inc. Hallwodd Group, Inc. Johnson Outdoors, Inc. Village Super Market, Inc. Pomeroy IT Solutions, Inc. ePlus, Inc. Merchants Bancshares, Inc. California First National Bancorp Firstbank Corp. Hancock Fabrics, Inc.
Measures of Risk (NYSE +AMEX+NASDAQ companies): ($ millions) Size: 99th percentile 75th percentile Median 25th percentile 1st percentile
Mkt Value Equity
OLS Beta
$161 $89 $54 $28 $5
5.54 1.69 0.80 0.25 1.79
Sum Beta 8.18 2.34 1.11 0.39 2.43
Measures of Risk (NYSE companies): ($ millions) Size: 99th percentile 75th percentile Median 25th percentile 1st percentile
Mkt Value Equity
OLS Beta
Sum Beta
$167 $129 $98 $61 $26
3.57 1.42 0.75 0.27 0.23
3.64 2.28 1.19 0.52 0.69
Source: Compiled from Standard & Poor’s Compustat Data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
214
Cost of Capital
Decile 10b is populated by many large (see companies as measured by Total Assets section of Exhibit 13.3) but highly leveraged companies with small-market capitalization that likely do not match the characteristics of financially healthy but small companies. Stocks of many of the troubled companies probably are trading like call options (large upside, limited downside). Even if you were to use the sum beta method, the beta estimates would likely be underestimated and the size premium overstated.
The Duff & Phelps studies screen out troubled companies and use the sum beta method. They still observe the size effect for a more recent period (since 1963), where size is measured by eight different size measures including six that are not market capitalization based.
DATA ISSUES Critics of the size effect point out various issues with the data used, resulting in anomalies which people mistakenly have observed as the size effect. These data issues are: seasonality, bid/ask bounce bias, transaction costs, and time-varying risk factors. We present a discussion of these issues in Appendix 13A. Some analysts have commented on the fact that small companies have not outperformed large companies consistently, particularly after 1982. The only reason for breaking the data between preand post-1982 periods is that Morningstar changed the methodology for calculating its ‘‘smallcompany’’ index returns in 1982.2 Through 1981, the Morningstar small-company series was calculated using the returns on a synthetic portfolio constructed from Center for Research in Security Prices (CRSP) data for stocks in the smallest quintile of the NYSE (ranked by market value). This is ‘‘synthetic’’ in the sense that it is not based on the returns of an actual fund. Actually, it is retrospectively calculated from a database of stock returns making assumptions about portfolio balance and reinvestment. From 1982 onward, Morningstar measured the small-company returns using the actual returns on the Dimensional Fund Advisors Small Company 9-10 Fund (DFA). The DFA returns are net of transaction costs and free of the delisting bias just discussed. For some time after 1982, small companies did not, on average, outperform larger stocks (as measured by the Morningstar large company returns). This observation sometimes is cited to cast doubt on the integrity of the pre-1982 small-company data. Some analysts contend that the smallstock effect disappeared after 1981 because Morningstar switched from the ‘‘biased’’ CRSP data to the ‘‘unbiased’’ DFA returns. This argument does not withstand scrutiny. If you want to illustrate the extent to which a ‘‘bias’’ is eliminated by using the DFA returns, it is not logical to compare the post1981 DFA premium to a pre-1982 premium derived from CRSP data. Rather, you would more appropriately compare the DFA returns to CRSP returns over the same period. Exhibit 13.4 presents size premium data for the CRSP deciles for various recent periods. These size premiums are calculated relative to the Morningstar income returns on long-term U.S. government bonds using annual betas. As you see, while the size premium has varied in magnitude, it still exists in the most recent 20-year period (even after 1981).
2
David King, ‘‘Do Data Biases Cause the Small Stock Premium?’’ Business Valuation Review (June 2003): 56–61.
Data Issues Exhibit 13.4
215 Returns in Excess of CAPM with Standard & Poor’s 500 Benchmark
Table 1. Long-term Returns in Excess of CAPM Estimation for Decile Portfolios of the NYSE/AMEX/NASDAQ, 1986–2005
Decile 1-Largest 2 3 4 5 6 7 8 9 10-Smallest
Beta*
Arithmetic Mean Return
Realized Return in Excess of Riskless Ratey
Estimated Return in Excess of Riskless Ratez
Size Premium (Return in Excess of CAPM)
Standard Deviation of Realized Excess Return
1.07 0.90 0.93 0.90 0.86 0.95 0.92 0.92 0.92 0.82
12.89% 14.11% 14.27% 14.09% 13.12% 14.02% 13.80% 14.26% 14.33% 15.32%
6.09% 7.30% 7.47% 7.29% 6.32% 7.22% 7.00% 7.45% 7.53% 8.52%
6.79% 5.71% 5.89% 5.71% 5.44% 6.01% 5.86% 5.84% 5.85% 5.20%
0.70% 1.59% 1.58% 1.58% 0.87% 1.20% 1.14% 1.61% 1.68% ‘ 3.32%
17.73% 15.67% 17.04% 16.59% 17.61% 20.02% 19.35% 21.32% 23.99% 27.70%
Table 2. Long-term Returns in Excess of CAPM Estimation for Decile Portfolios of the NYSE/AMEX/NASDAQ, 1976–2005
Decile 1-Largest 2 3 4 5 6 7 8 9 10-Smallest
Beta*
Arithmetic Mean Return
Realized Return in Excess of Riskless z Rate
Estimated Return in Excess of Riskless Ratey
Size Premium (Return in Excess of CAPM)
Standard Deviation of Realized Excess Return
1.05 0.92 0.91 0.91 0.85 0.89 0.92 0.93 0.89 0.80
13.19% 15.16% 16.02% 16.21% 16.24% 17.82% 17.45% 18.53% 18.17% 18.85%
5.31% 7.28% 8.15% 8.34% 8.36% 9.95% 9.58% 10.66% 10.30% 10.97%
6.27% 5.49% 5.42% 5.41% 5.06% 5.31% 5.47% 5.52% 5.30% 4.75%
0.96% 1.80% 2.73% 2.93% 3.31% 4.64% 4.10% 5.14% 5.00% 6.22%
16.40% 15.18% 15.90% 16.20% 16.92% 19.00% 19.03% 21.22% 22.42% 25.56%
Table 3. Long-term Returns in Excess of CAPM Estimation for Decile Portfolios of the NYSE/AMEX/NASDAQ, 1966–2005
Decile 1-Largest 2 3 4 5 6 7 8 9 10-Smallest
Beta*
Arithmetic Mean Return
Realized Return in Excess of Riskless Ratey
Estimated Return in Excess of Riskless z Rate
Size Premium (Return in Excess of CAPM)
Standard Deviation of Realized Excess Return
1.02 0.98 1.01 1.09 1.05 1.09 1.16 1.19 1.20 1.22
10.98% 12.51% 13.86% 14.01% 14.23% 15.39% 14.98% 16.36% 15.88% 17.61%
3.54% 5.08% 6.42% 6.57% 6.79% 7.95% 7.55% 8.92% 8.44% 10.18%
4.24% 4.10% 4.22% 4.54% 4.37% 4.55% 4.85% 4.97% 5.00% 5.09%
0.70% 0.97% 2.21% 2.03% 2.42% 3.41% 2.70% 3.95% 3.45% 5.09%
17.06% 17.16% 18.39% 20.38% 21.10% 22.64% 24.12% 26.95% 28.65% 33.66% (Continued )
216 Exhibit 13.4
Cost of Capital (Continued)
Table 4. Long-term Returns in Excess of CAPM Estimation for Decile Portfolios of the NYSE/AMEX/NASDAQ, 1956–2005
Decile
Beta*
Arithmetic Mean Return
1-Largest 2 3 4 5 6 7 8 9 10-Smallest
1.00 0.99 1.04 1.11 1.07 1.12 1.21 1.23 1.24 1.26
11.12% 12.81% 13.98% 14.19% 14.18% 15.14% 15.07% 16.16% 15.72% 17.15%
Realized Return in Excess of Riskless Ratey
Estimated Return in Excess of Riskless z Rate
Size Premium (Return in Excess of CAPM)
Standard Deviation of Realized Excess Return
4.41% 6.10% 7.27% 7.48% 7.47% 8.43% 8.36% 9.45% 9.01% 10.44%
5.03% 4.97% 5.19% 5.56% 5.38% 5.62% 6.07% 6.18% 6.19% 6.29%
0.61% 1.13% 2.08% 1.92% 2.09% 2.81% 2.29% 3.27% 2.83% 4.14%
16.74% 17.14% 18.58% 20.37% 21.07% 22.59% 24.24% 26.41% 27.87% 32.27%
*Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 total returns in excess of the 30-day U.S. Treasury bill, January 1956–December 2005, January 1966–December 2005, January 1976–December 2005, and January 1986–December 2005. y
Historical riskless rate is measured by the arithmetic mean income return component of 20-year government bonds for each period. Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 minus the arithmetic mean income return component of 20-year government bonds for each period. z
Source: Calculated (or derived) based on CRSP1 data, Copyright # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago. Calculations performed by Duff & Phelps LLC. Used with permission. All rights reserved.
RISKS OF SMALL COMPANIES Traditionally, small companies are believed to have higher required rates of return than large companies because small companies inherently are more risky. One study finds that analysts and investors have difficulty evaluating small, little-known companies and estimating traditional quantitative measures of risk. This ‘‘ambiguity’’ adds to the risk of investment and the return required to attract investors.3 However, this leaves the question of why small-stock returns have not consistently outperformed large-company stocks for various periods. The data suggest alternative views. Readers of the SBBI Yearbooks have long been aware that the small-stock premium tends to move in cycles, with periods of low premiums followed by periods of high premiums. Periods in which small firms have outperformed large firms have generally coincided with periods of economic growth. At least one study contends that the variability in the size effect over time is predictable since large firms generally outperform small firms in adverse economic conditions. Credit conditions are exceedingly important for all firms, but especially for small firms. Small firms generally are at a disadvantage when it comes to financing, and suppliers of debt capital are less likely to lend to small firms in periods of adverse economic conditions. For this reason, analysts should not be astonished to find stocks underperforming for a lengthy period of time. But even then, factors impacting profitability change over time. For 3
R. Olsen and G. Troughton, ‘‘Are Risk Premium Anomalies Caused by Ambiguity?’’ Financial Analysts Journal (March/April 2000): 24–31.
Risks of Small Companies
217
40%
0
Exhibit 13.5
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
–40%
Small-Stock Premium, 1982–2006, Small- Minus Large-Company Returns
Source: Calculated (or derived) based on CRSP1 data, Copyright # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
example, since the late 1990s companies have faced a perceived lack of pricing power. In this type of environment, small firms are likely to be at a disadvantage.4 Exhibit 13.5 plots the annual return premium for the returns of the CRSP tenth decile compared to the first decile from 1982 through 2006. The overall pattern since 1982 resembles the sort of cycles seen from 1926 to 1981. In this sense, small stocks have performed in recent years much as they have always performed. Some analysts claim that the historical average size premium is greatly reduced if you exclude the period 1974 through 1983. During that time, small stocks outperformed large stocks by an extraordinary margin. It makes little sense to exclude a 10-year period from the calculation of a historical average merely because its average premium was higher than that of any other 10-year period. Advocates of the size effect can find satisfaction in the erratic performance of small-cap stocks. If you believe that small stocks are riskier than large stocks, then it follows that small stocks should not always outperform large stocks in all periods. This is true even though the expected returns are higher for small stocks. Bond returns also occasionally outperform stock returns, yet few would contend that over time the average return on bonds is greater than the average return on stocks. One market observer has written: ‘‘An important question that is not answered by the doubters of the small stock effect is why smaller capitalization stocks have had performance cycles at all.’’5 The explanations of data bias that have been offered by the doubters are not such as would give rise to the small-stock cycles that can be observed in the historical data. For instance, stock delistings may follow cyclical business conditions, giving some cyclicality to the delisting bias. Nonetheless, the small-stock premium is not strongly correlated with the business cycle. For example, during bull markets, small stocks sometimes outperform and sometimes underperform larger stocks. Moreover, the delisting effect is much too small to account for the wide swings that are evident over time in the small-stock premium. It is even more difficult to imagine how transaction costs could give rise to the observed multiyear cycles because these transaction costs are incurred with every trade, every day. But some analysts analyze small firms as equivalent to scaled-down large firms. Practitioners know that small firms have different risk characteristics from large firms. One study frames the 4 5
Satya Dev Pradhuman, Small-Cap Dynamics: Insights, Analysis, and Models (Bloomberg Press, 2000), 23–28. Richard Bernstein, Style Investing: Unique Insights into Equity Management (New York: John Wiley & Sons, 1995), 142.
218
Cost of Capital
differences in terms of options.6 Potential competitors can more easily enter the ‘‘real’’ market (market for the goods and/or services offered to customers) of the small firm and ‘‘take’’ the value that the small firm has built. Large companies have more resources to better adjust to competition and avoid distress in economic slowdowns. Small firms undertake less research and development and spend less on advertising than large firms, giving them less control over product demand and potential competition. Small firms have fewer resources to fend off competition and redirect themselves after changes in the market occur. Those authors describe the value of the firm as (1) the value of assets in place plus (2) the present value of future growth options minus (3) an unwritten call option (a ‘‘real’’ option) on the business or the value that can be taken by potential competition that can enter the market and destroy value. The value of this unwritten call option increases with volatility. But even though company size and variance of returns are highly correlated, the authors find that this unwritten call option against the value of the small firm is larger than predicted by variance alone. Those authors find a size premium and an economic basis for its existence. The Duff & Phelps Risk Premium Report Risk Study finds that as company size decreases, measures of risk calculated from financial statement data generally increase and that the market demands a greater rate of return as company risks increase; hence the cost of equity capital for small firms is greater. In a recent study, Eugene Fama and Kenneth French studied the makeup of firms that have resulted in the greater than expected returns observed for smaller firms.7 They studied the migration of small (measured by market value) firms during the periods from 1927 to 1963 and 1963 to 2005 and found that a small percentage of successful small firms with their market capitalization increasing due to their success resulted in the preponderance of above-average return observed. Fama and French point out that when stocks are allocated to portfolios in one year, you do not know which stocks will change in size (a small company becoming larger due to its success). If stock prices are rational, the stock price set in one year is the best forecast of (1) the probability of changing size (i.e., succeeding) during the following year and (2) the stock price observed as a result of the success. The size (and value) premium in average returns ‘‘are the result of rational risks of concern to investors.’’8
RELATIONSHIP OF SIZE AND MEASURES OF RISK It has been pointed out in the financial literature that researchers may be mixing a ‘‘size’’ effect with a ‘‘risk’’ effect when measuring company size by ‘‘market value.’’ Market value is not just a function of ‘‘size’’; it is also a function of the discount rate. Therefore, some companies will not be risky (high discount rate) because they are small, but instead will be ‘‘small’’ (low market value) because they are risky. The Duff & Phelps Risk Study goes further in documenting indicators of risk in portfolios of stocks of small companies. It also goes beyond size and beta and investigates the relation between equity returns and fundamental risk measures drawn from company financial statements. In Chapter 14 on company-specific risk, we discuss the Risk Study. In one study the authors determine that after controlling for beta risk, the size effect disappears in ‘‘up markets’’ but appears in ‘‘down markets.’’9 The size effect in down markets appears to account for the size effect across both market conditions. As recessions deepen in down markets the assets of 6
7 8 9
M. S. Long and J. Zhang, ‘‘Growth Options, Unwritten Call Discounts and Valuing Small Firms,’’ EFA 2004 Maastricht Meetings Paper No. 4057, March 2004. Eugene Fama and Kenneth French, ‘‘Migration,’’ Financial Analysts Journal (May/June 2007): 48–58. Ibid., 57. Jungshik Hur and Vivek Sharma, ‘‘Stock Market Returns and Size Premium,’’ Working paper, March 2007.
Summary
219
small companies become more risky, causing investors to require a premium for investing in the small companies. The authors determine that the size premium is correlated to the size of residuals (from beta estimates using regressions of historical returns), casting doubt on market efficiency.
SUMMARY While there have been many criticisms of the size effect, it continues to be observed in data sources that utilize the CAPM methodology. Further, observation of the size effect is consistent with an expansion of the textbook CAPM. This chapter shows that if equilibrium capital asset prices are determined by a segmented model,10 the abnormal returns earned by small-company stocks are only apparent. The apparent small-firm effect is fully explained in a segmented market equilibrium, which explains why it persists for many years and in many countries. Since empirical evidence supports market segmentation, the apparent abnormal returns are explained without the need to assume the existence of systematic statistical errors, market inefficiency, and so on. Studies have shown the limitations of beta as a sole measure of risk. The size premium is an empirically derived correction to the textbook CAPM.
10
As suggested by Haim Levy, ‘‘Equilibrium in an Imperfect Market: A Constraint on the Number of Securities in a Portfolio,’’ American Economic Review (September 1978): 643–658; and Robert C. Merton, ‘‘A Simple Model of Capital Market Equilibrium with Incomplete Information,’’ Journal of Finance (July 1987): 483–510.
Appendix 13A
Other Data Issues Regarding the Size Effect
Seasonality Bid/Ask Bounce Bias Delisting Bias Transaction Costs Risk Factors Are Time-Varying
SEASONALITY The January effect is the empirical observation that rates of return for small stocks have on the average tended to be higher in January than in the other months of the year. The existence of a January effect, however, does not present a challenge to the small-stock effect. This is true unless it can be established that the effect is the result of a bias in the measurement of returns. Some academics have speculated that the January effect may be due to a bias related to tax-loss selling. Investors who have experienced a loss on a security may be motivated to sell their shares shortly before the end of December. An investor will make such a sale in order to realize the loss for income tax purposes. This tendency creates a preponderance of ‘‘sell’’ orders for such shares at year-end. If this is true, then (1) there may be some temporary downward pressure on prices of these stocks, and (2) the year-end closing prices are likely to be at the ‘‘bid’’ rather than at the ‘‘ask’’ price. The prices of these stocks will only appear to recover in January when trading returns to a more balanced mix of buy and sell orders (i.e., more trading at the ask price). Such ‘‘loser’’ stocks will have temporarily depressed stock prices. This creates the tendency for such companies to be pushed down in the rankings when size is measured by market value. At the same time, ‘‘winner’’ stocks may be pushed up in the rankings when size is measured by market value. Thus, portfolios composed of small-market-value companies will tend to have more losers in December, with the returns in January distorted by the tax-loss selling. A recent study finds that the January returns are smaller after 1963–1979 but have reverted to levels that appear before that period.1 More importantly, they find that trading volume for small companies in January does not differ from other months. They conclude that the January effect continues. This appendix draws on a number of works: David King, ‘‘Do Data Biases Cause the Small Stock Premium?’’ Business Valuation Review (June 2003): 56–61; Roger Grabowski and David King, ‘‘Equity Risk Premium,’’ in The Handbook of Business Valuation and Intellectual Property Analysis (New York: McGraw-Hill, 2004), 3–29; and Mathijs A. Van Dijk, ‘‘Is Size Dead? A Review of the Size Effect in Equity Returns,’’ Working paper, February 2006. The authors wish to thank Mr. King and Professor Van Dijk for their contributions to this important topic. 1 Kathryn E. Easterday, Pradyot K. Sen, and Jens A. Stephan, ‘‘The Small Firm/January Effect: Is it Disappearing in US Market Because of Investor Learning?’’ Working paper, June 2007.
220
Delisting Bias
221
This argument vanishes if you use a measure other than market value (e.g., net income, total assets, sales, etc.) to measure size; the size effect is evident in the Duff & Phelps Size Study using size measures other than market capitalization.
BID/ASK BOUNCE BIAS There is an argument that the existence of bid/ask spread adds a bias to all stock returns. Bid/ask spreads may add a bias particularly to portfolios of less liquid (generally smaller) companies that have larger bid/ask spreads. This bias results because the movement from a bid to an ask price creates a measured rate of return that is greater in absolute value than a movement from the same ask price to the same bid price. Since trades occur randomly at either the bid or the ask, a small bias can creep into measured returns. Most studies of the small-size effect (such as those by Morningstar and Duff & Phelps) use the Center for Research in Security Prices (CRSP) database, which generally uses the closing price to measure rates of return. The closing price will be either a bid or an ask. In cases where there were no trades on a given day (the most illiquid stocks with the greatest bid/ask spread), CRSP uses the average of the bid and ask price. This procedure automatically ameliorates the bias to some extent. But for thinly traded stocks, the ask is often a phantom price at which holders would like to sell. Market participants may not be offering stock, especially if they do not have long positions in the stock. This likely makes bids more realistic than asks. This bias can be most pronounced if you measure rates of return on a daily basis. Morningstar and Duff & Phelps calculate returns monthly at the portfolio level. Then they compound the portfolio returns for each 12 months of the year to get that year’s annual return. This procedure further mitigates much of the possible bid/ask bounce bias. The bid/ask bias has only a trivial impact on the observed small stock effect. Average bid/ask spreads are less than 4% of underlying stock price for the smallest decile of the New York Stock Exchange (NYSE). Spreads of even 4% would give rise to biases in measured returns that are, at most, only a few basis points. This assumes that annual returns are being compounded from monthly portfolio results, as in the Duff & Phelps Size Study. However, the size effect is observed even for midsize public companies—companies for which the bid/ask spread averages less than 1.5%. Some analysts have suggested that using the geometric average of realized returns would correct for the bid/ask bounce bias. However, this argument is completely spurious. The difference between the higher arithmetic average and the lower geometric average does not arise from the bid/ask bounce. Geometric averages are always less than arithmetic averages due simply to the principles of mathematics.
DELISTING BIAS A possible delisting bias exists in many studies that have used the CRSP database. The delisting bias may be due to the fact that CRSP in many (but not all) cases is missing prices for the period immediately after a stock is delisted from an exchange. This problem is not caused by a bias in the CRSP data per se because the database explicitly flags all instances of missing returns. The possible bias occurs in how these missing returns are handled when you calculate average returns for portfolios of companies. There are procedures for handling this issue effectively. When these procedures are used appropriately, the size effect still exists after making the adjustment.
222
Cost of Capital
Does delisting bias explain away the size effect? The evidence from the Duff & Phelps Size Study suggests otherwise. Grabowski and King have adjusted for the delisting bias in annual updates published since 1998. In fact, the adjustment for delisting makes little difference in the Duff & Phelps study results. In other words, the size effect is still present after making the delisting adjustment because companies with a history of losses (or with certain other indicators of poor financial performance) are placed in a separate high-financial-risk portfolio. Such companies are not included in any of the Duff & Phelps size-ranked portfolios. Companies with poor financial performance are much more likely to incur a performance-related delisting than are profitable companies. When Grabowski and King first started adjusting for the delisting bias, it caused the average return on the highfinancial-risk portfolio to decline by about 150 basis points. However, the delisting adjustment did not materially affect the average returns on the size-ranked portfolios. Moreover, CRSP completed a multiyear project of filling in the missing delisting data. The evidence from the CRSP white paper on the subject confirms that the delisting bias has been greatly exaggerated.2 First, CRSP now has returns for the large majority of performance-related delists on the NYSE, American Stock Exchange (AMEX), and NASDAQ. The average performance-related delisting across this population reflected a loss of about 22%. Thus, the 30% loss assumed for missing returns in the Duff & Phelps studies now appears overstated. Second, CRSP compared returns on the CRSP capitalization-based portfolios under alternate assumptions about missing delisting returns. For the tenth decile of the NYSE/AMEX/NASDAQ population, the average bias created by ignoring the missing delisting returns is at most about 20 basis points (0.2%) on a compound market-weighted basis for the period 1926 to 2005. This assumes the extreme case that companies with missing delisting returns incur a 100% loss. If you assume a 30% loss, the ‘‘bias’’ virtually disappears. This is important, because Morningstar uses the CRSP capitalization-based portfolios in deriving the size premiums. Accordingly, analysts can safely conclude that there is little bias in the Morningstar data.
TRANSACTION COSTS Capital Asset Pricing Model (CAPM) abstracts from the influence of liquidity on transaction costs. Some analysts have suggested that the size effect should be set aside because various studies have ignored transaction costs in measuring rates of return. The analysts point out that small stocks often have higher transaction costs than large stocks. In addition, the historical size premium can be greatly reduced if one makes certain assumptions about transaction costs and holding periods. However, in a discounted cash flow analysis, analysts typically use projected cash flows that do not make any adjustment for an investor’s hypothetical transaction costs. It may be that small stocks are priced in a way that increases the rates of return so as to reward investors for the costs of executing a transaction. If so, it would be a distortion to express the discount rate on a net-of-transaction-cost basis while the cash flow projections are on a before-transaction-cost basis. Academic studies support the hypotheses that illiquidity is a factor in pricing and returns of stocks and small firms are more sensitive to market liquidity, but the illiquidity factor does not capture the size effect completely. Moreover, any reasonable adjustment for transaction costs should recognize that investors can mitigate these costs on an annual basis by holding their stocks for a longer period. In fact, investors in small companies tend to have longer holding periods than investors in large companies.
2
CRSP Delisting Returns (Chicago: Center for Research in Security Prices, University of Chicago, 2001).
Risk Factors Are Time-Varying
223
RISK FACTORS ARE TIME-VARYING Many treat the CAPM as if beta estimates are constant over time. But considerable research indicates that betas vary considerably over time. Academic studies that allow for time-varying betas and other risk factors generally can explain some, but not all, of the size premium empirically observed.
Chapter 14
Company-Specific Risk
Introduction Estimating Company-Specific Risk Duff & Phelps Risk Study Total Beta Cost to Cure Other Company-Specific Factors Distress Valuing Firms in Distress Cost of Equity Capital of Distressed Firms Summary
INTRODUCTION Company-specific risk adjustments are intended to account for company-specific factors affecting a company’s competitive position in the industry or unique characteristics that cause investors to view the company’s risk differently from that of, say, the ‘‘pure plays’’ to which it might be compared. Practitioners often identify company-specific characteristics that they believe would cause investors to view the discount rate that should be applied to the expected cash flows of the subject company to differ from the discount rate investors would apply to the expected cash flows of those pure plays. According to the textbook Capital Asset Pricing Method (CAPM), unanticipated events arising from company-specific risk factors will affect the price of the stock through expected future cash flows, and only systematic risk will affect the cost of equity capital. Discount rates should be applied to expected cash flows, which should include the impacts of the full scope of possible cash flows, good outcomes and bad outcomes. Brealey, Myers, and Allen critique the use of the company-specific risk adjustment: Managers often add fudge factors to discount rates to offset worries. . . . This sort of adjustment makes us nervous. . . . the need for a discount rate adjustment usually arises because managers fail to give bad outcomes their due weight in cash flow forecasts . The managers then try to offset that mistake by adding a fudge factor to the discount rate.1
The proper estimation of beta or other systematic risk factor (e.g., downside beta) should help the practitioner better match the risk and return as priced by investors with the appropriate risk and return for the subject division, reporting unit, or closely held business. In Chapter 11 we discussed research that shows that investors are much less diversified than expected, ever with the efforts of investment 1
Richard A. Brealey, Stewart C. Myers, and Franklin Allen, Principles of Corporate Finance, 8th ed. (Boston: Irwin McGrawHill, 2006), 225.
225
226
Cost of Capital
advisors urging them to diversify. Further, they do not all hold the market portfolio as predicted by textbook CAPM. Based on these findings, it is reasonable that investor rates of return expectations are influenced by company-specific risk factors. Many analysts are able to express qualitative reasons for company-specific risk adjustments but rarely can provide data relating those qualitative factors to actual measurements in expected return. In this chapter we discuss approaches to better quantify the total risk and the related market returns of guideline public companies. When you use the total risk and the related return, you are including company-specific risk. Another company-specific risk issue is distress. We discuss issues surrounding distress in this chapter.
ESTIMATING COMPANY-SPECIFIC RISK DUFF & PHELPS RISK STUDY Practitioners typically have been able to quantify the relationship between risk and expected return only by measuring risk in terms of beta and size. While company size is a risk factor in and of itself, Grabowski and King were interested in understanding if the stock market recognized risk as measured by fundamental or accounting information. They used a database combining stock prices, number of shares, and dividend data by company from the Center for Research in Security Prices (CRSP) database with accounting and other data from the Standard & Poor’s Compustat database to analyze fundamental risk. Thereafter, Grabowski and King published a series of articles reporting their findings. That research correlates realized equity returns (and historical realized risk premiums) directly with measures of company risk derived from accounting information. The measures of company risk derived from accounting information may also be called ‘‘fundamental’’ or ‘‘accounting’’ measures of company risk to distinguish them from a stock market–based measure of equity risk such as beta. The Duff & Phelps Risk Premium Report Risk Study annually updates this research.2 Because Grabowski and King were interested in understanding how the stock market prices the risk of established companies, the Risk Study is limited to companies with a track record of profitable performance. They use three alternate measures of company risk: 1. Operating margin (The lower the operating margin, the greater the risk.) 2. Coefficient of variation in operating margin (The greater the coefficient of variation, the greater the risk.) 3. Coefficient of variation in return on equity (The greater the coefficient of variation, the greater the risk.) The data show a clear relationship between risk measures and historical rates of return and realized premiums. The Duff & Phelps studies separate companies into a separate portfolio for companies with any one of these characteristics was created for companies:
2
This section is adapted from the Duff & Phelps Risk Premium Report 2006. Used with permission. The Risk Premium Report was published as the Standard & Poor’s Corporate Value Consulting Risk Premium Report for reports titled 2002 to 2004 and as the PricewaterhouseCoopers Risk Premium Reports and Price Waterhouse Risk Premium Reports for years before 2002.
Estimating Company-Specific Risk
227
Identified by Compustat as in bankruptcy or in liquidation With five-year-average net income available to common equity for the previous five years less than zero (either in absolute terms or as a percentage of the book value of common equity) With five-year-average operating income for the previous five years (defined as sales minus [cost of goods sold plus selling, general and administrative expenses plus depreciation expense]) less than zero (either in absolute terms or as a percentage of net sales) Companies with negative book value of equity at any of the previous five fiscal year-ends With debt-to-total capital of more than 80% (with ‘‘debt’’ measured as preferred stock at carrying value plus long-term debt (including current portion) and notes payable in book value terms and total capital measured as book value of debt plus market value of equity)
These companies were excluded from the base set of companies and placed in a separate portfolio labeled the ‘‘high-financial-risk’’ portfolio. Segregating such companies into a separate portfolio isolates the effects of high financial risk. Otherwise, the results might be biased for smaller companies to the extent that highly leveraged and financially distressed companies tend to have both high returns and low market values. It is possible to imagine financially distressed (or highly risky) companies that lack any of the listed characteristics. It is also easy to imagine companies that have one of these characteristics but that would not be considered financially distressed. The resulting high-financial-risk portfolio is composed largely of companies whose financial condition is significantly inferior to the average, financially ‘‘healthy’’ public company. We discuss the high-financial-risk portfolio later in this chapter. To calculate realized risk premiums, Grabowski and King first calculate an average rate of return for each portfolio over the sample period. Returns are based on dividend income plus capital appreciation and represent returns after corporate-level income taxes (but before owner-level taxes). Then they subtract the average income return earned on long-term U.S. government bonds over the same period (using SBBI data) to arrive at an average realized risk premium. The Duff & Phelps Risk Study finds that as company size decreases, measures of risk calculated from financial statement data generally increase and that the market demands a greater rate of return as company risks increase; hence the cost of equity capital for riskier firms is greater.
Relationship of Size and Measures of Risk from Company Financial Statements Market value is not just a function of size; it is also a function of the discount rate. Therefore, some companies will not be risky (high discount rate) because they are small but instead will be ‘‘small’’ (low market value) because they are risky. The Risk Study goes further in documenting indicators of risk in portfolios of stocks of small companies. It also goes beyond size and investigates the relation between equity returns and fundamental risk measures. A variety of academic studies have examined the relationship between financial statement data and various aspects of business risk.3 Research has shown that measures of earnings volatility can be useful in explaining credit ratings, predicting bankruptcy, and explaining the CAPM beta. The Risk Study exhibits (e.g., Exhibit 14.1) document the relationship between the three risk measures and historical rates of return. Two of the risk measures are defined in terms of the coefficient of variation. The coefficient of variation is the standard deviation divided by the mean and measures volatility relative to the average 3
A survey of the academic research can be found in Gerald White, Ashwinpaul Sondi, and Haim Fried, The Analysis and Use of Financial Statements, 3rd ed. (New York: John Wiley & Sons, 2003), Chapter 18.
Duff & Phelps Risk Study: Risk Premiums for Use in Build-up Method
34.2% 27.1% 23.6% 21.1% 18.9% 17.5% 15.7% 14.5% 13.5% 12.6% 11.8% 11.2% 10.7% 10.0% 9.4% 8.8% 8.3% 7.8% 7.1% 6.5% 5.7% 4.8% 4.1% 3.3% 1.9%
Median Operating Margin
79 45 57 54 47 68 63 62 58 58 54 66 73 57 68 70 56 62 67 73 113 63 92 91 91
0.47 0.57 0.63 0.68 0.72 0.76 0.80 0.84 0.87 0.90 0.93 0.95 0.97 1.00 1.03 1.06 1.08 1.11 1.15 1.18 1.25 1.32 1.39 1.48 1.71
7.18%
7.20%
17.67%
12.01%
21.73%
14.51% 12.34% 13.69% 13.71% 14.84% 14.84% 16.28% 14.47% 17.44% 16.07% 14.26% 16.03% 17.02% 17.61% 17.01% 18.25% 18.76% 18.68% 19.77% 18.95% 19.55% 19.40% 19.90% 21.09% 19.41%
Arithmetic Average Return
10.47%
4.81%
14.53%
7.31% 5.14% 6.49% 6.51% 7.64% 7.64% 9.08% 7.27% 10.24% 8.87% 7.06% 8.83% 9.82% 10.41% 9.81% 11.05% 11.56% 11.48% 12.57% 11.75% 12.35% 12.20% 12.70% 13.89% 12.21%
Arithmetic Risk Premium 5.96% 6.69% 7.12% 7.48% 7.81% 8.05% 8.39% 8.64% 8.86% 9.09% 9.29% 9.45% 9.60% 9.82% 10.01% 10.20% 10.40% 10.60% 10.88% 11.13% 11.58% 12.11% 12.60% 13.24% 14.92%
Smoothed Average Risk Premium
Source: Derived from data from the Center for Research in Security Prices. # CRSP1, Center for Research in Security Prices. Graduate School of Business, The University of Chicago. Used with permission. All rights reserved. wwwcrsp.chicagogsb.edu. Calculations by Duff & Phelps LLC.
15.01%
16.49%
13.30% 11.15% 12.53% 12.44% 13.52% 13.31% 14.63% 12.84% 15.74% 14.11% 12.33% 14.13% 14.94% 15.35% 14.63% 16.05% 16.23% 16.07% 17.15% 16.09% 16.85% 16.11% 17.12% 17.91% 16.25%
Geometric Average Return
Long-term treasury Income (SBBI data)
38.05%
16.91% 16.43% 15.88% 16.86% 17.39% 18.82% 19.96% 19.17% 19.86% 21.39% 20.99% 21.27% 22.20% 22.73% 24.10% 22.46% 24.30% 24.69% 24.95% 26.28% 25.97% 28.22% 26.08% 28.22% 27.55%
Standard Deviation of Returns
Small Stocks (SBBI data)
1.62
0.81 0.77 0.80 0.95 0.99 1.11 1.15 1.12 1.20 1.20 1.21 1.19 1.21 1.19 1.23 1.18 1.27 1.27 1.29 1.27 1.26 1.29 1.30 1.32 1.29
Beta (SumBeta) Since ‘63
10.75%
680
Number as of 2005
Log of Median Op Margin
Large Stocks (SBBI data)
High financial risk
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Portfolio Rank by Size
47.51%
30.58% 34.49% 32.56% 26.87% 22.70% 19.17% 18.38% 20.20% 20.89% 21.57% 22.66% 22.83% 22.77% 23.86% 24.78% 26.52% 26.88% 27.84% 29.31% 31.12% 31.37% 32.07% 33.74% 33.66% 32.92%
Average Debt/ MVIC
Companies Ranked by Operating Margin Historical Equity Risk Premium: Average Since 1963 Data for Year Ending December 31, 2005
Exhibit 14.1
7.195% 0.796% 9.04
Regression Output: 2.607% 1.148% 78% 25 23
20% 18% 16% 14% 12% 10% 8% 6% 4% 2% 0% –1.8 –1.6 –1.4 –1.2 –1.0 –0.8 –0.6 –0.4 –0.2 Median Operating Margin
Smoothed Premium vs. Unadjusted Average
Smoothed Premium = 2.607% 7.195% * Log(Operating Margin)
Constant Std Err of Y Est R Squared No. of Observations Degrees of Freedom X Coefficient(s) Std Err of Coef. t-Statistic
Risk Premium Study: Data through December 31, 2005 Data Smoothing with Regression Analysis Dependent Variable: Average Premium Independent Variable: Log of Median Operating Margin
Equity Premium
228 0.0
Estimating Company-Specific Risk
229
value of the variable under consideration. Use of the coefficient of variation normalizes for differences in the magnitude of the subject variables. The Duff & Phelps study also documents the relationship of size and risk. For example, Exhibit 12.10 and Exhibit 12.11 display the relationship between two measures of size and the three measures of company risk. The exhibits present average risk measures for each of the size-ranked portfolios of companies that were used in the Size Study (e.g., Exhibits 12.7 and 12.8). While size may be considered a proxy for risk, the Risk Study investigates risk as represented by information in company financial statements. The results reported herein suggest a positive relationship; that is, the greater the risk as measured by historical accounting information, the greater the rate of return earned by equity investors. In addition, the Risk Study does document that size is correlated with these fundamental risk measures. Exhibit 12.10 displays 25 portfolios with size measured by market value of equity as displayed in Exhibit 12.7. Exhibit 12.10 shows, for each portfolio, the average historical realized premium since 1963. Also shown are five measures of risk corresponding to each portfolio: 1. Beta (calculated using the sum beta method applied to monthly returns for 1963 through the latest year) 2. Unlevered sum beta 3. Average operating margin (since 1963) 4. Average coefficient of variation of operating margin (since 1963) 5. Average coefficient of variation of return on book equity (since 1963) We see that the beta (both levered and unlevered) of the portfolios decreases (as expected) as market value of equity increases and that the average operating margin increases as market value of equity increases. We also see that the average coefficient of variation of operating margin and of variation of return on book equity decrease as market value of equity increases. And we see that generally the three fundamental measures of risk display increasing risk as size decreases, as the historical unlevered equity risk premium increases, and as the unlevered beta increases. When you measure company size based on sales or by number of employees, the Risk Study indicates that there is little differentiation in operating margin across the companies of various sizes. But the coefficient of variation of both operating margin and return on book equity indicates increasing risk as size decreases, as with other size measures. Why not just use measures of size as the measure of risk? First, certain measures of size (such as market value of equity) may be imperfect measures of the risk of a company’s operations. For example, a company with a large and stable operating margin may have a small and unstable market value of equity if it is highly leveraged. In this case the risk of the underlying operations is low while the risk to equity is high. Second, while small size may indicate greater risk, some small companies have been able to maintain near economic monopolies by holding a geographic or market niche such that their risk is less than indicated by their size. Alternatively, while larger size (e.g., as measured by sales) may indicate less risk, some companies may be more risky than the average of companies with similar sales. For example, assume the subject company was expecting to emerge from reorganization following bankruptcy. The risk premium appropriate for this company may be more accurately imputed from the pro forma operating profit (after removing nonrecurring expenses incurred during the bankruptcy) than from its size as measured by sales (i.e., the subject company may be more risky than companies with similar sales volume). Use of fundamental accounting measures of risk allows you to assess the risk of the subject company directly. For example, if you observe that the appropriate risk premium for the subject company
230
Cost of Capital
when measuring risk by one or more fundamental risk measures is greater than the risk premium based on size measures, this may be a measure of the investment-specific risk appropriate for the subject company. Using the Duff & Phelps Risk Study in the Build-up Method As an alternative to Formula 12.1 for the build-up method, EðRi Þ ¼ Rf þ RPm þ RPs þ RPu , you can use the Risk Study to develop a risk premium for the subject company that measures risk in terms of the total effect of market risk, size premium, and risk attributable to the specific company. The formula then is modified to be: (Formula 14.1) EðRi Þ ¼ R f þ RPmþsþu where: RPm+s+u ¼ risk premium for the ‘‘market’’ plus risk premium for size plus risk attributable to the specific company Three Measures of Risk, Twenty-Five Risk Categories The Risk Study exhibits (e.g., Exhibit 14.1) report average statistics for the period since 1963. For example, in Exhibit 14.1, the statistics on returns are for the period 1963 through 2005. To estimate historical realized premiums, Grabowski and King use the same methodology as in the Size Study. The Risk Study exhibits present summary data for companies ranked by various measures of risk. The measures are:
Operating margin (operating income divided by sales; operating income is defined as sales minus (cost of goods sold plus selling, general, and administrative expenses plus depreciation expense)) calculated as the mean operating income for the five prior years divided by the mean sales for the five prior years. For example, see Exhibit 14.1.
Coefficient of variation of operating margin calculated as the standard deviation of operating margin over the prior five years divided by the mean operating margin for the same years, where operating margin is operating income as defined above divided by sales. Coefficient of variation of return on book value of equity calculated as the standard deviation of return on book equity for the prior five years divided by the mean return on book equity for the same years (where return on book equity is net income before extraordinary items minus preferred dividends divided by book value of common equity).
The Risk Study exhibits include these statistics:
The median of the risk measure for the latest year (e.g., the median average operating margin for the latest five years before 2003). The reported average risk statistics in, for example, Exhibit 14.1, are calculated for portfolios grouped according to risk, independent of the size of the companies, and are not averages since 1963. They are not the same numbers as reported in, for example, Exhibit 12.10. Exhibit 12.10 reports statistics calculated for portfolios of companies grouped according to size and are averages since 1963. Log (base-10) of the median of the risk measure.
Estimating Company-Specific Risk
231
The number of companies in each portfolio in the latest year. Beta relative to the S&P 500 calculated using the sum beta method applied to monthly returns for 1963 through the latest year.
Standard deviation of historical annual equity returns. Geometric average historical equity return since 1963.
Arithmetic average historical equity return since 1963.
Arithmetic average realized risk premium (historical equity return over long-term government bonds) since 1963 (labeled ‘‘arithmetic risk premium’’). ‘‘Smoothed’’ average realized premium (i.e., the fitted premium from a regression with the average historical realized premium as the dependent variable and the logarithm of the average risk measure as the independent variable) (labeled ‘‘smoothed average risk premium’’). Average carrying value of preferred stock plus long-term debt (including current portion) plus notes payable (‘‘debt’’) as a percent of market value of invested capital (MVIC) since 1963 (labeled ‘‘average debt/MVIC’’).
Each exhibit shows one line of data for each of the 25 risk-ranked portfolios, plus a separate line for the high-financial-risk portfolio. In each case, the high-financial-risk statistics are drawn only from companies for which the ranking criterion (e.g., five-year-average operating margin, etc.) is available. For comparative purposes, the exhibits include average returns from SBBI series for Large Companies, Small Companies, and Long-term Government Bond Income Returns for the period 1963 through the latest year. Exhibit 14.2 displays the observed relationships for the three risk measures and the risk premiums. By each measure of risk that Grabowski and King study, the result is a clear relationship between risk and historical equity returns. The portfolios of companies with higher risk have yielded higher rates of return. Examples The data in the Risk Study can be used as an aid in formulating estimated cost of equity capital using objective measures of the risk of a subject company. In the build-up method, you want to determine a premium over the risk-free rate. The simplest approach is to use exhibits for each of the three risk characteristics and locate the portfolio whose risk is most similar to the subject company. For each guideline portfolio, the column labeled ‘‘smoothed average risk premium’’ gives an indicated historical realized premium over the risk-free rate, RPm+s+u. You could match, say, the operating margin of the subject company with the portfolio composed of stocks with a similar average operating margin. The smoothed premium for this portfolio can then be added to the yield on long-term U.S. government bonds as of the valuation date, resulting in a benchmark required rate of return. The ‘‘smoothed’’ average premium is a more appropriate indicator than the actual historical observation for most of the portfolio groups. Exhibits 14.3 and 14.4 illustrate the application of this method for a hypothetical company. Exhibit 14.3 shows, for a hypothetical company, the calculation of the mean (average) and standard deviation over the last five fiscal years of operating margin and return on book value of equity (ROE). The ratio of the standard deviation to the mean is the coefficient of variation. These risk
–1.4
–1.0
–0.8
–0.6
20% 18% 16% 14% 12% 10% 8% 6% 4% 2% 0% –1.5
Median Operating Margin
–1.2
0.0
Companies Ranked by CV(ROE)
–0.2
20% 18% 16% 14% 12% 10% 8% 6% 4% 2% 0% –2.0
–0.5 0.0 0.5 Log of Median CV(ROE)
–1.0
–0.5
0.0
1.0
1.5
Log of Median CV(Operating Income)
–1.5
Smoothed Premium vs. Unadjusted Average
Companies Ranked by CV (Operating Margin)
Smoothed Premium vs. Unadjusted Average
–1.0
–0.4
Smoothed Premium vs. Unadjusted Average
Equity Premium
Equity Premium
0.5
Exhibit 14.2 Duff & Phelps Risk Study: Risk Premiums for Use in Build-up Method Source: Derived from data from the Center for Research in Security Prices. # CRSP1, Center for Research in Security Prices. Graduate School of Business, The University of Chicago. Used with permission. All rights reserved. wwwcrsp.chicagogsb.edu. Calculations by Duff & Phelps LLC.
20% 18% 16% 14% 12% 10% 8% 6% 4% 2% 0% –1.8 –1.6
Companies Ranked by Operating Margin
Equity Premium
232
Estimating Company-Specific Risk Exhibit 14.3
233
Example of Calculating Risk Measures
Example 1: Coefficient of Variation of Operating Margin: (Standard Deviation of Operating Margin)/(Average Operating Margin)
Net Sales Operating Income Operating Margin Standard Deviation of Op. Margin Average Operating Margin Coefficient of Variation
2005
2004
2003
2002
2001
$900 $150 16.7%
$800 $120 15.0%
$850 $130 15.3%
$750 $80 10.7%
$900 $140 15.6%
2.3% 14.6% 15.8%
Example 2: Coefficient of Variation of Return on Book Value of Equity: (Standard Deviation of ROE)/(Average of ROE)
Book Value Net Income before Extraordinary Items Return on Book Equity (ROE) Standard Deviation of ROE Average ROE Coefficient of Variation
2005
2004
2003
2002
2001
$820 $110 13.4%
$710 $80 11.3%
$630 $90 14.3%
$540 $40 7.4%
$500 $100 20.0%
4.6% 13.3% 34.7%
Source: Duff & Phelps LLC Risk Premium Report 2006. Copyright # 2006. Used with permission. All rights reserved.
metrics can be used in conjunction with the exhibits in the Risk Study to estimate a premium over the risk-free rate. Exhibit 14.4 illustrates the procedure of estimating risk premiums. The indicated risk premium can be added to the risk-free rate to get an estimate of the cost of equity capital. Assuming a risk-free rate of 5.5% (say) and in isolation from other considerations, the results indicate a cost of equity capital in a range of 14.1% to 14.8%, with an average of 14.4%. Other fundamental company risk factors may cause one to adjust this indicated cost of equity capital. Practical Application of the Data The historical average debt/MVIC ratio does not appear to be strongly correlated with either the level or the volatility of the operating margin. This suggests that leverage does not explain the greater
Exhibit 14.4
Example of Estimating Risk Premiums1
Risk Premiums over Risk-free Rate: Using Guideline Portfolios Company Indicator Operating Margin CV(Operating Margin) CV(ROE) Mean premium over risk-free rate, RPm+s+u Median premium over risk-free rate, RPm+s+u 1
14.6% 15.8% 34.7%
Exhibit 14.1 (1) (1)
Guideline Portfolio
RPm+s+u
8 16 15
8.6% 9.3% 8.7% 8.9% 8.7%
From exhibits provided in the Risk Premium Report. Source: Duff & Phelps LLC Risk Premium Report 2006. Copyright # 2006. Used with permission. All rights reserved.
234
Cost of Capital
returns of the riskier portfolios. As expected, the leverage in the high-financial-risk portfolio is significantly greater than that of any of the other portfolios. The debt/MVIC ratio may have moderate correlation with the volatility of return on book equity. Higher leverage accordingly may explain some of the higher returns exhibited by the riskier portfolios (by this measure of risk). The companies that are riskier according to accounting information (operating margins and coefficients of variation) have also exhibited greater risk according to stock market–based risk statistics (betas and standard deviations of annual returns). The realized risk premiums reported are historical averages since 1963. Grabowski and King report the average realized premium over the same period for SBBI Large Company stocks (essentially the S&P 500). This average was 4.81% over the period 1963 to 2005, which is consistent with the evidence of the equity risk premium in Chapter 9. If your estimate of the equity risk premium for the S&P 500 on a forward-looking basis was materially different from the average historical realized premium since 1963, it may be reasonable to assume that the other historical portfolio returns reported here would differ on a forward-looking basis by approximately a similar amount. This forward-looking risk premium can then be added to the risk-free rate as of the valuation date to estimate an appropriate cost of equity capital for the subject company. The Risk Study data should not be used in isolation from other considerations about the subject company, its industry, or the general economic environment. For instance, a wholesale distributor might have thin operating margins compared to the average company on the New York Stock Exchange, yet those margins might exhibit unusually low variation due to a particularly strong position in a stable market niche. Alternatively, a company’s variation of operating income (calculated in the manner used in the study) might be uncharacteristically high due to an unusual event several years in the past. Appropriate knowledge of the company and its industry would give useful guidance in reconciling the historical realized premiums reported in the Risk Study and the historical realized premiums reported in the Size Study for portfolios of companies ranked by size. Size can be an important consideration in determining an appropriate cost of equity capital. The use of a portfolio’s average historical rate of return to calculate a discount rate is based (in part) on the implicit assumption that the risks of the subject company are quantitatively similar to the risks of the average company in the subject portfolio. If the risks of the subject company differ materially from the average company in the subject portfolio, then an appropriate discount rate may be lower (or higher) than a return derived from the average premium for a given portfolio. The data reported in the exhibits where risk statistics are reported for each size category (e.g., Exhibits 12.10 and 12.11) may be helpful in making such a determination.
TOTAL BETA The studies we cite in Chapter 11 suggest that investors in general are much less diversified than predicted by the textbook CAPM. Other studies suggest that at least for small companies (measured by market capitalization), returns are a function of more than beta. Is their risk meaningful information about risk of an investment in the R2 of the beta estimate? One study finds that firms with low R2 are characterized by low-quality earnings, low persistence of earnings, low predictability of earnings, and high volatility of returns. Low R2 firms are fundamentally weak. The results of the study support the view that R2 is an indicator of the uncertainty found by investors. This uncertainty is caused by investors receiving low-quality information and/or fundamental weakness in cash flows, making it
Estimating Company-Specific Risk
235
more difficult for investors to evaluate firm information. This leads to high firm-specific uncertainty associated with firm fundamentals.4 One method of adjusting beta is called total beta, which is beta adjusted for the total risk of the firm. The R2 of the regression of excess returns used to estimate beta regression measures proportion of risk that is market risk and can be used to adjust beta.5 For example, assume the beta for the ‘‘pure play’’ guideline public company = 1.10, the correlation of the regression used to estimate beta = 0.33 (i.e., R, not R2); Rf = 6%; ERP = 5%. We can calculate total beta: (Formula 14.2) Total beta ¼
1:10 ¼ 3:30 0:33
Total cost of equity ¼ 6% þ 3:30ð5%Þ ¼ 22:5% ðnot CAPM of 11:5%Þ Total beta equals the standard deviation of total returns of a stock divided by the standard deviation of total returns of the market portfolio. Total beta includes any risk premium for company size and company-specific risk premium inherent in the guideline public company used in the analysis. From the total cost of equity, we can then infer the company-specific risk premium using Formula 8.5, the expanded CAPM formula: (Formula 14.3) EðRi Þ ¼ Rf þ BðRPm Þ þ RPs þ RPu RPu ¼ EðRi Þ Rf BðRPm Þ RPs where: E(Ri) ¼ Expected rate of return on security i Rf ¼ Rate of return available on a risk-free security as of the valuation date B ¼ Beta RPm ¼ General equity risk premium for the market RPs ¼ Risk premium for small size RPu ¼ Risk premium attributable to the specific company (u stands for unique or unsystematic risk)
4
5
Siew Hong Teoh, Yong Yang, and Yinglei Zhang, ‘‘R-square: Noise or Firm-specific Information?’’ Working paper, October 2, 2006, rev. March 18, 2007. Aswath Damodaran, Damodaran on Valuation: Security Analysis for Investment and Corporate Finance, 2nd ed. (New York: John Wiley & Sons, 2006), 58–59; Peter Butler and Keith Pinkerton, ‘‘Company-Specific Risk—A Different Paradigm: A New Benchmark,’’ Business Valuation Review (Spring 2006): 22–28; Peter Butler and Keith Pinkerton, ‘‘Quantifying CompanySpecific Risk: A New, Empirical Framework with Practical Applications,’’ Business Valuation Update (February 2007): 1–11; Peter Butler and Keith Pinkerton, ‘‘Quantifying Company-Specific Risk: The Authors Answer Your Questions,’’ Business Valuation Resources (August 2007): 9–14; Peter Butler and Keith Pinkerton, ‘‘Comparing the Butler-Pinkerton Model to Traditional Methods Under Four Daubert Criteria,’’ Business Valuation Update (November 2007): 1, 4–7.
236
Cost of Capital
Continuing the example, we get: RPu ¼ 22:5% 6% 1:10ð5%Þ 7:2% ¼ 3:8% where: RPs ¼ Premium over CAPM from 25th portfolio of Duff & Phelps Risk Premium Report, Exhibit 12.12, of 7.2% which we are using as the size premium in this example Does such a measure capture the factors that cause company-specific risk? If you thoroughly analyze the risk factors of guideline public companies, the estimate of company-specific risk premium should reflect the market’s pricing of these risks. As in any use of guideline public companies as a proxy, you are dependent on the availability of good proxy companies and on the thoroughness of the analysis. This qualitative approach complements a qualitative assessment of the strengths, weaknesses, opportunities, and threats of the subject company compared to its peers by matching the subject company to the guideline public companies with comparable (not identical) strengths, weaknesses, opportunities, and threats relative to their peers. One study of the idiosyncratic or company-specific risk found that firms with low R2 are characterized by low-quality earnings, low persistence of earnings, and low predictability of earnings. Such firms are fundamentally weak, and the low R2 is an indication of the uncertainty faced by investors.6 ‘‘Low R2’’ firms are those where the beta estimate using regression techniques has a low R2. Low R2 firms would result in a relatively greater total beta than beta measures of risk. These results are consistent with the typical qualitative assessments of company-specific risk. In another study the authors found that time-varying idiosyncratic or company-specific risk can explain the difference in returns among stock in the U.S., and in the United Kingdom over time. The risk measure the authors use is total risk.7 As an alternative to total beta, you could similarly adjust the downside beta for the R2 of that risk measure. (See Chapter 11 for a discussion and example of calculating downside beta.) Most investors do not consider earning a return greater than expected to be risk; rather, they consider risk as earning a return less than expected. Downside beta and the respective downside total beta would match these characteristics.
COST TO CURE One way to account for company-specific risk is to estimate the cost to cure that risk. For example, if a company-specific risk is reliant on a key salesperson for a large amount of sales, then the cost of buying life insurance sufficient to reimburse the company for the possible loss of that person due to death is one measure of the cost to cure that risk. Another company-specific risk that may be accounted for by estimating the cost to cure is potential environmental cleanup costs. You can estimate the probability weighted costs of remediation given the possibility that a cleanup will be required and the possible timing of a required cleanup. Applying an adjustment for company-specific risk using the cost to cure is completely consistent with capital market theories, as these are adjustments to the expected cash flows. 6 7
See Siew Hong Teoh, Yong Yang, and Yinglei Zhang, ‘‘R-square.’’ Xiafei Li, Chris Brooks, and Joelle Miffre, ‘‘The Value Premium and Time-Varying Unsystematic Risk,’’ Working paper, April 2007.
Distress
237
OTHER COMPANY-SPECIFIC FACTORS Other factors specific to a particular company that affect risk could include, for example:
Concentration of customer base Key person dependence
Key supplier dependence
Abnormal present or pending competition Pending regulatory changes
Pending lawsuits A wide variety of other possible specific factors
Because the size premium tends to reflect some factors of this type, analysts should adjust further only for specific items that are truly unique to the subject company. Analysts must be careful not to include any adjustment for risk factors that may be included in other adjustments.
DISTRESS The standard cost of equity capital models (e.g., CAPM) and standard application of a discounted cash flow analysis assumes the business continues as a going concern. But a firm may be distressed. Its underlying operating business may be struggling (business or economic distress) (i.e., the firm may have suffered a loss of competitiveness, sales revenue may be declining, market share may be lost, costs of labor and materials may be increasing while the firm is unable to increase prices, causing margins to deteriorate, etc.) and/or its debt level may be too high relative to its current operating earnings (financial distress). When the debt level is too high, the firm suffers commercial costs of financial distress (e.g., suppliers may lose confidence and cease offering short-term, favorable payment terms and may eventually require payment on delivery or even in advance; customers may panic and switch in whole or in part to ‘‘safer suppliers’’; the best employees may leave for other jobs; management spends inordinate time working with creditors rather than on business operations; there exist legal costs of exploring restructuring options). The value of the firm in either case can be negatively impacted, and such distress can increase the cost of capital. The formulas for unlevering and relevering betas (and, therefore, capturing the effect of financial risk) are based on modest levels of debt financing and therefore do not adequately capture the impact in the cost of equity capital as levels of debt and distress increase. VALUING FIRMS IN DISTRESS One approach is to value the enterprise rather than equity with a changing capital structure over time. Beginning with the terminal value and working in reverse, you analyze normalized net cash flows (e.g., expected net cash flows following normalization of company operations and/or an amount reflective of industry average profit margins and industry average debt to equity capital structure). During the transition period from current distressed operations to normalized operations (a period that varies depending on the level of current distress and economic industry conditions), you project detailed cash flows. The cost of capital components change over time as does the weighted average of the overall cost of capital.
238
Cost of Capital
The cost of debt capital is reduced as debt is paid down and the credit rating improves. The cost of equity capital is reduced as financial distress is reduced.
Appendix 17B shows an example of estimating the value of the enterprise with a changing capital structure. An alternative approach is to value the firm using the adjusted present value (APV) approach. We discuss this approach in Chapter 17. The formulation of APV for valuation of a distressed company is: (Formula 14.4) PV ¼ PVkeu þ PVts where: PV ¼ Present value of net cash flows PVkeu ¼ Present value of net cash flows using unlevered cost of equity capital as the discount rate keu PVts ¼ Present value of tax shields due to interest expense on dept capital minus present value of distress-related costs In one study, the author quantifies the net costs of financial distress in various industries as the level if debt financing increases.8 He studies both direct and indirect costs of financial distress because the costs can be substantial even if a firm never files for bankruptcy. The study looks at the net cost of financial distress: the expected present value of lost future cash flows due to financing decisions minus the present value of the interest tax shield. That author uses a sampling of firms for the period 1994 to 2004 and finds the average net cost of financial distress to be 4% of total firm value. At levels of leverage at the time of default on debt, the net cost of leverage averages 13% to 26% of firm value at bankruptcy. COST OF EQUITY CAPITAL OF DISTRESSED FIRMS Often the observations of returns on equity capital for public firms during periods of distress do not represent expectations of investors. For example, as a firm begins to realize distress, investors reassess the firm’s expected cash flows and the firm’s risk, causing stock prices to adjust downward to reflect the new reality of the firm’s business. The result is that returns are in transition and do not reflect either the historical relationship to the market portfolio or the expected future relationship to the market portfolio once the market fully adjusts to the effects of distress on the firm. Risk measures such as beta estimate using realized returns during such transition periods will underestimate the risk of the distressed firm and underestimate its cost of equity capital. Further, once the stock price of a distressed firm ratchets downward, it often trades as an option rather than as a stock, reducing the validity of beta estimation methods (such as ordinary least squares [OLS]).9 You may substitute a forward-looking measure of relative volatility for a historic-based estimate based on observed yield spreads or observed volatility of traded options (see, for example, the discussion in 8 9
Arthur Korteweg, ‘‘The Cost of Financial Distress across Industries,’’ Working paper, January 15, 2007. In ‘‘Limited Liability, the CAPM and Speculative Grade Firms: A Monte Carlo Experiment,’’ Working paper, August 18, 2004, Carlos A. Mello-e-Souza shows that limited liability allows equity to be valued as a ‘‘call option’’ within the CAPM framework. When adjusting for measures of bankruptcy risk on beta estimation, he finds that when bankruptcy risk = 5%, OLS beta is underestimated by 10%, and when bankruptcy risk = 20%, OLS beta is underestimated by 23%.
Distress
239
Chapter 11 of using yield spreads as a risk measure and the discussion in Chapter 16 of the marketderived Capital Pricing Model or yield spread model). Any risk measure based on implied volatilities derived from options requires that the firm have traded options. Alternative methods available are:
Estimating betas for the subject distressed firms from beta estimates for guideline public companies not going through such a period of adjustment, relevering beta, and adding a companyspecific risk adjustment to account for the added risk due to distress. Estimating fundamental beta for the subject company (e.g., regressing operating earnings of subject company against operating earnings of S&P 500).
Estimating fundamental operating risk for the distressed firm and matching the fundamental risk with observed market returns. The Duff & Phelps Risk Study allows you to match the appropriate market returns with measures of operating risk. Because the database used excludes highfinancial-risk companies, you then need to add a company-specific risk adjustment to account for the added risk due to distress (the Study reports a separate high-financial-risk portfolio).
Value equity as a call option on the value of the firm’s assets. We show an example of this in Chapter 33.
Relevering Beta for a Distressed Company In Chapter 10 we discussed various relevering formulas. But these formulas likely underestimate the effect on beta due to distress. For example, the practitioners’ method formula for relevering beta (Formula 10.1.8) will result in the largest increase in levered betas as debt increases, but the relationship between leverage and the levered beta is linear. In fact, the correct relationship is likely nonlinear. An example of the relationship between beta (for equity and debt capital) as debt increases and the costs of financial distress increases is shown in Exhibit 14.5.
3 2.5 2 Beta 1.5 1 0.5 0
0
0.2
0.4 Leverage
0.6
Weighted average beta of equity and debt Bd BL
Exhibit 14.5 Beta as a Function of Leverage Source: Arthur G. Korteweg, ‘‘The Costs of Financial Distress across Industries,’’ Working paper, Stanford University, January 15, 2007, 65. Used with permission. All rights reserved.
240 Exhibit 14.6
Mean Median
Cost of Capital Estimated Company-Specific Risk Premium for Distressed Companies All Companies
NYSE & AMEX Only
1.5% 1.7%
2.1% 2.3%
Source: Compiled from Standard & Poor’s Compustat data. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
This figure depicts the relation between leverage and the beta of a firm’s debt, equity, and the weighted average beta with tax benefits and costs of financial distress. Leverage is defined as the market value of debt divided by the total market value of the firm. Bd is the beta of the company’s debt, and BL is the beta of the firm’s equity. The unlevered asset beta is assumed equal to 1. Company-Specific Risk Adjustment for a Distressed Company The Duff & Phelps Risk Study provides a risk premium for high-financial-risk companies (e.g., see Exhibit 14.1, the line ‘‘high financial risk’’). That data can be used in a build-up model (the arithmetic average equity risk premium of 14.53% added to the risk-free rate) as in a Capital Asset Pricing Model (CAPM). (A premium over CAPM can be calculated as 14.53% (1.62 4.81%) ¼ 6.74%.) That risk premium includes both any size effect and any company-specific risk premium due to the distressed nature of the companies involved in the high-financial-risk portfolio. Duff & Phelps analyzed the risk premium in excess of size premium that is observed in the companies that comprise the high-financial-risk portfolio. Exhibit 14.6 shows the findings. This company-specific risk adjustment estimate includes companies with high levels of debt, companies that are losing money, and companies that are in bankruptcy. Another indication of the specific-company risk adjustment for companies emerging from bankruptcy can be imputed from the rate of return, which equates the market value of public companies that emerge from bankruptcy and the expected cash flows. To the extent that the imputed cost of capital exceeds an industry average cost of capital, you can conclude that the market is adding a factor for company-specific risk due to the greater risks of the companies that recently emerged from bankruptcy. One such study indicates that such an imputed company-specific risk adjustment is in the range of 3.0% to 4.0%.10 Companies emerging from bankruptcy are generally more risky than peer companies because often they are still burdened with too much debt, they may not have worked through all of the problems that cause business distress, and they have a higher probability of returning to bankruptcy than do companies that have never been bankrupt. Any such company-specific risk premium is applicable during the time the company is in distress, as the premium reflects the added risk that plans to work out of the distress situation simply will fail. Some authors suggest looking at venture capital rates of return as a proxy for distressed company rates of return. These are at best a poor proxy because most of the rates observed are for newer ventures without a proven history in the market. Distressed firms often own proven technologies, products, and/or services. Often their problem is simply too much debt or poor execution by management. These risks differ from those of most venture capital or buyout fund investments.
10
Stuart C. Gilson, Edith S. Hotchkiss, and Richard S. Ruback, ‘‘Valuation of Bankrupt Firms,’’ Review of Financial Studies (Spring 2000): 56. The median is 3%; 4% is the mean with a standard deviation of 3.3%.
Summary
241
SUMMARY Quantifying company-specific risk is one of the most controversial and elusive areas of business valuation. We have identified several sources of data that will assist the analyst in this most difficult task. The Duff & Phelps Risk Study provides quantitative data for you to analyze the companyspecific risk of the subject company. Users of cost of capital data should make themselves aware of updates of this and other similar studies to incorporate the latest current quantitative data on measuring company-specific risk in cost of capital estimates, whether using build-up models, CAPM, or other cost of equity models.
Chapter 15
Alternative Cost of Equity Capital Models
Introduction Arbitrage Pricing Theory Explanation of the APT Model APT Model Formula Fama-French 3-Factor Model Market-Derived Capital Pricing Model Yield Spread Model Summary
INTRODUCTION Textbook CAPM (like Markowitz’ portfolio model on which it was built) provides fundamental insights about risk and return. In teaching CAPM as an introduction to fundamental concepts of asset pricing and portfolio theory, to be built on by more advanced models, a warning is needed: CAPM’s empirical problems probably invalidate textbook CAPM’s use in applications. Perhaps because of its simplicity, CAPM’s empirical record is poor.1 Because the textbook version of the Capital Asset Pricing Model (CAPM) has never been an empirical success, a number of alternative models have been developed to assist practitioners in more accurately estimating the cost of equity capital. Many of these models are multifactor models instead of the single-factor textbook CAPM.
ARBITRAGE PRICING THEORY The concept of the arbitrage pricing theory (APT) was introduced by academicians in 1976.2 However, it was not until 1988 that data in a commercially usable form became generally available to permit application of the theory to the estimation of required rates of return in day-to-day practice. Despite the theory’s longevity, it still is not widely used by practitioners today.
1
2
Eugene Fama and Kenneth French, ‘‘The CAPM: Theory and Evidence,’’ Journal of Economic Perspectives (January 2004): 25–46. Stephen A. Ross, ‘‘The Arbitrage Theory of Capital Asset Pricing,’’ Journal of Economic Theory (December 1976): 241–260; and Stephen A. Ross, ‘‘Return, Risk, and Arbitrage,’’ in Risk and Return in Finance, ed. Irwin I. Friend and I. Bisksler (Cambridge, MA: Ballinger, 1977): 189–218. See also Stephen A. Ross, Randolph W. Westerfield, and Jeffrey F. Jaffe, Corporate Finance, 8th ed. (Burr Ridge, IL: McGraw-Hill, 2006).
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Cost of Capital
EXPLANATION OF THE APT MODEL As noted in Chapter 8, the CAPM is a univariate model; that is, textbook CAPM recognizes only one risk factor: systematic risk relative to a market index. In a sense, APT is a multivariate extension of the CAPM. APT recognizes a variety of risk factors that may bear pervasively on an investment’s required rate of return, one of which may be a CAPM-type ‘‘market’’ or ‘‘market timing’’ risk. It may be argued that the CAPM and APT are not mutually exclusive, nor is one of greater or lesser scope than the other. It also can be argued that the CAPM beta implicitly reflects the information included separately in each of the APT ‘‘factors.’’ However, in spite of its more limited use, most academicians consider the arbitrage pricing theory model richer in its information content and explanatory and predictive power.3 Whereas the nature of the CAPM is a single regression, the nature of the APT is a multiple regression. In the APT model, the cost of capital for an investment varies according to that investment’s sensitivity to each of several different risk factors. The theoretic model itself does not specify what the risk factors are. Most formulations of the APT theory consider only risk factors of a pervasive macroeconomic nature, such as:
Yield spread. The differential between risky and less risky bonds as a measure of investors’ consensus confidence in economic prosperity
Interest rate risk. Measured by the difference between long-term and short-term yields Business outlook risk. Measured by changes in forecasts for economic variables such as gross national product (GNP)
Inflation risk. Measured by changes in inflation forecasts
The beta used in the CAPM may or may not be one of the risk factors included in any particular practitioner’s version of the APT. In some versions, more industry-specific factors may be included, such as changes in oil prices. Exhibit 15.1 explains one version of APT risk factors.
APT MODEL FORMULA The econometric estimation of the APT model with multiple risk factors yields this formula: (Formula 15.1) EðRi Þ ¼ R f þ ðBi1 K1 Þ þ ðBi2 K2 Þ þ þ ðBin Kn Þ where: E(Ri) ¼ Expected rate of return on the subject security Rf ¼ Rate of return on a risk-free security K1. . .Kn ¼ Risk premium associated with factor K for the average asset in the market Bi1. . .Bin ¼ Sensitivity of security i to each risk factor relative to the market average sensitivity to that factor Roger Ibbotson and Gary Brinson make these observations regarding APT: 3
See, for example, Richard Roll and Stephen A. Ross, ‘‘An Empirical Investigation of Arbitrage Pricing Theory,’’ Journal of Finance (December 1980): 1073–1103; Nai-fu Chen, ‘‘Some Empirical Tests of Arbitrage Pricing,’’ Journal of Finance (December 1983): 1393–1414; Nai-fu Chen, Richard Roll, and Stephen A. Ross, ‘‘Economic Forces and the Stock Market: Testing the APT and Alternative Pricing Theories,’’ Journal of Business 59 (1986): 383–403.
Arbitrage Pricing Theory
Exhibit 15.1
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Explanation of APT Risk Factors
Confidence Risk Confidence risk is the unanticipated changes in investors’ willingness to undertake relatively risky investments. It is measured as the difference between the rate of return on relatively risky corporate bonds and the rate of return on government bonds, both with 20-year maturities, adjusted so that the mean of the difference is zero over a long historical sample period. In any month when the return on corporate bonds exceeds the return on government bonds by more than the long-run average, this measure of confidence risk is positive. The intuition is that a positive return difference reflects increased investor confidence because the required yield on risky corporate bonds has fallen relative to safe government bonds. Stocks that are positively exposed to the risk then will rise in price. (Most equities do have a positive exposure to confidence risk, and small stocks generally have greater exposure than large stocks.) Time Horizon Risk Time horizon risk is the unanticipated changes in investors’ desired time to payouts. It is measured as the difference between the return on 20-year government bonds and 30-day Treasury bills, again adjusted to be mean zero over a long historical sample period. A positive realization of time horizon risk means that the price of longterm bonds has risen relative to the 30-day Treasury bill price. This is a signal that investors require a lower compensation for holding investments with relatively longer times to payouts. The price of stocks that are positively exposed to time horizon risk will rise to appropriately decrease their yields. (Growth stocks benefit more than income stocks when this occurs.) Inflation Risk Inflation risk is a combination of the unexpected components of short- and long-run inflation rates. Expected future inflation rates are computed at the beginning of each period from available information: historical inflation rates, interest rates, and other economic variables that influence inflation. For any month, inflation risk is the unexpected surprise that is computed at the end of the month (i.e., it is the difference between the actual inflation for that month and what had been expected at the beginning of the month). Since most stocks have negative exposures to inflation risk, a positive inflation surprise causes a negative contribution to return, whereas a negative inflation surprise (a deflation shock) contributes positively toward return. Industries whose products tend to be ‘‘luxuries’’ are most sensitive to inflation risk. Consumer demand for luxuries plummets when real income is eroded through inflation, thus depressing profits for industries such as retailers, services, eating places, hotels and motels, and toys. In contrast, industries least sensitive to inflation risk tend to sell ‘‘necessities,’’ the demands for which are relatively insensitive to declines in real income. Examples include foods, cosmetics, tire and rubber goods, and shoes. Also companies that have large asset holdings such as real estate or oil reserves may benefit from increased inflation. Business Cycle Risk Business cycle risk represents unanticipated changes in the level of real business activity. The expected values of a business activity index are computed both at the beginning and end of the month, using only information available at those times. Then business cycle risk is calculated as the difference between the end-of-month value and the beginning-of-month value. A positive realization of business cycle risk indicates that the expected growth rate of the economy, measured in constant dollars, has increased. Under such circumstances firms that are more positively exposed to business cycle risk—for example, firms such as retail stores that do well when business activity increases as the economy recovers from a recession—will outperform those such as utility companies that do not respond much to increased levels in business activity. Market Timing Risk Market timing risk is computed as that part of the S&P 500 total return that is not explained by the first four macroeconomic risks and an intercept term. Many people find it useful to think of the APT as a generalization of the CAPM, and by including this Market Timing factor, the CAPM becomes a special case: If the risk exposures (Continued )
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Cost of Capital
to all of the first four macroeconomic factors were exactly zero, then market timing risk would be proportional to the S&P 500 total return. Under these extremely unlikely conditions, a stock’s exposure to market timing risk would be equal to its CAPM beta. Almost all stocks have a positive exposure to market timing risk, and hence positive market timing surprises increase returns, and vice versa. A natural question, then, is: Do confidence risk, time horizon risk, inflation risk, and business cycle risk help to explain stock returns better than I could do with just the S&P 500? This question has been answered using rigorous statistical tests, and the answer is very clearly that they do. Source: Presented in a talk based on a paper, ‘‘A Practitioner’s Guide to Arbitrage Pricing Theory,’’ by Edwin Burmeister, Richard Roll, and Stephen A. Ross, written for the Research Foundation of the Institute of Chartered Financial Analysts, 1994. The exhibit is drawn from notes for ‘‘Controlling Risks Using Arbitrage Pricing Techniques,’’ by Edwin Burmeister. Reprinted with permission.
In theory, a specific asset has some number of units of each risk; those units are each multiplied by the appropriate risk premium. Thus, APT shows that the equilibrium expected return is the risk-free rate plus the sum of a series of risk premiums. APT is more realistic than CAPM because investors can consider other characteristics besides the beta of assets as they select their investment portfolios.4
Edwin Burmeister says this about APT: The APT takes the view that there need not be any single way to measure systematic risk. While the APT is completely general and does not specify exactly what the systematic risks are, or even how many such risks exist, academic and commercial research suggests that there are several primary sources of risk which consistently impact stock returns. These risks arise from unanticipated changes in the following fundamental economic variables:
Investor confidence
Interest rates
Inflation
Real business activity
A market index
Every stock and portfolio has sensitivity (or betas) with respect to each of these systematic risks. The pattern of economic betas for a stock or portfolio is called its risk exposure profile. Risk exposures are rewarded in the market with additional expected return, and thus the risk exposure profile determines the volatility and performance of a well-diversified portfolio. The profile also indicates how a stock or portfolio will perform under different economic conditions. For example, if real business activity is greater than anticipated, stocks with a high exposure to business activity, such as retail stores, will do relatively better than those with low exposures to business activity, such as utility companies.5
Research has shown that the cost of equity capital as estimated by the APT tends to be higher for some industries (e.g., oil) and lower for others (e.g., certain utility groups) than the cost of equity capital using the CAPM. Early research also suggests that the multivariate APT model explains expected rates of return better than does the univariate CAPM.6 4
5
6
Roger G. Ibbotson and Gary P. Brinson, Investment Markets (New York: McGraw-Hill, 1987), 32. For a more extensive discussion of APT, see Frank K. Reilly, Investment Analysis and Portfolio Management, 8th ed. (Fort Worth, TX: Dryden Press, 2005). Edwin Burmeister, ‘‘Using Macroeconomic Factors to Control Portfolio Risk,’’ Working paper, Duke University, March 9, 2003: 3. See, for example, Tim Koller, Marc Goedhart, and David Wessels. Valuation: Measuring and Managing the Value of Companies, 4th ed. (Hoboken: John Wiley & Sons, 2005), 317.
Arbitrage Pricing Theory
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Exhibit 15.2 Example of BIRR Risk Index for S&P 500 and Reebok The risk exposure profile for the S&P 500 and the corresponding prices of risk (the risk premia) are: Risk Factor
Exposure for S&P 500
Confidence Risk Time Horizon Risk Inflation Risk Business Cycle Risk Market Timing Risk
Price of Risk (%/yr)
0.27 0.56 0.37 1.71 1.00
2.59 0.66 4.32 1.49 3.61
For each risk factor, the contribution to expected return is the product of the risk exposure and the corresponding price of risk, and the sum of the products is equal to the expected return in excess of the 30-day Treasury bill rate:
Risk Factor Confidence Risk Time Horizon Risk Inflation Risk Business Cycle Risk Market Timing Risk
Exposure for S&P 500 0.27 0.56 0.37 1.71 1.00
Price of Risk (%/yr)
X X X X X
2.59 0.66 4.32 1.49 3.61
¼ ¼ ¼ ¼ ¼
Contribution of Risk Factor to Expected Return 0.70 0.37 1.60 2.55 3.61
Sum ¼ Expected Excess Return for the S&P 500 ¼ 8.09 The price of each risk factor tells you how much expected return will change due to an increase or decrease in your portfolio’s exposure to that type of risk. The risk exposure profile for Reebok International Ltd. is: Risk Factor Confidence Risk Time Horizon Risk Inflation Risk Business Cycle Risk Market Timing Risk
Exposure for Reebok 0.73 0.77 0.48 4.59 1.50
Exposure for S&P 500 0.27 0.56 0.37 1.71 1.00
These exposures give rise to an expected excess rate of return for Reebok equal to 15.71%/yr compared with the 8.09%/yr that is computed for the S&P 500. Source: Edwin Burmeister, ‘‘Using Macroeconomic Factors to Control Portfolio Risk,’’ Working paper, Duke University, March 9, 2003. (This paper is based on an early version of ‘‘A Practitioner’s Guide to Arbitrage Pricing Theory,’’ in A Practitioner’s Guide to Factor Models (Research Foundation of the Institute of Chartered Financial Analysts, 1994).
So, if the APT is more powerful than the CAPM, why is the APT not used more? For one thing, the variables are not specified. Also, there is no universal consensus about which variables are likely to have the greatest efficacy. Furthermore, implementing a model based on APT is complicated in that coefficients for several factors, rather than just one factor, must be worked out for each company for each specific time it is going to be applied. BIRR Portfolio Analysis, Inc., is a source for inputs to their version of the APT model. The BIRR Risk Index is a single overall risk measure for a stock or portfolio; you can think of this Risk Index as a multifactor equivalent to the single equivalent to the single-factor CAPM beta. Exhibit 15.2 shows an example of comparison of the exposures of the Standard & Poor’s (S&P) 500 and Reebok to the risk factors presented in Exhibit 15.1. Contact information for sources of information is given in Appendix II. Although the Alcar Group no longer provides APT cost of equity capital estimates, due to low demand for the inputs, William Roper, a vice president of Alcar, had this to say about APT theory:
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Cost of Capital
The practical application of APT theory is difficult because it is very hard to determine a valid statistical relationship between an individual company’s returns and the macroeconomic factors. There is simply too much ‘‘noise’’ in these relationships. In Exhibit 15.3, the relationship of an individual company is first measured against a portfolio of companies, then the relationship of the portfolio of companies to the macroeconomic factor is measured. However, while this two-step approach tries to relate the individual company to the macroeconomic factors, the relationship still tends to have too much noise. Therefore, Alcar’s formulation was to take a peer group of companies relative to the portfolios shown in Exhibit 15.3, and combine this with the relationship of the portfolios to the macroeconomic factors. This approach does tend to yield a better (statistically significant?) relationship for the peer group to the macroeconomic factors but the ability to extend this relationship and apply it to an individual company in the peer group remains problematic.
FAMA-FRENCH 3-FACTOR MODEL Because of the poor empirical record of textbook CAPM, Eugene Fama and Kenneth French (FF) conducted an empirical study confirming that firm size (as measured by market capitalization), earnings-to-price ratio, debt-to-equity ratio, and book value-to-market value ratios add to the explanation of realized returns provided by market beta. They found that the CAPM cost of equity estimates for high-beta stocks are too high and estimates for low-beta stocks are too low (relative to realized returns). The CAPM cost of equity estimates for high book-value-to-market-value stocks (so-called value stocks) are too low and estimates for low book-value-to-market-value stocks (so-called growth stocks) are too high (relative to realized returns). The implication of their research is that if market betas do not suffice to explain expected returns, the market portfolio, M, is not efficient and CAPM has potentially fatal problems. As a result, they introduce an empirically driven model to estimate cost of equity capital that is not dependent on beta alone.7 FF developed a 3-factor model that is empirically driven, not theoretically based. The factors are brute-force constructs. Do factors capture rational results of unknown risks or the result in irrational investor behavior? Opportunity cost of equity capital depends on premiums investors require to hold stocks, whether the premiums are rational or irrational. The FF 3-factor model is summarized in Formula 15.2: (Formula 15.2) EðRi Þ ¼ R f þ ðBi ERPÞ þ ðsi SMBPÞ þ ðhi HMLPÞ where: E(Ri) ¼ Expected rate of return on subject security i Rf ¼ Rate of return on a risk-free security Bi ¼ Beta of company i ERP ¼ Equity risk premium si ¼ Small-minus-big coefficient in the Fama-French regression SMBP ¼ Expected small-minus-big risk premium, estimated as the difference between the historical average annual returns on the small-cap and large-cap portfolios hi ¼ High-minus-low coefficient in the Fama-French regression
7
Eugene Fama and Kenneth French, ‘‘The Cross-Section of Expected Stock Returns,’’ Journal of Finance (June 1992): 427–486.
Fama-French 3-Factor Model Exhibit 15.3
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APT and CAPM Cost of Equity Capital Estimates Example APT Estimated CAPM Cost of Equity for Air Prods & Chems Inc. Beta Risk Premium ¼ Contribution
Risk-Free Rate + CAPM Equity Premium + Large Capitalization + Small Capitalization + High Cash Flow/Price + Low Cash Flow/Price
N/A 1.09 (0.58) 0.36 0.00 0.43
N/A 3.00% (0.23)% 3.30% 2.53% (3.76)%
10.00% 3.26% 0.13% 1.19% 0.01% (1.64)%
APT Cost of Equity Business Risk (Unlevered Ke) + Financial Risk APT Cost of Equity
12.95% 12.41% 0.54% 12.95%
Risk-Free Rate + Short-Term Inflation + Long-Term Inflation + Interest Yield Term Default Risk Monthly Production
10.00% (0.40)% 0.24% 0.20% 2.47% 0.43%
APT uses additional portfolios to overcome limitations of CAPM.
Three ways to look at equity risk.
APT techniques link the cost of equity to underlying economic factors. This business is quite sensitive to ‘‘default risk,’’ or investor confidence in the economy (the spread between high- and low-grade bonds).
12.95%
APT Cost of Equity
Selected Yield Term: Selected Market Risk Premium: Debt/Equity Ratio: R-Squared Specific Risk:
20 years Alcar Forecast 33.69% 43% 5% Estimated Cost of Equity for Air Prods & Chems Inc. CAPM/APT Reconciliation Economic Factors
Portfolio Factors
ShortTerm Infl.
‘‘Small capitalization,’’ Memo: or small stock, premium Average is due to this company’s LongInterest Default Monthly Risk higher sensitivity Term Infl. Yield Term Risk Prodn. TOTAL Premia to default risk.
Risk-Free Rate CAPM Eq. Prem. CAPM Ke
0.13%
0.47%
Large Cap Small Cap High CF/Price Low CF/Price
0.02% 0.11% 0.00% 0.40%
0.02% 0.10% 0.00% 0.36%
Difference APT Ke
0.27% 0.40%
0.24% 0.24%
Memo: Avg. Risk Premia
0.25%
0.31%
0.49%
1.84% 0.58%
10.00% 3.26% 13.26%
3.00%
0.02% 0.06% 0.02% 0.13% 0.23% This Low Cash 0.08% 0.73% 0.16% 1.19% 3.30% Flow-to-Price 0.00% 0.00% 0.00% 0.01% 2.53% effect indicates 0.39% 0.17% 0.33% 1.64% 3.76% stability and lower risk that more than 0.28% 0.63% 0.15% 0.31% offsets the small-cap 0.20% 2.47% 0.43% 12.95% effect, resulting in a lower estimated cost of equity under 0.19% 3.99% 0.60% APT than CAPM.
Selected Yield 20 years Term: Selected Market Alcar Forecast Risk Premium: Debt/Equity Ratio:33.69% AFT R-Squared 7% Improvement TM
Source: Figure highlights from APT!
: Alcar’s Financial Policy Information Service. Reprinted with permission
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Cost of Capital
HMLP ¼ Expected high-minus-low risk premium, estimated as the difference between the historical average annual returns on the high book-to-market and low book-to-market portfolios FF formed six return series (realized returns for companies in one of six categories):
Small Big
Low-Cap
Mid-Cap
High-Cap
x x
x x
x x
where ‘‘small’’ companies are those with market capitalization below the median New York Stock Exchange (NYSE) company and ‘‘big’’ companies are those with market capitalization above the median NYSE company. ‘‘Low-cap’’ companies have book-value-to-market-value ratios in the bottom 30% of the NYSE companies; ‘‘Mid-cap’’ companies have book-value-to-market-value ratios in the middle 40% of the NYSE companies; and ‘‘High-cap’’ companies have book-value-to-marketvalue ratios in the top 30% of the NYSE companies. Because the universe of stocks include the NYSE, American Stock Exchange (AMEX), and NASDAQ, the result is that there are more smallcapitalization companies by count than big-capitalization companies. FF then calculated average returns for the three portfolios of small-cap companies and for the three portfolios of big-cap companies. They then subtracted the average return for ‘‘big’’ from ‘‘small’’ to get the SMBP (small-cap minus big-cap risk premium). FF then calculated average returns for the two portfolios of high-cap book-value-to-market-value ratio companies and for the two portfolios of low-cap book-value-to-market-value ratio companies. They then subtracted the average return for high-cap from low-cap to get the HMLP (high-cap minus low-cap risk premium). Some people consider this a measure of financial distress. FF then ran regressions of historical security returns against the three time series and calculated the Bi, SI SMBP (SMBP, or size risk premium), and hi HMLP (HMLP risk premium). Bi is not equivalent to the single-factor CAPM beta. One source of the FF factors is the Morningstar Beta Book. Another source of the three factors is Kenneth French’s Web site: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. Generally, using the FF 3-factor model results in a large number of companies with high cost of equity compared to CAPM. This leads users to ask whether the FF 3-factor model is overcorrecting for size and/or financial distress or whether CAPM underestimating cost of equity capital. Exhibit 15.4 displays a comparison of the cost of equity capital obtained by using the textbook single-factor CAPM, the FF 3-factor model, and the BIRR version of APT. Researchers have studied the relative predictive power of the various models. In one such study, the author investigates the ability of models to capture time-varying predictability of returns. He studied the CAPM, FF 3-factor model, and a 5-factor economic model (e.g., an APT-type model). At the industry level, he finds that the CAPM is best in capturing time-variation of industry expected returns while the FF 3-factor model was the worst. His 5-factor economic model best captures predictability of size as measured by market capitalization and book-value-to-market-value ratio portfolios.8 In another study, the authors find that the degree of financial leverage explains the book-to-market effect observed by FF.9
8 9
Alex P. Taylor, ‘‘Conditional Factor Models and Return Predictability,’’ AFA 2006 Boston Meetings Paper, February 2005. Lorenzo Garlappi and Hong Yan, ‘‘Financial Distress and the Cross Section of Equity Returns,’’ Working paper, April 2007.
Market-Derived Capital Pricing Model
Exhibit 15.4
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Comparative Cost of Equity Capital Models: CAPM versus FF versus APT
Comparative Equity Return Models as of June 2006 Company
CAPM þSP1
CAPM
F-F 3- Factor
BIRR APT
CAPM Beta
F-F Beta
F-F SMB
F-F HML
General AT&T Corp Bristol Myers Squibb Coca-Cola Corp. General Motors Corp. IBM Microsoft Hewlett Packard McDonald’s Corp. Merck & Co. Procter & Gamble Walt Disney Co. Average
10.49% 9.79% 6.69% 11.84% 12.84% 10.59% 14.99% 10.94% 8.04% 5.79% 11.24% 10.29%
10.86% 10.16% 7.06% 12.21% 13.21% 10.96% 15.36% 11.31% 8.41% 6.16% 11.61% 10.66%
10.81% 6.61% 9.58% 19.11% 10.73% 8.94% 15.54% 12.59% 6.73% 5.48% 13.92% 10.91%
11.16% 12.77% 10.38% 14.64% 6.86% 2.60% 8.78% 15.18% 9.08% 10.44% 12.65% 10.41%
1.11 0.97 0.35 1.38 1.58 1.13 2.01 1.20 0.62 0.17 1.26
1.22 1.13 0.17 0.88 1.76 1.22 1.99 1.11 0.83 0.21 1.08
4.36% 3.40% 0.84% 2.78% 0.53% 0.06% 0.37% 0.26% 4.25% 0.04% 1.42%
3.76% 0.95% 2.58% 6.62% 2.85% 2.53% 0.09% 1.47% 1.52% 0.92% 1.79%
Integrated Petroleum Chevron Exxon Mobil Occidental Petroleum Average
8.19% 8.19% 7.94% 8.11%
8.56% 8.56% 8.31% 8.48%
11.04% 9.31% 10.23% 10.19%
11.57% 10.24% 12.15% 11.32%
0.65 0.65 0.60
0.46 0.61 0.43
1.28% 0.08% 1.58%
2.15% 0.87% 1.19%
11.89% 12.59% 13.54% 7.64% 12.89% 13.19% 6.74% 11.21%
12.26% 12.96% 13.91% 8.01% 13.26% 13.56% 7.11% 11.58%
12.46% 15.85% 17.20% 8.00% 15.71% 13.08% 5.67% 12.57%
12.84% 13.77% 10.89% 7.84% 10.95% 10.07% 10.78% 11.02%
1.39 1.53 1.72 0.54 1.59 1.65 0.36
1.37 1.33 1.50 0.57 1.31 1.67 0.49
0.02% 0.56% 0.70% 1.02% 2.23% 0.35% 1.17%
0.28% 3.33% 3.69% 0.86% 1.62% 0.93% 0.92%
Financial Services American Express Bank of New York JP Morgan Chase Bank of America Citigroup Morgan Stanley Wells Fargo Average 1
Size Premium ¼ 0.37. Source: Source for CAPM betas and 3-factor premiums: Ibbotson Associates’ Beta Book, First 2006 Edition. Copyright # 2006 Ibbotson Associates. Source for BIRR estimate: BIRR Risk and Returns Analyzer, July 2006 release. Source for Small Stock Premium (SSP): Stocks, Bonds, Bills, and Inflation1 Valuation Edition 2006 Yearbook. Copyright # 2006 Morningstar, Inc. Assumptions used in CAPM and 3-factor calculations: Rf ¼ 5.31% (20-year Treasury security yield on June 30, 2006), ERP ¼ 5%. Calculations by Duff & Phelps LLC. Used with permission. All rights reserved.
MARKET-DERIVED CAPITAL PRICING MODEL In cases when a company has troubled operations and is declining (negative returns) while the market returns are stable or rising, any of the risk measures that rely on comparing the historical realized returns of the subject company to the market returns will likely give measures that are unrepresentative of the company’s true risk. For example, you could get a very low beta indicating low risk when in fact the subject company is really high risk. What do you do? You can certainly turn to the fundamental risk studies, such as the Duff & Phelps Risk Study, and use the build-up method to estimate the cost of equity capital.
252
Cost of Capital
Alternatively, if the subject company is a public company with publicly traded options, you can extract implied variance statistics from publicly traded options and develop a risk measure that is current and forward-looking rather than based on historical returns. One such model is the MarketDerived Capital Pricing Model.10 The technique can be summarized in five steps for a public company with traded options. Step 1. Calculate the forward break-even price (the minimum amount equity investors must be compensated knowing that the return on stock must be greater than return on bonds of the subject company and the current bond yield reflects the specific-company risk of the company), and calculate the price a stock must reach at the end of the period to make the minimum rate of return. EðRi Þ ¼ EðRdiv Þ þ EðRcapgains Þ Minimum EðRcapgains Þ ¼ kd EðRdiv Þ ¼ company bond yield ðD=PÞ Pn ¼ P0 ð1 þ Kd D=PÞn where: E(Ri) ¼ Expected rate of return on equity i E(Rdiv) ¼ Expected equity rate of return on dividend E(Rcapgains) ¼ Expected equity rate of return on capital gains kd ¼ Discount rate for debt (net of tax affect, if any) D=P ¼ Dividend yield on stock Pn ¼ Stock price in period n P0 ¼ Stock price at valuation period Step 2. Estimate the stock’s future volatility; that is, use an option pricing model like the BlackScholes pricing model to solve for volatility. Step 3. Calculate the cost of ‘‘downside insurance’’; that is, using Black-Scholes, calculate the value of a theoretical put option with the strike price equal to the forward breakeven price Pn (step 1) and implied volatility (step 2) and the cost of funds (corporate interest rate). Step 4. Derive the annualized excess equity return; that is, divide the theoretical put option price (step 3) by P0 and convert it to an annual percentage rate following an annuity formula. This gives the rate of excess return required on the company’s shares. Step 5. Add the excess return to the corporate bond yield to derive E(Ri).
YIELD SPREAD MODEL Another model is based on yield spreads. You can look at the differences in market yields on bonds of different ratings. Using historical default rates on bonds, you can estimate expected default rates on bonds and a firm’s current cost of debt for use in its cost of capital. You can estimate market consensus risk premium by ratings class (i.e., the risk premium for specific ratings classes based on 10
James McNulty, Tony Yeh, William Schulze, and Michael Labatkin, ‘‘What’s Your Real Cost of Capital?’’ Harvard Business Review (October 2002): 114.
Summary
253
differences in leverage), which can be used to estimate firm-specific cost of equity given the firm’s rating. One study estimates risk premiums over Treasury bill rates ranging from 3.1% for AA-rated firms to 8.5% for B-rated companies.11 These premiums vary materially over time, and you should be sure to use current rather than historical yield spreads.
SUMMARY Various models have been proposed and are in active use by practitioners because the single-factor textbook CAPM has generally proven to provide unreliable estimates of the cost of equity capital. APT is a multivariate model for estimating the cost of equity capital. The risk factor variables are not specified, but most formulations use macroeconomic factors that may impact the rates of return of different companies to different degrees. The beta in the CAPM may or may not be one of the factors. Partly because of lack of consensus on the specific factors and the complexity of the model, it has not enjoyed wide usage. Moreover, the macroeconomic factors used in current applications of APT may have a considerably less significant systematic impact on the cost of capital for smaller companies or on individual divisional or project decisions than for large national companies. The FF 3-factor model is an empirically derived model that has gained wider acceptance. The three risk factors can be obtained from Morningstar’s Beta Book or from Kenneth French’s Web site, making implementation of the model relatively easy. However, the FF 3-factor model has not proven to provide a consistently reliable estimate of the cost of equity capital. The FF 3-factor model is widely used by academic researchers and is often used instead of the textbook CAPM in such research. The Market-Derived Capital Pricing Model and the yield spread model use current bond yields on the subject company bonds as a base risk measure. The bond yields incorporate current market conditions and the entire risk profile, including company-specific risk of the subject company. Appendix D contains an excerpt from the report submitted by Roger Grabowski in the case Herbert V. Kohler, Jr. et al. v. Commissioner of Internal Revenue. In that case Grabowski used the CAPM, the Duff & Phelps Risk Premium Report, and the FF 3-factor model in estimating the cost of capital. He submitted a report using multiple methods in the belief that no one method is likely to produce the true cost of capital. The use of multiple methods provides a range of market indications upon which the analyst then applies judgment to reach a final conclusion.
11
Ian Cooper and Sergei Davydenko, ‘‘Using Yield Spreads to Estimate Expected Returns on Debt and Equity,’’ Working paper, February 2003. In another paper, Harjoat Bhamra, Lars-Alexander Kuehn, and llya Strebuaev, ‘‘the Levered Equity Risk Premium and Credit Spreads: A Unified Framework,’’ working paper, July 18, 2007, study the substantial empirical evidence that stock returns can be predicted by credit spreads and movement in stock-return volatility can explain movements in credit spreads and explore the joint pricing of corporate bonds and stocks.
Chapter 16
Implied Cost of Equity Capital
Introduction Discounted Cash Flow Method Mechanics of the DCF Method Single-Stage DCF Model Using Analyst Forecasts Multistage DCF Models Residual Earnings Method Building a Forecast Sources of Information Summary
INTRODUCTION As discussed earlier in this book, there are several ways to estimate the cost of equity capital. Up to this point, all of the methods have had one thing in common: They begin with a risk-free rate and add one or many factors, based on the risks of the investment. You can also estimate the rate of return implied by the existing price for public companies. You can use either a discounted cash flow (DCF) method or a residual earnings (RE) method to reverse engineer the implied cost of equity capital.
DISCOUNTED CASH FLOW METHOD At least in theory, the DCF method is more direct and simpler than the build-up model or the Capital Asset Pricing Model (CAPM) for a public company. The important assumption of the DCF method is that the public company’s current stock price embodies the market’s expectation of the rate of return that will be realized by investing in that stock. In other words, the assumption is that the current stock price is actually the sum of the present values of the expected future returns to the investors (dividends and stock price change). The implied assumption is that the current stock price is equal to the expected future returns discounted to a present value at a discount rate that represents the equity cost of capital for that company. The theory of the DCF method to estimate cost of capital is to compute present value backward. That is, since the present value (i.e., the current stock price) is known, the calculations are reconfigured to solve for ke, the cost of equity capital. The relationship between the DCF method of valuing a business and the DCF method of estimating cost of capital is a matter of the known and unknown variables. In using the DCF method to value a company, division, or project, the cost of capital already has been estimated and is given as a known rate in the formula to estimate the present value. In using the DCF method to estimate the cost of capital, the 255
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Cost of Capital
present value (e.g., market price of the stock) is known and placed into the formula to solve for the discount rate (cost of capital). Thus we can also call this the implied method of estimating cost of equity capital, as we are estimating the cost of equity capital implied by the stock price and expected future cash flows. Two main types of models are used to implement the DCF method as it is applied to estimating cost of capital. The first, and most popular, is the single-stage model. The second, and most accurate (in most instances), is the multistage model. Although these models can be used to estimate the weighted average cost of capital, they typically are used to calculate the expected equity rate of return. The discussion that follows is based on equity rates of return only.
MECHANICS OF THE DCF METHOD All methods for estimating the cost of capital derive all or part of the expected rates of return from current capital market data. With the exception of possible adjustments for closely held companies, the DCF method derives all of the implied expected return from current market data used in conjunction with growth expectations. Although the models used are much different, some of the steps undertaken in estimating the cost of equity capital of a closely held company are the same as those used in the other methods. In particular, the DCF method of estimating cost of capital can be directly applied only to closely held companies with observed transactions in their stock (the current stock price is the essential ingredient here); therefore, for most closely held companies, a set of guideline public companies (i.e., those similar to the subject) must be identified. Alternatively, an industry average for companies in the subject’s industry may be used as the starting point. For public companies, the cost of equity estimated by the DCF method represents the entire cost of equity. That is, it encompasses in a single number all the factors considered in the build-up and CAPM methods: the risk-free rate, the equity risk premium, the beta, the size effect, and any company-specific factors. To apply the cost of equity capital developed from guideline public companies or guideline merged and acquired company transactions to a closely held company, the characteristics of the public companies or the merged and acquired companies must be compared with characteristics of the subject closely held company. Such comparisons could lead to adjustments for size and/or companyspecific risk factors to get from the cost of equity estimate for the public companies to an estimate for a particular closely held company.
SINGLE-STAGE DCF MODEL The single-stage DCF model is based on a rewrite (an algebraic manipulation) of a constant growth model, such as the Gordon Growth Model, presented earlier as Formula 4.6 and repeated here: (Formula 16.1) PV ¼
NCF0 ð1 þ gÞ ke g
where: PV ¼ Present value NCF0 ¼ Net cash flow in period 0, the period immediately preceding the valuation date ke ¼ Cost of equity capital (discount rate) g ¼ Expected long-term sustainable growth rate in net cash flow to investor
Discounted Cash Flow Method
257
When the present value (i.e., the market price) is known, but the discount rate (i.e., the cost of capital) is unknown, Formula 16.1 can be rearranged to solve for the cost of capital: (Formula 16.2) ke ¼
NCF0 ð1 þ gÞ þg PV
where the variables have the same definitions as in Formula 16.1. In public companies, the net cash flow that the investor actually receives is the dividend. We can substitute some numbers into Formula 16.2 and thus illustrate estimating the cost of equity capital for Alpha Utilities, Inc. (AUI), an electric, gas, and water utility conglomerate, by making these three assumptions: Dividend. AUI’s dividend for the latest 12 months was $3.00 per share. Growth. Analysts’ consensus estimate is that the long-term growth in AUI’s dividend will be 5%. Present value. AUI’s current stock price is $36.00 per share. Substituting this information into Formula 16.2, we have: (Formula 16.3) ke ¼ ¼
$3:00ð1 þ 0:05Þ þ 0:05 $36:00 $3:15 þ 0:05 $36:00
¼ 8:8 þ 0:05 ¼ 13:8 Thus, according to this computation, AUI’s cost of equity capital is estimated to be 13.8% (8.8% dividend yield plus 5.0% expected stock price increase). The preceding is the formulation used in Morningstar Cost of Capital Yearbook, ‘‘Analysts Single-Stage Discounted Cash Flow’’ cost of equity capital estimate. Morningstar source of growth estimates is the I/B/E/S database (now Thomson Financial) of long-term growth rate estimates. A number of other sources of growth estimates are included in Appendix B. This single-stage DCF model often is used in utility rate hearings to estimate a utility’s cost of equity.1 Like the capitalization ‘‘shortcut’’ version of the discounting model used for valuation, the singlestage DCF model for estimating cost of capital is deceptively simple. In utility settings, the dividend yield is assumed to be an appropriate estimate of the first input, cash flow yield. This is reasonable, because publicly traded utilities typically pay dividends, and these dividends represent a high percentage of available cash flows. In cases where the utility’s dividend yield is abnormally high or low, a ‘‘normal’’ dividend yield is used. It is difficult, however, to use dividend yields with all publicly traded companies. For many companies, dividend payments may have little to do with earnings or cash flows. A large number of companies do not pay dividends or pay only a token amount. In these cases, theoretically, the growth component, g, will be larger than that of an otherwise similar company that pays higher dividends. In practice, properly adjusting for this lack of dividends is extremely difficult. 1
For a concise discussion of the use of this model for utility rate-setting, see Richard A. Brealey, Stewart C. Myers, and Franklin Allen, Principles of Corporate Finance, 8th ed. (Boston: Irwin McGraw-Hill, 2006), 67–68.
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One way to avoid the dividend issue is to define cash flows more broadly. Instead of considering only the cash flows investors actually receive (dividends), the analyst might define net cash flows as those amounts that could be paid to equity investors without impeding a company’s future growth. As noted in Chapter 3, net cash flow is usually defined as: Net income ðafter taxÞ þNoncash charges ðe:g:; depreciation; amortization; deferred revenue; deferred taxesÞ Capital expenditures Additions to net working capital Changes in long-term debt ðadd cash from borrowing; subtract repaymentsÞ ¼ Net cash flow to equity
Only amounts necessary to support projected operations:
Of course, these cash flows are not those paid to investors, but, presumably, investors ultimately will realize the benefit of these amounts through higher future dividends, a special dividend, or, more likely, stock price appreciation. Some analysts assume that over the very long run, net (after-tax) income should be quite close to cash flows. Therefore, they assume that net income can be used as a proxy for net cash flow. This assumption should be questioned on a case-by-case basis. For a growing company, capital expenditure and working capital requirements may make the assumed equivalence of net income and net cash flow so remote as to be irrelevant. The other, and perhaps more problematic, input is the expected growth rate. An important characteristic of the growth rate is that it is the perpetual annual growth rate. Future growth rates do not have to be the same for every year; however, the ‘‘average’’ rate should be equal to this perpetual rate. For example, if a company is expected to grow at 10% per year for the next four years and 3% per year thereafter, then the average growth rate into perpetuity could be estimated as about 5%. If the company is expected to grow by 10% per year for the next 20 years and 3% per year thereafter, the average growth rate is probably closer to 9%. However, this would be an extreme case. It is theoretically impossible for the sustainable perpetual growth rate for a company to significantly exceed the growth rate in the economy. Anything over a 6% to 7% perpetual growth rate should be questioned carefully. USING ANALYST FORECASTS A common approach to deriving a perpetual growth rate is to obtain stock analysts’ estimates of earnings growth rates. The advantage of using these growth estimates is that they are prepared by people who follow these companies on an ongoing basis. These professional stock analysts develop a great deal more insight on these companies than a casual investor or valuation analyst not specializing in the industry is likely to achieve. There are, however, four caveats when using this information: 1. These earnings growth estimates typically are for only the next two to five years; they are not perpetual. Therefore, any use of these forecasts in a single-stage DCF model must be tempered with a longer-term forecast. 2. Most published analysts’ estimates come from ‘‘sell-side’’ stock analysts who work for firms that are in business to sell stocks. Thus, although their earnings forecasts fall within the range of ‘‘reasonable’’ possibilities, they may be on the high end of the range. Further, they rarely publicize negative reports.
Discounted Cash Flow Method
259
3. Usually these estimates are obtained from firms that provide consensus earnings forecasts; that is, they aggregate forecasts from a number of analysts and report certain summary statistics (mean, median, etc.) on these forecasts. For a small publicly traded firm, there may be only one or even no analyst following the company. The potential for forecasting errors is greater when the forecasts are obtained from a very small number of analysts. These services typically report the number of analysts who have provided earnings estimates, which should be considered in determining how much reliance to place on forecasts of this type. 4. The analysts’ estimates are denominated as net income. Any significant variations between net income and net cash flow require adjustment. Several authors have published studies on the usefulness and bias of analysts’ forecasts. For example, one study ‘‘examines the ability of naı¨ve investor expectations models to explain the higher returns to contrarian investment strategies.’’ The authors: find no systematic evidence that stock prices reflect naive extrapolation of past trends in earnings or sales growth. . . . [H]owever, we find that stock prices appear to naively reflect analysts’ biased forecasts of future earnings growth . Further, we find that naı¨ve reliance on analysts’ forecast of future earnings growth can explain over half of the higher returns to contrarian investment strategies. [T]he evidence suggests that stock prices naively incorporate analysts’ forecasts of long-term earnings growth. In particular, our results indicate that earnings tend to grow at less than half the rate predicted by analysts, but that stock prices initially reflect substantially all of the forecast earnings growth.2
In another study, the authors test the relationship of accounting information and firm value based on a residual earnings model (book value plus present value of future residual earnings, income in excess of the cost of capital) using analyst earnings forecasts (uses I/B/E/S consensus earnings forecasts to proxy for market expectations of future earnings). That study provides evidence on the reliability of I/B/E/S consensus forecasts for valuation (and a method for correcting predictable forecast errors).3 Are one set of analyst projections more accurate than another? In one study the authors compare I/B/E/S quarterly forecasts to Value Line and find that the I/B/E/S forecasts outperform Value Line in terms of accuracy and proxies for market expectation. I/B/E/S long-term forecasts are less biased and more accurate. Using more recent data . . . we reach different conclusions [than earlier studies] . . . . We find that . . . I/B/ E/S quarterly earnings forecasts significantly outperform Value Line in terms of accuracy and as proxies for market expectations. . . . We also evaluate long-term forecasts and find that I/B/E/S forecasts are less biased and more accurate.4
Those authors report the results of projected earnings amounts rather than growth rates. (They use the I/B/E/S long-term growth rate to project the earnings per share four years into the future, and compare this with the actual earnings per share four years out.) The results indicate that I/B/E/S mean
2
3
4
Patricia Dechow and Richard Sloan, ‘‘Returns to Contrarian Investment Strategies: Tests of Naı¨ve Expectations Hypotheses,’’ Journal of Financial Economics (January 1997): 3–27. Quotes 3, 4. Richard Frankel and Charles M.C. Lee, ‘‘Accounting Valuation, Market Expectation, and Cross-Sectional Stock Returns,’’ Journal of Accounting and Economics (June 1998): 283–319. Sundaresh Ramnath, Steve Rock, and Philip Shane ‘‘Value Line and I/B/E/S Earnings Forecast,’’ International Journal of Forecasting (January 2005): 185–198.
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Cost of Capital
forecast error in Year 4 can be translated into a typical growth rate adjustment for, say, 15% growth, implying a ratio of actual to forecast of 0.89.5 Many of the problems inherent in using the single-stage model to estimate cost of capital are addressed by using a multistage model. MULTISTAGE DCF MODELS Multistage models come closer to reversing the discounting process than do single-stage models that simply reverse the capitalization process. Multistage models do not incorporate specific expected return amounts for specific years, but they do incorporate different growth rates for different expected growth stages, most often three stages. Multistage models have one main advantage over single-stage models: Using more than one growth rate reduces reliance on a single such rate. Furthermore, it is unnecessary to compute a blended growth rate. The main disadvantage of a multistage model is its computational complexity relative to the single-stage model. Unlike the single-stage model, the multistage model must be solved iteratively. It also differs from the single-stage model in that there is no single form of the multistage model. Two main factors determine the form of the model: 1. Number of growth stages. Usually there are either two or three growth stages. 2. Length of each stage. Usually each stage is between three and five years long. In a three-stage model, the discounting formula that must be reversed to solve for k, the cost of capital, looks like this: (Formula 16.4) h i NCF10 ð1 þ g3 Þ 5 10 NCF5 ð1 þ g2 Þn5 X ½NCF0 ð1 þ g1 Þn X k e g3 þ þ PV ¼ n n ð1 þ k Þ Þ ð1 þ k e e ð1 þ ke Þ10 n¼1 n¼6 where: NCF0 ¼ Net cash flow (or dividend) in the immediately preceding year NCF5 ¼ Expected net cash flow (or dividend) in the fifth year NCF10 ¼ Expected net cash flow (or dividend) in the tenth year g1, g2, and g3 ¼ Expected growth rates in NCF (or dividends) through each of stages 1, 2, and 3, respectively ke ¼ Cost of equity capital (discount rate) These ‘‘stages’’ can be done in three-year increments or in increments of any number of years. Also, the length of the second stage can differ from the length of the first stage. As noted earlier, this equation must be solved iteratively for k. Fortunately, many spreadsheet software packages, such as Excel, can perform this calculation. Morningstar, for example, in its Cost of Capital Yearbook, uses two five-year stages and then a growth rate applicable to earnings over all future years after the first 10 years. In the first and second stages, Morningstar uses estimated cash flows instead of dividends. It defines cash flows for this purpose as net income plus noncash charges 5
Ibid. From Table 6, panel A. I/B/E/S mean forecast error in Year 4 can be translated into a typical growth rate adjustment for 15% growth in this way: ((1.15^4)(1 .0545))^.25 1 = 13.4%, implying a ratio of actual to forecast of 13.4/15 = 0.89.
Residual Earnings Method
261
less capital expenditures. This definition comes close to our definition of net cash flow to equity, except that it does not subtract additions to working capital or adjust for changes in outstanding debt principal. Morningstar’s third-stage (long-term) growth rate is the expected long-term inflation forecast plus the historical gross domestic product (GDP) growth rate.
RESIDUAL EARNINGS METHOD Like the DCF method, the residual earnings method (RE) (or the related abnormal earnings growth [AEG] method) is considered by some to be more direct and simpler than the build-up model or the CAPM for a public company. The single-stage RE model is based on a rewrite of a constant growth model presented in Formula 4.20 and repeated here: (Formula 16.5) PV ¼ BV0 þ
RE1 ðke gÞ
where: PV ¼ Present value BV0 ¼ Book value (net asset value) for period 0, the period immediately preceding the valuation date RE1 ¼ Residual earnings for period 0 ¼ V0 k e ke ¼ Cost of equity capital (discount rate) g ¼ Expected long-term sustainable growth rate in net cash flow to equity investors When the present value (i.e., the market price) is known, but the discount rate (i.e., the cost of capital) is unknown, Formula 16.5 can be rearranged to solve for the cost of capital, as shown: (Formula 16.6) PV0 BV0 RE1 þ ke ¼ g þ PV0 PV0 where the variables have the same definitions as in Formula 16.5. Similarly the AEG model is a rewrite of a constant growth model presented as Formula 4.21 and repeated here: (Formula 16.7) 1 AEG2 NI þ PV ¼ ðke gÞ ke where: PV ¼ Present value ke ¼ Cost of equity capital AEG2 ¼ RE2 RE1 NI ¼ Net income (after entity-level taxes) g ¼ Expected long-term sustainable growth rate in net cash flow to equity investors
262
Cost of Capital
Formula 16.7 can similarly be rearranged to solve for the cost of capital. The issues surrounding using analyst forecasts just described are equally applicable if you use the residual earnings method to estimate the cost of equity capital. Easton has used the concepts of the AEG model to improve on the popular PEG ratio.6 The PEG ratio (the price-to-earnings ratio divided by the short-term earnings growth rate) has become a fairly widely used means of combining prices and forecasts of earnings and earnings growth into a ratio. Advocates of the PEG ratio hold that it takes into account differences in short-run earnings growth. The author develops methodology that simultaneously estimates the expected rate of return and the rate of change in abnormal earnings growth in earnings beyond the short forecast horizon. He then demonstrates the use of the methodology using prices and analysts’ short-term earnings forecasts for years 1981 to 1995 and estimates the implied cost of capital and the long-run change in abnormal earnings growth. Another study by Easton highlights the errors that will be introduced if invalid assumptions are made about growth beyond the short horizon for which analysts’ forecasts of earnings are available.7 Easton concludes that in light of the analysts’ tendency to be optimistic, the estimate of the expected rate of returns are generally likely to be higher than the cost of capital.8
BUILDING A FORECAST While a detailed discussion of forecasting techniques are beyond the scope of this book, we highlight several methods that go beyond simple extrapolation of historical trends. For example, one consideration in forecasting is trend and cycle analysis. In one study (based on 505 firms from 1955 to 1994), the author decomposes earnings into:
Nonstationary trend component (explains 70.6% of earnings change) Cyclical component (explains 13.6% of earnings change)
Irregular component
That author finds that earnings cycles average 6.2 years (cycle peak to peak), and stock prices appear to rise and fall above and below their long-term trend contemporaneously with similar cyclical fluctuations in reported earnings.9 Another variation of the DCF method is called the sustainable growth method. In order to implement this method, you estimate the rate of return the company can earn on its retained capital.10 The main contributor to the growth of most companies is retained earnings and the rate of return earned on investments in new projects. The formula is shown next. (Formula 16.8) EðRi Þ ¼ ke ¼
6
7
8 9 10
D1 ð1 bÞNI1 þbr ¼ þbr P0 P0
Peter Easton, ‘‘PE Ratios, PEG Ratios, and Estimating the Implied Expected Rate of Return on Equity Capital,’’ Accounting Review 79 (2004): 73–96. Peter Easton, ‘‘Use of Forecasts of Earnings to Estimate and Compare Cost of Capital Across Regimes,’’ Journal of Business Finance & Accounting (April/May 2006): 374–394. Ibid., 376. Robert F. Halsey, ‘‘Stationary Components of Earnings and Stock Prices,’’ AFA 2001 New Orleans, October 2000. M. J. Gordon and L. I. Gould, ‘‘The Cost of Equity Capital: A Reconsideration,’’ Journal of Finance (June 1978): 849–861.
Sources of Information
263
where: D1 ¼ Dividend expected in period 1, the first period following the valuation date P0 ¼ Price of stock at valuation date NI1 ¼ Net income expected in period 1 b ¼ 1– Payout ratio = retention ratio r ¼ Expected marginal return on investing equity capital If the company gets equity capital from selling new stock besides retained earnings, we get: (Formula 16.9) ke ¼
ð1 qÞNI1 þ qr P0
where: q ¼ <1 q ¼ (bs þ s) s ¼ Rate of new equity financial investment This type of model leads analysts to ask whether, if a company is earning more (or less) than the industry average, that will continue, or whether the return will gravitate to the industry average because economic arguments say that in a competitive environment, profitability is mean reverting. One study11 found that profitability was mean reverting:
Rate of mean reversion is 38% per year but not linear. Profitability returns to the industry average at a faster rate when profitability is below the mean and when profitability is far from the mean in either direction (either far below or far above).
SOURCES OF INFORMATION To perform an implied cost of capital analysis rather than use data compiled by one of the services, a variety of inputs is necessary, including company-specific data, industry outlook data, and long-term macroeconomic forecasts. Company data can be obtained from Securities and Exchange Commission (SEC) filings or services such as Standard & Poor’s (a division of McGraw-Hill), Moody’s (published by Mergent, Inc.), or Value Line Publishing, Inc. Analysts’ estimates can be compiled from individual analysts’ reports or from one of the three earnings consensus reporting services: Thomson Financial (formerly First Call and I/B/E/S), Multex-Ace, and Zack’s Investment Research, Inc. There are a great number of different industry forecasts. For some industries, excellent material is available from industry trade associations, although they tend to focus primarily on revenues rather than on cash flows. There is also a wide variety of macroeconomic forecast information. Appendix B lists details on many sources providing data in all these categories. A more comprehensive compilation of the industry forecasts is the Business Valuation Data, Publications & Internet Directory, published annually by Business Valuation Resources, LLC, www.BVResources.com.
11
Eugene Fama and Kenneth French, ‘‘Forecasting Profitability and Earnings,’’ Journal of Business (April 2000): 161–175.
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Cost of Capital
SUMMARY The implied method of cost of capital estimation attempts to use current public stock price information to estimate implied costs of equity capital. You can use either a DCF method or an RE method. Single-stage models use a Gordon Growth Model type of formula, with the present value (i.e., the stock price) known, solving for k, the cost of equity capital. Multistage models use two or more growth estimates for different future periods. As with the CAPM, applying the method to closely held companies involves using public companies as proxies in a similar industry group to develop a proxy starting point, with modifications for differences in the characteristics between the public guideline companies and the subject company. Analysts can obtain DCF-based cost of capital estimates for public companies and industries from several services that compile them or can build their own estimates from scratch. Research continues to improve the methods for estimating the cost of capital. Recent research has been reported on using option prices on traded options of public stocks to imply the cost of equity capital. Options have been used to estimate expected volatility and these authors expand the option pricing models to imply the cost of equity capital that must be implied by the price and volatility of call and put options. Their results of applying the methodology to the stocks comprising the S&P 100 firms are promising in that their implied cost of equity estimates are reasonable and consistent with estimates obtained using the FF3 factor model.12
12
Antonio Camera, San-Lin Chung, and Yaw-Huei Wang, ‘‘The Cost of Equity Capital Implied by Option Market Prices,’’ Working paper, June 19, 2007.
Chapter 17
Weighted Average Cost of Capital
Introduction When to Use Weighted Average Cost of Capital Valuing the Levered Firm After-Tax Weighted Average Cost of Capital Optimal Capital Structure Computing WACC for a Public Company Computing WACC for a Non-Public Company Should an Actual or a Hypothetical Capital Structure Be Used? Should a Constant or Variable Capital Structure Be Used? Fixed Book-Value Leverage Ratio Pretax Weighted Average Cost of Capital Capital Cash Flows Equivalence of Valuation Methodologies Summary Additional Reading Appendix 17A Appendix 17B
INTRODUCTION In Chapter 6 we identified components of a company’s capital structure. Here we blend their costs together to estimate the company’s overall cost of capital. In other words, we want to estimate the weighted cost for all of the company’s invested capital or the capital to be committed to a specific project.
WHEN TO USE WEIGHTED AVERAGE COST OF CAPITAL The most obvious instance in which to use weighted average cost of capital (WACC) is when the objective is to value the overall firm. An example would be when considering an acquisition, and the buyer expects to pay off all equity and debt holders and refinance the whole company in a different way that better suits the buyer. Such an analysis may result in ‘‘investment value’’ instead of fair market value if the financing plan was significantly different from the industry average capital structure. Alternatively, WACC is also used even when the objective is ultimately to value only the equity. You would value the overall firm and then subtract the market value of the debt to estimate the value 265
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Cost of Capital
of the equity. Valuing the overall firm is frequently done in highly leveraged situations to understand the value of the operations separately from currently debt-burdened equity. Weighted average cost of capital is especially appropriate for project selection in capital budgeting. The proportions of debt and equity that could be available to finance various projects might differ according to the project (e.g., asset-intensive projects may be financed with more debt than the overall capital structure), and the cost of capital generally should be based on the debt capacity of the specific investment. The idea of differing proportions of debt and equity for financing various projects introduces the idea that we have to compute or estimate the weight (percentage of the total) for each component of the capital structure. The critical point is that the relative weightings of debt and equity or other capital components are based on the market values of each component, if we assume that debt remains a constant percentage of overall firm value (or its operating or unlevered net cash flow), not on the book values. In Appendix 10A of Chapter 2, we discussed the various formulas for adjusting the cost of equity capital for the amount of leverage. Even the Fernandez formula (10A.9 and 10A.10), which is based on debt capital (at market value) increasing/decreasing in proportion to the book value of equity capital, is based on market value weights of both debt capital and equity capital.1
VALUING THE LEVERED FIRM There are two equivalent formulations in the literature for valuing a levered firm: Value of levered firm ¼ Value of levered assets or alternatively Value of levered firm ¼ Value of unlevered firm þ Value of tax shield The tax shield is the reduction of the cost of debt capital due to the tax deductibility of interest expense on debt capital. Exhibit 10.3, which is reproduced here as Exhibit 17.1, describes these relationships. The first formulation uses as the discount rate the weighted after-tax cost of debt capital and the cost of equity capital components (after-tax weighted average cost of capital). It is applied to net after-tax (but before interest) net cash flows of the firm and its underlying assets. In the second formulation, the tax savings due to interest deductions are included in the cash flows. That is, the cash flows are measured by the tax savings due to the tax shield. Therefore, the discount rate is the pretax weighted cost of debt capital and the cost of equity capital components (pretax weighted average cost of capital). It is applied to the net after-tax (but before interest) net cash flows of the firm, the underlying assets, and the cash flows due to the tax shield. In the first formulation, you attach value to the assets of the business based on their being partially financed with debt capital. In the second formulation, you attach value to the assets of the business as if they were financed with all equity capital, and then the tax shield is valued separately.
AFTER-TAX WEIGHTED AVERAGE COST OF CAPITAL As noted in the discussion of debt in Chapter 6, the after-tax WACC is based on the cost of each capital structure component net of any corporate-level tax effect of that component. In the return to the debt component, interest is a tax-deductible expense to a corporate taxpayer. Whatever taxes are 1
The formulas are based on the relationship between the growth in book value of equity and market value of equity. This is also true for the Bodt-Levasseur formulas we reference in Appendix 10A.
After-Tax Weighted Average Cost of Capital
267
Value of Levered Firm = Value of Levered Assets Capital Assets Value of Levered Assets
Value of Debt Capital minus Value of Tax Shield plus Value of Equity Capital
In this formulation, cost of debt capital is measured after the tax affect (kd) as the value of the tax deduction on interest payment reduces the cost of debt capital. Value of the Levered Firm = Value of the Unlevered Assets + Present Value of Tax Shield Assets
Capital
Value of Unlevered Assets
Value of Debt Capital
plus
plus
Value of Tax Shield
Value of Equity Capital
In this formulation, the cost of debt capital is measured prior to the tax effect (kd(pt)) as the value of the tax deduction on the interest payments equals the value of the tax shield.
Exhibit 17.1
Value of a Levered Firm
paid are an actual cash expense to the company, and the returns available to equity holders are after the payment of corporate level income taxes. Because we are interested in cash flows after entity-level taxes, literature and practitioners refer to this formulation of the WACC as an after-tax WACC. The basic formula for computing the after-tax WACC for an entity with three capital structure components is: (Formula 17.1)
WACC ¼ ðke We Þ þ ðk p W p Þ þ ðkdð ptÞ ½1 t Wd Þ where: WACC ¼ Weighted average cost of capital (after-tax) ke ¼ Cost of common equity capital
268
Cost of Capital
We ¼ Percentage of common equity in the capital structure, at market value kp ¼ Cost of preferred equity Wp ¼ Percentage of preferred equity in the capital structure, at market value kd(pt) ¼ Cost of debt (pretax) t ¼ Tax rate Wd ¼ Percentage of debt in the capital structure, at market value
OPTIMAL CAPITAL STRUCTURE The traditional view of the optimal capital structure is that a company should increase debt until its weighted average cost of capital minimizes its WACC. Or the amount of debt should be increased until the after-tax cost of debt exceeds the increase in the risk of financial distress. This relationship is depicted in Exhibit 17.2 What is the optimal capital structure? Textbooks often contend that industry-wide factors are potentially important to firm capital structures. But research has shown that most variation in observed capital structures arises within industries, not between industries.2 Financial leverage is positively related to differences in profitability. As operating profitability increases, adding the fixed cost of debt financing is less risky than if operating profitability is low. Generally, large firms with tangible assets and few growth options tend to use relatively large amounts of debt. Firms with high corporate tax rates tend to have higher ratios of debt to assets. One study estimates the benefit from adding debt to the capital structure.3 The net benefit (net of cost of distress) is approximately equal to 4% of the book value of assets. The authors estimate different marginal cost curves for firms in different industries. They also find that the cost of being overleveraged appears to be more severe than the cost of being underleveraged.
Cost of Equity
Cost of Capital
WACC
Cost of Debt
Debt Total Capital
Exhibit 17.2
2
3
Optimal Capital Structure
Peter MacKay and Gordon Phillips, ‘‘How Does Industry Affect Firm Financial Structure?’’ The Review of Financial Studies 18 Issue 4 (2005): 1433–1465. Jules Van Binsbergen, John Graham, and Jie Yang ‘‘The Cost of Debt.’’ Working paper, September 2007.
After-Tax Weighted Average Cost of Capital
269
COMPUTING WACC FOR A PUBLIC COMPANY Assuming that the market price fairly represents the value for active publicly traded securities, you can compute the weights for each capital component by multiplying the amount of each component outstanding by the market value of each and then computing the percentage that each component represents of the total market value. The five steps for this procedure are: Step 1. Identify the number of shares or units of each component of the capital structure. Step 2. Determine the market price per unit of each component of the capital structure as of the valuation date. Step 3. Multiply the number of units of each component by the market price per unit. This gives the total market value for each capital structure component. Step 4. Sum the total market values of each component, from step 3. This gives the market value of invested capital (MVIC). (Alternative terms for market value of invested capital are enterprise value or business enterprise value.) Step 5. Divide the total market value of each component (from step 3) by the total MVIC (from step 4). This gives the percentage weight to be accorded to each component of the capital structure. To illustrate the process of computing weights for each capital structure component, let us make these assumptions for American Brainstorming Company (ABC):
5 million shares of common stock issued and outstanding Closing common stock price per share: $8.00
1 million shares of preferred stock issued and outstanding
Closing preferred stock price per share: $20.00 $10 million face value of bonds issued and outstanding
Closing bond price: 90 (This means 90% of face value. Because bonds usually have $1,000 face value, this would be $900 per bond.) From the preceding information, the capital structure weights can be computed:
Component Common stock Preferred stock Bonds MVIC
No. of Shares (or $ of face value)
Price (or % of face value)
Component Total
Weight
5,000,000 sh 1,000,000 sh $20,000,000
$ 8.00 $20.00 90%
$40,000,000 $20,000,000 $18,000,000 $78,000,000
51% 26% 23% 100%
We still need four more pieces of information before we can compute the WACC: 1. Cost of common equity. For the purpose of this example, we will assume that ABC’s cost of common equity is 20%. 2. Cost of preferred equity. The cumulative, nonparticipating dividend on the preferred stock is $2.50 per share per year. Since its market price is $20, the cost of preferred equity is 12.5% ($2.50 $20.00 ¼ 0.125).
270
Cost of Capital
3. Cost of debt (before tax effect). The bonds pay a 9% interest rate on their face value, or $90 per bond per year. Therefore, the current yield is 10% ($90 $900 = 0.10). However, remember that the cost of debt is the yield to maturity, not the current yield. We make the simplifying assumptions that the bonds mature three years from the valuation date and that the interest is paid only at the end of each year. This problem is very much like that addressed in Formulas 2.1 and 2.2, except that we know the present value (PV), but we have to solve for the cost of debt capital (kd(pt)) before tax effect. Putting it in the same form as Formulas 2.1 and 2.2 would look like: (Formula 17.2) $900 ¼
$90 $90 $90 $1;000 þ þ þ ð1 þ kdð ptÞ Þ ð1 þ kdð ptÞ Þ2 ð1 þ kdð ptÞ Þ3 ð1 þ kdð ptÞ Þ3
Instead of showing each step to solve for the independent variable as kdð ptÞ , we will simply compute it on our financial calculator and find that kdð ptÞ 13%. (Some readers may find it surprising that the example shows the pretax cost of the debt a half point [0.5%] higher than the cost of preferred stock, which is in a lower position of claims on the balance sheet. This sometimes happens when the preferred stock is attractive for taxable corporations to hold, because only a small portion of the dividends paid are taxable income to the receiving corporation.) 4. Tax rate. The combined federal and effective state income tax rate for ABC is 40%. Now we are prepared to substitute all of these numbers into Formula 17.1 to compute a weighted average after-tax cost of capital for ABC: (Formula 17.3) WACC ¼ ð0:20 0:51Þ þ ð0:125 0:26Þ þ ð0:13½1 0:40 0:23Þ ¼ 0:102 þ 0:0325 þ ð0:078 0:23Þ ¼ 0:102 þ 0:0325 þ 0:0179 ¼ 15:2% Many people prefer to set up this formula in tabular form: Component
Cost
Weight
Common stock Preferred stock Debt (after tax) WACC
0.20 0.125 0.078
0.51 0.26 0.23
Weighted Cost ¼ ¼ ¼
0.102 0.0325 0:0179 15.2%
Income Tax Rates Impact WACC Income tax rates do impact WACC. For example, assume that the tax rate assumed moves from 35% to 15%. The next example shows the impact on the WACC using Formula 17.1.
After-Tax Weighted Average Cost of Capital
271
(Formula 17.4) WACC ¼ ð0:15 0:50Þ þ ð0:10½1 0:35 0:50Þ ¼ 0:075 þ ð0:065 0:50Þ ¼ 0:075 þ 0:0325 ¼ 10:75% where: ke ¼ 15% We ¼ 50% kd(pt) ¼ 10% t ¼ 35% Wd ¼ 50% If t changes to 15%, we get: (Formula 17.5) WACC ¼ ð0:15 0:50Þ þ ð0:10½1 0:15 0:50Þ ¼ 0:075 þ ð0:085 0:50Þ ¼ 0:075 þ 0:0425 ¼ 11:75% U.S. tax code provisions also affect the assumed marginal tax rate:
Current tax code offers net operating loss carrybacks and carryforwards. Businesses can carry back losses 2 years.
Businesses can carry forward losses 20 years.
State income taxes do matter, and differences in the weighted average of the state income taxes do affect the cost of capital. In calculating the total effective income tax rate, the weighted average state income tax rate adjusted for the tax deductibility of the state income taxes against federal income taxes is added to the federal income tax rate. Do companies realize deductions at the statutory tax rate (get full benefit of interest tax deduction)? Researchers have developed an expected tax rate model that simulates taxable income into the future. This process has shown that many companies do not expect to pay the highest marginal rate for long periods of time. Because of tax-loss carrybacks and carryforwards and the cyclical nature of some industries, a substantial number of companies can expect a very low tax rate.4 Graham and Mills recently completed a simulation study of corporate marginal income tax rates. They used U.S. tax return data for public corporations from 1990 to 2000 to simulate the corporate marginal tax rates for 1998 to 2000. They used these data because financial statement data can vary greatly from tax return data. Actual taxes paid are the correct measure for the cost of debt capital, not financial statement taxes. These authors found that the simulated marginal tax rate most closely approximated future actual taxes paid. But when the simulated model is not available, they offer two formulas based on actual corporate income tax data to estimate the corporate marginal 4
John R. Graham, ‘‘Debt and the Marginal Tax Rate,’’ Journal of Financial Economics (May 1996): 41–73; Graham, ‘‘Proxies for the Corporate Marginal Tax Rate,’’ Journal of Financial Economics (October 1991): 187–221; Graham and Michael Lemmon, ‘‘Measuring Corporate Tax Rate and Tax Incentives: A New Approach,’’ Journal of Applied Corporate Finance (Spring 1998): 54–65.
272
Cost of Capital
Exhibit 17.3
Example of Valuing a Bond Using Excel ¼PRICE (a, b, c, d, e, f)
Inputs a b c d e f
Settlement Date: Maturity Date: Coupon Rate: Yield to Maturity: Redemption Value (%par): Coupons per year:
03/15/02 09/15/27 8.00% 6.16% 100.00 2
(Choose valuation date) (Choose a date of maturity) (Needs to be annual rate) (Needs to be annual rate) (Amount redeemed at maturity per $100 par) (Semi-annual payments)
Price(% of par):
123.51
Excel syntax: = PRICE(a,b,c,d,e,f)
Price:
tax rate.5 These formulas can be useful in estimating the expected cash tax rate instead of arbitrarily using the marginal income tax rate. Market Value of Debt In the WACC, we are to use market value weights based on the relative percentage of debt capital and equity capital in a company’s capital structure. You can calculate the value of the bond using the formula in Excel. Exhibit 17.3 is an example. For public companies, you can use the financial statement disclosures prepared under Financial Accounting Standards (FAS) No. 107, Disclosures about Fair Value of Financial Instruments (December 1991) to determine the market value weight of debt. Under FAS No. 107, fair value is defined as market prices, if available; otherwise, a discounted cash flow (DCF) value based on future obligations discounted at either: (1) the company’s current incremental borrowing rate on similar liabilities or (2) the rate required to induce a third party to assume the debt (‘‘settlement rate’’) can be used.6 Exhibit 17.4 shows such a disclosure. You need to reconcile the fair value disclosure with the balance sheet and the notes about outstanding debt. The fair value disclosure may not include all debt instruments; for example, capital leases may not be included in the fair value disclosure, and the fair value disclosure may or may not include current maturities. Often the instruments are not itemized, and the disclosure may include only one item for fair value of long-term debt. While it is often common practice to use book values of debt rather than market values, doing so when book values differ significantly from market values can distort cost of capital calculations.7 COMPUTING WACC FOR A NON-PUBLIC COMPANY In computing WACC for a closely held company, a reporting unit or division, a project, or proposed project, one important additional problem exists: Because there is no market for the securities, we have to estimate market values in order to compute the capital structure weightings. As we will see, estimating the weightings for each component of the capital structure becomes an iterative process 5
6 7
John R. Graham and Lillian F. Mills, ‘‘Using Tax Return Data to Simulate Corporate Marginal Tax Rates,’’ Working paper, January 24, 2007. FAS No. 107, Paragraphs 22–28 and 32. Richard J. Sweeney, Arthur D. Warga, and Drew Winters, ‘‘The Market Value of Debt, Market versus Book Value of Debt, and Returns to Assets,’’ Financial Management (Spring 1997): 5–21.
After-Tax Weighted Average Cost of Capital Exhibit 17.4
273
Sample Disclosure of Fair Value of Debt
Fair Values The carrying value of cash, cash equivalents, marketable securities, short-term deposits, trade accounts receivable, accounts payable, and other current liabilities approximates their fair value due to the relatively short maturity of these financial instruments. The carrying value of the revolving credit facility approximates fair value due to its variable interest rate. Estimated fair values of other financial instruments at December 31, 2006, and 2005 follows. 2006 ($1,000s) First Mortgage Bonds (a) Exchange Bonds (a) Real Estate Installment Note (b) 7% Notes (a) 7.625% Notes (a) 7.25% Notes (a) 7.8% Debentures (a) 7.9% Debentures (a) Trust Preferred Securities (a)
Carrying Value
Fair Value
Carrying Value
Fair Value
$200,000 $150,000 $52,563 $125,000 $240,000 $200,000 $300,000 $100,000 $300,000
$222,120 $161,550 $52,563 $126,975 $252,600 $204,420 $330,720 $109,400 $389,250
$300,000 $150,000 $54,821 $125,000 $240,000
$325,940 $161,537 $54,821 $126,781 $248,642
$300,000
$326,250
(a) The fair value of these instruments reflects quoted market prices. (b) The fair value of this financial instrument was estimated by discounting future cash flows.
Total Per Fair Value Disclosure Revolving Credit Facility Long-term Debt Instruments LT Debt Not Included in Disclosure Capital Leases Other Total Debt Less Revolving Credit Total Long-term Debt (including current) Less Current Maturities Total Long-term Debt (excluding current)
Book Value
Fair Value
166,000 1,667,563
166,000 1,849,598
55,334 4,268
55,334 4.268
$1,893,165 (166,000) 1,727,165 (11,908) $1,715,257
$2,075,200 (166,000) 1,909,200 (11,908) $1,897,292
!
)
2005
!
10.6% difference
for companies intending or assumed to operate with certain levels of debt. Fortunately, computers perform this exercise very quickly. To ‘‘iterate’’ means to repeat. An ‘‘iterative process’’ is a repetitious one. In this case, we estimate market value weights because the actual market values are unknown. We may reestimate weights several times until the computed market value weights come fairly close to the weights used in estimating the WACC.8
8
Pitabas, Mohanty ‘‘Solving the Circularity Problem in Estimating the Cost of Capital: A Practical Approach,’’ The Icfai Journal of Applied Finance (2007): 29–38.
274
Cost of Capital
The eight steps in the iterative process for estimating capital structure component weights for a closely held company can be summarized in this way: Step 1. Estimate the market value of senior securities (debt and preferred equity), and hold that dollar amount fixed throughout the process. Step 2. Make a first estimate of the market value weights of the senior securities and the common equity. (Generally, the farther above book value the equity market value is expected to be, the greater the first estimate of the equity percentage compared with its percentage at book value.) Step 3. Using the first-approximation weights, make a first-approximation computation of the WACC, using Formula 17.1. Step 4. Project (a) the net cash flows available to all invested capital, and (b) the projected growth rate necessary for either a discounting valuation model (Formula 2.1) or a capitalizing valuation model (Formula 4.4). Step 5. Using the first-approximation WACC from step 3 and the projected cash flows from step 4, compute a first-approximation MVIC. Step 6. Subtract from the MVIC from step 5 the value of the senior securities from step 1. This gives the first-approximation value of the common equity. Step 7. Compute the capital structure weights using the equity value from step 6. Step 8. Repeat the process, starting with step 3, until the computed market value weights come reasonably close to the weights used in computing the WACC. For simplicity, Exhibit 17.5 demonstrates this process using only a two-component capital structure, common equity and debt. To further simplify, we will use the capitalization model. (The iterative process works just as well with a discounting model, but a few more figures are involved.) The point is that the first approximation of the capital structure weighting led to a 30% overvaluation of the Donald E. Frump Company’s stock. This fact certainly demonstrates the importance of using capital structure component weightings at market value, not at book value, to estimate a company’s WACC. The iterative process can develop a good estimate of the WACC and therefore a sound and defensible estimate of the value of the overall capital, whether the valuation is using the WACC as a discount rate in the discounting method or as a base rate from which to subtract growth when applying the capitalization method. For detail about implementing the iterative process to develop WACC using CAPM with an assumed constant capital structure, see Appendicies 17A and 17B. This procedure could also be used to test if the market prices fairly reflect the true value of the securities. For example, is the market price of the stock for a thinly traded public company representative of the value of the business enterprise or its equity capital?
SHOULD AN ACTUAL OR A HYPOTHETICAL CAPITAL STRUCTURE BE USED? If a company or an interest in a company is to be valued as it is, assuming the capital structure will remain intact, then the amount of debt in the company’s actual capital structure should be used. For example, if a minority interest is to be valued by a procedure involving (first) valuing overall capital and (then) subtracting debt, the company’s actual amount of debt in its capital structure may be
After-Tax Weighted Average Cost of Capital
Exhibit 17.5
275
Example of the Iterative Process
We will carry out the example based on these six assumptions for the Donald E. Frump Company (DEF).
1. The balance sheet shows book values: Long-term debt Common equity
$400,000 $600,000
(40%) (60%)
1. Interest rate on the debt is 10%, and that approximates DEF’s current cost of borrowing. 2. DEF’s cost of equity has been estimated to be 25% (with the simplifying assumption that cost of equity is unaffected by differing levels of debt).
3. DEF’s tax rate is 40%. 4. NCFf,1 ¼ $250,000 (estimated net cash flow to all invested capital for the 12 months immediately following the valuation date).
5. Regarding growth, NCFf (net cash flow available to all invested capital) is expected to grow fairly evenly following the first year at 5% per year. If we start with the balance sheet book values as a first approximation of capital structure weightings, putting the assumed DEF balance sheet numbers into Formula 17.1, the first approximation of the capital structure weightings is: WACC ¼ ð0:25 0:60Þ þ ð0:10½1 0:40 0:40Þ ¼ 0:15 þ ð0:06 0:40Þ ¼ 0:15 þ 0:024 ¼ 17:4% This implies an overall cost of capital (WACC) of 17.4%. The next step in the iteration process is to compute the market value of all the invested capital at this WACC. Substituting numbers from the preceding information in the basic constant growth capitalization formula (Formula 4.4), we get: PVf
$250;000 0:174 0:05 $250;000 ¼ 0:124 ¼ $2;016;129
¼
Subtracting the debt of $400,000 implies a market value of equity of $1,616,129 ($2,016,129$400,000 ¼ $1,616,129). That is not even close to the book value of equity of $600,000. In fact, on this basis, the proportions of the market values of the components of the capital structure would be: Component
Value
Common stock Debt Market value of invested capital
$1,616,129 400,000 $2,016,129
Weight 80% 20% 100%
This certainly sends us back to the drawing board, because our first approximation was 60/40, and this calculation produced a significantly different (80/20) result. This time let us try these weights:
(Continued )
276 Exhibit 17.5
Cost of Capital (Continued)
Common stock 75% Debt 25% Substituting these weights in the formula for WACC produces: WACC ¼ ð0:25 0:75Þ þ ð0:10½1 0:40 0:25Þ ¼ 0:1875 þ ð0:06 0:25Þ ¼ 0:1875 þ 0:015 ¼ 20:25% This implies an overall cost of capital (WACC) of 20.25%, significantly higher than the 17.4% in our first approximation. Taking the next step, substituting this new estimate of WACC in the constant growth capitalization formula, we get: $250;000 0:2025 0:05 $250;000 ¼ 0:1525 ¼ $1;639;344
PVf ¼
Subtracting the debt of $400,000 implies a market value of equity of $1,239,344 ($1,639,344$400,000 ¼ $1,239,344). On this basis, the proportions of the market values of the components of the capital structure are: Component
Value
Weight
Common stock Debt Market value of invested capital
$1,239,344 400,000 $1,639,344
75.6% 24.4% 100.0%
This result is close enough for most applications. After all, computing WACC is not an exact science. A WACC of 20.25% is much more reasonable for this company than our first approximation of 17.4%. But it could be made more precise with further iterations. In Excel the computations are quite precise.
appropriate. The reason is because it would be beyond the power of a minority stockholder to change the capital structure. If a controlling interest is to be valued and the standard of value is fair market value or fair value, an argument can be made that an industry-average capital structure should be used, because a control buyer would have the power to change the capital structure and the industry average could represent the most likely result. However, it would be important to understand how the industry-average capital structure is derived and whether it is reasonable to expect the subject company to achieve it, given current conditions of the company itself and of the financial market. If the industry-average capital structure is comprised of public companies and the subject is closely held, the subject may not be able to achieve the public company average because public companies often have greater access to lower-cost senior capital than do closely held companies. If a controlling interest is to be valued under the standard of investment value (value to a particular buyer or seller rather than the hypothetical buyer or seller assumed under the fair market value standard), then the buyer’s or owner’s actual or desired capital structure could be used. Note that when using an industry-average capital structure, one must use formulas based on market value weights, not book value. Most composite industry statistics sources (e.g., RMA Annual
After-Tax Weighted Average Cost of Capital
277
Statement Studies and all the various services based on federal income tax return data) report balance sheet figures and ratios at book value. Industry-average capital structures at market value can be computed using data from selected guideline public companies in the industry or from sources such as Morningstar’s Cost of Capital Yearbook, remembering the caveat against assuming that closely held companies can achieve public company capital structures. SHOULD A CONSTANT OR VARIABLE CAPITAL STRUCTURE BE USED? Most analysts estimate a single WACC and apply it to each increment of the cash flow forecast. However, that procedure implies an underlying assumption that may or may not be true. The implied assumption is that a company has a constant capital structure at market values over its lifetime. That is, when the value of the company increases (e.g., expected cash flows have increased), the company increases its borrowing to maintain the same proportion of debt capital to equity capital (at market value weights) as that implied by the ‘‘target’’ capital structure. Similarly, when the value of the company decreases (e.g., expected cash flows have decreased), the company decreases its borrowings to maintain that same target capital structure (again at market value weights). Moreover, public companies may have a higher debt/equity ratio than intended if their stock price is depressed. To the extent that a company’s capital structure at market value weights varies over time, using a constant capital structure and constant WACC to discount each increment of the projected cash flows to invested capital will result in an incorrect value of the company. To the extent that the proportions of debt go down over time, using a constant WACC with the capital structure as in the beginning period usually will overvalue the company and vice versa because the cost of debt is usually lower than the cost of equity, so a large assumed portion of debt will lower the WACC, thus inflating the estimated value of the company. We illustrate this in Exhibit 17.6. For detail about implementing the iterative process to develop WACC using CAPM with a changing capital structure, see Appendix 17B. We used CAPM to estimate the cost of equity capital in Exhibit 17.5 and in Appendix 17B to highlight the change in the cost of equity capital as the leverage changes.
FIXED BOOK-VALUE LEVERAGE RATIO Many companies, closely held and public companies, utilize a fixed book-value leverage ratio (maintaining debt at a preset percentage of book equity) rather than maintaining a leverage ratio based on market values of debt and equity. Reasons include:
Rating agencies focus on book-value leverage ratios.9 The amount of debt does not depend on movements in the stock market (for public companies) or on unobservable market values (for closely held companies).
Empirical evidence suggests that leverage is more tied to book values than market values.10
9
Darren Kisgen, ‘‘The Influence of Credit Ratings on Corporate Capital Structure Decisions,’’ Journal of Applied Corporate Finance (Summer 2007): 65–73. 10 Pablo Fernandez, ‘‘APV and WACC with Constant Book Leverage Ratio,’’ Working paper, IESE Business School, April 19, 2007.
278
Cost of Capital
Exhibit 17.6
Example of Using Constant WACC When Capital Structure Changes
Assume a leveraged buyout of company A where the company initially borrowed 80% of the purchase price. It expects to repay the debt using all cash flows to invested capital; those cash flows will be used to pay interest on the outstanding debt with the remaining amount used to repay principle. Assume: Unlevered beta ¼ 1:50 Rf ¼ 5% RPm ¼ 5% RPs ¼ 2:5% keu ¼ unlevered cost of equity capital ¼ R f þ Bu ðRPm Þ þ RPs ¼ 0:05 þ 1:5ð0:05Þ þ 0:025 ¼ 15% kdð ptÞ ¼ 10% t ¼ 40% Expected long-term growth in cash flows to invested capital ¼ 5% Expected cash flows, value of the firm, and debt follows.
Year 0 1 2 3 4 5 6 )
Cash Flow to Invested Capital $100 105 110 116 122 128 134 (4)
Capitalized Value of Invested Capital (1)
Interest 10% (1– 0.4)
$1,050 1,100 1,160 1,220 1,280 1,340
50 47 43 39 34
Debt $
%
$840 785 (2) 722 649 566 536 (3)
80 71 62 53 44 40
(1) 1=ð0:15 0:05Þ next year’s expected cash flows to invested capital (2) $840 ½$105 $840 10% ð1 0:40Þ (3) $1;340 40% ¼ $536 (4) Thereafter growing at 5% per year
Assume you calculate the cost of equity capital based on the normalized debt equity ratio of 40% debt, 60% equity: ke ¼ 0:05 þ 2:1ð0:05Þ þ 0:025 ¼ 18% where the levered beta is estimated for illustrative purposes using the widely used Hamada formula (Formula 10A.2). But if you then use 18% for the cost of equity capital to calculate the WACC, using Formula 17.1, as of the acquisition date with the amounts of debt in the capital structure as of the acquisition date, we get: WACC ¼ ð0:18 0:20Þ þ ð0:10½1 0:40 0:80Þ ¼ 0:036 þ ð0:06 0:80Þ ¼ 0:036 þ 0:048 ¼ 8:40%
After-Tax Weighted Average Cost of Capital
279
If we then calculate the present value of the expected cash flows to invested capital using Formula 4.8, we get: 134ð1 þ 0:05Þ 105 110 116 122 128 134 PV ¼ þ þ þ þ 0:084 0:05 þ ð1 þ 0:084Þ ð1 þ 0:084Þ2 ð1 þ 0:084Þ3 ð1 þ 0:084Þ4 ð1 þ 0:084Þ5 ð1 þ 0:084Þ6 ð1 þ 0:084Þ6 140:7 ¼ 96:86 þ 93:61 þ 91:07 þ 88:36 þ 85:52 þ 82:59 þ 0:034 6 ð1:084Þ ¼ 96:86 þ 93:61 þ 91:07 þ 88:36 þ 85:52 þ 82:59 þ
4;138:24 ð1:084Þ6
¼ 96:86 þ 93:61 þ 91:07 þ 88:36 þ 85:52 þ 82:59 þ 2;550:58 ¼ $3089 But if we correctly relever the beta and calculate the varying WACC, we get: Year
D/E
BL
ke
WACC
0 1 2 3 4 5
4 2.45 1.63 1.13 .79 .67
5.1 3.71 2.97 2.52 2.21 2.10
33.0% 26.0 22.4 20.1 18.6 18.0
11.4% 11.8 12.2 12.6 13.1 13.2
You can then calculate the present value of the expected cash flows to invested capital using the varying WACC:
PV ¼
134ð1 þ 0:05Þ 105 110 116 122 128 134 0:132 0:05 þ þ þ þ þ þ ð1 þ 0:114Þ ð1 þ 0:118Þ2 ð1 þ 0:122Þ3 ð1 þ 0:126Þ4 ð1 þ 0:131Þ5 ð1 þ 0:132Þ6 ð1 þ 0:132Þ6
140:7 ¼ 94:25 þ 88 þ 82:13 þ 75:89 þ 69:17 þ 63:68 þ 0:082 6 ð1:132Þ ¼ 94:25 þ 88 þ 82:13 þ 75:89 þ 69:17 þ 63:68 þ
1;715:85 ð1:132Þ6
¼ 94:25 þ 88 þ 82:13 þ 75:89 þ 69:17 þ 63:68 þ 815:46 ¼ $1;289 This is quite a different result from the $3,089 calculated earlier as the present value using the constant WACC.
Appendix 10.1 presented the formula for unlevering betas (Formula 10A.9) and levering betas (Formula 10A.10) assuming a fixed book-value leverage ratio. These formulas are consistent with maintaining a fixed rate of debt to book value of equity. The formula for the WACC consistent with this approach is shown next.11 (Formula 17.6) Md ðkeu kni Þ NI1 keu þ WACC ¼ keu þ MVIC ðkni gni Þ BV0 11
Ibid., 7.
280
Cost of Capital
where: keu ¼ Cost of equity capital, unlevered (cost of equity capital assuming firm financed with all equity) MVIC ¼ Market Value of invested capital as of valuation date Md ¼ Market value of debt capital as of the valuation date kni ¼ Discount rate for equity capital when net income rather than net cash flow is the measure of economic income being discounted (equates Me to net income after-taxes) gni ¼ Rate of growth in net income NI1 ¼ Net income (after entity-level taxes) in year 1 BV0 ¼ Book value of net assets as of the valuation date
PRETAX WEIGHTED AVERAGE COST OF CAPITAL Because the cash flows include the income tax benefits of the interest expense on debt capital, the literature and practitioners refer to this formulation of the WACC as the pretax WACC. The basic formula for computing the pretax WACC for an entity with three capital structure components is: (Formula 17.7) WACCðptÞ ¼ ðke We Þ þ ðk p W p Þ þ ðkdð ptÞ Wd Þ where: WACC(pt) ¼ Weighted average cost of capital (pretax) ke ¼ Cost of common equity capital We ¼ Percentage of common equity in the capital structure, at market value kp ¼ Cost of preferred equity Wp ¼ Percentage of preferred equity in the capital structure, at market value kd(pt) ¼ Cost of debt (pretax) Wd ¼ Percentage of debt in the capital structure, at market value
CAPITAL CASH FLOWS The pretax WACC capital is applied to capital cash flows (CCFs), which include the tax savings from interest tax deductions on debt capital in the cash flows. If we modify Formula 3.2 we get: (Formula 17.8) Net income to common equityðafter taxÞ þNoncash charges ðe:g:; depreciation; amortization; deferred revenue; deferred taxesÞ Capital expenditures Additions to net working capital þDividends on preferred stock þInterest expense ¼ Net capital cash flows
Only amounts necessary to support projected operations.
Pretax Weighted Average Cost of Capital
281
or Net cash flow to invested capital þ Tax deductions resulting from interest as a tax deductible expense ¼ Net capital cash flows In using CCF methodology, the proper formula for unlevering beta is Formula 10A.5 and the proper formula for levering beta is Formula 10A.6.
EQUIVALENCE OF VALUATION METHODOLOGIES Valuation of after-tax net cash flow to invested capital, discounted using the after-tax WACC, yields equivalent results to valuation of CCF’s, discounted using the pretax WACC.12 The WACC method has also been shown to be equivalent to the adjusted present value (APV) methods, when consistent assumptions are applied.13 The general formulation of the APV method of valuation is:14 PV ¼ Present Value of Unlevered Firm þ Present Value of Tax Shield In this equation, the net cash flows of the unlevered firm are discounted at the unlevered cost of equity capital, keu, which is calculated using the next formula (assuming we are basing our discount rate on CAPM): (Formula 17.9) keu ¼ R f þ Bu ðRPm Þ þ RPs þ RPu where: keu ¼ Cost of unlevered equity capital Rf ¼ Rate of return available on a risk-free security as of the valuation date Bu ¼ Unlevered beta (i.e., financial risk removed) RPm ¼ General equity risk premium for the market RPs ¼ Risk premium for small size with effect of financial risk, if any, removed RPu ¼ Risk premium attributable to the specific company (u stands for unique or unsystematic risk) without regards to financial risk of debt financing The APV method has been touted as more flexible in that it can be applied when debt capital is not assumed to be a percentage of firm value (e.g., fixed amount of debt at valuation date is paid down over scheduled repayment process).15 It also can be very useful in valuing complex business ventures where taxes and subsidies may vary over time. For example, APV may be a more direct valuation methodology in valuing investments in developing economies. Exhibit 17.7 presents the format of an APV valuation of a business in a developing economy.
12
13
14
15
Richard S. Ruback, ‘‘Capital Cash Flows: A Simple Approach to Valuing Risky Cash Flows,’’ Financial Management (Summer 2002): 93–94. Laurence Booth, ‘‘Capital Cash Flows, APV and Valuation,’’ European Financial Management (January 2007): 29–48; and Pablo Fernandez, ‘‘Equivalence of Ten Different Methods for Valuing Companies by Cash Flow Discounting,’’ International Journal of Finance Education 1, no.1 (2005): 141–168. Marianne DeMario and Anthony Fazzone, ‘‘The Adjusted Present Value: An Alternative Approach to the Effect of Debt on Business Value,’’ Business Valuation Update (December 2006): 1–4. This is consistent with the Hamada formula. See Appendix 10A of Chapter 10.
282
Exhibit 17.7
Cost of Capital
Example of Using APV to Value Business in Developing Economy
Present Value ¼ PV of remittable after-tax operating cash flows (using unlevered cost of equity capital) during period of lease to operate business PV of capital outlays þ PV of tax savings from depreciation þ PV of financial subsidies þ PV of contribution to corporate debt capacity þ PV of other tax savings (e.g., tax holidays) þ PV of extra remittances þ PVof residual (residual may not be perpetual as business may revert to the government at the end of the license to operate business)
SUMMARY We have outlined the process of computing a WACC for both public and non-public companies and for proposed capital projects. Because the weights of the capital structure components must be at market value if you assume debt remains a constant percentage of overall firm value, and because private company stocks do not have market values, the process of computing the WACC for a private company is an iterative one, starting with approximations of market value weights of capital structure components. Under some circumstances (e.g., a minority interest valuation), a company’s actual (currently existing) capital structure may be used to estimate the WACC. If a controlling interest valuation is sought where it is reasonable to alter the company’s capital structure, a hypothetical capital structure may be used to estimate the WACC. There is much controversy about the potential impact that altering the capital structure has on the WACC. The assumption of a single WACC to discount each increment of expected cash flow implies a constant capital structure over time. If the capital structure varies significantly over time, using a constant WACC will likely result in the incorrect value of the company or project.
ADDITIONAL READING Booth, Laurence. ‘‘Finding Value Where None Exists: Pitfalls in Using Adjusted Present Value.’’ Journal of Applied Corporate Finance (Spring 2002): 8–17. Cooper, Ian, and Kjell G. Nyborg. ‘‘Valuing the Debt Tax Shield.’’ Journal of Applied Corporate Finance (Spring 2007): 50–59. Farber, Andre, Roland Gillet, and Ariane Szafarz. ‘‘A General Formula for the WACC.’’ International Journal of Business (Spring 2006): 211–218. Fernandez, Pable. ‘‘A General Formula for the WACC: A Comment.’’ International Journal of Business 12 No. 3 (2007). Massari, M., F. Rocaglio, and L. Zanetti.‘‘On the Equivalence between the APV and the WACC Approach in a Growing Leveraged Firm.’’ European Financial Management (in press). Velez-Pareja, Ignacio, Rauf Ibragimov, and Joseph Tham. ‘‘Constant Leverage and Constant Cost of Capital: A Common Knowledge Half-Truth.’’ Working paper, June 29, 2007.
Appendix 17A
Iterative Process Using CAPM to Calculate the Cost of Equity Component of the Weighted Average Cost of Capital When Capital Structure Is Constant Harold G. Martin, Jr. MBA, CPA, ABV, ASA, CFE Introduction Capital Asset Pricing Model and Beta Solution: The Iterative Process Step 1. Inputs for Debt and Equity Step 2. Calculation of Relevered Beta for Subject Company Step 3. Estimation of Cost of Equity Using the Capital Asset Pricing Model Step 4. Estimation of Weighted Average Cost of Capital Step 5. Capitalized Economic Income Method (Invested Capital Model) Iterative Process Using a Financial Spreadsheet Model Iteration 1 Iteration 2 Iteration 3 Iteration 4 Summary Additional Reading
INTRODUCTION In Chapter 17 the authors present an iterative process for computing the weighted average cost of capital (WACC) for a closely held company. In determining the WACC, the market values of the In developing the model presented here, I have received invaluable support and guidance from professional colleagues. In particular, I wish to thank James R. Hitchner of The Financial Valuation Group in Atlanta, Georgia, for sparking my initial interest in the invested capital valuation methodology; and Mark L. Zyla of Willamette Management Associates in Atlanta, Georgia, and Michael J. Mattson of The Financial Valuation Group in Chicago, Illinois, for their suggestions and critique of the model. Any errors relating to its application are solely my own. This model was first introduced in a presentation entitled ‘‘Cost of Capital’’ at the American Institute of Certified Public Accountants National Business Valuation Conference, December 4, 2001.
283
284
Cost of Capital
capital structure components—that is, debt and equity—are required to determine the relative weights of each component. However, this sets up a catch-22 scenario:
Our objective is to determine the market value of equity for the closely held company based on some unknown WACC.
To determine the WACC, we must solve for an unknown market value of equity.
Chapter 17 presents an estimation technique, the iterative process, that provides a method for circumventing this problem. This appendix expands on the technique and considers the additional complexities introduced to the iterative process when the Capital Asset Pricing Model (CAPM) is used to calculate the equity component of WACC. Further, it illustrates how to implement the iterative process using a financial spreadsheet model.
CAPITAL ASSET PRICING MODEL AND BETA Chapter 8 presents an overview of CAPM. The mathematical model for the expanded CAPM is expressed in Formula 8.5, which we repeat here as: (Formula 17A.1) EðRi Þ ¼ R f þ BL ðRPm Þ þ RPs þ RPu where: E(Ri) ¼ Expected rate of return on security i Rf ¼ Rate of return available on a risk-free security as of the valuation date BL ¼ Beta levered RPm ¼ General equity risk premium for the market RPs ¼ Risk premium for small size RPu ¼ Risk premium attributable to the specific company (u stands for unique or unsystematic risk) In determining the CAPM, betas for the subject company’s industry (as provided in such publications as Morningstar’s Cost of Capital Yearbook) or guideline public companies typically are used as proxies to estimate the beta for the closely held company. However, as noted in Chapter 10, the public company betas are ‘‘levered’’ betas. To unlever the public company beta, we will use for illustrative purposes Formula 10A.1 (commonly referred to as the Hamada formula), which we repeat here as: (Formula 17A.2) BL Bu ¼ 1 þ ð1 tÞWd =We where: Bu ¼ Beta unlevered BL ¼ Beta levered t ¼ Income tax rate for the company Wd ¼ Percent debt at market value in the capital structure We ¼ Percent equity at market value in the capital structure Once the public company beta is unlevered, then the beta may be relevered for the subject company using Formula 10A.2 for illustrative purposes, which we repeat here as:
Solution: The Iterative Process
285
(Formula 17A.3) BL ¼ Bu ð1 þ ð1 tÞWd =We Þ where the definitions of the variables are the same as in Formula 17A.2. In relevering the unlevered beta, we have introduced a third unknown: We need to know the market value of the subject company’s equity in order to determine the relative weights to be assigned to the subject company’s debt and equity for the purpose of relevering the beta.
SOLUTION: THE ITERATIVE PROCESS Each of the next three calculations depends on a single unknown value—the market value of the subject company’s equity: 1. Subject company’s relevered beta 2. WACC 3. Market value of equity We can solve each of these calculations by using the iterative process to estimate the market value of equity. The next example illustrates this methodology. For purposes of illustration, we have used a capital structure consisting of common equity and debt. Further, in applying the income approach, we have used the capitalization of economic income methodology instead of the discounted economic income methodology to simplify the calculations. Our example is based on seven assumptions: 1. 2. 3. 4. 5. 6. 7.
Book value of long-term interest-bearing debt: $400,000 Book value of common equity: $600,000 Interest rate for debt: 10% Income tax rate (combined federal and effective state rate): 40% Projected net cash flow to invested capital for year following valuation date: $250,000 Estimated annual compounded long-term growth rate for net cash flow to invested capital: 5% Cost of capital variables:
Rf : 4.61% RPm : 5.00%
Bu for industry: 1.52 RPs : 6.36%
RPu : 2.00%
STEP 1. INPUTS FOR DEBT AND EQUITY For this iteration, the book values of the subject company’s debt and equity will be used as proxies for the market values for purposes of calculating the weighting of the capital components of WACC: Capital Component Debt Equity Total )
Percentages expressed as decimal equivalents.
Estimated Market Value
Percent of Capital
$400,000 $600,000 $1,000,000
0.40 0.60 1.00
286
Cost of Capital
STEP 2. CALCULATION OF RELEVERED BETA FOR SUBJECT COMPANY The next step in the iterative process is to estimate the beta for the subject company. This involves relevering the unlevered industry beta. To calculate the relevered beta for the subject company, we substitute the unlevered industry beta, the subject company tax rate, and the initial book values for debt and equity into Formula 17A.4 to get Formula 17A.4: (Formula 17A.4) BL ¼ Bu ð1 þ ð1 tÞWd =We Þ ¼ 1:52½1 þ ð1 :4Þ0:4=0:6 ¼ 2:1280 STEP 3. ESTIMATION OF COST OF EQUITY USING THE CAPITAL ASSET PRICING MODEL Next we calculate an estimate of cost of equity using CAPM. We substitute the known values for the CAPM variables as well as the relevered beta just derived into Formula 17A.1 to get Formula 17A.5: (Formula 17A.5) EðRi Þ ¼ R f þ BL ðRPm Þ þ RPs þ RPu ¼ 0:461 þ 2:1280ð0:05Þ þ 0:0636 þ 0:02 ¼ 0:2361 STEP 4. ESTIMATION OF WEIGHTED AVERAGE COST OF CAPITAL After calculating the initial estimate of the cost of equity, we next estimate the WACC. Using the same book values of the subject company’s debt and equity as the weights and the cost of equity calculated using CAPM, we calculate the WACC as: (Formula 17A.6) WACC ¼ ðke We Þ þ ½kd ð1 tÞ Wd ¼ ð0:2361 0:6Þ þ ½0:1ð1 0:4Þ 0:4 ¼ 0:1657 As the WACC represents a discount rate for invested capital, we subtract the long-term growth rate of 5% to derive the capitalization rate of 11.57%. STEP 5. CAPITALIZED ECONOMIC INCOME METHOD (INVESTED CAPITAL MODEL) Finally, we use Formula 17A.7 to estimate the market value of invested capital and subtract the value of the debt to derive the estimated value of equity: (Formula 17A.7) PV ¼ where: PV ¼ Present value ¼ 250,000=0.1157 ¼ 2,160,761
NCF1 c
Iterative Process Using a Financial Spreadsheet Model
287
NCF1 ¼ Net cash flow expected in the first period immediately following the valuation date c ¼ Capitalization rate The market value of invested capital, $2,160,761, less the value of debt, $400,000, equals the estimated market value of equity, $1,760,761. However, this estimate of the market value of equity is materially different from the book value of $600,000 we used initially as a proxy and consequently results in very different market weights of debt and equity, as indicated in the next chart. Capital Component Debt Equity Total )
Estimated Market Value
Percent of Capital*
$ 400,000 $1,760,761 $2,160,761
0.1851 0.8149 1.0000
Percentages expressed as decimal equivalents.
Therefore, we must repeat the preceding calculations, substituting the book value of equity used in step 1, $600,000, with the calculated value of equity, $1,760,761. We continue to recalculate the value of equity until the value of the equity input in step 1 (the value used to estimate the market weights in steps 2 and 4) equals the calculated equity in step 5.
ITERATIVE PROCESS USING A FINANCIAL SPREADSHEET MODEL While we could repeat each of these calculations manually, the iterative process can be implemented more easily using a financial spreadsheet application and linking the cells containing the unknown weight of the equity value we are seeking to determine. The next illustration of a spreadsheet model is based on the previous example. This model is built in Microsoft Excel, and all formulas are presented using Excel definitions. Note that the version of the model presented requires a user to manually input the estimated market value of equity for each iteration. This presentation is useful in illustrating how the iterative process is performed. However, advanced users of Excel may wish to consider using the ‘‘Solver,’’ an Excel add-on tool, to calculate the value automatically. ITERATION 1 Worksheet 1.1 Inputs: Estimates of Debt and Equity As previously discussed, the estimated market values of debt (C7) and equity (C8) for Iteration 1 are based on book values and serve as our initial inputs to the model. The relative weights of debt (D7) and equity (D8) are calculated.
A 3 4 5 6 7 8 9
B
Long-term interest-bearing debt Equity Total capital
C
D
Estimated Market Value
Percent of Capital W 0.4000 0.6000 1.0000
400,000 600,000 1,000,000
288
Cost of Capital
A
B
3 4 5 6 7 8 9
C
D
Estimated Market Value Long-term interest-bearing debt Equity Total capital
Percent of Capital W ¼ ROUND(C7/C9,4) ¼ ROUND(C8/C9,4) ¼ SUM(D7:D8)
400,000 600,000 ¼ SUM(C7:C8)
Worksheet 1.2 Calculation of Relevered Beta for Subject Company Worksheet 1.2 presents the calculation of the relevered beta. The estimated market weights of debt (C17) and equity (C18) are linked to the values in Worksheet 1.1 (D7 and D8, respectively). The tax rate (D17) and beta (E19) are manual inputs to the model. The relevered beta (F19) is calculated using Formula 17A.4.
A 13 14 15 16 17 18 19
A 13 14 15 16 17 18 19
B
C
Debt Equity Total
Percent of Capital W 0.4000 0.6000 1.0000
B
C
Debt Equity Total
Percent of Capital W ¼D7 ¼D8 ¼SUM(C17:C18)
D
Tax Rate t 0.40 N/A
D
Tax Rate t 0.4 N/A
E
F
Industry (or Guideline Co.) Unlevered Beta Bui
Subject Company Levered Beta BL
1.52
2.1280
E
F
Industry (or Guideline Co.) Unlevered Beta Bui
Subject Company Levered Beta BL
1.52
¼ROUND((E19*(1 þ ((1-D17)*C17)/C18)),4)
Worksheet 1.3 Estimation of Cost of Equity Using CAPM Worksheet 1.3 presents the CAPM based on Formula 17A.6. All CAPM variables are manual inputs, except for beta (C26), which is linked to Worksheet 1.2 (F19). The cost of equity is calculated (D30).
Iterative Process Using a Financial Spreadsheet Model
A
B
23 24 25 26 27 28 29 30
Risk-free rate (Rf) Systematic risk Equity risk premium (RPm) Beta (B) Systematic risk Risk premium for size (RPs) Specific (unsystematic) risk (RPu) Cost of equity (ke)
289
C
A
B
23 24 25 26 27 28 29 30
Risk-free rate (Rf) Systematic risk Equity risk premium (RPm) Beta (B) Systematic risk Risk premium for size (RPs) Specific (unsystematic) risk (RPu) Cost of equity (ke)
D 0.0461
0.0500 2.1280 0.1064 0.0636 0.0200 0.2361
C
D 0.0461
0.05 ¼F19 ¼ROUND((C25*C26),4) 0.0636 0.02 ¼SUM(D23:D29)
Worksheet 1.4 Estimation of WACC Worksheet 1.4 calculates the WACC based on Formula 17A.6. As with Worksheet 1.2, the cells containing the estimated market weights of debt (C39) and equity (C40) are linked to the values in Worksheet 1.1 (D7 and D8, respectively). The cost of debt (D39) and tax rate (E39) are manual inputs and the tax-affected rate is calculated (F39). The cost of equity (D40) is linked to Worksheet 1.3 (D30). The weighted average cost of debt (G39) and equity (G40) are calculated and summed to derive the WACC (G41). The long-term growth rate (G45), a manual input, is deducted from the WACC (G44) to derive the capitalization rate (G46).
A
B
C
D
E
F
G
Rate k
Tax Rate t
Tax-Effected Rate k[1– t]
Weighted Average Cost WACC
0.10 0.2361
0.40 N/A
0.0600 0.2361
Cost of Captial 34 35 36 37 38 39 40 41 42 43 44 45 46
Percent of Capital W Calculation of WACC Debt Equity Total Calculation of Capitalization rate Discount rate for net cash flow Less long-term average growth rate Capitalization rate for net cash flow
0.4000 0.6000 1.0000
0.0240 0.1417 0.1657
0.1657 0.0500 0.1157
290
A
Cost of Capital
B
C
D
E
F
G
Cost of Capital 34 Percent 35 of 36 Capital 37 W 38 Calculation of WACC 39 Debt ¼D7 40 Equity 41 Total 42 43 Calculation of Capitalization Rate 44 Discount rate for net cash flow 45 Less long-term average growth rate 46 Capitalization rate for net cash flow
Rate k
Tax Tax-Effected Rate Rate t k[1-t]
0.1
0.4
¼D8 ¼D30 N/A ¼SUM (C39:C40)
Weighted Average Cost WACC
¼ROUND þROUND ((C39*F39),4) ((D39*(1-E39)),4) ¼þD40 þROUND ((C40*F40),4) þROUND (SUM(G39:G40),4)
þROUND(G41,4) 0.05 þ(G44-G45)
Worksheet 1.5 Capitalized Economic Income Method (Invested Capital Model) Worksheet 1.5 presents the calculation of the value of invested capital using the capitalized economic income method based on Formula 4.1, and also presents a calculation of the value of the equity. The net cash flow to invested capital (C50), a manual input, is multiplied by the capitalization rate (C51) linked to Worksheet 1.4 (G46) to derive the market value of invested capital (C52). From this amount, the market value of debt (C53), linked to Worksheet 1.1 (C7), is subtracted to derive the estimated market value of equity (C54). A
B
C
50 51 52 53 54
Adjusted net cash flow to invested capital Capitalization rate Indicated value of 100% of the Business Enterprise Less interest-bearing debt Indicated value of a 100% Marketable Equity Interest
250,000 0.1157 2,160,761 400,000 1,760,761
A
B
C
50 51 52 53 54
Adjusted net cash flow to invested capital Capitalization rate Indicated value of 100% of the Business Enterprise Less interest-bearing debt Indicated value of a 100% Marketable Equity Interest
250000 ¼G46 ¼ROUND(C50/C51,0) ¼C7 ¼C52-C53
As the value of the calculated equity (C54), $1,760,761, is not equal to the initial estimate of equity input in Worksheet 1.1 (C8), $600,000 (the value used to estimate the market weights in Worksheets 1.2 and 1.4), the market value of equity must be estimated again and the calculations repeated.
Iterative Process Using a Financial Spreadsheet Model
291
ITERATION 2 Worksheet 2.1 Inputs: Estimates of Debt and Equity In the second iteration, the value of equity in Worksheet 2.1 (C8) is set equal to the value derived in Iteration 1, Worksheet 1.5 (C54). The relative weights of debt (D7) and equity (D8) are then recalculated. The model then automatically performs the calculations in Worksheets 2.2, 2.3, 2.4, and 2.5.
A
B
3 4 5 6 7 8 9
Long-term interest-bearing debt Equity Total capital
C
D
Estimated Market Value
Percent of Capital W 0.1851 0.8149 1.0000
400,000 1,760,761 2,160,761
Worksheet 2.2 Calculation of Relevered Beta for Subject Company
A 13 14 15 16 17 18 19
B
C
D
Debt Equity Total
Percent of Capital W 0.1851 0.8149 1.0000
Tax Rate t 0.40 N/A
E
F
Industry (or Guideline Co.) Unlevered Beta Bui
Subject Company Levered Beta BL
1.52
1.7272
Worksheet 2.3 Estimation of Cost of Equity Using CAPM A
B
23 24 25 26 27 28 29 30
Risk-free rate (Rf) Systematic risk Equity risk premium (RPm) Beta (B) Systematic risk Risk premium for size (RPs) Specific (unsystematic) risk (RPu) Cost of equity (ke)
C
D 0.0461
0.0500 1.7272 0.0864 0.0636 0.0200 0.2161
292
Cost of Capital
Worksheet 2.4 Estimation of WACC A 34 35 36 37 38 39 40 41 42 43 44 45 46
B
C Percent of Capital W
Calculation of WACC Debt Equity Total
0.1851 0.8149 1.0000
D
E
F
G
Rate k
Tax Rate t
Tax-Effected Rate k[1- t]
Weighted Average Cost WACC
0.10 0.2161
0.40 N/A
0.0600 0.2161
Cost of Captial
Calculation of Capitalization rate Discount rate for net cash flow Less long-term average growth rate Capitalization rate for net cash flow
0.0111 0.1761 0.1872
0.1872 0.0500 0.1372
Worksheet 2.5 Capitalized Economic Income Method (Invested Capital Model) A
B
C
50 51 52 53 54
Adjusted net cash flow to invested capital Capitalization rate Indicated value of 100% of the Business Enterprise Less interest-bearing debt Indicated value of a 100% Marketable Equity Interest
250,000 0.1372 1,822,157 400,000 1,422,157
As the value of the calculated equity (C54), $1,422,157, is not equal to the estimate of equity input in Worksheet 2.1 (C8), $1,760,761, the market value of equity must be estimated again and the calculations repeated. ITERATION 3 Worksheet 3.1 Inputs: Estimates of Debt and Equity In Iteration 3, the value of equity in Worksheet 3.1 (C8) is set equal to the value derived in Iteration 2, Worksheet 2.5 (C54). The relative weights of debt (D7) and equity (D8) are then recalculated. The model then automatically performs the calculations in Worksheets 3.2, 3.3, 3.4, and 3.5. A 3 4 5 6 7 8 9
B
Long-term interest-bearing debt Equity Total capital
C
D
Estimated Market Value
Percent of Capital W 0.2195 0.7805 1.0000
400,000 1,422,157 1,822,157
Iterative Process Using a Financial Spreadsheet Model
293
Worksheet 3.2 Calculation of Relevered Beta for Subject Company A 13 14 15 16 17 18 19
B
C
D
Debt Equity Total
Percent of Capital W 0.2195 0.7805 1.0000
Tax Rate t 0.40 N/A
E
F
Industry (or Guideline Co.) Unlevered Beta Bui
Subject Company Levered Beta BL
1.52
1.7765
Worksheet 3.3 Estimation of Cost of Equity Using CAPM A
B
C
23 24 25 26 27 28 29 30
Risk-free rate (Rf) Systematic risk Equity risk premium (RPm) x Beta (B) Systematic risk Risk premium for size (RPs) Specific (unsystematic) risk (RPu) Cost of equity (ke)
D 0.0461
0.0500 1.7765 0.0888 0.0636 0.0200 0.2185
Worksheet 3.4 Estimation of WACC A
B
C
D
E
F
G
Rate k
Tax Rate t
Tax-Effected Rate k[1 t]
Weighted Average Cost WACC
0.10 0.2185
0.40 N/A
0.0600 0.2185
Cost of Capital 34 35 36 37 38 39 40 41 42 43 44 45 46
Percent of Capital W Calculation of WACC Debt Equity Total Calculation of Capitalization Rate Discount rate for net cash flow Less long-term average growth rate Capitalization rate for net cash flow
0.2195 0.7805 1.0000
0.0132 0.1705 0.1837
0.1837 0.0500 0.1337
294
Cost of Capital
Worksheet 3.5 Capitalized Economic Income Method (Invested Capital Model) A
B
C
50 51 52 53 54
Adjusted net cash flow to invested capital Capitalization rate Indicated value of 100% of the Business Enterprise Less interest-bearing debt Indicated value of a 100% Marketable Equity Interest
250,000 0.1337 1,869,858 400,000 1,469,858
As the value of the calculated equity (C54), $1,469,858, is not equal to the estimate of equity input in Worksheet 3.1 (C8), $1,422,157, the market value of equity must be estimated again and the calculations repeated.
ITERATION 4 Worksheet 4.1 Inputs: Estimates of Debt and Equity In the fourth iteration, the value of equity (C8) is set equal to the value derived in Iteration 3, Worksheet 3.5 (C54). The relative weights of debt (D7) and equity (D8) are then recalculated. The model then automatically performs the calculations in Worksheets 4.2, 4.3, 4.4, and 4.5. A
B
3 4 5 6 7 8 9
Long-term interest-bearing debt Equity Total capital
C
D
Estimated Market Value
Percent of Capital W 0.2139 0.7861 1.0000
400,000 1,469,858 1,869,858
Worksheet 4.2 Calculation of Relevered Beta for Subject Company
A 13 14 15 16 17 18 19
B
C
Debt Equity Total
Percent of Capital W 0.2139 0.7861 1.0000
D
Tax Rate t 0.40 N/A
E
F
Industry (or Guideline Co.) Unlevered Beta Bui
Subject Company Levered Beta BL
1.52
1.7682
Iterative Process Using a Financial Spreadsheet Model
295
Worksheet 4.3 Estimation of Cost of Equity Using CAPM A
B
C
23 24 25 26 27 28 29 30
Risk-free rate (Rf) Systematic risk Equity risk premium (RPm) Beta (B) Systematic risk Risk premium for size (RPs) Specific (unsystematic) risk (RPu) Cost of equity (ke)
D 0.0461
0.0500 1.7682 0.0884 0.0636 0.0200 0.2181
Worksheet 4.4 Estimation of WACC A 34 35 36 37 38 39 40 41 42 43 44 45 46
B
C Percent of Capital W
Calculation of WACC Debt Equity Total
0.2139 0.7861 1.0000
D
E
F
G
Rate k
Tax Rate t
Tax-Effected Rate k[1 t]
Weighted Average Cost WACC
0.10 0.2181
0.40 N/A
0.0600 0.2181
Cost of Capital
Calculation of Capitalization rate Discount rate for net cash flow Less long-term average growth rate Capitalization rate for net cash flow
0.0128 0.1714 0.1842
0.1842 0.0500 0.1342
Worksheet 4.5 Capitalized Economic Income Method (Invested Capital Model) A
B
C
50 51 52 53 54
Adjusted net cash flow to invested capital Capitalization rate Indicated value of 100% of the Business Enterprise Less interest-bearing debt Indicated value of a 100% Marketable Equity Interest
250,000 0.1342 1,862,891 400,000 1,462,891
As the value of the calculated equity (C54), $1,462,891, is approximately equal to the estimate of equity input in Worksheet 4.1 (C8), $1,469,858, we conclude that the market value of equity is approximately $1,463,000 in round numbers. We could continue the iterations until the two equity values equaled one another, but for purposes of illustration, the calculated value is considered reasonable.
296
Cost of Capital
SUMMARY This appendix has expanded on the iterative process presented in Chapter 17 to consider the additional complexities when the CAPM is used to calculate the equity component of WACC. Further, it has provided an example illustrating the use of a financial spreadsheet model to perform the calculations required for the iterative process.
ADDITIONAL READING Abrams, Jay B. Quantitative Business Valuation: A Mathematical Approach for Today’s Professionals. New York: McGraw-Hill, 2000. Bishop, David M., and Frank C. Evans. ‘‘Avoiding a Common Error in Calculating the Weighted Average Cost of Capital.’’CPA Expert (Fall 1997). Evans, Frank C., and Kelly L. Strimbu. ‘‘Debt and Equity Weightings in WACC.’’ CPA Expert (Fall 1998). Hitchner, James R., Financial Valuation: Applications and Models, 2nd ed. Hoboken: John Wiley & Sons 2006. Martin, Harold G., Jr. ‘‘Cost of Capital.’’ Joint presentation made with Ronald L. Seigneur at the American Institute of Certified Public Accountants National Business Valuation Conference, Las Vegas, NV, December 4, 2001. Pratt, Shannon P. Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed. New York: McGraw-Hill, 2007.
Appendix 17B
Iterative Process Using CAPM to Calculate the Cost of Equity Component of the Weighted Average Cost of Capital When Capital Structure Is Changing James R. Morris, Ph.D Introduction Assumptions Inherent in Weighted Average Cost of Capital Solution: Iterative Process with Changing Capital Structure Iterative Process Using Financial Spreadsheet Model Stage 4 Stage 3 Stage 2 Stage 1 Stage 0 Handling the Iterations Equity Value Summary Additional Reading
INTRODUCTION In Appendix 17A, Harold Martin explained how to use the iterative process to calculate the cost of capital and the value of the firm. The iterative process is necessary because the valuation problem is circular. That is, to calculate the cost of capital and the value of the firm, we need to know the value of the firm and value of its components—the debt and equity—which, in turn, are the things we are trying to determine. We use the iterative process to converge on value estimates where the values we use as input agree with the values we get as output. The purpose of this appendix is to build on the iterative process of Appendix 17A to show how to calculate the value of the firm and equity when the capital structure is changing over time.
297
298
Cost of Capital
ASSUMPTIONS INHERENT IN WEIGHTED AVERAGE COST OF CAPITAL The standard version of weighted average cost of capital (WACC) is based on the assumption that the capital structure will remain unchanged over the time period of the valuation. For example, the valuation developed in Appendix 17A was based implicitly on these assumptions:
The proportional mix of debt and equity in the capital structure, in terms of market values, would remain constant over the investment horizon. With a constant proportional mix of debt and equity, the costs of capital (cost of debt, cost of equity, and WACC) would remain unchanged over the investment horizon. The cash flow to invested capital will grow at a constant rate over an indefinitely long investment horizon.
But how do we handle it if the mix of debt and equity are expected to change over the investment horizon? The answer is that we still use the iterative technique, but the task is made slightly more complicated by the changing capital structure.
SOLUTION: ITERATIVE PROCESS WITH CHANGING CAPITAL STRUCTURE Basically, the iteration method is the same, except that we have to perform an iteration for each period where the capital mix has changed. The way we do this is to start at a future date when we expect the capital structure to reach long-run stability and calculate value at each date from the future, working backward in time to the present. For example, assume that by the end of period 4 in the future, the firm is expected to reach a point where its proportional capital structure will be stable for many years into the future. In the interim, with a given amount of debt currently outstanding, the firm is expected to repay part of the debt over the next three periods to reach that stable capital structure. To handle the changing capital structure with an iterative process, we start by calculating the value at time 4, when the firm is expected to reach its stable capital structure. Then we step back to time 3 and calculate the value at time 3, based on the capital structure and cost of capital prevailing at time 3. Next we calculate value at time 2 based on capital structure and cost of capital at time 2. We continue stepping backward in time until we reach the present and calculate the value based on the present capital structure. Essentially, when we use this process, we use a sequence of one-period valuation models, starting at the end and working backward, period by period, until we reach the present valuation date. We start the process by calculating the value of the firm at the horizon date when the firm is expected to reach a stable capital structure and stable future growth in future cash flows. In this case, assume the value at the horizon date (terminal value) is based on the constant growth model:1
1
The terminal value does not have to be based on constant growth. Constant growth is used here because it is a common method. The multistage iterative process explained here would work just as well if the terminal value was based on some other valuation method. It is just that we do need to have a terminal value with which to start working backward from the terminal date to the present. And, to generate consistent values, the terminal value of invested capital must be consistent with the terminal value of equity.
Iterative Process Using Financial Spreadsheet Model
(Formula 17B.1)
PV4 ¼ NCF5
1 ðWACC4 gÞ
299
where WACC4 ¼ WACC with capital structure proportions that prevail at time 4 NCF5 ¼ cash flow to invested capital for period 5 It is assumed that from time 5 forward, cash flows will grow at a constant rate g for the indefinite future. Having calculated terminal value for time 4 based on the capital structure at time 4, we step back to time 3 and use a one-period valuation model to calculate time 3 value: (Formula 17B.2) 1 1 þ PV4 PV3 ¼ NCF4 1 þ WACC3 1 þ WACC3 where WACC3 ¼ WACC with capital structure proportions prevailing at time 3 Then we continue stepping back, using a single-period valuation model to calculate value at each date based on the cost of capital and capital structure prevailing at that date. Our process stops when we reach the present, time 0. To calculate value, we not only have to step backward in time from the horizon to the present, but at each stage we have to use an iterative process so that the capital structure weights are based on market values instead of book values. At each stage, we start the iteration using the book values of debt and equity to calculate the weights in the WACC and the costs of equity, and perhaps debt to the extent that it depends on the capital weights. Using the book values as the starting point, we calculate the values, at that stage, of invested capital, equity, and debt. These first iteration values are used as input to calculate new capital proportions for the second iteration for that stage. The iterations continue until the calculated values equal the assumed values. That gives us the value for that stage. Then we step back to the previous stage and start the iterative value calculation over again. An example will help show this process. Our example will build on the valuation presented in Appendix 17A, but we will have to add some detail to reflect the changing capital structure.
ITERATIVE PROCESS USING FINANCIAL SPREADSHEET MODEL Consider the Martin Corporation, whose current and pro forma income statement and balance sheet is shown in spreadsheet format as Exhibit 17B.1. The statements are shown for the present (time t = 0), and forecasts for future periods 1 through 5. Martin’s sales, earnings before interest, taxes, depreciation, and amortization (EBITDA), and earnings before interest and taxes (EBIT) are stable for periods 1 to 4. Then from time 4 forward, it is assumed the firm’s sales and income will grow at an annual rate of 5% forever. Assets and current liabilities are assumed to be a constant percentage of 299
300
Cost of Capital
Exhibit 17B.1
Current and Pro Forma Financial Statements A
B
C
D
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
E
F
G
Martin Corporation Income Statement
Sales Operating Costs EBITDA Depreciation EBIT Interest Earnings Before Tax Income Tax Net Income Dividends Retained Earnings
Forecast 0
1
2
3
4
5
1,717,033 1,126,374 590,659 114,469 476,190 60,000 416,190 166,476 249,714
1,717,033 1,126,374 590,659 114,469 476,190 60,000 416,190 166,476 249,714
1,717,033 1,126,374 590,659 114,469 476,190 53,000 423,190 169,276 253,914
1,717,033 1,126,374 590,659 114,469 476,190 46,000 430,190 172,076 258,114
1,717,033 1,126,374 590,659 114,469 476,190 40,000 436,190 174,476 261,714
1,802,885 1,182,692 620,192 120,192 500,000 40,000 460,000 184,000 276,000
179,714 70,000
179,714 70,000
183,914 70,000
198,114 60,000
214,095 47,619
247,304 28,696
Martin Corporation Balance Sheet Forecast 0
1
2
3
4
5
Current Assets Net Fixed Assets Total Assets
331,960 858,516 1,190,476
331,960 858,516 1,190,476
331,960 858,516 1,190,476
331,960 858,516 1,190,476
348,558 901,442 1,250,000
365,986 946,514 1,312,500
Current Liabilities Long-term Debt Equity Liabilities & Equity
238,095 600,000 352,381 1,190,476
238,095 530,000 422,381 1,190,476
238,095 460,000 492,381 1,190,476
238,095 460,000 552,381 1,190,476
250,000 400,000 600,000 1,250,000
262,500 420,000 630,000 1,312,500
next period’s sales, so as sales grow after time 4, the firm will have to invest in new assets. With longrun sales growth at 5%, assets and current liabilities will also have to grow at 5%, forever. Debt: Martin’s current capital structure includes $600,000 of long-term debt at an interest rate of 10%. The borrowing rate is expected to remain at 10% for the indefinite future, and the market value of debt is equal to book value at each date. The company is expected to pay off some of its debt over the next three years until it has reduced its debt to $400,000 by time 3. If the firm did not grow, its debt would remain at $400,000. However, we expect growth after time 4, and as the firm grows, debt will be issued to finance part of the growth, with the amount of borrowing being just sufficient to maintain the book value debt-to-equity ratio at 0.667 in each future period. With the current book value of equity at $352,381, the debt-to-equity ratio is currently $600,000 / $352,381 ¼ 1.7, and repayment of debt will reduce it to 0.667 by time 4. Thus, we have a situation where the capital structure is going to change over the next four years and remain stable after that. Our task is to estimate the value of the firm and the equity so as to properly take account of the changing capital structure. Before calculating value, we need to specify some of the cost of capital parameters.
Iterative Process Using Financial Spreadsheet Model
301
Assume that market conditions and cost of capital parameters are the same as were used in the example in Appendix 17A. These parameters are: ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼
Rf RPm RPs RPu kd(pt) BU g t
4.61% 5.0% 6.36% 2.0% 10% 1.52 5% 40%
With these parameters, if the firm had no debt, its cost of equity capital would be: ke ¼ R f þ RPm Bu þ RPs þ RPu ¼ 4:61% þ 5:0% 1:52 þ 6:36% þ 2:0% ¼ 20:57% However, the firm has debt in its structure, so the cost of equity will be higher to reflect the financial leverage. Assume that the formula shown in Formula 8.5 and repeated as Formula 17B.1 (commonly known as the Hamada formula) for leveraged beta applies. Using book values of debt and equity as a first approximation, the beta for the leveraged equity at time 4 would be:
Debt4 ð1 tÞ BL ¼ Bu ½1 þ Equity4 400 ¼ 1:52½1 þ ð1 0:40Þ 600 ¼ 2:128 and the cost of leveraged equity would be: ke ¼ 4:61% þ 5% 2:128 þ 6:36% þ 2:0% ¼ 23:61% With the time 4 capital structure, using book values, the weighted average cost of capital would be: WACC4 ¼ Wd kdð ptÞ ð1 tÞ þ We ke ¼ 0:4 0:10ð1 0:40Þ þ 0:60 0:2361 ¼ 16:57% It must be emphasized that these cost of capital estimates are only a first approximation because the capital structure weights used to calculate beta and the weights in WACC should be based on the market values of debt and equity. We do not yet know the market value of equity because that is one of the things we are trying to determine. We know the market value of debt because it is assumed to be equal to book value. Our next step is to calculate the value of invested capital and equity at each date. Because the capital structure is changing until time 4, we will calculate value in stages, starting from the horizon date at time 4 and working backward to time 0. In addition, because the cost of
302
Cost of Capital
Exhibit 17B.2
Cash Flows to Invested Capital and Equity
A
B
C
D
34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
E
F
G
Martin Corporation Cash Flow to Invested Capital
EBITDA Depreciation EBIT Tax (Notional: T * EBIT) Operating CF (AT) NWC Investment Capital Investment Net Cash Flow to Invested Capital
1
2
3
4
5
590,659 114,469 476,190 190,476 400,183 0 114,469 285,714
590,659 114,469 476,190 190,476 400,183 0 114,469 285,714
590,659 114,469 476,190 190,476 400,183 0 114,469 285,714
590,659 114,469 476,190 190,476 400,183 4,693 157,395 238,095
620,192 120,192 500,000 200,000 420,192 4,928 165,264 250,000
Martin Corporation Equity Cash Flow
Net Income Depreciation Cash Flow from Earnings NWC Investment Capital Investment Debt Issued Equity Cash Flow
1
2
3
4
5
249,714 114,469 364,183 0 114,469 70,000 179,714
253,914 114,469 368,383 0 114,469 70,000 183,914
258,114 114,469 372,583 0 114,469 60,000 198,114
261,714 114,469 376,183 4,693 157,395 0 214,095
276,000 120,192 396,192 4,928 165,264 20,000 246,000
capital at each stage depends on the market values of debt and equity, we need to use an iterative process at each stage. We start at the horizon date using the constant growth model shown as Formula 17B.1. But first, we need to calculate the cash flows as input to our calculations. Exhibit 17B.4 shows the calculation of cash flow to invested capital along with the cash flow to equity. STAGE 4 This firm is the same that was discussed in Appendix 17A, so the time 4 terminal value is calculated the same way as in that example. At time 4, when the firm has reached a stable capital structure and long-run future growth is expected to stabilize at 5%, the first-iteration value of invested capital is based on book value capital weights. Using Formula .0000–0001A, iteration 1 value of invested capital at time 4 is: 1 PV4 ¼ NCFt;5 ðWACC4 gÞ 1 ¼ 250;000 0:1657 0:50 ¼ $2;160;761 where the NCFt,5 of $250,000 is from the last column of line 45 of Exhibit 17.2. Subtracting the debt from time 4 from the value of invested capital yields our iteration 1 estimate of the value of
Iterative Process Using Financial Spreadsheet Model Exhibit 17B.3
Stage 4 Iterations to Converge on Values of Invested Capital and Equity
Iteration Row 1 2 3 4 5 6 7
303
1
Assumed Equity Value Debt/Equity Beta ke WACC MVIC Derived Value Equity
2
3
4
5
" " " " "
600,000 66.67% 2.128 23.61% 16.65% 2,160,761 1,760,761
1,760,761 22.70% 1.727 21.61% 18.72% 1,822,563 1,422,563
1,422,563 28.12% 1.776 21.85% 18.37% 1,869,425 1,469,425
1,469,425 27.22% 1.768 21.81% 18.43% 1,861,758 1,461,758
1,461,758 27.36% 1.770 21.82% 18.42% 1,862,982 1,462,982
6 1,462,982 27.34% 1.769 21.82% 18.42% 1,862,786 1,462,786
equity as: Me ¼ ðMe;4 þ Md;4 Þ Md ¼ $2; 160; 761 $400; 000 ¼ $1; 760; 761 Note that if this were the market value of equity, the debt-to-equity ratio would be 400,000=1,760,761¼ 0.2272, instead of the 0.667, based on book values that were used to start our initial calculation of the leveraged beta. Similarly, the debt to total capital ratio (Wd in the WACC formula) would be 400,000=2,160,761 ¼ .1851 instead of .40. To improve our value estimate, we go to iteration 2, which uses the values and weights that we derived in iteration 1. The steps for iteration 2 are the same: We calculate the values of invested capital and equity using these revised capital weights and costs of capital. The iterations are continued until we reach a point where the derived values of invested capital and equity match the assumed values. Exhibit 17B.3 presents the results of six iterations, showing the final value of invested capital being $1,862,786, with an equity value of $1,462,786. A couple of more iterations would converge to the last dollar at $1,462,813. The number of iterations we take depends on the desired accuracy. The difference between the third iteration value and the final value is an error of about 0.4%. Note that the value at time 4, except for rounding differences, is the same as was derived in Appendix 17A. The idea is that the converged value in that appendix represents the value of the firm when it has reached its stable position at time 4. Now we continue to work through the stages to show how to handle the changes in capital structure that occur between time 0 and time 4.
Exhibit 17B.4
Stage 3 Iterations for Value of Invested Capital
Iteration Row 1 2 3 4 5 6 7
Assumed Equity Value Debt/Equity Beta ke WACC MVIC Derived Value Equity
1 552,381 72.41% 2.180 23.87% 16.37% 1,805,435 1,405,435
2
3
4
" " " " 1,405,435 28.50% 1.780 21.87% 18.35% 1,775,132 1,375,132
1,375,132 29.10% 1.785 21.90% 18.31% 1,775,700 1,375,700
1,375,700 29.10% 1.785 21.90% 18.32% 1,775,689 1,375,689
5 1,375,689 29.10% 1.785 21.89% 18.32% 1,775,689 1,375,689
304
Cost of Capital
STAGE 3 We use the one-period valuation model 17B.2 to calculate the value at time 3: 1 1 þ $1;862;783 PV3 ¼ $238;095 1 þ WACC3 1 þ WACC3 where the $238,095 is the cash flow to invested capital at time 4 from Exhibit 17B.2, and $1,862,783 is the converged value of invested capital at time 4 that we just finished calculating. We will need to use the iterative process to determine the discount rate at time 3, WACC3, which depends on the market value capital structure proportions at time 3. For the first iteration, we start with the book values of debt and equity, which, at the end of period 3, are $400,000, and $552,381 as shown in the balance sheet (Exhibit 17B.1) and shown as the initial Assumed Equity Value in row 1 of Exhibit 17B.4. Starting iteration 1 with book values, we have the debt to equity, cost of equity, and WACC as shown in the iteration 1 column. This yields derived values of invested capital and equity of $1,805,435 and $1,405,435 shown in the rows 6 and 7. The equity value of $1,405,435 is used as the assumed equity value for iteration 2, and calculations are repeated, to give values of $1,775,132 and $1,375,132 for invested capital and equity, respectively. The iterations are continued in this manner until, as shown for the fifth iteration, the derived value of equity that is the output agrees with assumed value of equity that is the input for calculating the capital ratios. We have concluded that the value of invested capital at the end of period 3 is $1,775,689, and equity is $1,375,689. Now we use that value as input in the next stage to calculate the values of invested capital and equity at time 2. STAGE 2 The one-period value of invested capital at time 2 is calculated as 1 1 þ $1;775;689 PV2 ¼ $285;714 1 þ WACC2 1 þ WACC2 where $285,714 is the cash flow to invested capital at time 3. From balance sheet we know that the time 2 book values of debt and equity are $460,000 and $492,381, respectively. Once again we have to go through the iterative process, starting with book values at time 2 and converging to value estimates for time 2. The reader undoubtedly gets the idea, so the iterations will not be shown here. The converged value of invested capital and equity at time 2 are calculated to be $1,747,905 and $1,287,905, respectively. STAGE 1 We go through the same steps, using the single-period valuation model that uses the cash flow at time 2 and the value at time 2 as the input. We go through the iterations again, starting with book values at time 1 and continuing until the process converges. The converged values at time 1 are $1,730,673 and $1,200,673 for invested capital and equity. STAGE 0 The last stage is the time 0 calculation of value. We use the values from stage 1, and start with book values to initiate the iterations. We end up with estimates of the value of the Martin Corporation at
Iterative Process Using Financial Spreadsheet Model Exhibit 17B.5
Model for Calculating Value of Invested Capital Showing Converged Values
A
B
C
D
59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
305
E
F
G
Martin Corporation Firm Valuation Period Weighted Average Cost of Capital Debt Equity Debt/Total Capital Equity/Total Capital Debt/Equity Cost of Debt Levered Beta Cost of Equity Weighted Average Cost of Capital
0
1
2
3
4
600,000 1,122,192 34.8% 65.2% 53.5% 10.0% 2.008 23.01% 17.08%
530,000 1,200,673 30.6% 69.4% 44.1% 10.0% 1.923 22.58% 17.50%
460,000 1,287,905 26.3% 73.7% 35.7% 10.0% 1.846 22.20% 17.94%
400,000 1,375,689 22.5% 77.5% 29.1% 10.0% 1.785 21.896% 18.32%
400,000 1,462,813 21.5% 78.5% 27.34% 10.0% 1.769 21.82% 18.42%
Cash Flow to Invested Capital PVt(CFt+1) PVt(Valuet+1)
285,714 243,152 1,487,521
285,714 242,263 1,505,642
285,714 201,238 1,574,451
238,095
244,028 1,478,164
1,862,813
MVIC less: Debt Value of Equity
1,722,192 600,000 1,122,192
1,730,673 530,000 1,200,673
1,747,905 460,000 1,287,905
1,775,689 400,000 1,375,689
1,862,813 400,000 1,462,813
5
250,000
time 0 of $1,722,192 for invested capital and $1,122,192 for the equity. These values are shown in the Period 0 column (column B) of Exhibit 17B.5, which shows the calculation of the converged values at each stage.
HANDLING THE ITERATIONS Exhibit 17B.5 shows the converged results for the iterations at each of the stages in the value calculation. Two ways to work through the iterations are manually and automatically. The manual approach was used to construct Exhibits 17B.3 and 17B.4, which were shown to demonstrate the steps in the iteration.
Manual Iterations Using the manual approach with a spreadsheet model like Exhibit 17B.5 requires that the user start at stage 4 and plug in the equity value in cell F64. For the first iteration, this would be the book value of equity referenced by equating cell F64 to equity in the balance sheet (¼ F31). The derived values for the first iteration would show in cells F77 and F79. The equity value in F79 from the first iteration would be plugged into cell F64 to start the second iteration. This would continue until cell F79 agrees with the input cell F64. Stage 3 would use these converged results from stage 4 and go through the iterations starting with the book value of equity in cell E64, with the derived value showing in cell
306
Exhibit 17B.6
Cost of Capital
Excel Menu Bar
E79. The stage iterations stop when E79 agrees with the input cell E64. Then we go to stage 2, reach convergence, then stage 1 and stage 0. These are the manual steps used to complete the values explained in the preceding text. Now let us look at the automatic approach. Automatic Iterations Excel will work through these iterations automatically, so you do not have to do it manually. The steps that Excel follows are much like the manual approach just explained, but they are performed instantly. In the Excel model shown in Exhibit 17B.5, we can set the input equity values in row 64 equal to the derived output equity values in row 79. For example, for stage 4 we enter in cell F64 the formula ‘F = 79.’ This causes a circular reference that brings up a dialog box chastising you for committing such a stupid and unforgivable error. The way to solve the circular reference is: 1. On the Excel Menu bar, select Tools>Options. The Options dialog box (shown in Exhibit 17B.6) pops up. 2. Choose the ‘Calculation’ tab, click ‘Iteration’ and ‘Ok’. The model is now set to do the iterations automatically. This automatic iteration method was used to generate the values shown in Exhibit 17B.5, and it does the iterations down to the point where the circular references agree within the .001 shown in the ‘Maximum Change’ box.2
2
A caution is in order. Automatic iteration works well in simple models where there are few circular references that do not conflict. However, complex models may contain numerous inconsistent circular references, and you may not be able to converge to consistent answers for all of them. The solution is simply to do a better job of model building so as to avoid the numerous circular references.
Equity Value
307
Exhibit 17B.7 Model of Equity Value First Iteration: Equity (line 90) at Book Value A
B
C
D
81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101
E
F
G
Martin Corporation Equity Valuation Period Risk-Free Rate Equity Risk Premium Size Premium Company-Specific Premium Unlevered Beta Debt Equity Debt/Equity Levered Beta Cost of Equity
0 4.61% 5.00% 6.36% 2.00% 1.52 600,000 352,381 1.70 3.073 28.33%
1
2
3
4
530,000 422,381 1.25 2.664 26.29%
460,000 492,381 0.93 2.372 24.83%
400,000 552,381 0.72 2.180 23.87%
400,000 600,000 0.67 2.128 23.61%
Equity Cash Flow PVt(CFt+1) PVt(Valuet+1)
179,714 145,626 912,193
183,914 158,707 993,319
198,114 172,836 1,067,125
214,095
140,036 824,269
1,321,870
964,305 600,000 1,564,305
1,057,820 530,000 1,587,820
1,152,026 460,000 1,612,026
1,239,961 400,000 1,639,961
1,321,870 400,000 1,721,870
Value of Equity Plus: Debt MVIC
5
246,000
EQUITY VALUE Our discussion so far has focused on the value of invested capital, with the value of equity being a residual. Often the appraisal task is to estimate the value of equity. The appraiser may want to attack the problem directly by using the equity approach, not the WACC. If we are using the equity approach with a changing capital structure, we use the same iterative approach over several stages. As with the invested capital approach, we start at the end of the investment horizon, when the firm is expected to reach a stable structure with constant growth. We will not repeat all the steps of the iterations and stages for the equity method, having shown them for the invested capital method. We will just show the beginning and end of the process. Exhibit 17B.7 shows the Excel model for calculating equity value. All the cost of capital parameters are the same as in the invested capital example, and the equity cash flow is from line 57 of Exhibit 17B.2. For the first iteration, the equity is set equal to book value (line 31 in Exhibit 17B.1), so the costs of equity in line 93 are based on the book value ratios. For iteration 1 of stage 4, using book value capital proportions, cell F97 shows the time 4 terminal value that is calculated with the constant growth model 1 Me;4 ¼ $246;000 ð0:2361 0:05Þ ¼ $1;321;870 where the long-run growth in equity cash flow is assumed to be equal to the growth of flow to invested capital. Line 96 is the present value at each stage t of the cash flow at time t þ 1, discounted
308
Cost of Capital
Exhibit 17B.8
Comparison of Costs of Capital and Value between First and Last Iterations
Period (Stage)
0
Cost of Equity—First Iteration —Last Iteration Value of Equity—First Iteration —Last Iteration Weighted Average Cost of Capital—First Iteration —Last Iteration MVIC—First Iteration —Last Iteration
28.33% 23.01%
1 26.29% 22.58%
2 24.83% 22.20%
3 23.87% 21.89%
4 23.61% 21.82%
$1,411,308 $1,482,481 $1,568,627 $1,662,121 $1,761,508 $1,122,192 $1,200,673 $1,287,905 $1,375,689 $1,462,813 14.26% 17.08%
15.00% 17.50%
15.74% 17.94%
16.37% 18.32%
16.57% 18.42%
$2,011,308 $2,012,481 $2,028,627 $2,062,121 $2,161,508 $1,722,192 $1,730,673 $1,747,905 $1,775,689 $1,862,813
at period t’s cost of capital, NCFe;tþ1 1=ð1 þ ke;t Þ . Line 97 is the present value at time t of the value at time t þ 1, PVtþ1 1=ð1 þ ke;t Þ . Line 99 adds the present value of cash flow to the present value of the end of period value to obtain the value of equity at each date. Thus, line 99 shows all the firstiteration values prior to iterating at each stage. We perform the iterations automatically by equating the equity value in line 90 with the equity value in line 99 and allowing Excel to do the iterations. The result of the converged iterations is shown in Exhibit 17B.8. Note that the value of equity (line 99) and the value of invested capital (line 101) at each stage match the values derived using the invested capital method shown in Exhibit 17B.5.
SUMMARY This appendix has discussed two complications to calculating and using the cost of equity and the weighted average cost of capital. First, both are functions of the capital proportions based on market values of the sources of capital, which makes the valuation problem circular. Second, both are valid for a stable capital structure, so if the capital structure is changing over time, we need to adjust the market-value-based capital proportions to calculate costs of capital and value at each stage. This appendix has shown how we can deal with these complications. To handle the requirement that the capital proportions are based on market values, we perform an iterative process, typically starting with book values and converging on a solution where the capital proportions are based on market value estimates. To handle the second problem when the capital structure is changing, we work in stages, starting at a terminal value and working backward in time to the present, using an iterative process at each stage to reach value estimates that are based on converged market values at each stage. To see how important these adjustments can be, consider Exhibit 17B.8, which compares the costs of capital and values at the first iteration with the last iteration. For example, at time 0, we see that the weighted average cost of capital has changed from 14.26% to 17.08%, and the value of invested capital has changed from $2.01 million to $1.72 million. These significant differences should be taken into account so that we can minimize any error in our valuation that might be due to errors in method or computation.
ADDITIONAL READING Morris, James R. ‘‘Reconciling the Equity and Invested Capital Methods of Valuation When the Capital Structure Is Changing.’’ Business Valuation Review (March 2004): 36–46.
Chapter 18
Global Cost of Capital Models
Introduction Risks Currency Risk Country Risks Sources of Information on Countries and Their Economies Cost of Equity Capital Models Local, Single-Country Version of the CAPM U.S. Cost of Equity Capital Adjusted for Country Yield Spreads U.S. Cost of Equity Capital Adjusted for Non-U.S. Volatility Spreads Global Version of CAPM Country Credit Rating Method Adjusting for Local Country Risk Exposure Other Sources of Global Cost of Capital Data Alternative Risk Measures to Beta Expanding Global Models to Incorporate Size Premium and Company-Specific Risk Firm-Size Phenomenon Company-Specific Risk Factor Expanded Cost of Capital Formula Should Projected Cash Flows and the Cost of Capital Be Nominal or Real? Capital Structure Summary Data Sources Additional Reading
INTRODUCTION Why is there an ‘‘international problem’’ in developing costs of equity capital? If people are everywhere alike and markets are integrated, then there is no problem. However, if markets are (entirely or partially) segmented, then we need to address the differences between the markets. The most common adjustments made by practitioners are aimed at this segmentation problem or at adding ad hoc ‘‘alphas’’ to the discount rate. There can be no doubt that some markets are at least partially segmented. The markets for goods, services, capital, and currencies may be segmented by a host of problems, such as taxation differences, legal factors, information, trading costs, and so on. But experts do not agree on the extent or effects of such segmentation. Consequently, it is plausible that expected returns are affected.
309
310
Cost of Capital
RISKS Practitioners typically are confronted with this situation: ‘‘I know how to value a cement company in the United States, but this one is in Country X, a developing economy. What should I use for a discount rate?’’ What are the issues? Currency risk? Country (economic) risk? Country (political) risk? Analysts need to reflect such risks, weighted by their probability of occurrence, in the cash flow projections. If they do not, then they do not really have expected cash flows. In the framework of the textbook Capital Asset Pricing model (CAPM), each of these is a problem for the discount rate only to the extent that it is unique and nondiversifiable. Remember, capital market theory divides risk into two components (other than maturity risk): market or systematic risk and unique or unsystematic risk. Stated in nontechnical terms, market risk or systematic risk (also known as undiversifiable risk) is the uncertainty of future returns owing to the sensitivity of the return on the subject investment to movements in the returns for a composite measure of marketable investments. Unique or unsystematic risk (also known as diversifiable risk, residual risk, or specific risk) is a function of the characteristics of the industry, the individual company, and the type of investment interest. The basic insight of capital market theory that expected return is an increasing function of market risk still holds when dealing with cost of equity capital in a global environment. But even in cases where the same market risks may exist, the variance of expected cash flows and therefore the risk of the cash flows differ. For example, assume that the expected cash flows from projects in two countries are identical, but the variance of expected future cash flows differs. The differences in variability (even in cases where expected or ‘‘mean’’ cash flows are identical) may reflect differences in risk and need to be reflected in the cost of capital.
CURRENCY RISK The currency of the cash flows always must match the currency of the discount rate. This is a good place to begin thinking about ‘‘adjustments.’’ Begin by considering a pure currency translation adjustment, as shown in Exhibit 18.1. If you use this rate, there is no adjustment for currency ‘‘risk’’ (i.e., exchange rate volatility), or for any other type of risk (e.g., country/economic/political risk). This is purely a currency translation, one that assumes, in effect, that parity conditions hold. This is a commonly used simplification but does not take into account the risks of changing currency relationships. Does currency risk impact the cost of capital? One team of researchers found that emerging market exchange risks have significant impact on risk premiums and are time-varying (for countries in the sample, including Mexico). They found that exchange risks impact risk premiums as a separate risk factor and represent over 50% of total risk premiums for investments in emerging market stocks. The exchange risk from investments in emerging markets even affects the risk premia for investments in developed market stocks.1 But actual foreign exchange risks differ from the assumed equilibrium party condition. One author has developed a formula for converting discount rates developed in terms of returns in one country (for example, U.S. dollars) to an equivalent discount rate in terms of returns in another country
1
Francesca Carrieri, Vihang Errunza, and Basma Majerbi, ‘‘Does Emerging Market Exchange Risk Affect Global Equity Prices?’’ Journal of Financial Quantitative Analysis (September 2006): 511–540.
Risks
311
Exhibit 18.1
Adjusting Cost of Equity Capital for Currency Translation
ke; local ¼
1 þ ke; u:s:
ð1 þ Inflationlocal Þ 1 ð1 þ Inflationu:s: Þ
or (approximately, but perhaps more intuitively): ke; local R f ; local þ ½Bu:s: RPu:s
where: R f ; local ¼
ð1 þ Inflationlocal Þ 1 1 þ R f ;u:s ð1 þ Inflationu:s: Þ
where: ke,local ¼ Discount rate for equity capital in local country for discounting expected cash flows in local currency ku.s. ¼ Discount rate for equity capital in U.S. Inflationlocal ¼ Expected rate of inflation in local country Inflationu.s. ¼ Expected rate of inflation in U.S. Rf,local ¼ Return on local government default-risk-free: debt Rf,u.s. ¼ U.S. risk-free rate Bu.s. RPu.s. ¼ Risk premium appropriate for a U.S. company in similar industry as subject company in local country.
(for example, Euro, Yen).2 In this way, projections of expected net cash flows can be made in the local country currency and the foreign exchange rate can be imbedded in the discount rate. COUNTRY RISKS Are there still country-specific risks, or have economies been so globalized that the issue of countryspecific risks is reduced? One researcher outlines an alternative to the neoclassical model that explains the limited impact of financial globalization where ownership is concentrated. He calculated the percentage of market value owned by corporate insiders (controlling shareholders plus other insiders) in 48 developing economies as of 2002. By investing in their firm, insiders cannot diversify away risks. Among the most concentrated ownership in 2002 (out of 48 countries) were Mexico, Peru, the Czech Republic, and the Philippines (over 70% owned by insiders).3
2
3
Thomas O’Brien, ‘‘The U.S. Dollar Global CAPM and a Firm’s Cost of Capital in Different Currencies,’’ Working paper, July 2005; ‘‘Foreign Exchange and Cross-Border Valuation,’’ Journal of Applied Corporate Finance (Spring/Summer 2004): 147– 154. Rene M. Stulz, ‘‘The Limits of Financial Globalization,’’ Journal of Finance (August 2005): 1595–1638.
312
Cost of Capital
In another study, the authors found that country risk matters.4 They decompose equity returns into cash flow and discount rate components and find:
Global cash flow variation explains 39% of the variation of country cash flows.
Global discount rates explain 55% of the variation of country discount rates.
Industry cash flow variation explains 72% of the variation of country cash flows. Industry discount rate variation explains 78% of country discount rates.
They conclude that because the lower degree of diversification of emerging markets to the world goods and financial markets, country risk differences still matter. What are legitimate reasons for country risk adjustments? Investors may view some country-level phenomena as unique or country-specific and demand a premium due to: Financial Risks
Currency volatility plus the inability to convert, hedge, or repatriate profits
Loan default or unfavorable loan restructuring Delayed payment of suppliers’ credits
Losses from exchange controls Foreign trade collection experience
Economic Risks
Volatility of the economy
Inflation: current and future expected Debt service as a percentage of exports of goods and services
Current account balance as a percentage of goods and services Parallel foreign exchange rate market indicators
Labor issues
Political Risks
Repudiation of contracts by governments Expropriation of private investments in total or part through change in taxation
Economic planning failures Political leadership and frequency of change
External conflict
Corruption in government Military in politics
Organized religion in politics Lack of law and order tradition
Racial and national tensions
Political terrorism
4
Kent Hargis and Jianping Mei, ‘‘Is Country Diversification Better than Industry Diversification?’’ European Financial Management 12, no. 3 (June 2006): 319–340.
Cost of Equity Capital Models
Civil war Poor quality of the bureaucracy
Poorly developed legal system
313
SOURCES OF INFORMATION ON COUNTRIES AND THEIR ECONOMIES There are a number of good sources of information: Political Risk Services, Standard & Poor’s, Moody’s, Institutional Investor, and Euromoney. We have listed those sources in the Data Sources section of this chapter. Political Risk Services, for example, provides country risk rankings. Are country risk rankings useful in measuring country-specific risks? One researcher analyzed risk ratings and cost of capital in countries with stock markets categorized into developed versus emerging. He found that lowest-rated countries have highest equity return volatilities. He concludes that country risk is priced in emerging markets: the greater the financial and economic risks, the greater the returns demanded by the market. The greater the risk of government instability and internal conflict, the greater the returns demanded by the market.5
COST OF EQUITY CAPITAL MODELS There is no consensus among academics and practitioners as to the best model to use in estimating the cost of equity capital in a global environment, particularly with regard to companies operating in ‘‘developing economies.’’ In choosing a model, the goal is to balance several objectives:
Similarity to models used by practitioners Available data for consistent and objective application of the model
Simplicity
In choosing models for developing the cost of equity capital for a company or project in a highly developed country, generally that economy is integrated into the global economy, and it can be expected that companies or projects with similar risks would require similar costs of capital. But when choosing models for developing the cost of equity capital for a company or project in a less developed or developing country, generally that economy is less integrated in the regional or world economy and local volatility is important. There are several common approaches to incorporating country factors into a discount rate. None is perfect. We present four broad categories of models for estimating the cost of equity capital. Most practitioners’ models fall into one of these categories. 1. 2. 3. 4.
5
Local, single-country version of the CAPM U.S. cost of equity capital adjusted for country yield spreads U.S. cost of equity capital adjusted for non-U.S. volatility spreads Global version of CAPM
Campbell R. Harvey, ‘‘Country Risk Components, the Cost of Capital, and Returns in Emerging Markets’’ Fuqua School of Business, Duke University, Durham, NC, November 2004.
314
Cost of Capital
Instead of a model, one could gather empirical data and directly estimate the cost of equity capital from the observed realized returns by country. The country credit rating method is one such approach. The four categories of models and the country credit rating method treat the risks of operating in a developing economy as affecting the relative business. We present another model that allows you to adjust for the relative business in and out of the developing economy.
LOCAL, SINGLE-COUNTRY VERSION OF THE CAPM (Formula 18.1) klocal ¼ R f ;local þ ½ Blocal RPlocal where: klocal ¼ Discount rate for equity capital in local country Rf,local ¼ Return on the local country government’s (default-risk-free) debt Blocal ¼ Market risk of the subject company measured with respect to the local securities market RPlocal ¼ Equity risk premium in local country’s stock market If one estimates all expected terms of rates of return in local currency (e.g., Brazilian Real), then the resulting discount rate can be used to discount expected net cash flows expressed in local currency. If one estimates all expected return in terms of rates of return in U.S. dollars, then the resulting discount rate is used to discount expected cash flows expressed in U.S. dollars (with the exchange risk treated in either the expected cash flows or as an adjustment to the discount rate). This approach has appeal because local investors provide capital to local firms in the local market. This approach allows more local factors to be incorporated in the measure of local market risks. This type of model works best in developed economies. For example, you can determine betas for U.S. firms relative to the Standard & Poor’s (S&P) 500, U.K. firms relative to the FT-SE 100, and Japanese firms relative to the TOPIX. In addition, you need to estimate a local estimated equity risk premium. Elroy Dimson, Paul Marsh, and Mike Staunton have published the most definitive work on equity risk premiums for 17 developed markets. They observe larger equity returns earned in the second half of the twentieth century compared to the first half because:
Corporate cash flows grew faster than investors anticipated due to rapid technological change and unprecedented growth in productivity and efficiency
Transaction and monitoring costs fell over the course of the final two decades of the century
Inflation rates generally declined Real interest rates rose, resulting in a reduced required rate of return due to diminished business and investment risks
Exhibit 18.2 displays the realized worldwide risk premiums relative to government bonds for 1900 to 2006. Using their data, you can estimate an equity risk premium (ERP) for each of the 17 developed economies. The data are available through Morningstar at http://global.morningstar.com/ uscofcresources.
Cost of Equity Capital Models Exhibit 18.2
315
Worldwide Risk Premiums Relative to Bonds, 1900–2006
Country Australia Belgium Canada Denmark France Germany* Ireland Italy Japan The Netherlands Norway South Africa Spain Sweden Switzerland United Kingdom United States World ex-U.S. World
Geometric Mean%
Arithmetic Mean%
Standard Error%
Standard Devn %
6.4 2.8 4.2 2.2 4.0 5.5 3.9 4.5 5.9 4.0 2.8 5.6 2.6 5.4 2.0 4.2 4.6 4.2 4.1
8.0 4.6 5.7 3.4 6.2 8.5 5.4 7.8 9.9 6.1 5.5 7.3 4.6 7.7 3.4 5.4 6.6 5.3 5.2
1.8 1.9 1.7 1.6 2.2 2.7 1.8 2.9 3.2 2.1 2.7 1.9 2.0 2.2 1.7 1.6 1.9 1.5 1.4
18.8 20.1 17.9 16.2 22.3 27.3 18.5 29.6 32.9 21.6 27.4 19.4 20.4 22.3 17.5 16.6 20.1 15.2 14.9
Source: Elroy Dimson, Paul Marsh, and Mike Staunton, Triumph of the Optimists (Princeton, NJ: Princeton University Press, 2002); Global Investment Returns Yearbook 2007 (ABN AMRO/London Business School, February 2007). *All statistics for Germany are based on 105 years, excluding 1922–23.
There are four problems with this approach. 1. It is most justified in developed economies (e.g., the United States). 2. Data are poor to nonexistent in segmented, developing country settings, especially for the local beta and ERP. 3. Many betas estimates using historical returns may be low because the local stock market may be dominated by a few firms. 4. The local country government’s debt is possibly not free of default risk.
U.S. COST OF EQUITY CAPITAL ADJUSTED FOR COUNTRY YIELD SPREADS (Formula 18.2) klocal ¼ R f ;u:s: þ ðRlocal euro $issue R f ;u:s: Þ þ ½Bu:s: RPu:s: where: klocal ¼ Discount rate for equity capital in local currency Rf,u.s. ¼ Current market interest rate of debt issued by U.S. government with the same maturity as debt issued by the local country government denominated in U.S. dollars Rlocal euro $issue ¼ Current market interest rate on debt issued by the local country government denominated in U.S. dollars (eurodollar debt)
316
Cost of Capital
Bu.s. RPu.s. ¼ Risk premium (rate of return expressed in terms of U.S. dollar returns) appropriate for a U.S. company in a similar industry as the subject company in the local country Because we are estimating expected returns in terms of U.S. dollars, this discount rate can be used for discounting expected net cash flows expressed in U.S. dollars (with the exchange risk treated in either the expected cash flows or as an adjustment to the discount rate). This approach has appeal where non-U.S. debt issued by the local country government can be observed. If that debt denominated in U.S. dollars has a higher expected return, that indicates a country-specific risk of default. This country-specific risk is clearly not included in the U.S. risk premium, so it must be added separately. The risk of government default is correlated with, and arguably proxies for, country risk. Exhibit 18.3 shows a sampling of yield spreads as of December 31, 2006. There are three problems with this approach. 1. In some cases, the local government’s credit quality may be a very poor proxy for risks affecting business cash flows. 2. This approach may double-count country-level risks that are already incorporated into projections of expected cash flows. 3. Many countries do not issue dollar-denominated debt. In such cases, you can correlate the Institutional Investor Country Credit Rating using the credit rating for countries that do issue dollardenominated debt. Then you can use the Institutional Investor Country Credit Rating for countries that do not issue dollar-denominated debt to input a yield spread. Exhibit 18.4 shows an example of such an analysis. U.S. COST OF EQUITY CAPITAL ADJUSTED FOR NON-U.S. VOLATILITY SPREADS (Formula 18.3) klocal ¼ R f ;u:s: þ ðBu:s: RPu:s: Þðs local =s u:s: Þ where:
Bu.s.
klocal ¼ Discount rate for equity capital in local country Rf,u.s. ¼ U.S. risk-free rate, adjusted if necessary for currency risk RPu.s. ¼ Risk premium (rates of return expressed in U.S. dollar returns) appropriate for a U.S. company in similar industry as the subject company in the local country slocal ¼ Volatility of local country’s stock market su.s. ¼ Volatility of U.S. stock market Exhibit 18.3 Austria Brazil China Ecuador Israel Lebanon
Example Yield Spreads as of December 31, 2006 0.21% 1.65% 0.26% 8.24% 1.16% 4.16%
Cost of Equity Capital Models Exhibit 18.4
Example of Guideline Yield Spreads Based on Country Credit Rating
S&P’s Rating (1) CC CCC CCC CCC+ B B B+ BB BB BB+ BBB BBB BBBþ A A Aþ AA AA AAþ AAA
317
Rating Score (2)
CCR Rating (3)
Guideline Yield Spread (4)
22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 2
0.0 9.2 13.7 18.2 22.7 27.3 31.8 36.3 40.8 45.3 49.8 54.3 58.8 63.3 67.8 72.4 76.9 81.4 85.9 92.6
6.23% 5.29% 4.49% 3.81% 3.23% 2.74% 2.33% 1.98% 1.68% 1.42% 1.21% 1.02% 0.87% 0.74% 0.63% 0.53% 0.45% 0.38% 0.32% 0.00%
(1) Standard & Poor’s credit rating (2) Numeric ranking of S&P’s credit rating (3) Institutional Investors Country Credit Rating (4) Guideline yield spread determined using regressed equation: Yield spread ¼ EXP½6:3874 þ 0:1642 ðS&P0 s debt ratingÞ Data as of December 31, 2006. Source: Calculations by Duff & Phelps, LLP.
Because we are estimating expected returns in terms of U.S. dollars, this discount rate can be used for discounting expected net cash flows expressed in U.S. dollars (with the exchange rate risk treated in either the expected cash flows or as an adjustment to the discount rate). This approach has appeal in cases where the stock market in the subject country is diversified. If it has higher volatility than the U.S. market, that higher volatility is evidence of differences in countrylevel market risk and therefore justifies a country risk premium. The adjustment shown ‘‘rescales’’ a U.S.-measured risk premium to local volatility norms. This approach has two problems: 1. The observed difference in volatilities may reflect mostly a difference in the composition of the subject country’s economy (e.g. lots of natural resources but not many service businesses). This is not a country effect but an industry effect. It is incorrect to apply it to other industries. 2. This adjustment is troublesome when the investor (e.g., a multinational firm) clearly has access to global markets. One variation of this model is the Goldman/Bank of America Model6 where Rf ¼ eurodollar bond yield. 6
Versions of this model have been published by analysts at Goldman Sachs and Bank of America, Stephen Godfrey and Ramon Espinosa, ‘‘A Practical Approach to Calculating Costs of Equity for Investments in Emerging Markets,’’ Journal of Applied Corporate Finance (Fall 1996): 80–89; J. Mariscal and R. Lee, ‘‘The Valuation of Mexican Stocks’’ (June 1993), and ‘‘The Valuation of Latin American Stocks: Part II’’ (May 1994); J. Mariscal and E. Dutra, ‘‘The Valuation of Latin American Stocks: Part III’’ (November 1995): all papers published by Goldman Sachs Latin American Research.
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Cost of Capital
Volatility versus Country Credit Rating 4.00
ln (volatility)
3.50 3.00 2.50 y = -0.0099x + 3.7703 R2 = 0.495
2.00 1.50 1.00 0.50 0.00 0.0
Exhibit 18.5
20.0
40.0
60.0 80.0 Country Credit Rating
100.0
120.0
Example of Using Country Credit Rating to Estimate Volatility
Again, some countries do not have local stock markets, or their markets are so thin that observed variance in returns may not be representative of the true risk from that country. You can correlate the Institutional Investor’s Country Credit Rating with the volatility of various stock markets and then use the Country Credit Rating to input an appropriate volatility. Exhibit 18.5 is an example of the relationship between the Country Credit Rating and observed stock market volatilities. Exhibit 18.6 shows how to estimate the relative volatility for two countries based on their respective country credit ratings. GLOBAL VERSION OF CAPM (Formula 18.4) ke ¼ R f ;u:s: þ ðBw RPw Þ where: ke ¼ Discount rate for equity capital Rf,u.s. ¼ U.S. risk-free rate Bw ¼ Market or systematic risk measured with respect to a ‘‘world’’ portfolio of stocks RPw ¼ Equity risk premium (rate of return expressed in terms of U.S. dollar returns) on a ‘‘world’’ diversified portfolio Because we are estimating expected returns in terms of U.S. dollars, this discount rate can be used for discounting expected net cash flows expressed in U.S. dollars (with the exchange risk treated in either the expected cash flows or as an adjustment to the discount rate). You can use the Dimson, Marsh, and Staunton data to estimate RPw . They then convert historical realized premium to a forward-looking ERP projection. They assume that:
The observed increase in the price/dividend ratio is attributable solely to the long-term decrease in the required risk premium (and the decrease will not continue).
Future standard deviation of annual returns will equal historical standard deviation of returns. The authors note:
Cost of Equity Capital Models Exhibit 18.6
319
Example of Estimating Relative Volatility using Country Credit Rating
Developed Economies Kazakhstan Jordan
CCR
s
s sB
80.0* 54.7 43.6
19.7y 25.2% 28.2%
1.00 1.28 1.43
*Lowest Country Credit Rating for 26 developed economies. y Average standard h deviation of return i for stock markets in 26 developed economies; serves as base standard deviation ¼ s B . ð3:77030:0099ðCCRÞÞ Volatility ¼ e 19:7
Further adjustments should almost certainly be made to historical risk premiums to reflect long-term changes in capital market conditions. Since, in most countries corporate cash flows historically exceeded investors’ expectations, a further downward adjustment is in order.
They conclude that a further downward adjustment of approximately 50 to 100 basis points in the expected ERP at the beginning of 2007 is plausible. Adjusting the realized risk premium for the increase in price-to-dividend ratio that resulted from a decrease in the discount rate and dividend yield to current levels, they estimate these ERPs at the beginning of 2007:
United States: In the range of 4.9% to 5.4% (arithmetic average over U.S. government bonds; 2.9% to 3.4% geometric average over U.S. government bonds)7
World index of stocks in 17 countries (denominated in US $): In the range of 3.6% to 4.1% (arithmetic average over government bonds; 2.5% to 3.0% geometric average over government bonds).8
Duff & Phelps publishes its Global Cost of Capital Report quarterly. It uses a global version of the CAPM to report risk premiums by industry for 40 industry groupings. It is available on the Duff & Phelps Web site at: www.duffandphelps.com/3_0_index.htm. This approach has intuitive appeal where markets are integrated. This method recognizes crossborder diversification opportunities and prices securities accordingly. This approach has five problems. 1. Markets may not (yet) be that integrated. In effect, this approach assumes away meaningful differences across countries. 2. High-quality data are still lacking in some places (which further suggests that integration is not complete). 3. Truly robust global versions of CAPM are multifactor models (but for which betas depend on unobservable variables). 4. The specification above is an idealized approximation unless there is complete integration. 5. This approach generally does not result in an increased cost of equity capital.
7
8
Based on this, Grabowski’s converting premium over total returns on bonds as reported by Dimson, Marsh, and Staunton, removing the impact of the growth in price-dividend ratios from the geometric average historical premium, reducing the historical average dividend yield to a current dividend yield and converting to an approximate arithmetic average. Ibid. Elroy Dimson, Paul Marsh, and Mike Staunton, ‘‘Global Evidence on the Equity Risk Premium,’’ The Journal of Applied Corporate Finance (Summer 2003): 27–38; ‘‘The Worldwide Equity Premium: A Smaller Puzzle,’’ EFA 2006 Zurich Meetings Paper, April 7, 2006; The Global Investment Returns Yearbook 2007 (ABN-AMBRO/London Business School, 2007): 44.
320
Cost of Capital
Because closely held companies have no market price, their betas cannot be measured directly. Thus, to use these models to estimate the cost of capital for a closely held company, reporting unit or division, it is necessary to estimate a proxy beta for that company. This usually is accomplished by using an average beta for the industry group or by selecting specific guideline public companies and using some composite, such as the average or median, of their betas. Does the choice of using local CAPM or a global CAPM matter for larger companies? One study compared the rates of return from S&P 500 companies using a domestic (U.S.) CAPM to rates of return for those same companies using a global CAPM model.9 They compare the two models to implied cost of equity capital estimates for these large U.S. companies for the period 1983 to 1998. They find only a small difference between the two versions of the CAPM, though the domestic CAPM provided estimates of cost of equity capital more consistent with the implied cost of equity capital estimates. In another study, the authors find that there was a relatively insignificant difference in cost if equity capital estimates between using a domestic (U.S.) CAPM and global CAPM for larger U.S. companies but does matter for smaller U.S. companies.10 They also study the difference in global CAPM estimates where the model is expanded to include foreign exchange risk. The difference in cost of capital estimates using different models also does matter in certain industries. In another study the authors find that for stocks in 9 developed economies, the differences in cost of equity capital estimates between a domestic CAPM model and a global CAPM model are not significant.11 The authors conclude that companies within a country by and large exhibit a joint exposure to international risk factors that is fully captured by an index of their local currency domestic market index. A variation of the global CAPM is the globally nested CAPM: (Formula 18.5)
kc ¼ R f þ ðbcw RPw Þ þ ðbcr dr Þ where: kc ¼ Local discount rate for equity capital in local country Rf ¼ U.S. risk-free rate bcw ¼ Country covariance with world RPw ¼ World equity risk premium (rate of return expected in terms of U.S. dollar returns) bcr ¼ Country covariance with region dr ¼ Regional risk not included in RPw This model is complex and requires proxies to measure covariances. That is, to implement this model, you must perform statistical analysis of representative economies data for the country, region, and world to estimate the respective covariances.
9
10
11
Robert S. Harris, Felicia C. Marston, Dev R. Mishra, and Thomas J. O’Brien, ‘‘Ex Ante Cost of Equity Estimates of S&P 500 Firms: The Choice Between Global and Domestic CAPM,’’ Financial Management (Autumn 2003): 51–66. Dev R. Mishra, and Thomas J. O’Brien, ‘‘A Comparison of Cost of Equity Estimates of Local and Global CAPMs,’’ The Financial Review 36 (2001): 27–48. Kees G. Koedijk, Clemens J.M. Kool, Peter C. Schotman, and Mathijs A. van Dijk, ‘‘The Cost of Capital in International Financial Markets: Local or Global?’’ Journal of International Money and Finance 21 (2002): 905–929.
Adjusting for Local Country Risk Exposure
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COUNTRY CREDIT RATING METHOD Another method for estimating the cost of capital is the Erb-Harvey-Viskanta country credit rating method.12 It is purely empirical in that the authors run a regression where the country credit rating is the independent variable and the historical equity returns are the dependent variable. While many countries have no data for risk-free debt or equity returns, they all have a country credit rating. This method is shown in Formula 18.6: (Formula 18.6) klocal ¼ a þ B logðCCRlocal Þ þ e where: klocal ¼ Cost of equity capital in local country a ¼ Regression constant B ¼ Regression coefficient CCRlocal ¼ Country credit rating of local country e ¼ Regression error term By performing a regression with the country credit ratings from a source such as Standard & Poor’s or Moody’s as the independent variable and returns for countries with equity return data (expressed in terms of U.S. dollar returns) as the dependent variable, you can estimate the appropriate returns for a specific country based on its credit rating to be applied to expected cash flows in U.S. dollars. But what do you do for a country with no rated debt? You can use the observed relationship between country risk ratings and country credit ratings to establish the proxy country credit rating based on the risk rating. Then you can extrapolate the credit rating that a country would have if it had rated debt from its risk ratings. This relationship has been documented.13 Risk ratings are available from Institutional Investor’s Country Credit Rating, Euromoney’s Country Risk Ratings, or Political Risk Services’ International Country Risk Guide. The International Cost of Capital and Risk Calculator estimates cost of capital for 136 countries. See www.duke.edu/charvey/applets/iccrc.html for information.
ADJUSTING FOR LOCAL COUNTRY RISK EXPOSURE The Damodaran model, shown in Formula 18.7,14 compares the volatility of the local country’s stocks and bonds (the relative risk between debt and equity for investors in that country): (Formula 18.7) klocal ¼ R f ;u:s: þ ½Bu:s: RPu:s: þ l ðCountry Risk PremiumÞ where: klocal ¼ Discount rate for equity capital in local country 12
13
14
Campbell R. Harvey, ‘‘The International Cost of Capital and Risk Calculator,’’ Fuqua School of Business, Duke University, Durham, NC, July 25, 2001. Claude Erb, Campbell Harvey, and Tadas Viskanta, ‘‘Expected Returns and Volatility in 135 Countries,’’ Journal of Portfolio Management (Spring 1996): 46–58. Aswath Damodaran, Investment Valuation, 2nd ed. (New York: John Wiley & Sons, 2002), 204–206; and Aswath Damodaran, Damodaran on Valuation, 2nd ed. (New York: John Wiley & Sons, 2006), 59–61.
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Rf,u.s. ¼ U.S. risk-free rate adjusted if necessary for currency risk Bu.s. RPu.s. ¼ Risk premium (in U.S. dollars terms) appropriate for a U.S. company in a similar industry as the subject company in the local country l ¼ Company’s exposure to the local country risk Country Risk Premium ¼ [Country Default Spread (sstock/sbond)] Country Default Spread ¼ Spread between government bonds issued by the local country versus U.S. government bonds sstock ¼ Volatility of local country’s stock market sbond ¼ Volatility of local country’s bond market Because we are estimating expected returns in terms of U.S. dollars, this discount rate can be used for discounting expected net cash flows expressed in U.S. dollars (with the exchange risk treated in either the expected cash flows or as an adjustment to the discount rate). The company’s exposure to the local company risk is measured relative to the average company in the local country. For example, if the average of local country companies has 80% revenue from operations in that local country, then you want to measure the subject company’s exposure to that country relative to the average local company. For countries without rated debt, you can use country risk ratings to estimate the credit rating and the spread. The country exposure measure in the Damodaran model is consistent with a study that measured global, country, and industry effects in firm-level returns between emerging and developed markets.15 The authors found that country effects dominate global and industry effects in emerging markets in contrast to developed markets. The implication of their results is that in applying country risk factor, you should consider the firm-level amount of international business in determining the impact of country risk versus global and industry risk.
OTHER SOURCES OF GLOBAL COST OF CAPITAL DATA Morningstar offers estimates of cost of capital by country for 170 þ countries:
International Cost of Capital Report (cost of equity estimates are from the perspective of a U.S. investor). In other words, these statistics in the International Cost of Capital Report represent estimates of the cost of equity from the perspective of a U.S.-based investor with an equity investment in the various countries. International Cost of Capital Perspectives Report (from the perspectives of investors based in each of six countries: Australia, Canada, France, Germany, Japan, and the United Kingdom, with an equity investment in the various countries. Methods presented in the International Cost of Capital Report are:
Country credit rating (risk rating) model (EHV model) Country-spread model
International CAPM
15
Kate Phylaktis and Xia Lichuan, ‘‘Sources of Firms’ Industry and Country Effects in Emerging Markets,’’ Working paper, 2005.
Alternative Risk Measures to Beta
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Globally nested CAPM Relative standard deviation model
Not all models are available for every country. The only method presented in the International Cost of Capital Perspectives Report is the country credit rating (risk rating) method. The cost of capital resources available through Morningstar are discussed in Chapter 19. The International Cost of Capital Report and International Cost of Capital Perspectives Report are available at corporate.morningstar.com.
ALTERNATIVE RISK MEASURES TO BETA Is beta a flawed measure of risk in emerging markets? We have already noted that in many local markets, beta measurements are flawed because ‘‘market’’ returns are dominated by a few large companies and returns on other ‘‘local market’’ companies may not be correlated with those large companies. Returns of the local market companies may even be highly correlated to one another and experience high variance (risk), but they look like low-risk companies because their betas are low. Researchers studied implied cost of capital estimates for individual stocks from 16 developing economies (sometimes called emerging market countries). They find that total risk (volatility of returns) is the most significant risk factor in explaining implied cost of capital estimates.16 For companies in those markets with global market presence, the global beta does explain, but to a lesser degree, differences in implied cost of capital estimates. Other researchers have determined that downside risk measures may result in more accurate risk measures in developing markets. One researcher found returns in emerging markets systematically related to downside risk, measured as the semistandard deviation of returns compared to a benchmark return.17 Another model that incorporates downside risk as the measure of risk is shown in Formula 18.8: (Formula 18.8) klocal ¼ R f ;u:s: þ ðDR j =DRw ÞRPw where: klocal ¼ Discount rate for equity capital in local country Rf,u.s. ¼ U.S. risk-free rate DRj ¼ Downside risk in the local market (measured in US $) DRw ¼ Downside risk in global (‘‘world’’) market (measured in US $) RPw ¼ General market risk premium in global ‘‘world’’ market Because we are estimating expected returns in terms of U.S. dollars, this discount rate can be used for discounting expected net cash flows expressed in U.S. dollars (with the exchange risk treated in either the expected cash flows or as an adjustment to the discount rate). DRj is the semideviation of returns in the local market (average of returns realized in the local market less the average returns of the global index), and DRw is the semideviation of returns in a 16
17
Dev R. Mishra and Thomas J. O’Brien, ‘‘Risk and Ex Ante Cost of Equity Estimates of Emerging Market Firms,’’ Emerging Market Review 6 (2005): 107–120. Brian Gendreau and Leila Heckman ‘‘Estimating the Equity Premium across Countries,’’ Salomon Smith Barney, 2002.
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global index (average of returns realized is global index less the average returns of the global index). You could use the respective downside betas as an alternative downside risk measure. The advantages of the model are its theoretical foundations and empirical support.18 Downside beta has also received support in the literature as a superior risk measure. That is, portfolios of company stocks with high downside betas realize greater returns than portfolios of company stocks with low downside betas, consistent with the theory of CAPM.19
EXPANDING GLOBAL MODELS TO INCORPORATE SIZE PREMIUM AND COMPANY-SPECIFIC RISK FIRM SIZE PHENOMENON Is there a size premium in countries other than the United States? Many empirical studies performed since CAPM was originally developed have indicated that the realized total returns on smaller companies have been substantially greater than returns on larger companies. There are currently two widely used sources of size premium data in the United States: SBBI Yearbook and the Duff & Phelps Size Study. The size effect and those sources are the subjects of Chapter 12. Chapter 13 discusses the criticisms of the size effect and shows that the size premium varies over time. Mathijs van Dijk summarized the studies on the size effect from 23 empirical studies in non-U.S. markets.20 The studies summarized in table 2 of his working paper for 17 out of 18 countries in emerging markets and Europe (outside the United Kingdom) appear at first glance to support the size premium. But the sample sizes are small for some markets, and many of the studies do not examine the differences in risk-adjusted returns across country companies; rather they simply report that smaller firms earned higher returns than larger firms in the respective market. Another issue that surfaces is size measurement. How should size be measured for European companies? Should size be defined with respect to companies in the country or with respect to companies throughout all of Europe? Other reported results indicate that the size premium varies over time in the United Kingdom. The author concludes that more study is needed. A number of other studies have shown evidence of the size effect in Canada.21 In another study, the authors report that they found evidence of the size effect in global stocks for the study period.22 They found strong size effect based on returns reported in the Compustat Global Vantage database for 1985 to 1996. Arithmetic average returns for the smallest quintile were 9.7% greater than for the largest quintile, and the results were statistically significant. In summary, in applying any method of estimating the cost of equity capital, you need to determine if a size premium is appropriate. 18
19 20 21
22
Javier Estrada and Ana Paula Serra, ‘‘Risk and Return in Emerging Markets: Family Matters,’’ EFMA 2004 Basel Meetings Paper; Javier Estrada, Finance in a Nutshell (Financial Times Prentice Hall, 2005), 96–108. Estrada and Serra, ‘‘Risk and Return in Emerging Markets.’’ Mathijs A. van Dijk, ‘‘Is Size Dead? A Review of the Size Effect in Equity Returns,’’ Working paper, February 2006. Jean-Francois L’Her, Tarek Masmoudi, and Jean-Marc Seret, ‘‘Evidence to Support the Four-Factor Pricing Model from the Canadian Stock Market,’’ Working paper, July 2003; John M. Griffin, ‘‘Are the Fama and French Factors Global or CountrySpecific?’’ Review of Financial Studies (Summer 2002): 783–803; Jimmy Liew and Maria Vassalou, ‘‘Can Book-to-Market, Size and Momentum Be Risk Factors that Predict Economic Growth?’’ Journal of Financial Economics (August 2000): 221– 245; Bala Arshanapalli, Daniel T. Coggin, John Doukas, and H. David Shea, ‘‘The Dimensions of International Equity Style,’’ Journal of Investing (Spring 1998). W. Scott Bauman, Mitchell C. Conover, and Robert E. Miller, ‘‘Growth versus Value and Large-Cap versus Small-Cap Stocks in International Markets,’’ Financial Analysts Journal (March/April 1998): 75–89.
Expanding Global Models to Incorporate Size Premium and Company-Specific Risk
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COMPANY-SPECIFIC RISK FACTOR The notion that the only component of risk that investors care about is market or systematic risk is based on the assumption that all unique or unsystematic risk can be eliminated by holding a perfectly diversified portfolio of risky assets that will, by definition, have a beta of 1.0. But you need to determine if company-specific risk factors are appropriate. Are there risks that will increase the variability of expected cash flows beyond the market/industry, country, and size factors we have addressed? The company-specific risk factor could be negative if the analyst concluded that the subject company was less risky than the average of the other companies from which the proxy estimates for the other elements of the cost of equity capital were drawn. For example, a company could have a well-protected, above-average price for its products as a result of a license to operate from the local country government, resulting in significantly less earnings volatility than experienced by its competitors. But in emerging markets, another risk factor enters the equation: the risk of expropriation. Is adding a political risk adjustment double counting other risks? Certain industries or ownerships (e.g., controlled by nonlocal country owners) may be considered politically sensitive from time to time within a specific country, increasing the risks of expropriation for that specific industry or company. For example, the Russian government has used its controlling interest in certain energy companies to effect expropriations of other energy companies. You should adjust the expected cash flows for this possible outcome. But quantifying expropriation possibilities explicitly can be ‘‘politically’’ imprudent at times; then you need to adjust the cost of capital only to be consistent with the probability of expropriation. For example, assume that in case 1 you determine the cash flows and present value of cash flows without consideration of expropriation. Case 1: No Political Risk Cash flow ¼ $100 next year if no expropriation
klocal ¼ 10% PV ¼ $100/(1.10) ¼ $90.91
In case 2 you adjust the expected cash flows for the 5% risk of expropriation. But this creates greater variability in the cash flows and requires a greater cost of capital. Case 2: 5% Chance of Expropriation ($0 Cash Flow) Expected cash flow ¼ ð:95Þ$100 þ ð:05Þ$0 ¼ $95
klocal ¼ 14% due to greater risk (variability) of cash flows PV ¼ $95=ð1:14Þ ¼ $83:33
Finally we can determine the cost of capital that is equivalent to the value resulting in case 2. That cost of capital adjusts for the risk of expropriation (increased variance of expected cash flows) without highlighting the issue specifically. Case 3: Case 2 Assumptions Applied to Case 1 Cash Flows
PV ¼ $100=ð1 þ klocal Þ ¼ $83:33 klocal ¼ 20% ¼ Imputed local country cost of equity capital
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Alternatively, you can obtain the cost of insurance from organizations providing political risk insurance; for example, the Overseas Private Investment Corporation, the Multilateral Investment Guarantee Agency, or the commercial insurance broker AON sell insurance to insure for risks of currency transfer, expropriation/contract infringement, and war and civil disturbance. Their premiums often are stated as a percent of invested capital or project value (equivalent to adding onto the discount rate). An example of the cost might be in the range of 2% of capital invested for risks in local countries with average credit ratings of approximately Ba2.
EXPANDED COST OF CAPITAL FORMULA If we expand the models to also reflect the size effect and specific risk, we can expand the cost of equity capital formula to add these two factors. For example, if we expand Formula 18.3, we get: (Formula 18.9)
klocal ¼ R f ;u:s: þ ½Bu:s: RPu:s: ðs local =s u:s: Þ þ RPs þ RPu where:
Bu.s.
klocal ¼ Discount rate for equity capital in local country Rf,u.s. ¼ U.S. risk-free rate RPu.s ¼ Risk premium appropriate for a U.S. company in similar industry as the subject company in the local country slocal ¼ Volatility of local country stock market su.s. ¼ Volatility of U.S. stock market RPs ¼ Risk premium for small size RPu ¼ Risk premium attributable to the specific company (u stands for unique or unsystematic risk). (See notes accompanying previous formulas.)
Note that the only difference between this formula and an international version of the build-up method formula is the addition of the beta coefficient. (See notes accompanying previous formulas.)
SHOULD PROJECTED CASH FLOWS AND THE COST OF CAPITAL BE NOMINAL OR REAL? In the models presented, we have developed nominal cost of capital estimates in that they reflect future expectations of inflation. Therefore, expected cash flow forecasts need to match; they need to reflect expected inflation. Some recommend using real cash flows (expected inflation removed) and discounting those cash flows using a cost of capital estimate with inflation removed. The consistency between cash flow forecasts and cost of capital estimates is not sufficient to get identical results (using nominal or real).23 In many instances using real cash flow forecasts and real discount rates results in an error in the concluded value. For example, taxable income on which income taxes is based most often on 23
Joseph Tham and Ignacio Velez-Pareja, ‘‘Top 9 (Unnecessary and Avoidable) Mistakes in Cash Flow Valuation,’’ Working paper, January 29, 2004.
Data Sources
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historical capital expenditures. Rarely is it correct to equate future depreciation with future capital expenditures.24 Tax credits for investment often are based on the amount of original investments. However, in countries where there is rampant and predictable inflation, denominating both the cash flows and discount rate in real terms may be the only reasonable alternative.
CAPITAL STRUCTURE Do comparable firms in different countries have comparable debt to equity ratios? In one study the authors find that the firm-specific factors (such as assets and profitability) determining the amount of leverage differ across countries.25 They also find that country-specific factors (such as better law enforcement systems and a healthy economy) also impact differences in leverage of all firms within those countries with positive factors compared to those with negative factors.
SUMMARY When you use the market approach of valuation, you are observing the market’s assessment of country risks (to the extent that they are priced risks). Country risk premiums sometimes appear to be the only plausible way to reconcile value indications from the market and income approaches. In today’s economy, there is often little theoretical justification for large country risk premiums. Such risk premiums must be carefully documented and address the risks inherent in the business mix of the subject company. Expect estimates of country risk premiums to have large standard errors. Real risk-adjusted free-market interest rates do not differ across countries for extended periods and generally not over the long horizons of most discounted cash flow valuation analyses. This fact has been empirically documented for large economies. From a theoretical perspective, discrete ‘‘event’’ risks, such as political risk, ideally should be reflected in the expected cash flows. Any systematic country risk should be treated in the discount rate, but there is no foolproof way to estimate the premium. Do not expect to be highly confident in your estimate of the country risk premium. Whenever possible, treat country considerations in the cash flow projections, and avoid allowing the discount rate to be a repository for fudge factors. We have included a list of data sources and references for additional reading for those interested in this evolving topic.
DATA SOURCES Political Risk Services (PRS) www.prsgroup.com Country report for 100 countries International country risk guides 24
25
Daniel L. McConaughy and Lorena Bordi, ‘‘The Long Term Relationships between Capital Expenditures and Depreciation across Industries: Important Data for Capitalized Income-Based Valuations,’’ Business Valuation Review (March 2004); Brant Armentrout, ‘‘A Sanity Test When Estimating Capital Expenditures in Excess of Depreciation,’’ Business Valuation Review (September 2003): 136–141. Abe de Jong, Rezaul Kabir, and Thuy Thu Nguyen, ‘‘Capital Structure Around the World: The Roles of Firm and CountrySpecific Determinants,’’ ERIM Report Series Research in Management (September 2007).
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Country data including ICRG Risk Rating Political Risk Yearbook Handbook of Country and Political Risk Analysis Country forecasts (semiannual for 100 countries) Standard & Poor’s www.sandp.com Ratings Yields and spreads Market Insights: Japan, Pacific Market, European Market, Asian Market, Canadian Market, Emerging Markets Industry Surveys Valordata Browser: global security information access for stocks, bonds, and derivatives Moody’s www.moodys.com Ratings Yields and spreads Institutional Investor www.institutionalinvestor.com Euromoney www.euromoney.com
ADDITIONAL READING Ammer, John, and Jon W. ‘‘Cash Flows and Discount Rates, Industry and Country Effects and Co-Movement in Stock Returns.’’ Financial Review (May 2007). Barnes, Mark A., Anthony Bercel, and Steven H. Rothmann, ‘‘Global Equities: Do Countries Still Matter,’’ Journal of Investing (Fall 2001): 43–48. Bruno, Solnik, Robert D. Arnott, Mark P. Kritzman, and Richard M. Levich, ‘‘Currency Risk in Investment Portfolios,’’ CFA Institute (AIMR) (June 1999). Budyak, ‘‘Developing Discount Rates in a Global Environment,’’ Valuation Strategies (January/February 2006 and May/June 2001). ______. ‘‘Getting Your Head Out of the Model: Due Diligence and Developing International Cost of Capital,’’ Business Valuation Update (May 2006): 5–8. ______. ‘‘Developing Discount Rates in a Global Environment.’’ Proceedings from the Sixth Joint Business Valuation Conference of the CICBVand the ASA, Toronto, October 19–20, 2006; The Journal of Business Valuation (2007): 361–393. Cantor, Richard, and Frank Packer. ‘‘Determinants and Impacts of Sovereign Credit Ratings,’’ Economic and Policy Review (October 1996): 37–53. Cavaglia, Stefano, Chris Brightman, and Michael Aked. ‘‘The Increasing Importance of Industry Factors,’’ Financial Analysts Journal (September 2000). Dimson, Elroy, Paul Marsh, and Mike Staunton. Triumph of the Optimists: 101 Years of Global Investment Returns, Princeton, NJ: Princeton University Press, 2002. Erb, Claude, Harvey Campbell, and Tadas Viskanta ‘‘Country Risk in Global Financial Management,’’ The Research Foundation of The Institute of Chartered Financial Analysts (March 1997). Erb, Claude, Harvey Campbell, and Tadas Viskanta, ‘‘The Influence of Political, Economic and Financial Risk on Expected Fixed-Income Returns,’’ Journal of Fixed Income (June 1996).
Additional Reading
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______. ‘‘The Risk and Expected Returns of African Equity Investments,’’ Duke Finance Research. Estrada, Javier. ‘‘Discount Rates in Emerging Markets: Four Models and an Application,’’ Journal of Applied Corporate Finance (Spring 2007): 72–77. Flannery, Sean P. ‘‘EMU and the Bond Markets of Western Europe.’’ Credit Analysis Around the World, CFA Institute (AIMR) (June 1998): 10–17. Godfrey, Stephen and Ramon Espinoza. ‘‘A Practical Approach to Calculating Costs of Equity for Investments in Emerging Markets,’’ Journal of Applied Corporate Finance (Fall 1996): 80–89. Goetzmann, William, and Philippe Jorion. ‘‘A Century of Global Stock Markets,’’ Journal of Finance (June 1999): 953–980. Goodwin and Ross, ‘‘Has Europe Outgrown Its Countries?’’ Old Dominion University & European Financial Management Association (February 2001). Campbell Harvey, R. ‘‘Emerging Market Corporate Finance,’’ Fuqua School of Business, Duke University, Durham NC. ______. ‘‘International Value Creation,’’ Fuqua School of Business, Duke University, Durham N.C. and National Bureau of Economic Research. ______. ‘‘Predictive Risk and Return in Emerging Markets,’’ Review of Financial Studies (1995). ______. ‘‘Risk Analysis and Project Evaluation,’’ Duke Center for International Development at the Stanford Institute, May 27–28, 2002. Larson, David, ‘‘Africa and the Middle East,’’ Credit Analysis Around the World, CFA Institute (AIMR) (June 1998): 26–37. Lessard, Donald R. ‘‘Incorporating Country Risk in The Valuation of Offshore Projects.’’ Journal of Applied Corporate Finance (Fall 1996): 52–63. Myers, Randy, ‘‘GM Remeasures the Bar in Latin America,’’ CFO (May 1998). Pereiro, Luis E., Valuation of Companies in Emerging Markets: A Practical Approach, Hoboken, NJ: John Wiley & Sons, 2002. Pettit, Justin, Mack Ferguson, and Robert Gluck. ‘‘A Method for Estimating Global Costs: The Case of Bestfoods,’’ Journal of Applied Corporate Finance (Fall 1999): 80–90. Qin, Yan, and Sitikantha Pattanaik. ‘‘Measuring Cost of Capital- Credit Rating vs Global CAPM,’’ Economic and Political Weekly (September 2000) 3325–3334. Rosenburg, Michael R. Currency Forecasting: A Guide to Fundamental and Technical Models of Exchange Rate Determination, Irwin Professional Publishing, 1996. Sabal, Jaime. Financial Decisions in Emerging Markets, London: Oxford University Press, 2002. Scholtens, Bert. ‘‘On the Co-movement of Bond Yield Spreads and Country Risk Ratings,’’ Journal of Fixed Income (March 1999). Vasan, Ashwin. ‘‘Eastern Europe,’’ Credit Analysis Around the World, CFA Institute (AIMR) (June 1998): 18–25.
Chapter 19
Using Morningstar Cost of Capital Data Michael W. Barad and Tara McDowell As Edited by James Harrington Introduction Stocks, Bonds, Bills, and Inflation Cost of Equity Models Equity Risk Premium Firm Size Premium Industry Risk Premium Morningstar Data and Taxes Morningstar Data: Minority or Controlling Interest? Cost of Capital Yearbook Organization of Data Cost of Equity Models Capital Asset Pricing Model Fama-French 3-Factor Model Implied or Discounted Cash Flow Models Morningstar Beta Book Beta Estimation Methodologies Levered and Unlevered Betas Morningstar (Adjusted) Betas Peer Group and Industry Betas Cost of Capital Resources Web Site
Notation for This Chapter: The notation used in this chapter is that used in the Morningstar data sources discussed herein and may differ slightly from the notation used elsewhere in this book. There are, however, no conceptual discrepancies between equations in this chapter and similar equations elsewhere in this book.
INTRODUCTION Morningstar, Inc. acquired Ibbotson Associates in 2006, a financial software, data, consulting, and training firm headquartered in Chicago, Illinois. Established in 1977 by Roger Ibbotson, it is a leading provider of financial information to business valuation analysts, corporate finance professionals, and investment analysts. Morningstar produces four publications that valuation and corporate finance professionals at all levels have found useful in the estimation of the cost of capital for companies of various industries and sizes.
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STOCKS, BONDS, BILLS, AND INFLATION Morningstar’s original benchmark publication is the Stocks, Bonds, Bills, and Inflation (SBBI) Yearbook, first published in 1983. Commonly referred to as the Classic Edition, the SBBI Yearbook is based on Roger Ibbotson and Rex Sinquefield’s original 1976 study of long-term market analysis. This publication has become a staple in the field of finance and is updated annually. The SBBI Classic Yearbook is a leading source of historical market data, including data on the equity risk premium and firm size premium, market commentary, and other historical analyses of the capital markets. While the SBBI Classic Edition Yearbook served as the foundation for discount rate, capitalization rate, and cost of capital estimates for many years, the Stocks, Bonds, Bills, and Inflation Valuation Edition Yearbook has become the new standard for such valuation data. The SBBI Valuation Edition Yearbook was introduced in 1999 to address the growing data needs of the valuation profession. The Valuation Edition was originally authored by Michael Annin and Dominic Falaschetti and expanded greatly on the cost of capital data already presented in the Classic Edition by drawing primarily from the cost of capital workshops then held by Ibbotson Associates. The Valuation Edition not only presents data along with examples on how to use it, but also addresses topical issues and controversies with alternative calculation methods and new studies as they become available. The Valuation Edition focuses on the equity risk premium, size premium, industry premium, beta, and other issues related to the cost of capital. The Valuation Edition Yearbook has undergone many augmentations over the years, from introducing a discussion of Professor Roger Ibbotson’s paper on using a supply side model for estimating the equity risk premium in the 2004 edition, to the expansion from three- to four-digit Standard Industrial Classification (SIC) code industry premia with the 2005 edition. The 2005 edition had yet another enhancement: the availability of quarterly updates. The SBBI Valuation Quarterly Report supplements the Valuation Yearbook, which includes data through December, by providing valuation practitioners additional information calculated with data through March, June, and September. Updated risk-free rates and updated industry risk premia for approximately 500 SIC codes are included. In addition, estimate of the ‘‘key variables’’ (equity risk premia and size premia) from the most recent Valuation Yearbook are included for the user’s convenience. The main benefit of the quarterly updates is the ability to choose analysis calculated closer to the valuation date, making cost of capital estimates even more accurate and defensible. The Valuation Edition discusses current issues and controversies related to cost of capital and includes any of Morningstar’s advances in the field of cost of capital analysis. Some examples of such coverage presented only in the Valuation Edition would be the inclusion of industry premia for use in the build-up method and alternative measures of firm size premia, including a further breakout of the smallest companies (the tenth decile) into even smaller divisions (10a and 10b). While the Classic Edition still provides much useful information to the valuation industry in the form of capital market analysis and discussions on the performance of the economy, the Valuation Edition is critical to anyone performing cost of capital analysis using the income approach and has become the industry standard for such data. For this reason, it is the Valuation Edition that serves as the basis for the discussion in this chapter. COST OF EQUITY MODELS The cost of equity capital is equal to the expected rate of return for a firm’s equity. There are several widely used models for estimating cost of equity for a firm, the two most common being the build-up method and the Capital Asset Pricing Model (CAPM) (see Exhibit 19.1). Other methods, such as the
Stocks, Bonds, Bills, and Inflation Exhibit 19.1
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Build-up versus CAPM Cost of Equity Models
Build-up Model
Capital Asset Pricing Model (CAPM)
Risk-free Rate þ Equity Risk Premium þ Firm Size Premium þ Industry Risk Premium? ¼ Cost of Equity Estimate
Risk-free Rate þ (Equity Risk Premium Beta) þ Firm Size Premium ¼ Cost of Equity Estimate
Fama-French (FF) 3-factor model and the implied or discounted cash flow (DCF) model, are discussed later. The build-up method and the CAPM are very similar, with the major exception being the use of beta. The risk-free rate, equity risk premium, and firm size premium are components shared by both the build-up method and the CAPM. These models should provide very similar if not identical results if implemented correctly. Let us take a closely-held company as an example. For a closely-held company, there are no market data from which to derive a beta. Therefore, to use the CAPM, the analyst must use a beta from guideline companies. If we assume that the beta used in this example is an industry beta for the subject company’s industry, then both the build-up and CAPM models have a provision for including industry risk. Theoretically, the industry premium in the build-up model and the industry beta used in the CAPM should lead both models toward identical results. Exhibit 19.1 compares the build-up versus CAPM cost of equity models. EQUITY RISK PREMIUM The equity risk premium is defined as the additional return investors expect to receive to compensate for the additional risk associated with investing in equities as opposed to risk-free assets. The equity risk premium is a critical component of many of the cost of equity models, including the build-up method, CAPM, and FF 3-factor model. While the equity risk premium (ERP) has many uses in the field of finance, for the purpose of business valuation, it should be a forward-looking measure of what investors can expect. Unfortunately, a forward-looking measure of the ERP is not directly observable in the market. The most common way of capturing expectations on the ERP is to measure the historical relationship of stocks to bonds. It is in measuring this historical relationship that such choices as benchmark selection, the appropriate range of data, and using arithmetic versus geometric averages become important decisions. Morningstar estimates the ERP by calculating the arithmetic average total return on the Standard & Poor’s (S&P) 500 Index over the arithmetic average income return on the appropriate horizon U.S. government security. ERP estimates are estimated for short-, intermediate-, and long-term horizons (30 days, 5 years, and 20 years, respectively). Since most companies do not have a defined life span and are valued as going concerns, the long-term discount rate typically is most appropriate for business valuation purposes. The appropriate horizon should be a function of the investment, not the investor. To estimate the long-horizon ERP, Morningstar calculates the arithmetic average total return on the S&P 500 less the arithmetic average income return on long-term U.S. government bonds using annual data from 1926 to the present. Price return (and ultimately total return) for a bond is sensitive to changes in interest rates and can lead to gains or losses. For the purpose of estimating the ERP, income return from a bond better represents the truly risk-free portion of the bond’s return.
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Cost of Capital
Choosing the components that comprise the estimated ERP is one of the first critical decisions. Morningstar has chosen the S&P 500 to represent the stock market and a 20-year bond to represent the risk-free asset. For stock market representation, other common benchmarks are the New York Stock Exchange (NYSE) Composite Index and NYSE 1-2 index (largest 20% of stocks by market capitalization traded on the NYSE). While the Dow Jones Industrial Average is a common investment reference for the market, it is too narrow for ERP calculation. Morningstar presents ERP estimates using both the S&P 500 and the NYSE 1-2 market benchmarks. However, the S&P 500 is most used throughout Morningstar publications because it represents a large sample of companies across a large sample of industries and is also one of the most widely known and accepted market benchmarks. All things considered, Morningstar believes that the S&P 500 is a good measure of the equity market as a whole. Morningstar’s methodology for estimating the long-horizon ERP makes use of the income return on a 20-year Treasury bond; however, the Treasury currently does not issue a 20-year bond. The 30-year bond that the Treasury recently began issuing again is theoretically more correct due to the long-term nature of business valuation, yet Morningstar instead creates a series of returns using bonds on the market with approximately 20 years to maturity. The reason for the use of a 20-year maturity bond is that 30-year Treasury securities have been issued only over the relatively recent past, starting in February of 1977, and were not issued at all through the early 2000s. The 10-year Treasury bond is not used for much the same reason: A long enough history of market data is not available for 10-year bonds. Morningstar has persisted in using a 20-year bond to keep the basis of the time series consistent. The SBBI equity risk premium covers the time range from 1926 to present. The original data source for the raw data series comprising the ERP is the Center for Research in Security Prices (CRSP) at the University of Chicago. The CRSP chose 1926 as a starting date for its data series because this is when good-quality financial data became available. This period was chosen also because it includes one full business cycle before the 1929 market crash. While Roger Ibbotson and other researchers have published data back to the early nineteenth century, these data are not of the same quality as the data that began in 1926. In basic terms, these are the main reasons why Morningstar uses a range back to 1926 in its historical risk premium calculations. The period from 1926 to the present is most relevant because it includes a number of different economic scenarios. Some practitioners argue for a shorter historical period, such as the last 20 or 30 years. This argument is based on the assumption that investors only factor in a more recent economic climate into their expectations and that ‘‘unusual’’ economic events prior to recent times are not likely to repeat in the future. However, all periods contain unusual events, some of which took place most recently. For example, the inflation of the late 1970s and early 1980s, the October 1987 market crash, the collapse of the Soviet Union, the development of the European Economic Community, and the September 2001 terrorist attacks on the United States are but a few of the ‘‘unusual’’ events that occurred in recent times. While we do not expect these events to occur again in the future, they are representative of the type of events that can occur unexpectedly and have massive effects on the economy. Focusing on a shorter historical date range would magnify the effect of the most recent unusual events. Using a longer range of data places less emphasis on each event and better captures long-term performance. By including market data measured over the entire set of economic scenarios available, Morningstar believes that the resulting computations can better anticipate similar events in the future. The equity risk premium estimate presented by Morningstar is an arithmetic average risk premium, as opposed to a geometric average risk premium. Morningstar believes that arithmetic averages are appropriate for use in discounting future cash flows. A geometric average is better for reporting past performance since it represents the compound average return. Mathematically, the arithmetic mean assumes that the cash flow being discounted each period is the expected value of the probability distribution of possible outcomes for that period.
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Arithmetic averages better incorporate the volatility in a data series. Take bonds and stocks as an example. Bonds have lower volatility than stocks, on average. When comparing the arithmetic mean with the geometric mean for each asset class, the difference between arithmetic and geometric will be greater for the asset class with higher volatility. The arithmetic mean captures the volatility of a time series. Since the historical risk premiums are a volatile data set and we are using it in a forwardlooking capacity, the arithmetic average will better capture the uncertainty associated with the ERP. In general terms, arithmetic averages are better forward-looking point estimates, and geometric averages are better for historical analysis of a defined data range. Numerous alternatives to using pure historical data for estimating the equity risk premium bear discussion. A few of these methods for estimating ERP are:
Use of survey results
Exponential weighting of historical periods
Supply-side perspective
The first of these alternatives takes the approach that a survey of ERP expectations from the appropriate people will yield more useful information. Typically, the survey is conducted on academics, money managers, or other professionals deemed to have an educated idea on the direction of the market. The difficulty in relying on this method stems from the subjective nature of the ‘‘opinions’’ submitted by the participants, along with a bias for participants to form estimates based heavily on the current economic condition. For those who struggle with the appropriate time period to use in their historical ERP calculation, exponential weighting offers a solution. Using an exponential weighting scheme to average historical data allows for more importance to be placed on current data (compared with an equal weighting scheme). Of course, this assumes that an unbiased reason exists for assuming that the future will bring with it an economic climate more similar to that of recent periods. The last alternative to estimating the ERP is the supply-side model. This method estimates what the economy can supply going forward as opposed to its actual historical performance. In general, research has shown that the supply-side estimate is lower than the historical estimate, indicating that the market cannot supply the type of long-term growth that it has demonstrated to date. All of the alternatives to estimating ERP have advantages and disadvantages. For cost of capital analysis, it is important that all of the cost of equity components are developed so they can work together in a model. If using a size premium, industry premium, or any other addition to the cost of equity, it is imperative that all of the components be on the same basis. For example, the time period and weighting scheme of the ERP and size premium should be identical. Similarly, both components should be from either a historical perspective or a supply side perspective. Consistency is a critical attribute in cost of capital analysis.
FIRM SIZE PREMIUM The relationship between firm size and return is one of the most remarkable discoveries of modern finance. This relationship cuts across the entire size spectrum but is most evident among smaller companies. While many studies have examined the size effect, Morningstar is the most cited source of size premium data as published in both the SBBI Classic Edition Yearbook and the SBBI Valuation Edition Yearbook. What is the firm size premium? Historically, small stocks have shown greater risk and greater return than their larger-capitalization counterparts. This makes perfect sense since investors will
336
Cost of Capital
demand higher return to compensate for increased risk. If small stocks did not provide a higher return to compensate for this risk, there would be no demand to invest in them. To capture the additional return exhibited by smaller stocks, we calculate a size premium that can be used as an addition to either the CAPM or the build-up model of estimating cost of equity. The first point worth noting is the evolution of Morningstar’s size premium and the difference between what is presented in the Classic Edition and Valuation Edition yearbooks. Through the 1994 yearbook, the Classic Edition simply presented what Morningstar calls the small-stock premium. The small-stock premium was measured as the simple difference between Morningstar’s Small Company Stock series and the S&P 500 total returns. The Small Company Stock series is a representation of publicly traded micro-cap stocks. Beginning in 1995, the SBBI Classic Edition presented a chapter on firm size that analyzed the small-stock effect across all 10 deciles of the stock market. At this point the CRSP data for companies traded on the NYSE was used in the firm size analysis. At the same time that data was introduced for all 10 deciles, a new method for measuring the size effect was introduced. This new method was calculated as the return in excess of what CAPM predicts given the beta for a decile, otherwise known as a beta-adjusted size premium. In 1999 the first SBBI Valuation Edition Yearbook was introduced, which was created to address current topics relating primarily to cost of capital analysis and to present advances made in this field. While both yearbooks contain a firm size chapter, the Valuation Edition has much more extensive coverage and analysis on the topic of firm size. The remainder of this section discusses some of the coverage offered in the Valuation Edition. The Valuation Edition Yearbook has continued to present advances in firm size analysis since its inception in 1999. Beginning with the 2001 edition, the yearbook revised all size premium calculations to include the population of stocks traded on the NYSE, American Stock Exchange (AMEX), and Nasdaq Stock Market. The AMEX and Nasdaq securities were added to the analysis to capture the performance of the many small stocks traded on these exchanges. The NYSE is used to create the breakpoints that define the deciles, to which AMEX and Nasdaq securities of similar size are then added. Also in the 2001 edition, size premia were added for deciles 10a and 10b. This breakout of the tenth decile into two components allows for further analysis of the smallest companies. Additional statistics relating to 10a and 10b were presented beginning in the 2002 yearbook. Exhibit 19.2 is a graph from the SBBI Valuation Edition 2006 Yearbook showing the actual returns achieved by the 10 deciles and the security market line on which the CAPM would predict the portfolios would fall. If the CAPM were functioning properly, all of the decile portfolios would fall directly on the line indicated on the graph. Instead, most of the deciles fall above the security market line, indicating that the CAPM underreports cost of equity for all but the largest companies. The vertical space between a decile and the security market line is the graphical representation of the size premium. This premium must be added back into the cost of equity to fully explain the returns of all but the largest companies. Exhibit 19.3 is a table from the SBBI Valuation Edition 2006 Yearbook detailing the calculation of the size premium for each decile. In addition to the 10 deciles, this table also presents size premia for the mid-, low-, and micro-cap size groupings for consolidation and generalization purposes. The first column of data next to the decile names represents the beta for each decile measured against the S&P 500 market benchmark. The next two columns show the actual historical returns and returns in excess of the risk-free rate for each decile. The second-to-last column represents the return predicted by CAPM in excess of the risk-free rate. This is calculated as beta multiplied by the equity risk premium. The last column shows the size premia, which is the difference between the actual returns (minus the risk-free rate) and the returns predicted by CAPM (minus the risk-free rate). As companies get smaller, their beta and CAPM-predicted return increase; however, beta does not fully explain the greater returns of these smaller companies, and a size premium must be added to complete the model.
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25%
Arithmetic Mean Return
10 20% 67 45 23
15% 1
9
S&P 500
10% 5%
8
Riskless Rate
0% 0
Exhibit 19.2
0.2
0.4
0.6
0.8 Beta
1
1.2
1.4
1.6
Security Market Line versus Size-Decile Portfolios of the NYSE/AMEX/NASDAQ (1926–2005)
Source: Stocks, Bonds, Bills, and Inflation1 Valuation Edition 2006 Yearbook. Copyright # 2006 Morningstar, Inc. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) To purchase copies of the Valuation Edition Yearbook, or for more information on other Morningstar publications, please visit global.morningstar.com/DataPublications. Calculated (or derived) based on CRSP1 data, Copyright # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago.
Exhibit 19.3 Returns in Excess of CAPM with Tenth-Decile Split Long-term Returns in Excess of CAPM Estimation for Decile Portfolios of the NYSE/AMEX/NASDAQ, with 10th Decile Split, 1926–2005
Decile
Beta*
Arithmetic Mean Return
1-Largest 2 3 4 5 6 7 8 9 10a 10b-Smallest Mid-Cap, 3–5 Low-Cap, 6–8 Micro-Cap, 9–10
0.91 1.04 1.10 1.13 1.16 1.18 1.23 1.28 1.34 1.43 1.39 1.12 1.22 1.36
11.29% 13.22% 13.84% 14.31% 14.91% 15.33% 15.62% 16.60% 17.48% 19.71% 24.87% 14.15% 15.66% 18.77%
Realized Return in Excess of Riskless Ratey
Estimated Return in Excess of Riskless Ratez
Size Premium (Return in Excess of CAPM)
6.07% 8.00% 8.62% 9.09% 9.69% 10.11% 10.40% 11.38% 12.26% 14.49% 19.65% 8.94% 10.44% 13.55%
6.45% 7.33% 7.77% 7.98% 8.20% 8.38% 8.73% 9.05% 9.50% 10.10% 9.82% 7.91% 8.63% 9.61%
0.37% 0.67% 0.85% 1.10% 1.49% 1.73% 1.67% 2.33% 2.76% 4.39% 9.83% 1.02% 1.81% 3.95%
* Betas are estimated from monthly portfolio total returns in excess of the 30-day U.S. Treasury bill total return versus the S&P 500 total returns in excess of the 30-day U.S. Treasury bill, January 1926–December 2005. y Historical riskless rate is measured by the 80-year arithmetic mean income return component of 20-year government bonds (5.22%). z Calculated in the context of the CAPM by multiplying the equity risk premium by beta. The equity risk premium is estimated by the arithmetic mean total return of the S&P 500 (12.30%) minus the arithmetic mean income return component of 20-year government bonds (5.22%) from 1926–2005.
Source: Stocks, Bonds, Bills, and Inflation1 Valuation Edition 2006 Yearbook. Copyright # 2006 Morningstar, Inc. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) To purchase copies of the Valuation Edition Yearbook, or for more information on other Morningstar publications, please visit global.morningstar.com/DataPublications. Calculated (or derived) based on CRSP1 data, Copyright # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago.
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Cost of Capital
Should these beta-adjusted size premia be used in both the CAPM and the build-up models for cost of equity analysis? Yes. The size premia calculated in SBBI are constructed within the context of CAPM. It is clear that this type of size premium can be used as an addition to the CAPM cost of equity. More debate surrounds the use of this data for addition to the build-up model. Some practitioners argue that the non–beta-adjusted, or simple excess return, method should be used instead. Morningstar believes that the beta-adjusted size premia constructed within the context of CAPM are appropriate for build-up use. But this will lead to a difference between estimates of the cost of equity capital based on the build-up model and the CAPM unless the industry risk premium also is included in the build-up model. In the CAPM, an adjustment for different types of risk (i.e., industry risk) are included in the beta measure. In the build-up model, beta is absent, and these additional risk factors must be added directly to the model in the form of risk premia. Many practitioners add a company-specific risk premium to the build-up model. The beta-adjusted size premium should be used in the build-up model because it makes no assumptions about the risk of the company by isolating the return due solely to size. The return due to beta (risk) for each decile has been removed from the actual returns to leave a size premium that is absent of risk assumptions. As mentioned, this risk is accounted for in the CAPM through the use of beta. In the build-up model, the risk that has been removed from the size premium calculation may be added back in through the use of other risk premia. This method for isolating size only in the size premium and accounting for other risk factors by using industry premia, company-specific premia, and the like presents a very clean model for estimating cost of equity. It also reduces the likelihood of double-counting risk factors. If you were to use a simple excess return small stock premium, you would be assuming that the beta of the subject company is the same as the beta of all small companies in the index. This contradicts the nature of most analysis to add or subtract risk premia to the model and assumes that there is no adjustment for industry risk. By using an excess return size premium such as this along with something like an industry premium, there is a high likelihood of double-counting risk factors. For the reasons presented here, Morningstar believes that the beta-adjusted size premia are appropriate for application to the CAPM and build-up models. In addition to the size premia presented in Exhibits 19.2 and 19.3, Morningstar publishes a variety of variations and additions to the analysis in its SBBI Valuation Edition Yearbook. Some of the additional information is meant to demonstrate that the size premium still exists even when altering the data in a number of ways suggested by critics, while other data add options for cost of equity analysis. Morningstar repeats the size premium graph and table:
Using the NYSE market benchmark instead of the S&P 500 Calculated with sum betas instead of raw ordinary least squares (OLS) betas Calculated with annual betas instead of monthly With the tenth decile split into 10a and 10b
All of the variations on the firm size analysis support the addition of a size premium for the smallest stocks. A common question among practitioners is whether to use the micro-cap decile, tenth decile, or 10a/10b split for analysis of the smallest companies. For example, say that we are analyzing a very small company whose market capitalization (or equivalent) would place it into the 10b size grouping. A company of this size also fits into the tenth decile and micro-cap aggregation of the ninth and tenth deciles. Which one should be used? Morningstar feels that this is up to the practitioner to determine, but suggests consistency across valuation assignments.
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INDUSTRY RISK PREMIUM Both the CAPM and build-up models should take the characteristics of the subject company’s industry into account when determining cost of equity. The CAPM has the ability to incorporate industry risk into the beta measure. For the build-up model, valuation practitioners often add an industry premium or incorporate industry risk into a company-specific premium. Prior to 2000, the formation of industry premia for use in the build-up model was not quantitative in nature. Since 2000, however, Morningstar has published industry premia for use in the build-up model in its SBBI Valuation Edition Yearbook. Initially Morningstar presented data on over 60 industries organized by two-digit SIC required; currently it publishes approximately 450 industry risk premia down to the four-digit level. The method Morningstar uses to form industry risk premia relies on the full-information beta estimation process outlined later in the Beta Book section. The full-information beta methodology uses data from all companies that participate in an industry to determine the risk characteristics of that industry. The approach provides a risk index for each industry that can be used to compare the risk level of the industry with that of the market as a whole. The industry risk premium methodology uses the equation shown in Formula 19.1: (Formula 19.1) IRPi ¼ ðRIi ERPÞ ERP where: IRPi ¼ Expected industry risk premium for industry i, or amount by which investors expect the future return of the industry to exceed that of the market as a whole (seen elsewhere in this book as RPi) RIi ¼ Risk index (full-information beta) for industry i ERP ¼ Expected equity risk premium For an industry with a risk index of 1.0 (the same as that of the market), the expected industry risk premium would be 0. For those industries with a risk index greater than 1.0, the industry premium will be positive; for those with a risk index less than 1.0, it will be negative. The industry risk premium can in fact be a negative number that actually must be subtracted from the cost of equity. This makes sense, since just as many industries should have less risk than the market as those that have more risk. Also remember that the beta-adjusted size premium is more appropriate than the simple excess returns size premium to use in conjunction with an industry premium. The systematic risk removed from a beta-adjusted size premium can be replaced by the risk included in the industry premium as a better measure of systematic risk. Although Morningstar started publishing IRP data with the SBBI Valuation Edition 2000 Yearbook, the ‘‘IRP Company List’’ was not created until the SBBI Valuation Edition 2003 Yearbook. The IRP Company List is a listing of all companies used to form the industry risk premia published in table 3-5. This report is available for the 2003, 2004, 2005, 2006, 2007 SBBI Valuation Edition Yearbooks and is also available for each of the SBBI Valuation Quarterly Updates from March 2005 to present. An example of the SBBI Valuation Quarterly Update is shown as Exhibit 19.4. These reports are available online from the SBBI Valuation Edition 2005 Yearbook on at corporate. morningstar.com.
MORNINGSTAR DATA AND TAXES All of the risk premium statistics presented in any Morningstar publication are derived from market returns earned by an investor. An investor receives dividends and realizes price appreciation after the
340
Exhibit 19.4
Cost of Capital
Sample of the SBBI Valuation Quarterly Update
Stocks, Bonds, Bills, and Inflation Valuation Update Data through September 2005 Cost of equity models Two primary methods for calculating the cost of equity Buildup model
Capital asset pricing model (CAPM)
Risk-free rate þ Equity Risk Premium þ Firm Size Premium þ Industry Risk Premium
Risk-free rate þ Equity Risk Premium Firm or Industry Beta þ Firm size Premium
¼ Cost of equity
¼ Cost of equity
Risk-free rate The risk-free rate is the starting point of the buildup method and the CAPM. Recent Treasury yields for longterm (20-year) government bonds are: January 2005 February 2005 March 2005 April 2005 May 2005 June 2005
4.65% 4.79% 4.88% 4.61% 4.40% 4.29%
July 2005 August 2005 September 2005
4.56% 4.32% 4.64%
Equity risk premium Historical long-horizon equity risk premium 1926–2004 Supply-side equity risk premium 1926–2004
7.17% 6.14%
Size premium 1926–2004 The long-term returns in excess of CAPM estimation for decile portfolios of the NYSE/AMEX/NASDAQ
Decile Mid-Cap, 3–5 Low-Cap, 6–8 Micro-Cap, 9–10 Breakdown of Deciles 1–10 1-Largest 2 3 4 5 6 7 8 9 10-Smallest Breakdown of the 10th Decile 10a 10b
Market capitalization of smallest company (in millions)
Market capitalization of largest company (in millions)
Size premium (return in excess of CAPM)
$1,607.931 $506.410 $1.393
$6,241.953 $1,607.854 $505.437
0.95% 1.81 4.02
$14,099.878 $6,258.530 $3,473.335 $2,234.146 $1,607.931 $1,098.284 $746.249 $506.410 $262.974 $1.393
$342,087.219 $14,096.886 $6,241.953 $3,464.104 $2,231.707 $1,607.854 $1,097.603 $746.219 $505.437 $262.725
0.37 0.60 0.75 1.07 1.44 1.75 1.61 2.36 2.86 6.41
$144.122 $1.393
$262.725 $143.916
4.54 9.90
Stocks, Bonds, Bills, and Inflation
Exhibit 19.4
341
(Continued)
Industry risk premium Data through September 2005 Note: The industry risk premium table presented below can be used to locate the appropriate industry adjustment to make in your cost of equity estimation. To use this table, simply locate the SIC code that corresponds to the subject company you are valuing and apply the corresponding industry risk premium. To find the description for each SIC code, please refer to the Stocks, Bonds, Bills and Inflation Valuation Edition 2005 Yearbook. SIC Code
# of Co’s*
01 017 02 08 10 12 122 1220 13 131 132 138 1381 1382 1389 14 15 152 1521 153 154 16 162 1623 1629 17 171 173 179 1799 20 201 2015 203 2033 204 289 2899 29 291 299
11 6 7 5 12 18 18 10 175 141 6 42 22 8 16 14 35 9 6 23 5 22 19 10 8 33 8 10 10 6 118 11 5 15 6 14 25 17 22 14 6
Industry Premium 3.45% 1.07% 6.36% 7.41% 4.69% 0.17% 0.12% 3.28% 2.79% 3.64% 6.67% 1.45% 1.03% 6.07% 1.97% 2.58% 1.05% 0.76% 1.83% 0.92% 3.15% 2.36% 2.18% 9.20% 1.10% 2.35% 1.77% 8.01% 1.62% 3.27% 5.18% 2.90% 1.96% 5.70% 5.97% 6.55% 0.33% 1.05% 2.97% 2.88% 2.14%
SIC Code 205 2051 2064 207 208 2084 2086 209 21 211 22 221 227 23 230 232 2329 233 2330 24 241 242 2421 243 245 2451 2452 25 251 2511 2512 252 253 26 261 262 3443 346 347 3479 348
# of Co’s* 11 5 7 5 30 8 13 21 7 5 23 6 6 52 11 16 8 16 7 34 8 12 10 5 12 7 5 29 13 5 5 6 5 49 5 15 13 9 9 6 7
Industry Premium
SIC Code
# of Co’s*
Industry Premium
2.03% 2.06% 3.06% 3.08% 4.67% 5.37% 4.44% 4.77% 2.96% 5.53% 5.84% 5.72% 3.25% 1.10% 0.75% 0.57% 0.40% 0.96% 0.25% 3.10% 6.86% 3.72% 2.03% 0.97% 8.61% 12.29% 1.67% 0.21% 0.61% 0.28% 2.96% 0.77% 1.00% 4.59% 3.26% 5.63% 2.07% 1.26% 6.44% 3.30% 7.14%
263 265 267 2671 2672 27 271 272 273 2731 2741 275 2750 2759 28 281 2812 2813 2816 2819 282 2821 2824 283 2833 2834 2835 2836 2842 2844 285 286 2869 287 2870 2879 3594 36 361 3612 362
9 6 25 6 11 76 18 16 10 9 13 15 7 6 447 43 8 5 5 26 35 23 11 293 11 148 56 88 13 25 11 24 17 17 5 10 6 470 11 7 34
1.92% 0.99% 3.24% 3.20% 2.85% 2.89% 4.17% 12.33% 5.48% 4.27% 3.79% 2.89% 2.98% 1.80% 2.66% 1.80% 1.43% 2.36% 3.50% 1.21% 0.59% 2.72% 10.60% 2.03% 3.09% 2.58% 2.89% 0.86% 5.91% 6.16% 2.20% 0.48% 0.56% 0.03% 0.60% 0.27% 1.23% 8.41% 0.40% 6.05% 1.82% (Continued )
342
Cost of Capital
Exhibit 19.4
(Continued)
SIC Code
# of Co’s*
Industry Premium
SIC Code
# of Co’s*
Industry Premium
SIC Code
# of Co’s*
Industry Premium
30 301 306 3069 308 3081 3089 31 314 3140 3143 32 322 3241 327 3273 33 331 3312 3316 3317 333 335 3351 3354 339 34 341 3411 3423 3429 343 344 3441 3442 3728 379 3799 38 382 3821 3823 3824 3825 3826 3827 3829 384 3841
81 5 8 7 62 10 38 24 16 5 5 43 6 5 13 9 84 36 20 7 8 9 30 5 5 6 108 6 6 6 8 7 32 6 5 24 9 6 390 151 11 25 5 37 35 14 28 202 56
1.89% 3.32% 4.47% 5.20% 0.31% 2.34% 0.97% 1.67% 0.84% 0.44% 7.27% 2.41% 3.91% 5.03% 0.73% 0.03% 7.16% 4.29% 5.52% 1.46% 3.98% 1.51% 9.72% 1.04% 11.02% 0.03% 6.90% 1.33% 0.43% 4.21% 5.26% 4.81% 1.11% 3.17% 0.31% 1.28% 4.16% 1.60% 3.00% 4.38% 6.74% 2.04% 3.71% 9.79% 1.92% 10.44% 1.00% 4.63% 4.95%
349 3499 35 351 3511 3519 352 3523 353 3531 3533 354 3541 3546 355 3555 3559 356 3561 3562 3563 3564 3565 3569 357 3571 3575 3576 3577 3578 3579 358 3585 3589 359 4512 4522 46 47 472 4724 473 48 481 4812 4813 483 4832 4833
24 9 370 12 5 7 12 10 38 9 20 22 6 6 59 7 49 63 12 6 7 13 5 14 144 24 5 39 42 9 5 39 22 16 14 20 9 8 32 6 5 20 172 79 34 59 45 19 32
0.24% 3.23% 5.83% 0.32% 4.63% 2.51% 1.69% 2.46% 0.11% 0.61% 0.48% 0.45% 0.20% 0.38% 10.86% 8.54% 10.97% 0.36% 0.16% 2.56% 2.05% 2.42% 1.17% 0.66% 7.78% 4.07% 0.28% 10.30% 7.33% 3.01% 1.96% 2.62% 2.02% 3.39% 3.87% 2.54% 5.70% 4.65% 1.47% 1.54% 1.17% 1.82% 1.81% 0.91% 4.59% 1.75% 6.64% 12.12% 4.38%
3621 3625 3629 363 3634 364 3643 3644 3646 365 3651 366 3661 3663 3669 367 3672 3674 3678 3679 369 3691 3692 3694 3699 37 371 3711 3713 3714 3715 3716 372 3721 3724 507 508 5084 5085 5088 509 5093 5094 51 511 5112 512 513 514
16 9 8 13 7 23 8 5 5 16 15 157 43 83 34 209 20 125 8 48 35 6 5 6 17 132 71 10 5 46 5 8 40 10 9 13 28 11 6 5 20 8 5 115 10 8 18 7 19
1.22% 2.50% 6.76% 1.93% 6.02% 0.60% 0.97% 3.07% 0.80% 4.22% 4.20% 5.89% 10.89% 4.12% 6.27% 10.87% 13.80% 10.87% 4.95% 11.85% 0.64% 1.02% 1.27% 2.58% 5.07% 2.15% 2.25% 2.16% 5.40% 2.33% 3.28% 4.27% 1.39% 2.08% 1.86% 0.19% 1.34% 0.24% 3.11% 0.73% 1.55% 3.55% 4.02% 3.73% 2.57% 7.12% 4.96% 2.66% 6.02%
Stocks, Bonds, Bills, and Inflation
Exhibit 19.4
343
(Continued)
SIC Code
# of Co’s*
3842 3843 3844 3845 385 386 39 394 3942 3949 399 3993 3999 40 401 4011 42 421 4213 4215 44 441 449 4499 45 451 58 5812 59 591 594 5944 5945 5947 596 5961 599 5999 60 602 6020 603 6035 6036 609 6099 61 611
58 11 7 83 5 15 54 27 7 12 21 5 14 12 12 10 36 34 26 8 16 7 5 5 32 23 82 78 129 18 30 8 5 6 56 54 18 15 634 452 444 168 128 40 13 13 115 6
Industry Premium 6.59% 4.28% 3.36% 2.63% 1.30% 1.77% 5.42% 5.78% 1.36% 0.32% 2.29% 0.04% 1.45% 2.32% 2.30% 2.34% 3.27% 3.17% 1.13% 3.96% 0.98% 1.01% 0.41% 0.29% 0.17% 0.68% 2.67% 2.69% 0.40% 3.36% 2.55% 6.92% 1.90% 2.97% 8.26% 8.60% 0.67% 1.02% 2.47% 2.21% 2.23% 4.52% 4.47% 4.87% 6.31% 1.38% 0.94% 5.42%
SIC Code
# of Co’s*
Industry Premium
SIC Code
# of Co’s*
Industry Premium
484 489 49 491 492 4922 4923 4924 493 4931 494 495 4953 4955 499 50 501 5013 503 504 5045 505 5051 506 5063 5065 637 64 65 650 651 6510 6512 6513 653 6531 655 6552 67 679 6792 6794 6795 6798 6799 70 701 72
23 42 167 79 67 26 14 40 8 7 12 36 13 19 23 177 13 8 9 55 28 12 11 31 5 23 6 45 110 14 56 10 40 9 23 19 32 29 303 300 7 71 7 160 57 21 21 20
1.03% 9.88% 4.16% 5.38% 3.24% 7.02% 3.54% 6.11% 3.91% 3.23% 6.70% 3.66% 3.23% 6.09% 8.84% 0.98% 2.88% 7.12% 13.51% 3.51% 5.38% 0.46% 0.56% 7.53% 2.97% 8.77% 13.63% 5.01% 1.25% 4.17% 5.77% 0.27% 6.25% 5.85% 4.35% 1.56% 3.02% 4.41% 4.77% 4.59% 5.40% 2.87% 5.56% 4.80% 4.42% 1.41% 0.99% 5.37%
516 5169 517 5172 519 52 53 531 533 54 541 5411 55 551 553 554 56 562 565 566 57 571 5712 5719 573 5731 7371 7372 7373 7374 7375 7379 738 7381 7382 7389 75 751 753 762 78 781 7812 783 7832 79 792 7922
8 6 39 36 10 8 26 8 15 29 26 23 27 9 8 5 61 18 20 14 30 14 7 7 15 9 21 322 140 29 131 53 91 5 7 78 19 8 7 5 40 27 22 6 6 68 6 6
5.06% 3.28% 3.07% 1.90% 2.04% 1.78% 1.79% 0.76% 2.58% 2.03% 2.00% 2.31% 0.87% 0.97% 2.83% 0.98% 2.55% 3.85% 2.46% 1.50% 4.76% 0.12% 0.26% 0.32% 6.83% 8.16% 11.38% 4.87% 7.07% 0.02% 11.80% 2.92% 4.31% 3.61% 2.26% 1.87% 5.25% 3.26% 0.21% 0.36% 9.03% 6.07% 5.68% 0.51% 0.24% 1.65% 0.46% 0.38% (Continued )
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Cost of Capital
Exhibit 19.4
(Continued)
SIC Code
# of Co’s*
614 615 6153 6159 616 6162 62 621 628 6282 6289 63 631 632 6321 6324 633 635 8243 83 836 87 871 8711 872 873 8731 8732 8734 874 8741 8742 8744
25 38 16 19 40 40 94 47 55 42 14 141 50 33 18 16 69 26 6 13 7 192 34 33 16 82 65 7 10 69 20 42 7
Industry Premium 3.74% 0.86% 7.73% 4.23% 4.87% 5.40% 4.44% 5.50% 0.82% 1.54% 2.35% 4.18% 2.28% 5.73% 4.42% 5.78% 3.35% 2.23% 3.50% 2.97% 2.67% 0.01% 0.43% 0.50% 1.07% 0.60% 2.57% 2.62% 3.73% 0.94% 3.05% 2.19% 1.67%
SIC Code
# of Co’s*
726 729 7299 73 731 7311 7319 732 7323 733 734 7349 735 7359 736 7361 7363 737
6 8 6 821 24 6 11 7 5 8 8 5 31 25 40 9 34 640
Industry Premium 4.98% 6.69% 6.56% 5.04% 3.42% 4.99% 2.67% 4.02% 4.24% 7.20% 6.21% 7.07% 4.45% 4.52% 3.80% 4.21% 3.74% 5.42%
SIC Code 794 7948 799 7993 7999 80 801 805 8051 807 8071 808 809 8093 8099 82 822 8221
# of Co’s* 16 12 48 11 28 96 8 8 7 20 19 13 33 18 13 29 8 6
Industry Premium 2.57% 3.79% 2.33% 1.41% 2.13% 6.35% 6.08% 1.27% 1.75% 4.26% 4.29% 6.01% 2.71% 0.72% 4.57% 6.41% 5.26% 5.31%
*To view the full list of companies, download the Industry Premia Company List Report at www.ibbotson.com/irp Source: For detailed information about the above data, please refer to the Stocks, Bonds, Bills, and Inflation Valuation Edition 2005 Yearbook. # 2005 Ibbotson Associates, Inc.
corporation has paid its taxes. Therefore, the underlying data used in these risk premia calculations represent returns after corporate taxes but before personal taxes. When performing discounted cash flow analysis, it is important that both the discount rate and the cash flows be on the same tax basis. Since most valuation settings rely on after-tax cash flows, the use of an after-tax discount rate is appropriate in most cases. However, there are some instances (usually because of regulations or statutes) in which it is necessary to calculate a pretax value. Should a pretax cost of capital be required, there is no easy way to accurately modify the underlying market returns to a pretax basis. This modification would require estimating pretax returns for all the publicly traded companies that comprise the market benchmark. Although not completely accurate, a commonly used way to convert an after-tax discount rate to a pretax basis is to divide the after-tax rate by (1 minus the tax rate). This will gross up the discount rate to an estimated pretax basis. See Chapter 32 for more information.
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The tax rate selected for use in this method can have a substantial effect on the results. While the tendency is to use the top marginal tax rate, each case should be analyzed to determine whether this is appropriate. Many companies do not always pay the top marginal tax rate. Determining value for an S corporation can be even trickier. An S corporation is a corporation that has elected to be taxed as a pass-through entity (similar to a partnership). S corporations must have 100 or fewer shareholders. For an S corporation, all taxes are passed through to the shareholder level (no corporate taxes). There has been much controversy regarding whether to tax-adjust data derived from publicly traded companies for application in discounting S corporations. Morningstar’s opinion is that in many cases it would make perfect sense to tax-adjust either the cash flow stream or the discount rate to put them on the same tax basis. However, the valuation practitioner should evaluate each case individually to determine what adjustments, if any, should be taken. Should an adjustment to the discount rate be warranted, methods other than the approach just described may be more appropriate. MORNINGSTAR DATA: MINORITY OR CONTROLLING INTEREST? Morningstar uses publicly traded company data in its risk premium calculations, but is a minority discount implicit in these data? This is an important issue for the valuation practitioner because applying a minority discount or control premium can have a material impact on the ultimate value derived in the appraisal. The Morningstar long-horizon equity risk premium is derived from returns on the S&P 500. The Morningstar size premia data are calculated from returns of stocks on the NYSE, AMEX, and Nasdaq stock exchanges. All of these indexes reflect a preponderance of transactions representing trades of minority positions in the companies. Because most of the transactions underlying Morningstar risk premium data represent minority positions, some valuation practitioners assume that the risk premia represent minority returns and therefore have an implicit minority discount. Morningstar does not believe this is entirely correct, however. The returns generated by the S&P 500, NYSE, and the like represent returns to equity holders. While most of these companies are in fact minority held, there is no evidence that higher rates of return could be earned if all of these companies were acquired by majority shareholders. The Morningstar risk premia represent expected premiums that holders of securities of a similar nature can expect to achieve, on average, into the future. There is no distinction between minority and controlling owners. The discount rate is meant to represent the underlying risk of a particular industry or line of business. There may be instances in which a majority shareholder can acquire a company and improve its cash flow, but that would not necessarily have an impact on the general risk level of the cash flows generated by that company. In applying the income approach to valuation, adjustments for minority or controlling interest value should be made to the projected cash flows of the subject company instead of to the discount rate. Adjusting the expected cash flows better measures the potential impact a controlling party may have while not overstating or understating the actual risk associated with a particular line of business.
COST OF CAPITAL YEARBOOK The Cost of Capital Yearbook is a comprehensive source of industry-level financial data. The yearbook presents statistics critical in applying the income and market approaches to business valuation. Cost of equity, cost of capital, capital structure ratios, growth rates, industry multiples, and other useful financial data are presented for more than 300 industries. For each statistic, Morningstar
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Cost of Capital
presents the median and average estimate along with estimates for the smaller and larger companies in the industry. This book is an excellent resource for industry analysis and is a necessary tool for obtaining comparable market data applicable to privately held company valuation. The Cost of Capital Yearbook is published annually containing data calculated through March, with June, September, and December Quarterly supplements available. ORGANIZATION OF DATA Those industries included in the yearbook are organized by SIC code ranging from one digit (the most general) to four digits (the most specific). Companies appearing in a four-digit SIC code also are included in three-, two-, and single-digit classifications. For example, the company Advanced Micro Devices (AMD) is located in industry 3674 as well as in industries 367, 36, and 3. In this way, companies of a similar type are classified together in a systematic manner. Only those industries that contain five or more companies are listed in the Cost of Capital Yearbook. The main provider of data for the Cost of Capital Yearbook is Standard & Poor’s Compustat data, copyright 2007, a division of the McGraw-Hill Companies, Inc. Compustat provides data for more than 10,000 companies, but the yearbook includes within a particular industry only those companies that meet the criteria of a rigorous sorting and screening process. This process attempts to provide the purest industry statistics possible by excluding companies that have incomplete data or contain other characteristics that would misrepresent a given industry’s financial statistics. A company may be excluded for any of these reasons:
A company does not have sales for the most recent fiscal year, or no stock price has been reported for the most recent month.
Company sales are less than $100,000 for the most recent fiscal year, or market value does not exceed $10,000.
A company has not reported financial results for each of the last three fiscal years or month-end stock prices for the last 24 months. A company has less than 75% of sales in a single SIC code.
The next example illustrates the selection process based on the sales of a company in a particular industry. As shown in the table, the total sales for fictitious companies A and B are distributed between more than one SIC code. Company A
Company B
SIC
$Sales
SIC
$Sales
3443 3533 3534 3559
$730 649 1,709 993
2531 3085 3691 3822
$5,308 968 774 2,960
$4,081
$10,010
Neither company A nor company B would be included at the four-digit level, because sales to any one SIC code are not greater than 75%. However, at the two-digit level, industry 35 represents 82% of company A’s sales. Thus company A would be found in industries 35 and 3. The analysis for company B reveals that industry 2 represents 53% of sales and industry 3 represents 47% of sales.
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Company B’s sales do not meet the 75% sales criteria for any of the industries in which it participates, and thus it would be excluded from the yearbook. Currently the yearbook includes statistics on more than 300 industries, which can be helpful in performing discounted cash flow analyses. For each industry, a comprehensive set of financial parameters (levels of profitability, capitalization requirements, capital structure, and risk) are displayed. In addition to these financial statistics, and unique to the Cost of Capital Yearbook, are multiple cost of equity and weighted average cost of capital (WACC) measures. COST OF EQUITY MODELS The yearbook calculates cost of equity and average cost of capital estimates based on five separate models for each industry. These models include the Capital Asset Pricing Model with beta estimated using the ordinary least squares methodology, variations of the implied or discounted cash flow model, and the FF 3-factor model. The results of each model can be seen in the bottom section of Exhibit 19.5. CAPITAL ASSET PRICING MODEL Most practitioners are familiar with the Capital Asset Pricing Model for calculating the cost of equity developed by William Sharpe and John Linter. The principal assumption behind the model is that a direct linear relationship exists between the risk of an asset relative to the market and the return that can be expected from that asset. The CAPM model determines the cost of equity for any company as equal to the risk-free rate plus an amount proportionate to its systematic risk: (Formula 19.2) ki ¼ R f þ ðBi ERPÞ where: ki ¼ Cost of equity Rf ¼ Rate of return on a risk-free security Bi ¼ Beta of company i ERP ¼ Expected equity risk premium The regression for each company is run using 60 months of total return data. All CAPM models in the yearbook use the yield on a 20-year U.S. government bond for the risk-free rate and the longhorizon equity risk premium for the equity risk premium. Values for both the expected risk-free rate and the expected equity risk premium can be found in the SBBI Valuation Edition Yearbook. The yearbook also provides industry betas that can be used to make modifications to the current CAPM assumptions. The Cost of Capital Yearbook displays two CAPM-based cost of equity estimates with identical OLS-adjusted betas; however, the second CAPM model incorporates a size premium. The size premium is included to account for the additional return provided by small companies over large companies but not captured by the standard CAPM model (see the section on firm size premium for more information). For a particular industry, the size premium is determined from the individual company size premia, which are based on the equity capitalization of each company. (A size premium is added only to mid-cap, low-cap, and micro-cap companies.) For composites, the size premium is an equitycapitalization-weighted average of the size premia of the companies included in the industry. When determining a cost of equity for an industry, the CAPM adjusted for size best represents the entire industry. The size adjustment for an industry dominated by large companies will be less than
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Cost of Capital
STATISTICS FOR SIC CODE 1381 Drilling Oil and Gas Wells This Industry Comprises 10 Companies Industry Description
Sales (million$)
Establishments primarily engaged in drilling wells for oil or gas field operations for others on a contract or fee basis. This industry includes contractors that specialize in spudding in, drilling in, redrilling, and directional drilling.
Total
Total Capital (million$) 7,368 736.8
Average Three Largest Companies
1,712.2 1,221.0
PRIDE INTERNATIONAL INC DIAMOND OFFSHRE DRILLING INC ENSCO INTERNATIONAL INC
1,046.9
Three Smallest Companies 185.2 168.5 4.4
S&P Debt Rating S&P 500
Large Cap
AAA, AA, A
70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00
BB, B, CCC, CC, D Not Rated Totals
Std Deviation
Annualized Statistics for Last 10 Years (%) Avg Return 10.29 33.38
Std Deviation 17.20 59.86
29.71 47.03
58.58 77.69
Large Composite Small Composite
DIAMOND OFFSHRE DRILLING INC ENSCO INTERNATIONAL INC PRIDE INTERNATIONAL INC
12,528.9 8,391.4 6,783.8
PARKER DRILLING CO PIONEER DRILLING CO TRI-VALLEY CORP
1,380.4 833.2 180.0
Mid Cap
0
1
0.0
12.5
1
0
0
0
1
8.4 0
0.0 1
0.0 2
0.0 0
8.4 3
0.0 0
6.8 2
3.1 2
0.0 1
9.9 5
0.0 2 20.9
9.4 3 16.1
2.5 4 5.6
0.2 1 0.2
12.0 10 42.8
Growth Over Last 5 Years (%)
14.89
14.88 21.73 18.16
32.63
30.27
12.47 7.87 16.89
Capital Structure Ratios (%)
Net Sales
Operating Income
Net Income
(companies) (capital)
Sales, Income & Market Capitalization (billion$) 10 Years 32.29 17.92
19.98
Small Composite
Totals
0 0.0
5 Years
25th Percentile SIC Composite Large Composite
Micro Cap
0 0.0
Compound Annual Equity Return (%) 75th Percentile Median
Low Cap
1 12.5
BBB
S&P 500 SIC Composite
4,282.1
Number of Companies & Total Capital (billion$)
SIC vs. S&P 500 for Last 10 Years (%)
Avg Return
42,821
Average Three Largest Companies
Three Smallest Companies
PIONEER DRILLING CO ATWOOD OCEANICS TRI-VALLEY CORP
SIC Composite
Total
Current Yr.
Sales 7.4
Operating Income 2.7
Last Yr. 2 Yrs. Ago 3 Yrs. Ago
5.7 4.6 5.4
1.4 1.2 1.8
4 Yrs. Ago
4.8
1.8
Net Income
Equity Capital 38.7
Debt Capital 4.2
1.0 0.1 0.0 0.4
25.4 15.9 13.6
5.0 4.7 4.4
0.7
16.4
3.9
Distribution of Sales & Total Capital (million$)
Debt/Total Capital Latest 5-Year Avg
Debt/MV Equity Latest 5-Year Avg
90th Percentile
Distribution of Sales Latest 5-Year Avg 1,270.1 925.7
Latest 8805.1
Total Capital 5-Year Avg 5,134.6
Median
17.68
20.17
18.16
5.66
16.84
6.00
20.38
75th Percentile
1,035.4
794.0
6467.3
3,842.6
SIC Composite Large Composite
16.98 17.04
21.98 24.26
44.50 40.53
5.88 5.66
18.06 20.77
6.25
22.04 26.21
Median 25th Percentile
748.9 271.9
2777.9 1447.7
1,573.3 822.0
Small Composite
18.31
6.59
9.08
3.40
13.78
15.99
10th Percentile
152.1
539.3 219.6 88.7
767.9
274.7
6.00 3.52
Margins (%)
Median
Operating Margin Latest 5-Year Avg 30.45 29.02
Net Margin Latest 5-Year Avg 8.42 15.69
SIC Composite Large Composite Small Composite
36.01 39.53 25.73
14.25
31.94 34.33 27.24
14.03 9.95
7.84 8.25 6.92
Asset Turnover Latest 5-Year Avg 46.42
42.13
45.65
38.95
35.63 49.84
30.97 45.31
Return on Inv. Cap. Latest 5-Year Avg 8.39 3.50 6.93 6.46 3.65
3.29 2.78 3.19
Return on Assets Latest 5-Year Avg
Return on Equity 5-Year Avg 2.61
Latest 2.42
7.82
3.07
6.50
3.05
2.95
5.00 4.96
2.56 3.13
2.44 1.52
Equity Valuation Ratios (Multiples)
Median
Price/Earnings Latest 5-Year Avg 41.40 38.37
SIC Composite Large Composite Small Composite
33.86 41.00 66.00
Growth Rates (%)
Median SIC Composite Large Composite Small Composite
17.17 19.89 29.21
Dividend Yield (% of Price) Market/Book Latest 5-Year Avg 2.02 3.87 3.57 3.52 4.10
2.07 1.90 2.60
4.66
2.98
4.82 5.75 6.57
3.09 3.58 3.25
48.15 62.44
CAPM CAPM + Size Prem 13.33 14.50 11.78 12.80 12.04 12.61
12.04 14.42
Price/Cash Flow Latest 5-Year Avg 54.79 NMF 51.25 73.12 120.93
Price/Operating Income Latest 5-Year Avg 14.26 10.07 13.40 14.55 25.53
213.54 162.00 NMF
Weighted Average Cost of Capital (%)
3-Factor Discounted Cash Flow Fama-French 1-Stage 3-Stage 15.13 48.89 14.30 14.81 49.19 18.50 15.23 16.62
Cost of Capital 2006 Yearbook, Data Through March 2006
Exhibit 19.5
Price/Sales Latest 5-Year Avg
Cost of Equity Capital (%)
Analysts' Estimate 48.89 48.89
2.53 2.31 2.13
49.48 48.89
17.80 12.40
CAPM 3-Factor CAPM + Size Prem Fama-French 12.89 13.17 14.70 11.34 12.27 14.10 11.44 12.39
11.44 14.13
14.28 16.23
Latest 0.00
5-Year Avg 0.00
0.97 1.38 0.00
0.70 0.92 0.00
Levered Betas
Discounted Cash Flow 1-Stage 3-Stage 47.30 13.55 45.40 17.46 44.82 47.19
9.69 10.41 11.94
16.57 12.18
Unlevered Betas
Raw Beta 1.21 1.12
Adjusted Beta 1.17 0.95
Adjusted Beta 1.09 0.89
1.17 1.35
0.98 1.07
0.91 1.04
© 2006 Ibbotson Associates
Sample Page from the 2006 Cost of Capital Yearbook (Data through March 2006)
Source: Cost of Capital 2006 Yearbook. Copyright # 2006 Morningstar, Inc. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) To purchase copies of the Cost of Capital Yearbook, or for more information on other Morningstar publications, please visit global.morningstar.com/DataPublications. The main provider of data for the Cost of Capital Yearbook is Standard & Poor’s Compustat data, Copyright # 2007, a division of the McGraw-Hill Companies, Inc.
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349
for an industry comprised mostly of small- or mid-cap companies. When valuing individual companies, however, it would be most appropriate to use the CAPM model that is not adjusted for size and instead add a size premium relative to the equity capitalization of the subject company. Full size premium analysis at the firm level is presented in the SBBI Valuation Edition Yearbook. FAMA-FRENCH 3-FACTOR MODEL The FF 3-factor model is a multiple linear regression model developed by Eugene Fama and Kenneth French. The model is estimated by running a time series multiple regression for each company. The dependent variable is the company’s monthly excess returns over Treasury bill returns. The independent variables are:
The monthly excess return on the market over Treasury bills SMB (small minus big): The difference between the monthly return on small-cap stocks and largecap stocks HML (high minus low): The difference between monthly returns on high book-to-market stocks and low book-to-market stocks The FF 3-factor model is presented as Formula 15.2 and is repeated in the next equation: (Formula 19.3) where:
ki ¼ R f þ ðBi ERPÞ þ ðsi SMBPÞ þ ðhi HMLPÞ
ki ¼ Cost of equity Rf ¼ rate of return on a risk-free security Bi ¼ Beta of company i ERP ¼ Expected equity risk premium si ¼ Small-minus-big coefficient in the Fama-French regression SMBP ¼ Expected small-minus-big risk premium, estimated as the difference between the historical average annual returns on the small-cap and large-cap portfolios hi ¼ High-minus-low coefficient in the Fama-French regression HMLP ¼ Expected high-minus-low risk premium, estimated as the difference between the historical average annual returns on the high book-to-market and low book-to-market portfolios The FF 3-factor model attempts to improve on the single-variable CAPM model by incorporating additional market variables to explain a company’s expected return more adequately. These variables include the size of the company and its book-to-market ratio (capturing the size effect and the financial distress of the firm), in addition to the single-market variable of the CAPM. Because this model incorporates more information into the cost of equity estimate than the typical CAPM, estimates on average tend to be higher. IMPLIED OR DISCOUNTED CASH FLOW MODELS The discounted cash flow model (DCF) or income approach was developed by John Burr Williams and elaborated by Myron J. Gordon and Eli Shapiro. The idea behind the DCF model is that the present value of a company can be estimated by discounting its dividends or expected cash flows using the firm’s appropriate discount rate. Therefore, the set of inputs needed to determine a company’s present value includes the value of future cash flows, the rate at which these cash flows will
350
Cost of Capital
grow, and the discount rate that will equate future cash flows to their present value. Alternatively, given these inputs, we can use the DCF model to solve for the discount rate or the cost of equity. Assuming that the present value of a company and its projected cash flows are known, there still exists the difficulty of obtaining a cash flow growth forecast, since cash flows tend not to grow at a constant rate forever. In this case, the yearbook uses the expected earning growth rates from the I/B/ E/S database of consensus long-term growth rate estimates. The one-stage and three-stage discounted cash flow models presented in the Cost of Capital Yearbook are both rooted in the constant growth/Gordon Growth Model as presented in Chapter 4 as Formula 4.6. The variables and formula used by Morningstar are shown next: (Formula 19.4) D Pi ¼ ðki gi Þ where: Pi ¼ Price per share for company i (seen elsewhere as PV) D ¼ Dividend per share for company i at the end of year 1 ki ¼ Discount rate for company i gi ¼ Dividend growth rate for company i To solve for the cost of equity capital, the formula is rewritten as: (Formula 19.5) Di ð1 þ gÞ þ gi ki ¼ Pi The single-stage growth model describes the cost of equity capital for a company that has a constant expected cash flow growth rate projected indefinitely into the future. One drawback of the single-stage model is that if a company pays no dividends, its cost of equity is equivalent to its growth rate. Given such shortcomings, the practitioner must recognize the limitations of the model on its own and view the results as a point of comparison with other models in estimating the cost of equity. It is probably unrealistic to assume that a firm’s cash flows will grow at a constant rate in perpetuity. To improve the predictability of the DCF cost of equity model, a more realistic assumption might be that the growth rate of cash flows changes over time. The three-stage DCF model estimates the cost of equity employing three different growth rate estimates at different future time periods. The Cost of Capital Yearbook calculates the three-stage DCF cost of equity for each industry assuming that cash flows will grow at the analyst’s company-specific rates for the first five years, at an industry-average growth rate for the next five years, and finally at a growth rate for the entire economy (expected real growth rate plus an inflation estimate) for all other time periods. The results of each model are shown in the bottom section of Exhibit 19.5.
MORNINGSTAR BETA BOOK The Beta Book rounds out Morningstar’s library of publications. Published semiannually since 1995, the Beta Book provides beta and 3-factor model information on approximately 5,000 companies. The Beta Book allows practitioners to select a company-specific measure of risk directly applicable to a publicly traded company or to construct a custom peer group for analysis of a private company. The Beta Book, published semiannually, includes company-specific betas for approximately 5,000 companies. Company betas are calculated for the CAPM with beta estimated using OLS methodology and FF 3-factor model with regression factors. A sample page from the Beta Book can be seen in Exhibit 19.6.
351
AP PHARMA INC APA ENTERPRISES INC APAC CUSTOMER SERVICES INC APACHE CORP APARTMENT INVT & MGMT-CLA
APO HEALTH INC APOGE E ENTERPRISES INC APOGEE TECHNOLOGY INC APOLLO GROUP INC –CLA APPLE COMPUTER INC
APPLEBEES INTL INC APPLERA CORP APPLIED BIOSYS APPLERA CORP CELERA GENOMICS APPLIANCE RECYCLING CTR AMER APPLICA INC APPLIED DIGITAL SOLUTIONS APPLIED FILMS CORP APPLIED IMAGING CORP APPLIED INDUSTRIAL TECH INC
APPLIED INNOVATION INC APPLIED MATERIALS INC APPLIED MICRO CIRCUITS CORP APPLIED NEURO SOLUTIONS INC APPLIED SIGNAL TECHNOLOGY APPLIX INC
APRIA HEALTHCARE GROUP INC APTARGROUP INC APTIMUS INC AQUA AMERICA INC
3APOA APOG ATA APOL AAPL
APPB ABI CRA 3ARCI APN ADSX AFCO AICX AIT
AINN AMAT AMCC 3APNS APSG APLX
AHG ATR APTM WTR
Page from Beta Book
APPA APAT APAC APA AIV
Exhibit 19.6
0.36 0.73 1.17 0.01
1.14 2.37 3.89 0.86 0.36 3.66
0.52 1.63 2.25 1.06 1.26 1.70 2.23 2.16 0.56
3.76 0.64 1.24 0.06 1.46
1.62 4.43 0.74 0.03
1.93 8.73 8.88 0.69 0.73 3.66
2.19 4.69 7.48 1.82 2.22 1.00 4.85 2.97 2.44
1.92 1.70 1.94 0.26 3.97
0.04 0.25 0.01 0.00
0.06 0.57 0.58 0.01 0.01 0.19
0.08 0.27 0.49 0.05 0.08 0.02 0.29 0.13 0.09
0.06 0.05 0.06 0.00 0.21
0.18 0.71 1.67 0.46
2.21 1.79 2.21 0.67 2.21 1.67
0.71 0.63 1.67 1.48 2.21 1.90 1.79 0.63 0.88
0.53 1.33 2.21 0.10 1.74
0.35 0.73 1.49 0.02
1.35 2.34 3.69 0.76 0.63 2.84
0.52 1.55 2.22 1.14 1.44 1.83 2.17 1.74 0.57
1.40 0.70 1.46 0.07 1.49
Beta 1.04 2.07 0.92 0.20 0.34
0.28 0.66 1.17 0.00
1.12 2.34 3.89 0.86 0.35 3.66
0.51 1.63 2.23 0.79 0.70 1.66 2.23 1.86 0.52
2.46 0.60 1.24 0.06 1.46
Beta 1.13 2.26 0.72 0.16 0.20
0.25 0.65 1.48 0.01
1.33 2.31 3.69 0.76 0.61 2.84
0.51 1.55 2.20 0.75 0.29 1.79 2.17 1.46 0.53
0.66 0.65 1.46 0.07 1.48
Beta 1.04 1.88 0.92 0.18 0.12
Beta 0.67 0.63 1.67 0.63 0.40
Beta 1.13 2.46 0.72 0.18 0.34
t-Stat R-Sqr 1.94 0.06 3.98 0.21 1.19 0.02 0.71 0.01 1.94 0.06
Pr Grp Ibbotson Raw Ibbotson
Raw
Unlevered
CAPM: Ordinary Least Squares Levered FF
SMB
SMB
0.32 0.72 0.24 0.02
0.71 2.10 3.97 1.13 0.13 3.07
0.42 1.79 1.97 0.82 0.71 0.56 2.19 1.83 0.53
3.53 0.45 0.83 0.13 1.16
1.44 4.25 0.15 0.12
1.18 8.14 10.04 0.86 0.26 2.94
1.71 5.01 6.58 1.32 1.25 0.36 4.54 2.39 2.20
1.82 1.14 1.33 0.55 3.10
2.02 0.95 8.09 0.97
3.83 4.63 4.51 0.04 2.14 4.41
1.86 0.08 2.24 2.90 7.18 20.72 2.61 5.61 1.51
6.69 4.15 3.63 3.89
4.69 13.33 8.47 0.02 3.05 3.14
5.58 0.17 5.55 3.49 9.45 9.94 4.03 5.46 4.70
20.27 7.78 2.80 5.27 9.47 11.33 3.45 10.70 3.93 7.80
Beta t-Stat Prem t-Stat 1.01 1.64 3.02 3.65 1.73 3.09 11.89 15.72 0.35 0.56 1.72 2.04 0.15 0.57 1.65 4.62 0.28 1.49 1.04 4.16
FF
2.85 2.06 13.48 2.47
5.93 0.52 11.48 8.63 2.88 10.05
0.68 5.03 4.35 1.88 3.48 30.68 4.02 0.49 2.00
32.87 0.50 5.76 0.66 1.78
Prem 2.24 0.62 8.54 2.39 0.07
HML
FF
0.15 0.31 0.06 0.08
0.14 0.66 0.70 0.03 0.04 0.24
0.12 0.33 0.56 0.08 0.22 0.29 0.32 0.17 0.14
0.21 0.09 0.23 0.15 0.30
(Continued )
8.62 8.20 5.52 9.01
6.62 1.36 19.69 4.43 3.76 6.54
1.87 9.53 9.84 2.07 4.18 13.43 5.65 0.43 5.65
11.51 0.86 6.29 1.86 3.23
t-Stat R-Sqr 2.46 0.08 0.75 0.44 9.28 0.11 6.11 0.06 0.27 0.09
HML
Fama-French Three-Factor Model
352
ARC WIRELESS SOLUTIONS INC ARCH CHENICALS INC ARCH COAL INC ARCHER-DANIELS-MIDLAND CO ARCHON CORP
ARCHSTONE-SMITH TRUST ARCTIC CAT INC ARDEN GROUP INC–CLA ARDEN REALTY INC ARENA PHARMACEUTICALS INC
3ARCS ARJ ACI ADM 3ARHN
ASN ACAT ARDNA ARI ARNA
0.42 0.96 1.05 0.29 1.73
2.34 0.50 0.35 0.73 1.40
0.86 2.09 0.67 2.87 0.66 0.27
Raw
3.34 4.26 4.22 1.78 4.04
4.23 2.22 0.77 3.50 1.97
0.95 4.51 1.38 4.39 3.36 1.19
0.16 0.24 0.24 0.05 0.22
0.24 0.08 0.01 0.17 0.06
0.02 0.26 0.03 0.25 0.19 0.03
0.38 0.67 0.83 0.38 0.98
1.12 0.67 0.94 0.32 0.80
1.79 1.67 0.45 0.63 0.74 0.98
Pr Grp
0.42 0.95 1.05 0.29 1.64
2.12 0.50 0.42 0.72 1.24
1.20 2.04 0.64 2.35 0.66 0.30
Ibbotson
0.32 0.96 1.05 0.22 1.61
1.95 0.40 0.30 0.61 1.03
0.85 2.03 0.41 2.19 0.49 0.26
Raw
0.29 0.95 1.04 0.20 1.52
1.69 0.38 0.35 0.57 0.79
1.18 1.97 0.23 1.62 0.43 0.28
Ibbotson
Unlevered
CAPM: Ordinary Least Squares Levered
0.42 0.64 0.97 0.21 1.48
2.05 0.32 0.02 0.67 1.45
0.49 1.85 0.76 2.78 0.53 0.26
FF
3.05 3.17 3.83 1.26 3.35
3.61 1.51 0.04 2.99 1.92
0.52 3.88 1.51 4.29 2.44 1.05
FF
7.67 0.64 3.95 2.92 2.67 0.36 13.60 7.52 6.44 7.34
0.07 3.72 2.58 1.47 4.37
5.14 7.30 1.53 7.67 6.99 3.46
SMB
5.86 0.18 2.46 0.88 2.73
6.78 4.71 1.05 6.70 1.96 1.08
SMB
3.02 16.08 8.18 0.82 3.33
2.53 5.10 5.58 0.27 3.72
2.00 8.52 6.75 2.00 1.26
0.42 2.59 6.93 10.98 2.04 2.62
0.69 1.83 5.19 10.50 0.73 1.13
0.40 2.55 2.53 0.50 0.82
HML
HML
Fama-French Three-Factor Model
0.16 0.46 0.31 0.11 0.28
0.30 0.26 0.10 0.19 0.08
0.06 0.32 0.07 0.36 0.27 0.05
FF
Source: Ibbotson Associates’ Beta Book, First 2006 Edition. Copyright # 2006 Ibbotson Associates. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) To purchase copies of The Beta Book, or for more information on other Morningstar publications, please visit global.morningstar.com/DataPublications. Calculated (or derived) based on CRSP1 data, # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago.
Note: Data through December 2005. *Companys with less than 60 months’ data (minimum 36 months).
AQUACELL TECHNOLOGIES INC* AQUANTIVE INC AQUILA INC ARADIGM CORP ARAMARK CORP* ARBITRON INC*
(Continued)
3AQUA AQNT ILA ARDM RMK ARB
Exhibit 19.6
Morningstar Beta Book
353
The Beta Book does not provide cost of equity estimates for individual companies; however, it does provide practitioners with the statistics necessary for calculating cost of equity under both the CAPM and the FF 3-factor model. Those companies included in the Beta Book are selected from the Compustat database based on three criteria:
A company must have at least 36 months of return data available.
It must have sales greater than $100,000 in the most recent year. It must have a market capitalization greater than $10,000 for the most recent month.
BETA ESTIMATION METHODOLOGIES For the CAPM model, the Beta Book provides several equity beta statistics including traditional unlevered and levered OLS beta estimates, peer group betas, and Morningstar adjusted betas. For the FF 3factor model, the beta factor in addition to size and value factors identified in the model are provided. All CAPM regressions in the Beta Book are run over a 60-month period, using the S&P 500 total returns as a proxy for the market returns and the yield on a 30-day Treasury bill as a proxy for the risk-free asset. If a company has less than 60 months of historical returns, then betas are calculated using its available return data with a minimum of 36 months being acceptable. Please refer to the ‘‘Cost of Capital Yearbook’’ section of this chapter for detailed information about the CAPM and FF 3-factor models. LEVERED AND UNLEVERED BETAS The OLS CAPM results for each company include both levered and unlevered betas. Whereas the levered beta incorporates both the business and financing risks undertaken by the company and borne by the equity shareholders, the unlevered beta excludes the risk implicit in the financial structure of a company and only reflects its business risk. This allows a practitioner to make adjustments to the capital structure inherent in a levered beta by relevering a company’s unlevered beta with a debt structure more similar to the subject company being valued. The unlevered beta is also useful when it may be difficult to make comparisons within an industry for a company that has much higher leverage than its peers. In this case, because the unlevered beta reflects only business risk and not financial risk, the practitioner could relever the company’s beta with that of its industry to make a more comparable peer group analysis. MORNINGSTAR (ADJUSTED) BETAS The Beta Book includes an adjusted or forward-looking beta for each of the CAPM models. The adjustment incorporates the theory that a company’s beta tends to revert toward its industry’s average beta over time. The adjusted beta is calculated using the Vasicek shrinkage technique, which takes the statistically weighted average of the company beta and the industry beta: (Formula 19.6) Adjusted Beta ¼ ð1 weightÞ peer group beta þ weight company beta where: Weight ¼ (cross-sectional standard error)2/[(cross-sectional standard error)2 þ (time series beta standard error)2]
354
Cost of Capital
The Vasicek adjustment focuses on the statistical significance of the beta estimate, using the standard error to appropriately weight the company and industry beta. If the historical company beta displays low statistical significance, the higher standard error will result in the company’s having a lower weighting than the industry, and vice versa. The greater the statistical confidence of the company’s regression beta, the closer that weight is to 1.0. The motivation behind adjusting a beta is to calculate a forward-looking estimate from a historical beta. An advantage of the Vasicek technique is that the adjustment does not need to be made toward the market as a whole but can be made toward an industry or a peer group. Also, if a company’s beta estimate seems statistically unreliable, confidence in the prospective beta can be increased by assigning a greater weight to its industry or peer group. PEER GROUP AND INDUSTRY BETAS In addition to individual company raw and adjusted betas, the Beta Book also provides peer group betas. Peer group betas are calculated by taking the sales-weighted average of the betas for each industry in which a company has sales. These betas can be useful for comparison purposes or in place of a company beta displaying poor regression statistics. The Beta Book includes OLS betas for industries defined by two-digit SIC codes. Previous versions of the publication constructed each industry beta using the market-capitalization–weighted average of the betas of all companies in the industry. Only companies with 75% of their sales in the industry as defined by the primary SIC codes of its business segments were included. However, this ‘‘pure play’’ approach tends to exclude many domestic conglomerates that are major participants in the industry. In order to calculate an industry beta using data from all companies participating in a particular industry, the Beta Book uses the Full Information Beta procedure developed by Paul Kaplan and James Peterson. In this procedure, a single market-capitalization–weighted cross-sectional regression is performed using individual company betas as the dependent variable and the percentage of exposure or sales to the industry as the independent variables. The resulting regression coefficients for each industry are the estimates of the pure play industry betas for which data from every company in a particular industry have been incorporated.
COST OF CAPITAL RESOURCES WEB SITE The Cost of Capital Resources Web site at global.morningstar.com/US/CofCResources.com is devoted to business valuation issues. As the name suggests, this site is the center of all things cost of capital. The site offers analysis on nearly 350 industries, approximately 5,000 companies, and 170 þ countries. Over 150,000 historical reports are currently available online for download. Morningstar uses the Cost of Capital Resources Web site, now found on Morningstar’s corporate site, as an outlet for much of its valuation-related data. Visitors to the site can purchase historical quarterly data from the Cost of Capital Yearbook and the Beta Book on a per-usage basis. Anyone interested in international cost of capital analysis will find the collection of historical international reports at the site critical in calculations. The Cost of Capital Resources Web site is segmented into four main product groups: 1. 2. 3. 4.
Individual Reports & Statistics (industry and company analysis and betas) U.S. Risk Premia Reports International Cost of Capital Reports International Risk Premia Reports
Cost of Capital Resources Web Site
355
Industry analysis available at the Cost of Capital Resources Web site is taken directly from the Cost of Capital Yearbook. Nearly 350 industries are organized by SIC code, are available going back to March 2001 on a quarterly basis, and can be downloaded immediately. Included in the analysis are multiple measures of cost of equity, WACC, beta, capital structure ratios, growth rates, industry multiples, and other important financial statistics. (See the ‘‘Cost of Capital Yearbook’’ section in this chapter for more information.) Company analysis presented on the Web site includes individual company betas and tax rates. Approximately 5,000 company betas from the Beta Book are sold at the site on a per-company basis and are available on a quarterly basis going back to December 2001. For each company, multiple measures of beta are displayed, including levered and unlevered betas, betas adjusted toward their peer group, and statistics necessary to calculate Fama-French 3-factor cost of equity. (See the ‘‘Morningstar Beta Book’’ section in this chapter for more information.) In addition to beta analysis at the company level, tax rate estimates are also available. Research has shown that using the top marginal tax rate in cost of capital calculations may be overstating the effect of taxes. Morningstar provides tax rate estimates on more than 5,000 companies that can be used in discounting projected future cash flows. Tax rate estimates based on the most recent fiscal year and the five-year average are presented for each company. Newly calculated company betas are added to the Web site quarterly, while individual company tax rates are updated annually (usually in the fall). The remaining sections of the Cost of Capital Resources Web site present data reports for global analysis and risk premia analysis. The international risk premia section provides equity risk premia and cost of equity estimates for a variety of countries. The International Equity Risk Premia Report provides ERP estimates on 16 different developed countries. The analysis can be customized to view the ERP for any time period covered for each country. When available, data are presented for both the long- and short-horizon ERP, in both U.S. dollars and local currency. Most of the ERP estimates use a historical date range that extends back to 1970. Using a longer string of data, Morningstar is also able to provide a Canadian Risk Premia over Time Report and a United Kingdom Risk Premia over Time Report. Some of the most popular reports available on the Web site are the International Cost of Capital Report and the International Cost of Capital Perspectives Report. The first presents cost of equity estimates on approximately 170 countries from the perspective of U.S. investors. This report offers estimates using up to five different cost of equity models for each country, based on data availability. The international ‘‘perspectives’’ report also covers approximately 170 countries but from the perspective of international investors. This report utilizes only one model for cost of equity estimation (the country risk rating model) and presents the estimates from the perspective of investors in Australia, Canada, France, Germany, Japan, and the United Kingdom. Examples of the data offered in both reports can be seen in Exhibits 19.7 and 19.8. All international reports are updated annually in late May, with data through the previous year’s end. In addition to the international reports available at the Cost of Capital Center, a number of U.S.based risk premium reports are presented in the U.S. risk premia section: specifically, the Risk Premia over Time Report and the Duff & Phelps Risk Premium Report (formerly the Standard & Poor’s Corporate Value Consulting Risk Premium Study). The Risk Premia over Time Report provides equity and size premia over all historical time periods dating back to 1926. The analysis can be customized by choosing the beginning and ending date for risk premia estimation. The report contains long-, intermediate-, and short-term equity risk premia and mid-, low-, and micro-cap size premia. All of the content in this report is from the SBBI Valuation Edition Yearbook, primarily from Appendix A.
356 Exhibit 19.7
Cost of Capital International Cost of Capital Report International Cost of Capital Models Country Risk Rating Linear Model
Country Spread
International CAPM Model
Globally Nested CAPM
Relative Standard Deviation Model
Thru 12-05
Thru 12-05
Thru 12-05
Thru 12-05
Country
Log Model
Afghanistan Albania Algeria Angola Argentina
Thru 44.23 32.89 22.16 38.94 28.48
Armenia Australia Austria Azerbaijan Bahamas
30.52 13.03 11.70 25.98 17.25
29.33 13.01 10.95 26.55 18.60
Bahrain Bangladesh Barbados Belarus Belgium Belize Benin Bhutan Bolivia Bosnia & Herzegovina
17.95 31.78 18.08 36.57 12.14 30.52 34.21 31.25 30.13 31.02
19.40 29.98 19.55 32.05 11.65 29.33 31.10 29.71 29.12 29.59
Botswana Brazil Bulgaria Burkina Faso Burundi
18.06 21.53 20.00 35.50 45.52
19.52 23.00 21.56 31.63 34.65
Cambodia Cameroon Canada Cape Verde Central African Republic
36.65 35.72 11.64 29.55 44.99
32.08 31.72 10.86 28.80 34.53
12.78
Chad Chile China Colombia Comoros
39.88 15.65 16.55 22.29 43.50
33.17 16.65 17.77 23.68 34.18
12.74 8.94 10.19
Congo Costa Rica Coˆte d’lvoire Croatia Cuba
42.35 21.82 41.91 19.67 44.23
33.88 23.27 33.76 21.23 34.35
Cyprus Czech Republic Dem. Republic of Congo (Zaire)
16.39 15.91 48.43
17.57 16.97 35.24
3-06 34.35 30.51 23.57 32.87 28.18
42.35
13.20
18.71
11.84 9.12
15.67 14.07
12.27
13.91
19.15
41.81
13.41
41.23
14.91
32.50
Available Models 2 2 2 2 6 2 4 4 2 2 2 2 2 2 4 2 2 2 2 2 2 6 2 2 2
13.41
2 2 4 2 2
20.65 26.44 18.87
2 5 4 4 2 2 2 2 2 2
10.95
18.97
2 4 2
Cost of Capital Resources Web Site Exhibit 19.7
357
(Continued) International Cost of Capital Models Country Risk Rating Country Spread
International CAPM Model
Globally Nested CAPM
Relative Standard Deviation Model
Country
Log Model
Linear Model
Denmark Djibouti
11.50 34.28
10.62 31.13
Dominican Republic East Timor Ecuador Egypt El Salvador
28.53 36.73 29.97 22.40 22.60
28.21 32.11 29.03 23.77 23.95
2 2 2 2 2
Eritrea Estonia Ethiopia Finland France
40.76 16.75 38.49 11.46 11.66
33.44 18.01 32.73 10.56 10.89
21.41 14.96
2 2 2 4 4
Gabon Gambia Georgia Germany
37.46 36.81 33.27 11.71
32.37 32.14 30.69 10.98
17.30
14.41
2 2 2 4
Ghana Greece Grenada Guatemala Guinea Guinea-Bissau
29.55 14.82 34.63 25.03 43.38 46.34
28.80 15.56 31.28 25.87 34.15 34.83
11.39
21.97
Guyana
32.02
30.10
12.43
Available Models
13.20
18.57 14.41
4 2
2 4 2 2 2 2 2
Source: International Cost of Capital Report 2006. Copyright # 2006 Morningstar, Inc. All rights reserved. Used with permission.
Exhibit 19.8
International Cost of Capital Perspectives Report 2006 International Cost of Capital Country Risk Rating Model from International Perspectives Australia Canada France Germany Japan U.K. Country Risk Country Risk Country Risk Country Risk Country Risk Country Risk Rating Rating Rating Rating Rating Rating
Country
Log Linear Log Linear Log Linear Log Linear Log Linear Log Linear Model Model Model Model Model Model Model Model Model Model Model Model
Afghanistan Albania Algeria Angola Argentina
Thru 43.57 32.88 22.76 38.59 28.72
Armenia Australia
30.64 29.30 30.03 28.71 30.05 29.01 29.35 28.34 27.24 26.01 29.93 28.67 14.15 14.25 12.26 12.30 14.62 14.58 13.45 13.37 11.30 11.36 13.97 14.05
3-06 33.94 30.40 23.99 32.58 28.24
Thru 43.97 32.44 21.54 38.59 27.97
3-06 33.76 29.89 22.91 32.27 27.55
Thru 42.15 32.14 22.67 37.49 28.26
3-06 33.46 30.06 23.91 32.15 27.99
Thru 41.81 31.50 21.75 37.00 27.50
3-06 32.95 29.43 23.05 31.60 27.28
Thru 39.74 29.40 19.62 34.92 25.38
3-06 30.52 27.07 20.83 29.19 24.97
Thru 42.44 32.09 22.30 37.62 28.07
3-06 33.18 29.73 23.51 31.85 27.64
(Continued )
358
Cost of Capital
Exhibit 19.8
(Continued) International Cost of Capital Country Risk Rating Model from International Perspectives
Austria Azerbaijan Bahamas
Canada France Country Risk Country Risk Rating Rating Log Linear Log Linear Model Model Model Model Thru 3-06 Thru 3-06 12.89 12.34 10.91 10.22 13.44 26.36 26.74 25.42 25.91 26.04 18.13 19.40 16.55 17.92 18.34
Germany Japan U.K. Country Risk Country Risk Country Risk Rating Rating Rating Log Linear Log Linear Log Linear Model Model Model Model Model Model Thru 3-06 Thru 3-06 Thru 3-06 12.75 12.24 11.47 10.08 9.50 12.76 12.19 26.56 25.22 25.79 23.10 23.51 25.79 26.18 19.52 17.29 18.49 15.15 16.37 17.83 19.06
Bahrain Bangladesh Barbados Belarus Belgium Belize Benin Bhutan Bolivia Bosnia & Herzegovina
18.79 31.83 18.91 36.35 13.31 30.64 34.13 31.33 30.28 31.12
20.14 29.90 20.28 31.81 13.00 29.30 30.94 29.66 29.11 29.55
17.26 31.32 17.40 36.18 11.36 30.03 33.79 30.78 29.64 30.55
18.72 29.36 18.87 31.44 10.93 28.71 30.49 29.09 28.50 28.97
18.96 31.17 19.08 35.39 13.83 30.05 33.31 30.70 29.71 30.50
20.23 29.59 20.36 31.42 13.38 29.01 30.58 29.35 28.83 29.25
17.92 30.49 18.04 34.85 12.64 29.35 32.71 30.01 29.00 29.80
19.23 28.94 19.36 30.84 12.12 28.34 29.97 28.69 28.15 28.59
15.78 28.39 15.90 32.75 10.49 27.24 30.61 27.91 26.89 27.70
17.09 26.59 17.22 28.45 10.14 26.01 27.60 26.35 25.82 26.25
18.46 31.08 18.58 35.45 13.16 29.93 33.30 30.60 29.58 30.39
19.77 29.26 19.90 31.11 12.83 28.67 30.26 29.02 28.49 28.91
Botswana Brazil Bulgaria Burkina Faso Burundi
18.89 22.16 20.72 35.34 44.79
20.25 23.47 22.13 31.43 34.21
17.37 20.90 19.34 35.09 45.28
18.84 22.34 20.89 31.02 34.06
19.05 22.12 20.77 34.45 43.29
20.33 23.42 22.14 31.05 33.72
18.02 21.17 19.78 33.87 42.98
19.34 22.54 21.21 30.46 33.22
15.88 19.04 17.65 31.78 40.91
17.20 20.33 19.03 28.08 30.78
18.56 21.73 20.33 34.48 43.62
19.88 23.00 21.71 30.74 33.44
Cambodia Cameroon Canada Cape Verde Central African Republic
36.43 35.55 12.84 29.73 44.29
31.84 31.51 12.26 28.81 34.10
36.26 35.32 10.85 29.05 44.74
31.47 31.11 10.13 28.17 33.94
35.46 34.64 13.39 29.20 42.82
31.45 31.13 12.67 28.54 33.62
34.92 34.08 12.19 28.46 42.50
30.86 30.54 11.39 27.85 33.12
32.83 31.98 10.03 26.35 40.43
28.47 28.16 9.42 25.53 30.68
35.53 34.68 12.71 29.05 43.14
31.14 30.82 12.12 28.20 33.34
Chad Chile China Colombia Comoros
39.47 16.62 17.47 22.89 42.89
32.85 17.60 18.64 24.10 33.78
39.54 14.93 15.84 21.68 43.23
32.57 15.95 17.08 23.03 33.58
38.31 16.93 17.73 22.79 41.51
32.41 17.79 18.79 24.02 33.30
37.85 15.83 16.65 21.87 41.15
31.87 16.70 17.74 23.16 32.79
35.77 13.69 14.51 19.74 39.07
29.46 14.62 15.63 20.94 30.36
38.47 16.37 17.19 22.43 41.78
32.12 17.31 18.31 23.61 33.02
Congo Costa Rica Coˆte d’lvoire Croatia Cuba
41.80 22.44 41.39 20.41 43.57
33.50 23.71 33.40 21.83 33.94
42.06 21.20 41.61 19.01 43.97
33.28 22.61 33.16 20.56 33.76
40.50 22.38 40.11 20.48 42.15
33.04 23.65 32.94 21.85 33.46
40.11 21.44 39.71 19.49 41.81
32.52 22.78 32.41 20.91 32.95
38.03 19.31 37.63 17.35 39.74
30.09 20.57 29.99 18.74 30.52
40.73 22.00 40.33 20.04 42.44
32.75 23.24 32.65 21.41 33.18
Cyprus Czech Republic Dem. Republic of Congo (Zaire) Denmark Djibouti
17.31 18.45 15.67 16.88 17.58 18.61 16.50 17.55 14.36 15.45 17.04 18.13 16.86 17.90 15.19 16.28 17.16 18.08 16.07 17.00 13.92 14.91 16.60 17.60 47.54 34.76 48.24 34.65 45.86 34.24 45.63 33.77 43.57 31.31 46.28 33.97
Dominican Republic East Timor Ecuador Egypt El Salvador
28.77 36.50 30.13 22.98 23.18
Country
Australia Country Risk Rating Log Linear Model Model Thru 3-06
12.70 12.04 10.70 9.89 13.26 12.46 12.05 11.17 9.90 9.21 12.57 11.90 34.19 30.97 33.86 30.52 33.37 30.61 32.77 30.00 30.67 27.63 33.37 30.29 28.27 31.87 29.03 24.18 24.34
28.02 36.35 29.48 21.78 21.99
27.58 31.50 28.41 23.12 23.30
28.30 35.53 29.57 22.88 23.07
28.02 31.47 28.75 24.10 24.25
27.54 34.99 28.85 21.96 22.15
27.31 30.89 28.07 23.24 23.40
25.43 32.90 26.74 19.84 20.02
25.00 28.50 25.74 21.02 21.18
28.12 35.60 29.43 22.52 22.71
27.67 31.16 28.41 23.69 23.85
Cost of Capital Resources Web Site Exhibit 19.8
359
(Continued) International Cost of Capital Country Risk Rating Model from International Perspectives
Country
Australia Country Risk Rating Log Linear Model Model Thru 3-06
Canada Country Risk Rating Log Linear Model Model Thru 3-06
France Country Risk Rating Log Linear Model Model Thru 3-06
Germany Country Risk Rating Log Linear Model Model Thru 3-06
Japan Country Risk Rating Log Linear Model Model Thru 3-06
U.K. Country Risk Rating Log Linear Model Model Thru 3-06
Eritrea Estonia Ethiopia Finland France
40.30 17.66 38.16 12.67 12.86
33.10 18.86 32.44 11.99 12.29
40.44 16.04 38.14 10.67 10.87
32.84 17.32 32.12 9.83 10.16
39.09 17.90 37.09 13.23 13.41
32.65 19.00 32.02 12.41 12.70
38.86 16.83 36.60 12.02 12.20
32.11 17.95 31.46 11.12 11.42
36.58 29.69 39.28 32.36 14.69 15.84 17.37 18.53 34.51 29.06 37.21 31.72 9.87 9.16 12.54 11.85 10.05 9.45 12.72 12.14
Gabon Gambia Georgia Germany Ghana
37.19 36.58 33.24 12.91 29.73
32.11 31.90 30.56 12.37 28.81
37.09 36.43 32.84 10.92 29.05
31.77 31.53 30.07 10.25 28.17
36.18 35.60 32.48 13.46 29.20
31.71 31.50 30.22 12.77 28.54
35.66 35.07 31.85 12.25 28.46
31.14 30.92 29.59 11.50 27.85
33.57 32.97 29.75 10.10 26.35
28.74 28.53 27.23 9.53 25.53
36.27 35.67 32.45 12.77 29.05
31.40 31.19 29.89 12.22 28.20
Greece Grenada Guatemala Guinea Guinea-Bissau
15.84 34.52 25.46 42.78 45.57
16.60 31.10 26.11 33.75 34.38
14.08 34.21 24.45 43.11 46.11
14.85 30.67 25.23 33.55 34.23
16.20 33.68 25.21 41.41 44.02
16.83 30.74 25.95 33.28 33.88
15.08 33.09 24.36 41.04 43.73
15.70 30.13 25.17 32.76 33.39
12.93 30.99 22.23 38.96 41.66
13.64 27.76 22.90 30.33 30.94
15.61 33.68 24.92 41.67 44.37
16.33 30.42 25.57 32.99 33.60
Guyana Haiti Honduras Hong Kong Hungary
32.06 37.43 30.43 15.55 18.54
30.01 32.20 29.20 16.21 19.87
31.56 37.35 29.81 13.77 16.99
29.48 31.86 28.59 14.44 18.42
31.38 36.40 29.86 15.93 18.73
29.69 31.79 28.91 16.46 19.97
30.71 35.89 29.15 14.80 17.68
29.05 31.22 28.23 15.32 18.96
28.61 33.80 27.04 12.65 15.54
26.70 28.82 25.90 13.27 16.83
31.30 36.50 29.73 15.33 18.22
29.36 31.48 28.57 15.96 19.51
Iceland India Indonesia Iran Iraq
14.60 20.69 25.69 26.00 49.61
14.90 22.10 26.28 26.50 35.11
12.75 19.31 24.70 25.03 50.47
13.01 20.86 25.41 25.64 35.04
15.04 20.74 25.42 25.71 47.80
15.21 22.11 26.11 26.32 34.58
13.88 19.76 24.58 24.87 47.63
14.02 21.18 25.33 25.55 34.12
11.74 17.62 22.46 22.75 45.57
12.00 19.00 23.06 23.27 31.66
14.41 20.31 25.14 25.44 48.29
14.69 21.68 25.73 25.94 34.32
Ireland Israel Italy Jamaica Japan
13.13 18.25 14.39 28.00 14.26
12.72 19.54 14.60 27.80 14.41
11.17 16.68 12.52 27.18 12.38
10.63 18.06 12.69 27.07 12.48
13.67 18.46 14.84 27.58 14.72
13.11 19.65 14.92 27.58 14.74
12.47 17.40 13.68 26.80 13.56
11.85 18.63 13.72 26.85 13.53
10.32 15.26 11.53 24.68 11.41
9.87 16.51 11.70 24.55 11.52
12.99 17.94 14.21 27.37 14.08
12.57 19.19 14.39 27.22 14.21
Jordan Kazakstan Kenya Kiribati Kuwait
23.85 20.92 32.70 30.08 16.84
24.89 22.32 30.31 29.00 17.88
22.71 19.58 32.25 29.42 15.16
23.89 21.10 29.80 28.38 16.25
23.69 20.95 31.98 29.52 17.14
24.78 22.32 29.98 28.73 18.06
22.80 19.98 31.33 28.80 16.05
23.95 21.40 29.34 28.04 16.98
20.67 17.84 29.23 26.69 13.90
21.71 19.21 26.99 25.71 14.89
23.36 20.52 31.92 29.38 16.58
24.38 21.89 29.65 28.38 17.57
Kyrgyzstan Laos Latvia Lebanon Lesotho
35.13 34.72 18.52 30.23 30.28
31.35 31.19 19.84 29.09 29.11
34.87 34.43 16.97 29.59 29.64
30.93 30.76 18.39 28.47 28.50
34.25 33.87 18.71 29.66 29.71
30.97 30.82 19.94 28.80 28.83
33.67 33.28 17.66 28.95 29.00
30.38 30.21 18.93 28.12 28.15
31.58 31.18 15.52 26.84 26.89
28.00 27.84 16.80 25.79 25.82
34.27 33.88 18.20 29.53 29.58
30.66 30.50 19.48 28.46 28.49
Liberia Libya
47.69 34.79 48.40 34.68 46.00 34.27 45.78 33.79 43.71 31.34 46.42 34.00 24.69 25.54 23.62 24.60 24.48 25.40 23.61 24.60 21.49 22.34 24.17 25.02
Source: International Cost of Capital Perspectives Report 2006. Copyright # 2006 Morningstar, Inc. All rights reserved. Used with permission. (Morningstar, Inc. acquired Ibbotson in 2006.) To purchase copies of the International Cost of Capital Perspectives Report, or for more information on other Morningstar publications, please visit global.morningstar.com/DataPublications.
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Cost of Capital
The Duff & Phelps Risk Premium Report is written by Roger Grabowski and David King. Companies are divided into 25 different size groups (see Chapter 12) based on:
Market value of equity
Book value of equity
Five-year average net income Market value of invested capital
Total assets Five-year average earnings before interest, taxes, depreciation, and amortization
Sales
Number of employees
Also into 3 different risk groups (see Chapter 14) based on:
Operating margin
Coefficient of variation of operating margin
Coefficient of variation of return on equity
Part 3
Corporate Finance Officers: Using Cost of Capital Data
Chapter 20
Capital Budgeting and Feasibility Studies Introduction Invest for Returns above Cost of Capital DCF Is Best Corporate Decision Model Focus on Net Cash Flow Capital Cash Flow and Adjusted Present Value Methods Use Target Capital Structure over Life of Project Summary
INTRODUCTION Good cost of capital estimation is essential to sound capital budgeting and feasibility analysis decisions. Because this issue has been the subject of many texts, many people take for granted that companies are effective in allocating capital to projects. But the evidence is not clear. For example, in one study the authors find that returns on real assets by corporations derived from actual cash flows (cash investments compared to cash flows realized) over long periods appear to be, on the average, lower than the returns expected by the providers of investment capital to the corporations and that the standard deviations of realized returns by corporations (i.e., risk) from such investments has been increasing.1 Such results point to the need for increased diligence in the capital budgeting process.
INVEST FOR RETURNS ABOVE COST OF CAPITAL When addressing capital budgeting and feasibility analysis decisions, popular phrases in contemporary corporate finance literature are shareholder value added (SVA) and economic value added (EVA). The essence of the way to add value is to invest funds in a project that will earn a higher rate of return than its cost of capital (see Chapter 24). As Brealey, Myers and Allen say in their capital budgeting chapter of their classic text on Principles of Corporate Finance, ‘‘Accept any project that more than compensates for the project’s beta.’’2 In the case of selection among multiple potential projects competing for limited funds, analysts recommend investing in those with the highest net present value (NPV). Net present value is 1
2
James S. Ang, Gregory Leo Nagel, and Jun Yang, ‘‘A Critical Long View of Capital Markets and Institutions: Realized Returns from Corporate Assets, 1950–2003,’’ Working paper, March 13, 2006. Richard A. Brealey, Stewart C. Myers, and Franklin Allen, Principles of Corporate Finance, 8th ed. (Boston: Irwin McGrawHill, 2006), 216.
363
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estimated by discounting the expected cash outflows and expected cash inflows from the project by the project’s cost of capital. Note two important points in the last sentence: 1. Cash flow is the preferred measure of economic income. 2. The project’s cost of capital is the preferred focus, as opposed to the company’s cost of capital. [T]he company cost of capital is not the correct discount rate if the new projects are more or less risky than its existing business. Each project should be evaluated on its own opportunity cost of capital.3
DCF IS BEST CORPORATE DECISION MODEL At a seminar on frontiers in corporate valuation, Tom Copeland, coauthor of Valuation: Measuring and Managing the Value of Companies, compared the use of ratios, formulas, and discounted cash flow (DCF) analysis for purposes of corporate decision making. In evaluating the three approaches, he noted: The most important criterion for comparing approaches is that they result in good decisions, because the model value is close to the equilibrium market value.4
Copeland asks these questions:
How well do the model values match market values?
Is the model logical? Is the approach easy to understand and use?
Does the approach easily lend itself to a wide variety of decision-making applications?
Copeland’s list of pros and cons for each of the three approaches to corporate decision making is shown in Exhibit 20.1. He concludes unequivocally that the DCF approach is superior.
FOCUS ON NET CASH FLOW Copeland notes that the DCF approach captures all elements of value. He also states: Managers who are interested in maximizing share value should use discounted cash flow analysis to make decisions, not earnings per share. . . . The market is not fooled by cosmetic earnings increases; only earnings increases that are associated with improved long-term cash flows will increase share prices. The evidence that the market focuses on cash flows can be grouped into four areas, showing that:
3 4
Accounting earnings is not very well correlated with share prices.
Earnings ‘‘window dressing’’ does not improve share prices.
Ibid. Tom Copeland, Seminar on Frontiers in Corporate Valuation, New York University Leonard N. Stern School of Business, November 6–7, 1997.
Focus on Net Cash Flow Exhibit 20.1
365
Pros and Cons of Approaches to Corporate Decision Making
Ratios are the oldest form of valuation methodology because they are easy to use. They provide a direct, simple link between easy-to-observe variables like earnings and market prices. Pros and Cons of Ratios Pros
Cons
Easy to use Based on comparables
Difficult to find exact comparables Heavily dependent on accounting standards No logic that leads back to a fundamental understanding (e.g., should earnings in a P/E ratio be normalized) P/E ratio does not focus on balance sheet, and market/book ratio does not focus on income statement Generally low correlation with actual market values Not particularly useful for day-to-day operating decisions
Formulas are fairly simple to use but are crude tools because their simplicity requires that they make strong (often unrealistic) assumptions.
Pros and Cons of Formulas Pros
Cons
Easy to use Logic does tie back to fundamentals (e.g., cash flows to the owner)
Make strong implicit assumptions (e.g., constant growth forever) Depend strongly on a point estimate of cash flows or earnings Require modest amounts of training regarding the underlying math Not useful for day-to-day operating decisions
Discounted cash flows are best for decision making but are more complex than the alternatives.
Pros and Cons of DCF Pros
Cons
Clear logical link to the underlying fundamentals Matches actual market values quite well Lends itself to a wide variety of decision-making applications Not dependent on changes in accounting principles, depends only on actual cash flow
Complex, requires training
Source: Tom Copeland, Seminar on Frontiers in Corporate Valuation, New York University Leonard N. Stern School of Business, November 6–7, 1997. Used with permission. All rights reserved.
The market evaluates management decisions based on their expected long-term cash flow impact, not the short-term earnings impact.
There are many decisions where cash flows and earnings per share give opposing results.5
In a capital budgeting context, the residual value may not be the typical perpetuity assumed in the valuation of a business as the investment may have a finite life. Cleanup costs, if any, that must be expended at the end of the life of the investment must be included as a cash outflow in the terminal 5
Ibid.
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Cost of Capital
value. The appropriate cost of capital (risk) for future expenditures for cleanup may be lower than the unlevered cost of equity capital used to discount the expected cash flows resulting from the investment.
CAPITAL CASH FLOW AND ADJUSTED PRESENT VALUE METHODS Generally speaking, most contemporary literature and seminars on corporate finance advocate discounting expected cash inflows and outflows at a weighted average cost of capital (WACC). The characteristics of a project, either risk or special financing opportunities unique to the project, may cause the WACC for the project to differ from the company’s overall WACC. However, two variations on DCF analysis, called the capital cash flow (CCF) method and adjusted present value (APV) method, advocates taking DCF analysis for project selection in a different direction. Instead of the WACC adjusted for the tax savings on interest expense, the CCF method uses a WACC(pt) and directly values the present value of the tax savings on debt financing (the tax shield). Instead of an overall project WACC, the APV approach estimates a base-case value by unbundling the components of value and analyzing each separately. APV starts with a base-case value, discounting all cash flows from the project as if they were financed entirely by equity. As such, if you are developing a cost of equity capital using the Capital Asset Pricing Model (CAPM), for example, you unlever the estimated beta; that is, you use an asset beta (see Chapter 10). APV then adds or subtracts increments or decrements of value from all financing side effects. The list includes:
Plus: interest tax shields (reduced income taxes due to ability to deduct interest payments)
Minus: cost of financial distress (loss of firm value due to the increase in the chance of default induced by the firm’s debt)6
Plus: subsidies
Plus: hedges Minus: issue costs
Minus: other costs7 Timothy A. Leuhrman, author of ‘‘Using APV,’’ claims that the particular version of DCF that has been accepted as the standard over the past 20 years—using the weighted average cost of capital (WACC) as the discount rate—is now obsolete. . . . Adjusted present value (APV) is especially versatile and reliable, and will replace WACC as the DCF methodology of choice among generalists.8
Some advocates of the APV method believe that it is more flexible where capital structure is expected to change (though in Appendix 17B we show how to adjust the WACC for changing capital
6
7 8
See Arthur Korteweg, ‘‘The Costs of Financial Distress across Industries,’’ Working paper, January 15, 2007, for an estimate of the costs of financial distress and measurement techniques. Timothy A. Luehrman, ‘‘Using APV: A Better Tool for Valuing Operations,’’ Harvard Business Review (May–June 1997): 145. Ibid., 145–153.
Summary
367
structure), develops a discrete value for the tax shields, and may provide a more accurate measure of value.9 We discuss both CCF and APV methods in Chapter 17.
USE TARGET CAPITAL STRUCTURE OVER LIFE OF PROJECT While the consensus advocates focusing on the cost of capital of the project rather than on the overall company cost of capital, to the extent that they differ, the focus should encompass the life of the project rather than any temporary effects. For example, if the project requires an abnormal level of debt financing that would temporarily change the company’s capital structure, the WACC should reflect the company’s target capital structure rather than the abnormal structure when the investment initially is made. We discuss the development of the WACC with a changing capital structure in Chapter 17 and present a comprehensive example in Appendix 17B. One author recently studied the financing of expansion projects and analyzed the process in terms of real options in an initial capital structure and an adjustment to that initial capital structure as more is learned about the outcome of the expansion project and the ultimate need for capital.10
SUMMARY This is a short chapter because the essential principles of using cost of capital for capital budgeting and project selection are basically the same as for other applications already discussed. The general consensus is:
Discounted cash flow is the best model for corporate finance decisions.
Focus on net cash flow as the economic income variable of choice. Each project should be analyzed in light of its own cost of capital characteristics, rather than automatically using the company’s overall cost of capital.
The cost of capital used should be the target cost of capital over the life of the project. New variations of cost of capital applications are constantly being developed.
Authors have recently concluded that the overall, firm-wide WACC is not the proper hurdle rate for the firm’s operating assets if the firm uses an active risk management strategy.11
9
Marianne DeMario and Anthony P. Fazzone, ‘‘The Adjusted Present Value: An Alternative Approach to the Effect of Debt on Business Value,’’ Business Valuation Update (December 2006): 1–4. 10 Sudipto Sarkar, ‘‘Expansion Financing and Capital Structure,’’ Working paper (January 2007). 11 Neil A. Doherty, ‘‘Risk Management, Risk Capital, and the Cost of Capital,’’ Journal of Applied Corporate Finance (Summer 2005): 119–123; and Thomas J. O’Brien, ‘‘Risk Management and the Cost of Capital for Operating Assets,’’ Journal of Applied Corporate Finance (Fall 2006): 105–109.
Chapter 21
Cost of Capital for Divisions and Reporting Units
Introduction Divisional Cost of Capital Estimating Divisional Cost of Equity Capital Divisional Size as a Risk Measure Reporting Unit Cost of Capital What Is a Reporting Unit? Testing for Impairment of Goodwill Determining Fair Value of Reporting Units Measuring the Cost of Capital of Reporting Units Reporting Unit Size as a Risk Measure Cost of Capital for Assets of Reporting Units New Rules for Accounting for Business Combinations Summary Additional Reading
INTRODUCTION In this chapter we discuss the factors that affect the cost of capital of divisions and reporting units, with particular emphasis on the appropriate cost of capital for divisions and reporting units within an integrated firm. Divisional costs of capital are important because according to modern finance theory, the overall cost of capital for the firm is the weighted average of the cost of capital (WACC) making up the company. The firm is viewed as a portfolio of businesses comprising the divisions, with each such business or division having distinctive risk characteristics. You cannot simply apply the company’s overall WACC to determine the value of each business. Nor can you apply the company’s overall cost of capital in making capital budgeting decisions. If the risk of divisional cash flows differs from that of the overall company cash flows, the appropriate discount rate for an investment decision at the division level should reflect the risk of that investment. Reporting units are a by-product of the Financial Accounting Standard Board’s (FASB) Statement of Financial Accounting Standard (SFAS) No. 142, Goodwill and Other Intangible Assets. That accounting standard calls for grouping of firm assets, including goodwill, by reporting units. With the adoption of SFAS No. 142, goodwill was not subject to amortization but tested for impairment at the reporting unit level, the same level as or one level below a SFAS No. 131, Disclosures about Segments of an Enterprise and Related Information, operating segment. Designating reporting units is Thank you to Nathan Levin, Duff & Phelps LLC, for his contribution in preparing this chapter.
369
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Cost of Capital
based on SFAS No. 131 operating segments before aggregation into reportable segments. (See ‘‘What Is a Reporting Unit?’’ later in this chapter). Determining the cost of capital of a reporting unit is the first step in testing for goodwill impairment. Because all company assets are assigned to reporting units and, if impairment is indicated under the step 1 test, those assets must be valued in testing for impairment of goodwill in step 2, we also discuss the appropriate cost of capital for the underlying assets of a reporting unit. That discussion is also relevant in the valuation of businesses accounted for under SFAS No. 141, Business Combinations.
DIVISIONAL COST OF CAPITAL The calculation of each division’s cost of capital is not a simple task. The main problem is the availability of information. For a public company, the only directly observable data generally are those pertaining to the overall cost of capital for the entire business. For example, assume you will use the Capital Asset Pricing Model (CAPM) to estimate the cost of equity capital. The tools available to directly estimate the company’s beta (e.g., ordinary least squares regression of company excess returns against the excess returns of the Standard & Poor’s [S&P] 500) measure the overall company beta, as those are the only stock return data available. These are the data on the returns for the entire company. How can you estimate the cost of capital for a division? The first task is to develop an overall cost of capital for the subject firm. Then you can estimate the risks and appropriate cost of capital for the individual divisions or other group of assets. Since generally you cannot observe rates of return for the individual divisions in the marketplace, ultimately you must reconcile the weighted average rate of return of the individual divisions (weighted by their values) to the overall firm cost of capital. Chapter 17 discussed the fact that the overall rate of return on invested capital, the weighted average cost of capital, embodies two risks, the financial risk of using debt capital and the unlevered or asset risk of the assemblage of the assets of the firm. Financing of firm assets is often undertaken at the corporate level as opposed to the divisional level. Therefore, it is useful to begin by developing the unlevered cost of equity capital for the firm as a whole and then the unlevered costs of equity capital for each division. Allocation of debt to the divisions can be based on the respective debt capacities of the divisions or on the relative values of the divisions. ESTIMATING DIVISIONAL COST OF EQUITY CAPITAL You can look to the market and locate guideline public firms for each division. The process is one of matching the business functions performed and the investment in the mix of underlying assets used in the business, and evaluating the risks of the business. This process is analogous to estimating the cost of equity capital for a closely held company. For example, the process begins by a search to locate ‘‘pure plays,’’ companies specializing in a very narrow business line that parallels the business of the subject division. You can unlever the observed risk measure—for example, the observed betas of the pure play guideline public companies—to estimate the business risk of the division (asset betas). The search for such narrow pure plays often leads to smaller companies. The business risk of the smaller pure plays may or may not be comparable to the business risk of the subject division, even if the description of the line of business appears that it is comparable. Comparability requires close matching of risk characteristics as well as general business function. Alternatively, you can use the full-information beta technique (using asset betas of the guideline public companies used in the analysis) to increase the sample size of potential guideline public companies for a particular division.
Divisional Cost of Capital
371
These methods are discussed in Chapter 10. Another tool you can use is the Duff & Phelps Risk Premium Report to help quantify the relative risks of the size of the division (contained in the Size Study portion of the report). We discussed using the Size Study to develop the cost of equity capital in Chapters 8 and 12. You can use the unlevered equity risk premiums in Exhibits C-1 through C-8 of the Risk Premium Report to estimate an asset or unlevered cost of equity capital using the build-up method based on the fundamental size of the division. Alternatively, you can use the premiums over CAPM indicated in the SBBI Valuation Edition Yearbook or the premiums over CAPM in Exhibits B-1 through B-8 of the Risk Premium Report and add the indicated size premium to the base indicated cost of equity capital for the division. In either case, you must be aware that the aggregate risk of the firm’s divisions may in fact be less than the build-up of firm risk that you get by adding the risks of the various divisions due, for example, to synergies among the divisions. Another tool is to match the fundamental risks of the divisions with the appropriate return. As discussed in Chapter 10, you could use fundamental or accounting betas (asset betas) as an alternative to market betas. The Duff & Phelps Risk Study (see Chapter 14) quantifies rates of return based on these fundamental risk measures: 1. Profitability (operating profit margin or operating profit / revenue) 2. Volatility of operating profit margin 3. Volatility of Return on equity (NI/book value of equity) Using such fundamental risk measures, you can directly measure the risks of each division and then reconcile the weighted average of the indicated returns to the overall rate of return required for investing in the firm. Regardless of the methodology used, you are basing the cost of equity capital estimates on observed market relationships of risk and return while reconciling to the overall firm unlevered cost of equity capital. Once you determine the appropriate amount of debt for each division, you can relever the cost of equity capital for each division, calculate the respective WACCs for each division, and reconcile (based on the relative estimated values) the WACCs of the divisions to the overall WACC for the firm. DIVISIONAL SIZE AS A RISK MEASURE While business size is certainly a risk factor in and of itself (see the discussion in Chapter 12), the resources of a much larger overall company can impact the relative risks of a company’s divisions vis-a`-vis their competitors. A division that is the fifth largest competitor in an industry likely is at a disadvantage to its larger competitors (whether they are stand-alone companies or divisions of other multidivisional firms). However, being a member division of a larger company can mitigate at least in part some of those risks. For example, the credit quality of the entire firm impacts the availability and cost of debt capital for the division when it is making its investments in fixed assets or product development. Thus with regard to debt capital, there may be an integration of the financing function firm-wide and a reduction in the apparent risks of business size of a division as a stand-alone entity. Therefore, you must measure division size compared to the division’s business competitors and evaluate the resources of the entire firm in overcoming competitive disadvantages inherent in being a small-size firm in an industry.
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Cost of Capital
REPORTING UNIT COST OF CAPITAL While this book is not a treatise on financial reporting under SFAS Nos. 141 and 142, it is helpful to review some of the background prior to discussing the cost of capital appropriate to apply. The standard of value applicable for SFAS Nos. 141 and 142 is fair value as defined in these and other standards issued by the FASB (e.g., SFAS No. 157, Fair Value Measurements). Therefore, when we use the term fair value in this chapter, we mean the accounting definition, not fair value in the context of shareholder disputes. WHAT IS A REPORTING UNIT? When is the reporting unit one level below the operating segment? If the components of the operating segment have different economic characteristics, the components with common economic characteristics become a reporting unit. Issues involved in identifying reporting units are:
Is it a business (Emerging Issues Task Force 98–3) for which discrete financial information is available? Does segment management regularly review the operating results of that component of the segment?
Two or more components of an operating segment are aggregated and considered a single reporting unit if they have similar economic characteristics (SFAS No. 131, par. 17). Companies have a great deal of discretion in identifying reporting units. TESTING FOR IMPAIRMENT OF GOODWILL Goodwill must be tested for impairment at least annually, though different reporting units may be tested for impairment at different times. In addition, interim impairment tests are required if an event occurs or circumstances change that would ‘‘more likely than not’’ reduce the fair value of a reporting unit below its carrying value, a so-called triggering event. Examples of such events are: significant adverse change in business climate, legal issue, regulatory/issue, change in competition, and loss of key personnel. Another reason for interim goodwill testing arises if a more-likely-than-not expectation surfaces that a reporting unit (or significant portion) will be sold or otherwise disposed of. Testing for goodwill impairment is a two-step test. Step 1. Compare fair value to book value (including goodwill) of reporting unit. If book value of the reporting unit is greater than the fair value of the reporting unit, then goodwill of the reporting unit is impaired, and Step 2 is required to measure impairment. Step 2. Measure excess of recorded goodwill over its implied fair value. Add the fair value of reporting unit to the liabilities of the reporting unit (whether carried on the books or not). Subtract the fair values of the reporting unit’s recognized (on the books) and unrecognized assets (not on the books), excluding goodwill, but including in-process research and development of the segment. The process of measuring the fair values of assets and liabilities is similar to a purchase price allocation under SFAS No. 141, though you do not record unrecognized or restate recognized assets, as this is only a test to determine the extent to which goodwill should be reduced. Exhibit 21.1 shows an example of a goodwill impairment calculation, comparing fair values (FVs) to book values (BVs).
Reporting Unit Cost of Capital Exhibit 21.1
373
Example Goodwill Impairment Calculation
Reporting Units: Step 1 FV of Reporting Unit BV of Reporting Unit Step 2 FV of Reporting Unit B FV of Reporting Unit’s Individual Assets/Liabilities (both recognized and unrecognized) Implied FV of Goodwill BV of Reporting Unit’s Goodwill Goodwill Impairment Charge
A
B
$1,000 600 $400
$500 600 $(100)
Step 2
$500
N/A
425 75 200 $125
Oftentimes managements of clients’ businesses ask if impairment charges are recognized by the equity markets. That is, do stock prices react to impairment charges? In one study, the authors find that goodwill impairments and goodwill balances are more closely associated with stock returns in the post–SFAS No. 142 period (after adjusting for the 1998 to 2000 stock market bubble and the substantial drop in stock prices after 2000) than in the period prior to enactment of SFAS No. 142 by the FASB.1 Those authors conclude that the equity markets recognize the improvement in financial information available to investors resulting from goodwill impairments under SFAS No. 142 and use that information in pricing stocks. The information is found to be most meaningful among companies with a high number of segments. In another study, the authors find that an impairment charge is associated with roughly an equivalent reduction in the market value of equity.2 Cost of capital can have a significant impact on determining the fair value of reporting units and such impairment charges. DETERMINING FAIR VALUE OF REPORTING UNITS You determine the fair value of a reporting unit by looking at:
Quoted market price of reporting unit’s stock (if publicly traded), although the aggregate market value need not be the sole measurement basis of fair value of the reporting unit (e.g., control premium may be appropriate to add)
Present value techniques (with reference to FASB Concepts Statement No. 7 and SFAS No. 157) Market multiples of ‘‘pure play’’ guideline publicly traded companies
Net cash flows of the reporting units and assets of the reporting units should be based on assumptions of marketplace participants, if available, under the premise that fair value is the price to sell an asset or liability and therefore represents an exit price, not an entry price (SFAS No. 157). Assets are grouped for valuation such that their fair value would be maximized (i.e., assuming the highest and best use of the assets to the market participants would be to bundle the assets together). 1
2
Anwer S. Ahmed and Lale Guler, ‘‘Evidence on the Effects of SFAS 142 on the Reliability of Goodwill Write-offs,’’ Working paper, May 25, 2007. Kevin Li and Geoff Meeks, ‘‘The Impairment of Purchased Goodwill: Effects on Market Value,’’ Working paper, November 28, 2006.
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Cost of Capital
According to SFAS No. 157, in assessing marketplace participant assumptions, you must evaluate the risks inherent in the particular valuation technique used to measure fair value (pricing model risk) and/or the risk inherent in the inputs to the valuation technique (input risks). Owner specific synergies are to be ignored. Cash flows resulting from such synergies flow to residual goodwill. MEASURING THE COST OF CAPITAL OF REPORTING UNITS The cost of capital for a reporting unit is not the overall cost of capital for the firm owning the reporting unit. Nor is it the overall cost of capital of market participants that make up the pool of likely hypothetical buyers of the reporting unit. Rather, it is the cost of capital that market participants would determine is appropriate for the risks of the reporting unit’s business and use in the valuation of the reporting unit. Thus synergies of the reporting unit with the parent company that are unlikely to be available to market participants who would likely buy the reporting unit should not enter into the estimation of the expected cash flows or of the cost of capital. How can we measure risk? As discussed in the section of this chapter ‘‘Estimating Divisional Cost of Equity Capital,’’ you can look to the stock market and locate guideline public firms providing a narrow range of products and services comparable to those of the reporting unit (‘‘pure plays’’). You can then estimate a beta appropriate for the risk of the reporting unit using the beta estimates (unlevered) of the pure plays. Examining the unlevered betas relative to the respective sizes of the pure play guideline companies being compared to the reporting unit will aid you in determining how market participants may assess their relative business risks. Alternatively, you can use the full-information beta technique (using asset betas of the guideline public companies included in the analysis) to increase the sample size of guideline public companies for the particular reporting unit. These methods are discussed in Chapter 10. Another tool you can use is the Size Study portion of the Duff & Phelps Risk Premium Report to help quantify the relative risks of the size of the reporting unit. We discussed using the Size Study to develop the cost of equity capital in Chapters 8 and 12. You can use the unlevered equity risk premiums in Exhibits C-1 through C-8 of the Risk Premium Report to estimate an asset or unlevered cost of equity capital using the build-up method. Alternatively, you can use the premiums over CAPM indicated in the SBBI Valuation Edition Yearbook or premiums over CAPM in Exhibits B-1 through B-8 of the Risk Premium Report and add the indicated size premium to the base indicated cost of equity capital for the reporting unit. Finally, another tool is to match the fundamental risks of the reporting units with the appropriate return. One can use fundamental or accounting betas (asset betas) as an alternative to market betas (see Chapter 10) or fundamental risk measure (see Chapter 14). REPORTING UNIT SIZE AS A RISK MEASURE Is size an appropriate proxy for the risk of a reporting unit? For example, the subject business may have a large segment made up of several reporting units. If you were estimating the cost of capital of the segment, the size may be such that little or no size premium needs to be added to correct the cost of equity capital estimate arrived at by using the CAPM. But sometimes the sizes of one or more of the reporting units are such that adding a size premium may be appropriate. Thus, the WACC for the reporting units may be greater than the cost of capital of the segment. How can this be? You must measure the risks of the reporting units relative to those of the competitors of the reporting units. We are measuring values of the reporting units as you would expect market participants to do.
Reporting Unit Cost of Capital
375
Market participants should not use their overall cost of capital in valuing a reporting unit either. Rather, they will evaluate the risks of the reporting units compared to the risks of the reporting unit’s competitors. For example, assume we are analyzing a company operating in multiple countries, and the segment of the company we are analyzing operates in multiple countries. The appropriate cost of capital for the segment is the WACC of its operations in the various countries. The segment may have integrated operations such that the size of the segment is considered large among its competitors and no size premium is determined to be appropriate. However, in this case, the segment is made up of multiple reporting units, each operating in a different geographic area. In developing appropriate costs of capital for the reporting units, you must evaluate the risks of each reporting unit relative to its competitors, including the relative size of the reporting unit to its competitors. Assume we are looking at a reporting unit operating in Africa, and the reporting unit, while small in an absolute sense if measured on a worldwide basis, is large in Africa. In fact, it is larger than any of its competitors when size is measured among African companies, and it holds the leading share in its industry in its geography. Size may become a meaningless proxy for business risk in such a case. Instead, you need to turn to fundamental risk measures to evaluate the risk of that African-based reporting unit. What about the appropriate debt of the reporting unit? You can look to the industry-average capital structure (based on market value weights) of the pure play guideline public companies being compared to the reporting unit as a proxy for the likely financing that market participants would employ in acquiring the reporting unit. Alternatively, if likely market participants can be identified (e.g., there are six likely companies that would acquire the reporting unit if it were sold), the average capital structure of those specifically identified market participants may be the most likely financing structure market participants would employ. COST OF CAPITAL FOR ASSETS OF REPORTING UNITS It is useful to begin with the definition of a business enterprise and relate it to the fair value of a reporting unit and the underlying assets of the reporting unit: (Formula 21.1) BE ¼ RU and RU ¼ NWCRU þ FARU þ IARU þ UIVRU where: BE ¼ Business enterprise RU ¼ Reporting unit NWCRU ¼ Net working capital of the reporting unit FARU ¼ Fixed assets of the reporting unit IARU ¼ Intangible assets of the reporting unit UIVRU ¼ Unidentified intangible value (i.e., goodwill) of the reporting unit As we discussed in Chapter 5, the cost of capital is equal to the return that could have been expected on alternative investments given a specific level of risk. Generally, the term cost of capital has three different meanings to three different users:
376
Cost of Capital
1. Asset view (discount rate used to discount future values of cash flows to be derived from assets to present value) 2. Liability view (economic cost to a firm of attracting and retaining capital where investors carefully analyze and compare all return-generating opportunities) 3. Investor’s view (return you expect from your investments in a firm’s debt or equity, given a specific level of risk for the investment) Following that thought process, the reporting unit can be valued as shown in Formula 21.2: (Formula 21.2) FVRU ¼ FVICRU and FVRU ¼ FVNWCRU þ FVFARU þ FVIARU þ FVUIVRU and FVICRU ¼ FVdRU þ FVeRU where: FVRU ¼ Fair value of reporting unit FVICRU ¼ Fair value of invested capital of the reporting unit FVNWCRU ¼ Fair value of net working capital of the reporting unit FVFARU ¼ Fair value of fixed assets of the reporting unit FVIARU ¼ Fair value on intangible assets, identified and individually valued, of the reporting unit FVUIVRU ¼ Fair value of unidentified intangibles value (i.e., goodwill) of the reporting unit FVdRU ¼ Fair value of debt capital of the reporting unit FVeRU ¼ Fair value of equity capital of the reporting unit Since you generally cannot observe the rates of return for assets in the marketplace, you can use the overall cost of capital for the reporting unit developed from observations of the appropriate rates of return for the invested capital side of the balance sheet as a tool to impute the appropriate rates of return on the underlying assets of the reporting unit. (See Exhibit 21.2.) Each of these rates of return is adjusted for the deduction of the debt financing portion of the assumed financing of the respective assets (the imputed interest on the assumed debt financing for the reporting unit) for income tax purposes. None of these rates of return reflect the returns that must be earned before tax to finance the assets; rather these rates are reduced by the benefit of deducting the interest cost of the debt financing implied. We need to match the appropriate rates of return to the risks of the assets (or grouping of assets) and reconcile with the appropriate rate of return for the overall reporting unit. In Chapter 17 we discussed that the overall rate of return on invested capital, the WACC, embodies two risks, the financial risk of using debt capital and the unlevered or asset risk of the assemblage of the assets of the firm. We discuss this further later. The underlying assets of the business enterprise including the identified intangible assets generally have finite lives (though that life may be unknown for any one or more such assets). This characteristic differentiates the valuation and estimation of the appropriate rates of return for the underlying assets from the valuation and the estimation of the overall business enterprise, as we typically assume the business enterprise has an ongoing, indefinite life. In analyzing the operations of any business, you must understand the functions and the underlying assets used by the business in performing its various functions. For example, assume we are
Reporting Unit Cost of Capital
Exhibit 21.2
377
Reconciling WACC of Reporting Unit to Rates of Return of Its Underlying Assets WACCRU ¼ ðkdRU WdRU Þ þ ðkeRU WeRU Þ
and WACCRU ¼ ðkNWCRU WNWCRU Þ þ ðkFARU WFARU Þ þ ðkIARU WIARU Þ þ ðkUIVRU WUIVRU Þ where: WACCRU ¼ Overall rate of return for the reporting unit ¼ Weighted average cost of capital for the reporting unit kdRU ¼ After-tax rate of return on debt capital of the reporting unit ¼ kd(pt)RU (1 tax rate) WdRU ¼ Weight of debt capital in capital structure of reporting unit ¼ Fair value of debt capital of the reporting unit/FVRU keRU ¼ After-tax rate of return on equity capital of the reporting unit WeRU ¼ Weight of equity capital in structure of reporting unit ¼ Fair value of equity capital of the reporting unit/FVRU kNWCRU ¼ Rate of return for net working capital of the reporting unit financed with debt capital (return measured after-tax) and equity capital WNWCRU ¼ Weight of net working capital in FVRU ¼ FVNWCRU /FVRU kFARU ¼ Rate of return for fixed assets financed with debt capital (return measured after-tax) and equity capital of the reporting unit WFARU ¼ Weight of fixed assets in FVRU ¼ FVFARU /FVRU kIARU ¼ Rate of return for identified and individually valued intangible assets financed with debt capital (return measured after-tax) and equity capital WIARU ¼ Weight of intangible assets in FVRU ¼ FVIARU/FVRU kUIVRU ¼ Rate of return for unidentified intangibles value of the reporting unit financed with debt capital (return measured after-tax) and equity capital WUIVRU ¼ Weight of unidentified intangibles value in FVRU ¼ FVUIVRU (i.e., ‘‘goodwill’’)/FVRU
analyzing a typical integrated manufacturing company. Exhibit 21.3 lists the typical functions and the typical intangible assets. Once the functions and assets are identified, you need to determine if the intangible asset is separable or not separable from goodwill, in accordance with the guidance of SFAS No. 141. You also need to understand the relative risks of the functions and assets within the context of the overall reporting unit. Differentiating Risks among Reporting Unit Assets How should you look on the relative risks? In Chapter 5 we defined risk in terms of the degree of uncertainty (or lack thereof) of achieving future expectations at the times and in the amounts expected.3 This means uncertainty as to both the amounts and the timing of expected economic income. 3
David Laro and Shannon P. Pratt, Business Valuation and Taxes: Procedure, Law, and Perspective (Hoboken, NJ: John Wiley & Sons, 2005), 160.
378
Exhibit 21.3
Cost of Capital
Typical Functions and Intangible Assets of Manufacturing Company
Management Assembled workforce, software, internal procedures, training programs Design product/processes Patents, secret processes and technical documentation (i.e., technical know-how), research procedures, government certification Purchase Raw Materials Supply contracts: raw material, transportation, energy costs Produce product Favorable labor rates, contract with contract manufacturer Advertise/Sell Product Brand name, sales force, sales reps, customers Distribute Product Distributor agreements, transportation agreements Collect Money Assembled workforce, software, internal procedures
Note that the definition implies as the reference point expected economic income, the expected value (mean average) of the probability distribution of possible economic income for each forecast period. This concept was explained in Chapter 3 in the discussion of net cash flow. The point to understand here is that the uncertainty encompasses the full distribution of possible economic income for each period both above and below the expected value. Reporting Unit Net Working Capital and Fixed Assets For working capital assets, you can look to the rate of return that would be charged for financing the net working capital as the debt capital component plus the equity component supporting such borrowing, as lenders typically will not lend against 100% of the value of these assets. Usually, though, the leverage will be greater than for the firm overall or the reporting unit. For fixed assets, the appropriate rate of return can be estimated from the rates a leasing company would charge to lease the subject assets. Some fixed assets can be employed in other businesses, and the appropriate rate for these assets is likely less than the overall cost of capital for the reporting unit but generally will be greater than the cost of debt capital of the overall firm or for the reporting unit). Leasing companies typically are taking on residual value risks of the subject assets as part of the lease in determining the rates they charge; the reporting unit owns the assets and is taking on the residual value risk just like the leasing company. Alternatively, you can look to the rate of return that would be charged for financing the fixed assets as the debt capital component plus the equity component supporting such borrowing, as lenders typically will not lend against 100% of the value of these assets. How does the rate of return on fixed assets of a typical reporting unit compare to the rate of return for a real estate investment trust (REIT)? While some commentators have hypothesized that the implied rates of return on investments in REITS (i.e., the overall cost of capital of REITs) can be used as a proxy for the rates of return on tangible assets, they generally would be only a poor estimate of the appropriate rate of return. First, REITs rarely hold specialized real properties (which often are inseparable with the specialized equipment housed therein, e.g., a steel mill). Second, the expected returns are based on expected returns of liquid securities. Investments in tangible assets made by firms are not liquid, and you would expect that the appropriate rate of return would exceed the overall
Reporting Unit Cost of Capital
379
cost of capital for REITs due to the illiquidity of the investment. Finally, expected returns on REITs are after their entity-level expenses. The expected lease payments that must be charged for the underlying fixed assets would need to be large enough to enable the REIT to pay its entity-level expenses and realize its expected return. Some fixed assets can be employed in other businesses. The appropriate rate of return for these assets is likely less than the overall cost of capital for the reporting unit. However, certain fixed assets may be specialized to the firm’s production process such that they would have little, if any, value were they sold separate from the business. In such cases, the appropriate rate of return may be equal to (or even greater than) the overall cost of capital of the reporting unit. In fact, the appropriate rate of return on such specialized fixed assets should likely be equal to the rate of return on the intangible assets associated with that specialized production process.
Reporting Unit Identifiable Intangible Assets SFAS No. 141 contains a list of intangible assets that meet the criteria for recognition as assets apart from goodwill. Some of the intangible assets identified as being separate and distinct from goodwill include:
Trademarks and trade names Newspaper mastheads Customer lists Customer contracts and relationships Advertising contracts Lease agreements
Employment contracts Patented technology Franchise agreements Broadcasting rights Literary and musical works Noncompetition agreements
SFAS No. 141 specifically excluded from identifiable intangibles a noncontractual workforce. However, as will be discussed, it may be necessary to value workforces separately if they are to be treated as contributory assets in the valuation of other intangibles. Intangible assets may be valued based on a variety of different methodologies. When valuing an identifiable intangible asset by the income approach, it is important to isolate the cash flows that are attributable to that particular intangible asset. This form of the income approach has been referred to as the multiperiod excess earnings method, meaning that the value of the intangible asset is equal to the present value of the incremental (or excess) after-tax cash flows attributable only to that intangible asset.4 In reality, most intangible assets do not exist on their own but produce profits and cash flow in connection with other tangible and intangible assets. A technology, for example, is used to manufacture a product that is produced in a factory with machinery and equipment. Perhaps the product produced using the technology is sold under a trade name. To attribute the cash flow from that product just to the technology would ignore, for example, the investment made in the factory, the machinery and equipment, and the trade name. Therefore, to isolate the cash flows from the product just to the technology requires that appropriate adjustments be made to account for all contributory assets that produced the product. These adjustments can be termed contributory asset charges. 4
American Institute of Certified Public Accountants, IPR&D Practice Aid (Jersey City, NJ: AICPA, 2001).
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Cost of Capital
Contributory Assets Contributory assets have been defined in this way: The fundamental premise of the multi-period excess earnings method is that the value of an intangible asset is equal to the present value of the net cash flows attributable to the subject intangible asset. The net cash flows attributable to the subject asset are those in excess of the fair returns on all the assets that are necessary to the realization of the cash flows. These assets include not only assets purchased in the instant transaction, but all assets required to realize the cash flows.5
One author described contributory assets in this way: The distinguishing characteristic of a contributory asset is that it is not income generating itself; rather it is an asset that supports the income generating asset.6
Contributory asset charges should be made for all assets that contribute to the realization of the cash flow of the subject asset. Examples of the most widely seen contributory assets are: Working capital Fixed assets Customer lists Trade names Trademarks
Technology Patents Recipes Noncompetition agreements Workforces
While workforce-related intangible assets generally are considered contributory assets, they are not reportable as separate identifiable intangible assets for financial statement purposes under SFAS Nos. 141 and 142 (unless they are contractual in nature); rather their fair value (while used in calculating contributory asset charges) is subsumed into goodwill. The principle behind a contributory asset charge is that the owner of each intangible asset ‘‘rents’’ or ‘‘leases’’ the underlying or requisite assets required to produce the total net cash flows from a specified group of assets. The analysis begins with the identification of the expected net cash flows attributable to a portfolio of assets utilized in conjunction with each other to generate those expected cash flows. The presumption is that the net cash flows cannot be isolated or attributed to a single asset. In determining which assets would be considered contributory to a subject asset, careful analysis must be made as to which assets are used in generating the resulting net cash flows of the subject asset. Furthermore, if a contributory asset supports more than one subject asset, then the fair return on the contributory asset needs to be allocated among all subject assets. For example, if we were valuing a product technology, we would need to deduct from the cash flow of the subject product line a charge for use of the factory space and all machinery and equipment used in the production of the product line using the technology; we would not deduct rent for machinery and equipment used in the production of products that do not use the technology. Thus, careful allocation of the machinery and equipment would be necessary to appropriately charge the cash flows in the valuation of the product technology. Use of contributory asset charges or economic rents is the most common method for representing the contributions of contributing assets. A contributory asset charge is akin to the producer of a
5 6
Ibid., par. 5.3.55. Lawrence B. Gooch, ‘‘Capital Charges and the Valuation of Intangible Assets,’’ Business Valuation Review (March 1992): 5–21.
Reporting Unit Cost of Capital
381
product paying rent for the use of the machinery, facilities, workforce, technology, and customer list to a third party that invested in the creation of each of those assets. Two methods of applying contributory asset charges appear in the literature: the hierarchy method and the cross-charges method.7 In the hierarchy method, intangible assets are categorized as the primary intangible asset and the other, supporting or contributing assets. The primary intangible asset is ‘‘charged’’ the full returns for the use of the contributory assets (net working capital, fixed assets, and contributory intangible assets). The present value of the excess earnings (earnings after charges for contributory assets) at an appropriate discount rate becomes the basis for the fair value estimate. In the cross-charges method, certain intangible assets are identified as interrelated rather than one being designated as primary, and the excess earnings are allocated to these interrelated intangible assets. The first step is to determine the appropriate contributory asset charges for such routine assets as net working capital, fixed assets, assembled workforce, and so on. The excess earnings are then allocated to each interrelated intangible asset through an iterative process. These two methods often result in different indicated values for the identified and individually valued intangible assets. Before concluding on any values, you must reconcile the rates of return used in any valuation of all of the assets, weighted by the relative values of each of the assets, with the overall rate of return appropriate for the reporting unit. Implied Overall Rate of Return for Reporting Unit Intangible Asset Assume we group the intangible assets (both the identified and individually valued intangible assets and the unidentified intangible value). We then can infer an appropriate overall rate of return for the intangible assets of a reporting unit by manipulating Formula 21.3: (Formula 21.3) WACCRU ¼ ðkNWCRU WNWCRU Þ þ ðkFARU WFARU Þ þ ðkIAþUIVRU WIAþUIVRU Þ or kIAþUIVRU ¼ ½ðWACCRU ðkNWCRU WNWCRU Þ ðkFARU WFARU Þ=½WIAþUIVRU where: kIA+UIVRU ¼ After-tax rate of return on all intangible assets, identified and individually valued, of the reporting unit plus the unidentified intangible value of the reporting unit WIA+UIVRU ¼ Weight of intangible assets in FVRU plus the weight of unidentified intangible value in FVRU ¼ (FVIARU þ FVUIVRU)/FVRU and all other variables are defined as above You can then segregate the values and returns of the various intangible assets to ensure consistency with the overall cost of capital for the reporting unit. This formulation is based on the standard WACC applied to net or free cash flows of the reporting unit. An alternative formulation can be thought of based on the concepts of capital cash flows (see Chapter 7). The resulting pretax WACCRU (WACC(pt)RU) of the reporting unit can be thought of as the expected return on the assets. It is intended to better represent the composite business risk of the assets of the reporting unit. 7
Marc Asbra, ‘‘Contributory Asset Charges in the Excess Earnings Method,’’ Valuation Strategies (March/April 2007): 4–17.
382
Cost of Capital
Exhibit 21.4
Reconciling WACC(pt) of Reporting Unit to Rate of Return of its Underlying Assets WACCð ptÞRU ¼ ðkdð ptÞRU WdRU Þ þ ðkeRU WeRU Þ
or WACCð ptÞRU ¼ ðkNWCð ptÞRU WNWCRU Þ þ ðkFAð ptÞRU WFARU Þ þ ðkIAþUIVð ptÞRU WIAþUIVRU Þ þ ðkTSRU WTSRU Þ or
kIAþUIV ð ptÞRU ¼
½ðWACCð ptÞRU ðkNWCð ptÞRU WNWCRU Þ ðkFAð ptÞRU WFARU Þ ðkTSRU WTSRU ÞÞ ½WIAþUIVRU
where: WACC(pt)RU ¼ Pretax WACC of the reporting unit kd(pt)RU ¼ Rate of return on debt capital of the reporting unit without taking into account the tax deduction on interest expense (pretax cost of debt capital) kNWC(pt)RU ¼ Rate of return for net working capital of the reporting unit financed with debt capital (measured pretax) and equity capital kFA(pt)RU ¼ Rate of return for fixed assets of the reporting unit financed with debt capital (measured pretax) and equity capital kIA+UIV(pt)RU ¼ Pretax rate of return on all intangible assets, identified and individually valued, plus the unidentified intangible value of the reporting unit financed with debt capital (measured pretax) and equity capital kTSRU ¼ Rate of return used to present value tax savings due to deducting interest expense on debt capital financing of the reporting unit WTSRU ¼ Weight of tax savings in FVRU ¼ Tax savings of the reporting unit/FVRU and all other variables are defined as above.
The pretax returns on the various assets are estimated without regard to the tax deductibility of the interest on the debt capital used to finance the respective asset. For example, in estimating the appropriate rate of return for working capital based on the cost of financing, say 60% of the working capital would be financed with debt capital and 40% with equity capital. The rate of return on the debt portion is the interest cost on debt not reduced by the tax deductibility of that interest. In estimating the appropriate rate of return for fixed assets based on the imputed cost of leasing those assets, the rate of return is not reduced by the tax deductibility of the leasing expense. Based on that formulation, we get the relationships shown in Exhibit 21.4, which better relate the rates of return required on assets with the cash costs of providing the capital to finance the assets (before the tax savings that might result from the tax-deductibility of the cost of debt). Using the capital cash flow concept, one study estimated the rates of return on total intangible assets (identified and individually valued plus the unidentified intangible value) for eight industries studied for companies included in the S&P 500.8 The analysis implicitly assumes that intangible assets are financed in part by debt financing, which may understate the appropriate rate of return on intangible assets if intangible assets are financed more by equity capital than by a mix of debt and equity capital. Their results indicate: 8
Rudolf Stegink, Marc Schauten, and Gijs de Graaff, ‘‘The Discount Rate for Discounted Cash Flow Valuations of Intangible Assets,’’ Working paper, March 2007.
Additional Reading
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The appropriate rates of return on the overall intangible assets are greater than the WACC; that is, intangible assets are more risky than the firm as a whole. The appropriate rates of return on the overall intangible assets are greater than the unlevered cost of equity capital of the companies as a whole. (Their results are inconclusive for the utility sector of the eight sectors studied.) The levered cost of equity appears to be the best proxy for the appropriate rate of return on intangible assets of the possible implied rates of return on the overall intangible assets tested (WACC, unlevered cost of equity capital, and levered cost of equity capital), although the levered cost of equity capital generally underestimates the implied rate of return on the overall intangible assets. (Their results are inconclusive in three of the eight industries).
NEW RULES FOR ACCOUNTING FOR BUSINESS COMBINATIONS The new rules for accounting for business combinations (to be effective for business combinations completed after January 1, 2009) will increase the complexity of estimating the cost of capital. Currently, contingent consideration (i.e., contingent purchase price) is not recorded until the amount is determined based upon the events occurring in the year upon which the contingency is based. Under the new rules, contingent cash consideration (e.g. amounts payable based on future earnings) will be recorded as a liability and measured at fair value (both at the time of the combination, but also at subsequent periods). Changes in fair value will be recorded in the income statement. Contingent equity consideration will be recorded at fair value at the acquisition date and not remeasured subsequently. The measurement of these contingencies at fair value requires that the discount rate factors in the risk that the contingency will in fact be triggered. The contingent consideration will typically increase the recorded goodwill and increase the amount of goodwill for which impairment testing will be required.9
SUMMARY The cost of capital is a function of the risk of the investment, and risk is the degree of uncertainty regarding the realization of the expected returns from the investment. In the case of divisions and reporting units, the appropriate cost of capital is not the overall cost of capital for the firm. Rather the business risks of the division or reporting unit must be evaluated against competitors or appropriate guideline public companies operating in a line of business with similar risks.
ADDITIONAL READING Chua, Jess, Philip C. Chang, and Zhenyu Wu. ‘‘The Full-Information Approach for Estimating Divisional Betas: Implementation Issues and Tests,’’Journal of Applied Corporate Finance (Spring/Summer 2006): 53–61. Conine, Thomas E. Jr., and Maurry Tamarkin. ‘‘Divisional Cost of Capital Estimation: Adjusting for Leverage,’’ Financial Management (Spring 1985): 54–58. 9
Formica, John, ‘‘Thinking of a Deal? New Accounting, New Strategies,’’ Accounting Policy & Practice Report (October 19, 2007).
Chapter 22
Cost of Capital in Evaluating Acquisitions and Mergers Introduction Invest for Returns above Cost of Capital Common Mistakes DCF Is Best Corporate Decision Model Focus on Net Cash Flow Cost of Capital in Acquisitions and Mergers Use Target Capital Structure of the Combined Company New Rules for Accounting for Business Combinations Summary
INTRODUCTION Good cost of capital estimation is essential to sound evaluation of acquisitions and mergers. The literature is replete with analyses of acquisitions and mergers indicating that many acquisitions and mergers are failures. We consider that a failure in acquisitions and mergers occurs when the rate of return earned by the owners of the acquiring company is less than the benchmark return of its peer companies that did not make major acquisitions. Because this issue has been the subject of many texts, many people take for granted that companies are effective in estimating the appropriate cost of capital to be used in analyzing acquisitions and mergers. But the evidence is far from convincing, and the results of so many failed acquisitions point to the need for increased diligence in the assessment of acquisitions and mergers.
INVEST FOR RETURNS ABOVE COST OF CAPITAL As we discussed in Chapter 20, popular phrases in contemporary corporate finance literature are shareholder value added (SVA) and economic value added (EVA) when addressing capital budgeting and feasibility analysis decisions. The essence of the way to add value is to invest funds in a project that will earn a higher rate of return than its cost of capital (see Chapter 24). An acquisition or merger should be looked at in a similar fashion. Valuation of potential acquisitions and mergers is more than simply an analysis of a large capital project. While most capital projects are not ‘‘pay completely up front’’ propositions, acquisitions and mergers often are such projects. Even in cases where part of the consideration is contingent and the actual price paid will vary based on near-term success, once the acquisition is closed, the owner is fully committed to the business (i.e., the owner that has taken over responsibility to make it work), even if it fails to live up to expectations. Most capital projects get phased in, reducing the risks to the 385
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Cost of Capital
firm. If the project does not work, there are many points along the way where the company can pull the plug, or shut down and reduce risk of future low or negative cash flows. In an acquisition or merger, the acquiring firm is accepting full ownership of the acquisition up front. If the expected cash flows do not result, the acquisition can easily result in returns less than the cost of capital.
COMMON MISTAKES What are some of the most common mistakes in mergers and acquisitions? Here is a list of mistakes we believe are made:
Treating stock of the acquiring company as if it were ‘‘free money’’ instead of having a cost. The cost of equity capital is the minimum return investors require. Otherwise, the share price will fall. The stock issued in an acquisition or merger should be treated the same way as existing stock.
Using a flawed short-term earnings per share accretion/dilution test of an acquisition value rather than the cost of capital.1 The earnings per share accretion/dilution test does not reflect the actual value created by the acquisition. Investors quickly see through the accounting and evaluate acquisitions based on their longer-term economic impact.
Using the acquiring firm’s overall cost of capital as the required return in valuing the acquisition. The correct cost of capital matches the risks in the expected cash flows being valued. This error has led to many overpayments in acquisitions. Professor Damodaran points out that the cost of equity capital should reflect the risk characteristics of the investor who raised the funds; risky businesses cannot become safe just because the buyer of these businesses is in a safer business.2 Further, an acquiring firm may be able to borrow much more than the target firm can on its own and at a lower cost of debt. Building the debt capacity and costs of debt characteristics into the valuation of the target firm, transfers wealth from the acquiring firm their stockholders to the stockholders of the target firms. The correct cost of debt capital should reflect the debt capacity and the cost of debt capital of the target firm. Failure to differentiate the risks along the way and use the cost of capital reflecting the risk in the expected cash flows. You should differentiate:
The appropriate (low) discount rate for determining the present value of the investments that must be made to integrate an acquisition or merger into the acquiring company’s business from The appropriate (greater) discount rate that should be used in valuing the cash flows the acquired company brings along from The appropriate (much greater) discount rate that should be used in valuing hoped-for synergistic cash flows resulting from integrating the acquired business with the acquirer’s existing business
What does the stock market say about acquisitions for which the acquirer overpays? In one study of acquisitions made from 1995 through 2001,3 the authors examined longer-term returns on significant acquisitions (market capitalization of acquired firms averaged nearly 50% of the market 1
2
3
Richard Dobbs, Billy Nand, and Werner Rehm, ‘‘Merger Valuation: Time to Jettison EPS,’’ McKinsey Quarterly (Spring 2005): 17–20. Aswath Damodaran, ‘‘Acquirers Anonymous: Seven Steps Back to Sobriety,’’ Presentation at Duff & Phelps Seminar, Paris France, November 15, 2007. Mark L. Sirower and Sumit Sahni, ‘‘Avoiding the ‘Synergy Trap’: Practical Guidance on M&A Decisions for CEOs and Boards,’’ Journal of Applied Corporate Finance (Summer 2006): 83–95.
Focus on Net Cash Flow
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capitalization of the acquiring firms). Of the 302 transactions studied, 64% were viewed negatively initially (the share price of the acquiring company declined). After one year, 61% of the acquirers lagged their industry peers. After one year, 67% of the transactions that were initially viewed negatively were still negative. The larger the acquisition premium paid, the worse are the subsequent returns for the acquiring firm. The average acquisition premium paid for the acquired company’s stock was over 40% by those acquirers that were persistent negative performers after the acquisition, while persistent positive performers paid an average premium of less than 26%. Acquisition premiums are measured over trading prices, not over intrinsic value (e.g., discounted cash flow [DCF]) of the acquisitions. In attempting to make a deal, the underlying assumption of valuation (e.g., net cash flow and cost of capital) are often stretched to justify an inflated price. The results of this study should make management seek to use increased diligence in evaluating potential acquisitions and mergers. Two themes that should drive any such evaluation are: 1. Cash flow is the preferred measure of economic income. 2. The cost of capital of the acquired business is the preferred focus, as opposed to the acquiring company’s cost of capital. Some have argued that making acquisitions to diversify the business leads to value creation by reducing the combined firms’ cost of capital (i.e., rating agencies give a better rating to a company that is more diversified) and, therefore, this reduction in the cost of capital should be reflected in the cost of capital used to value the target company. But, research has shown that diversified conglomerates are valued at a discount from the sum of the values of the underlying businesses. That discount eliminates the observed benefit from a reduced cost of capital.4
DCF IS BEST CORPORATE DECISION MODEL As we discussed in Chapter 20, Tom Copeland, coauthor of Valuation: Measuring and Managing the Value of Companies, compared the use of ratios, formulas, and discounted cash flow analysis for purposes of corporate decision making. In evaluating the three approaches, he noted that ‘‘the most important criterion for comparing approaches is that they result in good decisions, because the model value is close to the equilibrium market value.’’5 Copeland concludes unequivocally that the DCF approach is the superior approach. But successful use of DCF is dependent on comprehensive analysis of expected net cash flows.
FOCUS ON NET CASH FLOW Copeland notes that the DCF approach captures all elements of value. He also states: Managers who are interested in maximizing share value should use discounted cash flow analysis to make decisions, not earnings per share. : : :The market is not fooled by cosmetic earnings increases; only earnings increases that are associated with improved long-term cash flows will increase share prices. The evidence that the market focuses on cash flows can be grouped into four areas, studies showing that: 4
5
Manual Ammann, and Michael Verhofen, ‘‘The Conglomerate Discount: A New Explanation Based on Credit Risk,’’ International Journal of Theoretical and Applied Finance, 9 No. 8, (2006): 1201–1214; Markus M. Schmid, and Ingo Walter, ‘‘Do Financial Conglomerates Create or Destroy Economic Value?’’ Working paper, August 28, 2007. Tom Copeland, Seminar on Frontiers in Corporate Valuation, New York University Leonard N. Stern School of Business, November 6–7, 1997.
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Accounting earnings is not very well correlated with share prices.
Earnings ‘‘window dressing’’ does not improve share prices.
The market evaluates management decisions based on their expected long-term cash flow impact, not the short-term earnings impact.
There are many decisions where cash flows and earnings per share give opposing results.6
But making projections of net cash flows and terminal values, particularly for hoped-for synergies between acquiring firms and assumed businesses, is a difficult task.
COST OF CAPITAL IN ACQUISITIONS AND MERGERS As discussed in Chapter 5, probably the most widely accepted definition of risk in the context of business valuation is the degree of uncertainty (or lack thereof) of achieving future expectations at the times and in the amounts expected.7 This means uncertainty as to both the amounts and the timing of expected income. Note that the definition implies as the reference point expected returns. By expected returns, in a technical sense, we mean the expected value (mean average) of the probability distribution of possible returns for each forecast period. The cost of capital of any potential acquisition should reflect those risks. The goal is to analyze the appropriate cost of capital and earn a greater return. This sounds easy; it is not. One study found that 61% of acquisition programs did not earn a sufficient return (cost of capital) on the funds invested.8 Any acquisition or merger can be viewed as three distinct streams of expected cash flows. First, in a typical acquisition, the acquiring company will make investments beyond those captured in the expected cash flows of the acquired business. Typically there are integration costs that need to be expended to get the two businesses operating together. The variability of those cash outflows is negligible, and the appropriate cost of capital should be as low as the after-tax cost of the debt that will be used to finance the acquisition. Second, the risk of the ‘‘stand-alone’’ cash flows that will be realized from the business the acquired company already had should be analyzed consistent with the methods we have presented herein. If the target company is publicly traded, you can use the returns realized on that firm’s stock. For example, assume you will use the Capital Asset Pricing Model (CAPM) to estimate the cost of equity capital. The tools available to directly estimate the company’s beta (e.g., ordinary least squares regression of company excess returns against the excess returns of the Standard & Poor’s [S&P] 500) measure the overall company levered beta. But the overall capital structure and the cost of debt capital may change as a result of the merging of the companies. If the target company is a closely held business, you must estimate the risk of the business using the methods we have described in previous chapters. For example, you can locate pure plays, companies specializing in a very narrow business line that parallels the business of the target. You can unlever the observed risk measure—for example, the observed betas of the pure play guideline public companies—to estimate the business risk of the target company. As we discussed in Chapter 17, the overall rate of return on invested capital, the weighted average cost of capital (WACC), embodies two risks: the financial risk of using debt capital and the unlevered 6 7
8
Ibid. David Laro and Shannon P. Pratt, Business Valuation and Taxes: Procedure, Law, and Perspective (Hoboken, NJ: John Wiley & Sons, 2005), 160. See Tim Koller, Marc Goedhart, and David Wessels. Valuation: Measuring and Managing the Value of Companies, 4th ed. (Hoboken, NJ: John Wiley & Sons, 2005), chap. 15.
Use Target Capital Structure of the Combined Company
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or asset risk of the assemblage of the firm’s assets. Therefore, it is useful to begin by developing the unlevered cost of equity capital for the target firm as a whole. You can then relever the cost of equity capital based on the overall target capital structure of the combined firm. Thirdly, the risk of cash flows resulting from synergies expected requires added analyses. As one commentator puts it: Since shareholders do not have to pay a premium to buy the shares of the target on their own, these payoffs, the synergies, must represent something that shareholders cannot get on their own. They must mean improvements in performance greater than those already expected by the markets. If these synergies are not achieved, the acquisition premium is merely a gift from the shareholders of the acquiror to the shareholders of the target company. Current share prices at various multiples already have substantial projected improvements in profitability and growth built into them. Hence our operational definition of synergy is this: Synergy is the increase in performance of the combined firm over what the two firms are already expected or required to accomplish as independent firms.9
One study found that of successful mergers (i.e., those that resulted in an increase in the combined equity value), operating synergies generated primarily by reductions in capital expenditures and investments in net working capital, rather than increased operating profits, accounted for the major contribution to the increased equity value. If the target company is in several businesses and synergies will result from the integration of various divisions of the acquiring company with those of the acquired company, you should begin by assessing the divisional risks of both the acquiring company and the acquired company. We discussed those considerations in Chapter 21. The synergies may in fact be tiered such that there are several sets of expected cash flows. For example, melding of the expanded product offerings from the two companies and selling the expanded portfolio of products with the existing sales forces may be relatively easy, and the WACC for the divisions may adequately reflect the risk of those cash flows. In fact, the cost of capital may be reduced as operating synergies change the operating leverage of the firm.10 The next tier of synergies may involve, for example, combining product features and introducing a new product. The appropriate cost of equity capital for the expected added cash flows from such synergies of these divisions is greater than the weighted average cost of equity capital of the divisions as they exist before integration. Ultimately, the added risk premium for the expected cash flows from synergies is a matter of judgment. A final synergy is often the reduction of corporate overhead by eliminating duplicate functions. While this type of synergy is easy to theorize, it often is difficult to implement in as short a time frame as was originally planned.
USE TARGET CAPITAL STRUCTURE OF THE COMBINED COMPANY The focus of the capital structure analysis should encompass the long-term financing of the combined company rather than any temporary effects. Remember that the appropriate cost of debt is the cost of debt of the target and the debt capacity of the target firm. For example, if the acquisition requires an abnormal level of debt financing that would temporarily change the combined company’s capital structure, the long-term WACC should reflect the debt capacity of the target company added to the target debt of the acquiring company rather than the abnormal structure when the investment initially 9 10
Mark L. Sirower, The Synergy Trap: How Companies Lose the Acquisition Game (New York: The Free Press, 1997), 19–20. See, e.g., Marco Vulpiani, ‘‘Cost of Capital and Valuation of Merging and Acquisition Operations,’’ Business Valuation Review (January 2006): 157–165.
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is made. We discuss the development of the WACC with a changing capital structure in Chapter 17 and present a comprehensive example in Appendix 17B. But financing risks actually may increase rather than decrease, as is often assumed. One recent study determined that, on the average, a merger increases the default risk of the acquiring company.11
NEW RULES FOR ACCOUNTING FOR BUSINESS COMBINATIONS The new rules for accounting for business combinations (to be effective for business combinations completed after January 1, 2009) will add a layer of complexity to the evaluation of target companies. For example, contingent consideration will be rewarded at fair value upon closing of the transaction (see Chapter 21 for a discussion) requiring that the cost of capital for the contingency reflect the risks that the contingent payments will be triggered. In-process research and development will be capitalized instead of deducted at the time of the acquisition (and amortized if the research is successful or written off when it is determined that the research is abandoned). Acquired contingencies (e.g., indemnification provisions, litigation, environment issues) will be recorded at fair value (if certain conditions are met). Finally, restructuring charges will generally be expensed as incurred instead of being included as part of the initial consideration. This provision will more properly measure net cash flows and highlight the amounts and timing of restructuring expenses.12
SUMMARY This is a relatively short chapter, because the essential principles of using cost of capital in evaluating potential mergers and acquisitions are essentially the same as for other applications already discussed. But the ramifications are huge. The market views acquisitions with great skepticism because:
While acquisitions are a quick way to grow, full payment is required up front. Stock prices of the acquirer and target companies often reflect significant performance improvements as stand-alone companies even before the acquisition, making synergistic improvements even more difficult to attain. Synergies require investments. Unwinding a failed acquisition is much more expensive and difficult than halting a typical failed capital project.13
A recent study of over 1,200 acquisitions between 1990 and 2005 found target shareholders receive 55% more if a publicly held firm makes the acquisition instead of a private equity fund. Publicly held firms where management controls 20% or more of the equity pay premiums comparable to those paid by private equity funds. The implications are that managers of firms with diffuse
11
12
13
Craig H. Furfine and Richard J. Rosen, ‘‘Mergers and Risk,’’ Federal Reserve Bank of Chicago, Working paper 2006-09 (September 2006). John Formica, ‘‘Thinking of a Deal? New Accounting, New Strategies,’’ Accounting Policy & Practice Report (October 19, 2007). See Sirower and Sahni, ‘‘Avoiding the ‘Synergy Trap,’’ 86.
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ownership pay too much for acquisitions.14 We hope that the discussion in this chapter will help corporate practitioners better organize their analyses and better evaluate the true economics of potential acquisitions. The general consensus is:
Discounted cash flow is the best model for corporate finance decisions.
Focus on net cash flow as the economic income variable of choice. Each potential merger or acquisition should be analyzed in light of its own cost of capital characteristics and not the acquirer’s overall cost of capital.
14
Leone Bargeron, Frederik P. Schlingemann, Rene´ M. Stulz, and Chad J. Zutter, ‘‘Why Do Private Acquirers Pay So Little Compared to Public Acquirers?’’ Charles A. Dice Center Working paper 2007-8 and Fisher College of Business Working paper 2007-03-011, April 2007.
Chapter 23
Cost of Capital in Transfer Pricing
Introduction Transfer Pricing Analysis Functional Analysis Differentiating Risks of Company Functions Differentiating Risks among Company Assets Quantifying Appropriate Costs of Capital Differentiating Risks Cost of Capital for Functions and Assets Internal Revenue Service Regulations Relating Valuation of Intangible Assets for Transfer Pricing to SFAS No. 141 Summary
INTRODUCTION In this chapter we discuss the factors that affect the pricing of property for transfer among related parties, with particular emphasis on the appropriate cost of capital for the valuation of functions (groups of tangible and intangible assets within an integrated firm) and assets of a firm, particularly intangible assets. A transfer pricing analysis most often arises within the context of an integrated company. Such companies are portfolios of assets and functions, and the entity operates, in theory, in a cooperative fashion to maximize its long-term cash flow (i.e., its overall value). Because such firms likely operate in several taxing jurisdictions, the intercompany pricing of goods, services, and assets affects the income taxation of the entity in the various jurisdictions. The tax rules of most countries do not simply allocate income (i.e., worldwide income allocated based on relative sales of the business to third parties in the various countries, or assets in a particular country or wages paid in a particular country or some combination). Rather, the income taxed in a particular country is based on the profits generated in that taxing jurisdiction. As such, the value of goods and services provided by other parts of the integrated company become an input to the computation of taxable income in a particular jurisdiction. Property transfers among controlled entities in different taxing jurisdictions are subject to review by taxing authorities. Transfer prices used between controlled parties must reflect the appropriate income to prevent the avoidance of taxes. The test applied is: Are the prices paid between related parties comparable to what would have been paid had the parties not been related (the arm’s length principle)? The arm’s length principle requires that the transfer prices charged between controlled parties are ‘‘consistent with the results that would have been realized if uncontrolled taxpayers had engaged in the same transaction under the same circumstances.’’ One significant area of controversy is the value of intangible assets being transferred to a controlled entity that will operate thereafter under a cost sharing agreement. The value of the ‘‘buy-in’’ Thanks to Dan Peters and Timothy Reichert of Duff & Phelps, LLC, Transfer Pricing Practice, for their assistance in preparing this chapter.
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Cost of Capital
payment for transfer of the intangible assets requires analysis of the cash flows and an appropriate discount rate for the intangible assets. In addition, as the companies expand around the world, it is increasingly common for firms to operate in jurisdictions in whole or in part with related party entities where the parent company owns a controlling but not an absolute controlling interest. Property often gets transferred to such joint ventures. The price charged or paid to such an entity by an owner with more than 50% ownership is also subject to review by taxing authorities under the prevailing transfer pricing rules. These reviews may include retroactive adjustments in certain circumstances.
TRANSFER PRICING ANALYSIS The valuation of intellectual capital and functions within an integrated firm begins with a thorough functional analysis, dividing the firm into its component parts and identifying the assets of the firm by function (grouping of tangible and intangible assets). In analyzing the cost of capital, the tasks are to first develop an overall cost of capital for the subject integrated firm and then develop rates of return for functional groupings of assets or individual assets based on their relative risks. Since we cannot observe rates of return appropriate for many functional groupings of assets or individual assets in the marketplace, particularly special purpose tangible assets and intangible assets, you must ultimately reconcile the estimated appropriate asset returns to the weighted average rate of return of the individual functional grouping of assets or individual assets (weighted by their relative values) to the overall firm cost of capital. It is useful to begin with the definition of a business enterprise: (Formula 23.1) BE ¼ NWC þ FA þ IA þ UIV where: BE ¼ Business enterprise NWC ¼ Net working capital FA ¼ Fixed assets IA ¼ Intangible assets UIV ¼ Unidentified intangible value (i.e., ‘‘goodwill’’) Graphically, we can display the relationship as shown in Exhibit 23.1.
FUNCTIONAL ANALYSIS In analyzing the operations of any business, you must understand the functions and the underlying assets that are used by the business in performing the various functions. For example, assume we are analyzing a typical integrated manufacturing company. Exhibit 23.2 lists the typical functions and the typical intangible assets. The overall classification of intangible assets is often divided into two categories: intellectual property and the broader descriptor, intangible assets. Intellectual property is generally viewed as intangible assets that can be legally protected and transferred to another party without transfer of the business enterprise itself.
Transfer Pricing Analysis
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Assets Current Assets
Liabilities and Equity Current Liabilities
Net Working Capital Interest-Bearing Debt Fixed Assets
Intangible Assets • Identified and Individually Valued • Unidentified
Exhibit 23.1
Stockholders' Equity
Business Enterprise
Examples of intellectual property are:
Brands (groupings of intangible assets that differentiate a specific product or service)
Patents Trademarks and trade names
Copyrights
Technical know-how
Exhibit 23.2
Typical Functions and Intangible Assets of Manufacturing Company
Management Assembled workforce, software, internal procedures, training programs Design product/processes Patents, secret processes and technical documentation (i.e., technical know-how), research procedures, government certification Purchase raw materials Supply contracts—raw material, transportation, energy costs Produce product Favorable labor rates, contract with contract manufacturer Advertise/Sell product Brand name, sales force, sales reps, customers Distribute product Distributor agreements, transportation agreements Collect money Assembled workforce, software, internal procedures
396
Designs Formulas
Trade secrets
Computer software
Cost of Capital
Examples of other intangible assets that generally cannot be transferred to another party without transfer of the business enterprise itself are:
Procurement procedures and supply contracts Internal procedures Manufacturing practices (though often not a stand-alone asset, as practices often are integral with the actual equipment used in manufacturing, the technical know-how, the formulas, etc.) Research procedures (including documentation of prior research successes and failures)
Customer lists and relationships Licenses, government certifications
Sales and distribution networks
Assembled, trained workforce
Once the functions and assets are identified, you then need to understand the relative risks of the functions and assets within the context of the overall business enterprise. How should you look on the relative risks? While some try to differentiate the risks of the various functions of the firm in terms of capital employed in each function, capital employed is not risk. In Chapter 5 we defined risk in terms of the degree of uncertainty (or lack thereof) of achieving future expectations at the times and in the amounts expected.1 This means uncertainty as to both the amounts and the timing of expected economic income or cash flows. Note that the definition implies as the reference point expected economic income, the expected value (mean average) of the probability distribution of possible economic income for each forecast period. This concept was explained in Chapter 3 in the discussion of net cash flow. The point to understand here is that the uncertainty encompasses the full distribution of possible economic incomes for each period both above and below the expected value. So in analyzing the risks of the various functions, you must examine the variability of the cash flows attributable to the function. Often that variability depends on what activity that function provides during the life cycle of company products and services. And that variability changes over the typical product life cycle. For example, Exhibit 23.3 displays the graph of the typical product life cycle. During the product development stage, no revenues are earned, but costs are expended. The product development stage is really multiple stages: initial investigation (e.g., scientific and economic feasibility), product prototype building, production process development (often including specialized equipment design), market testing, and so on. The investment required at each of these development stages often increases as you draw closer to product introduction. The costs of development typically are known with much more certainty than are the revenues that will be realized upon introduction of the product. The revenues realized during introduction phase typically are more uncertain than during later phases as the product develops its customer following.
1
David Laro and Shannon P. Pratt, Business Valuation and Taxes: Procedure, Law, and Perspective (Hoboken, NJ: John Wiley & Sons, 2005), 160.
Transfer Pricing Analysis Product Development Introduction
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Growth
Maturity
Decline Sales
Volume Profit Time
Exhibit 23.3
Typical Product Life Cycle
DIFFERENTIATING RISKS OF COMPANY FUNCTIONS How does this difference in risk affect a transfer pricing analysis and the appropriate cost of capital? Each function has a revenue and expense risk, and often the functions must be separately analyzed. Generally, the literature distinguishes functions and the assemblage of assets used in the functions into ‘‘routine’’ functions and nonroutine or entrepreneurial functions. Routine functions are presumably relatively simple functions that could, at least in theory, be subcontracted. Examples of routine functions include: distribution or sales and marketing function; manufacturing or assembly functions; research and development activities; procurement services; back-office support services. Entrepreneurial functions involve financing the development of valuable intangible assets and/or assuming substantial risks. Entrepreneurial functions generate non-routine profits, or residual profits. Non-routine profits are those profits above and beyond a return on routine functions. Non-routine profits are attributed to returns on different forms of intangible property, such as technology, know-how, processes, trademarks, or trade names. Example: Manufacturing Function versus Distribution Function For example, a multinational company, XYZ Products, Inc., has traditionally performed all product development at its New Jersey–based development center while manufacturing of its products has been done at local plants. XYZ Products has determined that its manufacturing functions should be more centralized in Latin America, for example, to take advantage of economies of scale and allow it to expand into other Latin American countries without setting up manufacturing operations in each country. Its Latin American manufacturing function (XYZ Latin America Manufacturing) will act as, in essence, a contract manufacturer for its Latin American distribution company (XYZ Latin America Distributing), which in turn will sell products to either a local country affiliated sales company or third-party sales companies, taking the risks of selling the product. XYZ Latin America Distributing will take on the risks of raw material procurement because it will purchase and supply raw materials to XYZ Latin American Manufacturing. XYZ Latin American Manufacturing will process the raw materials, engage the labor force, own the manufacturing facilities, and earn a profit based on a return for its fixed asset investments and its manufacturing costs (i.e., it will earn a markup on its costs). XYZ Latin American Distributing licenses valuable product intangible assets (e.g., formulas, trade names, etc.) and pays a royalty on sales to XYZ Products. XYZ Latin American Manufacturing licenses the valuable manufacturing know-how and pays a royalty on units manufactured to XYZ Products (and that royalty is one of the operating expenses of XYZ Latin American Manufacturing).
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Cost of Capital
What is the appropriate rate of return for this contract manufacturing business? Is the overall cost of capital for XYZ Products the appropriate rate of return? The business of XYZ Products is a portfolio of business functions, and the overall cost of capital for XYZ Products represents the market’s composite analysis of the risks of all of its products and functions. XYZ Latin American Manufacturing will be performing a routine function while XYZ Latin American Distributing will be performing an entrepreneurial function. The appropriate rate of return for XYZ Latin American Manufacturing should be sufficient to earn a fair rate of return on the fair market values of its assets. Its cash flows will reflect operating expenses (labor, utilities, etc.), needed future capital expenditures for maintaining its manufacturing capabilities, and the operating risks it is taking on. XYZ Latin American Manufacturing is in essence a contract manufacturer with relatively low risk. If the markup will be calculated based on XYZ Latin American Manufacturing’s actual costs (actual cost plus), XYZ Latin American Manufacturing’s risk are lower than many comparable contract manufacturers, as those firms often enter into contracts based on a markup over their estimated costs and accept the risks as to whether the expected markup actually is realized. Given the risks, the margin is likely low. The goal is to match the compensation paid to XYZ Latin American Manufacturing to the compensation paid to unrelated contract manufacturers in true arm’s length contracts. XYZ Latin American Manufacturing should earn a low margin since its risks are relatively low and its expected cash flow will be relatively more stable than the expected cash flow of XYZ Latin American Distributing, which is accepting more of the risks (raw material pricing and distribution pricing risks) and should earn a greater margin. Variability in expected margins and cash flows are the principle risk determinants in concluding the appropriate costs of capital.
Example: New Product Development Function As XYZ Products has expanded throughout the world, it has had to differentiate the products for the various markets. As products were introduced and manufactured in various countries, XYZ Products has charged a royalty on products manufactured in local countries. Lately its local country managers have requested development of products specifically for local market consumers instead of relying on product extensions of products initially designed for and introduced in the United States. XYZ Products has now grown to such a size that it has decided to transfer the product development business (as it pertains to its European-based business) to XYZ Development, a newly formed Swiss subsidiary. XYZ Development does not start de novo. Rather XYZ Development will acquire development procedures and results of prior research endeavors of XYZ Products, reducing future development time. XYZ Development will acquire an assemblage of intangible assets (i.e., the resulting value of the development business is termed the ‘‘buy-in’’ payment for this activity) and will charge a royalty on its future developments from its European-affiliated companies (subsidiaries of XYZ Products) that will manufacture the products it develops. What is the appropriate rate of return for this development business? Is the overall cost of capital for XYZ Products the appropriate rate of return? The business of XYZ Products is a portfolio of business functions, and the overall cost of capital for XYZ Products represents the market’s composite analysis of the risks all of its products and functions. If you follow the product life cycle graph in Exhibit 23.2, XYZ Products has a portfolio of products in the various stages of the typical product life cycle. XYZ Development will not acquire any of the existing products or acquire any of the assets used in the functions pertaining to XYZ Products’ business beyond the product development stage. XYZ Development will invest its capital in return for an unknown stream of royalties in the future. XYZ Development will be performing an entrepreneurial function.
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If you divide XYZ Development into its relatively stable investment function (e.g., on the average XYZ Development will spend 5 million annually on development) from its more risky recovery of its investment through future royalties, you should use a relatively low rate of return for discounting the future investments (possibly by capitalizing the investment outflow with the capitalization rate equal to 1/(k g), where k = discount rate for a relatively certain outflow and g = the expected growth rate in development expenditures, possibly expected inflation) and a much higher rate of return for discounting the expected stream of royalties (possibly by capitalizing expected future royalties at a capitalization rate equal to 1/(k g), where k = discount rate for a relatively uncertain inflow of royalties and g = the expected growth rate in expected royalties). DIFFERENTIATING RISKS AMONG COMPANY ASSETS The discussion thus far has focused on the risks and appropriate rates of return by company function. If you divide a firm into its component assets, you can identify the risks inherent in one asset (or grouping of asset) and the other assets. For example, if XYZ Products were to transfer its product trade names to an intellectual property holding company (XYZ Trade Name Holding) and pay that holding company a royalty based on product sales, what is the appropriate rate of return for this royalty? Is the overall cost of capital for XYZ Products the appropriate rate of return? Again, the business of XYZ Products is a portfolio of business functions, and the overall cost of capital for XYZ Products represents the market’s composite analysis of the risks of all of its products and functions. While XYZ Trade Name Holding is bearing a risk that future product sales will vary and likewise its cash flows, it is not bearing the risks of investment and the risks of variability of costs. Therefore, the appropriate rate of return should be less than the overall cost of capital of XYZ Products. Even where profit margins are agreed to by contract, there is risk of variability in cash flows. Variability of cash flows makes the appropriate rate of return greater than the risk-free rate of return.
QUANTIFYING APPROPRIATE COSTS OF CAPITAL In transfer pricing, the valuation methods are broadly categorized in two ways: comparable uncontrolled transactions (CUT) method or a profit split method for the valuation of intangible assets. The CUT method is a form of the market approach. The CUT method is used to determine the amount to be charged for a transfer of intangible property to a related party by reference to an amount charged in a comparable transaction between unrelated parties (a comparable transactionbased application of the method). For example, the CUT method can be used for royalties on trade names where third-party royalty agreements can be identified for comparable trade names. The cost-plus method is a CUT method for routine functions, provided comparable companies can be identified providing comparable services on a cost-plus basis (profitability-based application of the method). The economic circumstances and contractual parameters must be closely comparable to use the CUT method. This makes use of the CUT method problematic in many cases. The profit split methods (overall or residual profit split methods) look to third-party evidence between unrelated parties for:
Allocation of overall profits based on functions performed and risks taken or
Returns on assets used typically in routine functions with the remaining profit remaining allocated to the entrepreneurial functions
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Cost of Capital
The profit split methods should reflect the economic income for the functions performed and the risks taken. These methods are subject to review and possible adjustment (even on a retroactive basis under the ‘‘commensurate with income’’ principal of U.S. Treasury Regulations Section 482.2
DIFFERENTIATING RISKS In Chapter 5 we categorized risk in terms of capital market theory into three components: maturity risk (also called horizon risk or interest rate risk); market risk (also called systematic risk or undiversifiable risk); and unique risk (sometimes called unsystematic risk or undiversifiable risk or residual risk or company-specific risk).3 Maturity risk is the risk that the value of the investment may increase or decrease because of changes in the general level of interest rates. The longer the term of an investment, the greater its maturity risk. Some assets are short-lived in nature (short maturity), and their appropriate costs of capital should reflect a shortened maturity. For example, net working capital is a relatively short-term investment compared to fixed assets or products. As such, it should reflect a lower rate of return than for other longer-term assets. Market risk is the uncertainty of future returns because of the sensitivity of the return on a subject investment to movements in returns for the investment market as a whole. We commonly use the term beta as a measure of market risk. While beta has come to have a specific meaning in the context of the Capital Asset Pricing Method (CAPM), beta is used in the literature as a more general term meaning the sensitivity of an investment to overall market factors (e.g., changes in the economy). Product sales (and to a lesser degree costs) of most firms are, to varying degrees, highly subject to market risks. The theoretical concept of the asset (unlevered beta) and fundamental beta (see Chapter 10) is that a firm’s sales and operating profits move with the economy as represented by a proxy, the stock market index. Unique risk is the uncertainty of expected returns arising from factors other than the market itself. These factors typically include characteristics of the industry and the individual company. In international investing, these risks also include characteristics of a particular country. You can think of the unique risks of the firm’s functions causing the appropriate rate of return for that function to be more or less than the overall cost of capital. Determining the cost of capital in transfer pricing is about measuring and pricing the risks of the integrated firm’s functions and assets. COST OF CAPITAL FOR FUNCTIONS AND ASSETS We have discussed extensively the methods available to quantify the cost of equity capital for a business. What tools are available to quantify the risks of the functions of the firm? As we discussed in Chapter 5, the cost of capital is equal to the return that could have been expected on alternative investments given a specific level of risk. Generally, there are three different meanings of the term cost of capital to three different users: 1. The asset view (discount rate used to discount future values of cash flows to be derived from assets to present value) 2 3
Treas. Reg. Sec. 1.482-4(f), ‘‘Special Rules for Transfers of Intangible Property.’’ See Richard A. Brealey, Stewart C. Myers, and Franklin Allen, Principles of Corporate Finance, 8th ed. (Boston: Irwin McGraw-Hill, 2006), 162.
Quantifying Appropriate Costs of Capital
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2. The liability view (the economic cost to a firm of attracting and retaining capital where investors carefully analyze and compare all return-generating opportunities) 3. The investor’s view (return a person expects from investments in a firm’s debt or equity, given a specific level of risk for the investment) Following this thought process and assuming that market value of debt and equity capital equal their fair market values, the business enterprise can be valued as shown in Formula 23.2: (Formula 23.2) FMVBE ¼ MVIC where FMVBE ¼ FMVNWC þ FMVFA þ FMVIA þ FMVUIV and MVIC ¼ Md þ Me where: FMVBE ¼ Fair market value of the business enterprise MVIC ¼ Market value of invested capital FMVNWC ¼ Fair market value of net working capital FMVFA ¼ Fair market value of fixed assets FMVIA ¼ Fair market value on intangible assets FMVUIV ¼ Fair market value of unidentified intangibles value (i.e., ‘‘goodwill’’) Md ¼ Market value of debt capital Me ¼ Market value of equity capital Graphically we can display the relationship in Exhibit 23.4. In transfer pricing, we desire to develop the appropriate rate of return for the assets (or grouping of assets) that support a particular function of the integrated firm. We generally cannot directly observe the appropriate returns in the market, particularly for intangible assets. Consequently, as a first step, you will look to identify guideline public companies (‘‘pure plays’’) that own comparable assets and perform comparable functions (‘‘comparables’’). You then calculate the overall cost of capital for each guideline public company. You may then impute the rates of return for grouping of assets from the overall cost of capital of the guideline public companies based on the relative risks of the assets and functions of the guideline public companies. That is, we can use the overall cost of capital developed from observations of the appropriate rates of return for the invested capital side of the balance sheet for such guideline public companies as a tool to impute the appropriate rates of return on the underlying assets for the groupings of assets used in a specific function of the integrated firm. The formulation of imputing returns may be based on the standard weighted average cost of capital (WACC) applied to net or free cash flows. Alternatively, the formulation of imputing returns may be based on the pretax WACC (WACC(pt)) applied to capital cash flows (see Chapter 17). The pretax WACC (WACC(pt)) can be thought of as the expected return on the assets. It is intended to better represent the composite business risk of the assets. It is also consistent with the purpose of valuing intangible assets in transfer pricing analysis. The purpose is to value pretax income (i.e., appropriate royalty before tax effecting) attributable to the intangible assets (i.e., the present value of the taxable income upon which the tax will be levied).
402
Cost of Capital
Assets FMV of Current Assets
Liabilities and Equity FMV of Current Liabilities
Net Working Capital Market Value of Debt FMV of Tangible Assets
FMV of Intangible Assets • Identified • Unidentified
Exhibit 23.4
Market Value of Equity
Business Enterprise Value or Fair Market Value Balance Sheet
The returns on the various assets are estimated without regard to the tax deductibility of the interest on the debt capital used to finance the respective asset. For example, in estimating the appropriate rate of return for working capital based on the cost of financing, say 60% of the working capital would be financed with debt capital and 40% with equity capital. The rate of return on the debt portion is the interest cost on debt not reduced by the effect of the tax deduction on that interest. In estimating the appropriate rate of return for fixed assets based on the imputed cost of leasing those assets, the rate of return is not reduced by the tax deductibility of the leasing expense. Based on that formulation, we get the relationships among the rates of return depicted in Exhibits 23.5. Reconciling the rates of return on the underlying assets to the pretax WACC (WACC(pt)) better relates the rates of return required on assets with the cash costs of providing the capital to finance the assets (before the tax savings that might result from the tax-deductibility of the cost of debt). The imputed rates of return should reconcile as shown in Exhibit 23.5. Graphically we can display the relationship in Exhibit 23.6. Once we have imputed the appropriate rates of return for the various functions (or groupings of assets used in performing the functions) of the integrated firm from the comparables by matching the appropriate rates of return to the risks of the assets (or grouping of assets into functions), we finally reconcile those rates of return with the appropriate rate of return for the overall integrated firm. The underlying assets of the business enterprise including the identified intangible assets generally have finite lives (though that life may be unknown for any one or more such assets). This characteristic differentiates the valuation and estimation of the appropriate rates of return for the underlying assets from the valuation and the estimation of the overall business enterprise, as we typically assume the business enterprise has an ongoing, indefinite life. You can look to the market and locate guideline public companies providing a narrow range of functions and estimate risk measures appropriate for those functions. For example, you can locate
Quantifying Appropriate Costs of Capital Exhibit 23.5
403
Reconciling WACC(pt) to Rates of Return of Underlying Assets
WACCð ptÞBE ¼ ðkdð ptÞ Wd Þ þ ðke We Þ or WACCð ptÞBE ¼ ðkNWCð ptÞ WNWC Þ þ ðkFAð ptÞ WFA Þ þ ðkIAþUIVð ptÞ WIAþUIV Þ þ ðkTS WTS Þ or
kIAþUIV ð ptÞ
WACCð ptÞ ðkNWCð ptÞ WNWC Þ ðkFAð ptÞ WFA Þ ðkTS WTS Þ ¼ ½WIAþUIV
where: WACC(pt)BE ¼ Pretax WACC of the business enterprise kd(pt) ¼ Rate of return on debt capital without taking into account the tax deduction on interest expense (pretax cost of debt capital) kNWC(pt) ¼ net working capital financed with debt capital (measured pretax) and equity capital kFA(pt) ¼ Rate of return for fixed assets financed with debt capital (measured pretax) and equity capital kIA+UIV(pt) ¼ Pretax rate of return on all intangible assets, identified and individually valued, plus the unidentified intangible value financed with debt capital (measured pretax) and equity capital TS ¼ Present value of tax savings due to deducting interest expense on debt capital financing kTS ¼ Rate of return used to present value tax savings due to deducting interest expense on debt capital financing FMVBE ¼ Fair market value of business enterprise WTS ¼ Weight of TS in FMVBE = TS/FMVBE and all other variables are defined as other equations in the chapter. pure plays, companies specializing in a single (or very narrow) business line that parallel the functions of the subject firm. You can unlever the observed risk measure—for example, the observed betas of the pure plays—to estimate the business risk of the function. The search for such narrow pure plays often leads to smaller companies. The business risk of the smaller pure plays may or may not be comparable to the business risk of the subject function even if the description of the line of business appears to be comparable. Comparability in functional analysis requires close matching of risk characteristics as well as general business line. Alternatively, you can use the full-information beta technique to increase the sample size. These methods are discussed in Chapter 10. Another tool one can use is the Risk Study portion of the Duff & Phelps Risk Premium Report to help quantify the relative risks of the functions and the appropriate return. As we discussed in Chapter 14, the Risk Study reports observed rates of return based on three risk measures:
404
Cost of Capital
FMV of Net Working Capital
Assets
Liabilities and Equity
FMV of Current Assets
FMV of Current Liabilities
kNWC(pt) Market Value of Interest-Bearing Debt FMV of Fixed Assets
kd(pt)
kFA(pt)
FMV of Intangible Assets kIA + UIV(pt)
Market Value of Stockholders’ Equity
FMV of Tax Savings kTS
Exhibit 23.6
ke
Business Enterprise Reconciliation of Assets and Rates of Return
1. Profitability (operating profit margin or operating profit/revenue) 2. Volatility of operating profit margin 3. Volatility of return on equity (NI/book value of equity) You can allocate overall profit margin to the functions and allocate overall rate of return based on the relative volatility of profit margins, for example. Assume XYZ Products has a history of operating for the five years prior to the valuation date as shown in Exhibit 23.7. If we use Exhibit D-2 from the Risk Study (Chapter 14, Exhibit 14.1), we can develop the estimated cost of equity capital by adding the appropriate risk premium over the risk-free rate for companies in the study. We look up the appropriate portfolio in D-2 based on coefficient of variation of operating margin. Exhibit 23.7 Products
Example: Coefficient of Variation of Operating Margin for XYZ
(Standard Deviation of Operating Margin)/(Average Operating Margin) Year 2005 2004 2003 Net Sales $900 $800 $850 Operating Income $150 $120 $130 Operating Margin 16.7% 15.0% 15.3% Std. Dev. of Op. Margin 2.3% Ave. Operating Margin 14.6% Coefficient of Variation 15.8% Risk Premiums over Risk-free Rate: Using Guideline Portfolios Company Relevant Guideline Indicator Exhibit Portfolio CV (Operating Margin) 15.8% D-2 16
2002 $750 $80 10.7%
2001 $900 $140 15.6%
Premium over Risk-free Rate 9.3%
Quantifying Appropriate Costs of Capital
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Exhibit 23.8 Example: Coefficient of Variation of Operating Margin for XYZ Products Licensing Trade Name from XYX Trade Name Holdings (Standard Deviation of Operating Margin)/(Average Operating Margin) Year
2005
2004
2003
Net Sales $900 $800 $850 Operating Income $150 $120 $130 Operating Margin 16.7% 15.0% 15.3% Std. Dev. of Op. Margin 2.3% Ave. Operating Margin 9.6% Coefficient of Variation 24.0% Risk Premiums over Risk-free Rate: Using Guideline Portfolios Company Relevant Guideline Indicator Exhibit Portfolio CV (Operating Margin) 24.0% D-2 11
2002
2001
$750 $80 10.7%
$900 $140 15.6%
Premium over Risk-free Rate 10.1%
The indicated risk premium can be added to the risk-free rate to get an estimate of the required rate of return on equity. Assuming a risk-free rate of 5.5% (say) and in isolation from other considerations, this suggests an appropriate cost of equity capital of 14.8%. Now assume XYZ Products transfers its trade name to another entity, XYZ Trade Name Holdings, in return for a 5% royalty. The restated operating results for XYZ Products are shown in Exhibit 23.8. The indicated risk premium can be added to the risk-free rate to get an estimate of the required rate of return on equity. Assuming a risk-free rate of 5.5% (say) and in isolation from other considerations, this suggests an appropriate cost of equity capital of 15.1%. The appropriate cost of equity capital for XYZ Trade Name Holdings LLC is lower. While its profits will vary in the future as sales vary and, therefore, the return on equity it will earn on the investment in XYZ Trade Name Holdings LLC can be expected to vary, another indicator of the lower risk is the coefficient of variation of its expected operating margin, which is negligible. For products under development and newly introduced products, the rates of return that can be inferred from venture capital investments can be particularly useful. We discuss observed returns on venture investments at various stages of development in Chapter 29. Using the capital cash flow concept, one study estimated the rates of return on total intangible assets (identified and individually valued plus the unidentified intangible value) for eight business sectors for companies included in the S&P 500.4 While this study formulates the analyses in terms of fair values for financial reporting purposes (see Chapter 21), its results are drawn from publicly traded stocks and are applicable to rates of return relative to the fair market value of the total intangible assets. The analysis implicitly assumes that intangible assets are financed in part by debt financing, which may understate the appropriate rate of return on intangible assets if intangible assets are financed more by equity capital than by a mix of debt and equity capital. The study results indicate that:
The appropriate rates of return on the overall intangible assets are greater than the WACC; that is, intangible assets are more risky than the firm as a whole.
4
Rudolf Stegink, Marc Schauten, and Gijs de Graaff, ‘‘The Discount Rate for Discounted Cash Flow Valuations of Intangible Assets,’’ Working paper (March 2007).
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Cost of Capital
The appropriate rates of return on the overall intangible assets are greater than the unlevered cost of equity capital of the companies as a whole. (Results are inconclusive for the utility sector of the eight studied.) The levered cost of equity appears to be the best proxy for the appropriate rate of return on intangible assets of the possible implied rates of return on overall intangible assets tested (WACC, unlevered cost of equity capital, and levered cost of equity capital), though the levered cost of equity capital generally underestimates the implied rate of return on overall intangible assets. (Results are inconclusive in three of the eight sectors.)
INTERNAL REVENUE SERVICE REGULATIONS The U.S. Treasury has proposed changes to the Section 482 regulations pertaining to testing the reasonability of discount rates used in calculating the present value of expected cash flows associated with a particular function, for example, the so-called buy-in payments pertaining to cost-sharing arrangements.5 Buy-in payments can take the form of a one-time, lump sum amount, equivalent installment payments, or equivalent royalties. Generally these proposed regulations emphasize the matching of risks and returns with a seeming default to the overall WACC, which clearly may understate the appropriate rate of return on risky functions and intangible assets. Exhibit 23.9 contains these proposed regulations. The proposed regulations more closely tie the cost of capital for the intangible assets subject to the buy-in payment to the rate of return for the subject business enterprise rather than allowing for an abstract determination of rates of return without regard to the appropriate rate of return on the overall business. These proposed regulations imply that it is imperative to reconcile the rates of return of each function with the overall rate of return for the firm. Many times transfer pricing studies only address certain firm functions in isolation. But the firm is a portfolio of functions, some lower risk, some higher risk. One needs to study the relative risks and reconcile the rates of return if one is to ‘‘prove’’ that the rates of certain functions are not over- or understated.
RELATING VALUATION OF INTANGIBLE ASSETS FOR TRANSFER PRICING TO SFAS NO. 141 Often as part of an acquisition where the purchase price is being allocated to the underlying assets in accordance with Financial Accounting Statement (SFAS) No. 141, Business Combinations (see Chapter 21), intangible assets may be transferred to a controlled entity from the acquired entity. While the data gathering, identification of functions, assets, and overall scope of the analysis are determined, there are differences between the valuation of intangible assets. The principal differences that may result are:
5
The net cash flows (i.e., appropriate royalty rate before tax effecting) have no deduction for income taxes since the theory of transfer pricing is to get the present value of the taxable income on which a tax is levied. We are valuing the stream of royalties upon which income taxes would be paid. Proposed Treas. Reg. Sec. 1.482-7(g)(2)(vi).
Relating Valuation of Intangible Assets for Transfer Pricing to SFAS No. 141
Exhibit 23.9
407
Proposed 1.482-7(g)(2)(vi)
(A) In general. Some calculations set forth in this paragraph (g) and elsewhere in this section require determining a rate of return which is used to convert a future or past monetary sum associated with a particular set of activities or transactions into a present value. For this purpose, a discount rate should be used that most reliably reflects the risk of the activities and the transactions based on all the information potentially available at the time for which the present value calculation is to be performed. Depending on the particular facts and circumstances, the risk involved and thus the discount rate may differ among a company’s various activities or transactions. Normally, discount rates are most reliably determined by reference to market information. For example, the weighted average cost of capital (WACC) of the relevant activities and transactions derived using the capital asset pricing model might provide the most reliable discount rate; in such cases, this WACC might most reliably be based on information from uncontrolled companies whose business activities as a whole constitute comparable uncontrolled transactions. Where a company is publicly traded and its cost sharing arrangement (‘‘CSA’’) involves substantially the same risk as projects undertaken by the company as a whole, then the WACC of the relevant activities and transactions might most reliably be based on the company’s own WACC. Depending on comparability and reliability considerations, including the extent to which the company’s hurdle rate reflects market information and is used in a similar manner in the controlled and uncontrolled transactions, in some circumstances discount rates might be most reliably determined by reference to other data such as a company’s internal hurdle rate for projects of comparable risk. (B) Examples. The following examples illustrate the principles of this paragraph (g)(2)(vi): Example 1. USPharm, a publicly traded U.S. pharmaceutical company, enters into a CSA with FPharm, its wholly owned foreign subsidiary. Under the agreement both controlled participants agree to share the research costs of developing a specific drug compound called T. USPharm is also engaged in another development project for compounds U and V, which involves different risks than the T development project and which is not part of the CSA. However, there are a large number of uncontrolled publicly traded U.S. companies for which information can be reliably derived that are highly comparable to USPharm but that conduct research only on compounds similar to T involving risks similar to those of the T development project. At the commencement of the CSA (Year 1), USPharm and FPharm enter into a PCT with respect to external contributions owned by USPharm in the form of the RT Rights in its preexisting drug research. As part of the method that USPharm determines will most reliably calculate PCT Payments, a discount rate needed to convert future monetary sums into a present value. After analysis, USPharm concludes that the discount rate is most reliably determined by calculating a WACC based on the information relating to the comparable uncontrolled companies, with suitable adjustments for factors such as differences in capital structure between USPharm and the comparables, and for the stability and other statistical properties of the beta measurement of the comparables. Example 2. The facts are the same as in Example 1 except that the T development project is the only business activity of USPharm and FPharm and no reliable data exists on uncontrolled companies undertaking similar activities and risk as those associated with the CSA. After analysis, USPharm concludes that the discount rate is most reliably determined by reference to its own WACC. USPharm funds its operations with debt and common stock. Debt comprises 40% of its financing and USPharm’s cost of debt is 6%. Equity comprises the remaining 60% of financing, USPharm is publicly traded and its equity beta is 1.25. Using third-party information, USPharm concluded that the appropriate risk-free rate and equity risk premium are X% and Y%, respectively, implying a return on USPharm’s equity of Z%½X% þ ð1:25Y%Þ. The weighted average cost of capital is calculated by blending and weighting the after-tax cost of debt and the cost of equity according to percentage of total financing. USPharm’s weighted average cost of capital is W%½ð6% 0:4Þ þ ðZ% 0:6Þ. Example 3. Use of a documented discount rate. The facts are the same as Example 1 except that no data exist on uncontrolled companies undertaking similar activities and risks as those associated with the CSA. USPharm has documented a hurdle rate of 12% that it uses as the minimum anticipated return for its business investments having a comparable risk profile. The commissioner examines USPharm’s documentation and concludes that the hurdle rate provides a reliable discount rate in this case.
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Cost of Capital
This can be illustrated with a simple example. Assume that the legal entity that owns an asset wishes to sell it to a related party. Assume that the appropriate cash flow attributable to the asset in each period (in perpetuity) equals $100, the appropriate discount rate for the asset equals 10%, and the income tax rate equals 40%. If no sale of the asset were to take place, the selling entity would have paid a present value of future taxes on the cash flow of $400 (¼ $100 40%/.10) to the tax authority. The typical calculation of fair value (or, for that matter, fair market value) would equal $600 (¼$100 (1 .40)/.10). If the selling entity is paid $600 for the asset, it currently pays $240 ($600 40%) in tax. By contrast, if the selling entity is paid $1,000 (¼ $100/.10) for the asset, it pays $400 tax (¼$1,000 40%), which is equal to the present value of the tax the selling entity would otherwise have paid. The ratio of return on net working assets, fixed assets, and intangible assets are estimated consistent with WACCð ptÞ . Specifically, cost of capital estimates are derived for each asset grouping in a manner that is consistent with the overall WACCð ptÞ (which is the weighted average cost of capital for all asset groups). The value excludes the value of the tax shield for the tax deductibility of interest expenses because the tax shield is valued separately.
In addition, analysts often use the relief from royalty method to value trademarks. That valuation method often underestimates the value of a trade name because it only includes the value for a specific licensed use while the owner of a trademark has the ability (and takes on the risk) to use trademarks in a multitude of uses.6 This ‘‘lost royalty’’ approach is equivalent to a ‘‘lost profits’’ analysis.
SUMMARY Cost of capital is a function of the risk of the investment, and risk is the degree of uncertainty regarding the realization of the expected returns from the investment. In the case of firms performing multiple functions in multiple taxing jurisdictions, you often need to determine the appropriate rate of return for groups of assets performing a specific function or even a single asset with reference to transactions among unrelated parties. As such, you need first to identify the functions and/or assets and then measure their relative risks. While many times transfer pricing consultants assemble an analysis of an isolated function or isolated asset of an integrated firm, such an analysis can easily lead to an inappropriate rate of return for that function or asset relative to the risks of the portfolio of functions and assets comprising an integrated firm. In estimating the appropriate costs of capital for the functions and/or assets of the firm, you begin with the overall cost of capital for the business enterprise. In estimating the appropriate cost of capital for specific functions, you first look to guideline public companies performing similar functions so you can use a comparable uncontrolled transactions (CUT) method. If guideline public companies are not available, you can turn to a fundamental analysis of the risks and the returns of the specific functions. In either case, you need to reconcile the resulting cost of capital estimates to the overall cost of capital of the business enterprise. 6
Nestle Holdings, Inc. v. Commissioner, T.C. Memo. 1995-441, affd. in part, revd. and remanded in part 152 F.3d 83 (2d Cir. 1998); T.C. Memo.2000-374.
Chapter 24
Central Role of Cost of Capital in Economic Value Added Joel M. Stern, G. Bennett Stewart, III, and Donald H. Chew, Jr. Introduction EVA Financial Management System EVA and the Corporate Reward System EVA Bonus Plan: Simulating Ownership Leveraged Stock Options: Making Ownership Real Summary
INTRODUCTION As was discussed in the preface to this book, one of the four traits of great chief executives is their understanding of the fundamental reality of wealth creation. Successful organizations invest to earn a rate of return in excess of their cost of capital. These executives pass that understanding onto their organization and its business managers. An economic value added (EVA)–based performance measurement system makes the cost of capital explicit. In its simplest form, EVA is net operating profit after taxes less a charge for the capital employed to produce those profits. The capital charge is the required, or minimum, rate of return necessary to compensate all the firm’s investors, debt holders, and shareholders for the risk of the investment. EVA is charged for capital at a rate that compensates investors for bearing the firm’s explicit business risk. The assessment of business risk is based on the Capital Asset Pricing Model (CAPM), which allows for a specific, market-based evaluation of risk for a company and its individual business units using the concept of beta. In addition, the tax benefit of debt financing is factored into the cost of capital, but in such a way as to avoid the distortions that arise from mixing operating and financing decisions. To compute EVA, the operating profit for the company and for each of the units is charged for capital at a rate that blends the after-tax cost of debt and equity in the target proportions each would plan to employ rather than the actual mix each actually uses year by year. Moreover, operating leases are capitalized and considered a form of debt capital for this purpose. As a result, new investment opportunities are neither penalized nor subsidized by the specific forms of financing employed. To illustrate, a company with a 10% cost of capital that earns a 20% return on $100 million of net operating assets has an EVA of $10 million. This says the company is earning $10 million more in profit than is required to cover all costs, including the opportunity cost of tying up scarce capital on This chapter is adapted with permission from a portion of Joel M. Stern, G. Bennett Stewart, III, and Donald H. Chew, Jr., ‘‘The EVA1 Financial Management System,’’ Journal of Applied Corporate Finance (Summer 1995): 32–36.
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Cost of Capital
the balance sheet. In this sense, EVA combines operating efficiency and balance sheet management into one measure that can be understood by business managers. For operating heads and top management alike, EVA holds out three principal ways of increasing shareholder value: 1. Increase the return derived from the assets already tied up in the business. Run the income statement more efficiently without investing any more capital on the balance sheet. 2. Invest additional capital and aggressively build the business so long as the return earned exceeds the cost of that new capital. (Targets based on rates of return such as return on earnings [ROE] or return on investment [ROI], incidentally, actually can discourage this objective when divisions are earning well above their cost of capital, because taking on some EVA-increasing projects will lower their average return.) 3. Stop investing in, and find ways to release capital from, activities that earn substandard returns. This means everything from turning working capital faster and speeding up cycle times to consolidating operations and selling assets worth more to others. Besides making the cost of capital explicit, the EVA performance measure also can be designed to encourage tax-minimizing accounting choices and to incorporate a number of other adjustments intended to eliminate distortions of economic performance introduced by conventional accounting measures such as earnings or ROE. For example, one notable shortcoming of generally accepted accounting principles (GAAP) accounting stems from its insistence that many corporate outlays with longer-term payoffs (such as research and development [R&D] or training) be fully expensed rather than capitalized and amortized over an appropriate period. While well suited to creditors’ concerns about liquidation values, such accounting conservatism can make financial statements unreliable as guides to going-concern values. More important, to the extent GAAP’s conservatism is built into a company’s performance measurement and compensation system, it can unduly shorten managers’ planning horizon. In setting up EVA systems, we sometimes advise companies to capitalize portions of their R&D, marketing, training, and even restructuring costs. In cases of other ‘‘strategic’’ investments with deferred payoffs, we have also developed a procedure for keeping such capital off the books (for internal evaluation purposes) and then gradually readmitting it into the manager’s internal capital account to reflect the expected payoffs over time. As these examples are meant to suggest, EVA can be used to encourage a more farsighted corporate investment policy than traditional financial measures based on GAAP accounting principles. In defining and refining its EVA measure, Stern Stewart & Co. has identified over 120 shortcomings in conventional GAAP accounting. In addition to GAAP’s inability to handle R&D and other corporate investments, we have addressed performance measurement problems associated with standard accounting treatments of:
Inventory costing and valuation
Depreciation Revenue recognition
Writing-off of bad debts
Mandated investments in safety and environmental compliance Pension and postretirement medical expense
Valuation of contingent liabilities and hedges
EVA Financial Management System
Transfer pricing and overhead allocations Captive finance and insurance companies
Joint ventures and start-ups
Special issues of taxation, inflation, and currency translation
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For most of these accounting issues, we have crafted a series of cases to illustrate the performance measurement problem and devised a variety of practical methods to modify reported accounting results in order to improve the accuracy with which EVA measures real economic income. Of course, no one company is likely to trigger all 120 measurement issues. In most cases, we find it necessary to address only some 15 to 25 key issues in detail, and as few as 5 or 10 key adjustments actually are made in practice. We recommend that adjustments to the definition of EVA be made only in those cases that pass four tests: 1. 2. 3. 4.
Is it likely to have a material impact on EVA? Can the managers influence the outcome? Can the operating people readily grasp it? Is the required information relatively easy to track or derive?
For any one company, then, the definition of EVA that is implemented is highly customized with the aim of striking a practical balance between simplicity and precision. To make the measure more user-friendly, we have also developed a management tool called ‘‘EVA Drivers’’ that enables management to trace EVA through the income statement and balance sheet to key operating and strategic levers available to them in managing their business. This framework has proven to be quite useful in focusing management’s attention, diagnosing performance problems, benchmarking with peers, and enhancing planning. More generally, it has helped people up and down the line to appreciate the role they have to play in improving value. It also can help guard against an excessive preoccupation with improving individual operational metrics to the detriment of overall performance. For example, a drive to increase productivity or, say, a single-minded obsession with winning the Malcolm Baldrige Award could lead to unwarranted capital spending or to shifts in product mix that result in less EVA and value, not more. In the end, management must be held accountable for delivering value, not improving metrics.1
EVA FINANCIAL MANAGEMENT SYSTEM The real success of business today depends not on having a well-thought-out, far-reaching strategy but rather on reengineering a company’s business systems to respond more effectively to the new business environment of continuous change. Our contention at Stern Stewart is that just as this information revolution has created a need for business process reengineering, it also has precipitated a need to reengineer the corporate financial management system.
1
Nevertheless, our research suggests a remarkably strong correlation between a company’s EVA performance, its shareholder value added (or MVA), and its standing in Fortune’s Most Admired survey, a ranking based on an assessment of such criteria as customer responsiveness, innovation, time to market, and management quality. See Bennett Stewart, ‘‘EVA: Fact and Fantasy,’’ Journal of Applied Corporate Finance 7, no. 2 (Summer 1994).
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Cost of Capital
What do we mean by a financial management system? A financial management system consists of all those financial policies, procedures, methods, and measures that guide a company’s operations and its strategy. It has to do with how companies address such questions as:
What are our overall corporate financial goals and how do we communicate them, both within the company and to the investment community? How do we evaluate business plans when they come up for review?
How do we allocate resources—everything from the purchase of an individual piece of equipment, to the acquisition of an entire company, to opportunities for downsizing and restructuring?
How do we evaluate ongoing operating performance? Last but not least, how do we pay our people, what is our corporate reward system?
Many companies these days have ended up with a needlessly complicated and, in many respects, hopelessly obsolete financial management system. For example, most companies use discounted cash flow analysis for capital budgeting evaluations. But when it comes to other purposes, such as setting goals and communicating with investors, the same companies tend to reach for accounting proxies— measures like earnings, earnings per share (EPS), EPS growth, profit margins, ROE, and the like. To the extent this is true, it means there is already a disconnect between the cash flow–based capital budget and accounting-based corporate goals. To make matters worse, the bonuses for operating people tend to be structured around achieving some annually negotiated profit figure. This widespread corporate practice of using different financial measures for different corporate functions creates inconsistency, and thus considerable confusion, in the management process. And, given all the different, often conflicting, measures of performance, it is understandable that corporate operating people tend to throw up their hands and say, ‘‘So, what are you really trying to get me to do here? What is the real financial mission of our company?’’ With EVA, all principal facets of the financial management process are tied to just one measure, making the overall system far easier to administer and understand. That is, although the process of coming up with the right definition of EVA for any given firm is often complicated and timeconsuming, the measure itself, once established, becomes the focal point of a simpler, more integrated overall financial management system—one that can serve to unite all the varied interests and functions within a corporation. Why is it so important to have only one measure? As we noted earlier, the natural inclination of operating managers in large public companies is to get their hands on more capital to spend and grow the empire. This tendency in turn leads to an overtly political internal competition for capital—one in which different performance measures are used to gain approval for pet projects. And because of this tendency toward empire building, top management typically feels compelled to intervene excessively, not in day-to-day decision making but in capital spending decisions. Why? Because they do not trust the financial management system to guide their operating managers to make the right decisions. There is no real accountability built into the system, and there is no real incentive for operating heads to choose only those investment projects that will increase value. EVA is the internal measure that management can decentralize throughout the company and use as the basis for a completely integrated financial management system. It allows all key management decisions to be clearly modeled, monitored, communicated, and rewarded according to how much value they add to shareholders’ investment. Whether reviewing a capital budgeting project, valuing an acquisition, considering strategic plan alternatives, assessing performance, or determining bonuses, the goal of increasing EVA over time offers a clear financial mission for management and a means of improving accountability and incentives. In this sense, it offers a new model of internal corporate governance.
EVA and the Corporate Reward System
413
EVA AND THE CORPORATE REWARD SYSTEM Incentive compensation is the anchor of the EVA financial management system. The term incentive compensation is not quite right, however, for in practice too much emphasis gets placed on the word compensation and not enough on the word incentive. The proper objective is to make managers behave as if they were owners. Owners manage with a sense of urgency in the short term but pursue a vision for the long term. They welcome change rather than resisting it. Above all else, they personally identify with the successes and the failures of the enterprise. Extending an ownership interest is also the best way to motivate managers in the information age. As the pace of change increases and the world becomes ever less predictable, line managers need more general as opposed to specific measures of performance to which they will be held accountable. They need more leeway to respond to changes in the environment. They need a broader and longer-range mandate to motivate and guide them. Maximizing shareholder value is the one goal that remains constant, even as the specific means to achieve it are subject to dramatic and unpredictable shifts. Making managers into owners should not be undertaken as an ‘‘add-on’’ to current incentive compensation methods. Rather, it should replace them. In place of the traditional short-term bonus linked to budget and ordinary stock option grants, the EVA ownership plan employs two simple, distinct elements: 1. A cash bonus plan that simulates ownership 2. A leveraged stock option (LSO) plan that makes ownership real EVA BONUS PLAN: SIMULATING OWNERSHIP The cash bonus plan simulates ownership primarily by tying bonuses to improvements in EVA over time. Paying for improvements in, rather than absolute levels of, EVA is designed mainly to solve the problem of unequal endowments. This way managers of businesses with sharply negative EVA can be given a strong incentive to engineer a turnaround, and those managers of businesses already producing large positive EVA do not receive a windfall simply for showing up. Besides leveling the playing field for managers inheriting different circumstances, bonuses tied to improvements in, rather than levels of, EVA are also ‘‘self-financing’’ in this sense: To the extent that a company’s current stock tends to reflect current levels of EVA, it is only changes in current levels of EVA that are likely to be correlated with changes in stock price.2 And, to the extent the managers of a given company succeed in increasing a company’s EVA and so earn higher bonus awards for themselves, those higher bonuses are more than paid for by the increase in shareholder value that tends to accompany increases in EVA. As with a true ownership stake, EVA bonuses are not capped. They are potentially unlimited (on the downside as well as upside), depending entirely on managerial performance. But, to guard against the possibility of short-term gaming of the system, we have devised a ‘‘bonus bank’’ concept that works in this way: Annual bonus awards are not paid out in full but instead are banked forward and held at risk, with full payout contingent on continued successful performance. Each year’s bonus 2
Our own research indicates that the changes in companies’ EVAs over a five-year period account for nearly 50% of the changes in their market value added (MVAs) over that same time frame. (MVA, which is a measure of the shareholder value added by management, is roughly equal to the difference between the total market value and the book value of the firm’s equity.) By comparison, growth in sales explained just 10% of the MVA changes, growth in earnings per share about 15% to 20%, and return on equity only 35%. For a description of this research, see Bennett Stewart, ‘‘Announcing the Stern Stewart Performance 1,000,’’ Journal of Applied Corporate Finance 3, no. 2 (summer 1990).
414
Cost of Capital
award is carried forward from the prior year, and a fraction—for example, one-third—of that total is paid out, with the remainder banked into the next year. Thus, in a good year, a manager is rewarded—much like a shareholder who receives cash dividends and capital appreciation—with an increase in both the cash bonus paid out and in the bonus bank carried forward. But in a poor year—again, much like a shareholder—the penalty is a shrunken cash distribution and a depletion in the bank balance that must be recouped before a full cash bonus distribution is again possible. Because the bonus paid in any one year is an accumulation of the bonuses earned over time, the distinction between a long-term and a short-term bonus plan becomes meaningless. When combined with such a bonus bank system, EVA incentive plans tied to continuous improvement also help to break the counterproductive link between bonuses and budgets. EVA targets are automatically reset from one year to the next by formula, not annual negotiation. For example, if EVA should decline for whatever reason, management will suffer a reduced, possibly negative bonus in that year. In the following year, however, the minimal standard of performance for the next year’s bonus will be set somewhat lower again, by a preset formula. This automatic lowering of expectations is designed to help companies retain and motivate good managers through bad times by giving them a renewed opportunity to earn a decent bonus if they can reverse the company’s fortune. At the same time, however, it avoids the problem inherent in the stock option ‘‘repricing’’ practices of so many public companies of rewarding managers handsomely when the stock drops sharply and then simply returns to current levels. In combination with a bonus bank, then, the use of objective formulas to reset targets eliminates the problems of sandbagging on budgets and encourages collaborative, long-range planning. Instead of wasting time managing the expectations of their supervisors, managers are motivated to propose and execute aggressive business plans. Moreover, because it compensates the end of creating value rather than the means of getting there, the EVA bonus plan is entirely consistent with the movement to decentralize and empower. In sum, the banking of bonuses tied to continuous improvements in EVA helps companies to smooth cyclical bumps and grinds, extends managers’ time horizons, and encourages good performers accumulating equity in their bank accounts to stay and poor performers running up deficits to go. In so doing, the EVA bonus bank functions as both a long-term and short-term plan at one and the same time. LEVERAGED STOCK OPTIONS: MAKING OWNERSHIP REAL The annual EVA cash bonus is intended to simulate an owner’s stake. In many cases, however, it is often valuable to supplement the bonus plan with actual stock ownership by management. Pursuit of that goal, however, runs headlong into this fundamental contradiction: How can managers with limited financial resources be made into significant owners without unfairly diluting the current shareholders? Showering them with stock options or restricted stock is apt to be quite expensive for the shareholders, notwithstanding the incentive for the managers. And asking the managers to buy lots of stock is apt to be excessively risky for them. One approach we recommend to resolve this dilemma is to encourage (or require) managers to purchase common equity in the form of special leveraged stock options (LSOs). Unlike ordinary options, these are initially in the money and not at the money, are bought and not granted, and project the exercise price to rise at a rate that sets aside a minimal acceptable return for the shareholders before management participates. Although managers’ purchase of LSOs could be funded by them as a one-time investment, we typically recommend that managers be allowed to buy them only with a portion of their EVA
EVA and the Corporate Reward System
415
bonuses. Besides providing even more deferred compensation, this practice helps ensure that only those managers who have added value in their own operations are allowed to participate in the success of the entire enterprise. To illustrate how an LSO operates, consider a company with a current common share price of $10. The initial exercise price on the LSO is set at a 10% discount from the current stock price, or $9, making the option worth $1 right out of the gate. But instead of just handing the LSOs to management, managers are required to purchase them for the $1 discount, and that money is put at risk. Another difference between LSOs and regular options is that the exercise price is projected to increase at a rate that approximates the cost of capital (less a discount for undiversifiable risk and illiquidity)—let us say 10% per annum. In this case, over a five-year period (and ignoring compounding for simplicity), the exercise price will rise 50% above the current $9 level to $13.50. In sum, management pays $1 today for an option to purchase the company’s stock (currently worth $10) for $13.50 five years down the road. Only if the company’s equity value grows at a rate faster than the exercise price will management come out ahead. Indeed, if the exercise price rises at a rate equal to the cost of capital (less the dividend yield), then the LSOs will provide exactly the same incentives as an EVA bonus plan. It rewards management for generating a spread between the company’s rate of return on capital and the cost of that capital (as reflected by the rate of increase in the exercise price) times the capital employed by management to purchase the shares. Perhaps a better comparison, however, is between the incentives held out by LSOs and those provided by leveraged buyouts. LSOs can be seen as putting management in the position of participating in an LBO but without requiring an actual LBO of the company. By virtue of their being purchased 10% in the money, LSOs effectively replicate the 90% debt and 10% equity that characterized the structure of the LBOs of the 1990s. At bottom, then, LSOs (and LBOs, as we have seen) also boil down to EVA, to the idea that management should participate only in those returns in excess of a company’s required rate of return. But while conceptually identical to an EVA bonus plan, LSOs are likely to be an even more powerful motivator because they amplify the risks and rewards for management. Any improvement in EVA that investors think will be sustained is capitalized into the value of the shares; for example, a company with a cost of capital of 10% that increases its EVA by $1 million will see its value appreciate by $10 million. For managers holding the LSOs, such capitalized increases in value are themselves further leveraged 10 to 1, thus creating $100 of added managerial wealth for each $1 improvement in EVA. This leveraging effect makes LSOs a potent way to get management to concentrate on building EVA over the long haul. In sum, the EVA ownership plan replaces the traditional short-term bonus linked to budget and ordinary stock option grants with two components: 1. A cash bonus plan that simulates ownership 2. A leveraged stock option plan that confers actual ownership The cash bonus plan simulates ownership by tying bonuses to sustained improvements in EVA over time, with a large portion of awarded bonuses held in escrow and subject to loss to ensure that improvements are permanent. The LSO plan corrects the deficiencies of normal stock option plans in two ways: 1. The leverage factor allows managers to purchase significantly more stock for a given amount of dollars (thus replicating an LBO’s effect on ownership). 2. A steadily rising exercise price ensures that managers win only if shareholders do.
416
Cost of Capital
SUMMARY An EVA financial management system represents a way to institutionalize the running of a business in accordance with basic microeconomic and corporate finance principles. When properly implemented, it is a closed-loop system of decision making, accountability, and incentives—one that has the potential to make the entire organization and not just the chief executive officer responsible for the successes and failures of the enterprise. It can result in a self-regulated and self-motivated system of ‘‘internal’’ governance. As a concept, EVA starts simple, but in practice it can be made as comprehensive as necessary to accommodate management’s needs and preferences. EVA is most effective, however, when it is more than just a performance measure. At its best, EVA serves as the centerpiece of a completely integrated framework of financial management and incentive compensation. The anchor of the EVA financial management system is a powerful incentive compensation plan that consists of two parts: 1. A cash bonus plan tied to continuous improvement in EVA, in which a significant portion of the awarded bonuses is carried forward in a bonus bank and held at risk 2. A leveraged stock option plan, in which managers use part of their cash bonus awards to make highly leveraged purchases of company stock Such an EVA reward system holds out major benefits over more conventional compensation plans:
Rewarding managers for continuous improvement in (rather than levels of) EVA means that new managers neither receive windfalls for inheriting already profitable divisions, nor are they penalized for stepping into turnaround situations.
In contrast to compensation plans that continually revise performance criteria to provide ‘‘competitive’’ compensation levels each year, the EVA bonus plan has a long-term memory in the form of a bonus bank that ensures that only consistent, sustainable increases in value are rewarded.
EVA bonuses are tied to a performance measure that is highly correlated with shareholder value, thus aligning the interests of managers with those of shareholders. The strength of the correlation between changes in EVA and in shareholder value also means that the EVA compensation system is effectively self-financing; that is, managers win big only when shareholders are winning, and managers are truly penalized when shareholders lose.
Cost of capital plays an integral role in such a compensation plan, driving management to invest in projects whose returns are greater than the cost of capital. Proper internal governance is certainly no guarantee of success, and it is no substitute for leadership, entrepreneurship, and hustle. But an EVA financial management and incentive system can help. We like to say that EVA works like the proverbial Trojan horse: What is wheeled in appears to be an innocuous new financial management and incentive program, but what jumps out is a new culture that is right for times of rapid change and decentralized decision making. By increasing accountability, strengthening incentives, facilitating decentralized decision making, establishing a common language and integrated framework, and fostering a culture that prizes building value above all else, it significantly improves the chances of winning. That is all any shareholder can reasonably expect from governance in today’s business environment of continuous change.
Part 4
Cost of Capital For Closely Held Entities
Chapter 25
Handling the Discount for Lack of Marketability for Operating Businesses
Introduction Discrete Percentage Discount for Lack of Marketability Minority Ownership Interests Controlling Ownership Interests Building the Discount for Lack of Marketability into the Discount Rate Venture Capitalists’ Required Rates of Return Quantifying the Marketability Factor in the Discount Rate Summary
INTRODUCTION As noted earlier, whether the cost of capital estimation is based partly or entirely on historical market data or on current market data, the data typically used for estimating rates of return represent for returns on publicly traded stock in the highly liquid U.S. public stock markets. Investors in companies without an established trading market for their stock place a high premium on liquidity or, conversely, demand a high discount for lack of liquidity compared with companies with an established trading market for their stock. Having estimated required rates of return from market data for publicly traded stocks, there are two ways to adjust for the lack of liquidity for closely held stock: 1. After estimating a value as if publicly traded, subtract a percentage discount for lack of marketability. 2. Build the lack of marketability factor into the discount rate by adding some number of percentage points into the discount or capitalization rate, developed from any of the models discussed in earlier chapters of this book.
419
420
Cost of Capital
DISCRETE PERCENTAGE DISCOUNT FOR LACK OF MARKETABILITY The most common way to handle the lack of marketability issue is by a percentage deduction from the value indicated after discounting or capitalizing expected cash flows at a rate derived from public market data.1 MINORITY OWNERSHIP INTERESTS Many empirical studies have provided extensive transaction data to help quantify the amount of such a discount in the case of minority interest transactions. The studies consistently show a central tendency for discounts for lack of marketability for minority interests to be 30% to 50% from the value if they were freely traded. However, there are many transactions above and below this range. For any given valuation developed by the income approach, it is tempting to simply take the average from the studies and apply that as a discount for lack of marketability. However, with the broad ranges around the measures of central tendency, such as the minority discount/control premium issue, it is more accurate (and more convincing to a court) to select from the available databases those transactions with characteristics closest to the subject company to estimate the discount for lack of marketability. Fortunately, since the first edition of this book, two databases have been put online to enable researchers to do this. One is a restricted stock study and the other is a pre–initial public offering (IPO) study. Incidentally, SFAS No. 157, Fair value measurements, specifically requires discounts for restricted and otherwise illiquid securities. Restricted Stock Studies A ‘‘restricted stock’’ is a stock of a public company that is identical in all respects to the stock that trades publicly, except that it is restricted from trading on the public market. It could be, for example, stock issued in an acquisition, stock issued in a financing, or stock of insiders not registered in a public offering. Such stock is, however, eligible for block transactions with institutional and other qualified investors. The essence of restricted stock studies is to compare the price at which a restricted stock transaction takes place with the public market price on the same day. The percentage difference is a proxy for the discount for lack of marketability. A summary of the restricted stock studies published to date is shown as Exhibit 25.1. The Securities and Exchange Commission (SEC) loosened the restrictions in 1990, and the average discount went down from the mid-30s to the mid-20s. In 1997 the SEC reduced the required holding period under Rule 144 from two years to one year, and the average discount was 13% in the only post-1997 study as of press time. The reduction in discounts for restricted stocks should not be interpreted to indicate a reduction in the discount for lack of marketability for minority interests in closely held companies, but merely as a reaction to the loosening of restrictions. The most detailed study to date is the FMV Restricted Stock StudyTM by FMV Opinions, Inc. It covers 475 transactions from 1980 through 1997 (the year the SEC cut the required holding period 1
For a comprehensive discussion of discounts for lack of marketability, see chapters 3 through 11 in Shannon P. Pratt, Business Valuation Discounts and Premiums (Hoboken, NJ: John Wiley & Sons, 2001), 45–211; see also Chapter 17, ‘‘Discounts for Illiquidity and Lack of Marketability,’’ in Shannon P. Pratt, Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed. (New York: McGraw-Hill, 2008).
Discrete Percentage Discount for Lack of Marketability Exhibit 25.1 Time Period 1/66–6/69 1/68–12/70 1/68–12/72 1/68–12/723 1/69–12/73 10/78–6/82 1/81–12/88 1/79–4/97 1/80–I2/96 1/91–12/95 1/96–4/97 5/97–12/98
421
Summary of Restricted Stock Transaction Studies Study SEC Institutional Investor Milton Gelman Robert Trout Robert Moroney Michael Maher Standard Research Consultants William Silber FMV Opinions, Inc5 Management Planning, Inc. Bruce Johnson Columbia Financial Advisors Columbia Financial Advisors
Number of Transactions 398 89 60 148 33 28 69 475 53 72 23 15
Average Discount
Time Period1
25.8%2 33.0% 33.5% 35.6% 35.4% 45.0%4 33.8% 23.0% 27.1% 20.0% 21.0%6 13.0%7
A A A A A A A B B C C D
1
A Pre-1900 (before SEC loosened reporting requirements). B Straddles 1990 (some before, some after, but more pre-1997). C Post-1990 but pre-1997. D Post-1997 (after SEC reduced required holding period under Rule 144 from two years to one year). 2 The average was 32.6% for OTC companies not required to file reports with the securities and exchange commission. 3 The exact ending month is not specified. 4 Median. 5 FMV Opinions has updated its study through 1997 and now includes 475 transactions. It is available online at www.BVMarketData.com. 6 Median was 14.0. 7 Median was 9.0. Source: Adapted from Shannon P. Pratt, Business Valuation Discounts and Premiums (Hoboken, NJ: John Wiley & Sons, 2001), 81, copyright # 2001. Used with permission. All rights reserved.
from two years to one year), with 53 data items for each transaction, and has recently been updated through 2005. A sample transaction report from the FMV study is shown as Exhibit 25.2. It was placed online in 2001 and is fully searchable at www.BVMarketData.com. When an analyst is trying to quantify a discount for lack of marketability for a particular company, he or she can search the database to find companies with comparable characteristics to use for guidance. Such characteristics might include company size (measured by either sales or assets), size of the block (as a percentage of the total outstanding), earnings (or deficit), and so on. As we go to press, the new LiquiStatTM database of restricted stock transactions is gaining recognition. It is based on transactions on the Restricted Securities Trading Network (RSTN). Exhibit 25.3 demonstrates how the discount for illiquidity increases as the days of illiquidity remaining increase. With 10 days of illiquidity remaining, the discounts range from about 10% to about 20%. With 350 days of illiquidity remaining, the discounts range from about 30% to over 60%.
Pre–Initial Public Offering Studies When a company goes public for the first time, it is required by the SEC to disclose in its prospectus all the transactions in its stock for the previous three years. A comparison of the prices of those transactions with the initial public offering (IPO) price is the essence of the ‘‘pre-IPO studies.’’ The percentage below the IPO price at which the transactions took place (adjusted for changes in company fundamentals) is a proxy for the discount for lack of marketability. For a long time, only two such series of studies existed, the Willamette Management Associates studies and the
422 Exhibit 25.2
Cost of Capital FMV Restricted Stock StudyTM Transaction Report
Company SIC Name Ticker Exchange Transaction Data Transaction Month Registration Rights Holding Period (yrs.) Discount (Prior Month) Discount (Transaction Month) Discount (Subsequent Month) Offering Price Prior Month High Prior Month Low Prior Month High-Low Average Prior Month Volume Transaction Month High Transaction Month Low Transaction Month High-Low Average Transaction Month Close Transaction Month Volume Subsequent Month High Subsequent Month Low Subsequent Month High-Low Average Subsequent Month Volume Shares Placed to Volume Ratio Shares Outstanding Shares Placed Placement Amount Shares Placed/Shares After (%) % of Prior Month Volume to Total Shares Outstanding (%)
4412 Deep Sea Foreign Transportation of Freight OMI Corporation OMM NYS
2/2000 M 1 7.25% 34.02% 46.22% $2.00 $2.56 $1.75 $2.16 4,529,700 $3.88 $2.19 $3.03 $3.81 9,051,500 $4.06 $3.38 $3.72 5,323,000 1.06 49,394,000 9,583,000 $19,166,000 16.2% 16.2%
Financial Data ($000s) Market Value Book Value MTB Ratio (absolute value) Intangible Assets Current Assets Current Liabilities Total Assets Debt Retained Earnings Total Revenues Depreciation Expense Interest Expense Pretax Income Net Income Prior Year Dividend ($) Dividend Yield (%) EBITDA Operating Profit Margin (%) Net Profit Margin (%) Volatility (%) Z-Score (absolute value)
106,505.80 171,766.00 0.62 0.00 121,195.00 77,239.00 472,415.00 267,747.00 62,966.00 115,992.00 23,835.00 17,945.00 80,796.00 87,747.00 0.00 0.00% 39,016.00 54.2% 75.6% 90.50% 0.03
N/A ¼ Not Available. Source: Copyright # FMV Opinions, Inc., 2006. Used with permission. All rights reserved. Available at www.BVMarketData.com.
Emory & Co. studies (formerly the Baird & Co. studies). Both indicated average discounts in the mid-40%s. A summary of the Willamette studies is shown as Exhibit 25.4. Because the Willamette studies incorporate transactions back three years from the IPO, discounts are computed in terms of relative price/earnings ratios instead of absolute dollar comparisons. A summary of the Emory studies is shown as Exhibit 25.5. Because the Emory studies collect transactions only five months prior to the IPO, discounts are computed on unadjusted prices. Finally, the broadest pre-IPO study was instituted by Valuation Advisors in 2000, called the Valuation Advisors’ Lack of Marketability Discount StudyTM. While the Willamette and Emory studies set limiting criteria for transactions considered, Valuation Advisors recorded every transaction for two years prior to the IPO date. They recorded 17 data points for each transaction: 1. Standard Industrial Classification (SIC) code 2. North American Industry Classification System (NAICS) code
Discrete Percentage Discount for Lack of Marketability
423
70.0%
Illiquidity Discount
60.0% 50.0% 40.0% 30.0% 20.0% 10.0%
35 0
0 31 0 33 0
29
0
0
27
25
10 0 12 0 14 0 16 0 18 0 20 0 23 0
60
80
40
0 20
0.0%
Days of Illiquidity Remaining
LiquiStatTM Discounts for Restricted Stocks Source: Espen Robak, ‘‘Discounts for Illiquid Shares and Warrants: The LiquiStatTM Database of Transactions on the Restricted Securities Trading Network,’’ Pluris Valuation Advisors White Paper (January 2007): 30. All rights reserved. Used with permission. Please visit www.plurisvaluation.com for more information.
Exhibit 25.3
3. 4. 5. 6. 7.
Company name Company description Sales EBIT (earnings before interest and taxes) Assets
Exhibit 25.4 Summary of Discounts for Private Transaction P/E Multiples Compared to Public Offering P/E Multiples Adjusted for Changes in Industry P/E Multiples
Time Period 1975–78 1979 1980–82 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
Number of Companies Analyzed 17 9 58 85 20 18 47 25 13 9 17 27 36 51 31 42 17 34
Number of Transactions Analyzed 31 17 113 214 33 25 74 40 19 19 23 34 75 110 48 66 22 44
Standard Mean Discount 34.0% 55.6% 48.0% 50.1% 43.2% 41.3% 38.5% 36.9% 41.5% 47.3% 30.5% 24.2% 41.9% 46.9% 31.9% 32.2% 31.5% 28.4%
Trimmed Mean Discount 43.4% 56.8% 51.9% 55.2% 52.9% 47.3% 44.7% 44.9% 42.5% 46.9% 33.0% 28.9% 47.0% 49.9% 38.4% 47.4% 34.5% 30.5%
Median Discount
Standard Deviation
52.5% 62.7% 56.5% 60.7% 73.1% 42.6% 47.4% 43.8% 51.8% 50.3% 48.5% 31.8% 51.7% 53.3% 42.0% 58.7% 44.3% 35.2%
Source: Copyright # Willamette Management Associates, www.willamette.com. Used with permission. All rights reserved.
58.6% 30.2% 29.8% 34.7% 63.9% 43.5% 44.2% 49.9% 29.5% 18.6% 42.7% 37.7% 42.6% 33.9% 49.6% 76.4% 45.4% 46.7%
424
Cost of Capital
Exhibit 25.5
Value of Marketability as Illustrated in Initial Public Offerings of Common Stock Discount
Study 1997–2000 1995–1997 1994–1995 1991–1993 1990–1992 1989–1990 1987–1989 1985–1986 1980–1981 All 9 studies
Number of IPO Prospectuses Reviewed
Number of Qualifying Transactions
Mean
Median
1,847 732 318 443 266 157 98 130 97 4,088
266 84 45 49 30 17 21 19 12 543
50% 43% 45% 45% 34% 46% 38% 43% 59% 46%
52% 41% 47% 13% 33% 40% 43% 43% 68% 47%
Source: John D. Emory Sr., John D. Emory Jr., and F. R. Dengel III, ‘‘Discounts for Lack of Marketability Emory Pre-IPO Discount Studies 1980–2000 As Adjusted October 10, 2002,’’ Business Valuation Review (December 2002): 190. See Emory & Co., LLC’s Web site, www.EmoryCo.com, for a free downloadable spreadsheet of the underlying data.
8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
IPO price IPO date Transaction price Transaction date Whether transaction was Common stock Option Convertible preferred stock Percentage discount from IPO price Industry description
Transactions may be searched online on any of these fields at www.BVMarketData.com. Results of the Valuation Advisors study for the year 2000 are presented in Exhibit 25.6. As can be seen clearly from the exhibit, the discounts diminish rapidly as they approach the IPO date. Three sample transaction reports from the Valuation Advisors study are shown as Exhibit 25.7. Since these are all recent IPOs, if additional data regarding a transaction are desired, they can be readily obtained from public company filings. The pre-IPO studies are the only ones that actually represent transactions in private company stock (although the parties in most cases probably had hopes for a public offering, and the discount may reflect risk associated with the company not going public), and thus come closest to a proxy for a discount for lack of marketability for stock of a privately held company. Nevertheless, there are some challenges to the use of these studies, and the appraiser should be aware of the challenges when relying on them to support the discount.2 Discounts inputted from pre-IPO studies are biased high because they represent the results of successful IPO’s. For example, assume that an investment fund buys stock in 10 private companies
2
See, e.g., Shannon Pratt, ‘‘Lack of Marketability Discounts Suffer More Controversial Attacks,’’ editor’s column in Shannon Pratt’s Business Valuation Update1 (February 2002): 1–3; see also Mukesh Bajaj, ‘‘Dr. Bajaj Responds to Dr. Pratt’s February 2002 Editorial,’’ reader/editor exchange in Shannon Pratt’s Business Valuation Update1 (March 2002): 12–14.
Discrete Percentage Discount for Lack of Marketability Exhibit 25.6
425
Results of Valuation Advisors Study for 2000 Table 1. Complete Study Results
Time of Transaction before IPO Number of transactions Average discount
1–90 Days 535 27.7%
91–180 Days 786 37.40%
181–270 Days 604 49.10%
271–365 Days 541 54.40%
1–2 Yrs. 937 60.70%
271–365 Days 323 55.10%
1–2 Yrs. 542 61.20%
271–365 Days 82 58.20%
1–2 Yrs. 203 59.60%
271–365 Days 136 50.50%
1–2 Yrs. 192 60.60%
271–365 Days 82 63.10%
1–2 Yrs. 110 68.20%
Table 2. Complete Study: Option Transactions Only Time of Transaction before IPO Number of transactions Average discount
1–90 Days 367 27.4%
91–180 Days 480 36.5%
181–270 Days 351 50.70%
Table 3. Complete Study: CPS Transaction Only Time of Transaction before IPO Number of transactions Average discount
1–90 Days 41 33.80%
91–180 Days 108 41.20%
181–270 Days 85 46.30%
Table 4. Complete Study: Stock Transactions Only Time of Transaction before IPO Number of transactions Average discount
1–90 Days 127 26.70%
Time of Transaction before IPO Number of transactions Average discount
1–90 Days 90 31.70%
91–180 Days 197 37.30%
181–270 Days 167 47.10%
Table 5. SIC 7372: Software Publishers 91–180 Days 107 37.40%
181–270 Days 74 56.80%
Source: Brian K. Pearson, ‘‘2000 Marketability Discounts as Reflected in Initial Public Offerings,’’ Shannon Pratt’s Business Valuation Update1 (September 2001): 1–7, tables at 4. Used with permission. More comprehensive data and searches are also available for purchase with an annual license fee as the Valuation Advisors’ Lack of Marketability database at bvresources.com.
that may go public. Assume 5 companies go public 2 years after the investment and the discount from IPO price observed averages 40%. But assume the 5 other companies never go public and in fact go out of business within 2 years. The implied annual rate of return on the investment in the 5 successful IPO’s is 20% ([40/100]/2) (without regards to the typical ‘‘lock up period’’ following IPO; the lock up period restricts the pre-IPO investors from selling their shares for a period of time following the IPO). But the return on the investments in the other 5 companies is zero. The average return is 10%. The implied average discount from IPO price is therefore 10% ([20% 50%] þ [0% 50%]). The inclusion of only successful IPO’s results in a discount that is biased high. The average implied rate of return is 10% ([20/100]/2 years).
CONTROLLING OWNERSHIP INTERESTS The case for discounts for lack of marketability for controlling interest transactions has not been without controversy. A controlling interest holder cannot merely call a stockbroker, execute a transaction in seconds, and have cash in hand within three business days. It may take months to prepare a controlling interest for sale, in the process of which significant legal, accounting, and management time costs are incurred. Furthermore, compared with public companies, most private companies have much less ready access to the capital markets to raise additional equity and/or debt capital. Courts frequently have recognized discounts for lack of marketability for controlling stock interests held in estates. Discounts for lack of liquidity (marketability) for controlling ownership interests,
426 Exhibit 25.7
Cost of Capital Valuation Advisors’ Lack of Marketability Discount StudyTM Transaction Report
Sample Transactions Company Products, Service, or Business SIC NAICS
Double-Take Software Data Protection Software for Business Systems 7372 Prepackaged Software 511210 Software Publishers
Transaction Data Pre-IPO Time Frame Transaction Date Transaction Price per Share CPS, S or O IPO Date IPO Price per Share Company Products, Service, or Business SIC NAICS
Financial Data 12 mths 12/31/2005 $1.96 S 12/15/2006 $11.00
Company Products, Service, or Business SIC NAICS
Financial Data 11 mths 7/15/2005 $5.17 CPS 6/27/2006 $6.50
Net Sales Marketability Discount Total Assets Operating Income Operating Profit Margin
$42,804,000 20.462% $76,976,000 $(17,385,000) 40.615%
Corel Corporation Productivity, Graphics, and Digital Imaging Software 7372 Prepackaged Software 511210 Software Publishers
Transaction Data Pre-IPO Time Frame Transaction Date Transaction Price per Share CPS, S or O IPO Date IPO Price per Share
$41,787,000 82.182% $30,911,000 $5,227,000 12.509%
Omniture, Inc. Online Software for Business Optimization 7372 Prepackaged Software 511210 Software Publishers
Transaction Data Pre-IPO Time Frame Transaction Date Transaction Price per Share CPS, S or O IPO Date IPO Price per Share
Net Sales Marketability Discount Total Assets Operating Income Operating Profit Margin
Financial Data 9 mths 7/15/2005 $10.77 O 4/26/2006 $16.00
Net Sales Marketability Discount Total Assets Operating Income Operating Profit Margin
$164,044,000 32.688% $120,836,000 $16,886,000 10.294%
Source: Copyright # 2006. Valuation Advisors’ Lack of Marketability Discount StudyTM. All rights reserved. Available at www.BVMarketData.com. Used with permission. More comprehensive data and searches are also available for purchase with an annual license fee as the Valuation Advisors’ Lack of Marketability database at bvresources.com.
Building the Discount for Lack of Marketability into the Discount Rate
427
when appropriate (such as those recognized in the U.S. Tax Court), are often in the range of 10% to 25%,3 not as great as for minority ownership interests.4 We discuss these discounts in Chapter 26, the Private Company Discount.
BUILDING THE DISCOUNT FOR LACK OF MARKETABILITY INTO THE DISCOUNT RATE VENTURE CAPITALISTS’ REQUIRED RATES OF RETURN Venture capitalists typically say that they look for expected rates of return between 30% and 50% on their portfolios, which means higher rates on very risky start-ups. One reason why these rates are so high is the illiquidity of the companies and securities in which venture capitalists invest, even though they virtually always have an exit strategy in place if everything works out as projected. Unfortunately, there are no data available to indicate how much of their required rate of return is for illiquidity. (If any reader can shed light on this issue, please contact the authors at the phone numbers or addresses shown in the preface.) We discuss realized rates of return in venture capital investments in Chapter 29.
QUANTIFYING THE MARKETABILITY FACTOR IN THE DISCOUNT RATE In building the lack of marketability factor into the discount rate, determining how many percentage points to add to the discount rate is difficult and quite subjective. Z. Christopher Mercer, chief executive officer of Mercer Capital, has compiled a list of factors to consider, generally adding somewhere between zero and four percentage points for each factor considered important in the particular case. This list is shown in Exhibit 25.8. In most of his examples, Mercer considers about four to six factors, and his cumulative adjustments tend to run between one and six percentage points.5 The applicable cash flow for Mercer’s ‘‘Quantitative Marketability Discount Model’’ discount rate are those expected to be available to the minority investor. Of course, no empirical basis exists for assigning numbers in a matrix like this, and doing so may give the valuation report a sense of accuracy that does not actually exists. When using a table like this, the analyst might want to include a disclaimer to the effect that the numbers are presented not for precise quantification but merely to show the thinking of the analyst. Several other authors have proposed models for imbedding the marketability discount in the discount rate.6
3
4
5
6
See reference in note 1; see also Bradley A. Fowler, ‘‘How Do You Handle It?’’ part of a special report, ‘‘ASA Conference Offers Valuable Insights,’’ Shannon Pratt’s Business Valuation Update1 (July 1997): 1–2. See also Jim Hitchner’s discussion of marketability, liquidity, level of value, and valuation methodology in James R. Hitchner, Financial Valuation: Application and Models, 2nd ed. (Hoboken, NJ: John Wiley & Sons, 2006). Z. Christopher Mercer, Quantifying Marketability Discounts: Developing and Supporting Marketability Discounts in the Appraisal of Closely Held Business Interests (Memphis: Peabody Publishing, LP, 1997). This book also comprehensively covers empirical studies of discounts for lack of marketability conducted over the 30 years up until its publication. Francois M. De Visscher, Craig E. Aronoff, and John L. Ward, Managing Capital and Liquidity in the Family Business (Marietta, GA: Family Enterprise Publisher, 1995); Daniel McConaughy, ‘‘Is the Cost of Capital Different for Family Firms?’’ Family Business Review (December 1999): 353-359; David Tabak, ‘‘A CAPM-Based Approach to Calculating Illiquidity Discounts,’’ NERA Economic Consulting, Working paper, November 11, 2002.
428 Exhibit 25.8
Cost of Capital Estimating Cost of Capital, Including Illiquidity Factor Range of Returns
Components of the Required Holding Period Return
Lower
Higher
Base equity discount rate (adjusted Capital Asset Pricing Model) Current yield-to-maturity composite long-term Treasuries + Adjusted Ibbotson large stock premium Applicable beta statistic = Beta-adjusted large stock premium + Adjusted Ibbotson small stock premium = Base equity discount rate
0.0% 0.0% 1.0 0.0% 0.0% 0.0%
0.0%
Investment-Specific Risk Premiums: Factors to Consider Uncertainties related to length of expected holding period General illiquidity of the investment Lack of expected interim cash flow Uncertainties related to expected interim cash flow Potential for adverse cash flow from tax pass-through entity Uncertainties related to potential for favorable exit from investment General unattractiveness of the investment Lack of diversification of assets Unattractive asset mix Unlikely candidate for merger/sale/acquisition/initial public offering Uncertainties related to buy-sell agreement Small shareholder base Adjustment for large size of the entity Large size of the investment limits market Other Range of specific risk premiums for the investment Initial range of required returns Concluded range of required holding period returns
0.0% 0.0% 0.0%
0.0% 0.0% 0.0%
0.0% 0.0% 0.0%
Source: Z. Christopher Mercer, Quantifying Marketability Discounts (Memphis: Peabody Publishing, LP, 1997), 323. Reprinted with permission.
SUMMARY Investors, especially in the United States, cherish liquidity and abhor illiquidity. Because our empirical data to estimate cost of equity capital all come from the public stock market, the comparative lack of liquidity must be addressed when using cost of capital data to estimate value for privately held interests or companies. There are two ways to handle the liquidity difference between public company interests and private company interests: 1. Use a discrete percentage discount for lack of marketability. Value the interest as if it were publicly traded, and then subtract a discount for lack of marketability from the estimated publicly traded equivalent value. Two sets of studies to provide quantitative guidance for this are: a. Restricted stock studies b. Pre–initial public offering studies 2. Adjust the discount rate. Add percentage points to the discount rate used to discount the expected cash flows to present value.
Chapter 26
Private Company Discount Introduction Discrete Percentage Discount for Lack of Marketability Quantifying the Private Company Discount Building the Discount for Lack of Marketability into the Discount Rate Venture Capital Returns Include Return for Lack of Marketability Reasons for the Private Company Discount Summary
INTRODUCTION In Chapter 25 we discussed discounts for lack of marketability for minority interests. The empirical studies discussed therein provide data to help quantify the amount of such a discount in the case of minority interest transactions. In this chapter we discuss the appropriate discount, if any, for 100% of a private company compared to the value of a publicly traded equivalent company: the private company discount.
DISCRETE PERCENTAGE DISCOUNT FOR LACK OF MARKETABILITY The case for discounts for lack of marketability for controlling interest transactions is not as clear as for minority interests. A controlling interest holder cannot merely call a stockbroker, execute a transaction in seconds, and have cash in hand within three business days. It may take months to prepare a controlling interest for sale, with significant legal, accounting, and management time costs incurred in the process. Furthermore, compared with public companies, most closely held companies have less ready access to the capital markets to raise additional equity and/or debt capital. In addition, the quality of the accounting information of closely held companies is considered inferior to that of public companies. Also, most private companies are less well known to potential investors than are most public companies. Despite these limitations, some analysts would say that discounts for lack of marketability are not applicable to controlling interests. These same analysts may, however, recognize the realities of these factors under the rubric of ‘‘liquidity.’’ Some analysts have attempted to quantify the discount for lack of marketability by measuring the hypothetical cost of taking the closely held firm public as a proxy for the discount. This approach has two problems: 1. The closely held company may not be of the size to go public. 2. Even if it were a potential public company, the time and risk of failure of a public offering is not embodied in the costs to go public. Therefore, if anything, a proxy likely underestimates the appropriate discount. 429
430
Cost of Capital
Courts frequently have recognized discounts for lack of marketability for controlling stock interests held in estates. Discounts for lack of liquidity (marketability) for controlling ownership interests in closely held firms, when appropriate (such as those recognized in the U.S. tax court), are often in the range of 10% to 25%, not as great as for minority ownership interests. Several recent studies that have assembled data to help analysts quantify the private company discount.
QUANTIFYING THE PRIVATE COMPANY DISCOUNT John Koeplin, Atulya Sarin, and Alan Shapiro conducted a study of the multiples paid for public companies compared to closely held companies.1 In their study of matched pairs, they identified all acquisitions of closely held companies between 1984 and 1998 (excluding financial companies and regulated utilities) that were made by public companies. In those instances the acquiring company often must include information about the acquisition for the prior three years in its public filings. Closely held company acquisitions studied were limited to transactions in which a controlling interest was acquired and those in which sufficient information was disclosed in the public filing of the acquiring company. For each of these transactions, the authors identified an acquisition of a public company in the same country, in the same year, and in a similar industry. Of the matched pairs, 87% were in the same four-digit Standard Industrial Classification (SIC) code. In instances where there was more than one comparable public company, they chose the public company that was closest in size (as measured by sales) to that of the closely held company. These authors were able to develop a database of matched pair transactions in the U.S. and foreign transactions for transactions between 1984 and 1998. Comparing the sizes of the companies, the net sales and assets of the sample of closely held companies were smaller than those of the comparable public company transactions. Comparing growth of earnings, the earnings of the U.S. closely held targets for the three years prior to the acquisition increased at a higher rate than the earnings of the matched public companies. However, the earnings of the foreign closely held targets increased at a lower rate than the earnings of the matched public companies. Exhibit 26.1 presents select statistics about the closely held firms (domestic acquisitions) and the comparable public company transactions. The authors calculated valuation multiples for the transactions: enterprise value to earnings before interest and taxes (EBIT), enterprise value to earnings before interest, taxes, depreciation, and
Exhibit 26.1
Net Sales Assets
Descriptive Statistics of Sample Transactions Private Firms (1)
Public Firms (2)
$56.3 $40.6
$91.2 $60.1
$ millions (1) Median of 84 closely held companies acquired. (2) Median of 84 matched public companies acquired. Source: John Koeplin, Atulya Sarin, and Alan Shapiro, ‘‘The Private Company Discount,’’ Journal of Applied Corporate Finance, Winter 2000: 97. Blackwell Publishing Ltd. Used with permission. All rights reserved. 1
John Koeplin, Atulya Sarin, and Alan C. Shapiro, ‘‘The Private Company Discount,’’ Bank of America Journal of Applied Corporate Finance 12, no. 4 (Winter 2000): 94–101.
Quantifying the Private Company Discount Exhibit 26.2
431
Private Company Discounts PCD (1)
Enterprise Value/EBIT Enterprise Value/EBITDA Enterprise Value/Sales
30% 18% <1% (2)
(1) Based on median multiples for domestic acquisitions. (2) Difference not statistically significant. Source: John Koeplin, Atulya Sarin, and Alan Shapiro, ‘‘The Private Company Discount,’’ Journal of Applied Corporate Finance (Winter 2000) 99. Blackwell Publishing Ltd. Used with permission. All rights reserved.
amortization (EBITDA), enterprise value to book value, and enterprise value to sales. They compared the multiples and calculated the private company discount (PCD) as: PCD ¼ 1 ðClosely Held ðPrivate CompanyÞ Multiple=Public Company MultipleÞ Exhibit 26.2 summarizes their results. What causes the difference? Could the differences be due to differences in size? Growth? Need for liquidity of the selling owners of the closely held targets? In another study, Micah Officer documents the average acquisition discounts for stand-alone closely held firms and unlisted subsidiaries of public firms.2 He compares acquisition multiples for unlisted targets paid by public companies to acquisition multiples for portfolios of comparable (matched by industry and size) public companies and calculates the PCD. The sample covers the period 1979 through 2003. The author was able to develop a database containing over 2,800 standalone private firms acquired by public firms and over 5,300 unlisted subsidiaries of public firms acquired by other public firms. For each unlisted acquired company, Officer forms portfolios of comparable public targets where comparable acquisitions are in the same two-digit SIC code as the unlisted target and met certain other screens for comparability. For example, he identified over 1,100 matching portfolios of comparable transactions drawn from over 4,000 acquisitions of public firms to use in comparing the enterprise value-to-sales multiple paid for the unlisted acquired companies. The results are shown in Exhibit 26.3. The author also studies the differences in prices paid between acquisitions paid for in cash versus stock of the acquiring firm. Exhibit 26.4 summarizes his results. Exhibit 26.3
Assets
Descriptive Statistics of Sample Transactions Private Firms (1)
Unlisted Sub (2)
Public Firms (3)
$52.5
$255.2
$292.6
$ millions (1) Median of 417 closely held companies acquired. (2) Median of 416 unlisted subsidiaries acquired. (3) Median of 4,206 public firms acquired. Source: Micah S. Officer, ‘‘The Price of Corporate Liquidity: Acquisition Discounts for Unlisted Targets,’’ Journal of Financial Economics 83 (2007): 571–598.
2
Micah S. Officer, ‘‘The Price of Corporate Liquidity: Acquisition Discounts for Unlisted Targets,’’ Journal of Financial Economics 83 (2007): 571–598.
432 Exhibit 26.4
Cost of Capital Private Company Discounts Private Firms (1)
Unlisted Sub (2)
22% 12% 17%
28% 28% 28%
Average—cash acquisitions Average—stock acquisitions Average—overall
(1) Based on average difference in multiples (price paid for equity to book value of equity, price paid for equity to earnings, enterprise value to EBITDA, and enterprise value to sales) paid for private firms and comparable public firms (difference in arithmetic average of multiples). (2) Based on average difference in multiples (price paid for equity to book value of equity, price paid for equity to earnings, enterprise value to EBITDA, and enterprise value to sales) paid for unlisted subs and comparable public firms (difference in arithmetic average of multiples). Source: Micah S. Officer, ‘‘The Price of Corporate Liquidity: Acquisition Discounts for Unlisted Targets,’’ Journal of Financial Economics 83 (2007): 571–598.
Officer looks to see if the PCD is a function of alternative sources of liquidity for the selling owners. For example, during easy credit periods (lower spread between corporate interest rates and the federal funds rate), the PCD is lower (PCD = 14% for closely held firms and 25% for unlisted subsidiaries) than during times of more costly debt financing (PCD = 23% for closely held firms and 34% for unlisted subsidiaries). While you might hypothesize that during periods of above average initial public offering (IPO) activity, the PCD might be lower (as going IPO is an alternative method of gaining liquidity), Officer finds no evidence that the PCD varies with IPO activity. In the most comprehensive study to date, Gus De Franco, Ilanit Gavious, Justin Jin, and Gordon Richardson build a database of many more transactions.3 They build a database of closely held company acquisitions reported in Pratt’s Stats, where the acquisitions were made by public companies. In this manner they were able to use the public filings of the acquiring companies to extract more data about the acquired company than was available in Pratt’s Stats. Publicly acquired firm data was extracted from Compustat. Their database contains data on 664 acquired closely held firms and 2,225 acquired public firms. Exhibit 26.5 displays some discipline statistics of the companies comprising their database. The authors calculate the PCD based on differences in capitalization rates (rather than multiples to ensure that the denominators are always positive numbers): EBITDA=Enterprise Value and Sales=Enterprise Value They performed a multifactor analysis so that the regression statistics could help them better understand the reason for the differences between the observed multiples. The regression models control for size (log of total assets), sales growth (drawn from acquiring public company filings as Exhibit 26.5
Descriptive Statistics of Sample Transactions
Net Sales Assets
Private Firms (1)
Public Firms (2)
$15.8 $8.7
$130.1 $131.1
$ millions (1) Median of 673 closely held companies acquired. (2) Median of 2,249 public companies acquired. 3
Gus De Franco, Ilanit Gavious, Justin Yiqiang Jin, and Gordon D. Richardson, ‘‘The Existence and Explanations for the Private Company Discount,’’ Working paper, April 27, 2007.
Venture Capital Returns Include Return for Lack of Marketability Exhibit 26.6
433
Private Company Discounts PCD (1)
Enterprise Value/EBITDA Enterprise Value/Sales
37% 21%
(1) Based on mean of capitalization rates. Source: Univariate analysis in Gus De Franco, Ilanit Gavious, Justin Yiqiang Jin, and Gordon D. Richardson, ‘‘The Existence and Explanations for the Private Company Discount,’’ Working paper, April 27, 2007.
they present pro forma historical financial results for the acquired firm, closely held or public), research and development expenditures as a percentage of sales, and profit margin (EBITDA as a percentage of sales). They also control for industry by normalizing their results based on the median industry values (based on industry groupings of public companies). The authors determined the resulting private company discount statistics after controlling for differences among the acquisitions due to size, sales growth, research and development expenditures, and profit margins. Their results are displayed in Exhibit 26.6. These results are consistent with the Koeplin et al. and the Officer results in that the multiples for the acquisitions of the closely held firms are lower than the multiples for the acquired public companies. The results of these three studies are consistent with studies of the rates of return realized by shareholders of acquiring companies.4 These studies generally conclude that shareholders of public acquiring firms benefit from the companies acquiring closely held firms or nonpublic subsidiaries of public firms when compared to shareholders of public acquiring firms acquiring public companies.
VENTURE CAPITAL RETURNS INCLUDE RETURN FOR LACK OF MARKETABILITY In Chapter 29 we present rates of return venture capitalists typically say that they demand before making an investment. Such rates of return range between 30% and 50% on their portfolios, which means higher rates on very risky start-ups. One reason why these rates are so high is the illiquidity of the companies and securities in which venture capitalists invest, even though they virtually always have an exit strategy in place if everything works out as projected. These rates of return also are used for securing potential investments and do not represent expected average rates of return across many investments. We also discuss observations of historical rates of return earned on venture investments in Chapter 29. Unfortunately, there are no data available to indicate how much of their required rate of return is for illiquidity. In addition, these rates of return are for what venture capitalists believe to be a limited investment period. Venture capitalists do not make the investment believing they will hold onto it for an indefinite period (though for some investments they never realize a profitable exit).
4
See, e.g.: James Ang and Ninon Kohers, ‘‘The Take-over Market for Privately Held Companies: The US Experience,’’ Cambridge Journal of Economics 25 (2001): 723–748; Kathleen Fuller, Jeffry Netter, and Mike Stegemoller, ‘‘What Do Returns to Acquiring Firms Tell Us? Evidence from Firms that Make Many Acquisitions,’’ Journal of Finance 62, no. 4 (2002): 1763– 1793; Paul Draper and Krishna Paudyal, ‘‘Acquisitions: Private versus Public,’’ European Financial Management 12, no. 1 (2006): 57–80.
434
Cost of Capital
Building the lack of marketability factor into the discount rate, determining how many percentage points to add to the discount rate, is difficult and quite subjective.
REASONS FOR THE PRIVATE COMPANY DISCOUNT De Franco et al. study the differences in the quality of the financial data using several standard techniques. They find larger differences between the ‘‘cash earnings’’ and the ‘‘accrual earnings’’ of the private companies than the public companies in the year prior to the acquisition. This is consistent with the theory that acquirers are more suspect of the earnings quality of the closely held firm. They find that choice of an audit firm for the closely held firm can reduce the observed PCD; use of a large audit firm by a closely held firm results in an increase in the enterprise value paid for the closely held firms of between 19% and 25% compared to closely held firms not audited by a large audit firm. They conclude that the PCD is consistent with lower-quality accounting information. The median closely held firms in all three studies are smaller than the comparable public firms on which the PCD is based. As a result, these firms are likely less diversified and have greater variability of earnings than the comparable public firms. Other reasons for the private company discounts may hinge in part on the very sales process used in the sale of a closely held company. Often the entrepreneur restricts the sales process to be followed by the business broker engaged to sell the business. For example, say the owner of the closely held company has a friend who tried to sell his closely held company. Key employees of his friend’s business learned of the possible sale and became nervous. Some accepted offers of employment from other firms that heard of the possible sale and made lucrative offers to get the key employees to leave their ‘‘uncertain world’’ (i.e., no one knew who the new owner might be) for a new, more certain world (i.e., the new boss was not selling his business). Ultimately the possible sale of his friend’s business fell through after months of parading possible buyers through the company. It took the friend three years to get his business stabilized in the condition it was in before the sales process began. As a result, the owner of the closely held business tells the business broker that he or she can sell the business as long as no one learns of the possible sale. This is similar to trying to sell a house without putting up a ‘‘for sale’’ sign or listing the house with a multiple listing service. If you restrict the salesperson to contacting only potential buyers whom he or she knew might be interested, the owner of the house may not get the top dollar price. Another explanation for the private company discounts of the parties to the transaction may in part result in the ability to customize the structure of the purchase of the closely held company such that the after-tax proceeds to the owner may be higher than if the owner were to receive all cash proceeds at closing. In the sale of a public company, fewer opportunities exist for such customized structuring.
SUMMARY We presented three studies that provide data to quantify the appropriate private company discount. The PCD is an entity-level discount accounting for the differences between acquisition prices paid for closely held businesses and comparable public companies. There are basic differences in buyers’ assessment of the risks of acquiring closely held companies. The PCD represents in part the cautionary approach of acquiring companies. Other authors have presented evidence of the PCD.5 5
Nancy Fannon, and Heidi Walker, ‘‘Rates of Return: Don’t Ignore Public Market or Transactional Data,’’ Business Valuation Update (September 2007): 1, 4–6.
Summary
435
In addition, public company shareholders almost always benefit from higher prices because their firms generally are auctioned to the highest bidder. Closely held firms are less liquid than public company stock, and owners of closely held businesses have more limited avenues to liquefy their interests. Given the evidence, it is unreasonable to extrapolate public company acquisition prices and resulting multiples when valuing 100% of smaller, closely held businesses or even nonpublic subsidiaries of public companies.
Chapter 27
Cost of Capital of Interests in Pass-Through Entities Introduction Characteristics of Pass-Through Entities Gross Decision Delaware Court Adjusts for Tax Differences Market Evidence of Value of Interests in Pass-Through Entities Risks of Investments in Pass-Through Entities Summary Additional Reading
INTRODUCTION1 In the past several years a series of court decisions has challenged what was the traditional thinking of many regarding the valuation of pass-through entities. Appraisers often used tax effecting as a means to address risks of owning interests in pass-through entities. In the Gross decision, the tax court rejected the traditional approach of tax effecting, pointing out that by tax effecting the subject S corporation earnings, the petitioner’s expert: Introduced a fictitious tax burden, equal to an assumed corporate tax rate of 40%, which he applied to reduce each future period’s earnings, before such earnings were discounted to their present value.
The court found that risk should be measured in the cost of capital. Due to the Gross decision2 and a series of subsequent decisions, practitioners have had to change their thinking. In this chapter we discuss some of the issues in developing the cost of equity capital for a pass-through entity.
1
2
For a complete discussion of the valuation considerations in valuing pass-through entities, see Roger Grabowski and William McFadden, ‘‘Applying the Income Approach to S Corporation and Other ‘Pass-Through Entity’ Valuations,’’ chapter 5 in Robert Reilly and Robert Schweihs, The Handbook of Business Valuation and Intellectual Property Analysis (New York: McGraw-Hill, 2004). Gross, TCM 1999-254; affirmed Gross v. CIR, US Court of Appeals for the Sixth Circuit, Nos. 97-04460; 97-04469, Nov 19, 2001.
437
438
Cost of Capital
CHARACTERISTICS OF PASS-THROUGH ENTITIES The issue of the appropriate valuation method is broader in terms of application than simply to S corporations. There are a variety of so-called pass-through entities that require valuation: subchapter S corporations,3 partnerships (general or limited liability), real estate investment trusts (REITs), closed-end investment funds, and limited liability companies (LLCs). These entities ‘‘pass through’’ their reported tax characteristics directly to owners including income, gains, losses, deductions, and credits. Owners include these items on their individual income tax returns. Passed-through tax items also retain their tax character. For example, capital gains pass to owners still as capital gain income and not as ordinary income. For pass-through entities, the federal income tax resulting from the entities’ taxable income is owed directly by the owners regardless of the actual cash distributed to the owners. In addition, there is no second income tax due on distributions (as is due on dividends received by owners of shares of a C corporation). The avoidance of double taxation is a key feature of pass-through entities and has become a central consideration in their proper valuation, as evidenced in Gross. Today pass-through entities are an extremely popular and preferred form of entity structure for small to moderate-size businesses. Even larger businesses are often held as LLCs. With the rise of private equity ownership of many businesses, it is common for those businesses to be held through an LLC. So how should you develop the appropriate cost of capital for a pass-through entity? If we are valuing shares of a private REIT, we could derive expected rates of return for publicly traded REITs directly. The publicly traded REITs have the same tax characteristics as the private REIT being valued and the issues arising in the recent tax court cases are not applicable. See Chapter 37 for a discussion of developing cost of capital for a REIT. But analysts are often called on to value pass-through entities where data on rates of return can be derived only from entities with tax structures that differ from that of the pass-through entity.
GROSS DECISION The valuation experts in Gross took extremely opposed and simplified positions. The petitioner’s (taxpayer) expert fully tax effected the S corporation’s earnings as if it were a C corporation. The respondent’s (government) expert applied no income tax to the S corporation’s earnings because S corporation distributions to its shareholders are not taxed at the corporation or entity level. In its commentary, the court discussed the concept of properly matching the tax characteristics of the company’s cost of equity capital applied with the projected cash flow as better methodology: If in determining the present value of any future payment, the [cost of equity capital] is assumed to be an after-shareholder-tax rate of return, then the cash-flow should be reduced (‘‘tax affected’’) to an aftershareholder-tax amount.
The court further stated: We believe that the principal benefit that shareholders expect from an S corporation election is a reduction in the total tax burden imposed on the enterprise. The owners expect to save money, and we see no reason why that savings ought to be ignored as a matter of course in valuing the S corporation.
3
Owners must elect to be taxed as a small business corporation within the meaning of IRC Section 1371.
Gross Decision Exhibit 27.1
439 Company A: Year 1 Expected Net Cash Flow
Revenue Income before Tax Entity-Level Tax Rate Entity-Level Tax Net Income Net Depreciation Capital Expenditures Net Working Capital Net Cash Flow
}
(1) S Corporation
(2) As if C Corporation
$5,000,000 625,000 1.5% (9,375)
$5,000,000 625,000 40% (250,000)
615,625
375,000
0
0
$615,625
$375,000
The nature of the controversy may be made clearer through an example. Consider Company A with projected revenue, net income, and net cash flows for the first projected year in Exhibit 27.1. Company A has elected S corporation status, and its entity-level income taxes are limited to certain state levies (no federal income tax is due at the entity level) (column 1). Assume we are appraising a 5% interest in Company A. Assume for simplicity that depreciation expense minus capital expenditures minus changes in net working capital net to zero. The traditional approach and the one used by the taxpayer expert in Gross has been to treat the corporation identically except reduce the net income by a hypothetical income tax as if it were a C corporation (column 2). Assume that the appropriate cost of capital for an equivalent C corporation equals 15%. Assume further that the expected long-term stabilized growth rate in cash flows equals 5%. If you discount the expected future cash flows in column 2 by capitalizing the cash flow assuming a constant stabilized growth rate into perpetuity (converting the discount rate to a capitalization rate by subtracting longterm expected growth, commonly referred to as the constant perpetual growth model or the Gordon growth model), you arrive at an indicated value of $375,000/(15% 5%) ¼ $3,750,000. You then multiply this indicated value for the entire equity by the 5% ownership interest being appraised, subtract a discount for lack of control (if appropriate), and adjust for lack of marketability of the closely held nature of the pass-through entity.4 The tax court recognized that the federal income tax subtracted was hypothetical. The two controversies are: 1. Should such a hypothetical income tax be subtracted in the valuation process? 2. What is the appropriate discount rate to use in converting the expected future cash flows to their present value equivalent (through either the discounted cash flow method or a single-period capitalization method), given that appraisers most often derive the discount rate from expected returns on investments in C corporations? Exhibit 27.2 extends the example in Exhibit 27.1 by subtracting owner-level income taxes.
4
As S corporations are closely held entities, any indicated values derived by reference to publicly traded stock data should be discounted for the relative lack of ready marketability of the subject private company stock compared to publicly traded stocks. See Chapter 25 in this volume with regard to minority interests and Chapter 26 with regard to controlling interests.
440
Cost of Capital Exhibit 27.2
Net Cash Flow to Owner (1) S Corporation
(2) As if C Corporation
Revenue Income before Tax Entity-Level Tax Rate (1) Entity-Level Tax Net Income
$5,000,000 625,000 1.5% (9,375) 615,625
$5,000,000 625,000 40% (250,000) 375,000
Net Cash Flow (2) Owner-Level Tax Rate (3) Owner-Level Taxes
$615,625 41.5% 255,484
$375,000 41.5% 155,625
Net Cash to Owner
$360,141
Increase in Cash Flow
$140,756
$219,385
(1) Assumed state income tax rate for S corporation and federal rate plus effective state income tax rates for C corporation. (2) Pretax to owner. (3) Income tax rates as S corporation ordinary income and C corporation dividends were approximately the same rate.
The data used by both appraisers in Gross to derive the appropriate cost of equity capital were rates of return on shares of C corporations after paying entity-level income taxes but before ownerlevel income taxes. The cost of equity capital was appropriate to apply to the net cash flow. In the traditional method, you would apply the discount rate to the $375,000 in net cash flow as if it were a C corporation (column 2). That cash flow is before owner-level income taxes. Therefore, the discount rate is appropriate to convert to present value the pre–owner-level-tax net cash flow. The court compared the S corporation’s net cash flow and noticed that the subject company in the Gross case was, in fact, subject to no entity-level income tax.5 The pre–owner-level-tax net cash flow for the S corporation in the example is $615,625 (column 1). The court reasoned that since the historical and expected cash distributions were equivalent to interest on a bond in which only owner-level taxes are due, the discount rate should be applied to the net cash flows before owner-level taxes. At the valuation date, the income tax rate on S corporation income passed through to the owners and the income tax rate on C corporation dividends for noncorporate investors were approximately the same. The court simply recognized that $140,756 in total income taxes were saved (the combination of entity-level taxes and owner-level taxes) and believed that the expected tax savings should be included in the value. The court applied the cost of equity capital to the $615,625 in column 1, ignoring the hypothetical income taxes applied by the taxpayer’s expert. [The IRS expert] assumed that [the subject company] would continue to distribute all of its earnings annually. He made no explicit adjustment for any shareholder level taxes, although, undoubtedly he knew such taxes would be due. [He] did not, however, ignore shareholder level taxes. He simply disregarded them both in projecting [the company’s] available cash and in determining the appropriate discount rate. . . . If, in determining the present value of any future payment, the discount rate is assumed to be after-shareholder-tax rate of return, then the cash-flow should be reduced (‘‘tax affected’’) to an after-shareholdertax amount. If, on the other hand, a pre-shareholder-tax discount rate is applied, no adjustment for taxes 5
The company was incorporated and operated in Ohio. In Ohio, S corporations were not subject to state income tax.
Gross Decision Exhibit 27.3
441 Net Cash Flow to Owner
Revenue Income before Tax Entity-Level Tax Rate (1) Entity-Level Tax
(1) S Corporation
(2) As if C Corporation
$5,000,000 625,000 1.5%
$5,000,000 625,000 40%
(9,375)
(250,000)
Net Income
615,625
375,000
Net Cash Flow (2) Owner-Level Tax Rate (3) Owner-Level Taxes
$615,625 41.5% 255,484
$375,000 20% 75,000
Net Cash to Owner
$360,141
Increase in Cash Flow
$60,141
$300,00
(1) Assumed state income tax rate for S corporation and federal rate plus effective state income tax rates for C corporation. (2) Pretax to owner. (3) Assumed federal rate plus effective state income tax rate for S corporation income and assumed federal rate plus effective state income tax rate for C corporation dividends.
should be made to the cash-flow. Since, in applying his discounted cash-flow approach, [the IRS expert] assumed a pre-shareholder-tax discount rate, he made no error in failing to tax affect expected cash flow.6
Today the income tax rates applicable to the ordinary income passed-through taxable to the owners of pass-through entities differs from the income tax rate on C corporation dividends and taxes on owners’ capital gains, reducing the difference in net cash flow to the owners (see Exhibit 27.3). The total income taxes saved would now equal $60,141. The taxpayer’s expert suggested tax effecting as a way of taking into account the risks of the investment. One risk he cited was the risk that the S corporation would not distribute sufficient cash for the shareholders to pay the owner-level income tax on the S corporation income passed through to the shareholders. The court was unconvinced that such a risk was reasonable, given the history of growth of the subject business and its making distributions that nearly equaled its entire income. Further, as a theoretical matter, we do not believe that ‘‘tax-affecting’’ an S corporation’s projected earnings is an appropriate measure to offset the potential burden associated with S corporations.7
Another risk cited was the risk that the S corporation might lose its favorable tax status. The court found that while [w]e might consider an approach that sought to determine the probability of such an occurrence, and which utilized a tax rate equal to the product of such probability and the corporate tax rate in an effort to quantity that potential loss, [w]e do not, however, think it is reasonable to tax affect an S corporation’s 6
7
Gross, TCM 1999-254; affirmed Gross v. CIR, US Court of Appeals for the Sixth Circuit, Nos. 97-04460; 97-04469, Nov 19, 2001. Ibid., 24.
442
Cost of Capital
projected earnings with an undiscounted corporate tax rate without facts and circumstances sufficient to establish the likelihood that the election would be lost.8
Finally, the taxpayer’s expert argued that an S corporation is at a great disadvantage in raising capital given the limits the law places on numbers and types of shareholders. The court found that [t]his concern is more appropriately addressed in determining the cost of capital. In any event, it is not a justification for tax affecting an S corporation’s projected earnings under a discounted cash-flow approach.9
The tax court in Gross and in subsequent decisions did not adjust for the total tax differences (combined entity level and owner level) between owning an interest in an S corporation and an interest in an otherwise identical C corporation. The authors of this book disagree with the tax court on its analysis. Grabowski has written on variations of the income approach for valuing either minority or control interests in a pass-through entity such as an S corporation. These methods use a consistent cost of capital reflecting the risk of the investment but take into account the differences in taxation between a C corporation and its shareholders and S corporation shareholders.10
DELAWARE COURT ADJUSTS FOR TAX DIFFERENCES Tax effecting on S corporation was the tax subject of a recent Delaware fair value case.11 The valuation expert for defendant treated the valuation of the subject company, Delaware Radiology, as if it were a C corporation. The valuation expert for appraisal petitioner did not tax effect its earnings (a`la Gross). The court found that Delaware Radiology: is a very small entity. The record reveals no set of circumstances in which it is likely that Delaware Radiology will convert to a C corporation status. It is a highly profitable entity that generates and distributes income well in excess of the stockholder taxes its stockholders must pay.
The court ruled: Under Delaware law, an appraisal petitioner is ‘‘entitled to be paid for that which has been taken from him. . . . ’’ In this case, the [appraisal petitioner] was involuntarily deprived of the benefits of continuing as stockholders in a profitable S corporation. . . . it would be highly misleading to do a market-based comparable acquisition valuation of an S corporation using sales of comparable C corporations to C corporations, and then assume that the S corporation would sell at a higher price because of its tax status. In other words, I am not trying to quantify the value at which Delaware Radiology would sell to a C corporation; I am trying to quantify the value of Delaware Radiology as a going concern with an S corporation structure and award the (appraisal petitioner) their pro-rata share of that value.
8 9 10
11
Ibid., 25. Ibid., Roger J. Grabowski, ‘‘S Corp Valuation in the Post Gross World-Updated,’’ Business Valuation Review (September 2004): 139– 166. Delaware Open MRI Radiology Associates, P.A. v. Howard B Kessler et al. (Court of Chancery of the State of Delaware, Cons C.A. No. 275-N (April 26, 2006).
Market Evidence of Value of Interests in Pass-Through Entities
443
The court found a precedent In re Radiology Associates (611 A.2d at 495), noting that: Under an earnings valuation analysis, what is important to an investor is what the investor ultimately can keep in his pocket.
In rendering its decision, the vice chancellor ruled: Refusing to tax affect at all produces . . . a windfall . . . to ignore personal taxes would overestimate the value of an S corporation and would lead to a value that no rational investor would be willing to pay to acquire control. This is a simple premise—no one should be willing to pay for more than the value of what will actually end up in her pocket . . . .
The vice chancellor applied a hypothetical 29.4% effective tax rate to the earnings of Delaware Radiology: treating the S corporation shareholder as receiving the full benefit of untaxed dividends, but equating its after-tax return to the after-dividend return to a C corporation shareholder as shown next:
Affecting to Equate Income before income tax Corporate tax rate Available earnings Dividend or personal income tax rate equals: Cash available for shareholders
Corporation Returns to Shareholders
C Corporation
Tax S
$100 40% $60
$100 – $100
$100 29.4% $70.60
15% $51
40% $60
15% $60
MARKET EVIDENCE OF VALUE OF INTERESTS IN PASS-THROUGH ENTITIES Is there market evidence that interests in pass-through entities sell at a premium over interests in an otherwise identical C corporation? Let us look at Canada’s income trusts. Income trusts are hybrid structures that do not pay corporate-level income taxes but distribute taxable income to unit holders as fully taxed interest income. Income trusts avoid paying tax only if they distribute income each year. Distributions in excess of taxable income are treated as tax-free returns of capital to investor. In Canada, diverse operating companies have organized or converted to income trusts; publicly traded pass-through entities are comprised of REITs (15%), oil and gas royalty trusts (39%), pipe and power trusts (11%), and other (35%). In a recent study, the authors find that earnings are valued higher for Canadian income trusts than for a set of matched business operations operating as corporations, consistent with marginal investor in income trusts being low-tax rate investors.12 For example, assume the corporation (paying
12
Klassen and Mescall, ‘‘Valuation of Income Trusts: An Exploration of Clienteles and Implicit Taxes,’’ Working paper (April 2006).
444
Cost of Capital
entity-level taxes) and the income trust in the same business each has $1,000 of earnings. The market prices each such that the return to the owners, on an after-tax basis, are:
Earnings Multiple Market value Return to investor:
Corporation
Income Trust
$1,000 5 $50,000 $1,000 (1–50%) $500/$50,000 ¼ 10%
$1,000 6 $60,000 $1,000 (1–40%) $600/$60,000 ¼ 10%
The authors find income trusts are valued about 18.75% greater per dollar of pretax income than the otherwise identical corporation, consistent with marginal investor in income trust having a tax rate of approximately 38%. In circumstances where the pass-through entity net cash flow to the owners is greater than it would be as an identical C corporation, those savings in variable expense (combined effective entity plus owner income taxes) result in the entity having an incremental value because its cash flows are greater, not because its cost of capital is lower. The price the buyer is willing to pay for the benefits of owning an interest in a pass-through entity will depend on the income tax status of the buyer, the nature of the interest being purchased, and, in part, on the peculiar risks that may offset those benefits. The Canadian income trust transactions represent minority interest transactions. Do people pay a premium for controlling interests of a pass-though entity? In a June 2001 article, Brian H. Burke calculates the value of selling assets (instead of C corporation stock) and notes that in his experience, ‘‘the difference in value will usually have an order of magnitude in the range of 15% to 20%.’’13 In a 2002 study, Erickson and Wang report the median acquisition multiples paid by acquiring C corporations measured for ‘‘matched pairs’’ of (comparable) S and C corporations; the median acquisition multiple paid for S corporations exceeded that paid for C corporations (e.g., median price to revenue multiple for S corporation acquisitions were 31% greater than for matched C corporation acquisitions). Their study includes only taxable transactions (i.e., no transactions in which stock was exchanged for stock).14 Why should there be a difference in value? The reason for the premium is that the buyer can realize a step-up in tax basis of the underlying assets, resulting in an increase in future tax deductions and increased future cash flow. This result is not due to any differences in the cost of capital. These observations are not without controversy. Practitioners studying information on prices paid for sales of 100% interests in corporations contained in transaction databases that have compared prices paid for S corporations versus C corporations. Their results indicate virtually no price differences, except for larger corporations.15 These results are not surprising because shareholders of smaller corporations typically are involved in operating the business, and controlling owners can theoretically mimic an S corporation’s elimination of double taxation by paying themselves additional salary. The entity will get a tax deduction for the added compensation and the owners will be taxed (only once). But the added 13 14
15
Brian H. Burke, ‘‘The Impact of S Corporation Status,’’ Business Valuation Review (June 2001): 15–24. Merle Erickson and Shiing-wu Wang, ‘‘The Effect of Organizational Form on Acquisition Price,’’ Working paper, May 16, 2002. For a discussion of the impact of the S corporation election on value, see Sidney R. Finkel, ‘‘Is There an S Corporation Premium?’’ Valuation Strategies (July/August 2001): 14–27. That article addresses a premium for a control position. It briefly addresses the S corporation election benefits when valuing a minority interest, but that discussion is incomplete. Also see Mark O. Dietrich, ‘‘Computing Premium for S Status Based on Buyer’s Benefit,’’ Valuation Strategies (May/June 2003). For example, Michael J. Mattson, Donald S. Shannon, and David E. Upton, ‘‘Some Evidence on ‘S’ Premiums,’’ Shannon Pratt’s Business Valuation Update (November 2002 and December 2002); John Phillips, ‘‘S-Corp or C-Corp? M&A Deal Prices Look Alike,’’ Shannon Pratt’s Business Valuation Update (March 2004).
Market Evidence of Value of Interests in Pass-Through Entities
445
compensation may be subject to employment taxes and may subject the entity to IRS scrutiny due to the overly aggressive compensation. Further, the sellers of 100% of the stock of a small business taxed as a C corporation can mimic the proceeds they would receive as if they were selling assets of an S corporation. They can realize proceeds upon sale, outside of the selling price for their stock, by receiving payments under employment agreements and noncompetition agreements that are tax deductible to the buyer. The sellers can realize total sales proceeds equivalent to those that would be paid to tax owners of an identical corporation taxed as an S corporation. The value of the step-up in basis can be passed through to the buyers via the tax deductions they will realize on employment agreements and noncompetition agreements. Sellers will use these agreements as a way to circumvent the ‘‘built-in’’ gains tax that would result if the C corporation sold assets directly to the buyer. These values allocated to employment agreements and noncompetition agreements are added to the price paid for the stock when the total consideration paid for the corporation is reported in transaction databases, at least in some cases. Such an allocation can be challenged and changed upon audit by the Internal Revenue Service; the transaction databases do not reflect the final allocation results.16 Further, the reported transaction prices in the databases do not allow the researcher to differentiate whether the transaction was structured to be tax-free to some or all of the selling S corporation shareholders. In determining fair market value, you need to convert the ‘‘value’’ of any consideration received to its cash-equivalent basis. Researchers or practitioners who do not (or cannot) convert the proceeds reported in the databases to their cash-equivalent basis will come to faulty conclusions.17 But for larger corporations, there is typically a separation between management and shareholders. Nonmanagement shareholders will not be able to participate in employment agreements or noncompetition agreements. In these cases, sellers must receive value for their stock through the sale of the stock. Buyers will pay for the step-up in basis of assets to reduce their future taxes, and this added price will be reflected in the price paid for the stock of an S corporation and the value realized by the willing buyer. The observed transaction prices reflect this difference. Thus while some commentators have concluded that there is no evidence or logic indicating that S corporations are worth more than C corporations,18 the data on which they rely is incomplete and their observations fail to account for the myriad of possible unique facts and circumstances that negate a blanket assertion. These types of conclusions fail to account for the fact that analysts typically are asked to value a specific interest with all of its characteristics and attributes (including tax attributes). Other commentators have observed that since the current financial accounting standards require all acquisitions to be accounted for as a purchase of assets, any difference in the prices paid for C corporations versus S corporations should go away. But the change in financial reporting standards does not alter the analyses presented herein because the step-up in asset basis we address affects income taxes.19 16
17
18
19
See, e.g., Langdon v. Commissioner, 2003 U.S. App. LEXIS 2714, February 14, 2003, per curiam. The appeals court upheld the tax court’s reallocation of an amount originally allocated to a noncompetition agreement to the company’s intangible assets. The corporation had sold its assets for a price equal to its operating assets and accounts receivable, with no amount allocated to the intangible assets. John D. Finnerty, ‘‘Adjusting the Comparable Company Method for Tax Differences when Valuing Privately Held ‘S’ Corporations and LLCs,’’ Journal of Applied Finance (Fall/Winter 2002): 7–22. Chris Treharne, Nancy J. Fannon, and Jim Hitchner, ‘‘Valuation of Pass-Through Entities,’’ paper presented at the 23rd ASA Annual Advanced Business Valuation Conference, October 8, 2004, 36. SFAS No. 141 mandates financial reporting requirements only and not income tax accounting. There will still be acquisitions that are nontaxable to the sellers (i.e, exchange of stock of the acquiring corporation for stock of the seller) for which no step-up in income tax basis of the corporation will be realized by the buyer. The step-up in income tax basis of the corporation’s assets can occur only in a taxable transaction.
446
Cost of Capital
Do the changes brought about by the Jobs and Growth Tax Relief Reconciliation Act of 2003 (which equated federal income tax rates on dividends and certain capital gains) eliminate the benefit of being a pass-though entity? The change in the law did not eliminate the corporate tax on the sale of appreciated property (built-in gain tax). For example, if a C corporation owns appreciated property and distributes such property as a dividend to its shareholders, the gain on the property (difference between the fair market value of the property and its income tax basis) is subject to corporate income tax. Stock in an S corporation that owns appreciated property and is not subject to the built-in capital gains tax would be valued at a greater amount than stock in that same S corporation where it currently is subject to the built-in gains tax. While the shareholders will pay only personal income tax on the dividend at the reduced rate, there still is double taxation. In one bankruptcy court decision, the judge disagreed with this analysis. In Doctors Hospital of Hyde Park, the judge accepted the testimony of one expert witness that had tax-effected the cash flows of the subject S corporation because ‘‘it’s standard methodology to tax-affect the normalized cash flow of an S corporation.’’20 The expert relied on a book by two experts in business valuation who opined that this was the correct way to value 100% of an S corporation that was the subject of the proceeding. The judge commented: [ . . . ] it is not logical to suggest that a buyer would pay substantially more for [the subject company] just because the buyer is an S corporation. The object of an insolvency analysis is to determine the value of [the subject company] to a theoretical buyer, regardless of the nature of the buyer.
While there had been testimony from the opposing expert that the likely buyer would have been a nonprofit or another S corporation, the ‘‘pool of likely buyers’’ as a factor appears not to have been explored. In addition, the dates at which insolvency was being tested were August 1997 through August 2000, a period before much of the current literature on S corporation valuations had been written.
RISKS OF INVESTMENTS IN PASS-THROUGH ENTITIES What are some of the unique risks of an investment in an interest in a pass-through entity? These depend on the specific facts and circumstances surrounding the interest. For example, buyers of a minority interest are unable to determine distribution policy. Unless buyers are protected from being required to pay personal income taxes in excess of distributions received, they will not pay a ‘‘full’’ premium justified by only theoretical benefits. Even historical precedent of distributions does not provide the same level of risk reduction as written agreement among the owners. Absent the protection of a written agreement, the theoretical benefit of avoiding double taxation may be offset in whole or in part by an increased discount for the reduced marketability that results.21 Controlling owners may reduce distributions for any number of reasons, including retaining income for capital investments or squeezing out nonconforming minority shareholders. While such reduction in distributions may serve as grounds for an oppressed
20
21
In Re: Doctors Hospital of Hyde Park Inc. v. Dr. James H. Desnick, U.S. Bankruptcy Court, Northern District of Illinois, Eastern Division, Bankruptcy No. 00B11520, March 2, 2007. This might be accomplished by either increasing the discount rate or increasing the percentage discount for lack of ready marketability applied to the indicated value at the end of the valuation process; see Chapter 25 in this volume.
Additional Reading
447
shareholder action against the controlling owners, such remedies are costly to pursue. These specific risks should be weighed against the theoretical advantages of the interest in the pass-through entity. Minority investors in a closely held entity can rarely fully capture the theoretic appreciation in the value of their shares. Willing buyers (at least those unrelated to existing owners) are typically scarce. Absent sale of the entire business (control of which is in the hands of the controlling owners only), owner liquidity, in fact, may be realized only through distributions from the entity itself. Sometimes the documents creating the entity (e.g., articles or incorporation or by-laws) and/or agreement among the owners (e.g., shareholders agreement) provide for some level of distributions (in excess of the income taxes owed by the owners as a result of the pass-through entity status) and/or some sort of a ‘‘market mechanism’’ to be created by the entity or controlling owner(s). Absent such distributions or mechanism, minority owners generally are at the mercy of the controlling owner(s) to create a liquidity event. The risks in investing in partnerships and LLCs are determined in large part by the partnership agreement and the agreement establishing the LLC. Some risks parallel those confronting the S corporation shareholder. But other risks may be reduced because in the process of forming the partnership or LLC, the parties need to consider every aspect of their relationships to the entity and to each other. These deliberations often result in establishing protections through the agreements that may be overlooked by S corporation shareholders when establishing the corporation. In addition, the investor in a pass-through entity is confronted with the risk of lack of ready marketability. Handling that risk was discussed in Chapter 25 for minority interests and in Chapter 26 for controlling interests.
SUMMARY This is a chapter on risks in investing in interests in pass-though entities. All risk assessment requires consideration of benefits also. Tax-effecting of pass-through entity income is not a substitute for assessing the inherent risks in the business and in the subject interest being valued. The risks differ between minority interests and controlling interests and even between the size of the controlling interests. In general, some differences in the cost of capital between C corporations and pass-through entities may apply, for the reasons stated in this chapter. However, most of the differences in the values of interests in C corporations and similar pass-through entities are accounted for by differences in cash flows available to shareholders. A valuation formula has a numerator (cash flow) and a denominator (discount rate). Each must be considered separately. The expected cash flows of a pass-through entity do not include federal entitylevel income taxes. The tax court has indicated that any unique risks faced by the owners of interests in pass-through entities should be addressed through the cost of capital, not by tax effecting. This chapter speaks to the need to analyze and quantify the advantages and disadvantages of the subject interest based on the specific facts and circumstances of the subject business and the likely buyers for the ownership interest being valued.
ADDITIONAL READING Hitchner, James R. Financial Valuation: Applications and Models, 2nd ed. Hoboken, NJ: John Wiley & Sons, 2006.
Chapter 28
Cost of Capital in Private Investment Companies Will Frazier, ASA Introduction Characteristics of a Private Investment Company Relationship between Investment Period and Value PICs Are Very Long-Term Investments Mean Reversion Control and Marketability Considerations in Investments in PICs Lack of Control Determining the Increment to the Cost of Capital for Lack of Control Lack of Marketability or Illiquidity Determining the Increment to the Cost of Capital for Lack of Marketability Example: Valuing LP Interests in McCord v. Commissioner Partnership Assets Applying the Income Approach Partnership Portfolio Returns Incremental Rate of Return for Lack of Control Incremental Rate of Return for Lack of Marketability Calculating the Low-End and High-End Cost of Capital Determination of Curve of Best Fit Reconciliation of McCord Adjusted Net Asset Method Valuation with the NICE Method Summary
INTRODUCTION The most common way of determining the fair market value of equity interests in closely held investment entities, such as family limited partnerships and limited liability companies (referred to herein as private investment companies [PICs]), is the adjusted net asset method, a version of the assetsbased approach.1 In applying that approach, you first determine the net asset value (NAV) of the entity and then apply valuation discounts to the subject interests for factors such as lack of control and lack of marketability. An alternative methodology is to apply an income-based approach. In applying the income-based approach, you must determine the appropriate cost of equity capital. Because PICs are closely held, the cost of equity capital will include an added return related to the fact that an interest in a PIC has reduced marketability compared to a direct ownership of the underlying assets or in a freely traded equivalent entity.
1
See American Society of Appraisers, Business Valuation Standards-Glossary (Herndon, VA: American Society of Appraisers, revised 2005).
449
450
Cost of Capital
The nonmarketable investment company evaluation (NICE) method is a valuation method designed especially to determine the fair market value of interests in PICs that directly takes into account investment risks by embodying them into the appropriate cost of equity capital for the subject interest.2 The NICE method solves for the price you would pay for the interest in view of the investment’s risks and expected returns. This is, in fact, what investors in the marketplace actually do every day.
CHARACTERISTICS OF A PRIVATE INVESTMENT COMPANY PICs may hold investment assets of any type, but among the most common assets are stocks of public companies or closely held companies, bonds, and real estate. In this chapter, we concentrate our discussion on PICs holding these types of assets. PICs are generally pass-through entities (limited partnerships [LPs] or limited liability companies [LLCs]) established to maximize long-term asset appreciation. As such, PICs often distribute cash only to the extent that the equity owners owe income taxes on the taxable income passed through to them. The remaining income is reinvested. The economic return to the equity owners from a PIC with such a distribution policy ultimately results from liquidation of the entity. As we explain later, the likely liquidation date of a PIC can be a very distant event, with a practical range of no less than 10 years from the valuation date and ending, in most cases, at a date 50 years from the formation of the entity. The fair market value of an equity interest in a PIC is based entirely on the rates of return required by both the buyer and the seller. Each has his or her own view of what these returns should be. In the case of the willing buyer, the required rate of return will be the expected ex ante rate of return from the investment. In the case of the willing seller, the price at which he or her is willing to sell will be influenced by the historical rate of return from the investment, available reinvestment rates of return in the marketplace, and, of course, the expected rate of return of the interest should the seller choose not to sell. Because of lack of control and the unfamiliarity with the operating and entity management of the PIC, a willing buyer will require a rate of return higher than could be otherwise obtained in the public marketplace by investing directly in assets similar to those held by the entity. The degree of the rate of return enhancement will vary based on the asset class. Generally speaking, the safer (less volatile) the assets currently held by the PIC and expected to be held in the future through reinvestment of retained income, the lower the required adjustment. The availability of expected return data will also vary based on the asset class. For example, data on public securities, such as stocks and bonds, are plentiful. However, reliable, published return data on investment types such as private equity, real estate, or timberland are relatively thin. However, this does not mean returns for these asset classes cannot be observed historically and estimated in the future—after all, these assets are bought and sold every day by investors who have no better information. What is required is for the analyst to build a solid, reasonable case based on the same information available to these risk-taking investors. The required rate of returns of the hypothetical buyer and seller would reasonably require during a lengthy but uncertain period until a liquidity event occurs will be expressed by a range, or spread, above the weighted average rate of return of the underlying assets held by the PIC (i.e., an entitylevel rate of return). Furthermore, because of the uncertainty as to the length of time before a liquidity event occurs (at which time distribution of the underlying investments of the PIC occurs and
2
William H. Frazier, ‘‘Nonmarketable Investment Company Evaluation,’’ Valuation Strategies (November/ December 2006).
Relationship between Investment Period and Value
451
investors can liquefy their investment position through sale of the assets distributed), you must analyze the degree of mean reversion and varying levels of illiquidity based on the expected holding period; as a result, the expected rate of return will vary over time. That is, the cost of capital will differ depending on the times to expected future liquidity events. We will determine two paths of possible annual returns representing a range of low end and high end of reasonable returns for the PIC based on the assets it holds. While there is uncertainty as to the length of time before a liquidity event occurs, we do know that, if we can determine a price that satisfies the best possible compromise between the buyer’s and seller’s objectives, we have identified a reasonable estimate of the fair market value. Willing sellers have their own outlook and expectations for the financial characteristics of the interest in the PIC. Willing buyers develop their own unique views too. These individual views are examples of investment value, not fair market value. But the synthesis of these two viewpoints is the point at which the transaction takes place. This is the essence of fair market value. The NICE method attempts to replicate the most likely investment behavior of the buyer and the seller. We assume that both parties are motivated to conclude a transaction and seek to individually maximize their economic benefit but are rational and their behavior conforms to the realities of the marketplace.
RELATIONSHIP BETWEEN INVESTMENT PERIOD AND VALUE Pratt states: value . . . depends upon an estimate of the future benefits and the required rate of return at which those future benefits are discounted back to the valuation date .’’3
Fair market value, then, is the price a hypothetical buyer would pay (and at which a hypothetical seller would sell) based on (1) the expected economic returns to the interest, (2) the expected risks of realizing those expected returns, and (3) consideration of alternative investments and rates of return available in the marketplace. The length of the period until the investor expects to realize cash distributions is critical to the determination of fair market value under the income approach. In all financial calculations, time is an essential element. You cannot calculate the interest cost of a loan, the present value of an annuity, or the future value of an investment without the element of time. Ignoring the time element in the valuation violates the primary principle of the time value of money. We must examine further what we mean when we say ‘‘time to a liquidity event.’’ What do we mean when we say ‘‘short time to a liquidity event’’ or ‘‘long time to a liquidity event’’? Is there a typical or ‘‘average’’ period until a liquidity event that can be used as a measuring stick? You probably will not be shocked to learn that there is no definite answer to this question. Investors gravitate to investments whose economic return patterns best fit their particular needs. This phenomena was noted and analyzed by Amihud and Mendelson: Illiquidity can be measured by the cost of immediate execution. An investor willing to transact faces a tradeoff: He may either wait to transact at a favorable price or insist on immediate execution at the current bid or ask price. The quoted ask (offer) price includes a premium for immediate buying, and the bid price similarly reflects a concession required for immediate sale. . . . Our model predicts that higher-spread 3
Shannon Pratt, Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed. (New York: McGraw-Hill, 2008).
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Cost of Capital
assets yield higher expected returns, and that there is a clientele effect whereby investors with longer holding periods select assets with higher spreads . The resulting testable hypothesis is that asset returns are an increasing and concave function of the spread.4
Thus, the authors show that the more illiquid an asset (or asset class) is, the higher the required rate of return, although this rate of return increases at a decreasing rate (i.e., the relationship of return and illiquidity is not a linear one). Also, the authors do not focus on how the return on a specific asset class might change over varying holding periods. Rather, they observe that in pricing of assets (stocks in this case), there are groups of investors (‘‘clients’’) with varying degrees of risk tolerance and investment horizons. Assets with poor liquidity will be rejected by most investors, but there is a group of investors seeking such investments for the higher returns to be realized (the ‘‘clientele effect’’). It stands to reason that, if a specific asset has additional trading restrictions placed on it above its normal relative level of liquidity (or lack thereof), its rate of return will rise by some marginal function. That is, the ‘‘clients’’ willing to accept a 5-year period until an expected liquidity event may be unwilling to wait 10 years. To attract the 10-year client, the rate of return will have to be increased.5 The illiquidity of an investment in a PIC is not in its assets but in the timing of the economic return that will be realized by the investor (i.e., the timing of the liquidity event that will cause the assets of the PIC to be distributed to the investors). In this way, the value of an interest in a PIC is more like an option or a zero coupon bond. Perhaps the leading research related to this notion has been performed by Francis Longstaff, who looks at the opportunity cost, using options analysis, of being unable to trade an asset during a given period of illiquidity.6 These costs are significant. PICS ARE VERY LONG-TERM INVESTMENTS A fundamental assumption of NICE is that the length of the holding period in most PICs is uncertain and difficult to estimate. In those cases where the period until an expected liquidity event is known or reasonably predictable, the NICE method is not needed. Value can be calculated by a simple discounted cash flow analysis. In this writer’s experience in hundreds of PIC valuations, having a certain time until a liquidity event is the rare exception. Given the considerable variance in the definition of ‘‘long term’’ in the investment world, we are contemplating is a method of calculating the value of an investment in a potentially very long-term investment vehicle. Investment analysis for the very long term is somewhat more complicated than the normal investment analysis used for merely ‘‘long-term’’ investments. In the first place, what is meant by the concept of long term?
4
5
6
Yakov Amihud and Haim Mendelson, ‘‘Asset Pricing and the Bid-Ask Spread,’’ Journal of Financial Economics (1986): 223–250. Another view on this subject is that the market is dominated by institutional investors with a long-term objective who have a preference for equities with a long-term ‘‘duration.’’ These investors tend to avoid short-duration equities and, thus, require a premium to compensate for risks and transaction costs. Thus, unlike the upward-sloping debt yield curve, the equity yield curve is downward sloping. Interestingly, an implied duration of more than 20 years is too great for these investors. After this point, the equity yield curve begins rising again. The point for our discussion is that, as a passive and long-term investor in a PIC, you cannot be assured that the general partner will select an equity portfolio with long duration equities. See Patricia M. Dechow, Richard G. Sloan, and Mark T. Soliman, ‘‘Implied Equity Duration: A New Measure of Equity Security Risk,’’ Review of Accounting Studies (June 2004): 197–228. Francis A. Longstaff, ‘‘How Much Can Marketability Effect Security Values?’’ Journal of Finance (December 1995): 1767– 1774.
Relationship between Investment Period and Value
453
A debt with a maturity of greater than one year is considered long-term debt. Long-term capital gains, for tax purposes, are gains realized on the sale of investments held more than one year. Steven Sharp of the Federal Bureau of Statistics states: The long-term growth forecasts of equity analysts do not have well-defined horizons, an ambiguity of substantial import for many applications. . . . The estimated coefficients on consensus long-term growth forecasts suggest that the market applies these forecasts to an average horizon somewhere in the range of five to ten years .’’7
The NICE method, designed to value investments in PICs, assumes a very long-term, illiquid investment. PICs are established, among many other reasons, as a very long-term vehicle to provide for intergenerational capital appreciation. An investment horizon of less than 10 years would certainly not represent an ‘‘intergenerational’’ investment entity. The contractual term of the majority of LLPs we have seen is 50 years. While LLCs have, theoretically, an infinite life, we use 50 years herein as the practical maximum termination date of a PIC, unless we know otherwise. The very long-term nature of the PIC investment may be what would attract certain hypothetical buyers. There are few, if any, investment products available to those investors seeking excess returns via investing in illiquid, long-lived investment vehicles. While the universe of potential buyers would be small for an investment in a PIC, this type of investment could represent an attractive investment for an institutional investor with a (near) perpetual time horizon. Most likely, this buyer would be a foundation, endowment, or charity that allocates small portions of its portfolios for alternative investments. Yale University’s chief investment officer puts it this way: Active [investment] managers pursuing inefficiencies frequently gravitate toward relatively illiquid markets, since rewarding investments tend to reside in dark corners, not in the glare of the floodlights. . . . By avoiding the highly liquid securities favored by market players, serious active investors focus on much more interesting opportunities . In embracing less liquid assets, investors often identify opportunities to establish positions at meaningful discounts to fair value.8
To better describe the potential buyer universe, we must first recognize that an investment in a PIC would be considered an alternative investment, such as venture capital or hedge funds might be. Typically, alternative investments are no more than 10% of an investor’s portfolio. Because of the idiosyncratic risks found in investing an individual PIC, a prudent investor in this asset subclass would have to make many such investments in order to diversify away these risks. The typical private equity fund of funds invests in 20 funds with about 20 investments each, or 400 separate investments.9 Current research indicates that a diversified portfolio would be made up of over 100 investments.10 Furthermore, such an investor would not confine its alternative investments solely to PICs. The willing buyer of an investment in a PIC would certainly have a higher allocation in private equity and/or hedge funds. Thus, by this reasoning, it would appear that a prudent buyer of a $1 million investment in a PIC would likely have total assets of at least $3 billion.11 7
8
9
10 11
Steven A. Sharpe, ‘‘How Does the Market Interpret Analysts’ Long-term Growth Forecasts?’’ Federal Reserve Board, Finance and Economics Discussion Series Paper 2002-7 (September 2002). David F. Swensen, Pioneering Portfolio Management: An Unconventional Approach to Institutional Investment, (New York: The Free Press, 2000). Tom Weidig, Andreas Kemmerer, and Bjorn Born, ‘‘The Risk Profile of Private Equity Fund-of-Funds,’’ Working paper, March 2004. Meir Statman, ‘‘How Much Diversification Is Enough?’’ Working paper, October 2002. Assuming $1 million as one of 100 such investments comprising 3.33% of total alternative investments, or .0333% of total assets.
454
Cost of Capital
MEAN REVERSION The ability of any investment manager of a given asset to outperform the benchmark associated with that asset class (the manager’s ‘‘alpha’’) declines over time. Thus, the alpha is the highest it will ever be at the beginning of the PIC measurement periods of possible liquidity events (assumed herein to be the tenth year) and the lowest it will ever be at the last period of possible liquidity events. The acceptable rate of return for an investment in a small, closely held investment entity is actually a reasonable range within the bounds of the low-end and high-end return thresholds. The magnitude (width) of the range will decline each year due to a well-documented phenomenon known as mean reversion. The implication here is that, in order to attract the hypothetical buyer, the investment in the PIC must offer the prospect of above-average returns. In the early years of the investment, the amount by which these unrealized returns exceed the weighted benchmark returns for the underlying assets of the PIC may be significant. However, over time, this margin will shrink. At the last period of possible liquidity events for the PIC, the margin should be much smaller. The magnitude of the shrinkage in the margin will vary depending on the mix of assets held by the PIC and, therefore, the risk of the underlying investments of the PIC.12
CONTROL AND MARKETABILITY CONSIDERATIONS IN INVESTMENTS IN PICS The typical investment we are valuing using the NICE method is a noncontrolling, relatively illiquid interest in the PIC. LACK OF CONTROL A noncontrolling investor in a PIC has no control over entity management issues, such as market timing of purchases and sales of underlying assets, the hiring and firing of investment managers, investment strategy and timing, and amount of cash distributions. The noncontrolling investor also has very limited influence on governance issues, such as replacing the managing general partner, amending the partnership agreement, or the early liquidation of the PIC (prior to legal end of the entity). Academic studies indicate that corporate governance significantly affects financial policy and performance and, therefore, enters into pricing considerations.13 Because of lack of control and the unfamiliarity with the operating and entity management of the PIC, a willing buyer will require a rate of return greater than could be otherwise obtained in the observable marketplace for similar assets. Following are some well-researched topics describing the reasons for demanding incremental returns.
12
13
Asymmetrical information. This condition exists when one side of the market possesses information lacked by others in that market. Certainly an investor holding an assignee or nonmanaging interest in a PIC suffers from this disadvantage. Monitoring costs. If a minority owner wished to monitor (or second guess) the actions of the managing partner or member, this would have to be done at the minority owner’s own expense. K. Bhanot, ‘‘What Causes Mean Reversion in Corporate Bond Index Spreads? The Impact of Survival,’’ Journal of Banking and Finance (June 2005): 1385–1403. Yunguang Mike Yang, ‘‘Corporate Governance, Agency Conflicts, and Equity Returns along Business Cycles,’’ Working paper, October 20, 2005.
Control and Marketability Considerations in Investments in PICs
455
This assumes that the managing partner or member would even provide the limited partner with enough information to conduct the analysis. Depending on the LP or LLC agreement governing the PIC, the managing partner or member may not be required to provide such information; hence, the asymmetrical informational problem. By law, the limited partner or nonmanaging member may not act in the capacity of a managing partner or member.
Agency costs. Jensen defines an agency relationship as: a contract under which one or more persons (the principal(s)) engage another person (the agent) to perform some service on their behalf which involves delegating some decision making authority to the agent. If both parties to the relationship are utility maximizers, there is good reason to believe that the agent will not always act in the best interests of the principal. . . . Since the relationship between the stockholders and the managers of a corporation fits the definition of a pure agency relationship, it should come as no surprise to discover that the issues associated with the ‘‘separation of ownership and control’’ in the modern diffuse ownership corporation are intimately associated with the general problem of agency .14
Fama and Jensen have further identified the agency costs associated with a small, closely held entity wherein the decision makers are also the majority wealth owners of the entity.15 Yang16 and Gompers17 note the negative market pricing consequences of corporations with weak governance that does not allow stakeholders a voice in management. DETERMINING THE INCREMENT TO THE COST OF CAPITAL FOR LACK OF CONTROL An effective way to begin the process of estimating the incremental returns a hypothetical investor in the PIC would require for lack of control is to examine rates of return realized by top-ranked investment funds generally available in the marketplace. The better-performing funds (those whose returns exhibit the highest alphas) set a threshold rate of return for a minority investment in a closely held investment entity with a comparable portfolio. The reason this is a valid minimum return threshold is the knowledge that a willing seller would realize that the willing buyer will demand a return higher than that which is generally available in the marketplace. Of course, the willing seller is not interested in giving the willing buyer a bargain and thus needs some objective benchmark by which to gauge the enhanced return offered. One method of accomplishing this task is, where available, to compare the PIC returns by asset class held with returns from mutual fund returns investing in comparable assets. Such comparative returns are found in various sources but the most widely used source may be Morningstar, Inc. These statistics can be found by asset class over various time periods. The return information is provided by asset class (municipal bonds, government bonds, largecap equity, small-cap equity, etc.). The ‘‘Quick Rank’’ function on Morningstar’s Web site will provide its list of ‘‘Top Performers’’ in each category. The information is also presented over various time periods, with the longest comparison period being 10 years. We are interested in the 10-year data since that is our minimum assumed expected time until a liquidity event. 14
15
16 17
Michael C. Jensen and William H. Meckling, ‘‘Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure,’’ in Michael C. Jensen, A Theory of the Firm: Governance, Residual Claims and Organizational Forms (Cambridge, MA: Harvard University Press, 2000). Michael C. Jensen and Eugene F. Fama, ‘‘Separation of Ownership and Control,’’ in Michael C. Jensen, Foundations of Organizational Strategy (Cambridge, MA: Harvard University Press, 1998), and Journal of Law and Economics (June 1983): 301–350. Yang, ‘‘Corporate Governance.’’ Paul A. Gompers, Joy L. Ishii, and Andrew Metrick, ‘‘Corporate Governance and Equity Prices,’’ Quarterly Journal of Economics (February 2003): 107–155.
456
Cost of Capital
A suggested framing of the buyer-seller negotiation of the sales process vis-a`-vis the Morningstar data would be to set the low-end required rate of return at the spread between the average ROR of all funds in the Morningstar universe for that asset class (as reported, e.g., in the SBBI Yearbook) and the lower end of the ‘‘Top Performing’’ funds. Similarly, the high-end required rate of return for lack of control would be represented by the spread between the average of all funds versus the average of the ‘‘Top Performers.’’ Besides this suggested approach, many other constructs could effectively illustrate the ROR differential between the buyer and seller. It is up to the user to choose the method to convincingly delineate these parameters. LACK OF MARKETABILITY OR ILLIQUIDITY Longstaff presents examples in which a liquid asset can be worth up to 25% more than an illiquid asset even though both have identical cash flow dynamics. Quoting the study: A large percentage of the wealth of the typical household is held in the form of illiquid assets such as human capital, sole proprietorships, partnerships, and equity in other closely-held firms, deferred compensation, pension plans, tax-deferred retirement accounts, savings bonds, annuities, trusts, inheritances, and residential real estate. On the institutional side, an increasing amount of wealth is being allocated to illiquid asset classes such as private equity, emerging markets, venture capital, commercial real estate, and the rapidly-growing hedge fund sector. In each of these examples, an investor might have to wait months, years, or even decades before being able to unwind a position. 18
The terms liquid and illiquid can be misleading. In truth, liquidity is a continuum. The very most liquid securities are represented by U.S. government securities and the typically very least degree of liquidity (virtually none) are represented by an equity interest in a closely held entity such as a PIC. What some of the research we cite indicates clearly is that just because a security is publicly traded does not mean it is completely liquid. The degree to which a publicly traded security is illiquid will be reflected in its market price. When we estimate the illiquidity of the PIC interest, then, we are extrapolating what the additional illiquidity cost would be associated with a security if its liquidity went from its present state (as held outside the PIC) in the marketplace to a state of virtual illiquidity (the PIC equity interest is an indirect holding of the underlying securities held by the PIC). DETERMINING THE INCREMENT TO THE COST OF CAPITAL FOR LACK OF MARKETABILITY We have a few observations of this ‘‘virtually’’ illiquid state. One is a study we performed of implied rates of return in the equity private placements found in the various restricted stock studies.19 While the virtually illiquid state of the restricted stocks is relatively temporary compared to an investment in a PIC, the imputed rates of return are instructive. In that study, we estimate that the premium required due to illiquidity is in the range of 500 to 600 basis points compared to the expected returns on the freely tradable underlying stocks. At the opposite end of the risk spectrum a study of is the difference in returns between publicly and privately issued government bonds in Germany.20 Kempf and Uhrig-Homburg provide a study of 18
19
20
Francis A. Longstaff, ‘‘How Much Can Marketability Effect Security Values?’’ Journal of Finance (December 1995): 17671774. William H. Frazier, ‘‘Quantitative Analysis of the Fair Market Value of an Interest in a Family Limited Partnership,’’ Valuation Strategies (January/February 2005). In this chapter we are describing the applied mechanics we have developed to the basic premise expressed in the original article. A. Kempf and M. Uhrig-Homburg, ‘‘Liquidity and Its Impact on Bond Prices,’’ Schmalenbach Business Review (January 2000).
Control and Marketability Considerations in Investments in PICs
457
bonds issued by the German Government (BUND) and its state-operated funds (BAHN, POST). Generally speaking, the BUND are liquid and the BAHN and POST are illiquid. All of the bonds can be viewed as default-risk free. At 10 years, cost of illiquidity is about 100 basis points.21 This study corroborates the statement by Swenson that debt issued by U.S. agencies and backed by the full faith and credit of the U.S. government but which are less liquid than U.S. Treasury bonds often trade with a yield of 50 to 100 basis points to the far more liquid U.S. Treasury bonds.22 Another manner of approaching this subject is from the study of the effects of ‘‘liquidity shocks’’—situations where liquidity in a marketplace has quickly evaporated. One such study found that, subsequent to such shocks, illiquid portfolios have higher unconditional average returns than liquid portfolios. The return spread between the two extreme deciles is 0.48% per month. The study covered all New York Stock Exchange (NYSE) stocks between 1964 and 2004. On an annualized basis, the spread in illiquidity costs equates to an annualized return of 5.9%.23 This is comparable to the 500 to 600 basis points we estimated through a study of restricted stock transactions. Another observation is provided in a study by Simon Kwan, who supplies this information regarding the illiquidity premium associated with junk bonds in 1998, a time when the liquidity had virtually disappeared from this market. Between June 1998 and October 1998, the junk bond premium rose 334 basis points. The rise was not associated with an increase in expected default risk as no recession followed this period. The liquidity shock of this period is one of those rare glimpses the market provides into the cost of liquidity. This situation is about as close as is possible to simulating the pricing of a completely nonmarketable security, such as in interest in a closely held entity. This information was helpful in our modeling of the additional required return component appropriate a PIC holding junk bonds in the portfolio. 24 Exhibit 28.1 illustrates the increasing illiquidity cost (in DM) of risk-free bonds over time25.
Price Discount (DM)
1.2 1 0.8 0.6 0.4 0.2 0 1
Exhibit 28.1 21 22 23
24
25
2
3
4
5 6 Time to Maturity (years)
7
8
9
10
Risk-Free Bonds over Time
Ibid. Swensen, Pioneering Portfolio Management. Akiko Watanabe, and Masahiro Watanabe, ‘‘Time-Varying Liquidity Risk and the Cross Section of Stock Returns,’’ Eighth Annual Texas Finance Festival, January 9, 2007. S. H. Kwan, ‘‘Firm-Specific Information and the Correlation between Individual Stocks and Bonds,’’ Journal of Financial Economics 40 (1996): 63–80. Kempf and Uhrig-Homburg, ‘‘Liquidity and Its Impact on Bond Prices.’’
458
Cost of Capital
Exhibit 28.2 Estimated Incremental Illiquidity Premiums with Historical Returns and Standard Deviation by Asset Class Asset Class U.S. Government Bonds (10 Yr.) (a) Municipal Bonds (b) Corporate Bonds (c) Junk Bonds (c) U.S. Large-Cap (a) International Large-Cap North American Real Estate Equities (b) U.S. Small-Cap (a)
Historical Volatility
Low-End PIC Illiquidity Premium (bp)
5.1% 5.1% 8.7% 22.0% 20.3% 19.4% 20.4% 34.1%
50 75 100 300 200 225 275 500
High-End PIC Illiquidity Premium (bp) 100(e) 125 150 350 250 275 325 600(f)
Boldface-sourced results; italics: interpolated result; bp ¼ basis points Sources: (a) Stocks, Bonds, Bills and Inflation1 1997 Yearbook (Chicago: Ibbotson Associates, 1997), Copyright # 1997. Used with permission. qlobal.morningstar.com/SBBIYrBks. All rights reserved. (b) Commercial Real Estate 2006 (Chicago: Ibbotson Associates, 2006), Copyright # 2006. Used with permission. qlobal.morningstar.com/SBBIYrBks. All rights reserved. (c) Ian Cooper and Sergei Davydenko. ‘‘Using Yield Spreads to Estimate Expected Returns on Debt and Equity,’’ Working paper (February 2003). (d) Lehman Brothers Municipal Bond Index, 1995–2005. (e) Alexander Kempf and Marliese Uhrig-Homburg. ‘‘Liquidity and Its Impact on Bond Prices.’’ Schmalenbach Business Review (January 2000). (f) Frazier, William H. ‘‘Quantitative Analysis of the Fair Market Value of an Interest in a Family Limited Partnership.’’ Valuation Strategies (January/February 2005).
Another observation is provided in a study cited by Damodaran. That study estimates that private investors earn excess returns of 5% to 8% relative to the public equity market and this premium generates about 24% in risk-adjusted additional value to a private equity investor over 10 years. The securities are for the most part small-cap and micro-cap stocks.26 Exhibit 28.2 provides this author’s guide to the additional increments of return required for various asset classes held in many PICs. At this writing, we have direct sources of information for the data points related to risk-free government bonds, junk bonds, and small-cap common stocks. We have interpolated the estimated required return components for the other asset classes by comparing volatility and relative risk—the two key components to the cost of liquidity. In our calculation, we first determined the differences between the ‘‘known’’ components of the riskfree and small-cap asset classes and extrapolated the indicated required return based on the volatility of the asset class. However, based on our research, we know that risk is a major player in the cost of illiquidity. The price of an asset with less than optimal liquidity but with low risk will not be influenced by nearly the same degree as an asset with poor liquidity and significant default risk.27
26
27
Aswath Damodaran, ‘‘Marketability and Value: Measuring the Illiquidity Discount,’’ Working paper, July 30, 2005; In this paper professor Damodaran cites Alexander Ljungqvist and Matthew P. Richardson, ‘‘The Cash Flow, Return and Risk Characteristics of Private Equity,’’ New York University, Finance Working Paper No. 03-001, January 9, 2003. Maria Vassalou, Jing Chen, and Lihong Zhou, ‘‘The Relation between Liquidity Risk and Default Risk in Equity Returns,’’ EFA 2006 Zurich Meetings, July 16, 2006.
Example: Valuing LP Interests in MCCORD V. Commissioner Exhibit 28.3
459
Estate of McCord v. Commissioner, 120 T.C. Memo No. 13 (May 2003) Discount Percentages for All Categories Taxpayer
Overall Discount Minority Interest Discount Common Stocks Municipal Bonds Real Estate Partnerships Real Estate Oil & Gas Lack of Marketability Discount
IRS
Average
Tax Court
49%
16%
32.5%
32%
16% 11% 40% 40% 33.5%
6% 6% 9% 40% 33.5%
11% 8.5% 24.5% 40% 33.5%
10% 10% 23% 40% 33.5%
35%
7%
21%
20%
EXAMPLE: VALUING LP INTERESTS IN MCCORD V. COMMISSIONER The following example shows how to use the NICE methodology to value the LP interests that were at issue in McCord v. Commissioner.28 McCord Interests, Ltd., L.L.P. was formed on June 30, 1995. Our firm originally valued the partnership on January 12, 1996, when Mr. and Mrs. McCord each transferred by gift 41% limited partnership interests (subject interest).29 The transfer, including the valuation of the interests, was challenged by the Internal Revenue Service upon audit. What ensued was a protracted legal and valuation dispute too complicated and lengthy for our purposes here. We illustrate the NICE method by using the facts (somewhat simplified) of the McCord case. When we originally valued the interests in McCord, we used the traditional method of applying valuation discounts to the NAV for lack of control and lack of marketability. The IRS expert followed the same approach. His value was far lower than the fair market value we determined. The tax court, in its decision, exactly split the difference between the taxpayer and the IRS. This unsatisfying result was the genesis of the NICE method. Exhibit 28.3 presents the discounts applied to the NAVs. PARTNERSHIP ASSETS About 70% of the partnership’s assets were marketable securities. (See Exhibit 28.4.) The partnership’s securities portfolio was approximately 22% common equities and 48% municipal bonds. Both Exhibit 28.4
McCord Interests, Ltd., L.L.P., Net Asset Value
Assets Equities Municipal Bonds Real Estate Partnerships Total Net Assets
$ $3,640,00 8,040,000 5,190,000 $16,870,000
% of Total 21.6% 47.7% 30.8% (a)
(a) The actual McCord NAV was $17,653,760. For simplification purposes, we have omitted assets from two additional asset classes. The partnership also held $581,553 in directly owned undeveloped real estate and $215,098 in oil and gas working and partnership interests. Because of the small size of the omitted assets, one may still reasonably compare the NICE model valuation of McCord with the original work. 28 29
Estate of McCord v. Commissioner, 120 T.C. Memo No. 13 (May 2003). What we actually valued was an ‘‘assignee’’ interest. However, that distinction is an unnecessary complication here.
460 Exhibit 28.5
Cost of Capital McCord Interests, Ltd. L.L.P. Common Stock Portfolio
Stock PHILIP MORRIS UNION PACIFIC COCA-COLA MERCK & COMPANY AMERICAN GENERAL CORPORATION MOTOROLA GENERAL ELECTRIC TYCO INTERNATIONAL ROYAL DUTCH PETROLEUM ANADARKO PETROLEUM CORP.
Shares Held
1/11 Price
6,200 88.880 6,000 67.750 4,900 73.630 5,700 61.500 6,400 34.250 4,000 50.130 2,400 70.500 4,200 33.250 1,000 137.630 2,000 51.500 Top 10 stocks (by % held) Total Portfolio
Market Value
% Portfolio
Cumulative % Portfolio
551,056.00 406,500.00 360,787.00 350,550.00 219,200.00 200,520.00 169,200.00 139,650.00 137,630.00 103,000.00 2,638,093.00 $ 3,641,955.83
15.13% 11.16% 9.91% 9.63% 6.02% 5.51% 4.65% 3.83% 3.78% 2.83%
15.13% 26.29% 36.20% 45.82% 51.84% 57.35% 61.99% 65.83% 69.61% 72.44%
portfolios were managed by either a local bank or stockbroker. Approximately 30% of the partnership’s assets were investments in four operating real estate partnerships also owned and controlled by the family. The partnership’s $8 million municipal bond portfolio consisted of primarily AAA-rated (or insured) hospital, school, and general obligation bonds of Louisiana cities and parishes. It had a weighted average maturity of about 11 years. Most of the bonds were taxable. As of the valuation date, the partnership had a net asset value of $16,870,000. The partnership’s primary holdings included municipal bonds totaling $8,040,220 and interests in real estate partnerships totaling $5,194,933. The $3 million common stock portfolio was predominantly large cap but was not adequately diversified. (See Exhibit 28.5.) Ten stocks made up 72% of the portfolio’s value. Over 50% was in just five stocks. Over the prior three years (1991 to 1995), the portfolio had earned a compound return of about 24%. This compares very favorably with total return of Large Company Stocks (15.3%) reported in the SBBI Yearbook. However, the benchmark is a diversified portfolio and the partnership’s portfolio was not. Just three of the 39 companies held in the portfolio accounted for 45% of its gains. Recent research documents that undiversified portfolios require higher returns and that, to be adequately diversified, a stock portfolio may need as many as 130 stocks.30 The partnership held about $5.2 million worth of partnership interests in a family-owned real estate operating partnership. Each of these operating partnerships owned a medium-size office building in Houston, Texas. Each of these operating partnerships owed significant debt secured by their respective office buildings. While the operating partnerships were profitable and had a positive cash flow, the properties were in a generally weak market and struggled with occupancy rates. Given the debt that had to be serviced and the need for maintenance reserves, there were no foreseeable prospects for distributions. The interest held by the partnership in each of the operating partnerships was approximately 40%. When originally valued for purposes of calculating the McCord Partners NAV, these operating partnership interests were valued at their undiscounted pro rata NAV because the controlling general partners of McCord were also the controlling general partners of these operating partnerships. 30
Statman, ‘‘How Much Diversification Is Enough?’’ Gerald T. Garvey, ‘‘What Is an Acceptable Rate of Return for an Undiversified Investor?’’ Working paper, September 2001.
Example: Valuing LP Interests in MCCORD V. Commissioner
461
APPLYING THE INCOME APPROACH The economic return in the case of the subject interest was expected to be realized only when the partnership liquidated. No interim distributions, other than to provide distributions to the partners to pay tax obligations passed through to the partners, were expected prior to liquidation. The primary purpose of the partnership was capital appreciation. As we will show, the fair market value of the subject interest in the partnership must reflect a price wherein the expected future return at any given point during the expected term of the partnership is reasonable. That is, a return inherent in the fair market value is neither too high (from the willing seller’s standpoint), nor too low (from the willing buyer’s standpoint). The important difference between this analysis and a simple internal rate of return analysis is that there is no way to know with certainty the timing of a liquidity event with respect to the subject interest. Therefore, our analysis encompasses the range of potential periods until a liquidity event. The reasonable range of the possible liquidity events for the partnership, as of the valuation date, would be from the minimum assumed period of 10 years and a maximum of the specified termination date of the partnership, 2041, or 45 years from the valuation date.31 Thus, the model will calculate 105 separate internal rate of returns: 35 each for the partnership, the hypothetical buyer, and the hypothetical seller. PARTNERSHIP PORTFOLIO RETURNS The weighted average expected return of any portfolio of securities may be calculated by determining (i) the various asset classes or categories comprising the portfolio (also referred to as asset allocation); (ii) the expected holding period or investment horizon of the portfolio (duration); and (iii) the appropriate benchmark returns for the various asset classes corresponding to the expected holding period. Given the state of the stock and bond markets in 1996, we were not assuming any difference between the 10-year expected outlook and long-term historical averages. In hindsight, we are, of course, aware that the equity markets took off like a rocket between 1996 and 1999. But they fell just as fast. The 10-year average return on the Dow Jones Industrial Average between 1995 and 2005 was just 7.7%. Real estate equity returns in 1996 were not as well researched as other markets. However, our research shows that the outlook for the next five years was for returns in the 12% to 15% range.32 Furthermore, the National Association for Real Estate Investment Trusts reports returns for real estate equity at 13.1% for the period 1979 to 1998. INCREMENTAL RATE OF RETURN FOR LACK OF CONTROL Morningstar provides mutual fund return data on all three of the McCord asset classes. Ordinarily, to measure the minimum incremental rate of return for lack of control offered by the seller, we suggest taking the difference between the average mutual fund and the low end (e.g., 25th percentile) of the top performer’s list. For purposes of our illustration here, we did not have access to such data from Morningstar for 1996. Accordingly, for the low-end increment we use one standard deviation above the mean; for the high-end increment, two standard deviations above the mean (see Exhibit 28.6). The adjustments made for lack of control are derived from the range of returns exhibited by the marketplace for that particular asset class. While the incremental return we are suggesting increases 31
32
Of course, it is possible that the partnership might liquidate at any time, but the expectation that the partnership might liquidate in any time period other than the very long term is highly unlikely and therefore disregarded. Todi Gutner, ‘‘Who’s Afraid of Real Estate?’’ Business Week, December 30, 1996.
462 Exhibit 28.6
Cost of Capital Indicated Incremental Required Returns for Lack of Control
Asset Class Large-cap Muni Bonds Real Estate Equity
Historical Total Returns
Standard Deviation
Low-end Incremental ROR (bp)*
High-end Incremental ROR (bp)
11.0% 7.6% 13.1%
20.2% 5.2% 14.4%
222 40 189
444 79 377
*(bp) = basis points ROR = rate of return
the expected return from that particular asset class of the PIC, the adjusted return may not exceed maximum returns experienced in the marketplace for that asset class. However, this process assumes the asset held by the PIC has a risk profile reasonably comparable to the assets comprising the database of market returns. In some cases, this may not be true, and in such instances, a specific risk increment may be necessary. The McCord common stock and municipal bond portfolio, while small, was comprised of publicly traded securities. Therefore, no further risk adjustments were necessary beyond the process we have already described. Such was not the case with the real estate portfolio held by the McCord partnership, however. The benchmark returns for this asset class comes from real estate investment trusts (REITs), since this is the most readily available source of market return information for the U.S. publicly traded real estate securities market. However, the partnership’s real estate partnership investments were so much riskier than the REIT universe that an additional risk increment must be included. To simplify matters, the McCord real estate investment was tiny, nondiversified, leveraged, and could not pay distributions to partners due to loan covenants and cash flow needs. In addition to the financial characteristics, from the perspective of a hypothetical investor in the partnership, this asset class suffers from asymmetrical information, the need for monitoring costs, and the possibility of agency problems.33 We are adding 200 basis points to the required return for these risk factors. Our source for this measure of incremental return is research done on estimating equity risk premiums from bond ratings. When a bond’s rating changes from investment grade to junk, 400 basis points is the approximate additional equity risk premium indicated. We think this is an appropriate comparison here.34 However, we are not using the full measure of this adjustment since we have already increased the rate of return over the benchmark before adding this adjustment factor. INCREMENTAL RATE OF RETURN FOR LACK OF MARKETABILITY Earlier we developed a general framework for lack of marketability associated with several asset classes commonly found in a PIC. (See Exhibit 28.7.) Generally speaking, the magnitude of the 33
34
In an interview, Joseph Pagliari Jr., a noted author and professor in real estate investments, cites the idiosyncratic risks of private real estate investing and describes such investments as ‘‘imprudent’’ for most investors. Portfolio: What advice would you give to an individual investor weighing the option of investing in private vs. public real estate? Pagliari: For the lion’s share of individual investors, public real estate is certainly the preferable investment vehicle. For most of us, the exposure to the idiosyncratic risks (i.e., non-market risks which otherwise can be diversified away) of holding a concentrated real estate portfolio (because we simply lack enough wealth to be able to create a well-diversified private real estate portfolio) is imprudent. See M. Bechard, ‘‘Weighing Public and Private Real Estate,’’ Real Estate Portfolio, National Real Estate Investment Trusts (November/December 2003). Ian Cooper and Sergei Davydenko, ‘‘Using Yield Spreads to Estimate Expected Returns on Debt and Equity,’’ London Business School IFA Working Paper, EFA 2003 Annual Conference Paper No. 901 (December 2003).
Example: Valuing LP Interests in MCCORD V. Commissioner
463
Exhibit 28.7 General Framework for Lack of Marketability Associated with Several Asset Classes: Incremental Rates of Return Asset Class Large cap Equity Municipal Bonds Real Equity Partnership
Low-End
High-End
Base Year
200 bp 75 bp 275 bp
250 bp 125 bp 325 bp
6 10 6
bp = basis points
discount here is associated with risk and volatility (standard deviation of returns), with risk being the most important factor. Based on the partnership’s three asset classes, we have set the incremental rates of return for the low-end and high-end cases as shown in Exhibit 28.7. The ‘‘Base Year’’ is the year applicable to the illiquidity analysis for the particular asset class. For stocks, using the restricted stock studies, we have estimated that an estimated restricted holding period of 6 years for small-cap common stocks results in a return premium of 500 to 600 basis points. For municipal bonds, the Federal Reserve Board study denotes a 51 basis point premium for liquidity on a 10-year AAA bond relative to a 1-year bond. What would the additional premium be if that bond could not be sold at all between year 1 and 10? We are estimating a premium of 75 to 125 basis points. We know that the direct (not extrapolated) illiquidity cost for a 10-year risk-free bond is 50 to 100 basis points. The illiquidity cost for a municipal bond must be greater than this since the Federal Reserve Board study reported that municipal bonds were nowhere nearly as liquid as U.S. government securities. We have extrapolated the real estate illiquidity cost. It has a greater historical return than largecap equity, although over a much shorter period. Its volatility is lower than large-cap equity. However, the market capitalization of the average REIT is far lower than large-cap equity. Balancing the lower volatility with the smaller size, we conclude that the real estate equity illiquidity cost should, at least, equal that of large-cap equity. CALCULATING THE LOW-END AND HIGH-END COST OF CAPITAL When we add the incremental rates of return for lack of control and illiquidity for the low-end and high-end cases, we now have all of the data points required to complete our analysis. Exhibit 28.8 summarizes the partnership’s expected returns by asset class and for the partnership as a whole. Exhibit 28.9 shows the individual asset class incremental returns for lack of control and illiquidity for both the low-end and high-end cases. The underlying assets of the partnership are expected to earn between 10.0% to 9.7%. The willing seller is asking the willing buyer to accept a scenario (low-end cost of capital) that begins with a rate of 13.4% in year 10 and declines to 12.2% in year 45. The willing buyer is bidding a price that results in a rate of return (high-end cost of capital) that begins with 14.8% in year 10 and declines to 13.2% in year 45. Exhibit 28.8
McCord Partners Expected Returns
Rate of Return of Internal Interest Partnership Expected Return High-end Expected Return (buyer view) Low-end Expected Return (seller view)
10
20
30
40
45
17.56% 10.04% 14.79% 13.38%
13.64% 9.70% 14.07% 12.81%
12.31% 9.70% 13.69% 12.58%
11.60% 9.70% 13.30% 12.34%
11.44% 9.70% 13.11% 12.23%
Exhibit 28.9
Summary of Inputs to Exhibit 28.8 Summary of Low-end Return Differential [Cost of Capital of Seller]
I. Average Expected Returns by Asset Class long-term Avg.
10 yr
20 yr
30 yr
40 yr
45 yr
11.0% 12.0% 7.6%
11.0% 13.1% 7.6% 10.0%
11.0% 12.0% 7.6% 9.7%
11.0% 12.0% 7.6% 9.7%
11.0% 12.0% 7.6% 9.7%
11.0% 12.0% 7.6% 9.7%
II. Low-end Marginal Required Return Component for Lack of Control 10 yr
20 yr
30 yr
40 yr
45 yr
Large company stocks Real estate Municipal bonds Weighted Average Lack of Control Component
2.2% 2.9% 0.4% 1.6%
1.8% 2.4% 0.4% 1.3%
1.4% 1.8% 0.3% 1.0%
1.0% 1.3% 0.3% 0.7%
0.8% 1.0% 0.3% 0.6%
10 yr
20 yr
30 yr
40 yr
45 yr
2.3% 2.8% 0.9% 1.8%
2.4% 2.8% 0.9% 1. 8%
2.4% 2.9% 1.0% 1.9%
2.5% 3.0% 1.0% 1.9%
2.5% 3.0% 1.0% 1.9%
10 yr
20 yr
30 yr
40 yr
45 yr
15.5% 18.8% 8.9% 13.4%
15.2% 17.2% 8.9% 12.8%
14.8% 16.7% 8.9% 12.6%
14.5% 16.3% 8.9% 12.4%
14.3% 16.0% 8.9% 12.2%
long-term Avg.
10 yr
20 yr
30 yr
40 yr
45 yr
11.0% 12.0% 7.6%
11.0% 13.1% 7.6% 10.0%
11.0% 12.0% 7.6% 9.7%
11.0% 12.0% 7.6% 9.7%
11.0% 12.0% 7.6% 9.7%
11.0% 12.0% 7.6% 9.7%
II. High-end Marginal Required Return Component for Lack of Control 10 yr
20 yr
30 yr
40 yr
45 yr
Large company stocks Real estate Municipal bonds Weighted Average Lack of Control Component
4.4% 3.8% 0.8% 2.5%
3.8% 3.2% 0.7% 2.1%
3.1% 2.6% 0.6% 1.8%
2.4% 2.0% 0.5% 1.4%
1.5% 1.3% 0.5% 1.0%
10 yr
20 yr
30 yr
40 yr
45 yr
2.8% 3.2% 1.4% 2.3%
2.8% 3.3% 1.4% 2.3%
2.9% 3.3% 1.5% 2.4%
2.9% 3.4% 1.5% 2.4%
3.0% 3.5% 1.6% 2.5%
10 yr
20 yr
30 yr
40 yr
45 yr
18.2% 20.1% 9.8% 14.8%
17.6% 18.5% 9.7% 14.1%
17.0% 17.9% 9.8% 13.8%
16.3% 17.4% 9.7% 13.5%
15.5% 16.8% 9.7% 13.2%
Large company stocks Real estate Municipal bonds Weighted Average ROR of Partnership
III. Low-end Marginal Required Return Component for Illiquidity
Large company stocks Real estate Municipal bonds Weighted Average Lack of Illiquidity Component IV. Low-end Required Return (I+II+III) Large company stocks Real estate Municipal bonds Weighted Average Cost of Capital of Seller Summary of High-end Return (Cost of Capital of Buyer) I. Average Expected Returns by Asset Class
Large company stocks Real estate Municipal bonds Weighted Average ROR of Partnership
III. High-end Marginal Required Return Component for Illiquidity
Large company stocks Real estate Municipal bonds Weighted Average Illiquidity Component IV. High-end Required Return (I+II+III) Large company stocks Real estate Municipal bonds Weighted Average Cost of Capital of Buyer
464
Example: Valuing LP Interests in MCCORD V. Commissioner
465
DETERMINATION OF CURVE OF BEST FIT In order to determine the fair market value of the subject interest using the income approach, we have analyzed the implied rates of return to a hypothetical willing buyer of the subject interest over a range of possible periods until a liquidity event occurs from 10 to 45 years. We assume an equal probability of liquidation in any one year. The indicated price (fair market value) is where the buyer expects never to receive a return that is too low in view of the risks and the seller can expect the buyer will not be receiving a return that is too high (at the seller’s expense). The model solves for the one price that best satisfies this condition. That price was $3,569,749 for the 41% subject interest. Graphically this is illustrated in Exhibit 28.10, where the dashed line (internal rate of return of interest) appears between the low-end rate of return (lower dotted line) and the top-end rate of return (upper dotted line) lines as equally as is possible. The indicated price (fair market value) is where the buyer expects never to receive a return that is too low in view of the risks and the seller can expect the buyer will not be receiving a return that is too high (at the seller’s expense). RECONCILIATION OF MCCORD ADJUSTED NET ASSET METHOD VALUATION WITH THE NICE METHOD The price and, therefore, the fair market value that best satisfies the constraints just described for the subject interest is $3,569,749. This is an implied 48.4% discount from NAV. Our original valuation in the McCord case resulted in a discount from NAV of 46.7%. If we adjust our original valuation for the simplifications involved in our illustration here, the total discount from NAV under the conventional approach would have been 44.2%.35 We believe we have provided ample evidence and sources NICE Method McCord Partners, Ltd. 18.00% 16.00%
Return
14.00% 12.00% 10.00% 8.00% 6.00% 10
13
16
19
22
25
28 31 Years
Rate of Return (ROR) - Interest High-end expected return
Exhibit 28.2 35
34
37
40
43
45
Partnership expected return Low-end expected return
Curve of Best Fit
Our original valuation in the McCord case resulted in a discount from NAV of 48.7%. However, this was for an ‘‘assignee’’ interest. Our value for the McCord partnership interest as a limited partnership interest was 5% higher, representing a total discount from NAVof 46.7%. With the simplifications of the McCord facts for this illustration, the adjusted discount from NAV would be about 44%.
466
Cost of Capital
for every step taken in our analysis. While another appraiser may have chosen different inputs, we believe, because the sources for all of the data are objective and well defined (though subject to interpretation and judgment), the deviation between two separate appraisals due to purely subjective judgments should be less than under other approaches. It may not always be the case that the adjusted net asset method and the NICE method result in estimated values quite so close because the studies used to estimate percentage discounts may not be very comparable to the underlying illiquidity of an interest in a PIC. Fair market value then needs to be determined by a synthesis of the two results. Such a synthesis does not imply taking an average. Rather, it means examining the comparability of the underlying studies used to estimate RROR and discounts to the subject PIC and evaluating the ‘‘strengths’’ and ‘‘weaknesses’’ inherent in the alternative approaches. However, this is no different from valuing an operating company by the income approach and the market approach and determining a final value based on a synthesis of these two results.
SUMMARY The NICE method is not a replacement for the more traditional PIC valuation methodology. However, neither is it merely a corroboration or sanity check. It is a complementary methodology. Whereas the traditional method uses investment analysis in a general and indirect manner, in NICE, investment returns serve as the engine for calculating results. Exhibit 28.11 summarizes the steps involved in the NICE method. Exhibit 28.11
Nice Method to Appraise an Equity Interest in a PIC
1. Determine the long-term expected return of the PIC a. Projection of liquidity events over typically 40–50 year period b. Requires detailed look at asset classes held 1. How has the PIC performed historically relative to benchmark for the asset class? 2. What is the benchmark for each class? a. Historical returns b. Current market expectations c. Mean reversion 3. Will the asset mix of the PIC stay constant or change? 2. Distribution policy of the PIC a. Affects reinvestment rate (‘‘leakage’’) b. Include ‘‘tax-only’’ distributions in your calculations but adjust benchmark accordingly. 3. Incremental required rate of return a. Lack of control. 1. Minimum or low-end increment a. The Seller’s ‘‘ask’’ price b. Asking price must result in a return higher than PICs for this asset class 2. Minimum or high-end increment a. The Buyer’s ‘‘bid’’ price b. Price is lower than seller’s asking price c. Results in rate of return higher than that resulting from Minimum Increment d. High-end cost of capital must not be outside of the normal bounds for the asset class
Summary
467
3. Specific risk a. Can be present when PIC asset is uniquely risky b. Do not double-count risks 4. Mean reversion a. Low-end and high-end incremental ‘‘spread’’ over the PIC return will decline overtime (mean reversion) b. At end of projection period low-end and high-end spread should typically be small c. Risk of change in investment policy b. Illiquidity 1. Based on research of premia for illiquidity by asset class
a. Research indicates a range (high-low) b. Low side of range serves as incremental rate of return for low-end case c. High side of range for high-end case 2. Two-step function (Amihud and Mendelson)
a. Annual cost of illiquidity rises sharply to ‘‘inflection point’’ 1. Inflection point represents the clientele effect a. Six years for equity
b. Ten years for bonds b. After inflection point, cost of illiquidity rises slowly and at a decreasing rate of increase 4. The Price is fair market value a. The IRR is calculated for each year of the expected holding period for both the low-end case and the high-end case
b. Price, determined through an iterative process, describes the balance point between the low-end rate of return and high-end rate of return
c. The Price results in the ‘‘curve of best fit’’ d. The foregoing process replicates the negotiated price between a willing seller and a willing buyer.
Chapter 29
Relationship between Risk and Returns in Venture Capital Investments
Introduction Benchmark Data on Venture Fund Investments Benchmark Returns on Venture Project Investments Realized Returns on Venture Project Investments Cochrane Study Das, Jagannathan, and Sarin Study Realized Returns on Buyout Investments Summary
INTRODUCTION We are often confronted with the issue of choosing appropriate rates of return with which to discount cash flows estimated for venture capital investments. This issue can arise when valuing in-process research and development (IPR&D) in the context of a SFAS No. 141, on business combinations, engagement, or equity investments.1 Aggregate returns on venture capital funds (portfolios) have been reported by Cambridge Associates and Venture Economics, for example. These are useful for general benchmarking of fund results. But most often we are interested in expected rates of return on individual venture capital investments. Little is available to guide the analyst in selecting the appropriate cost of capital to use in discounting expected cash flows from venture capital investments. In this chapter we report on research into the rates of returns and risks of venture capital investments. The research has focused on expected returns (and volatility) from individual investments in venture projects based on actual success and failures observed in such investments by venture investors.
BENCHMARK DATA ON VENTURE FUND INVESTMENTS Cambridge Associates (www.cambridgeassociates.com) reports on the aggregate returns reported by venture capital funds each quarter. Typically, venture capital funds report changes to their portfolio investments for liquidity events only during the first three quarters and revalue all investments once per year. 1
See, e.g., U.S. Private Equity Valuation Guidelines, Private Equity Industry Guideline Group, December 1, 2003.
469
470
Cost of Capital
Venture Economics (www.thomson.com) also reports on returns reported by funds. Moskowitz and Vissing-Jorgensen summarize the data for buyout and mezzanine funds and venture capital funds.2 Chen, Bariel, and Kaplan analyzed 148 venture funds that liquidated through June 30, 1999.3 They summarize their returns from 1960 through 1999 in this way: Arithmetic average annual return ¼ 45% for fund Standard deviation ¼ 115.6% Correlation between venture capital fund Investment and public stocks ¼ .04% The authors note that the returns may suffer from survivor bias (i.e., only successful funds last throughout the period and report their results, making the measured returns possibly overstated). And they do not have access to data on market values of venture capital projects between the time of investment and exit. The typical returns to initial public offerings (IPOs) or acquisitions are meaningful returns, since venture capital investors must hold investments all the way to IPO, acquisition, or failure. Firms go public when they have experienced a good return. But many firms remain private. Start-up firms are fraught with failure. For example, 66% of private firms fail in their first 10 years. Return to IPO measures only the winners. As a result, it is an upward-bias measure of ex ante returns to potential venture capital investors.4
BENCHMARK RETURNS ON VENTURE PROJECT INVESTMENTS Typically, analysts rely on surveys of required returns (e.g., IPR&D AICPA Practices Aid).5 That document describes sources of venture capital rates of return and provides guidance on estimating the cost of capital for venture investments. It identified two publications that provide guidance about rates of return commanded by venture capital investors at various stages of an entity’s development.6 Exhibit 29.1 displays the results of surveys of ‘‘hurdle rates’’ used by venture capital investors.
Exhibit 29.1
Sample Rates of Return Cited in IPR&D Practices Aid
Stage of Development
Plummer
Scherlis and Sahlman
Start-up First stage or ‘‘early development’’ Second stage or ‘‘expansion’’ Bridge/IPO
50%–70% 40%–60% 35%–50% 25%–35%
50%–70% 40%–60% 30%–50% 20%–35%
Source: IPR&D AICPA Practices Aid (#2001 AICPA). Used with permission. All rights reserved. 2
3
4
5 6
Tobias J. Moskowitz and Annette Vissing-Jorgensen, ‘‘The Private Equity Premium Puzzle,’’ Center for Research in Security Prices working paper no. 524 (November 2000). P. Chen, G. Bariel, and P. Kaplan, ‘‘Venture Capital and Its Role in Strategic Asset Allocation,’’ Journal of Portfolio Management (Winter 2002): 83–89. Robert M. Conroy, and Robert S. Harris, ‘‘How Good Are Private Equity Returns?’’ Journal of Applied Corporate Finance (Summer 2007): 96–108. American Institute of Certified Public Accountants. IPR&D Practice Aid. Jersey City, NJ: AICPA, 2001. James L. Plummer, ‘‘QED Report on Venture Capital Financial Analysis,’’ Palo Alto: QED Research, Inc. (1987); Daniel R. Scherlis and William A. Sahlman, A Method for Valuing High-Risk, Long-term, Investments: The Venture Capital Method (Boston: Harvard Business School Publishing, 1987).
Benchmark Returns on Venture Project Investments
471
These rates of return represent a method for venture capitalists to screen potential investments. The presentations from entrepreneurs typically do not represent expected cash flows; rather they typically represent ‘‘success case’’ cash flows; the hurdle rates help venture capitalists initially screen potential investments for more analysis. These high rates of return reflect forecast overoptimism. The lower rates of return for later-stage investments reflect the greater likelihood of achieving the forecasts. Exhibit 29.2 displays the calculation of the weighted average cost of capital of a sampling of young public companies as it appears in the Practices Aid. Finally, the Practices Aid provides guidance on the expected behavior of the cost of capital over the life of a venture research project. The task force’s conclusions about the expected behavior of discount rates over the life of an IPR&D project and presumed lower boundary from which discount rates may be selected for young, single-product companies is shown in Exhibit 29.3.
Exhibit 29.2
Weighted Average Cost of Capital for Young Public Companies Expected Returns
Networking and Communication Devices Biotechnology Internet Software and Services
Number of Companies
Mean
Trimmed Meany
Median
25 62 20
19.90% 19.30% 29.30%
19.50% 19.30% 28.10%
19.60% 19.20% 25.60%
The returns computations use a size-adjusted capital asset pricing model, assuming a risk-free rate of 6% (see note), an equity or market premium of 7.8%, and size adjustment of 3.3%. Betas were retrieved from Hoover’s Online by selecting all companies in the indicated subindustry with a market capitalization less than or equal to $250 million. The Capital Asset Pricing Model and basic input date (long-term Treasury rate, equity risk premium, size adjustment) were taken from Ibbotson Associates: Stocks, Bonds, Bills and Inflation 1998 Yearbook: Market Results for 1926–1997, 162–65. y Excludes the smallest and largest 5% of observed returns from the computation. Note: In developing the statistics in this table, the task force made use of the size-adjusted Capital Asset Pricing Model (CAPM). The use of the CAPM in the task force’s report is not intended to proscribe the use of other widely accepted approaches to estimating an entity’s cost of equity capital. Rather, the task force chose to use a version of the CAPM to illustrate the goals of arriving at an estimated weighted average cost of capital (WACC) when valuing in-process research and development because of its broad acceptance in the finance community. The task force notes that debt financing is not commonly used to finance the entities that the task force believes are appropriate proxies. This simplifies the WACC estimation to estimating the required return on equity of proxy entities. The formula used, together with an explanation of the variables used, is: ke ¼ R f þ B ðRm R f Þ þ P Each of these inputs is discussed in further detail. Risk-free Rate (Rf): The risk-free rate is the return on government securities with a term similar to that of the investment being valued. Equity or Market Risk Premium (ERP ¼ Rm Rf): The equity or market risk premium (ERP), also known as the equity premium, is defined as the additional rate of return over the risk-free rate that is expected by investors from investments with systematic risk equal to the ‘‘market portfolio’’. The market portfolio can be thought of as a broadly diversified investment portfolio, often thought of as the return on an index such as the S&P 500. Beta (b): The theory and application of beta as a modifier of the ERP are well documented and widely accepted. Beta is a measure of the risk of an entity’s stock relative to the risk of a diversified portfolio (the ERP). Rather than explain the nature of how to estimate beta, the task force notes that there are many available sources of betas. Because the estimation procedure is not controversial, those sources may normally be relied on. Size premium (P): Research has shown that small companies have larger betas than large companies. The adjustment is necessary because small stocks outperform large stocks, even after adjusting for the systematic risk (beta) of small stocks. This phenomenon is widely known as the size effect. Source: IPR&D AICPA Practices Aid (# 2001 AICPA). Used with permission. All rights reserved.
472
Cost of Capital
Discount Rates Used to Value IPR&D
Start-up (50%–70%)
Discount Rate
Young Company Startup (20%–30%)
0
Stage Complete
100
Substance Demonstrated
Exhibit 29.3 Expected Behavior of Discount Rates over Life of IPR&D Project Source: IPR&D AICPA Practices Aid (#2001 AICPA). Used with permission. All rights reserved.
REALIZED RETURNS ON VENTURE PROJECT INVESTMENTS COCHRANE STUDY One of the most comprehensive studies of realized returns from venture capital investments at the individual investment level was conducted by John Cochrane.7 The objectives of his work are to measure the historic returns for individual venture capital projects:
Estimate mean, standard deviation, and other characteristics of venture capital investments and compare to publicly traded securities. Correct for selection bias because we do not see returns for projects that remain private.
Cochrane models how the returns we observe are generated from the underlying value process and the decision to go public or out of business. He addresses selection bias. (We observe valuation only when the firm goes public, receives new financing, or is acquired.) He addresses the problem through maximum likelihood simulation. Let us explore the selection bias issue a bit further. Assume investment in a venture capital project is successful and increases in value at 10% per year with constant standard deviation of 50% per year. If the probability of going public is independent of the project value, simple analyses would measure underlying return characteristics in this way: For projects that take 2 years to go public: Average return ¼ 2 10% ¼ 20% and Variance ¼ 2 .502 7
John Cochrane, ‘‘The Risk and Return of Venture Capital,’’ Journal of Financial Economics (January 2005): 3–52, revision of National Bureau of Economic Research working paper, March 19, 2004.
Realized Returns on Venture Project Investments
473
For projects that take 3 years to go public: Average return ¼ 3 10% ¼ 30% and Variance ¼ 3 .502 Average of (return/time to IPO) would provide an unbiased estimate of expected annual return. Average of (return2/time to IPO) would provide an unbiased estimate of variance of annual returns. Derivation of these statistics (assuming probability of going public is independent of project value, where each venture capital investment is treated as a separate ‘‘project’’) is: Rt ¼ log returns at time t 2 period return ¼ Rt þ Rtþ1 Mean ¼ EðRt þ Rtþ1 Þ ¼ 2EðRt Þ Variance ¼ s 2 ðRt þ Rtþ1 Þ ¼ 2s 2 which implies that there is no covariance term. But the problem is that the decision to go public is not absolute; rather, the probability of going public is an increasing function of the project’s value. That is, as the project is more successful over time and its value increases, the probability of going public increases. Measuring only successes results in an observed mean return greater than true mean return and observed volatility less than true volatility of investments in projects. For example, assume that a venture capital investor makes 100 investments (and over time such an investor may invest multiple times in the same company as the company raises new capital in later rounds of financing). Assume that 40% of the investments result in success; that is, the companies in which the investments are made either go public or are acquired. Assume that 60% of the investments are unsuccessful; that is, the companies in which the investments are made either remain private and do not increase in value sufficiently to go public, or get acquired or go out of business. Assume that the rate of return from the successful investments is 50% per annum and from the unsuccessful investments is zero. We observe payoffs only for the successful investments. It appears the rate of return is 50%. But 60% of the investments resulted in a rate of return of zero. The true rate of return for the 100 investments is: 40% 50% þ 60% 0 ¼ 20% This illustrates the bias in calculated returns created by using only successes in the calculation. This bias analysis of counting only returns on successful IPOs points to why some say that the rates of return imputed from pre-IPO discount studies are biased high. Cochrane uses the Venture One database for investment information for the period 1987 through June 2000. Each round of financing is considered a single investment; if the investor makes multiple investments in different rounds in the same company, each is considered a separate investment. The data include:
Financing round (sample includes 16,613 financing rounds in 7,765 companies). Amount raised in each round (aggregate total of the sample investments equals $112,613 million). ‘‘Value’’ of the investment made in round t measured by looking at round t þ 1 and calculating the value assigned to the company using the ‘‘postmoney’’ valuation of the next round of investment. If the round t þ 1 is an IPO or acquisition, then the IPO price or acquisition price is used in valuing the investment in time t. Firm-specific characteristics (industry, location, etc.).
474
Cost of Capital
In building his database of outcomes, Cochrane obtained IPO data from the SDC Corporation New Issue database and acquisition prices from the SDC Merger and Acquisitions database. The round-to-round statistics of outcomes from the sample investments following each round of investment are:
Companies go IPO after 21.4% of investment rounds. Companies are acquired after 20.4% of investment rounds. Companies go out of business after 9% of rounds. Companies remain private after 45.5% of rounds.
On the average, after about five years, 50% of the investment rounds have either resulted in the company going public or the companies have been acquired. After five years, the chance of success decreases. Cochrane’s observations can be summarized in this way:
Overall (geometric) mean log return ¼ 15% on venture capital investments (where an investment is measured as money invested in a round of financing) compared to 14% for Nasdaq (geometric average return) during 1987 through 2000. Overall standard deviation log return ¼ 89% on venture capital investments compared to: 14.9% for Standard & Poor’s 500
50% for typical individual large publicly traded stock 97% for typical Nasdaq stock
96% for typical individual small Nasdaq stock (market value of equity < $10 million)
High volatility results in high arithmetic mean return. Overall arithmetic E(R) ¼ 59%, s(R) ¼ 107%, Beta ¼ 1.9 compared to: E(R) ¼ 16%, and s(R) ¼ 118% for typical individual small Nasdaq stock (market value of equity < $10 million). Chance of company ending up as an IPO or acquisition rises from 37% for a first-round investment to 50% for a fourth-round investment.
DAS, JAGANNATHAN, AND SARIN STUDY In another comprehensive study, Sanjiv Rangan Das, Murali Jagannathan, and Atulya Sarin (Das et al.) estimate the probability of ‘‘exit’’ from the investment in the venture capital project through IPO or acquisition/buyout and estimate valuation multiples (Exit Proceeds/Investment Amount).8 The authors use the Venture Xpert (www.thomson.com) database with data from 1980 through 2000. The data included:
8
Financing round (sample includes 52,322 financing rounds in 23,208 companies) Data from 700 þ venture and 250 þ buyout funds
Sanjiv Rangan Das, Murali Jagannathan, and Atulya Sarin, ‘‘Private Equity Returns: An Empirical Examination of the Exit of Venture-Backed Companies,’’ Journal of Investment Management (first quarter 2003): 152–177, and ‘‘The Private Equity Discount: An Empirical Examination of the Exit of Venture Backed Companies,’’ Working paper, January 22, 2002.
Realized Returns on Venture Project Investments
475
They used the data to estimate the resulting total probability of ‘‘exit’’ through either IPO or acquisition; that result is equal to 30% to 45%. The authors observe that:
Probability of exit increases rapidly after first two financing rounds, indicating that the probability of failure is greater after the early financing rounds.
Probability of exit increases slowly thereafter. Probability of exit increases with stage of financing.
Das, et al present their observed probability of exit due to liquidity events of IPO or acquisition or either during the years after the investment and calculate valuation multiples measured post-money, adjusted for effects of dilution; that is, a valuation multiple equals the value on exit divided by dollars invested. The multiple for failure to exit via IPO or acquisition in their analyses equals zero. Exhibit 29.4 presents an example of their adjustment for dilution. Das et al. present both raw and industry-adjusted (excess over industry stock price change during time from investment until exit) multiples (i.e., value realized/investment). Using their results you can calculate the expected industry adjusted multiple: Probability of exit via an IPO or an Acquisition=Buyout Industry Adjusted Multiple The equally weighted average expected industry adjusted multiple for their study period (1984 to 1997) are: Buyout/acquisition ¼ 2.03 Early stage ¼ 5.12 Expansion stage ¼ 2.04 Later stage ¼ 1.12 Other ¼ .69 For example, these multiples can be used to calculate the discount from expected value at IPO or acquisition/buyout: D ¼ 1 1=E
Exhibit 29.4
Example of Adjustment for Effects of Dilution
Assume first-round investment ¼ $100 Second-round investment ¼ $100 with postmoney valuation ¼ $500 (i.e., the value of the company is estimated at $500 following the second round of investment. Implies: Original investors parted with 20% of firm (¼100/500) Retention ratio ¼ 80% IPO ¼ $1000, capital raised from new investors ¼ $300 Implies: dilution of 30% ( ¼ 300=1000) Retention ratio ¼ 70% Cumulative/Retention ratio for first round investors ¼ 80% 70% ¼ 56% Multiple before dilution ¼ 10 ¼ 1000=100) Multiple for first round adjusted for dilution ¼ 10 56% ¼ 5.6 Multiple for second round adjusted ¼ 1000=500 70% ¼ 1.4
476
Cost of Capital
where D ¼ Private equity discount E ¼ Exit multiple The resulting discounts are: Later stage: (1 1=1.12) ¼ 11% Early stage: (1 1=5.12) ¼ 80% You can use this discount plus the expected time until exit to impute a rate of return. You can refine the probabilities and expected multiples instead of using simple averages by using their three multivariate analyses based on specific characteristics of the round, the industry, etc. 1. Probability of exit either by IPO or acquisition 2. Expected valuation given exit 3. Expected time to exit9 You can use the results of applying the three multivariate analyses to calculate the private equity discount: Probability of exit Expected multiple given exit determined for financing round ¼ E D ¼ 1 1=E You can use expected time to exit to estimate how long before you expect an exit to occur and impute an estimate expected annual return. For example, assume that the private equity discount equals 60% and the expected time until IPO equals three years. The imputed return until exit can be calculated as: $60 ¼ present value of $100 in 3 years at k return k ¼ 18.56% (compounded annually) A word of caution whenever you impute a return from any of these venture capital studies using exit via IPO. The time to exit, for example, is measured from the investment until the IPO occurs. Investors typically are restricted from liquefying their investment completely at the time of the IPO (‘‘look up period’’). The restriction period until a subsequent secondary offering must be added to the period until IPO in calculating the entire period before liquidity occurs. The imputed return also includes compensation due to the illiquidity of the venture investment until an exit. The private equity discount (D) measures the extra return required on the private investment over the return earned on investing in the public firm. This is akin to buying high-risk discount security (discounted from face) where maturity date is unknown.
REALIZED RETURNS ON BUYOUT INVESTMENTS Ljungqvist, Richardson, and Wolfenzon study the rates of return realized by investments in buyout funds.10 Compared to typical venture capital investments, buyout funds typically purchase 9 10
Das, Jagannathan, and Sarin, ‘‘Private Equity Discount.’’ Alexander Ljungqvist, Matthew Richardson, and Daniel Wolfenzon, ‘‘The Investment Behavior of Buyout Funds: Theory and Evidence,’’ European Corporate Governance Institute Working paper, June 2007.
Summary
477
controlling interests in established firms using large amounts of debt capital. The authors study the returns using a proprietary data set of one of the largest multinational investors in private equity representing investments in over 2,200 portfolio companies by over 200 buyout funds between 1981 and 2000. The data show investments and returns for the period 1981 through 2003 for buyouts. The data set accounts for 35% of all buyout fund capital raised during this period. The data allow the authors to compute annualized compound returns on their investments at the level of the individual portfolio company (instead of at the fund level). They measure returns as: 1
½Cash return=Cash investedh 1 where: h ¼ Holding period Among 53 mature buyout funds, the equal average weighted annual compound (geometric) returns equaled 12.7%. Though the distribution is highly skewed; the median return equaled 4.9%. The arithmetic average return equaled 34%.11
SUMMARY We have presented several studies that help analysts quantify the cost of capital appropriate for an investment in venture capital projects. The observed returns reflect the risks of the projects. Probably the most widely accepted definition of risk in the context of business valuation is the degree of uncertainty (or lack thereof) of achieving future expectations at the times and in the amounts expected.12 This means uncertainty as to both the amounts and the timing of expected income. Note that the definition implies as the reference point expected returns. By expected returns, in a technical sense, we mean the expected value (mean average) of the probability distribution of possible returns for each forecast period. The point to understand here is that the uncertainty encompasses the full distribution of possible returns for each period both above and below the expected value. Investments in venture capital projects suffer from: maturity risk (horizon risk or interest rate risk), given the relative long time period before likely realization of any cash flows; market risk (systematic risk or undiversifiable risk), given the uncertainty of future returns because of the sensitivity of the return on a subject investment to movements in returns for the investment market as a whole; unique risk (investment or company specific or unsystematic risk); and illiquidity risk (as the investments once made are not liquid until a liquidity event occurs). The observed returns compensate the investor for the combination of all these risks.
11 12
Ibid., 22. David Laro and Shannon P. Pratt, Business Valuation and Taxes: Procedure, Law, and Perspective (Hoboken, NJ: John Wiley & Sons, 2005), 160.
Part 5
Other Topics
Chapter 30
Minority versus Control Implications of Cost of Capital Data Introduction Minority versus Control Has Little or No Impact on Cost of Capital Company Efficiency versus Owner Exploitation Impact of the Standard of Value Under What Circumstances Should a Control Premium Be Applied? Projected Income May Not Reflect What a Control Owner Would Achieve Investment Value Reflecting Synergies Factors Affecting a Control Premium a Financial Buyer Might Pay A Tale of Two Markets Many Takeovers at Less than Public Trading Price Summary
INTRODUCTION There is much confusion about whether the results of applying cost of capital data, as discussed in this book, produce a minority value or a control value. The difference between the per-share value of a share that represents control and the per-share value of a share that represents a minority interest can be quite significant. (See Exhibit 30.1.) As with many such questions in economics and finance, the answer is: It depends. More than anything else, when the cost of capital is used in the context of valuation, the question of whether the result of discounting or capitalizing represents a minority or a control value depends primarily on the nature of the cash flows being discounted or capitalized rather than on the discount or capitalization rate. In some cases, the answer to this question may hinge on the definition of value sought, for example, fair market value (the value to a hypothetical buyer and/or seller) or investment value (the value to a particular buyer and/or seller).1
1
For a detailed discussion of definitions of various standards of value in commonly encountered legal contexts, see Jay E. Fishman, Shannon P. Pratt, and William Morrison, Standards of Value: Theory and Application (Hoboken, NJ: John Wiley & Sons, 2007).
481
482
Cost of Capital
MINORITY VERSUS CONTROL HAS LITTLE OR NO IMPACT ON COST OF CAPITAL Regardless of which of the major approaches is used to estimate cost of capital (e.g., build-up method, Capital Asset Pricing Model, discounted cash flow method, arbitrage pricing model, Fama-French 3-factor model, etc.), the information is derived from publicly traded stocks. Because these public market transactions represent minority ownership interests, some analysts think that the cost of capital should be adjusted upward in valuing a controlling ownership interest. This generally is not true! Recall that the discounting method of valuation and the capitalization method of valuation have two basic elements in common: 1. A numerator consisting of an amount or amounts of expected economic income 2. A denominator consisting of a rate of return at which the economic income is discounted or capitalized Almost all the difference in the control value versus the minority value in the income approach to valuation is found in the numerator—the expected economic income available to the investor—rather than in the denominator—the discount or capitalization rate. As Roger Ibbotson has succinctly stated: When you are purchasing a company you are acquiring the ability to potentially control future cash flows. To acquire this option to exercise control, you must pay a premium. Holding all else constant, it should not impact the discount rate.2
Generally speaking, investors will not accept a lower expected rate of return for purchase of a controlling interest than for purchase of a minority interest. Control buyers pay premiums because they expect to do something to increase the cash flows, not because they are willing to accept a lower expected rate of return. What they may do to increase cash flows can range from eliminating inactive relatives from the payroll to eliminating duplicative sales forces to consolidating products and distribution functions. Of course, many a public stock has taken a huge tumble in its market price as a result of an acquisition. This usually is because the acquisition failed to achieve the expected increase in cash flows for the target and/or the acquirer. If the market perceives that the returns a company is likely to achieve will fall short of the market’s required rate of return, then the market simply adjusts the stock price downward until the expected returns do meet the market’s required rate of return. The ‘‘control premium’’ in Mergerstat/Shannon Pratt’s Control Premium StudyTM includes both the ‘‘control premium’’ and the ‘‘synergistic’’ or ‘‘strategic’’ premium, as shown in Exhibit 30.1.
COMPANY EFFICIENCY VERSUS OWNER EXPLOITATION Benefits available to a minority owner are a function of two distinct factors: 1. Efficiency at the overall company level 2. Differential benefits between control owners and minority owners (e.g., cash flow that could be available for dividends used for extra compensation to controlling owners) 2
Ibbotson Associates Cost of Capital Workshop (Chicago: Ibbotson Associates, 1998), chaps. 1, 12.
483
45% total discount for lack of marketability (25% + 20%) may be taken additively Additional 20% discount for private company stock (taken from publicly traded equivalent value $8.00 per share)
25% discount for lack of marketability for restricted stock
or Minority Discount
Additional discount for private company stock.
Discount for restricted stock of public company
Control Premium
Value of nonmarketable minority (lack of control) shares $ 4.40
$ 6.00
“Publicly traded equivalent value” or “stock market” value” of minority shares if freely traded Value of restricted stock of public company
$ 8.00
Value of control sharesa
$10.00
Source: Jay E. Fishman, Shannon P. Pratt, and J. Clifford Griffith, Guide to Business Valuations, 17th ed. (Fort Worth, TX: Practitioners Publishing Company, 2007), 8–8, Copyright # 2007. All rights reserved. Reprinted with permission of Practitioner’s Publishing Company. Copies of this Guide can be ordered by calling PPC at (800) 323–8724 or log onto www.ppc.thomson.com.
Exhibit 30.1 ‘‘Levels of Value’’ in Terms of Characteristics of Ownership
A combined 20% discount and a 45% discount for lack of marketability equals a total of 56% discount from value of control shares.a
20% minority interest discount; 25% control premium
20% strategic acquisition premium
Synergistic (Strategic) Value
$12.00
Per-Share Value
484
Cost of Capital
Controlling stockholders enjoy a number of prerogatives of control, which can have an impact on both of the aforementioned benefits as they affect minority stockholders. Some of the more common prerogatives of control include the ability to:
Appoint or change operational management.
Appoint or change members of the board of directors.
Determine management compensation and perquisites.
Set operational and strategic policy and change the course of the business.
Acquire, lease, or liquidate business assets, including plant, property, and equipment.
Select suppliers, vendors, and subcontractors with whom to do business and award contracts.
Negotiate and consummate mergers and acquisitions.
Liquidate, dissolve, sell out, or recapitalize the company.
Sell or acquire Treasury shares.
Register the company’s equity securities for an initial or secondary public offering.
Register the company’s debt securities for an initial or secondary public offering.
Declare and pay cash and/or stock dividends.
Change the articles of incorporation or by-laws.
Set one’s own compensation (and perquisites) and the compensation (and perquisites) of related-party employees.
Select joint venturers and enter into joint venture and partnership agreements.
Decide what products and/or services to offer and how to price those products/services.
Decide what markets and locations to serve, to enter into, and to discontinue serving.
Decide which customer categories to market to and which not to market to.
Enter into inbound and outbound license or sharing agreements regarding intellectual properties.
Block any or all of the above actions.3
It is apparent that exercise of some of these prerogatives may have an impact on the total cash flows available to the firm, and others will affect the relative benefits ultimately realized by control shareholders versus minority shareholders. It should also be apparent that in projecting expected cash flows, the amounts available to a control owner may not be the same as those available to a minority owner. For example, in many companies, control owners set their own compensation (often reflecting their own perceived genius) rather than having an independent compensation committee. In any case, whether a result of company efficiency or differential shareholder benefits, it is the expected cash flows to investors that drive the value to them, not differences in cost of capital between minority investors and control investors. Enron and its ilk notwithstanding, the exploitation of minority shareholders is far less prevalent in public companies than in private companies, at least in larger public companies. If company cash flows are already maximized and the returns are already distributed pro rata to all shareholders, then there may be no difference between a control value and a minority value.
3
Shannon Pratt, Valuing a Business, 5th ed. (New York: McGraw-Hill, 2008), chap. 15.
Under What Circumstances Should a Control Premium Be Applied?
485
IMPACT OF THE STANDARD OF VALUE Some analysts suggest that the appropriate cost of capital for an acquisition should be that of the acquirer rather than the target. As we point out in Chapter 22, the cost of capital should reflect the risk of the target, not the risk of the acquiring company. This position also departs from the standard of fair market value (the price at which the property would change hands between hypothetical buyers and sellers, with no special motivations). If the standard of value is fair market value, then the principle that ‘‘the cost of capital is a function of the investment, not the investor’’ clearly applies. The idea of fair market value is that there is a consensus value that, in economic terms, ‘‘clears the market.’’ If the cost of capital is a function of the investment, not the investor, then it is conceivable that the risk perceived by one investor may depart from the market consensus regarding the investment’s risk. If the estimated cost of capital for a particular investment for a particular investor is driven by a view that departs from the market consensus, then we are moving away from the standard of fair market value (a consensus value) and toward investment value (value to some particular investor, driven by that investor’s unique perceptions or circumstances).
UNDER WHAT CIRCUMSTANCES SHOULD A CONTROL PREMIUM BE APPLIED? We have made the case that the cost of capital developed from public company data does not differ for minority or controlling interests. But we know that acquisitions are made at prices reflecting a control price premium over public market minority share trading prices.4 So if we are valuing a controlling interest by the discounting or capitalizing method, and if we are using the cost of capital that we have estimated, under what circumstances should we add a control premium? PROJECTED INCOME MAY NOT REFLECT WHAT A CONTROL OWNER WOULD ACHIEVE We said earlier that the control premium would be reflected as a result of the increased cash flows that a control owner would expect to achieve. If such control cash flows have been either discounted or capitalized, then little or no further control premium should be applied. However, if the projected cash flows used do not reflect a control owner’s expectations, then a control premium may be warranted. INVESTMENT VALUE REFLECTING SYNERGIES If a buyer can achieve strategic or synergistic benefits by an acquisition, then that buyer may be willing to pay a control premium. For example, if the target is a direct competitor, then the buyer may benefit by raising his or her own prices as well as those of the target. Remember, however, that a price premium reflecting benefits to such a particular buyer brings in the element of investment value as opposed to a pure fair market value. In the context of this thinking, the ‘‘levels of value’’ chart (Exhibit 30.1) added another level at the top since the first edition of this book was published, ‘‘synergistic value,’’ reflecting a potential premium over control value on a stand-alone basis. 4
See, e.g., Mergerstat/Shannon Pratt’s Control Premium StudyTM (Los Angeles: Mergerstat, LP), available online, updated quarterly, at www.BVMarketData.com.
486
Cost of Capital
FACTORS AFFECTING A CONTROL PREMIUM A FINANCIAL BUYER MIGHT PAY Financial buyers sometimes pay control premiums, even if they do not have any opportunities for synergistic benefits, albeit typically much lower premiums than those paid by synergistic buyers. For example, one control prerogative that control owners can implement that minority owners cannot is to register a public offering (i.e., create liquidity). Other control prerogatives would be to sell interests to employees or to others, to repurchase outstanding minority interests, or to recapitalize. Some will pay a premium to ‘‘call the shots’’. Some may perceive psychological advantages to control of certain companies.
A TALE OF TWO MARKETS In our opinion, a strong case could be made that when the share price of a public company is wildly out of line with its intrinsic value (to a financial buyer and even possibly to a normal strategic buyer), then perhaps the public market value is meaningless and should be disregarded entirely. In fact, the Delaware Court of Chancery frequently gives no weight at all to prior trading prices in dissenting stockholder actions.5 In 2001 Mark Lee, a well-known business valuation analyst for over 30 years, went public with his views on the issue. Lee observed: The stock market is a market for minority interests in common stock. The principal buyers and sellers are individuals, mutual funds, and financial institutions. The market is highly liquid, individual investment horizons may be short, and risk tolerances can be greater than in illiquid markets. Financing is often readily available from banks and brokers at short-term money rates. Investors are generally passive. Individual investments are usually purchased as part of diversified portfolios, which leads to greater tolerance to risk. The [mergers and acquisitions] market is a market for whole companies. The principal buyers and sellers are controlling shareholders, corporations, and [leveraged buyout] houses. The market is not liquid; as a result, individual investment horizons tend to be longer. Risk tolerances in the short term tend to be lower than in a liquid market. Transactions are financed using long-term debt from banks, insurance companies, mezzanine funds, equity of large corporations, and private equity funds. [Mergers and acquisition] investors take an active role in managing their companies. The relationship of the two markets is not linear [as shown in the single bar of the levels of the value chart]. [This linearity] presupposes that acquisition premiums apply in all situations; and acquisition premiums are roughly the same amount generally or in each industry. The relationship of the two markets is better shown as the two overlapping forms as shown in [Exhibit 30.2] [. . .] . Clearly, the existence of an acquisition premium and its magnitude is a ‘‘facts and circumstances’’ test for each individual valuation.6
5
6
See, e.g., In re Emerging Communications, Inc. Shareholders Litigation, 2004 Del. Ch. LEXIS 70 (Del. Ch. 2004) (‘‘Delaware law recognizes that, although market price should be considered in an appraisal, the market price of shares is not always indicative of fair value. Our appraisal cases so confirm.’’), citing Cede & Co v. Technicolor, Inc., 684 A.2d 289, 301 (Del. 1996) (the ‘‘market price of shares may not be representative of true value.’’); Harris v. Rapid-American Corp., C.A. No. 6462, 1992 WL 69614, at * 1, * 4. (Del. Ch. 1992) ($28 merger price, representing a 28% premium over unaffected trading price was barely one-third of adjudicated fair value of $73.29); In re Shell Oil Co., 1990 Del Ch. LEXIS 199 (Del Ch. 1990)), aff’d, 607 A.2d 1213 (Del. 1992) (market price $44, adjudicated fair value $71.20). Mark Lee, ‘‘Control Premiums and Minority Discounts: The Need for Specific Economic Analysis,’’ Shannon Pratt’s Business Valuation Update1 (August 2001): 1–5. Used with permission.
A Tale of Two Markets
Exhibit 30.2
487
Schematic Relationship of Stock Market and M&A Market
Stock Market Acquisition Value Exceeds Market Value if a Buyer Exists
M&A Market
Acquisition Value Exceeds Market Value
Market Value Exceeds Acquisition Value
1. The oval in the chart is the M&A market. The box is the stock market. (The sizes of the two are not proportionate.) 2. If a potential acquirer believes that it can create sufficient added economic benefits, the acquisition value of the company will exceed its market value. The additional economic benefit can pay for the cost of the acquisition premium. These are the transactions reported in the Control Premium Study and similar publications. 3. Only a small fraction of publicly traded companies are taken over in a given year. Generally, there is no market available that can create benefits large enough to justify payment of the premium required for the acquisition of the companies that remain public in view of other alternatives. If there is no M&A market available to sell a company at a premium to its stock market value, then there is little or no acquisition premium, much less a ‘‘theoretical’’ premium based on an average of acquisitions of dissimilar companies. 4. In emerging industries, such as the Internet in 1998 and 1999, the value of the common stock of a corporation as a whole often is worth less than the aggregate market value of common stock trading as minority interests. While the new industry is viewed as very attractive for investment, entire corporations are perceived as too risky. As a result, individual and institutional investors will pay more for minority interests as part of a diversified industry portfolio than individual acquirers will pay for the entire company. Investors are willing to risk a small amount that an investment in a minority interest requires but not the large amount acquiring an entire business requires. 5. Similarly, many companies spin off units or sell them in an IPO rather than sell the units in the M&A market because a higher price can be obtained in the market than in an M&A transaction. Source: Adapted from Mark Lee, ‘‘Control Premiums and Minority Discounts: The Need for Specific Economic Analysis,’’ Shannon Pratt’s Business Valuation Update1 (August 2001):1–5. Reprinted in Shannon P. Pratt, Business Valuation Discounts and Premiums (Hoboken, NJ: John Wiley & Sons, 2001), 41, Copyright # 2001. Used with permission.
488
Mean Premium w/o Negatives
55% 50% 47% 45% 53% 58% 49% 48% 54% 49% 42% 51% 60% 56% 48% 49% 36% 36% 38% 36% 30% 34% 31% 41%
Quarter
1Q2000 2Q2000 3Q2000 4Q2000 1Q2001 2Q2001 3Q2001 4Q2001 1Q2002 2Q2002 3Q2002 4Q2002 1Q2003 2Q2003 3Q2003 4Q2003 1Q2004 2Q2004 3Q2004 4Q2004 1Q2005 2Q2005 3Q2005 4Q2005
48% 33% 35% 30% 37% 42% 30% 26% 42% 36% 21% 36% 50% 56% 42% 40% 36% 28% 30% 26% 22% 21% 22% 30%
Mean Premium w/Negatives 36% 38% 37% 36% 37% 42% 35% 30% 40% 42% 26% 32% 37% 41% 32% 37% 30% 25% 24% 28% 21% 24% 22% 33%
Mean Premium w/o Negatives 32% 28% 31% 23% 27% 33% 23% 22% 34% 28% 17% 26% 33% 40% 28% 32% 30% 22% 19% 22% 17% 15% 15% 24%
Mean Premium w/Negatives 165 268 244 248 228 203 223 186 179 118 180 126 134 113 99 90 86 123 103 126 104 114 104 133
Total Count
Mergerstat/Shannon Pratt’s Control Premium StudyTM Takeovers from 2000 to 2005
ALL Foreign and Domestic Transactions Control Premiums by Quarter, with and without Negative Premiums and TIC/EBITDA
Exhibit 30.3
16 56 39 54 43 38 53 49 27 22 53 26 15 7 9 12 1 19 14 24 18 27 19 27
Total Negative 10% 21% 16% 22% 19% 19% 24% 26% 15% 19% 29% 21% 11% 6% 9% 13% 1% 15% 14% 19% 17% 24% 18% 20%
Percent Negative
11.92 10.45 10.14 8.88 7.75 7.59 8.35 8.11 7.02 7.33 7.94 7.22 7.83 8.44 7.74 8.99 8.15 9.27 10.00 9.57 8.56 8.71 10.15 10.19
Median TIC/EBITDA*
489
(continued)
Mean Premium w/o Negatives
59% 52% 51% 50% 56% 64% 51% 54% 63% 49% 46% 59% 66% 74% 57% 50% 38% 36% 43% 40% 32% 38% 36% 39%
Quarter
1Q2000 2Q2000 3Q2000 4Q2000 1Q2001 2Q2001 3Q2001 4Q2001 1Q2002 2Q2002 3Q2002 4Q2002 1Q2003 2Q2003 3Q2003 4Q2003 1Q2004 2Q2004 3Q2004 4Q2004 1Q2005 2Q2005 3Q2005 4Q2005
52% 30% 41% 34% 38% 50% 36% 37% 56% 37% 30% 47% 58% 72% 56% 43% 38% 32% 36% 36% 30% 29% 30% 36%
Mean Premium w/Negatives 34% 43% 42% 45% 35% 51% 39% 33% 50% 45% 41% 32% 35% 58% 41% 37% 31% 25% 24% 32% 27% 29% 26% 30%
Mean Premium w/o Negatives 32% 29% 37% 32% 26% 38% 32% 27% 47% 32% 23% 31% 41% 55% 40% 33% 31% 25% 22% 30% 26% 24% 22% 30%
Mean Premium w/Negatives
Only Domestic Transactions Control Premiums by Quarter, with and without Negative Premiums and TIC/EBITDA
Exhibit 30.3
103 139 137 148 121 107 112 106 80 64 59 54 78 44 63 57 49 69 64 67 48 62 54 71
Total Count 10 37 17 30 24 17 18 22 6 10 13 6 8 1 1 6 0 6 8 5 3 10 7 5
Total Negative 10% 27% 12% 20% 20% 16% 16% 21% 8% 16% 22% 11% 10% 2% 2% 11% 0% 9% 13% 7% 6% 16% 13% 7%
Percent Negative
(continued )
13.01 10.84 11.15 9.18 8.75 8.86 11.62 9.36 7.51 8.01 7.65 8.58 10.56 10.10 7.65 8.70 7.61 10.17 10.68 9.69 11.21 9.69 11.26 10.97
Median TIC/EBITDA*
490
(Continued)
47% 47% 42% 38% 50% 51% 45% 38% 45% 49% 39% 45% 53% 55% 28% 47% 35% 34% 28% 29% 28% 27% 26% 44%
1Q2000 2Q2000 3Q2000 4Q2000 1Q2001 2Q2001 3Q2001 4Q2001 1Q2002 2Q2002 3Q2002 4Q2002 1Q2003 2Q2003 3Q2003 4Q2003 1Q2004 2Q2004 3Q2004 4Q2004 1Q2005 2Q2005 3Q2005 4Q2005
40% 37% 28% 25% 36% 33% 24% 13% 30% 34% 16% 28% 40% 46% 18% 34% 33% 23% 20% 13% 16% 13% 15% 24%
Mean Premium w/Negatives 37% 32% 32% 24% 37% 36% 31% 25% 32% 35% 22% 30% 36% 36% 20% 37% 30% 23% 19% 20% 19% 14% 14% 35%
Mean Premium w/o Negatives 34% 27% 26% 17% 28% 27% 18% 15% 24% 24% 13% 16% 26% 34% 16% 25% 29% 18% 17% 9% 15% 8% 11% 11%
Mean Premium w/Negatives 62 129 107 100 107 96 111 80 99 54 121 72 56 69 36 33 37 54 39 59 56 52 50 62
Total Count 6 19 22 24 19 21 35 27 21 12 40 20 9 6 8 6 1 11 6 19 15 17 12 22
Total Negative 10% 15% 21% 24% 18% 22% 32% 34% 21% 22% 33% 28% 16% 9% 22% 18% 3% 20% 15% 32% 27% 33% 24% 35%
Percent Negative
10.74 10.17 9.10 7.86 6.74 6.48 7.56 6.81 6.66 6.24 7.95 6.71 6.50 6.96 8.69 9.73 8.35 8.91 7.77 8.83 7.82 6.90 9.44 9.53
Median TIC/EBITDA*
*Excludes negative TIC/EBITDA. Includes companies with negative Control Premiums. TIC = Target Invested Capital = Target company’s implied total invested capital based on the sum of implied market value of equity (MVE) plus the face value of total interest-bearing debt and the book value of preferred stock outstanding prior to the annoucement. Sources: FactSet Mergerstat Control Premium StudyTM, 2000–2005, inclusive. Copyright # 2000–2005. FactSet Mergerstat, LLC. Mergerstat/Shannon Pratt’s Control Premium StudyTM, 2002–2005. Copyright # 2005. FactSet Mergerstat, LLC. Mergerstat/Shannon Pratt’s Control Premium StudyTM (Los Angeles: FactSet Mergerstat, LLC), distributed by Business Valuation Resources, LLC, Portland, Oregon, available online, updated quarterly, at wwwBVMarketData.comTM.
Mean Premium w/o Negatives
Quarter
Only Foreign Transactions Control Premiums by Quarter, with and without Negative Premiums and TIC/EBITDA
Exhibit 30.3
A Tale of Two Markets
491
05 20 3Q
05 20 1Q
04 3Q
20
04 20 1Q
03 3Q
20
03
02
20 1Q
20
02 3Q
20 1Q
01 20 3Q
01 20 1Q
20 3Q
20 1Q
00
70% 60% 50% 40% 30% 20% 10% 0% 00
Control Premium
Mergerstat/Shannon Pratt's Control Premium Study™ Median Control Premium w/Negatives Excluded
Quarter Mergerstat/Shannon Pratt's Control Premium Study™ Median Control Premium w/Negative Included Control Premium
60% 50% 40% 30% 20% 10% 05 20 3Q
05 20 1Q
04 3Q
20
04 20 1Q
03 3Q
20
03 20 1Q
02 3Q
20
02 20 1Q
01 20 3Q
01 1Q
20
00 20 3Q
1Q
20
00
0%
Quarter
05 20 3Q
05 20 1Q
04 3Q
20
04 20 1Q
03 3Q
20
03 20 1Q
02 3Q
20
02 20 1Q
01 20 3Q
01 20 1Q
20 3Q
20 1Q
00
14.00 12.00 10.00 8.00 6.00 4.00 2.00 0.00 00
Control Premium
Mergerstat/Shannon Pratt's Control Premium Study™ MedianTIC/EBITDA
Quarter All
Exhibit 30.3
Domestic
Foreign
(Continued)
It is obvious that one must be extremely cautious about applying a control premium to public market values to determine a control level of value. Conversely, if guideline stocks are trading at or near control value in a given case, valuation of a minority interest by applying a discount for lack of control from the guideline indicators (in addition to a lack of marketability discount) might be supported, since the minority owner lacks the control prerogative of taking the company public or registering his or her stock in an offering.
492
Cost of Capital
MANY TAKEOVERS AT LESS THAN PUBLIC TRADING PRICE Many people are surprised to learn just how many takeovers occur at prices below the public trading price just prior to the takeover announcement. In 2001, Business Valuation Resources assumed distribution of the Mergerstat Control Premium StudyTM, renamed it Mergerstat/Shannon Pratt’s Control Premium StudyTM, and put it online so that people could access and analyze it electronically. Utilizing this, Exhibit 30.3 is a summary of the takeovers of public companies from 2000 through 2005. In the 24 quarters analyzed, over 16% of the takeovers were at prices below their recent public market trading prices! Also as shown in Exhibit 30.3, including the ‘‘negative premiums’’ in the medians and averages has a dramatic impact. The database is searchable by Standard Industrial Classification (SIC) code, North American Industry Classification System (NAICS) code, time frame, and size of company (by several measurements). Before naively applying an ‘‘average’’ control premium or implied minority discount, we would recommend searching the database to select those transactions that are truly relevant to the subject at hand.7
SUMMARY Generally, the cost of capital is the same for minority interest investments as for controlling interest investments. Investors typically do not reduce their required rate of return because they are buying a controlling interest rather than a minority interest. Therefore, although empirical data used to estimate the cost of capital are drawn almost entirely from the public stock market (which represents transactions in minority shares), the cost of capital thus estimated is applicable to either control or minority investments. Premiums above current market trading prices often are paid to acquire controlling interests. However, these premiums are paid because of anticipated increases in the cash flows available to the controlling investors, not because of a lower cost of capital. Increased cash flows to control buyers may come as a result of improved operating efficiency, synergies with a buying company, or redistribution of already available cash flows to new control owners. The standard of value conceivably could affect the cost of capital. Fair market value assumes a market consensus cost of capital, whereas an investment value standard may reflect a cost of capital driven by a particular investor’s perceptions or circumstances, which may depart from the market consensus. The merger and acquisition market is a distinct market from the public stock market. While most takeovers occur at prices above the stock’s public market price prior to the acquisition, a significant number occur at prices below the public market trading price. Careful research should be undertaken before applying a ‘‘control premium’’ or ‘‘implied minority discount’’ to a private company valuation to determine whether such a premium or discount is warranted.
7
See, e.g., Daniel L. McConaughy, ‘‘Negative Takeover Premia and Stock Price Levels in Internet Stocks,’’ Valuation Strategies (March/April 2002): 20–29.
Chapter 31
How Cost of Capital Relates to the Excess Earnings Method of Valuation Introduction Basic ‘‘Excess Earnings’’ Valuation Method Conceptual Basis for the Method Steps in Applying the Excess Earnings Method Example of the Excess Earnings Method Cost of Capital Reasonableness Check Computing the Weighted Average Excess Earnings Capitalization Rate Estimating a Build-up Model Capitalization Rate Discussion of the Example Vagaries of the Excess Earnings Method Summary
INTRODUCTION The excess earnings method of valuation was originally created for the purpose of valuing intangible assets, specifically intangible value in the nature of goodwill. It was devised to determine how much the U.S. government would compensate brewers and distillers for the economic loss of their goodwill as a result of Prohibition. This valuation method has since been embodied in Revenue Ruling 68-609, included as Exhibit 31.1. Although it was originally designed to value only intangible assets, it is widely used (and misused) today in the valuation of small businesses and professional practices. This chapter has a single point: An estimate of the cost of capital, developed by methods discussed in this book, can be used as a test of the reasonableness of the assumptions and results achieved by using the excess earnings method. This test can be applied either by a person preparing an excess earnings method valuation or by someone reviewing an excess earnings method valuation prepared by someone else. This chapter gives only enough of the skeletal basics of the excess earnings method to allow the reader to understand how to apply the reasonableness test proposed herein. Most basic texts on business valuation contain a full chapter, or a major portion of a chapter, on the excess earnings method.1
1
See, e.g., Jay E. Fishman, Shannon P. Pratt, and J. Clifford Griffith, PPC’s Guide to Business Valuations, 17th ed. (Fort Worth, TX: Practitioners Publishing Company, 2007, updated annually in May), 7-19 to 7-31; Shannon P. Pratt, Robert F. Reilly, and Robert P. Schweihs, Valuing Small Businesses and Professional Practices, 3rd ed. (New York: McGraw-Hill, 1998), chap. 23; Shannon P. Pratt, Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed. (New York: McGraw-Hill, 2007), chap. 13.
493
494
Exhibit 31.1
Cost of Capital
Revenue Ruling 68-609
The ‘‘formula’’ approach may be used in determining the fair market value of intangible assets of a business only if there is no better basis available for making the determination; A.R.M. 34, A.R.M. 68, O.D. 937, and Revenue Ruling 65-192 superseded. Ruling is to update and restate, under the current statute and regulations, the currently outstanding portions the currently outstanding portions of A.R.M. 34, C.B. 2, 31 (1920), A.R.M. 68, C.B. 3, 43 (1920), and O.D. 937, C.B. 4, 43 (1921). 26 CFR 1.1001-1: Computation of gain or loss. Rev. Rul. 68-609/1/. The question presented is whether the ‘‘formula’’ approach, the capitalization of earnings in excess of a fair rate of return on net tangible assets, may be used to determine the fair market value of the intangible assets of a business. The ‘‘formula’’ approach may be stated as follows: A percentage return on the average annual value of the tangible assets used in a business is determined, using a period of years (preferably not less than five) immediately prior to the valuation date. The amount of the percentage return on tangible assets, thus determined, is deducted from the average earnings of the business for such period and the remainder, if any, is considered to be the amount of the average annual earnings from the intangible assets of the business for the period. This amount (considered as the average annual earnings from intangibles), capitalized at a percentage of, say, 15 to 20 percent, is the value of the intangible assets of the business determined under the ‘‘formula’’ approach. The percentage of return on the average annual value of the tangible assets used should be the percentage prevailing in the industry involved at the date of valuation, or (when the industry percentage is not available) a percentage of 8 to 10 percent may be used. The 8 percent rate of return and the 15 percent rate of capitalization are applied to tangibles and intangibles, respectively, of businesses with a small risk factor and stable and regular earnings; the 10 percent rate of return and 20 percent rate of capitalization are applied to businesses in which the hazards of business are relatively high. The above rates are used as examples and are not appropriate in all cases. In applying the ‘‘formula’’ approach, the average earnings period and the capitalization rates are dependent upon the facts pertinent thereto in each case. The past earnings to which the formula is applied should fairly reflect the probable future earnings. Ordinarily, the period should not be less than five years, and abnormal years, whether above or below the average, should be eliminated. If the business is a sole proprietorship or partnership, there should be deducted from the earnings of the business a reasonable amount for services performed by the owner or partners engaged in the business. See Lloyd B. Sanderson Estate v. Commissioner, 42 F.2d 160 (1930). Further, only the tangible assets entering into net worth, including accounts and bills receivable in excess of accounts and bills payable, are used for determining earnings on the tangible assets. Factors that influence the capitalization rate include (1) the nature of the business, (2) the risk involved, and (3) the stability or irregularity of earnings. The ‘‘formula’’ approach should not be used if there is better evidence available from which the value of intangibles can be determined. If the assets of a going business are sold upon the basis of a rate of capitalization that can be substantiated as being realistic, though it is not within the range of figures indicated here as the ones ordinarily to be adopted, the same rate of capitalization should be used in determining the value of intangibles. Accordingly, the ‘‘formula’’ approach may be used for determining the fair market value of intangible assets of a business only if there is no better basis therefore available. See also Revenue Ruling 59-60, C.B. 1959-1, 237, as modified by Revenue Ruling 65-193, C.B. 1965-2, 370, which sets forth the proper approach to use in the valuation of closely-held corporate stocks for estate and gift tax purposes. The general approach, methods, and factors, outlined in Revenue Ruling 59-60, as modified, are equally applicable to valuations of corporate stocks for income and other tax purposes as well as for estate and gift tax purposes. They apply also to problems involving the determination of the fair market value of business interests of any type, including partnerships and proprietorships, and of intangible assets for all tax purposes. A.R.M. 34, A.R.M. 68, and O.D. 937 are superseded, since the positions set forth therein are restated to the extent applicable under current law in this Revenue Ruling. Revenue Ruling 65-192, C.B. 1965-2, 259, which contained restatements of A.R.M. 34 and A.R.M. 68, is also superseded. /1/ Prepared pursuant to Rev. Proc. 67-6, C.B. 1967-1, 576.
Basic ‘‘Excess Earnings’’ Valuation Method
495
BASIC ‘‘EXCESS EARNINGS’’ VALUATION METHOD The excess earnings method is a form of a capitalization method requiring separate estimation of two capitalization rates. The reason for the two rates is that the income stream being capitalized is divided into two parts: 1. Income attributable to tangible assets. Less risky, lower required rate of return 2. Income attributable to intangible assets. More risky, generally higher required rate of return The rule is simply that the weighted average of the two rates based on asset components (weighted at market values, of course) should approximately equal capitalization rates based on capital structure components estimated by methods discussed in this book. CONCEPTUAL BASIS FOR THE METHOD The Guide to Business Valuations explains the concept of the excess earnings method: The model for the excess earnings method computes the company’s equity value based on the appraised value of tangible assets, plus an additional amount for intangible assets. A company’s tangible assets should provide a current return to the owner. Since there are risks associated with owning the company’s assets, the rate of return on those assets should be commensurate with the risks involved. That rate of return should be either the prevailing rate of return required to attract capital to that industry or an appropriate rate above the risk-free rate. Any returns produced by the company above the rate on tangible assets are considered to arise from intangible assets. Accordingly, the weighted average capitalization rate for tangible assets and intangible assets should be equivalent to the capitalization rate for the entire company.2
STEPS IN APPLYING THE EXCESS EARNINGS METHOD The Guide to Business Valuations lists the steps required in implementing the excess earnings method: Step 1. Obtain the company’s financial statements. Apply the necessary GAAP (generally accepted accounting principles) and normalization adjustments (including adjustments for nonoperating assets). Recompute federal and state income taxes, if necessary, based on normalized pretax earnings. Many small companies only have tax-basis financial statements. Step 2. Determine the value of the company’s net tangible assets. Step 3. Determine a reasonable rate of return (as of the valuation date) on the appraised value of the company’s net tangible assets (assets minus liabilities). Step 4. Multiply the reasonable rate of return (step 3) times the company’s net tangible asset value (step 2). That amount is the ‘‘reasonable return’’ on those net assets. Step 5. Subtract the calculated reasonable return (step 4) from normalized net earnings (step 1). That difference is the company’s ‘‘excess earnings.’’ Step 6. Determine an appropriate capitalization rate (as of the valuation date) for the company’s excess earnings, which are assumed to be attributable to goodwill or other intangible assets. Step 7. Capitalize the excess earnings (divide excess earnings by the capitalization rate). Step 8. Add the amount computed in step 7 and the value of the net tangible assets (step 2). Step 9. Perform ‘‘sanity checks’’ to determine the reasonableness of the value determined in steps 1 through 8. 2
Jay E. Fishman, Shannon P. Pratt, and J. Clifford Griffith, PPC’s Guide to Business Valuations, 17th ed. (Fort Worth, TX: Practitioners Publishing Company, 2007, updated annually in May), 7–19.
496
Cost of Capital
Step 10. Determine an appropriate value for any excess or nonoperating assets that were adjusted for in step 1. If applicable, add the value of those assets to the value determined in step 8. If asset shortages were identified in step 1, determine if the value estimate should be reduced to reflect the value of such shortages. If the normalized income statement was adjusted for identified asset shortages, it is not necessary to further reduce the value estimate. Step 11. Determine if the value of the company computed in step 8 should be adjusted for a minority interest discount, discount for lack of marketability, or other discounts.3 A very good sanity check, as referred to in step 9, is the cost of capital reasonableness check outlined in this chapter. EXAMPLE OF THE EXCESS EARNINGS METHOD For an example, we will use a company with 100% equity in its capital structure. This simplifies the example, although it works just as well in valuing overall invested capital. As a practical matter, though, a majority of the companies to which this method is applied have no long-term debt. We are reviewing an excess earnings method valuation prepared by Sam Shoveler for a company owner’s wife in a divorce proceeding. The company is Kenny’s Landscaping Mob (KLM), a sole proprietorship with several years of history in a residential area primarily populated by employees of lumber, plywood, and papermill companies. Mill shutdowns are frequent, impacting KLM’s business, and there has even been talk of permanent closures. Kenny, now 45, supervises a high-turnover workforce whose members are paid a small fraction of the hourly rate that Kenny charges his clients for the gardening and landscaping work performed. There is substantial client turnover, but Kenny advertises heavily and finds new customers, at least when the mills are fully operating. To illustrate a simple valuation of KLM by the excess earnings method, we will make five assumptions: 1. An appraiser accredited by the American Society of Appraisers in Machinery and Equipment Appraisal and with experience in landscaping and gardening equipment has appraised KLM’s tangible assets on a value-in-use basis at $200,000. We assume there is zero debt. 2. Shoveler has determined that a reasonable rate of return on the company’s net tangible assets is 8%. 3. Shoveler has also determined that an appropriate capitalization rate for the company’s excess earnings is 20%. 4. Normalized after-tax net cash flow for KLM, after reasonable compensation to Kenny, is $50,000 per year. 5. Because Kenny is always scrambling for both customers and workers, and because the community’s industrial base is flat at best, growth in net cash flow is expected to be only at the rate of inflation, estimated at 3%. Shoveler’s summary of the excess earnings method of valuation of KLM is: Tangible asset value $200,000 Net cash flow $50,000 Required return on tangible assets: 0.08 $200,000 ¼ 16,000 3
Ibid., 7–19 to 7–20.
Cost of Capital Reasonableness Check
497
Return attributable to intangible assets $34,000 Intangible asset value (capitalized excess earnings) $34,000 0.20 170,000 Total value of KLM $370,000
COST OF CAPITAL REASONABLENESS CHECK The cost of capital reasonableness check is a fairly simple two-step process: Step 1. Estimate a reasonable capitalization rate for the subject company by one or more of the cost of capital estimation methods discussed in this book. Step 2. Compute the weighted average capitalization rate (the weighted average of the returns on tangible assets and excess earnings, the latter representing the return on intangible assets) implied in the excess earnings valuation, and compare it with the capitalization rate estimate in step 1. If the results of step 1 and step 2 are close, this implies passing marks on one test of the reasonableness of the rates used in the excess earnings method. (The analyst should recognize, of course, that the weighted average of the excess earnings method rates could have been close to the overall capitalization rate by accident and that different tangible asset values or cash flows could still produce an unreasonable result.) COMPUTING THE WEIGHTED AVERAGE EXCESS EARNINGS CAPITALIZATION RATE Returning to the excess earnings method valuation, we see that the company’s estimated value of $370,000 was composed of $200,000 tangible asset value and $170,000 intangible asset value. Computing the relative weights of these asset values, we have: Tangible assets $200,000 $370,000 ¼ 54.1% Intangible assets $170,000 $370,000 ¼ 45.9% ¼ 100.0% Weighting the required rates of return on the tangible and intangible asset value components gives us: Tangible asset value 0.541 0.08 ¼ 0.043 Intangible asset value 0.459 0.20 ¼ 0.092 Weighted asset-based capitalization rate ¼ 0.135 ESTIMATING A BUILD-UP MODEL CAPITALIZATION RATE For a very small company like KLM, the build-up method, presented in Chapter 1, is usually the best method for estimating an equity capitalization rate. To implement the build-up method, we will make four assumptions: 1. Risk-free rate. At the valuation date, 7.0%. 2. Equity risk premium. As discussed in Chapter 9, 5.0%.
498
Cost of Capital
3. Size premium. Tenth-decile size premium from SBBI Valuation Edition Yearbook, 5.33%. 4. Company-specific risk premium. The company is tiny compared with Morningstar’s tenth-decile New York Stock Exchange stocks. The company has high specific risk because of lack of stability of the customer base and economic vulnerability of its customer base due to conditions in the industry on which it is dependent. In addition, there is a key person issue: How easily could Kenny be replaced? Although this decision is quite subjective, it seems reasonable to add a specific risk factor of 5.0%. Adding up the pertinent factors gives us this discount rate: Risk-free rate 7.00% Equity risk premium 5.00% Size premium 5.33 Company-specific premium 5.00 Estimated KLM cost of equity (discount rate) 22.33% We then subtract the estimated growth rate from the discount rate to get the estimated capitalization rate: Discount rate 22:33% Estimated long-term growth rate 3:00 ¼ Estimated capitalization rate 19:33% A 13.5% asset-based capitalization rate certainly is significantly different from a 19.33% capitalization rate based on capital structure components. If we divided the $50,000 cash flow by the 13.5% asset-based capitalization rate, we would, of course, get the excess earnings method value of $370,000 (=$50,000 0.135). If we divided the $50,000 by the 19.33% build-up method capitalization rate, we would get an indicated value of $258,665 (=$50,000 0.1933). Which do you believe?
DISCUSSION OF THE EXAMPLE Considering the risks involved, it is unlikely that anyone would pay $170,000 for the blue sky (a colloquial term used loosely to refer to intangible assets) in KLM. Obviously, the capitalization rates for tangible assets and excess earnings used by Shoveler in his excess earnings exercise are considerably too low. Note that the asset appraisal assumes value in use. This is the value to an operating business, not a liquidation value. There appears to be plenty of risk associated with these tangible assets. Accordingly, one point over the risk-free rate is not nearly an adequate risk premium. Capitalizing excess earnings at 20% implies that a buyer will pay for five years of expected excess earnings (1 0.20 ¼ 5). Typically, buyers will pay that implied multiple only for a very stable customer base. The KLM customer base certainly is not stable. Obviously, this is an extreme example. Its purpose is merely to illustrate the mechanics of using cost of capital as a reasonableness check on an excess earnings method valuation. However, there have been worse abuses. There are even people who think that the 30-day U.S. Treasury bill rate is a satisfactory return rate of the tangible assets employed in a business. Watch out for such abuses!
Summary
499
VAGARIES OF THE EXCESS EARNINGS METHOD Revenue Ruling 68-609 is not very specific on many points, such as how income is defined. Definitions of income other than net cash flow may require some adjustment to the capitalization rate, as we illustrated its development. The many vagaries of the excess earnings method have been explored at great length and are beyond the scope of this book.4 The purpose here is simply to show the mechanics of demonstrating whether the weighted capitalization rate implied in an excess earnings valuation is within a reasonable range.
SUMMARY The excess earnings method uses two capitalization rates: 1. A required return on tangible assets 2. A rate at which to capitalize ‘‘excess earnings,’’ returns over and above amounts necessary to support the tangible assets in a business The position presented in this chapter is that the weighted average of these two rates (weighted at market value, of course) should be approximately equal to a company’s capitalization rate (developed as discussed in this book). This chapter has illustrated the mechanics of how to make such a comparison. To explore the many vagaries of implementing the excess earnings valuation method, readers are encouraged to avail themselves of the references listed in the notes.
4
See the preceding references plus ‘‘Practitioners Disagree Strongly on Excess Earnings Methodology,’’ Shannon Pratt’s Business Valuation Update1 (April 1997): 1–3. These references provide guidance on estimating rates of return on tangible and intangible assets, among other things.
Chapter 32
Adjusting the Discount Rate to Alternative Economic Measures Introduction Converting from Net Cash Flow to Another Economic Income Variable Converting from After-Tax Rate to Pretax Rate Converting After-Tax Capitalization Rate to Pretax Capitalization Rate Converting After-Tax Discount Rate to Pretax Discount Rate Summary
INTRODUCTION Throughout most of this book, we have focused on deriving a discount rate applicable to net cash flow. But sometimes analysts may desire to discount returns to some other economic income variable, such as net income. The key to a valid discount rate for any variable other than net cash flow is a fairly consistent relationship between that variable and net cash flow.
CONVERTING FROM NET CASH FLOW TO ANOTHER ECONOMIC INCOME VARIABLE The procedure is the same for converting a discount rate applicable to net cash flow to a discount rate applicable to net income or any other measure of economic income. The first step is to ascertain that there is a reasonably constant relationship over time between the income variable of interest and net cash flow. If that is not the case, then it is impossible to convert the discount rate applicable to net cash flow to a discount rate applicable to another income variable. Assuming there is a reasonably constant relationship, the next step is to quantify what that relationship is. To do that, we might observe the relationship over a period of five years or so. The analyst should be as sure as possible that the relationship over the period observed is likely to continue to be the same relationship over future periods. For example, say the relationship between net cash flow and net income was as shown over the last five years: Period
–1
–2
–3
–4
–5
NCF NI NCF/NI X
100 120 0.8333 0.8234
95 115 0.8261
90 112 0.8036
92 114 0.8070
80 95 0.8421
501
502
Cost of Capital
where: NCF ¼ Net cash flow NI ¼ Net income NCF X ¼ average relationship of NI This probably would be a consistent enough relationship to satisfy most people. If you thought that there was a trend, you might take a weighted average rather than a simple average. The next step would be to divide the discount rate applicable to net cash flow by the average relationship between net cash flow and net income. Using the most recent table, assuming a discount rate applicable to NCF of 0.15 the computation would be: (Formula 32.1) 0:15 ¼ 0:1824 0:8234 Thus the discount rate applicable to net income would be 18.24%. To convert to a capitalization rate applicable to net income, you would subtract the long-term expected growth rate for net income. The same procedure would apply for converting a weighted average cost of capital (WACC) to a discount rate applicable to earnings before interest and taxes (EBIT) or earnings before interest, taxes, depreciation, and amortization (EBITDA). And having solved for the discount rate applicable to EBIT or EBITDA, to get a capitalization rate for EBIT or EBITDA, you would have to subtract the expected long-term growth rate in EBIT or EBITDA. Remember, the validating of this assumes not only a constant relationship between WACC and EBIT or EBITDA, but also a constant capital structure over the future periods.
CONVERTING FROM AFTER-TAX RATE TO PRETAX RATE We have emphasized that the cash flows that we are capitalizing are after taxes. We can convert aftertax capitalization rates to pretax capitalization rates,1 and even to pretax discount rates, provided that we assume zero or constant growth. CONVERTING AFTER-TAX CAPITALIZATION RATE TO PRETAX CAPITALIZATION RATE To convert an after-tax capitalization rate to a pretax capitalization rate, the formula is: (Formula 32.2) c cð ptÞ ¼ 1t where: c ¼ Capitalization rate (on after-tax cash flows) cð ptÞ ¼ Capitalization rate on pretax cash flows t ¼ Tax rate 1
For an earlier exposition of this concept, see Mary Ann Lerch, ‘‘Pretax/Aftertax Conversion Formula for Capitalization Rates and Cash Flow Discount Rates,’’ Business Valuation Review (March 1990): 18–22.
Converting from After-Tax Rate to Pretax Rate
503
Assuming a tax rate of 30%, substituting in Formula 4.16, we have: (Formula 32.3) 0:10 0:10 ¼ ¼ 14:3% 1 0:30 0:70 But the result of Formula 32.3 is not a discount rate, unless the assumption is that there will be no growth. CONVERTING AFTER-TAX DISCOUNT RATE TO PRETAX DISCOUNT RATE Suppose that we arrived at the capitalization rate of 10% by starting with a discount rate of 15% and subtracting an estimated sustainable growth rate of 5% (0.15 0.05 = 0.10). We are not going to apply a discount rate of 14.3% to pretax cash flows! To get a discount rate applicable to pretax cash flows, we have to add the growth rate to the pretax capitalization rate. In this case, we have 14.3% + 5% = 19.3% as a discount rate for pretax cash flows. (Formula 32.4) kð ptÞ ¼ cð ptÞ þ g where: kð ptÞ ¼ Discount rate applicable to pretax cash flows cð ptÞ ¼ Capitalization rate applicable to pretax cash flows g ¼ Growth rate If we estimated the 10% capitalization rate on after-tax cash flows by estimating a 15% discount rate less a 5% growth rate, substituting in Formula 32.3, we have: (Formula 32.5) kð ptÞ ¼ 14:29 þ 5:00 ¼ 19:29 So this gives us a 19.29% discount rate applicable to pretax cash flows. If this is correct, discounting after-tax cash flows at 15% should derive the same answer as discounting pretax cash flows at 19.29%. To test this, we assumed for period 1 (the estimate for the pretax immediately following the valuation date), $10,000 in pretax cash flow and a 30% tax rate, resulting in $7,000 of after-tax cash flows. We tested the equivalency with a model consisting of two discrete forecast periods plus a terminal value. First, discounting the after-tax cash flows at 15%, we have Formula 32.6: (Formula 32.6) Terminal Value Period 1
Period 2
ðPeriod 3 and beyondÞ
$7;000 $7;000ð1:05Þ þ þ 1:15 ð1:15Þ2 $7;000 $7;352 ¼ þ 1:15 1:3225
$7;000ð1:05Þð1:05Þ 0:15 0:05 ð1:15Þ2
$7;350ð1:05Þ 0:10 þ 1:3225
504
Cost of Capital
$7;000 $7;352 ¼ þ 1:15 1:3225 $7;000 $7;352 þ ¼ 1:15 1:3225
$7;717:50 þ 0:10 1:3225 $77;175 þ 1:3225
ffi $6;086:96 þ $5;557:66 þ $58;355:39 ffi $70;000 For discounting the pretax cash flows at 19.29%, we have Formula 32.7: (Formula 32.7) Terminal Value Period 1 $10;000 1:1929
Period 2
þ
$10;000ð1:05Þ ð1:1929Þ2
$10;000 $10;500 ¼ þ 1:1929 1:4230 $10;000 $10;500 þ 1:1929 1:4230 $10;000 $10;500 ¼ þ 1:1929 1:4230 ffi $8;382:93 þ $7;378:78 ffi $69;979:45 ¼
ðPeriod 3 and beyondÞ $10;000ð1:05Þð1:05Þ 0:1929 0:05 þ ð1:1929Þ2 $10;500ð1:05Þ 0:1429 þ 1:4230 $11;025 þ 0:1429 1:4230 $77;151:85 þ 1:4230 þ $54;217:74
(The difference between this amount and $70,000 is due to rounding.)
SUMMARY To summarize, there are three steps in converting an after-tax discount rate to a pretax discount rate: Step 1. Convert the after-tax discount rate to an after-tax capitalization rate by subtracting the estimated growth rate. Step 2. Convert the after-tax capitalization rate to a pretax capitalization rate by dividing the aftertax capitalization rate by 1 minus the tax rate. Step 3. Convert the pretax capitalization rate to a pretax discount rate by adding the estimated growth rate to the pretax capitalization rate. The strict validity of this conversion is subject to two limiting assumptions: 1. The relationship between after-tax cash flows and pretax cash flows remains constant over time. 2. The growth rate is a long-term sustainable growth rate that remains constant over time.
Chapter 33
Estimating Net Cash Flows Introduction Net Cash Flow Equity Cash Flow Method Invested Capital Method Residual Income Method Adjusted Present Value Method Economic Value Added Method Financial Analysis of Historical Operating Results Revenue and Profitability Estimates Noncash Charges and Investments in Fixed Assets Investments in Net Working Capital Reasonableness of Estimated Profit Margins and Asset Turnovers Testing Net Cash Flow Estimates Estimating Alternative Net Cash Flows Common Errors in Estimating Net Cash Flows Summary Appendix 33A
INTRODUCTION In a recent survey of executives, approximately 50% of the respondents indicated their sales and cost forecasts were ‘‘too optimistic.’’1 According to the same survey, corporate-level respondents indicated that 17% of the capital invested by their companies went toward underperforming investments that should be terminated and that 16% of their investments were a mistake to be financed in the first place. Business unit heads and front-line manager respondents indicated that 21% of the investments should not have been approved and that another 21% should be terminated. As a result, the authors thought it would be useful to include guidance on this most important element of using any discounted cash flow (DCF) analysis: projecting the net cash flows. Valuation analysts are rarely in a position to produce credible projections independently. Rather, they can either act as facilitators to assist operating management in assembling projections or as testers of the projections prepared by operating management.
NET CASH FLOW As we discussed in Chapter 3, we are estimating net cash flows. In that chapter we presented formulations of net cash flow, which we revisit here. 1
McKinsey & Company, ‘‘How Companies Spend Their Money: A McKinsey Global Survey,’’ The McKinsey Quarterly, June 2, 2007. Survey conducted in April and May 2007. Responses: 2,507 executives from around the world: 26% corporate-level executives, 26% business unit or division leaders, 28% front-line managers.
505
506
Cost of Capital
EQUITY CASH FLOW METHOD In the equity cash flow method, the value of equity equals present value net cash to equity. The net cash flow to equity (NCFe ) is defined as: (Formula 33.1) Net income (after subtracting interest expense and income taxes) þNoncash charges (e.g., depreciation, amortization, deferred taxes) Capital expenditures ( the net changes in fixed and other noncurrent assets)* Changes in net working capital* þ Net changes in longterm debt* ¼ Net cash flow to equityy *
Assumes that the amounts are the levels necessary to support projected business operations. If there are preferred dividends, they would have to be subtracted.
y
In the cash flow to equity method, earnings (after interest expense and after income taxes) are adjusted for various items to produce net cash flow, including:
Noncash expenses that are subtracted from revenues but do not affect cash flow, including depreciation, amortization, depletion allowance, and in some cases changes in deferred taxes.
Amounts necessary to augment net working capital as levels of production increase. Net working capital does not include current portion of long-term debt, any other permanent invested capital financing of a short-term nature, or increases in cash above the level necessary to sustain the business.
Amounts invested in plant, property, and equipment to establish or maintain productive capacity in line with increases, or decreases, in revenues. Reflection of amounts to cover scheduled repayments of debt principal or additions to debt principal.
INVESTED CAPITAL METHOD In the invested capital method, the value of the invested capital equals the present value of the cash flows to invested capital (or the firm). The value of equity is the value of invested capital minus the market value of debt capital at the valuation date. The net cash flow to invested capital or net cash flow to the firm (NCF f ) is defined as: (Formula 33.2) Net income (after interest expense and income taxes) available to common shareholders þNoncash charges Capital expenditures* Changes in working capital* þInterest expense, net of the tax effect (interest expense [1 tax rate]) þPreferred dividends, if any ¼Net cash flow to overall invested capital *
Assumes that the amounts are the levels necessary to support projected business operations.
An alternative formula for net cash flow to invested capital is:
Net Cash Flow
507
(Formula 33.3) Earnings before interest and taxes Taxes on EBIT at effective tax rate (¼ earnings before interest, after tax) þNoncash charges Capital expenditures* Changes in working capital ¼Net cash flow to overall invested capital *Assumes that the amounts are the levels necessary to support projected business operations.
The earnings (before interest expense and after income tax) are adjusted for various items to produce net cash flow, including:
Noncash expenses that are subtracted from revenues but do not affect cash flow, including depreciation, amortization, depletion allowance, and in some cases changes in deferred taxes.
Amounts necessary to augment net working capital as levels of production increase. Net working capital does not include current portion of long-term debt, any other permanent invested capital financing of a short-term nature, or increases in cash above the level necessary to sustain the business. Amounts invested in plant, property, and equipment to establish or maintain productive capacity in line with increases, or decreases, in revenues.
Debt is not subtracted or added in the invested capital model since it is deducted at the conclusion of the process to derive the value of equity. RESIDUAL INCOME METHOD In the residual income method, the value of equity equals the book value of equity at the valuation date plus the present value of the expected residual income discounted at the cost of equity capital. Residual income is defined as the net income (after interest expense and after income taxes) minus the return on book value of equity (cost of equity capital times book value of equity). Residual income is defined as: (Formula 33.4) Net income (after subtracting interest expense and income taxes) Book value of equity ke (Cost of equity) ¼RI ¼ Residual income to equity* * If there are preferred dividends, they would have to be subtracted. Net income is not as reported; rather it is comprehensive income derived by using ‘‘clean samples’’ accounting (see Chapter 3).
ADJUSTED PRESENT VALUE METHOD In the adjusted present value method, the value of equity equals the present value of equity cash flows as if the firm were financed solely with equity capital plus the present value of the expected benefits to equity from financing part of the firm capital with debt (the present value of the tax shield). The net cash flow to unlevered equity (NCFue ) is defined as: (Formula 33.5) Earnings before interest and taxes Taxes on EBIT at effective tax rate (¼ earnings before interest, after tax)
508
Cost of Capital
þ ¼ *
Noncash charges Capital expenditures Changes in working capital* Preferred dividends, if any Net cash flow to unlevered equity (assuming the firm is financed only with equity)
Assumes that the amounts are the levels necessary to support projected business operations.
As in the cash flow to equity method, earnings (before interest expense, after income tax) are adjusted for various items to produce net cash flow, including:
Noncash expenses that are subtracted from revenues but do not affect cash flow, including depreciation, amortization, depletion allowance, and in some cases changes in deferred taxes. Amounts necessary to augment net working capital as levels of production increase. Net working capital does not include current portion of long-term debt, any other permanent invested capital financing of a short-term nature, or increases in cash above the level necessary to sustain the business. Amounts invested in plant, property, and equipment to establish or maintain productive capacity in line with increases, or decreases, in revenues.
Debt is not subtracted or added in the adjusted present value method since the present value of the net benefits and costs of debt are added to the present value of the cash flows to unlevered equity to derive the total value of equity. ECONOMIC VALUE ADDED METHOD In the economic value added (EVA) method, the value of the invested capital equals the book value of equity plus the book value of debt plus the present value of the economic value added. The economic value added equals the net income (before interest expense, after income taxes) multiplied by the weighted average cost of capital (WACC). The value of equity is determined by subtracting the value of debt from the value of invested capital. The formula for the annual economic value added is: (Formula 33.6) Earnings before interest and taxes Taxes on EBIT at effective tax rate (¼ earnings before interest, after tax) ¼ Net cash flow to overall invested capital WACC ¼ EVA While the various measures of economic income differ in format, they all are composed of similar elements and require comparable estimates of their future components: sales, operating expenses, noncash charges, investments in fixed assets (capital expenditures), and investments in net working capital.
FINANCIAL ANALYSIS OF HISTORICAL OPERATING RESULTS The first step is to analyze historic performance. You likely will find it helpful to begin by removing the effects of inflation from historical results:
Financial Analysis of Historical Operating Results
509
Determine a common unit of measure to determine (e.g., tons of paper, gallons of beer, thousands of courses taught, etc.). Calculate the real increase in prices and use that as a beginning point in any forecast. Determine the real increase in cost of goods sold (and the relationship to unit sales) and overhead expenses.
The goal of any historical analysis is not just to calculate ratios. Rather, it is to understand the relationships between the income statement and balance sheet elements both for the subject business and the guideline public companies to which you are comparing the subject business. One framework for understanding the relationship of value drivers is the DuPont analysis, a ratio analysis named for the firm that popularized the methodology. One variation expands that methodology and divides the firm into operating and financing activities to better understand the components of return on common equity.2 The basic analysis is accomplished by applying ‘‘clean-surplus’’ accounting (see Chapter 3 for a discussion) between operating and financing items (assets and liabilities on the balance sheet and income and expense on the income statement) to match net operating assets with operating income and net financial liabilities to net financial expense. Formula 33.4 shows the basic formula: (Formula 33.4) ROCE ¼ RNOA þ ½FLEV SPREAD where: ROCE ¼ Return on common equity RNOA ¼ Return on net operating assets FLEV ¼ Net financial obligations/(Net operating assets net financial obligations) (i.e., financial leverage) SPREAD ¼ RNOA Net borrowing costs [(financial expense financial income, after tax)/ (financial obligations financial assets)] RNOA can be broken down in the standard DuPont analysis as in the next formula: (Formula 33.5) RNOA ¼ ðOI=SalesÞ ðSales=OA OLÞ where: OI ¼ Operating income OA ¼ Operating assets OL ¼ Operating liabilities and other variables are as defined. The return on net operating assets can be further broken down to account for the leverage provided by operating liabilities. This leverage differs from financial leverage because it arises from operations:
2
Doron Nissim and Stephen H. Penman, ‘‘Ratio Analysis and Equity Valuation: From Research to Practice,’’ Review of Accounting Studies 6 (2001): 109–154.
510
Cost of Capital
(Formula 33.6)
ðOI þ ioÞ OA io OL RNOA ¼ OA ðOA OLÞ OL ðOA OLÞ where: io ¼ Implicit interest charges on operating liabilities (other than deferred taxes) and other variables are as defined above. While operating liabilities (accounts payable and accrued expenses) may look ‘‘free,’’ suppliers presumably charge for the credit in terms of higher prices. You can estimate the implicit interest on operating liabilities, io, using a short-term borrowing rate. Understanding seasonality is an important issue in studying historical results and extrapolating current year growth. It is helpful to lay out monthly/quarterly volume sales and dollar sales for each of the prior several years to understand the seasonal pattern.
REVENUE AND PROFITABILITY ESTIMATES A good beginning point is the estimation of the real growth in volume and the real growth in prices. The simplest and least reliable method is simply to extrapolate the rate of historical volume growth. A better method is to look to the real growth in an underlying series that is driving real unit growth (e.g., population growth in general or growth in population of a certain age group that most uses the company’s products, real gross domestic product growth, real growth in the number of car registrations, etc.) and tie volume growth for the subject business to projections of real growth of that underlying series. This type of analysis requires research about the industry and the underlying series driving subject company real growth. What has been the change in real prices? Will that trend continue? You then can develop estimated inflation from services that report on expected inflation forecasts of economists (e.g., Blue Chip Economic Indicators) or derive expected inflation from the term structure of zero-coupon government debt instruments. Multiplying expected real volume times expected real growth in prices times expected inflation in prices grounds the sales forecast in reality. Ideally this sort of analysis should be performed by (major) customer, by (major) product line, or by business unit. More sophisticated time-series models take into account both the level of revenues and the trend of revenues (e.g., Holt’s two-parameter exponential smoothing model, or Winter’s additive and multiplicative smoothing methods3). Operating expenses (excluding depreciation and amortization) should be divided into fixed and variable, and the historical relationships of real expense growth compared to real revenue growth should form the basis for future projections. Fixed operating expenses are rarely fixed in the long run. Most often they move up in step fashion as the business grows. It is useful to understand estimated capacity utilization of existing production and distribution facilities to better understand how much more volume a company can handle before its fixed operating expenses move up to the next step. 3
Lon-Mu Liu, Time Series Analysis and Forecasting, 2nd ed. (Villa Park, IL: Scientific Computing Associates Corp., 2006).
Noncash Charges and Investments in Fixed Assets
511
Regressing historical variable operating expenses account by account against revenues is a useful tool to understand the sensitivity of one to the other. Often some categories of operating expenses that on the surface appear variable in fact are more semi fixed than variable. Variable operating expenses should likewise be projected based on real volume growth times real cost growth times expected inflation whenever possible.
NONCASH CHARGES AND INVESTMENTS IN FIXED ASSETS Investment in fixed assets usually does not increase in lockstep with increases in sales (though often that is the simplifying assumption). As volume increases, some increase in fixed asset investment typically is required. But where a firm recently has added capacity to production or distribution facilities, major increases in fixed assets may not be required for some period of time. It is useful to understand estimated capacity utilization of existing production and distribution facilities to better understand how much more volume can a company handle before making its next major investment in fixed assets. You then estimate the percentage of new capital investments that will be land (nondepreciable), buildings and improvements and equipment. Often the historical relationships of the gross investment in these asset categories can serve as a guideline for the expected percentage of each type of asset in future periods. The best way to estimate future depreciation and amortization is to develop depreciation lapsing schedules. We are interested in cash flows. Cash taxes are impacted by tax depreciation. Estimating future depreciation and amortization begins with the income tax returns and constructing estimated lapsing schedules (i.e., how depreciation and amortization will run out over their remaining depreciation periods until they have zero remaining balance) for the existing investments in fixed and (amortizable for income tax purposes) intangible assets. Depreciation for future years is a combination of the lapsing schedules for depreciation and amortization of existing fixed and intangible assets and lapsing schedules for depreciation of future estimated investments in fixed assets. One common assumption made in the terminal value estimate is to equate capital expenditures with depreciation in the net cash flow. Generally if the net cash flows are expected to grow in future years, this is an erroneous assumption.4 You will get the correct relationship by estimating growth in capital expenditures and then calculating the estimated depreciation using lapsing schedules. Another problem can develop when a large capital expenditure that significantly expands volume is expected to occur say two years prior to the terminal value calculation and the projected depreciation then exceeds the more normalized level of capital expenditure in the year just prior to the terminal value calculation. You should then extend the period of the direct cash flow forecast until depreciation and capital expenditures reach a more normalized equilibrium amounts. There is no hard and fast rule as to the number of years to forecast annual net cash flows before capitalizing net cash flows thereafter in a terminal value calculation. The guidance is to estimate individual-year cash flows until the growth rates for two consecutive years for all of the components of the net cash flows reach normalized long-term relationships.
4
See, e.g., Brant H. Armentrout, ‘‘A Sanity Test When Estimating Capital Expenditures in Excess of Depreciation,’’ Business Valuation Review (September 2003): 136–141; Gilbert Mathews, ‘‘CAPX ¼ Depreciation Is Unrealistic Assumption for Most Terminal Values,’’ BV Update (March 2002): 1–3; Dan McConaughy and Lorena Bordi, ‘‘The Long-Term Relationships between Capital Expenditures and Depreciation across Industries: Important Data for Capitalized Income Based Valuation,’’ Business Valuation Review (March 2004): 14–18.
512
Cost of Capital
INVESTMENTS IN NET WORKING CAPITAL Many analysts erroneously assume that the cash balances as of the valuation can be added dollar for dollar to the present value of future cash flows (or used to reduce outstanding debt); such an analysis is equivalent to assuming that all cash is surplus. Companies need some level of cash to operate. Assuming one can strip all cash from the company may change the risk characteristics of the firm. For smaller, risky companies, cash can serve as a value-preserving buffer against downturns, as well as a means of funding investment opportunities at less cost than raising new capital.5 The analysis of the minimum level of cash needed requires an analysis of the cyclicality of the business and the variability of cash operating profits, as well as the availability and cost of funds to finance research and development and fixed assets. The most reliable way to estimate investments in net working capital is to tie estimates of inventory investment and inventory turns to estimates of sales growth, estimates of accounts payable and accrued expenses to inventory and sales growth, flow the sales estimates into estimates of accounts receivable, and ultimately cash collections based on estimates of days receivables outstanding. Estimating net working capital investment in a seasonal business can be particularly difficult. We recommend getting quarterly/monthly historical balances of cash, accounts receivable, inventory, accounts payable, and accrued expenses as well as sales for the prior two years to better understand the flow of working capital as the company moves through the seasons.
REASONABLENESS OF ESTIMATED PROFIT MARGINS AND ASSET TURNOVERS When you discover that the subject company has been or is expected to perform better than the guideline public companies, is there any evidence that such differences can be sustained, or will such superior performance revert to an industry average? In one study, the author decomposes the return on net operating assets into profit margin and operating asset turnover (see Formula 33.2).6 He finds that decomposing return on net operating assets within an industry is a useful tool in forecasting changes in return on net assets. He finds that firms with higher-than-average net operating asset turnover (compared to the industry average) are more likely to continue with that higher-than-average net operating asset turnover and that firms with higher-than-average operating profit margins are more likely to revert to the mean operating profit margins. In another study, the author examines the life cycle of a typical firm and the tendency and speed to mean reversion of return on net assets based on the stage in a firm’s life cycle.7 The five life cycles are: 1. 2. 3. 4. 5.
5
6 7
Introductory stage (innovation is first produced) Growth stage (number of producers increases dramatically) Maturity stage (number of producers reaches maximum) Shakeout stage (number of producers begins to decline) Decline stage (nearly no new producers)
Lee Pinkowitz and Rohan Williamson, ‘‘What is the Market Value of a Dollar of Corporate Cash?’’ Journal of Applied Corporate Finance (Summer 2007): 74–81. Mark T. Soliman, ‘‘Using Industry-Adjusted DuPont Analysis to Predict Future Profitability,’’ Working paper, February 2004. Victoria Dickinson, ‘‘Future Profitability and the Role of Firm Life Cycle,’’ Working paper, September 2006.
Testing Net Cash Flow Estimates
513
TESTING NET CASH FLOW ESTIMATES An analyst often is required to test estimates provided by operating management for their reasonableness. One important first step is to go through the steps just outlined and see what relationships are embedded in management’s estimates. Make sure to get detailed textual descriptions of the underlying assumptions for each line item. If you discover discrepancies between the text and the spreadsheet extrapolations built using those assumptions, start by investigating whether there are mechanical errors in the spreadsheet. Such errors are more common than you would expect. Another method is to compare management’s past forecasts with historical results. First, determine the reason for management’s forecasts. Do the forecasts represent goals for operating management to aspire to, or are they realistic estimates of likely results? If aspirational, then you must be prepared to work to recast those forecasts into expected forecasts. You know that forecasts will be wrong, especially as the length of time from the forecasting date increases. But the near-term portion of the forecast can be compared with results for the first few years to determine whether management is prone to bias its estimates high or low. The most common basis used by business to prepare future estimates of revenues, expenses, and cash flows is to make those estimates only for the existing business. The resulting net cash flow estimates assume retention of sufficient cash to fund capital expenditures necessary to generate the expected future revenues. The net cash flows resulting from the estimates of revenues and the like are available to distribute to shareholders or available to reinvest in new business ventures. If the company chooses to reinvest its available net cash flow as opposed to distributing it, the net present value of the net cash flows during that discrete period are reduced accordingly. However, the terminal value would increase assuming the company earns an incremental rate of return on the net cash flows employed for new business ventures. Historical revenues and net cash flows include both the results from then-existing businesses plus the revenues and net cash flows that resulted from new investments made in prior years. For example, assume you were to compare business plans prepared at the beginning of year 2000, 2001, and 2002 with the actual results for those years. The typical business plan prepared at the beginning of year 2000 included the expected revenues and net cash flows for the business as it existed at that time. But the actual results for 2000 and 2001 include the historical results for the then-existing business at the beginning of year 2000 plus the historical results of new business opportunities entered into during year 2000 and 2001. Those new business opportunities typically result from reinvestment of cash retained in excess of those amounts needed to fund capital expenditures and investments in net working capital for the existing business plan. While the typical business plan does not directly include the increased revenues, expenses, and net cash flows resulting from the reinvestment of the net cash retained, that retained cash adds value to the firm. To test future estimates of revenues and net cash flows based on a comparison to historical revenues and net cash flows, you must make some assumption as to the expected returns from expected reinvestments of future retained cash in business ventures other than the subject company. The examples in Exhibits 33.1 and 33.2 help explain the theory embedded in the valuation methodology due to this cash retention. The net cash flows in this example are assumed to be distributed in the year created. Assume the firm in this example retains all net cash flows and reinvests the retained net cash flows in new investments expected to earn the cost of capital. What exactly is the economic assumption underlying this discounted cash flow result if the owners are receiving no dividends? The capital expenditures (line 13, Exhibit 33.1) are sufficient to allow the business to generate net cash flows. Because the corporation is retaining the net cash flows and reinvesting this amount, the result of the
514
Cost of Capital
Exhibit 33.1
Value Based on Present Value of Net Cash Flows
Assumptions
(1) (2) (3) (4) (5) (6)
Growth rate Pretax margin Depreciation as a % of sales Reinvestment rate Net working capital as a % of sales Rate of return on equity
5.0% 12.5% 4.0% 150.0% 10.0% 15.0%
Projected Fiscal Year 1 (7) (8) (9) (10) (11) (12) (13)
Revenue Income before tax Entity level tax rate Entity level tax Net income Depreciation Capital expenditures
Networking capital (increase)/decrease Net cash flow Present value factor Discounted net cash flows Sum of discounted net cash (18) flows (19) PV Terminal Value (20) Indicated value
(14) (15) (16) (17)
ð2Þ ð7Þ ð8Þ ð9Þ ð8Þ ð10Þ ð3Þ ð7Þ ð4Þ ð12Þ ð5Þ Dð7Þ Sð11Þ to ð14Þ 15.0% ð15Þ ð16Þ Sð17Þ ð18Þ þ ð19Þ
2
Terminal
3
4
Value
$5,000,000 $5,250,000 $5,512,500 $5,788,125 $6,077,531 625,000 656,250 689,063 723,516 759,691 40.0% 40.0% 40.0% 40.0% 40.0% (250,000) (262,500) (275,625) (289,406) (303,877) 375,000 393,750 413,438 434,109 455,815 200,000 210,000 220,500 231,525 243,101 (300,000) (315,000) (330,750) (347,288) (364,652) (23,810) 251,190 0.8696 $218,427 766,207 1,745,843 $2,511,050
(25,000) 263,750 0.7561 $199,433
(26,250) 276,938 0.6575 $182,091
(27,563) 290,784 0.5718 $166,257
(28,941) 305,324
Terminal Value: Capitalization rate Terminal value Present value factor @ 15% Present value
10.0% 3,053,240 0.5718 $1,745,843
reinvestment must be an increased expected terminal value and reduced values during the discrete projection period, i.e., years 1 through 4. In these examples, we have assumed that the cost of capital is 15%. Assume that the controlling owners and management are rational and reinvest these retained amounts to earn that same 15%. Exhibit 33.2 displays the cumulative effect of retaining net cash flows. The expected terminal value from the business without this reinvestment equals $3,053,240 (present value equal to $1,745,843). The additional terminal value due to retention of the net cash flows during years 1 through 4 equals $1,340,101 (from Exhibit 33.2). The present value of the additional terminal value due to retention of the net cash flows during years 1 through 4 equals $766,207 (Exhibit 33.2), which exactly equals the present value of the net cash flows for those same years (line 18, Exhibit 33.1). The reduction in the present value from the reduced net cash flows in years 1 through 4 exactly equals the increase in terminal value at the end of year 4. We see from this analysis that the underlying methodology of the discounted cash flow equates the value of the net cash flow as distributed to the owners or as retained by the corporation and reinvested by the corporation at the discount rate. The owners are assumed to be indifferent between
Testing Net Cash Flow Estimates Exhibit 33.2
515
Value Added Due to Reinvestment of Net Cash Flows Year 1
Net cash flow (NCF) Reinvestment at 15%
2
Line 15, Exhibit 33.1 $251,190 $263,750 Year 1 NCF 251,190 288,869 Year 2 NCF 263,750 Year 3 NCF Year 4 NCF Additional Terminal Value due to retention and reinvestment of free cash flow Present value factor @ 15% at 4 years Present Value of reinvested net cash flow (equals line 18 of Exhibit 33.1)
3
4
$276,938 332,199 303,313 276,938
$290,784 382,029 348,809 318,478 290,784 $1,340,101 0.571 $766,207
receiving current distributions and having the corporation retain the cash and reinvest that cash in new business opportunities because the owners will realize an identical value. While that is the theory, this situation points to a basic difference between public corporations and closely held corporations. If a public corporation retains net cash flows rather than declaring dividends, theoretically the price of the stock should rise. An owner desiring a current return can create a ‘‘homemade’’ dividend by selling some stock and capturing the appreciated value.8 If management of the public corporation pursues policies that are contrary to shareholder interests (e.g., reinvesting cash at a rate of return lower than the owners’ discount rate, shifting benefits to management and/or controlling owners by paying exorbitant compensation), shareholders will sell their holdings. Widespread selling will decrease the public corporation stock price. In situations where management owns only a small percentage of the corporation stock, such a downward pressure on stock price will expose management to removal. In such situations, commentators have argued that publicly held corporation management’s self-interest would independently restrain poor dividend decisions.9 The ability to create homemade dividends and create pressure on management through selling of shares is premised on the existence of a functioning market for the stock. But in a closely held entity (e.g., an S corporation, typical limited partnership, etc.), these market protections are inapplicable. Such closely held entities, by definition, lack a market for the interests.10 As such, minority investors in a closely held entity can rarely fully capture the theoretic appreciation in the value of their shares. Willing buyers (at least those unrelated to existing owners) typically are scarce. Absent sale of the entire business (control of which is in the hands of the controlling owners only), owner liquidity, in fact, may be realized only through distributions from the entity itself. Sometimes the documents creating the entity (e.g., articles of incorporation or by-laws) and/or agreement among the owners (e.g., shareholders agreement) provide for some level of distributions (in excess of the income taxes owed by the owners as a result of the pass-through entity status) and/or some sort of a ‘‘market mechanism’’ to be created by the entity or controlling owner(s). Absent such distributions or mechanism, the minority owner generally is at the mercy of the controlling owner(s) to create a liquidity event. 8 9 10
Daniel R. Fischel, ‘‘The Law and Economics of Dividend Policy,’’ Virginia Law Review (May 1981): 702, note 2. Ibid., notes 81–84 and accompanying text. Donahue v. Rodd Electrotype, 328 N.E.2d 505, 514 (Massachusetts 1975) (‘‘In a large public corporation, the oppressed of dissident minority stockholder could sell his stock in order to extricate some of his invested capital. By definition, this market is not available for shares in the closed corporation.’’ note 33).
516
Cost of Capital
Exhibit 33.3
Value Based on Present Value of Reinvestment of Net Cash Flows
Assumptions (1) (2) (3) (4) (5) (6)
Growth rate Pretax margin Depreciation as a % of sales Reinvestment rate Net working capital as a % of sales Rate of return on equity
(7) (8) (9) (10)
Revenue Income before tax Entity income tax rate Entity level tax
(11) (12) (13)
Net income Depreciation Capital expenditures Net working capital (increase)/decrease
(14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24)
Free cash flow Cash retained beyond capital expenditures Cash distributions Present value factor Discounted distributions Sum of discounted distributions PV terminal value of future distributions Sum of discounted cash retained and reinvested PV of added terminal value due to cash retained Indicated value (marketable, 100%)
5.0% 12.5% 4.0% 150.0% 10.0% 15.0% 1
2
3
4
ð 8Þ ð 9Þ
$5,000,000 625,000 40.0% (250,000)
$5,250,000 656,250 40.0% (262,500)
$5,512,500 689,063 40.0% (275,625)
$5,788,125 723,516 40.0% (289,406)
$6,077,531 759,691 40.0% (303,877)
ð8Þ ð10Þ ð3Þ ð7Þ ð4Þ ð12Þ
375,000 200,000 (300,000)
393,750 210,000 (315,000)
413,438 220,500 (330,750)
434,109 231,525 (347,288)
455,815 243,101 (364,652)
ð5Þ Dð7Þ
(23,810)
(25,000)
(26,250)
(27,563)
(28,941)
Sð11Þ to ð14Þ
251,190
263,750
276,938
290,784
305,324
(251,190) 0.8696 $
(263,750) 0.7561 $
(276,938) 0.6575
(290,784) 0.5718 $
(305,324)
ð 2 Þ ð 7Þ
ð17Þ ð15Þ Zero 15.0% ð17Þ ð18Þ Sð19Þ
$
ð22Þ þ ð23Þ
766,207 1,745,843 $ 2,512,050
$
Terminal Value:
Sð16Þ ð18Þ
Terminal Value
Capitalization rate Terminal value Present value Factor @ 15% Present value
10.0% 3,053,240 0.5718 $1,745,843
Exhibit 33.3 is the value of the business where we valued the retained net cash flow in excess of the capital expenditures sufficient to generate the projected net cash flow from the existing business investment. The exhibit displays the additional terminal value resulting from reinvestment of the net cash flow retained during projection years 1 through 4 ($1,340,101 from Exhibit 33.2). The present value of that added terminal value equals $766,207, the sum of the present value of the cash retained.
ESTIMATING ALTERNATIVE NET CASH FLOWS Because we are looking to estimate expected net cash flows, it is useful to project net cash flows under various scenarios. Some theoreticians recommend using Monte Carlo simulation techniques. But such techniques are simply a tool. You can assemble more limited scenarios and use such scenarios as tools to transmit information to both operating and executive management as well as serve as a basis for a better valuation. Such scenarios are particularly useful alongside option valuation methods in capital budgeting, valuation of start-up companies, and valuation of companies in distress.
Summary
517
Appendix 31A presents an example of valuing a firm in financial distress using both a scenario analysis of the DCF method and an option pricing model.
COMMON ERRORS IN ESTIMATING NET CASH FLOWS Some of the more common errors are:
Unsupported assumptions Sales growth not supported by industry analysis Company lacks the ability to reach projections with available capital or organization structure
Significant sales growth projected without commensurate investments in fixed assets and net working capital All operating costs assumed to be variable with no supporting analysis
Income tax projections that either ignore the impact of net loss carryforwards or that do not adjust income taxes for loss carryforwards only for the future periods until existing loss carryforwards are used up. Valuing the enterprise using the WACC and failing to take into account how interest or debt financing will stretch out the periods over which loss carryforwards will reduce income taxes (interest payments imbedded in the cost of debt capital in the WACC reduce taxable income, stretching out the periods over which loss carryforwards are used) Long-term growth in terminal value unreasonably high, unsupported by analysis of volume
Capital expenditures made equal to depreciation in terminal value calculation
No balance sheet projected to check relationships among working capital accounts Balance sheet is increased by the net cash flow in the DCF forecast even though the underlying assumption and premise of value is the distribution of that net cash flow. It is informative to see that courts increasingly scrutinize projections and will even adjust the projections of the experts in arriving at the concluded value.11
SUMMARY We have shown that five cash flow methods that are discussed regularly in the literature provide consistent results provided consistent assumptions are employed. Because the weights of the capital structure components must be at market values, the process of determining the value of equity capital (independent of any market value) and computing the WACC is an iterative one, starting with approximations of market value weights of capital structure components. Under some circumstances (e.g., a minority interest valuation), a company’s actual (currently existing) capital structure may be used to estimate the WACC. If a controlling interest valuation is sought where it is reasonable to alter the company’s capital structure, a hypothetical capital structure may be used to estimate the WACC. There is much controversy about the potential impact that altering the capital structure has on the WACC. The assumption of a single WACC to discount each increment of expected cash flow implies a constant capital structure over time. If the capital structure varies significantly over time, using a constant WACC will likely result in the wrong value of the company or project. 11
See, for example, Legal & Court Case Update, ‘‘Delaware Chancery’s Preference for DCF Turns on Credible Projections,’’ and ‘‘Inconsistent DCF Analysis Fails to Stop Merger of Lear Corp,’’ Business Valuation Update (September 2007): 7–12.
Appendix 33A
Estimating the Value of a Firm in Financial Distress Introduction Potential Future Value Discounted Cash Flow Method Using Scenarios Option Method Relationship of Value of Call Option to Independent Variables Probability that FMVBE Exceeds Face Value of Debt Discounted Cash Flow Method Using Scenarios Option Method Other Considerations Summary
INTRODUCTION Net cash flows (and the resulting value of a business) in any one future given year are unknown with certainty but follow a probability distribution. Less risky net cash flows (businesses) have a ‘‘tighter’’ distribution, while more risky net cash flows (businesses) have a ‘‘wider’’ distribution. Standard application of the discounted cash flow (DCF) method is based upon expected net cash flows to estimate the value of a business. An expected net cash flow is the probability weighted net cash flow of the entire distribution of possible net cash flows. But assume that we are valuing a firm in financial distress where the value of the equity (measured as the present value of expected net cash flows to equity capital) appears to be less than the value of the debt based on the face value of the debt. Should anyone be willing to pay anything to acquire the equity? In essence, will the future value of equity possibly exceed the face value of debt? In estimating (1) the value of the possibility that the value of the business enterprise will exceed the face value of debt at some future point in time and (2) the probability that this will occur at some future point in time, you are explicitly considering the right ‘‘tail’’ of the probability distribution of net cash flows (i.e., the probability that net cash flows will be greater than the mean, X).
Thanks to Joanne Fong, Deloitte Financial Advisory Services, LLP, and Christopher Bordener, Duff & Phelps, LLC, for assistance in preparing this chapter.
518
Potential Future Value
519
POTENTIAL FUTURE VALUE Black and Scholes1 note that all ownership claims, such as common stock, corporate bonds, and warrants, can be viewed as combinations of simple option contracts. For example, equity holders own the equivalent of an option to buy the assets of the company, given that they repay the debt holders. In other words, the value of equity can be viewed as the value of a call option on the assets, with an exercise price equal to the face value of debt. Debt holders, however, have the risk-free right to receive the return of their loaned monies minus the value of default risk. In other words, the value of debt can be viewed as a risk-free bond minus the value of a put option on the assets. The value of equity as a call option is the price a hypothetical buyer would pay for the possibility that the fair market value of the business enterprise will exceed the face value of debt over a specified future horizon. This can be depicted as follows: FAIR MARKET VALUE Assets ¼ Liabilities þ Equity Assets Assets ¼
Debt Equity Business Enterprise
¼ Risk-Free Bond Put Option ¼ Call Option ¼ Underlying Assets
We present a DCF analysis based on a probability distribution of risky future cash flows and an options approach to valuing equity based on unlevered, observed equity volatilities of guideline public companies. Both methods directly estimate the value of equity as a call option. DISCOUNTED CASH FLOW METHOD USING SCENARIOS In the standard application of the DCF method applied to invested capital, you estimate the fair market value of equity based on the present value of expected (i.e., probability-weighted net cash flows to invested capital minus the face value debt). This application provides an estimate of the liquidating value of equity as of the valuation date. In the case where the fair market value of the business enterprise is less than the face value of debt, zero value is ascribed to the fair market value of equity for the possibility that the business enterprise may exceed the face value of debt in the future. Adopting the standard DCF method using scenarios, though, we can use a one-step binomial model (on the premise of no arbitrage) to value the possibility that the fair market value will exceed the face value of debt (i.e., we can estimate the value of equity as a call option). The fair market value of equity is determined based on a hypothetical construction of a risk-free portfolio at time 0 consisting of owning some percentage (p, expressed as a decimal; e.g., 15% ¼ .15) of the business enterprise (BE) and shorting the equity. As the constructed portfolio is risk-free, the liquidating payoff at time n is the same in the ‘‘up’’ scenario and the ‘‘down’’ scenario. Additionally, the value of the risk-free portfolio at time 0 is equal to the present value of the liquidating payoff at time n discounting at the risk-free rate.
1
Fischer Black and Myron Scholes, ‘‘The Pricing of Options and Corporate Liabilities,’’ Journal of Political Economy (May 1973): 637–654.
520
Cost of Capital
The DCF analysis indicates the fair market value of equity at time 0 based on a probability distribution of risky cash flows that a business can be expected to generate in the future. Our application of the DCF method is comprised of six steps:
FMV of Risk Portfolio
p FMVBE ;0 þ minus: FMVe;0
Liquidating Payoff p FMVBE;n;up minus: FMVe;n;up p FMVBE;n;down minus: FMVe;n;down
where: p ¼ percentage owned of business enterprise FMVBE;0 ¼ Fair Market Value of business enterprise at valuation date FMVe;0 ¼ Fair Market Value of equity at valuation date FMVBE;n;up ¼ Fair Market Value of business enterprise at time ¼ n assuming ‘‘up’’ scenario (value of BE increases) FMVe;n;up ¼ Fair Market Value of equity at time ¼ n assuming ‘‘up’’ scenario (value of BE increases) FMVBE;n;down ¼ Fair Market Value of business enterprise at time ¼ n assuming ‘‘down’’ scenario (value of BE decreases) FMVe;n;down ¼ Fair Market Value of equity at time ¼ n assuming ‘‘down’’ scenario (value of BE decreases)
Steps for Time n 1. Discount the expected ‘‘up’’ (‘‘down’’) future net cash flows to time n value at a rate of return that considers the relative risk of achieving the cash flows and the time value of money. This will provide indications of FMVBE;n;up and FMVBE;n;down . 2. FMVBE;n;up ðFMVBE;n;down Þ less the face value of debt (Fd) equals FMVe;n;up (FMVe;n;down ). 3. Solve for p, the liquidating payoff, which is the same in the ‘‘up’’ and ‘‘down’’ scenario, under our premise of no arbitrage, p FMVBE;n;up FMVe;n;up ¼ p FMVBE;n;down FMVe;n;down .
Steps for Time 0 4. Discount the expected future cash flows to present value at a rate of return that considers the relative risk of achieving the cash flows and the time value of money. This will provide an indication of FMVBE;0 . 5. Discount the liquidating payoff to present value at the risk-free rate. This will provide an indicated value of the riskless portfolio. 6. p FMVBE;0 minus the value of the riskless portfolio equals FMVe;0 .
Potential Future Value
521
Exhibit 33A.1 Valuation of Firm in Financial Distress Value of Possibility that FMVBE;n Exceeds Fd Discounted Cash Flow Method Dollars in Thousands Probability
1 <20% 20–80% >80%
20% 60% 20% Expected Net Cash Flows, X
Net Cash Flows for Projection Year n 2 3 4 5
Terminal Value
$86 $62 $38
$95 $71 $47
$106 $82 $58
$118 $94 $70
$132 $108 $84
$1,137 $931 $725
$62
$71
$82
$94
$108
$931
Other Assumptions WACC (midyear convention used in calculating PV Factors) Long-Term Growth Rate Rf Fd
15.0% 3.0% 5.0% $ 1,000
Expected Net Cash Flows for Projection Year n 1
2
3
4
5
Expected Net Cash Flows PV Factor Present Value of Net Cash Flows
$62 0.9325 $58
$71 0.8109 $58
$82 0.7051 $58
$94 0.6131 $58
$108 0.5332 $58
Sum of Present Value of Net Cash Flows Minus: Debt Fd Indicated FMVe,0
$785 $1,000 $0
STANDARD DCF METHOD
Terminal Value $931 0.5332 $496
RESULTS OF SCENARIO ANALYSIS AND BINOMIAL OPTION MODEL Projection Year n 1
2
3
4
5
FMVBE,n,up (i.e., 20%) FMVBE,n,down (i.e., 80%) FMVe,n,up (i.e., 20%) FMVe,n,down (i.e., 80%) p FMVBE,0 p FMVBE;0 Riskless Portfolio0 ð p FMVBE;0 FMVe;0 Þ
$1,036 $787 $36 $0 $0 $785 $115
$1,090 $835 $90 $0 $0 $785 $276
$1,139 $878 $139 $0 $1 $785 $419
$1,184 $915 $184 $0 $1 $785 $538
$1,219 $943 $219 $0 $1 S785 $623
$109
$266
$404
$513
$582
FMVe,0 % of FMVBE,0
$5 1%
$11 1%
$16 2%
$25 3%
$40 5%
See Exhibit 33A.1 for an example, under the discounted cash flow method, on valuing the possibility that the business enterprise will exceed the face value of debt at some future point in time. From the example, the FMVBE;0 is directly correlated with time, and is approximately 1% of expected FMVBE;0 assuming a 2-year horizon (i.e., n ¼ 2).
522
Cost of Capital
OPTION METHOD Using the Black-Scholes option pricing model,2 we can estimate the fair market value of equity as a call option using estimated volatilities drawn from guideline public company data based on a few input assumptions. The basic Black-Scholes call option pricing model is: (Formula 33A.1) R ðniÞ
FMVe;0 ¼ FMVBE;0 Nðd1 Þ Fd f
Nðd2 Þ
where: FMVBE;0 ¼ Fair market value of business enterprise value at time 0 N (*) ¼ Cumulative normal density function log
d1 ¼
FMVBE;0 Fd
þðR f þ12 s 2 ÞðniÞ pffiffiffiffiffiffi s ni
log
¼
FMVBE;0 Fd
þR f ðniÞ pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi þ 12 s n i s ni
Fd ¼ Face value of outstanding debt Rf ¼ Risk-free rate n i ¼ Time to maturity of debt or time to a liquidating event from period i to period n s ¼ Standard deviation of the value of the business enterprise pffiffiffiffiffiffiffiffiffiffi d 2 ¼ d1 s n i The option method indicates the fair market value of equity at time 0 based on unlevered, observed equity volatilities of guideline public companies (used as proxy for the subject company). Our application of the option method is comprised of two steps: 1. Gather estimates for FMVBE;0, n, s, and Rf. An estimate of s can be observed from guideline public companies. 2. Using the Black-Scholes option pricing model, calculate FMVe;0 . See Exhibit 33A.2 for an example of an analysis using Formula 33A.1, under the option method, on valuing the possibility that the business enterprise will exceed the face value of debt at some future point in time. From the example, the FMVe;0 is directly correlated with time and is approximately 1% of FMVBE;0 assuming a 2-year horizon (i.e., n ¼ 2). RELATIONSHIP OF VALUE OF CALL OPTION TO INDEPENDENT VARIABLES In Exhibit 33.A.3, Line A represents the intrinsic value (or payoff) from a call option at time n. When the FMVBE is less than the face value of debt (i.e., FMVBE < Fd ), the equity holder will let the option expire worthless (i.e., default on the debt). When the FMVBE is greater than the face value of debt (i.e., FMVBE > Fd ), the equity holder will exercise the option (i.e., repay the debt holders and own the assets). Exhibit 33.A.3 also illustrates the value of a call option in relation to its intrinsic value. Viewing equity as a call option is more significant when the FMVBE is approximately equal to the face value of debt. When near the money, the value of a call option is the most above intrinsic value. When deep out of the money or deep in the money, the value of a call option is closer to intrinsic value. 2
Ibid.
Probability that FMVBE Exceeds Face Value of Debt Exhibit 33A.2
523
Analysis Using Black-Scholes Call Option Pricing Model
Assumptions FMVBE,0 Fd ¼ Face Value of Debt s ¼ Standard Deviation R f ¼ Risk-Free Rate
$ 785 $ 1,000 10.0% 5.0%
RESULTS OF ANALYSIS
Projection Year ni
d1 d2 FMVe,0 % of FMVBE,0
1
2
3
4
5
1:867 1:967 $1 0%
0:931 1:072 $10 1%
0:443 0:616 $27 3%
0:108 0:308 $49 6%
0.149 0:074 $73 9%
PROBABILITY THAT FMVBE EXCEEDS FACE VALUE OF DEBT Although the FMVBE may be less than the face value of debt today, there is some probability that the FMVBE will exceed the face value of debt over a specified future horizon. Based on statistical theory, we present a method based on a probability distribution of risky future net cash flows (DCF method) and a method based on a probability distribution of observed volatilities of market values of stocks of guideline public companies (option method).
DISCOUNTED CASH FLOW METHOD USING SCENARIOS Continuing with the earlier DCF example, assume that the risky future net cash flows follow a normal distribution, which can be described by its mean and standard deviation.
Payoff Value of Option
X
Exhibit 33A.3 Value of a Call Option
Business Enterprise Value
524
Cost of Capital
The DCF indicates the probability that the FMVBE will exceed the face value of debt at some future point in time based on a probability distribution of risky net cash flows that a business can be expected to generate in the future. Depending on expectations, the probability distribution may or may not be a normal or other standard statistical distribution. Our generalized application of the DCF is comprised of three steps: Step 1. Gather estimates for FMVBE;0, X, s, and n. Step 2. Based on the probability distribution of the cash flows and an estimated probability, calculate FMVBE;n . Step 3. Repeat step 2, using a different estimated probability, until the calculated FMVBE;n approximately equals the face value of debt. See Exhibit 33A.4 for an example using the DCF method of estimating the probability that the FMVBE will exceed the face value of debt at some future point in time. From the example, the probability is directly correlated with time and is approximately 20%, assuming a one-year horizon (i.e., n ¼ 1).
OPTION METHOD The Black-Scholes option pricing model assumes that continuously compounded single-period returns are normally distributed, which implies FMVBE;n is lognormally distributed, see Appendix VI. Formula 33A.2 is the equation3 that uses the distribution’s mean and standard deviation to indicate the probability the business enterprise is equal to a certain value: (Formula 33A.2) h pffiffiffiffiffiffiffiffiffiffii ln FMVBE;0;ni f ln FMVBE;0 þ ðWACC s 2 =2Þðn iÞ; s n i where: WACC ¼ Expected rate of return on the business enterprise and other definitions are as in Formula 33A.1. f ¼ standard deviation of returns on the business enterprise The option method indicates the probability that FMVBE will exceed the face value of debt at some future point in time based on unlevered, observed equity volatilities of guideline companies. The probability is a function of the expected volatility and time of FMVBE . Our application of the option method is comprised of three steps: Step 1. Gather estimates for FMVBE;0, WACC, s, and n. An estimate of s can be observed from guideline companies. Step 2. Using the equation for a lognormal distribution and an estimated probability, calculate FMVBE;n . Step 3. Repeat step 2, using a different estimated probability, until the calculated FMVBE;n approximately equals Fd. 3
For a derivation and discussion of this equation, see John C. Hull, Options, Futures and Other Derivative Securities, 6th ed. (Englewood Cliffs, NJ: Prentice-Hall, 2005), chaps. 10 and 11.
Probability that FMVBE Exceeds Face Value of Debt
525
Exhibit 33A.4 Valuation of Firm in Financial Distress Probability that FMVBE exceeds Fd Discounted Cash Flow Method Dollars in Thousands Net Cash Flows for Projection Year n Probability 20% 60% 20% Expected net cash flows, X
<20% 20–80% >80%
1
2
3
4
5
Terminal Value
$86 $62 $38 $62
$95 $71 $47 $71
$106 $82 $58 $82
$118 $94 $70 $94
$132 $108 $84 $108
$1,137 $931 $725 $931
Other Assumptions WACC (using midyear convention) Long-Term Growth Rate Rf Fd
15.0% 3.0% 5.0% $ 1,000
RESULTS OF ANALYSIS
Net Cash Flows for Projection Year n Probability 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
1
2
3
4
5
Terminal Value
$109 $100 $91 $86 $81 $77 $73 $69 $65 $62
$118 $110 $101 $95 $90 $86 $82 $78 $75 $71
$129 $120 $111 $106 $101 $97 $93 $89 $85 $82
$141 $133 $124 $118 $113 $109 $105 $101 $98 $94
$155 $147 $138 $132 $128 $123 $119 $116 $112 $108
$1,333 $1,259 $1,183 $1,137 $1,095 $1,058 $1,024 $992 $960 $931
FMVBE for Projection Year n Probability 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
0
1
2
3
4
$1,168 $1,098 $1,026 $981 $942 $907 $874 $844 $813 $785
$1,227 $1,155 $1,082 $1,036 $996 $960 $927 $896 $865 $837
$1,284 $1,211 $1,136 $1,090 $1,048 $1,012 $978 $946 $915 $886
$1,338 $1,264 $1,187 $1,139 $1,097 $1,060 $1,025 $993 $960 $931
$1,388 $1,311 $1,232 $1,184 $1,140 $1,102 $1,066 $1,033 $1,000 $969
Note: the scenarios in the box represent the scenarios when FMVBE exceeds Fd.
5 $1,429 $1,351 $1,269 $1,219 $1,174 $1,135 $1,098 $1,064 $1,030 $998
526
Cost of Capital
Exhibit 33A.5
Standard Normal Probability Distribution
Standard Normal Probabilities: (The table is based on the area P under the standard normal probability curve, below the respective z-statistic.) z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0
0.00 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7258 0.7580 0.7882 0.8159 0.8414 0.8643 0.8849 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.9713 0.9773 0.9821 0.9861 0 9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.9987 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 1.0000 1.0000
0.01 0.5040 0.5438 0.5832 0.6217 0.6591 0.6950 0.7291 0.7612 0.7910 0.8186 0.8438 0.8665 0.8869 0.9049 0.9207 0.9345 0.9463 0.9564 0.9649 0.9719 0.9778 0.9826 0.9865 0.9896 0.9920 0.9940 0.9955 0.9966 0.9975 0.9982 0.9987 0.9991 0.9993 0.9995 0.9997 0 9998 0.9999 0.9999 0.9999 1.0000 1.0000
0.02 0.5080 0.5478 0.5871 0.6255 0.6628 0.6985 0.7324 0.7642 0.7939 0.8212 0.8461 0.8686 0.8888 0.9066 0.9222 0.9358 0.9474 0.9573 0.9656 0.9726 0.9783 0.9830 0.9868 0.9898 0.9922 0.9941 0.9956 0.9967 0.9976 0.9983 0.9987 0.9991 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000
0.03 0.5120 0.5517 0.5910 0.6293 0.6664 0.7020 0.7357 0.7673 0.7967 0.8238 0.8485 0.8708 0.8907 0.9082 0.9236 0.9370 0.9485 0.9582 0.9664 0.9732 0.9788 0.9834 0.9871 0.9901 0.9925 0.9943 0.9957 0.9968 0.9977 0.9983 0.9988 0.9991 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000
0.04 0.5160 0.5557 0.5948 0.6331 0.6700 0.7054 0.7389 0.7704 0.7996 0.8264 0.8508 0.8729 0.8925 0.9099 0.9251 0.9382 0.9495 0.9591 0.9671 0.9738 0.9793 0.9838 0.9875 0.9904 0.9927 0.9945 0.9959 0.9969 0.9977 0.9984 0.9988 0.9992 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000
0.05 0.5199 0.5596 0.5987 0.6368 0.6737 0.7088 0.7422 0.7734 0.8023 0.8290 0.8531 0.8749 0.8944 0.9115 0.9265 0.9394 0.9505 0.9599 0.9678 0.9744 0.9798 0.9842 0.9878 0.9906 0.9929 0.9946 0.9960 0.9970 0.9978 0.9984 0.9989 0.9992 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000
0.06 0.5239 0.5636 0.6026 0.6406 0.6772 0.7123 0.7454 0.7764 0.8051 0.8315 0.8554 0.8770 0.8962 0.9131 0.9279 0.9406 0.9515 0.9608 0.9686 0.9750 0.9803 0.9846 0.9881 0.9909 0.9931 0.9948 0.9961 0.9971 0.9979 0.9985 0.9989 0.9992 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000
0.07 0.5279 0.5675 0.6064 0.6443 0.6808 0.7157 0.7486 0.7794 0.8079 0.8340 0.8577 0.8790 0.8980 0.9147 0.9292 0.9418 0.9525 0.9616 0.9693 0.9756 0.9808 0.9850 0.9884 0.9911 0.9932 0.9949 0.9962 0.9972 0.9980 0.9985 0.9989 0.9992 0.9995 0.9996 0.9997 0.9998 0.9999 0.9999 1.0000 1.0000 1.0000
0.08 0.5319 0.5714 0.6103 0.6480 0.6844 0.7191 0.7518 0.7823 0.8106 0.8365 0.8599 0.8810 0.8997 0.9162 0.9306 0.9430 0.9535 0.9625 0.9700 0.9762 0.9812 0.9854 0.9887 0.9913 0.9934 0.9951 0.9963 0.9973 0.9980 0.9986 0.9990 0.9993 0.9995 0.9996 0.9998 0.9998 0.9999 0.9999 1.0000 1.0000 1.0000
0.09 0.5359 0.5754 0.6141 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 0.8621 0.8830 0.9015 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.9936 0.9952 0.9964 0.9974 0.9981 0.9986 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 1.0000 1.0000 1.0000
See Exhibit 33A.6 for an example, applying the option method, on estimating the probability that the business enterprise will exceed the face value of debt at some future point in time. From the example, the probability is directly correlated with time and is approximately 15%, assuming a oneyear horizon (i.e., n ¼ 1).
Summary Exhibit 33A.6
527 Analysis Using Lognormal Probability Distribution
Assumptions FMVBE;0 Expected return ¼ WACC s ¼ Standard Deviation Fd
$ 785 15.0% 10.0% $ 1,000
RESULTS OF ANALYSIS
FMVBE for Projection Year n Probability 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0% 45.0% 50.0%
0
1
2
3
4
5
$1,071 $1,032 $1,006 $987 $971 $956 $944 $931 $920 $908
$1,132 $1,086 $1,056 $1,034 $1,015 $998 $983 $968 $955 $941
$1,195 $1,142 $1,107 $1,082 $1,060 $1,040 $1,024 $1,006 $992 $976
$1,259 $1,199 $1,160 $1,131 $1,106 $1,084 $1,066 $1,046 $1,030 $1,012
$1,538 $1,447 $1,388 $1,345 $1,308 $1,275 $1,248 $1,220 $1,196 $1,170
$1,776 $1,657 $1,582 $1,527 $1,479 $1,438 $1,403 $1,367 $1,337 $1,305
Note: the scenarios in the box represent the scenarios when FMVBE exceeds Fd.
OTHER CONSIDERATIONS Any company with amounts of debt such that its equity is potentially deemed worthless may also find it difficult to meet all interim principal and interest payments and continue operations until some future time n. As such, the equity holders may be faced with interim decisions whether to contribute additional equity capital or let the company enter bankruptcy. Although the law generally does not require additional equity capital infusions, it may be economically advantageous to do so. Therefore, as part of a complete analysis, it is also necessary to consider the company’s expected future net cash flows as the expected cash flow relates to compliance with debt covenants.
SUMMARY We have presented here a methodology to estimate the value of the possibility and the probability that the fair market value of the business enterprise will exceed the face value of debt at some future point in time. Viewing equity as a call option, there is always some value to the possibility of a future payoff. This is similar to a lottery ticket, where many are willing to pay some nominal amount for the chance, however remote, of hitting the jackpot. Moreover, there is always some statistical probability that a specified event outcome will materialize in the future.
Chapter 34
Common Errors in Estimation and Use of Cost of Capital
Introduction Confusing Discount Rates with Capitalization Rates Using the Firm’s Cost of Capital to Evaluate a More or Less Risky Acquisition or Project Mistaking Historical Rates of Return for Expected Rates of Return Blindly Accepting Morningstar’s Long-term Average as Today’s Equity Risk Premium Using an Inappropriate Beta in the CAPM Using an Inappropriate Beta in a Multifactor Model Mismatching the Discount Rate with the Economic Income Measure Using a Safe Rate to Discount or Capitalize a Risky Return Applying a Discount Rate in Real Terms to an Economic Income Projection in Nominal (Current) Terms Applying Costs of Capital Derived from After-Tax Returns to Pretax Returns Subtracting a Short-term Super Growth Rate from the Discount Rate to Get a Capitalization Rate Applying a Discount Rate Applicable to Net Cash Flow to Net Income Performing an Excess Earnings Method Valuation that Results in an Unrealistic Cost of Capital Projecting Growth Beyond that which the Capital Being Valued Will Support Internally Inconsistent Capital Structure Projection Using a Constant WACC with a Varying Capital Structure Using the Same WACC to Value Different Businesses Owned by a Diversified Company Assumptions that Produce a Standard of Value Other than that Specified in the Valuation Engagement Incorrect or Inadequately Supported Data in Estimating the Cost of Equity Using an Unattainable Growth Rate in Calculating the Terminal Value Summary
INTRODUCTION This chapter calls attention to some of the errors frequently encountered in estimation and applications of the cost of capital. We point out these errors partly so that readers will not fall into the same traps themselves when estimating or using cost of capital. Another reason is to help readers readily identify such errors when reviewing the work of others and understand how the errors should be corrected. Still another aim is to call attorneys’ attention to common errors when settling cases or in cross-examining expert witnesses.
CONFUSING DISCOUNT RATES WITH CAPITALIZATION RATES The discount rate is the cost of capital, and it applies to all prospective economic income. This includes all distributions and realized or readily realizable capital appreciation. The capitalization rate is a divisor applied to some particular economic income (e.g., earnings, cash flow, etc., for the latest 529
530
Cost of Capital
12 months, upcoming 12 months, or some other period). Only when the expected level of economic income is constant in perpetuity are these two rates equal, other than by sheer coincidence. Nevertheless, some analysts fall into the trap of using the discount rate (i.e., cost of capital) as a capitalization rate. The opposite is also seen from time to time: the use of a capitalization rate to discount prospective cash flows or other expected economic income to a present value. The relationship between discount rates and capitalization rates is the subject of Chapter 4.
USING THE FIRM’S COST OF CAPITAL TO EVALUATE A MORE OR LESS RISKY ACQUISITION OR PROJECT We have emphasized throughout this book that the cost of capital is market driven and that it is a function of the investment, not the investor. If an acquirer uses its own cost of capital (or its own beta) to set an acquisition price by discounting the expected cash flows of a riskier acquiree, then the result will be some increase in the risk of the acquiring company after the acquisition. This will result in an increase in the company’s overall risk and cost of capital, to which the market would be expected to respond by reducing the stock price. Decreases in acquirers’ stock prices as a result of acquisitions are very common phenomena, although it is not possible to sort out the extent to which this is a result of perceived overestimation of future cash flows or a market adjustment to the company’s cost of capital. The same principle applies to internal capital budgeting and project selection as to acquisitions. If the project under consideration is more or less risky than the activities of the company as a whole, then the expected cash flows from the project should be evaluated by a correspondingly higher or lower discount rate. In deciding among competing potential projects, an analyst should be certain to appropriately reflect the risk of each project in the discount rate applied to the respective project.
MISTAKING HISTORICAL RATES OF RETURN FOR EXPECTED RATES OF RETURN Remember, cost of capital is a forward-looking concept. Cost of capital is the expected rate of return that the market requires to induce investment in a subject security. Historical returns rarely are what investors expect in the future. Even if you were to extrapolate historical returns into the future, you would be wrong most of the time. The analyst should use historical returns only for guidance about what to expect in the future. If extrapolating historical returns into the future, the analyst should have some basis for the assumption that the future will resemble the past on an extrapolated basis. This assumption should be articulated in the analyst’s report. Rarely are conditions in the economy, the industry, and the specific company comparable to what they were in the past. The common error is for the analyst to naively assume that the future will fall somewhere near the line of extrapolation of the past. If this is, indeed, the assumption, the analyst should demonstrate that he or she has done the analysis and concluded that this will be true or that, at least, it is the best estimate of the future. The correct risk-free rate to use with the estimated equity risk premium is the risk-free rate as of the valuation date, not the average risk-free rate for some historical period. For example, the average total returns reported for long-term U.S. government bonds in Stocks, Bonds, Bills, and Inflation Yearbook (SBBI Yearbook) are historical returns, not the correct risk-free rate to use in estimating the cost of equity capital.
Using an Inappropriate Beta in a Multifactor Model
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A related error is to take the recent average historical rates of return that have been achieved for an industry, often from a source of industry composite statistics, such as the Risk Management Association’s (RMA) (formerly Robert Morris Associates) Annual Statement Studies, and to assume that this average is the expected return required to attract investment in that industry. The returns actually achieved for a particular industry in recent past years may be well above or below the level of expected return required to attract capital to the industry and certainly do not represent a reliable indicator of the cost of capital. Furthermore, returns shown in sources like the RMA Annual Statement Studies are based on book values, whereas the relevant measure is return on market values.
BLINDLY ACCEPTING MORNINGSTAR’S LONG-TERM AVERAGE AS TODAY’S EQUITY RISK PREMIUM In their SBBI Yearbook, Morningstar calculates an arithmetic average equity risk premium from 1926 through the present time. Many analysts use this equity risk premium in developing their equity discount rate by the Capital Asset Pricing Method (CAPM) or build-up methods. However, recent research, as presented in Chapter 9, has concluded that this long-term arithmetic average is too high under today’s conditions.
USING AN INAPPROPRIATE BETA IN THE CAPM You need to evaluate the quality of the beta estimates derived from guideline public companies (or for the subject company itself if publicly traded). Different beta sources calculate their betas differently (e.g., using different market portfolios, measuring returns over different intervals, etc.). Always use betas from the same source (or calculate your own beta estimates) for a valuation. Unlevering the observed beta estimates of the guideline companies is always a good first step. But make sure you use an appropriate formula to unlever the observed beta estimates. The most commonly used formula is the Hamada formula. This formula is not consistent with constant debt-toequity. The Miles-Ezzell and Harris Pringle formulas are consistent with a constant debt-to-equity ratio. Upon comparing beta estimates for the guideline public companies, if they fall within a relatively tight range, then the estimates will likely provide a reasonably accurate estimate of the appropriate beta for the subject company. But if there is wide divergence in the unlevered betas, you need to investigate the estimates further and not just blindly take the median or average of the observations. For example, one of the companies may be going through difficult times, and its return over the past few years may have moved in the opposite direction from its peers (or from the general economy as represented by the returns in, say, the Standard & Poor’s [S&P] 500). The beta estimate for that company may be low relative to its peers, yet it may be the most risky of the guideline companies you are investigating. Do not use a ‘‘dumb beta’’ just because it results from a calculation (even from a reliable source). The beta estimate should make economic sense.
USING AN INAPPROPRIATE BETA IN A MULTIFACTOR MODEL Beta estimates derived for use in the CAPM should not be used in a multifactor model, such as the Fama-French 3-factor model. The multifactor beta estimates represent the sensitivity of a return on an individual stock to changes in the returns on the S&P 500, for example, but given
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the influence simultaneously of other factors, the multifactor betas need to be estimated using a multifactor analysis, not a single-factor analysis as is often used in estimating beta for use in the CAPM.
MISMATCHING THE DISCOUNT RATE WITH THE ECONOMIC INCOME MEASURE The most common type of error in application of the income approach to valuation is to use a discount or capitalization rate that is not appropriate for the definition of economic income being discounted or capitalized. This general category of error has almost infinite variations. Those discussed in the next paragraphs are only a few. USING A SAFE RATE TO DISCOUNT OR CAPITALIZE A RISKY RETURN Although not the most common version of the mismatching error, the use of a safe rate to discount or capitalize a risky return certainly is one of the most egregious. On occasion, analysts erroneously discount a highly risky series of projected economic income by the U.S. Treasury bill rate. They claim that weighting cash flow outcomes by the probability of each outcome is a sufficient adjustment for the future risk of the cash flows. In such a case the cash flows are expected to have a variance of possible outcomes in future years. A safe rate assumes low variability (if any) in expected cash flows. Cash flows that could vary widely in future periods are not safe and deserve an appropriate risk adjustment to the discount rate. APPLYING A DISCOUNT RATE IN REAL TERMS TO AN ECONOMIC INCOME PROJECTION IN NOMINAL (CURRENT) TERMS In discounting or capitalizing, some analysts erroneously subtract the anticipated inflation rate from the discount rate and then apply the adjusted discount rate to an economic income projection that includes inflation (and vice versa). It is noteworthy that all the Morningstar data are presented in nominal terms—that is, they include inflation. The most common way of performing the income approach to valuation in the United States and in other mature economies is to express the cash flows in nominal terms (including the effect of inflation) and use a nominal discount rate. Although it is more common to express expected cash flows in real terms and to use a discount rate not including expected inflation in countries with hyperinflation, this can lead to incorrect conclusions. Depreciation expense and therefore income taxes are most often based on historical costs for investments in plant and equipment. During periods of inflation, the amount of depreciation from prior investments shrinks relative to the current costs of new equipment. The results are that the effective income tax rate increases and the difference between historical cost-based depreciation and the cost of replacement equipment increases. Assuming every expense will increase uniformly with inflation is most often a wrong assumption. APPLYING COSTS OF CAPITAL DERIVED FROM AFTER-TAX RETURNS TO PRETAX RETURNS Whether costs of capital are estimated by the build-up model, the CAPM, a multifactor model such as the Fama-French 3-factor model, or the discounted cash flow (DCF) method, in all cases they are returns realized after the payment of corporate-level income taxes. If the entity being valued is
Excess Earnings Method Valuation that Results in an Unrealistic Cost of Capital
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subject to entity-level income taxes, then it is inappropriate to apply the cost of capital estimated by those methods to pretax return flows. As we go to press, three controversial U.S. tax court cases have been issued that many analysts believe are guilty of this error.1 The cases all involved S corporations, and the tax court applied discount rates developed on an after-tax basis to S corporation earnings, which are pretax, on the theory that the corporation itself did not pay the taxes on the earnings. But someone had to pay the taxes. All S corporation status does is pass through the tax liability to the owners and thus avoid double taxation. But S corporation status does not avoid, or even defer, the obligation to pay the taxes on the earnings, though the total tax burden (entity level plus owner level) may be less than for an identical C corporation. The issues are discussed in Chapter 27 on valuing interests in pass-through entities. Most public companies have a rather low payout ratio of dividends to earnings, if they pay dividends at all. But in the case of S corporations, the earnings are all taxed to the owners, regardless of whether the earnings actually are distributed. We will undoubtedly hear more about this issue in the months and years to come. SUBTRACTING A SHORT-TERM SUPER GROWTH RATE FROM THE DISCOUNT RATE TO GET A CAPITALIZATION RATE Converting a discount rate to a capitalization rate involves subtracting an estimate of the long-term sustainable growth rate. Many companies expect high short-term growth that will tend to dampen over time. If the high short-term growth rate is subtracted from the discount rate, the proper capitalization rate will be understated, resulting in overvaluation. In such circumstances, a two-stage or three-stage DCF valuation model usually will produce a more valid valuation than a straight capitalization model. APPLYING A DISCOUNT RATE APPLICABLE TO NET CASH FLOW TO NET INCOME One of the reviewers of this book said that applying a discount rate applicable to net cash flow to net income is the most common error he sees in practice. Morningstar data produces a discount rate that is applicable to net cash flow, which usually is lower than net income. In such cases, the discount rate developed for net cash flow (or the capitalization rate derived by subtracting growth from the discount rate) would result in overvaluation if applied to net income. If a consistent relationship exists between net cash flow and net income, then it is possible to adjust the discount rate by the proportion of net income to net cash flow. In a capitalization model, this is a reasonable approximation. However, very few companies have an adequately consistent relationship between net cash flow and net income to make this any more than an approximation.
PERFORMING AN EXCESS EARNINGS METHOD VALUATION THAT RESULTS IN AN UNREALISTIC COST OF CAPITAL One very useful application of the cost of capital analysis is to do a sanity check on the reality of a valuation performed by the excess earnings method. In the excess earnings method, two capitalization rates are estimated: 1
Gross v. Commissioner, T.C. Memo 1999-254, 78 T.C.M. (CCH) 201 (U.S. Tax Ct. 1999), affirmed, 272 F.3d 333 (6th Cir. 2001); Estate of Heck v. Commissioner, T.C. Memo 2002-34, 83 T.C.M. (CCH) 1181 (U.S. Tax Ct. 2002); Estate of Adams v. Commissioner, T.C. Memo 2002-80 (U.S. Tax Ct. 2002).
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1. A capitalization rate for tangible assets 2. A capitalization rate for excess earnings (return over and above the amount required to support the company’s tangible assets) The excess earnings method derives its capitalization rates by very different methods from those discussed earlier in this book. It is based on required returns to categories of assets rather than on required returns to categories of capital. Nevertheless, at the end of the day, the value as estimated by the excess earnings method should reflect a capitalization rate very similar to that which would be derived if we developed a discount rate by any of the cost of capital estimation methods presented in this book and subtracted a reasonable estimate of long-term sustainable growth. An example of such a sanity check follows. Sanity Check. Is the overall equity capitalization rate approximately equal to what you would expect using a build-up capitalization rate? 1. Analysis of overall equity cap rate using excess earnings method: Net cash flow to equity $270 Divided by: indicated equity value $1; 205 Equals implied cap rate on equity: 22:4% ($270 $1,205 = 22.4%) 2. Build-up cap rate: 20-year government bond rate 7.0% Small-stock equity risk premium (combined general equity premium and small-stock premium) 15.8% Specific risk premium for subject 5:0% Total required rate of return (discount rate) 27.8% Less: expected sustainable growth rate 4:0% Equals cap rate applicable to net cash flow: 23:8% According to the sanity check, the results of the excess earnings method seem reasonable. If we capitalize the $270 net cash flow to equity at 23.8%, we would have an indicated value of $1,134, compared with $1,205 achieved by the excess earnings method. This is a reasonable range of difference. If the results were significantly different, we would reexamine all our calculations and assumptions. In the example, we dealt only with a capitalization rate for equity, because most of the data sources used to perpetrate this error show only returns to equity rather than returns to total capital. The excess earnings method, however, is used more often to value controlling interests than minority interests. Consequently, the return to total capital, as measured by the weighted average cost of capital (WACC), is relevant, and thus the capitalization rate for overall invested capital also should be considered in the reasonableness test. This use of cost of capital as a reasonableness check for an excess earnings method valuation is the subject of Chapter 17. That example demonstrated a significant overvaluation by the excess earnings method.
PROJECTING GROWTH BEYOND THAT WHICH THE CAPITAL BEING VALUED WILL SUPPORT As businesses expand, they typically need additional working capital and capital expenditures to support the increased level of operations. One of the many advantages of using net cash flow as the
Using a Constant WACC with a Varying Capital Structure
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prospective economic income measure is that it forces the analyst to consider these needs explicitly. Nevertheless, they often are underestimated. When cost of capital is used for valuation, it values only the investment as of the valuation date. The calculation of net cash flow allows for reinvestment for capital expenditures and additions to working capital necessary to support projected operations. However, if the projections being discounted will not be totally supported by the capital expenditure and working capital allowances in the net cash flow projections, and additional investment will be required to achieve those projected results, then the existing investment will be overvalued. Many analysts do not make adequate deductions for capital expenditures and additions to working capital. Analysts should be sure that these items bear a reasonable relationship to revenue, especially to revenue growth. A good idea is to project balance sheets as well as income statements. This helps to show potential asset deficiencies. These items also should be examined when calculating the terminal value. If growth is assumed when calculating the terminal value, then capital expenditures following the discrete projection period should necessarily exceed depreciation following the discrete projection period. Many analysts assume capital expenditures to equal depreciation when estimating the terminal value, which results in overestimation of expected net cash flow and overvaluation, where growth is expected.2
INTERNALLY INCONSISTENT CAPITAL STRUCTURE PROJECTION Methods using WACC and betas adjusted for leverage require projections about the subject company’s capital structure. These projected capital structures are on the basis of market value. Analysts often assume a capital structure in the process of estimating a market value of equity, and the resulting estimated market value of equity makes the capital structure, at the estimated market value, different from that which was assumed. In such cases, the projected capital structure has to be adjusted and the process iterated until the estimated market value of equity results in a capital structure consistent with that which is projected in estimating the cost of capital. Even worse, of course, is to not even estimate a market value capital structure but simply to use book value. If the company is earning good returns, then the market value of equity is likely to exceed book value. This is true not only for the subject company but also for peer companies that may be used to estimate an industry-average capital structure. If the market value of equity is understated, then the assumed proportion of low-cost debt in the capital structure will be too high. This will result in an understatement of the WACC and an overstatement of value. Chapter 17 addresses estimating capital structure by the iterative process, and Appendices 17A and 17B illustrate using the iterative process in the context of CAPM.
USING A CONSTANT WACC WITH A VARYING CAPITAL STRUCTURE Most analysts use a single WACC when valuing all invested capital (sometimes referred to as enterprise value). This has the potential to misvalue the company. For example, as shown in Chapter 17, when a highly leveraged company uses the WACC based on the high leverage but pays down the debt 2
For a good discussion of this common error, see Gilbert E. Matthews, ‘‘Cap X ¼ Depreciation Is Unrealistic Assumption for Most Terminal Values,’’ Shannon Pratt’s Business Valuation Update1 (March 2002): 1–3.
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over time, use of a single WACC to discount all future expected cash flows will overvalue the enterprise, often substantially.
USING THE SAME WACC TO VALUE DIFFERENT BUSINESSES OWNED BY A DIVERSIFIED COMPANY You should match the risk of the business being valued with the cost of capital used to value the business. Different businesses have different risks. Even the overall cost of capital of a public company derived from estimates of its beta, using its own stock returns, represents the cost of capital of a portfolio of businesses. The risks of each of the businesses owned by the diversified company need to be reflected in a unique cost of capital. This is particularly true of operations in developing countries. Those businesses have a unique set of risks such that a country-risk premium should be thoroughly investigated. You should not assume that just because the majority of operations of the parent company reside in developed economies that the business in the developing economy faces identical risks.
ASSUMPTIONS THAT PRODUCE A STANDARD OF VALUE OTHER THAN THAT SPECIFIED IN THE VALUATION ENGAGEMENT A common error is to project a capital structure other than the company’s actual capital structure (thereby deriving a WACC different from the company’s actual WACC) when the standard of value is fair market value on a minority basis. If an acquirer were to use its own WACC, then the implied result would be investment value to that acquirer instead of fair market value. Moreover, if the equity ownership interest is a minority interest, the holder could not force a change in capital structure. Another enormous assumption that would lead to investment value rather than fair market value would be to inject the benefits of synergies into the projected cash flow stream. This would produce the value to a particular buyer that could take advantage of the synergies rather than a hypothetical buyer.
INCORRECT OR INADEQUATELY SUPPORTED DATA IN ESTIMATING THE COST OF EQUITY The first mistake sometimes made in this category of incorrect or inadequately supported data in estimating the cost of equity is to mismatch the risk-free rate with the equity risk premium. Morningstar has equity premiums series that attach to 30-day Treasury bill maturities, five-year Treasury note maturities, and 20-year Treasury bond maturities. Based on its historical data, the equity risk premium should be selected to match one of those maturities. Morningstar’s SBBI Valuation Edition Yearbook specifies the range for each of the size premia, and these vary from year to year. The size is measured in terms of market value of common equity capital. The size premium decreases as the market value increases. Mismatching the company size to the company size premium can either understate or overstate the equity risk premium and therefore understate or overstate value. Another common error is inadequate support for the company-specific risk premium. Within the CAPM, a portion of the company-specific risk may be captured in beta. Certainly major portions of the company-specific risk are captured in the size premium. The remaining companyspecific premium is totally a matter of the analyst’s judgment. Ideally it should be reflected when at all possible in arriving at the expected cash flows. It is theoretically more correct (and likely less likely to be challenged) when adverse scenarios are weighted in arriving expected cash flows.
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For example, it is more proper to analyze possible cleanup costs of an environmental problem and deduct that probability weighted cost from the expected cash flows than to add an arbitrary company-specific risk premium. Any adjustment to either the expected cash flows or the cost of capital by adding a factor for company-specific risk should be based on quantitative and/or qualitative analysis, which should be detailed in the report. The company-specific risk premium added to the cost of capital should be as small as possible—sometimes we see 10 percentage points in the company-specific risk premium, and that, depending on the company and the industry, is normally too much. Ten points would push the discount rate close to a venture capital or start-up company rate. In any case, the companyspecific risk premium should be supported with a very strong narrative.
USING AN UNATTAINABLE GROWTH RATE IN CALCULATING THE TERMINAL VALUE The growth rate assumed in calculating the terminal value is a compound growth rate in perpetuity, which is a very long time. At a growth rate of 20% compounded annually, the company’s revenues would soon exceed the gross domestic product (GDP) of the United States and eventually the world. Long-term growth rates exceeding the real growth in GDP plus inflation are generally not sustainable. Most analysts use more conservative growth rates in calculating the terminal value.
SUMMARY Cost of capital is one of the most critical components in valuation, capital budgeting, and other financial decision making. There are many ways to err in both estimating the cost of capital and applying it in practice. Numerous errors are seen regularly in actual practice. Some of the major areas that require careful consideration include:
Properly distinguishing between discount rates and capitalization rates Making sure that the data supporting discount and capitalization rates represent expected returns (current market-required returns), not past returns that do not represent future expectations Making sure that the discount or capitalization rate used matches the definition of expected returns being discounted or capitalized Making sure that the implied weighted capitalization rate used in an excess earnings valuation procedure is reasonably close to capitalization rates developed by the cost of capital estimation methods discussed in this book
Being careful that projected returns being discounted or capitalized can be achieved without having to dilute the existing capital with additional outside capital
Being sure that capital structure assumptions fully reflect the market values of the capital structure components
Being sure that valuation results are estimated consistently with the definition of value specified in the valuation assignment
Making sure that the cost of equity is calculated correctly and supported adequately
Avoid all of these traps and you get a gold star. More important, your company and your clients will be well served, and your cost of capital work should withstand rigorous scrutiny.
Chapter 35
Cost of Capital in the Courts
Introduction Cost of Capital in Shareholder Disputes Cost of Capital in the Tax Court Cost of Capital in ESOP Stock Valuation Cost of Capital in Family Law Cost of Capital in Bankruptcy Reorganizations Setting Interest Rates Valuation of Stock by the Income Approach Cost of Capital Included in Damages Cost of Capital in Utility Rate-setting Taxicab Lease Rates Cost of Capital in Ad Valorem Taxation Summary
INTRODUCTION Cost of capital is getting ever-increasing attention in the courts within many contexts, such as valuations for many judicial purposes, allowed rates of return as a component in rate setting, and other applications. This chapter touches briefly on many of the contexts in which many millions of dollars can hinge significantly on the court’s determination of the relevant cost of capital. For each context, we cite one or more cases that are typical of contemporary court deliberations on the subject.
COST OF CAPITAL IN SHAREHOLDER DISPUTES Delaware traditionally has been the case law trendsetter in shareholder disputes. A landmark Delaware Supreme Court case in 1983 reversed a lower court case because it did not consider future earnings projections. The court made the point that a determination of fair value (the statutory standard of value in Delaware, as well as in most other states, for dissenting stockholder actions) ‘‘must include proof of value by any techniques or methods which are generally considered acceptable in the financial community.’’1
Note: Months in parentheses after case citations refer to the issue in which the case was abstracted, either in Shannon Pratt’s Business Valuation Update1 (BVU), or in Judges & Lawyer’s Business Valuation UpdateTM (J&L) (now merged with BVU), as noted. The full texts of most cases abstracted in either BVU or J&L are available online at www.BVLibrary.com. 1 Weinberger v. UOP, Inc., 457 A.2d 701 (Del. 1983).
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Since that time, Delaware courts have increasingly embraced the discounted cash flow (DCF) method of valuation. In a 1997 case, the Delaware Chancery Court characterized the DCF method as ‘‘increasingly the model of choice for valuations in this Court.’’2 While several methods are accepted by the Delaware Chancery Court, the DCF method continues to be the preferred method. Typical of the quotes from this court is this one: The DCF model of valuation is a standard one that gives life to the finance principle that firms should be valued on the expected value of their future cash flows, discounted to present value in a manner that accounts for risk. The DCF method is frequently used in this court, and [the court] [ . . . ] prefer[s] to give it great, and sometimes even exclusive, weight when it may be used responsibly.3
As early as 1993, the Delaware court rejected the cost approach in favor of the DCF method: In determining the value of a shareholder’s interest in a company as a going concern, the appraiser must take into account the future prospects of the merged corporation. Weinberger, 457 A.2d at 713. This is generally accomplished through the discounted cash flow analysis, which theoretically values the future earnings of an entity and then discounts them to present value. Neal v. Alabama By-Products Co., 1990 Del. Ch. LEXIS 127, Del Ch., C.A. No. 8282, Chandler, V.C. (Aug. 1, 1990), aff’d, Del. Supr., 588 A.2d 255 (1991). S. Pratt, Valuing a Business: The Analysis and Appraisal of Closely Held Companies 67–85 (2d ed. 1989). The Merrill Lynch valuation does not use a discounted cash flow analysis, but rather uses the cost approach, an approach typically used in contemplation of liquidation. While a cost (or ‘‘asset value’’) approach may occasionally be appropriate in valuing a going concern, see Pratt, Valuing a Business at 106–109, it tends to undervalue intangible factors of a business (i.e., goodwill and synergy), making it less accurate than the discounted cash flow method in valuing an existing and viable business. ‘‘The notion that a business interest is worth the value of its underlying assets is basically fallacious in most cases, at least for an operating company.’’4
Another case used the DCF method exclusively over the comparable transactions method: Although the experts relied upon three basic valuation technologies, I conclude that only one technique can be reliably applied by me on this record—the discounted cash flow method. Neither of the market approaches—comparable company or comparable acquisition—relied upon by the parties’ experts can be rationally deployed by me. Neither of those market-based methods is backed up by sufficiently reliable testimonial and record evidence. At trial, the experts evidenced little familiarity with the actual details of their comparables. Moreover, my own review of their comparables suggests reason to doubt that they provide a sound basis to assess PNB’s value.5
Another quote expands on the foregoing: In recent years, the DCF valuation methodology has featured prominently in this Court because it ‘‘is the approach that merits the greatest confidence’’ within the financial community. In appropriate cases, this Court has relied exclusively on DCF models.* Regardless of the methodology, however, this Court prefers valuations based on management projections available as of the date of the merger and holds a healthy skepticism for 2 3
4 5
Grimes v. Vitalink Comm. Corp., 1997 Del. Ch. LEXIS 124 (Del. Ch. 1997) (Oct. 1997 BVU). Andaloro v. PFPC Worldwide, 2005 Del. Ch. LEXIS 125 *35 (Del. Ch. Aug. 19, 2005). Also quoted in Richard S. Gesoff, plaintiff, v. IIC industries Inc., CP Holdings Limited, Kenyon Phillips Acquisition, LLC, Bernard Schreier, John Smith, Robert M. Levy, Robert Glatter, and Alfred L. Simon, defendants. CEDE & Co., Petitioner, v. IIC Industries Inc. and Kenyon Phillips Acquisition, LLC, respondents, 902 A.2d 1130; 2006 Del. Ch. LEXIS 91. TV58 Limited Partnership v. Weigel Broadcasting Co., 1993 Del. Ch. LEXIS 146. In Re PNB Holding Co. Shareholders Litigation, 2006 Del. Ch. LEXIS 158.
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post-merger adjustments to management projections or the creation of the new projections entirely.y Expert valuations that disregard contemporaneous management projections are sometimes completely discounted.6 *Ryan v. Tad’s Enterprise, Inc., 709 A.2d 682, 702 (Del. Ch. 1996) aff’d, 693 A.2d 1082 (Del. 1997) (TABLE). y
See, e.g., Gilbert v. MPM Enterprises, Inc., 709 A.2d 663, 668 (Del. Ch. 1997), aff’d, 731 A.2d 790 (Del. 1999).
Although the DCF method is clearly favored, it will be rejected where its fundamental inputs, such as projected revenues, expenses, and cash flows, are found to not be reasonably reliable.7 For similar reasons, the court may be reluctant to use the DCF method where the company is a short-lived niche company without much of an earnings history8 or where the appraisers have not conducted an adequate DCF analsysis.9 In such instances, however, the court may perform its own DCF analysis. In a typical case before the Delaware Supreme Court, both experts used the DCF method as well as other methods. The court rejected the other methods and focused on the DCF method. The court accepted one expert’s Capital Asset Pricing Model (CAPM) for the cost of equity capital, with minor modifications to the beta (‘‘[T]he beta employed shall be based on the average beta of [the subject company’s] comparable companies.’’) The court made some minor adjustments to the cash flow projections because ‘‘it was apparent by the date of the merger [the effective valuation date] that [the subject company] would have a very difficult time meeting this projection.’’ Both experts used market multiples for their terminal values. The court accepted the multiple of the expert who had ‘‘convincingly demonstrated the appropriateness of [his] selection of [comparable companies].’’10 The weight given to the DCF method will vary from case to case. In one case, for example, DCF was given 30% weight,11 in another case it was given 70% weight,12 and in another it was given 75% weight.13 However, in another case before the Delaware Chancery Court, both experts used the DCF method, with one using a 12% discount rate and the other an 18% discount rate. The court determined that the difference between the experts’ discount rates was ‘‘attributable primarily to their different estimates of [the subject company’s] cost of equity capital, and their different assumptions of the company-specific risks confronting [the subject company] at the time of the merger.’’ The court disagreed with certain of the other assumptions applied by both of the parties’ experts. The Chancery Court ultimately concluded that it could not rely on the DCF valuation opinion of either party’s expert. The Delaware Supreme Court affirmed, stating: Similarly, by recognizing the discounted cash flow model as one proper valuation technique, the Court of Chancery was not required to use that methodology to make its own independent valuation calculation by either adapting or blending the factual assumptions of the parties’ experts. The ultimate selection of a valuation framework is within the Court of Chancery’s discretion.14
6 7 8 9 10 11
12 13 14
Cede & Co., v. JRC Acquisition Corp., (2004 Del. Ch. LEXIS 12). Doft & Co. v. Travelocity.com Inc., 2004 Del. Ch. LEXIS 75. Lane v. Cancer Treatment Centers of America, Inc., 2004 Del. Ch. LEXIS 108. Gholl v. eMachines, Inc., 2004 Del. Ch. LEXIS 171. M.P.M. Enter., Inc. v. Gilbert, 731 A.2d 790 (Del. 1999). Dobler v. Montgomery Cellular Holding Co., Inc., 2004 Del. Ch. LEXIS 139, aff’d on valuation issue, 2005 Del. LEXIS 295, 880 A.2d 206 (Del. 2005). In re United States Cellular Operating Co., 2005 Del. Ch. LEXIS 1. Andaloro v. PFPC Worldwide, 2005 Del. Ch. LEXIS 125. M.G. Bancorp., Inc. v. LeBeau, 737 A.2d 513 (Del. 1999).
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Cost of Capital
Thus, in another case, the court rejected both sides’ experts’ DCF valuations, and the DCF method altogether, because it was not comfortable with the adjustments the experts made to management projections and other inputs they used.15 In yet another case, the court found the appraiser’s DCF analysis ‘‘incredible’’ because the appraiser eschewed any reliance on the real-world beliefs of the company’s management team about the company’s prospects and, in the absence of any management projections of cash flows, invented his own.16 In one case where the court accepted CAPM, it accepted the small-stock premium but rejected the company-specific risk premium because defendants could find no support in the literature for increasing the discount rate for the extra risk they claimed.17 One of the most famous cases was ultimately decided in 2006. In that case, greater credibility was found with the DCF method. The opinion is that case contains some colorful quotes: As shall be seen, using even an income-based approach such as a DCF model to value such an entity has its challenges, principally in the area of calculating a proper cost of capital. In this situation, the absence of both market information about the Subject Company and good public comparables force the court to rely even more than is customary on the testimonial experts. Testimonial feuds about discount rates often have the quality of a debate about the relative merits of competing alchemists. Once the experts’ techniques for coming up with their discount rates are closely analyzed, the court finds itself in an intellectual position more religious than empirical in nature, insofar as the court’s decision to prefer one position over the other is more a matter of faith than reason. This unfortunate reality flows from the status of principles of corporate finance. Even as to public companies, there is much dispute about how to calculate the discount rate to use in valuing their future cash flows, even when one tries to stick as closely as possible to the principles underpinning the capital asset pricing model and the semi-strong form of the efficient capital markets hypothesis. Witness the serious academic debate about whether the so-called size premium received by investors in smaller public companies is a durable indicia of their greater risk, or whether there are attributes of stocks with a low book-tomarket (value) ratio that require the consideration of that factor in estimating a discount rate. . . . Situations like this one inspire even less confidence, when experts are required to calculate a cost of capital for a very small, non-public company, for which neither of the experts has identified reliable public companies. In this context, the ability of the experts or the courts to hew literally to the teaching of the high church of academic corporate finance is essentially non-existent [ . . . ]. At best, the experts and the court can express their reverence by trying to come up with a proxy that takes into account concerns addressed by CAPM. The experts in this case have used the proxy that has found the most favor among professional appraisers: the so-called ‘‘build-up model.18
But sometimes the court fails to match the discount rate chosen with the risk of the subject company.19 The Delaware court rejects adding a control premium to a value derived by the DCF method (although it does add a control premium to the values derived from the comparable companies method). The court describes its reasoning in this way: 15 16 17 18
19
The Union Illinois 1995 Investment Limited Partnership v. Union Financial Group, Ltd., 847 A.2d 340 (Del. Ch. 2003). Finkelstein v. Liberty Digital, Inc., 2005 Del Ch. LEXIS 53. In Re Emerging Communications Inc. Shareholders Litigation, 2004 Del. Ch. LEXIS 70. Delaware Open MRI Radiology Associates, P.A. v. Kessler, 898 A.2d 290. (2006 Del. Ch. LEXIS 84). Footnote to case, n130: That is, both experts essentially calculated the discount rate consistent with the leading nonacademic treatise. See Shannon Pratt, Valuing a Business, 5th edition (New York: McGraw-Hill, 2007), 163. Gilbert, Matthews, ‘‘Errors and Omissions in DCF Calculations: A Critique of Delaware’s Dr. Pepper Appraisal,’’ Business Value Update (October 2007): 9.
Cost of Capital in the Tax Court
543
Finally, I reject [the expert’s] addition of a 20% control premium to correct for an alleged minority discount arising from the inclusion of market data in his model. Some analysts believe that the income approach always produces a publicly traded minority basis of value because the Capital Asset Pricing Model (CAPM) and the buildup model develop discounts and capitalization rates from minority transaction data in the public markets. This is a very common and highly flawed conclusion.20 There is little or no difference in the rate of return that most investors require for investing in a public, freely tradable minority interest versus a controlling interest.21
COST OF CAPITAL IN THE TAX COURT The tax court has rejected the DCF method in cases where it believed that the model used by the expert was far too sensitive to minor changes in assumptions, such as the discount rate and/or the growth rate.22 The tax court also has been known to reach its conclusion by giving partial weight to a DCF method and partial weight to a market approach method. For example, one case gave 70% weight to the market method and 30% weight to the DCF method.23 One tax court judge, obviously very knowledgeable about CAPM, rejected testimony offered in the context of the DCF but gave this critique of the testimony for the guidance of other appraisers: Beta of 1.00 too low. Beta, a measure of systematic risk, is a function of the relationship between return on an individual security and the return on the market as a whole [ . . . ]. However, because the betas for small corporations tend to be larger than the betas for larger corporations, it may be difficult to find suitable comparables when valuing a small, closely held corporation [ . . . ]. [T]here are substantial differences in size and operations between [the subject company] and the banks on the VL bank list [Value Line Investment Survey (4th ed., Apr. 9, 1993)]; we do not believe that their betas are representative of the greater business risks faced by [the subject company]. We do not believe that an investment in [the subject company], a small, single location bank, whose earnings were susceptible to impending interest rate mismatches and sluggish local economic conditions, presents the same systematic risk as an investment in an index fund holding shares in 500 of the largest corporations in the United States.24 Failure to add small stock premium. Although [the witness] cited Ibbotson [25] as his source for equity risk premium, in his initial report he ignored a crucial aspect of the Ibbotson approach to constructing a cost of capital—the small stock premium. In his rebuttal report, [the witness] unsuccessfully tried to persuade us that the small stock premium is not supported by financial theory, characterizing the risk associated with a firm’s size as unsystematic risk, for which the market does not compensate. The relationship between firm size and return is well known. Size is not an unsystematic risk factor and cannot be eliminated through diversification. ‘‘On average, small companies have higher returns than large ones.’’ Ibbotson at 125. [ . . . ] [I]t has been found that the greater risk of small stocks is not fully reflected by CAPM, in that actual returns may exceed those expected based on beta [ . . . ] Consequently, when calculating a cost of capital under CAPM on a small stock [ . . . ], it is appropriate to add a small stock premium to the equity risk 20
21 22 23 24
25
For additional reading see Shannon Pratt, Business Valuation Discounts and Premiums (Hoboken, NJ: John Wiley & Sons, 2001). Lane v. Cancer Treatment Centers of America (2004 Del. Ch. LEXIS 108). Morton v. Commissioner, T.C. Memo 1997-166, 73 T.C.M. (CCH) 2520 (U.S. Tax Ct. 1997) (June 1997 BVU). Estate of Freeman v. Commissioner, T.C. Memo 1996-372, 72 T.C.M. (CCH) 373 (U.S. Tax Ct. 1996) (Oct. 1996 BVU). Estate of Hendrickson v. Commissioner, T.C. Memo 1999-278, 78 T.C.M. (CCH) 322 (U.S. Tax Ct. 1999) (Oct. 1999 J&L) (Oct. 1999 BVU). Morningstar acquired Ibbotson Associates in 2006.
544
Cost of Capital
premium, to reflect the greater risk associated with an investment in a small stock in comparison to the large stocks from which the equity-risk premium is calculated. Based on [the subject company’s] size, a microcapitalization equity size premium of 3.6 percent should have been added. See Ibbotson at 161 [ . . . ].26 Failure to account for unsystematic risk. [B]ecause CAPM assumes that an investor holding a diversified portfolio will encounter only systematic risk, the only type of risk for which an investor can be compensated is systematic or market risk, which represents the sensitivity of the future returns from a given asset to the movements of the market as a whole [citing Brealey & Myers, Principles of Corporate Finance 137–138, 143–144 (4th ed. 1991); Pratt et al., Valuing a Business 166 (3rd ed. 1996)] [ . . . ]. [The witness] followed the principles of CAPM and did not make any provision for [the subject company’s] unsystematic risk, based on the assumption that such risk was diversifiable[ . . . ]. [R]espondent and [the witness] have overlooked the difficulties in diversifying an investment in a block of stock they argued is worth approximately $8.94 million. Construction of a diversified portfolio that will eliminate most unsystematic risk requires from 10 to 20 securities of similar value. See Brealey & Myers, supra at 137–139. Thus, proper diversification of an investment in the [the subject company] shares owned by petitioner, as valued by respondent, would require a total capital investment of at least $89 million. We do not think the hypothetical buyer should be limited only to a person or entity that has the means to invest $89 million in Peoples and a portfolio of nine other securities[ . . . ].27
In another case, an expert added a small stock premium applicable to companies much smaller than the subject company. For this reason, the court rejected that expert’s cost of equity developed by the CAPM model and accepted the cost of equity capital developed by the opposing expert, also by the CAPM model.28 In another case, the court rejected the DCF model for a small company because it did not believe that CAPM and the WACC were ‘‘the proper analytical tools to value a small, closely held corporation with little possibility of going public.’’29 Another case rejected the conclusion of an expert because he failed to apply a small-stock premium and used too low a beta: Respondent relies on an article by Bajaj & Hakala, ‘‘Valuation for Smaller Capitalization Companies,’’ published in Financial Valuation: Business and Business Interests, ch. 12A (Hanan & Sheeler ed. 1998), for the proposition that there is no small-stock premium. We find [petitioner’s expert’s] analysis to be more persuasive.’’ [Respondent’s expert] testified that it is appropriate to use the Ibbotson Associates data from the 1978–92 period rather than from the 1926–92 period because small stocks did not consistently outperform large stocks during the 1980’s and 1990’s. We give little weight to [respondent’s expert’s] analysis. [He] appeared to selectively use data that favored his conclusion. He did not consistently use Ibbotson Associates data from the 1978–92 period; he relied on data from the 1978–92 period to support his theory that there is no small-stock premium but used an equity risk premium of 7.3 percent from the 1926–92 data (rather than the equity risk premium of 10.9 percent from the 1978–92 period). If he had used data consistently, he would have derived a small stock premium of 5.2 percent and an equity risk premium of 7.3 percent using the 1926–92 data, rather than a small-stock premium of 2.8 percent and an equity risk premium of 10.9 percent using the 1978–92 data.
26 27 28
29
Ibid. Ibid. Gross v. Commissioner, T.C. Memo 1999-254, 78 T.C.M. (CCH) 201 (U.S. Tax Ct. 1999) (Sept. 1999 J&L) (Sept. 1999 BVU), affirmed, 272 F.3d 333 (6th Cir. 2001) (Jan. 2002 BVU). Estate of Maggos v. Commissioner, T.C. Memo 2000-129, 79 T.C.M. (CCH) 1861 (U.S. Tax Ct. 2000) (July 2000 BVU).
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We conclude that [petitioner’s expert] appropriately applied a small-stock premium in valuing the [subject company’s] stock.30
In the same case, another issue in the income approach was the petitioner’s expert’s build-up method versus the respondent’s expert’s CAPM method. Respondent’s expert lowered his equity discount rate by multiplying it by a beta of 0.7. The judge stated: We disagree with [respondent’s expert’s] use of a .7 beta because [the subject company] was a small, regional company, had customer concentrations, faced litigation and environmental claims, had inadequate insurance, was not publicly traded, and had never paid a dividend. A beta . . . can only be correctly estimated on the basis of the betas of comparable publicly traded companies. . . . [Respondent’s expert] stated that he selected the beta based on a review of comparable companies. However, he did not identify these comparable companies or otherwise give any reason for his use of a .7 beta. We believe [his] use of a .7 beta improperly increased his estimate of the value of the [subject company’s] stock.31
In one case involving a 19.99% interest in a boat-building business, both experts capitalized income, using the build-up method. The respective expert’s equity discount rates were calculated in this way:
Risk-free rate ERP Premium-small stock Company/Industry risk Total discount rate Less: Growth Capitalization rate
Taxpayer Expert
IRS Expert
6.14% 7.90 5.78 3:00 22.82 5:50 17.5%
6.56% 7.5 5.78 ð5:20Þ 14.64 5:50 10.01%
The Internal Revenue Service (IRS) expert used Ibbotson’s industry adjustment, and the court adopted the IRS expert’s cap rate with this explanation: Although the 5.2-percent premium was based on some data from years subsequent to 1997, we are satisfied that the 5.2-percent is within a reasonable range. In part we base our conclusion on [the subject company’s] tendency to generally outperform the industry and economy, so that the 5.2-percent premium may be on the conservative side. . . . [The taxpayer’s expert’s] figures are without empirical support or explanation and appear to be purely subjective.32
However, the tax court rejected CAPM in a case involving the valuation of 30% of stock in an exclusive Burger King franchise in four Florida counties. The tax court ruled: We do not believe CAPM and WACC are the proper analytical tools to value small, closely-held corporation with little possibility of going public.
The court used the public company EBITDA multiple method.33
30 31 32 33
Estate of Klauss v. Commissioner, T.C. Memo 2000-191, (U.S. Tax Ct. 2000) (July 2000 BVU) (July 2000 J&L). Ibid. Estate of Deputy v. Comm., (TCM 2003-176). Maude G. Furman, et al. v. Comm. of Internal Revenue (TCM 1998-157).
546
Cost of Capital
In one case, the tax court rejected in its entirety a 12% ‘‘technology-related risk factor (‘‘companyspecific risk’’) particularly in light of their failure to project any additional income from technology-related expenditures . . .’’ thereby reducing the estate’s capitalization rate from 30.5% to 18.5%. The court also added to the value by the income approach $68 million of nonoperating assets.34 Three cases involving S corporations were decided. Since S corporation earnings are pretax, many appraisers valuing S corporation stock either tax-affect the earnings (apply hypothetical taxes as if they were a C corporation) or increase the discount or capitalization rate by dividing the aftertax rate by 1 minus the effective tax rate to derive a rate applicable to pretax earnings.35 The correct method for converting and after-tax discount rate to the pre-tax equivalent is discussed in Chapter 32. The first such case was Gross v. Commissioner.36 One expert tax-affected the S corporation earnings and the other did not. The tax court accepted the procedure of not tax-affecting the earnings. The case was appealed to the Sixth Circuit Court of Appeals, where the tax court decision was upheld by a two-to-one vote of the deciding judges. The minority judge wrote a lengthy dissenting opinion.37 The next case was Estate of Heck v. Commissioner.38 In this case neither the expert for the estate nor the expert for the IRS tax-affected the earnings or adjusted the after-tax discount rate. Since both agreed, it was not an issue in the case, and the after-tax discount rate applied to the S corporation’s pretax earnings was allowed to stand. The expert for the taxpayer in that case was the same expert who testified for the IRS in the Gross case. The last case was Estate of Adams v. Commissioner.39 In the Adams case, one appraiser adjusted the capitalization rate (derived from Ibbotson after-tax discount rates) to apply to pretax earnings and the other did not. The tax court accepted the nonadjusted rate, resulting in an outcry from the professional business appraisal community. It is our opinion that these cases, if allowed to stand unchallenged and cited as precedent, represent bad case law and a misinterpretation of fair market value. Taxes on S corporation earnings have to be paid. In S corporations the liability for the taxes is just shifted from the corporation to the stockholders. The only saving is avoiding the double taxation at the corporate and individual levels. We believe that we will see some modification of these results in future cases.40
COST OF CAPITAL IN ESOP STOCK VALUATION Both the IRS and the U.S. tax court traditionally have leaned more toward the market approach than the income approach. The reason is partly because of language in Revenue Ruling 59-60, written before the development of modern capital market theory, which evolved in the 1960s. The market approach has also been favored partly because of concern about possible manipulation of both cash 34
35
36 37
38 39 40
Estate of Josephine T. Thompson v. Commissioner of Internal Revenue. T.C. Memo 2004-174; 2004 Tax Ct. Memo LEXIS 180; 88 T.C.M. (CCH) 48. Tax-effecting S corporation earnings is advocated by the IRS Valuation Training for Appeals Officers Coursebook (Chicago: CCH Incorporated, 1998), 7–12. Gross v. Commissioner, T.C. Memo 1999-254, 78 T.C.M. (CCH) 201 (U.S. Tax Ct. 1999) (Sept. 1999 J&L) (Sept. 1999 BVU). Gross v. Commissioner, 272 F.3d 333 (6th Cir. 2001). For an analysis of this discussion, see George Hawkins, ‘‘A Gross Result in the Gross Case Calls into Question Circumstances in Which Tax Affecting Is Valid,’’ (Jan. 2002 BVU). Estate of Heck v. Commissioner, T.C. Memo 2002-34, 83 T.C.M. (CCH) 1181 (U.S. Tax Ct. 2002) (March 2002 BVU). Estate of Adams v. Commissioner, T.C. Memo 2002-80 (U.S. Tax Ct. 2002) (May 2002 BVU). See Gregory A. Barber, ‘‘Valuation of Pass Through Entities,’’ Valuation Strategies (March/April 2001): 4–11, 44–45; David Laro and Shannon P. Pratt, Business Valuation and Taxes: Procedure, Law, and Perspective (Hoboken, NJ: John Wiley & Sons, 2005).
Cost of Capital in Family Law
547
flow forecasts and discount rates in the DCF method. Nonetheless, as the DCF method has achieved greater utilization in the professional financial community, it has also achieved greater acceptance in the tax court. In a 1985 case the IRS challenged income tax returns reflecting deductions for a company’s contributions to the employee stock ownership trust at $61.35 per share, based on the fair market value estimated by an independent appraisal firm. The IRS asserted that the value was between $5.36 and $8.00 per share. The independent appraisal heavily emphasized earning power and dividend-paying capacity, whereas the IRS stressed net asset value (book value was $7.05 per share). The court agreed with the emphasis on earning power and dividend-paying capacity. The court was somewhat concerned ‘‘that the appraisal took into account a 20-year earnings projection’’ but thought it was ‘‘not unreasonable in light of past earnings increases.’’ The court concluded that the only reasonable appraisal presented to it was the one at $61.35 per share.41 Holders of employee stock option plan (ESOP) stock sued for trustees’ breach of fiduciary duty in overpaying for a purchase of 66% of the shares of a company for $34,427,353. At trial the parties’ experts used both a guideline companies method and an income approach, but the court focused primarily on the income approach. One of the court’s criticisms of the defendant’s expert was that the ‘‘capitalization rate of 16% was improperly low because it included an adjustment for a 9% steady growth rate despite the expectation that the company’s growth would lead off after two years.’’ Also ‘‘[the defendant’s expert’s] discount rate numbers were not credible because of [the defendant’s expert’s] failure to explain the basis for the numbers.’’ The court stated: the special master found the [plaintiff’s expert’s] report a conceptually completer application of the discounted cash flow method, the preferred valuation method [ . . . ]. [The plaintiff’s expert] was clearer about the source of significant data used and provided some narrative supporting his judgment, whereas [the defendant’s expert] provided details in the form of numbers without any substantiation.
The court also noted to the extent that [the plaintiff’s expert] used a 1997 Grabowski/King study that would not have been available in March 1994, the court finds that such error does not materially affect the credibility of the [plaintiff’s expert’s] report.’’ The court’s concluded value for the ESOP stock was $29,310,000, resulting in the participants being awarded $8,139,116.42
COST OF CAPITAL IN FAMILY LAW Cost of capital is getting increasing attention in family law courts as those courts are becoming more receptive to the DCF method of valuation of closely held businesses for marital property divisions. In a 1996 Ohio case, for example, the trial judge stated from the bench that the DCF method had never been used before within her family law jurisdiction. She was willing to consider it, based on testimony that members of the professional financial community would be likely to use the method in valuing a company of the particular type at issue in the case. Ultimately the court not only accepted
41 42
Las Vegas Dodge, Inc. v. United States, 1985 U.S. Dist. LEXIS 21577 (D. Nev. 1985). Thomas Horn v. Robert McQueen. 353 F. Supp. 2d 785; 2004 U.S. Dist. LEXIS 27413 (December 1, 2004, decided).
548
Cost of Capital
the method but used the value indicated by the DCF method as its final conclusion of value. The case was appealed and upheld.43 Other courts have similarly followed suit.44 Business Valuation Update1 consistently reports family law cases that recognize or reject the DCF method.
COST OF CAPITAL IN BANKRUPTCY REORGANIZATIONS Cost of capital arises in bankruptcy proceedings in at least two contexts: 1. Setting interest rates 2. Valuing companies or interests in companies by the income approach SETTING INTEREST RATES The concept of the cost of capital as described in this book is recognized for the purpose of setting interest rates in the case of a bankruptcy reorganization. For example, the Seventh Circuit Court of Appeals rejected a trustee’s notion that the interest rate a creditor should receive should be the Treasury bill rate. The court stated that the creditor was entitled to indubitable equivalence of its property interest, which means a stream of payments including interest that adds up to the present value of its claim [ . . . ]. [T]he creditor must get the market rate of interest [ . . . ] for loans for equivalent duration and risk.
The court then added: To say that the lender is limited to its ‘‘cost of capital’’ [ . . . ] is therefore to say that the lender is entitled to the market rate of interest, for that is what its cost of capital is: the price it must pay to its own lenders, plus the costs of making and administering loans, plus reserves for bad debts (that is, the anticipated rate of nonpayment).45
Another court of appeals case in a different circuit stated the same concept. In considering a reorganization plan involving interest payments, it stated that the issue is whether the interest rate provides the plaintiffs with the ‘‘present value’’ of their claims. The court explained: ‘‘Present value’’ is a market rate concept, determined by the use of an interest rate which fairly compensates the creditor for not receiving the amount of its secured claim upon confirmation of the debtor’s plan.
The same court added: ‘‘[A]n entity forced to delay payment that it is entitled to receive is, in effect, extending a loan.’’ The court further stated: [T]he purpose [ . . . ] is [ . . . ] ‘‘to put the secured creditor in an economic position equivalent to the one it would have occupied had it received the allowed secured amount immediately.’’ [ . . . ] [T]he appropriate 43
44 45
Sergi v. Sergi, 1996 Ohio App. LEXIS 3241 (Ohio Ct. App. 1996), appeal denied, 673 N.E.2d 147 (Ohio 1996) (Sept. 1996 BVU). Guiffre v. Baker, 1996 Ohio App. LEXIS 3673 (Ohio Ct. App. 1996) (Nov. 1996 BVU). Koopmans v. Farm Credit Serv., 102 F.3d 874 (7th Cir. 1996).
Cost of Capital in Bankruptcy Reorganizations
549
rate of interest is ‘‘that which the secured creditor would charge, at the effective date of the plan, for a loan similar in character, amount and duration to the credit which the creditor would be required to extend under the plan.’’46
The preceding case quoted the Third Circuit’s case of first impression on this issue, a frequently quoted case. In effect, the case rejected use of the prime lending rate and required a market rate for similar credits: Some courts, including the bankruptcy court in the cases we are here reviewing, have suggested a ‘‘cost of funds’’ theory which would determine present value by looking to the creditor and the market in which the creditor borrows capital. There is more involved, however, than the mere cost of funds [ . . . ]. It is only by acknowledging the coerced loan aspects of a cram down and by compensating the secured creditor at the rate it would voluntarily accept for a loan of similar character,* amount and duration that the creditor can be placed in the same position he would have been in but for the cram down. We hold that the bankruptcy and district courts erred in utilizing the prime rate to determine whether the proposed plan, as required by [the bankruptcy code], provided for payments to the creditor having a present value equal to the value of its allowed secured claim. The appropriate interest rate for this purpose is the rate of interest currently being charged by the creditor in the regular course of its business for loans similar in character, amount and duration to the loan being coerced in the cram down.47 * By a loan of ‘‘similar character’’ we mean a loan that the creditor regularly extends to other debtors who are not in bankruptcy but who are otherwise similarly situated to the debtor who is the recipient of the loan coerced by the Chapter 13 proceeding and who are seeking the same kind of credit (e.g., auto loan, home equity loan, etc.).
The Fifth Circuit reached a similar conclusion in a case decided September 8, 1997.48 A common issue is setting appropriate interest rates to establish present value in ‘‘cram-down’’ situations. In these situations, the bankruptcy court, in effect, forces the creditor to accept a new loan for the property rather than allowing the creditor to repossess the secured property. In a consolidated 1998 case,49 the debtors’ Chapter 13 plan proposed to provide a 9% interest rate on the balances due the creditors on automobiles in the debtors’ possession. Both creditors maintained that a 9% rate was inadequate to provide them with an amount equal to the present value of their claims as required by the bankruptcy code. Both creditors argued that the appropriate capitalization rate should be based on the rate of interest they currently charge for similar loans in the region. According to the creditors, the appropriate rate should be 20.19% in one case and 21% in the other. The court determined that any analysis of this issue necessarily begins with the Tenth Circuit opinion of In re Hardzog.50 The Tenth Circuit held that ‘‘in the absence of special circumstances, such as the market rate being higher than the contract rate, bankruptcy courts should use the current market rate of interest used for similar loans in the region.’’ The debtors argued that the ‘‘current market rate of interest’’ should be some variation on the ‘‘prime lending rate’’ or ‘‘prevailing market rate’’ as reflected, for example, in The Wall Street 46 47 48 49 50
Rankin v. DeSarno, 89 F.3d 1123 (3d Cir. 1996), certiorari denied, 519 U.S. 1108 (U.S. Sup. Ct. 1997). General Motors Acceptance Corp. v. Jones, 999 F.2d 63 (3d Cir. 1993). Green Tree Fin. Serv. Corp. v. Smithwick, 121 F.3d 211 (5th Cir. 1997), rehearing denied, 57 F.3d 1190 (D.C. Cir. 1991). In re Oglesby and Jones, 221 B.R. 515 (1998). In re Hardzog, 901 F.2d 858 (10th Cir. 1990).
550
Cost of Capital
Journal. The creditors argued that the correct interpretation of ‘‘current market rate of interest,’’ as used in Hardzog, means the rate charged by the particular or objecting creditor for similar loans in the region in the recent past. Citing Hardzog, the court determined that ‘‘similar’’ loans means a loan that the creditor regularly extends to other borrowers who are not in bankruptcy but who are otherwise similarly situated to the debtor. Thus, the court ordered that the appropriate rates for the debtors should be 20.1% and 21%, respectively. Another case that followed shortly thereafter articulated the same conclusion:51 The remaining matter for the Court to decide is the appropriate cram down discount, or interest rate n1 for payment for Household on the secured portion of its claim under [the bankruptcy code]. Debtors’ Chapter 13 plan proposed to pay an interest rate of 10% on the secured portion of Household’s claim, and Household objected to this interest rate as being insufficient. The testimony of the witness from Household indicated that based on the Debtors’ credit history, Household’s current interest rate would be in a range between 18.95% and 24.95%. Debtors’ contract rate of interest is 22.95% [ . . . ]. For the sake of clarity, the Court will refer to ‘‘interest rate’’ though ‘‘discount rate’’ or ‘‘capitalization rate’’ may be more appropriate terms. [The code] requires that a secured creditor receive payments that provide the present value of the secured amount of its claim. In determining the appropriate interest rate, this Court must begin its analysis with Memphis Bank & Trust Co. v. Whitman, 692 F.2d 427 (6th Cir. 1982). In Memphis Bank, the Sixth Circuit stated that it would be inappropriate to arbitrarily establish an interest rate for cram down under [the code], but instead ‘‘bankruptcy courts should use the current market rate of interest used for similar loans in the region.’’ Memphis Bank, 692 F.2d at 431. In making this determination, the Court must ‘‘assess interest on the secured claim for the present value of the collateral [ . . . ] in order not to dilute the value of that claim through delay in payment. In effect, the law requires the creditor to make a new loan in the amount of the value of the collateral rather than repossess it, and the creditor is entitled to interest on his loan.’’ Memphis Bank, 692 F.2d at 429. The Sixth Circuit subsequently ruled that ‘‘the most equitable rate to establish in this type of situation is the prevailing market rate of interest on similar types of secured loans at the time of allowance of the creditor’s claim and the confirmation of the plan in bankruptcy with a maximum limitation on such rate to be the underlying contract rate of interest.’’ In re Colegrove, 771 F.2d 119, 123 (6th Cir. 1985). The use of the ‘‘current market rate’’ of interest for cram down under [ . . . ] [the bankruptcy code], was also adopted in U.S. v. Arnold, 878 F.2d 925 (6th Cir. 1989). The Arnold court noted that the contract interest rate maximum set forth in Colegrove was applicable only for fully secured creditors who were not required to write-down any portion of a loan. Arnold, 878 F.2d at 929, 930 [ . . . ]. In light of Memphis Bank, Arnold and Colegrove, interest rates offered to low risk borrowers are not necessarily appropriate for cram down [ . . . ]. Other circuits have adopted a ‘‘coerced loan’’ approach, consistent with Memphis Bank, for determining appropriate cram down interest rate [ . . . ]. See General Motors Acceptance Corp. v. Jones, 999 F.2d 63 (3d Cir. 1993); In re Hardzog, 901 F.2d 858 (10th Cir. 1990). The various approaches to determining the appropriate cram down interest rate were analyzed in a recent article, David G. Epstein, Don’t Go and Do Something Rash About Cram Down Interest Rates, 49 Ala. L.Rev. 435 (1998): Accordingly, in applying ‘‘value, as of the effective date of the plan,’’ bankruptcy courts should endeavor to leave the secured creditor as well off as if it had been paid the amount of its secured claim in cash. The cram down interest rate should reflect what the secured creditor would have earned had it taken that cash and reinvested it in loans with terms comparable to the terms proposed by the debtors’ plan and with risks comparable to the risks presented by the debtor’s nonpayment [ . . . ].
51
In re Glueck, 223 B.R. 514 (1998).
Cost of Capital in Bankruptcy Reorganizations
551
This court finds that evidence of the relevant creditor’s recent loan rate for similar loans within the region will be instrumental for setting the proper cram down interest rate [ . . . ]. In this case, Debtors presented no testimony or evidence concerning the market rate of interest that was available for borrowers with similar credit histories, but simply proposed an arbitrary interest rate of 10% for cram down [ . . . ]. Absolutely no support was provided for this rate, and the Court cannot accept such an arbitrary rate in light of Memphis Bank. The only evidence requiring an adjustment of the contract rate of interest, to accurately reflect the current market interest rate for similar loans, came from Household’s witness who testified that the current market rate of interest for similar loans ranged from 18.95% to 24.95%. The Court believes that the reduced risk associated with Debtors’ payments to the Chapter 13 trustee, and discharge of debts on completion of their Chapter 13 plan supports the use of the interest rate at the low end of Household’s ‘‘range,’’ and will set 18.95% as the interest rate to be paid on the secured portion of Household’s claim under § 1325(a)(5)(B).
This case contains references to many other cases espousing this position. One bankruptcy reorganization case concluded: ‘‘The primary reason the current joint plan is patently unconformable, and thus, why no reorganization is in prospect: the interest rate proposed on the Chevron secured claims is not sufficient.’’ The case earlier stated: [ . . . ] one of the most significant issues relevant to whether the Current Joint Plan is confirmable is whether the treatment proposed for Chevron’s secured claims would provide Chevron with a stream of payments over the life of the plan, the present value of which will equal the secured claims of $940,000. This turns on whether the 8% per annum interest rate proposed is an appropriate rate of interest with regard to the Chevron loans.
The court concluded that, even if the questionable projected cash flows were attainable, the proposed 8% rate would be insufficient to be comparable to the rate that would be available on a similar loan with comparable risks.52
VALUATION OF STOCK BY THE INCOME APPROACH A bankruptcy case decided January 18, 2007, gave weight to the DCF method, the comparable companies method, and the comparable transactions method, with the greatest weight to the DCF method. The court weighted the three experts’ conclusions, as corrected by the court, 40% to the opinion of one expert and 30% each to the other two experts, based on the experts’ credentials and the quality of their reports. The court’s opinion contained considerable discussion of each expert’s development of the equity discount rate within the WACC.
Company-specific risk. One expert used zero company-specific risk, one expert used about 2%, and one expert used 6%. The court case cut the 6% to 4%, stating that ‘‘[the witness] could provide little explanation of the basis for making such a significant adjustment to the discount rate.’’
Size premium. Two of the experts used Ibbotson’s microcap size premium (3.95%), and the third expert used the tenth decile premium (6.41%). The court went with the microcap size premium because the subject company was at the bottom of the ninth decile.
52
In Re: Northwest Timberline Enterprises, Inc., In Re: Construction and Real Estate information Services, Inc., 348 B.R. 412. (2006 Bankr. LEXIS 1994).
552
Cost of Capital
Terminal value. The court stated that the terminal value could be based on either the Gordon Growth Model or multiple of a variable such as EBITDA. Since all three experts used the multiple method in estimating the terminal value, the court accepted the multiple method.53 Different discount rates for ‘‘base business’’ and ‘‘growth ideas.’’ One of the experts used a higher discount rate for the portion of the company’s projected operations that were beyond the company’s historical operations. The court accepted this, noting ‘‘Valuation experts agree that corporate projects should be valued using a discount rate that is commensurate with a project’s risk.’’ ‘‘Emergence risk premium.’’ Two of the experts included an ‘‘emergence premium’’ of about 2% to account for the increased risk to earning capacity that the debtors face as a result of being in bankruptcy and emerging from bankruptcy. The court accepted this premium to the discount rate. (The witness who testified to the 6% company-specific risk premium, which the court cut to 4%, included the emergence premium in his company-specific risk premium. Thus, the court, in effect, accepted about 2% for the emergence premium and another 2% for the company-specific risk premium.) Nonoperating assets. Two of the experts added the value of nonoperating assets to their values derived from the DCF method. One did not, although he added the value of the nonoperating assets to the results from his comparable companies and comparable transactions methods. The court added the nonoperating assets to the value derived by his DCF method, explaining in no uncertain terms that his failure to do so was an error. Cash flow projections. All three experts relied on projections provided by the debtor-in-possession management that the court found to be biased upward. The court corrected for this by making a deduction to the weighted average of the experts’ conclusions of value.54
The most recent bankruptcy case that involved a cost of capital issue as we go to press, decided March 2, 2007, involved differences between experts in the company-specific risk factor. Both experts used the DCF method to decide whether the company was insolvent at the time when transfers were made. They both used a WACC, but one expert’s WACC reflected a 5% company-specific risk factor while the other expert’s WACC reflected a 10% company-specific risk factor. The expert with the 5% company-specific factor based his estimation solely on ‘‘the nature of the related party transactions with (the controlling owner) and his associated entities.’’ He opined that the additional risk factors were ‘‘baked into the industry’’ and thus captured in the industry beta. The expert with the 10% company-specific premium cited several factors unique to the subject company, including depth of management, fraud occurring at the hospital, management’s reputation, unreliability of financial statements, and the greater effect that the Balanced Budget Act of 1997 would have on the subject hospital because of its high percentage of Medicare/Medicaid patients. The court came down on the side of the 10% company-specific risk premium, adding that ‘‘[the expert] was thus conservative in choosing a 10% risk premium.’’55 One case found flaws in the application of the discounted cash flow method.56 In discussing [the expert’s] application of the discounted cash flow method, the court found several flaws in [his] report and testimony:
53 54 55 56
For reasons described elsewhere, the authors prefer the Gordon Growth Model method of estimating the terminal value. Nellson Nutraceutical, Inc. et al., Chapter 11, case No. 06-10072 (CSS) (January 18, 2007). Doctors Hospital of Hyde Park, Inc. v. Dr. James H. Desnick, et al., B.R. 11520 (March 2, 2007). ‘‘Bankruptcy Court Determines Fair Market Value Under Pennsylvania Judgment,’’ Judges & Lawyers Business Valuation UpdateTM (May 2000): 7.
Cost of Capital in Bankruptcy Reorganizations
553
He failed to include information regarding additional working capital or capital expenditures that would be required for QSA to expand its business as he projected,
He projected earnings without management input,
He failed to account for Mahoney’s salary as president and CEO of QSA, and
He assumed that QSA would terminate a distributorship contract, and further assumed an estimated cost savings associated with this termination.57
The court ultimately rejected this expert witness’s valuation and accepted the valuation of the opposing expert witness. The issue in another interesting adversary proceeding58 was whether the transfer of stock of Danbury Surgical Center, Inc. (DSC) and Bridgeport Surgical Center, Inc. (BSC) by debtors Googel and Sisti to the defendants Steinberg and Simons were fraudulent transfers under the bankruptcy code. The transfer agreement recited the consideration as $100,000 for all of the stock. There was conflicting testimony regarding whether the release of debtors’ liability on the center’s financing was part of the consideration and whether additional consideration was promised to be paid ‘‘after the debtors’ financial troubles were over.’’ The trustee’s expert used the discounted net cash flow method to value the stock, projected net cash flows for three years, used the industry average capital structure of 24% debt and 76% equity, computed a discount rate of 17.5%, and determined that DSC’s business enterprise value was $7,124,000. From this value he subtracted interest-bearing debt of $3,798,000, applied a 20% discount for lack of marketability, and applied an additional 5% discount for restrictions on voting rights. Based on Googel and Sisti’s ownership percentages of the total stock of DSC, the trustee’s expert concluded that each debtor’s ownership interest was worth $349,100. He further tested the validity of his valuation by comparing the results with the value of publicly traded surgical centers and with comparable centers that were traded within a reasonable period before the subject transfer. Defendants provided expert valuation testimony but did not independently appraise the value of the DSC stock. Instead, the expert provided a critical review of the trustee’s expert’s appraisal. Defendant’s expert’s criticisms fell into three main areas. He testified that:
[Trustee’s expert] failed to fully consider the impact of the Connecticut economy, which was in a recession;
The discount rate and weighted average cost of capital [he] used did not account for the ‘‘unsystematic risks’’ associated with valuing future cash flows of a small, privately owned, highly leveraged business; and
[His] selection of a 20% discount for lack of marketability was too low—based upon a number of discount studies, a 35% discount for lack of marketability was appropriate.59
Defendant’s expert recommended changes in the calculations and concluded that each debtor’s ownership interest in DSC was worth $126,000. The court concluded that the trustee had not proven his claim of actual fraud because the only evidence that additional consideration for the stock would be paid at a later date was the testimony of Googel. (It is of some interest that Googel testified by videotape due to his incarceration in federal prison for wire fraud, bank fraud, and impeding administration of IRS laws.)
57 58 59
In re Mahoney, 251 B.R. 748 (2000) (May 2000 J&L) (June 2000 BVU). In re Colonial Realty Co. 202 B.R. 185 (Bankr. D. Conn. 1996). ‘‘Stock Recipients Liable for Fraudulent Transfer Underpayment,’’ BVU (Jan. 1999): 10.
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Cost of Capital
Regarding the trustee’s constructive fraud claim, the defendants conceded that debtors were insolvent at the time of the transfer. Therefore, the trustee needed to prove that debtors did not receive reasonably equivalent value for their stock. Based on the expert valuation testimony, the court concluded that the debtors indeed did not receive reasonably equivalent value for the DSC stock and the trustee therefore could void the transfer as fraudulent. The court generally credited the testimony of the trustee’s expert but adjusted his valuation conclusion by applying the 35% lack of marketability discount suggested by defendant’s expert.
COST OF CAPITAL INCLUDED IN DAMAGES In a District of Columbia (D.C.) case, the plaintiff appealed the district court’s decision to award the cost of its lost capital, calculated on the basis of the total amount of damages. The D.C. court of appeals ruled: It remains unclear whether prejudgment interest [interest from the time of the tort to the date of court judgment] is available in a negligence action. Nonetheless [ . . . ] [i]n addition to finding Williams negligent, the district court found that Straight had breached its contract with Smoot. Further, because Williams agreed to indemnify Straight in full, the court did not err by including the cost of capital in the damage award assessed against Williams—whether or not District of Columbia law allows a cost of capital award in a negligence action.
The court of appeals did, however, require an adjustment in the district court’s calculation of the time period for which portions of the cost of capital were awarded. The district court had awarded cost of capital on the full amount of the damages through the last day of the trial. The court of appeals noted, however, that portions of the damages, such as increased insurance premiums and legal fees, were incurred over an extended period of time, and ordered a recalculation based on time of actual incurrence of damages.60
COST OF CAPITAL IN UTILITY RATE-SETTING Many providers of essential services are subject to federal or state regulation in respect to the rates they can charge for their services. In setting rates, it is virtually universally recognized that one of the costs the service provider is entitled to recover is its cost of capital. This generally is interpreted to mean its weighted average cost of capital, as discussed in Chapter 7. This principle was articulated by the U.S. Supreme Court more than 50 years ago: The Supreme Court has stated that a just and reasonable rate should be ‘‘sufficient to assure confidence in the financial integrity of the enterprise, so as to maintain its credit and to attract capital’’; the rate should also be ‘‘commensurate with returns on investments in other enterprises having corresponding risks.’’61
The next quote from a case appealing a Federal Communications Commission (FCC) rate order is typical: 60
61
Williams Enter., Inc. v. The Sherman R. Smoot Co., 938 F.2d 230 (D.C. Cir. 1991), rehearing denied, 57 F.3d 1190 (D.C. Cir. 1991). Federal Power Comm’n v. Hope Natural Gas Co., 320 U.S. 591 (U.S. Sup. Ct. 1944), quoted in Illinois Bell Tel. Co. v. Federal Comm. Comm’n, 988 F.2d 1254 (D.C. Cir. 1993).
Taxicab Lease Rates
555
The FCC relied on ‘‘classic’’ DCF methodology, which assumes that the price of a share of stock is equal to the present value of the cash flows the stock will generate. J. Bonbright et al., Principles of Public Utility Rates 318 (2d ed. 1988).* These cash flows are in the form of dividends.y Because a dollar available now is worth more than a dollar available only later, the future cash flows must be reduced by a rate that reflects investors’ opportunity costs, i.e., their required rate of return or discount rate, Id. Assuming that this discount rate and the growth rate of dividends both remain constant, one calculates the price of the stock using the following formula: P = D/(r g), where P is the current price of the stock, D is the total dividend in the first year, r is the rate of return, and g is the expected annual growth of dividends. Id.; see also A. Kolbe et al., The Cost of Capital: Estimating the Rate of Return for Public Utilities 53–54 (1984). Since regulatory commissions are interested in the rate of return, they rearrange the equation to solve for r: r = D/P + g. * The DCF method ‘‘has become the most popular technique of estimating the cost of equity, and it is generally accepted by most commissions. Virtually all cost of capital witnesses use this method, and most of them consider it their primary technique.’’ Id. at 317–18. y
Cash flows also result from the ultimate sale of the stock. R. Brealey and S. Myers, Principles of Corporate Finance 49 (4th ed. 1991). However, the theory is that the next investor will be willing to buy the stock at a price based on his estimate of future dividends and the price at which he will be able to sell; so too the third investor and the fourth, ad infinitum. The most basic form of the DCF model therefore assumes that the stock is held forever. Bonbright et al., supra at 318. For a detailed explanation, together with the mathematics, see 1.62
Similarly, a case challenging a Federal Energy Regulatory Commission (FERC) rate order supports the use of the Gordon Growth Model version of DCF analysis for estimating the cost of equity. Courts reviewing rate decisions generally will not require the use of one method rather than another to estimate the cost of equity capital but will accept methods in common use in the financial community. The next excerpt is typical of approval of regulatory methodology. In fact, the Commission appears quite wedded to DCF analysis and to efficient market theory as its theoretical mainstay. In Montaup Electric Co., 38 FERC ô 61,252 (1987), for example, the Commission adopted the DCF methodology over risk premium analysis for a period of rapidly declining interest rates and reasoned that ‘‘a market-oriented analysis such as a DCF analysis accounts for all risk factors perceived by investors.’’ Id. at 61,866. At about the same time as this court’s first remand, it published its third annual ‘‘generic Determination of Rate of Return on Common Equity for Public Utilities,’’ in which it defended the use of the DCF methodology against attacks based on criticism of the Efficient Market Hypothesis. Order No. 461, III FERC Regulations Preambles ô 30,722 (1987). It declared enthusiastically, ‘‘The concept of an efficient market is astonishingly simple and remarkably well supported by the facts.’’63
TAXICAB LEASE RATES The City of Chicago Commissioner of Consumer Services retained a consulting firm to recommend the rate of return on invested capital that Yellow Cab Company should be allowed to include in its maximum allowable lease rate for taxicabs. The commissioner adopted the consultant’s recommended rate of 14%, and Yellow Cab appealed to the U.S. District Court. According to the court:
62 63
Ibid. Tennessee Gas Pipeline Co. v. Federal Energy Regulatory Comm’n, 926 F.2d 1206 (D.C. Cir. 1991).
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Cost of Capital
Based on extensive research and the concept of a weighted average cost of capital, which resulted in a 12 percent rate of return assigned to the debt and a 20 percent rate of return given to the equity, [the consultant] determined that the maximum lease rates should afford a 14 percent rate of return.
Yellow Cab’s actual cost of debt at the time was 7.25%, so the cost of capital was based on the risks and costs of the lease transaction, not on Yellow’s debt cost. In granting summary judgment for the defendants, the court stated, ‘‘Yellow Cab did not show that the risk of the taxicab industry in Chicago entitled it to a rate of return exceeding 20 percent.’’64
COST OF CAPITAL IN AD VALOREM TAXATION The state of Georgia traditionally has used three approaches to valuation of property for ad valorem purposes: (1) a stock market approach, (2) a DCF approach, and (3) a market multiple approach. Against one party’s position that a single approach should always be used, the U.S. district court of appeals said ‘‘the fact that CSXT’s true market value is an educated guess weighs against the court requiring the Department to use a particular valuation method.’’ In this case, the court concluded that the department’s DCF valuation was the most reliable indicator of value, and issued a conclusion based on that number.65 Many states use a capitalization of net operating income method for valuation of property, especially utilities, for property taxation. The property tax forum is an organization of tax representatives from a majority of the natural gas pipeline companies in the United States with representation in Canada. The forum does an annual capitalization rate study, which the member companies support. The court in this case apparently relied on that study in upholding the board of tax appeals decision.66 One court found that a 30% rate of return was fair for an investment in a financially distressed company. The company had contemplated paying off a debt with proceeds from the sale of a major asset, but the sale fell through. To avoid bankruptcy, the company sold convertible preferred stock to a trust controlled by the controlling stockholder. A minority stockholder filed suit. There was testimony that a 30% to 40% return was ‘‘in the range of appropriateness for this investment given that that is typically what private equity and what venture capital funds expect for their return.’’67
SUMMARY In matters such as valuation and allowed rates of return or interest rates, courts attempt to reflect the realities of financial decision making as practiced in the contemporary financial environment. This includes the attempt to embrace modern capital market theory in reaching determinations of the appropriate cost of capital in many contexts. These contexts include but are not limited to:
Shareholder disputes
Gift and estate tax valuations
64 65
66
67
Yellow Cab Company v. City of Chicago, 938 F.Supp. 500, U.S. Dist. N.D. Ill. (September 10, 1996). CSX Transportation, Inc., v. The State Board of Equalization of the State of Georgia, et al., 448 F. Supp. 2d 1330, (2005 U.S. Dist. LEXIS 43390). In the matter of the appeal of ANR Pipeline Co. from a decision of the director of property valuation of the State of Kansas, 276 Kan. 702; P.3d 751; 2003 Kan. LEXIS 613; 158 Oil & Gas Rep. 1165. Chinyun Kim v. The Grover C. Coors Trust, Court of Appeals Nos.: 04CA0583 & 04CA1203. 2007 Colo. App. LEXIS 394.
Summary
Marital property valuations Bankruptcy reorganizations
Damage awards
Rate-setting Lease rates
557
Courts are moving away from arbitrary cost of capital decisions and relying heavily on expert witnesses who use current market data in conjunction with the cost of capital estimation methods discussed in this book.
Part 6
Real Estate and Ad Valorem
Chapter 36
Cost of Capital of Real Property–Individual Assets James MacCrate, MAI, CRE, ASA Introduction Typical Structure of a Real Estate Transaction Real Property Competes with Other Asset Classes Direct Capitalization Method Overall Direct Capitalization Band of Investment Method Elwood Formula Estimating the Capitalization Rate Residual Methods Discounted Cash Flow Method Estimating the Property Discount Rate Summary Appendix 36A
INTRODUCTION This chapter presents development of the cost of capital for individual real property investments and provides practical applications for the valuation of income-producing assets, such as apartment or office buildings, industrial properties, and development properties. In conjunction with the other chapters in this book, this chapter assists the reader in understanding the differences between the current practices applied in business valuation and those applied in real estate valuation. The income and the cost of capital associated with the ownership of real property rights are the focus of this section. This is different from the income and cost of capital that might be earned by a business enterprise operating on the property, such as a marina, hotel, fitness club, or restaurant. Real estate is a unique asset class with distinguishing characteristics. Real estate is immobile, durable, or indestructible, and each parcel is different in that no two parcels can be in the same location. As a result, a body of law has evolved concerning real property rights or interests in real estate or realty. The rights inherent in the ownership of real estate are generally referred to as the bundle of rights. These include the rights of possession, control, enjoyment, and disposition. These rights are divisible and separable and can be transferred by legal documents, such as a lease, a mortgage, or a deed. The value of real estate is the value of the real property or the rights inherent in the ownership of real estate or realty and is based on its capacity to support and house economic activities. In essence, real property value is a function of its physical attributes, rights inherent in the I thank Terry Vaughn Grisson, PhD, Professor of Real Estate at Georgia University, J. Mack Robinson College of Business Administration, for his assistance with this chapter. Subsequent to authoring this chapter, the market for CMOs changed considerably.
561
562
Cost of Capital
ownership of real estate or realty, and its economic location. The property’s comparative ability to generate income becomes its basis of value. While there are three traditional approaches to value—the cost, sales comparison, and income approaches—this chapter focuses on the income approach for income-producing properties. Market value is the present worth of the anticipated future benefits derived from the ownership of real estate. Market value is based on typical financing, which influences the future benefits that affect the price that investors pay for real estate. The cost of capital includes those benefits or returns to the equity and debt positions. Definitions of terms such as net income and cash flow differ from those used previously in this text. This chapter defines these terms in the context of real estate valuation; they should not be confused with the terms as defined in financial textbooks.
TYPICAL STRUCTURE OF A REAL ESTATE TRANSACTION Because of the special characteristics associated with real property investments, such investments can be analyzed based on their physical, legal, or financial components. The financial components include debt and equity investments. Equity investments can be in various forms, such as an individual investor, joint ventures, partnerships, syndications, or public securities. Since most real estate is acquired with debt financing, the cash flow from the real property investment must satisfy the return requirements of debt investors in order to attract debt as well as equity investors. The mortgage or debt component may include various categories and can be obtained from commercial banks, life insurance companies, agencies (Federal National Mortgage Association, Federal Home Loan Mortgage Corporation, Federal Housing Association, etc.), pension plans, real estate investment trusts (REITs), mutual funds, hedge funds, opportunity funds, credit companies, and private lenders. Commercial collateralized mortgage obligations (CMOs) had become an increasingly important vehicle for debt financing. These are rated by Moody’s, Fitch, or Standard & Poor’s. The secondary markets have considerable influence on real estate finance. Historically, it was recommended that real estate should be valued free and clear of all encumbrances including mortgage debt.1 If the typical investor obtains debt to acquire the real property interests, then you should consider the typical financial structure that is utilized to acquire the asset. The definition of market value has evolved to assume cash to the seller or a cash-equivalent price.2 More important, market participants consider debt to be crucial to the consummation of a satisfactory transaction. Many investors prefer financial leverage to improve the actual return on the investment and allow for diversification. Since market value is the most probable price that a typical investor is willing to pay and if the transaction price is influenced by financing, the cost and typical terms of financing should be considered in estimating market value. This idea supports the position that the source of capital and structure of the capital vehicle used in financing the property can have a significant affect on the value of the property that is collateralized. The capital structure associated with an entity that utilizes the real property as part of its business operations can be different from an owner/investor who leases the property to third parties. For example, a corporation that has a high credit rating may be able to obtain unsecured debt to acquire real property assets at a substantially lower cost. There may also be additional tax benefits that accrue to 1 2
William N. Kinnard Jr., Income Property Valuation (Lexington, MA: Heath-Lexington Books, 1971), 145. Cash equivalent price is defined as ‘‘a price expressed in terms of cash, as distinguished from a price expressed totally or partly in terms of the face amounts of notes or other securities that cannot be sold at their face amounts. Calculating the cash-equivalent price requires an appraiser to compare transactions involving atypical financing to transactions involving comparable properties financed at typical market terms.’’ Appraisal Institute, The Dictionary of Real Estate Appraisal, 4th ed. (Chicago: Appraisal Institute, 2002).
Real Property Competes with Other Asset Classes
563
owner-users that lower their after-tax effective cost of capital. When the real property is acquired as an investment, the real property is provided as collateral to obtain mortgage financing. The cost and the amount of financing are primarily driven by the capital markets.
REAL PROPERTY COMPETES WITH OTHER ASSET CLASSES Investors have many investment alternatives available in the current environment. In order to attract equity and debt investors, the expected returns or forward-looking returns must be commensurate with the perceived investment risks as compared to alternative investments (mortgage investments, stocks, bonds, etc.) and other factors influencing the return on real estate. Many real estate analysts use the convention of benchmarking the property rate of return to the risk-free rate using 10-year U.S. government bonds. The expected inflation rate and perceived risk over 10 years is factored into the yield on a 10-year bond. In comparison to real estate investments, 10-year U.S. government bonds are highly liquid, require no investment management, and are perceived to have assured income. Real estate investments in individual real property assets are highly illiquid, require intensive management, and have substantial investment risks that affect the cost of capital. Investors in real estate should be compensated for the additional investment risk over and above the risk-free rate for relative lack of liquidity, and for the additional management burden.3 The investment risk4 premium should include:
Market or business risk
Financial risk
Capital market risk Inflation risk
Environmental risk Legislative risk
Market or business risk is related to factors that occur in the real estate market that may affect the operations of the real estate. This may include changes in demand and supply impacting the forecasted net operating income. Market risks can be influenced by property type, location, and position of the real estate market cycle. By leveraging the property, the investor increases the financial risk associated with that particular investment, but, ideally, the expected return may also be increased. Positive leverage occurs when cost of debt is less than the unleveraged return on the real property. The loan-to-value ratio is defined as the ratio of money borrowed on a property to the property’s fair market value. As the loan-to-value ratio increases, the risk associated with a specific investment increases. The cost of debt also increases as the loan-to-value ratio increases. The degree of financial risk is directly related to the amount of debt and type of debt. Capital market risk is associated with changes that might occur in the capital markets that impact mortgage rates, expected equity, and property yield rates. The value of the investment may be affected if these rates increase or decrease. Changes in mortgage interest rates, the availability of debt 3
4
The discount for lack of marketability is built into the discount or capitalization rate, as it is in venture capital rates in business appraisals. Appraisal Institute, Advanced Income Capitalization (Chicago: Appraisal Institute, 2001), 7-3; William B. Brueggeman and Jeffrey D. Fisher, Real Estate Finance and Investment, 13th ed. (New York: McGraw-Hill, 2006), 385–387.
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Cost of Capital
and equity, and the expected rates of return on alternative investments can affect investment performance. Inflation risk is always present because real estate investments are highly illiquid. The expected cash flow from the operation of the real estate investment may lose its purchasing power. A real estate investment may not keep pace with inflation if the leases are not properly structured. Environmental issues are always present and continuously changing from the risks associated with new contaminants at the property level as well as in the market in which the property is located. Environmental issues may include a nuclear accident, a gasoline spill, or a new product that has been used that has been reclassified as an environmental hazard. In addition, weather conditions can affect the cost of operating the property (e.g., insurance expense for properties along the Gulf Coast). Legislative risk is always present in real estate investments at the local, state, and federal level. The 1986 Tax Reform Act had a negative impact on the demand for real estate by decreasing tax depreciation benefits to investors and, hence, real property values, especially as the 1986 act directly followed the 1981 Tax Reform Act, which created generous benefits to corporations and real estate investments. Despite the volatility generated by these extreme regulatory shifts, additional uncertainty can arise as local municipalities control zoning, building codes, and other regulations that can impact the cost of development, the operation of the real estate, and the net proceeds from sale of the property, such as a transfer tax. The cost of capital for real property is affected by the same risk factors that affect the cost of capital for a corporation. It is the degree of risk that varies between the macro- and microeconomic factors for each type of investment that may be different.
DIRECT CAPITALIZATION METHOD In real property valuation, direct capitalization is defined as: A method used to convert an estimate of a single year’s income expectancy into an indication of value in one direct step, either by dividing the income estimate by an appropriate rate or by multiplying the income estimate by an appropriate factor. A capitalization technique that employs capitalization rates and multipliers extracted from sales. Only the first year’s income is considered. Yield and value change are implied, but not identified.5
Embedded in a market-derived overall rate are the market-oriented assumptions concerning the future income expectations or the performance of similar properties. The market-oriented assumptions result in changes in projected income and value over time. The expected annual compound rate of change in income and value can be added to the overall capitalization rate to indicate the property yield or discount rate. OVERALL DIRECT CAPITALIZATION The capitalization formula for business valuation was presented in Chapter 4 as: (Formula 4.1) PV ¼
5
NCF1 c
Brueggeman and Fisher, Real Estate Finance and Investment.
Direct Capitalization Method
565
where: PV ¼ Present value NCF1 ¼ Net cash flow expected in first period c ¼ Capitalization rate In real property valuation, the direct capitalization formula becomes: (Formula 36.1) PVp ¼
Ip cp
where: PVp ¼ Overall value or present value of the property Ip ¼ Overall income to the property cp ¼ Overall property capitalization rate Using the reconstructed operating statement shown in Exhibit 36A.1 in Appendix 36A, the property’s net operating income is $524,052. If the market-supported capitalization rate for a project at stabilized occupancy was 10%, the indicated value is: PVp ¼
Ip $524;052 ¼ ¼ $524;052; Rounded $524;000 cp 10%
Note that Io is measured before income taxes. This basic formula can be modified to analyze the financial, physical, or legal interests in real property if the appropriate income stream can be estimated. Multipliers are a derivative of the direct capitalization overall rate. The net income multiplier is the reciprocal of the overall rate. Multipliers can be applied to the potential gross income, effective gross income, net operating income, or the equity cash flow. If income factors or multipliers are applied, the formulas generally are used to produce an indication of the property’s value. It is important to adequately define the type of income being estimated in order to employ the correct techniques to estimate proper value. Exhibit 36.1 displays the various relationships. The financial components are established by debt and equity interests; the legal components are established by contracts, such as leases creating the leasehold and leased fee interests; the physical components include land, building, furniture, fixtures, equipment, and other personal property. Based on the preceding information, the property value can be estimated by summing the parts of the components: (Formula 36.2) Property Value ðPVp Þ ¼ Equity Value ðMe Þ þ Mortgage Value ðMm Þ ¼ Land Value ðMLÞ þ Building Value ðMBÞ ¼ Leased Fee Value ðMLF Þ þ Leasehold Value ðMLH Þ If the financial components, the value of the equity positions, and the value of the mortgages are added, the overall value of the property is indicated. The financial components may include various
566
Cost of Capital
Exhibit 36.1
Income Components, Rates, Factors, Symbols, and Formulas for Direct Capitalization
Value Property Value (PVp) Property Value (PVp) Property Value (PVp)
Income Streams
Income Factors
Potential gross income (PGI) Effective gross income (EGI) Net operating income (NOI, Ip)
Potential gross income multiplier (PGIM) Effective gross income multiplier (EGIM) Net income multiplier (NIM)
Financial Components
Formula PVp ¼ PGI PGIM PVp ¼ EGI EGIM PVp ¼ NOI or Ip NIM
Rates
Equity Value (Me)
Equity income (Ie)
Mortgage Value (Mm)
Mortgage income (Im)
Equity Dividend Rate or Equity Capitalization Rate (ce) Mortgage Capitalization Rate (cm)
Me ¼ Ie/ce
Mm ¼ Im/Mm
Physical Components Land Value (ML) Building Value (MB)
Land income (IL) Building income (IB)
Land Capitalization Rate (cL) Building Capitalization Rate (cB)
ML ¼ IL/cL MB ¼ IB/cB
Income to the leased fee (ILF) Income to the leasehold (ILH)
Leased Fee Capitalization Rate (cLF) Leasehold Capitalization Rate (cLH)
MLF ¼ ILF/cLF
Legal Components Leased Fee Value (MLF) Leasehold Value (MLH)
MLH ¼ ILH/cLH
Note: The symbols in parentheses are based on the standard symbols used by the Appraisal Institute. Different symbols may be used by different authors and organizations.
equity and debt positions that are entitled to receive specific cash flows from an investment in real property. The value of the property may also be estimated by adding the physical components, the land and building values, which may be expanded to include fixtures, equipment, and other specific items commonly referred to as personal property. If personal property is included, the indication of value includes more than the real property. In theory, the sum of the parts equals the whole, indicating that the value of the leased fee plus the value of the leasehold provides an indication of the overall value of the property. This is true if the value of all of the parts is known, including the value associated with special benefits, such as tax benefits. This is not always the case in the valuation of the legal components of real property rights. The property yield rate can be estimated at stabilized occupancy if the long-term growth in cash flow and value are stable. Formula 4.3 from Chapter 4 was: (Formula 4.3) c¼kg where: c ¼ Capitalization rate k ¼ Discount or yield rate g ¼ Expected long-term sustainable growth rate in the cash flow available to subject investment
Direct Capitalization Method
567
This is quite similar to the formula presented in real estate texts,6 which is: (Formula 36.3) c¼kA where: c ¼ Capitalization rate k ¼ Discount or yield rate A ¼ Expected change in income and value (adjustment factor) A represents the relative change in value and is often expressed as D a. To calculate A, the adjustment factor represents the anticipated periodic change in value that is multiplied by the total change in value. Subscripts are used to indicate the applicable rates to the various components, such as equity and debt. Exhibit 36.2 illustrates the development of overall rates from competitive property sales of comparable properties. Multipliers often can be extracted from transactions of similar properties. If the effective gross income multiplier (EGIM) can be developed from similar properties that are comparable, the overall rate can be established as long as the operating expense ratios (OER) are similar. The operating expense ratio is defined as the ratio of the total operating expenses to the effective gross income. The basic formula is: (Formula 36.4) ð1:00 OERÞ co ¼ EGIM where: OER ¼ Operating expense rates EGIM ¼ Gross income multiplier Exhibit 36.2
Derivation of Indicated Overall Capitalization Rates from Comparable Sales for Apartments
Sale Number
1
2
3
4
5
Date of Sale Sale Price Address City State Total Units Potential Gross Income Vacancy & Credit Loss Free Rent Concessions Additional Income
10/1/2005 12/14/2005 $3,350,000 $3,300,000 4112 Fourth Ave 555 E 21st St Johnstown Johnstown New York New York 100 58 $596,085 $593,688 ($46,048) ($20,779) ($16,806) ($5,937) $5,600 $3,500
10/25/2005 $4,100,000 19 Linden Blvd Johnstown New York 53 $559,044 ($21,261) ($2,689) $5,590
1/24/2006 $4,275,000 829 E 9th St Johnstown New York 54 $606,759 ($16,314) ($2,952) $4,500
2/25/2006 $3,750,000 2516 Bedford Ave Johnstown New York 52 $579,996 ($20,025) ($2,800) $5,800
Effective Gross Income Operating Expenses Capital Reserve
$538,831 ($297,931) ($24,247)
$570,472 ($326,528) ($20,300)
$540,684 ($251,570) ($18,550)
$591,993 ($303,379) ($18,900)
$562,971 ($303,379) ($18,900)
Net Operating Income
$216,653
$223,644
$270,564
$269,714
$240,692
6.78%
6.60%
6.31%
6.42%
Indicated Overall Rate (cO) 6.47% 6
Charles B. Akerson, Capitalization Theory and Techniques Study Guide (Chicago: Appraisal Institute, 1984), 59.
568
Cost of Capital
Exhibit 36.3
Derivation of Effective Gross Income Multipliers and Overall Property Capitalization Rates
Sale Number Date of Sale Sale Price Effective Gross Income Multiplier (EGIM) Operating Expense Ratio (OER) Indicated Overall Rate (cp)
1
2
3
4
5
10/1/2005 $3,350,000 6.22 59.79% 6.47%
12/14/2005 $3,300,000 5.78 60.80% 6.78%
10/25/2005 $4,100,000 7.58 49.96% 6.60%
1/24/2006 $4,275,000 7.22 54.44% 6.31%
2/25/2006 $3,750,000 6.66 57.25% 6.42%
Exhibit 36.3 summarizes the development of effective gross income multipliers and the extraction of overall rates from the five comparable sales provided in Exhibit 36.2. BAND OF INVESTMENT METHOD The band of investment method estimates the overall rate based on the weighted average of the financial components of a capital investment. The net operating income can be used only to satisfy the debt and equity requirements. The dividend and equity capitalization rate (ce) is a single year’s cash flow to the equity position divided by the equity invested. The mortgage capitalization rate (c m ) is the annual debt service (ADS or I m ) divided by the principal amount or face value of the loan (Fd ). Generally, the typical loan-to-value ratio (Fd=PVp) is known as well as the typical terms of the loan. The annual debt service can be calculated based on this information. The equity capitalization rate, also known as the equity dividend rate or cash on cash return, can be extracted from comparable sale information or obtained by interviewing or surveying market participants. The basic formula, which can be modified for various classes of equity and debt, is: (Formula 36.5) Equity Component = 1[1 (Fd=PVp)] ce Plus : Debt Component ¼ ðFd =PVp Þ cm Equals : Overall Rate ¼ cp where: ce ¼ Dividend capitalization rate 1 (Fd=PVp) ¼ Equity to value ratio Fd=PVp ¼ Loan to value ratio cm ¼ Mortgage capitalization rate or constant cp ¼ Overall property capitalization rate The ‘‘band of investment’’ method is a term used in real estate appraisal that is analogous to the WACC in business appraisal for the overall cost of capital for the firm (see Chapter 17) except that the cost of debt includes repayment of principal and the equity component includes return ‘‘of’’ as well as ‘‘on’’ equity investment. This approach is most appropriate when the equity dividend capitalization rate can be well supported based on extraction from comparable sales. The preceding sales are utilized to estimate the equity capitalization rate or the cash on cash return in Exhibit 36.4. Exhibit 36.4 indicates a range in equity dividend capitalization rates between 5.00% and 5.99%. Greatest emphasis would be placed on the most comparable property, taking into consideration the quality, quantity, and the reliability of the data that was analyzed.
Direct Capitalization Method Exhibit 36.4
569
Derivation of Equity Dividend Capitalization Rates from Comparable Sales for Apartments
Sale Number
1
2
3
4
5
Date of Sale Sale Price Loan-to-Value Ratio Mortgage Amortization Term Interest Rate Annual Debt Service
10/1/2005 $3,350,000 73% 30 5.68% $169,953
12/14/2005 $3,300,000 75% 30 5.80% $174,266
10/25/2005 $4,100,000 75% 30 5.70% $214,168
1/24/2006 $4,275,000 68% 30 5.65% $201,363
2/25/2006 $3,750,000 72% 30 5.70% $188,050
Cash Flow to Equity Equity Invested Indicated ce
$46,700 $904,500 5.16%
$49,378 $825,000 5.99%
$56,396 $1,025,000 5.50%
$68,351 $1,368,000 5.00%
$52,642 $1,050,000 5.01%
The indicated overall rate for the subject property can now be developed using Formula 36.5 on these assumptions: Typical Mortgage Terms Loan-to-value ratio Interest rate Amortization period Payments Balloon payment The formula is as follows:
70% 5.70% 30 years Monthly 10 years Equity Component ¼ ½1 ðFd =PVp Þ ce Plus : Debt Component ¼ ðFd =PVp Þ cm Equals : Overall Rate ¼ cp
Inserting the sample data, we get: Equity Component ¼ 30% 5:49% ¼ 1:65% Plus : Debt Component ¼ 70% 6:96% ¼ 4:88% Equals : Overall Rate ¼ cp ¼ 6:52% The indicated overall rate falls within the range provided by the comparable property sales. ELWOOD FORMULA Prior to the introduction of financial calculators and desktop computers, L. W. Ellwood developed a mortgage-equity capitalization formula that takes into account the equity yield rate (ke) and the mortgage terms, including equity build-up through the amortization of the loan and the anticipated change in value over the investment holding period. The Ellwood formula is applicable only for level income streams or income streams that change systematically. Mathematical factors can be used to convert a systematically changing income pattern to a level annuity. The required equity yield rate on the investment is known. The equity yield rate is not equal to the equity dividend rate, which represents a cash flow rate. Assuming a level income stream, the Elwood formula is:
570
Cost of Capital
(Formula 36.6) cp ¼ ½ðFd =PVp Þ cm þ ½ð1 Fd =PVp Þ ke ½ðFd =PVp Þ P 1=Sn Þ Dp 1=Sn where: P ¼ Principal paid off over the holding period 1=Sn ¼ Sinking fund factor at the equity yield rate (ke ) Dp ¼ Change in value over the holding period and all other variables as defined in Formula 36.5. For example, based on market research, this information has been developed: Typical Mortgage Terms Loan-to-value ratio Interest rate Amortization period Payments Monthly Balloon payment Typical holding period Required equity yield rate Change in value over the holding period Type of income stream
70% 5.70% 30 years 10 years 10 years 12% 20% Level
Applying Formula 36.6 we get: cp ¼ ½ðFd =PVp Þ cm þ ½ð1 Fd =PVp Þ ke ½ðFd =PVp Þ P 1=Sn Þ Dp 1=Sn ¼ ð0:70 0:0696Þ þ ½ð1 0:70Þ 0:12 ð0:70 0:15726 0:0570Þ ð0:20 0:0570Þ ¼ 6:71% The debt service coverage ratio (DSCR or DCR) equals the ratio of net operating income to the annual debt service. Lenders utilize this ratio as an underwriting tool for risk management. The lender establishes the maximum ratio that will be permitted in order to provide sufficient cash flow to cover the debt. However, lenders may lower the debt coverage ratio for certain clients and under specific conditions (e.g., loan guarantees provided by the equity holder). The DSCR method can be well supported in an active mortgage market when properties are generally acquired with debt (as witnessed between 2003 and 2007). It is unreliable during periods when debt is difficult to obtain, such as during the early 1990s. The property should be at stabilized occupancy. One of the strengths of this approach is that all the factors can be derived from market participants. Mortgage terms, including the debt coverage ratio, loan-to-value ratio, amortization period, interest rate, maturity, and number of payments per year, can be obtained from lenders. Published information from the American Council of Life Insurance and other sources can provide additional support. The basic formula is: (Formula 36.7) cp ¼ DSCR cm ðFd =PVp Þ where: DSCR ¼ Debt service coverage ratio and all other variables as defined above.
Direct Capitalization Method
571
Exhibit 36.5 Example Derivation of Overall Property Capitalization Rates from Comparable Sales for Apartments, Debt Service Coverage Ratio Method Sale Number
1
Debt Service Coverage Ratio Mortgage Constant Loan-to-Value Ratio Indicated Overall Property Rate (cp)
1.27 6.95% 73% 6.47%
2
3
4
5
1.28 7.04% 75% 6.78%
1.26 6.96% 75% 6.60%
1.34 6.93% 68% 6.31%
1.28 6.96% 72% 6.42%
Exhibit 36.5 illustrates the development of the overall rate using the DSCR method based on the sale information from Exhibit 36.2. This method supports the previous overall capitalization rate estimates. The overall rate can be abstracted from property yield rates if the assumptions concerning the anticipated changes in value can be supported. For example, by interviewing market participants and researching published data, property yield rates were estimated to be approximately 8.25%, and the expected compound rate of change in income and value was reported to be 2.0%. Applying Formula 36.3, we get the indicated overall property capitalization rate: cp ¼ k A ¼ 8:25% 2:0% ¼ 6:25%
ESTIMATING THE CAPITALIZATION RATE Any real property interest that produces an income can be valued by direct capitalization. Several methods are available to estimate the appropriate capitalization rate for the specific real property interest being valued. The approach that is most applicable depends on the quantity, quality, and reliability of the available market information. More than one approach may be necessary to develop the appropriate capitalization rate. Methods to develop a capitalization rate include:
Interviewing market participants
Reviewing published surveys Abstracting from comparable sales
Abstracting from multipliers developed from comparable sales Developing by the band of investment method
Mortgage-equity analysis Estimating by the debt service coverage ratio method
Abstracting from yield rates
Potential buyers determine the assumptions that are utilized to estimate the transaction price that is paid for real property interests. Various published surveys are available that indicate the overall rates that are being applied to estimate value. Examples of these sources include:
RERC Real Estate Report
RealtyRates.comTM Quarterly Investor Survey
572
Cost of Capital
Korpacz Real Estate Investor Survey1 American Council of Life Insurance Quarterly Report
Commercial real estate brokers, such as Cushman & Wakefield, CB Richard Ellis, and Colliers International, also publish surveys. These reports provide broad parameters of the appropriate rates based on the expectations and experience of market participants. They also may not reflect the type of property and associated risks that are being analyzed. Actual transactions provide a clear indication of the market interaction between buyers and sellers. The ‘‘going-in’’ capitalization rate can be extracted from the sale information. The ‘‘going-in’’ capitalization rate is obtained by dividing a property’s net operating income for the first year after purchase by the sale price of the property.7 Recent comparable sales provide excellent support for market-derived capitalization rates if the information has been confirmed by the participants involved in the transaction. The comparable sales must represent a competitive investment with similar risk characteristics to the property that is being evaluated. These factors include:
Market conditions Buyer and seller motivation
Property type
Property rights
The method that should be used to develop the overall rate is based on a number of factors, and the analyst must realize that each approach has certain strengths and weaknesses. More than one method should be employed. The methods applied to develop the overall rate must be supportable and defensible. Market value is estimated based on the actions of typically informed and knowledgeable investors. Therefore, the most appropriate method is the method that reflects the typical actions of the most probable investors. The quantity and quality of data is important to provide support for the indicated overall rate. The information collected must also be reliable. Overall rates developed from each method can be very persuasive and easy to understand. Confirmation of the information, however, is difficult and time consuming, but it is extremely important because many services that provide this information do not have the expertise to extract the correct information. Thus, erroneous data may be provided. A number of adjustments might be required based on the information that is developed, such as:
Property rights conveyed Property type
Nonrealty components included
Near-term capital expenditures Adjustment for rent concessions
Rent loss due to absorption Present value adjustment for tenant improvement costs and leasing commissions
Adjustment for above- or below-market rents
Excess land
7
Appraisal Institute, Dictionary of Real Estate Appraisal.
Discounted Cash Flow Method
573
The preceding list is not all-inclusive but may have an impact on the transaction or sale price. It must be remembered that the going-in capitalization rate must be consistent with market expectations and reflect the expected income pattern from the real property investment. If the net income is declining or stable, the capitalization rate will be higher than a similar asset with an increasing income stream, and vice versa. The basic formula for a capitalization rate can be modified by factors to adjust for changing income patterns, such as increasing and decreasing annuities. Different investors treat capital outlays differently. It is important to understand the calculation that was used to develop the overall rate. Some investors deduct an annualized amount for nonrecurring capital expenditures, leasing commissions, and tenant improvement costs prior to capitalizing the income into value, while others do not. As long as the rates are developed in a similar method, it should not make a difference. The estimated market value is the same if these expenses are handled correctly. An appraisal is a snapshot in time based on observations at a specified point in time. Any changes in market conditions that occur in the future can impact the future estimates of market value. If mortgage rates increase and the debt coverage ratio changes in the future, the estimated market value of the property can be severely impacted by negative leverage. If market participants do not factor future market expectations into the analysis correctly, any refinancing of the property can have a negative impact of the performance of the property. RESIDUAL METHODS Today the traditional residual methods are rarely employed to develop capitalization rates. Today the residual methods generally are used for special-purpose properties, leasehold valuation, and feasibility analysis and in built-up areas with limited transactions. In the residual methods, it is assumed that the income is divided among the physical, financial, and legal components. The residual methods include land, building, mortgage, equity, property, leasehold, and leased fee. These methods should be employed only if the assumptions concerning the known information are supportable and defensible. If the information concerning one component includes its present value, its capitalization rate, the capitalization rate for the unknown component, and the net operating income for the real property, the residual income for the unknown component can be estimated and capitalized into value. The residual income is the amount that remains after the income required to support the investment in the other components has been met. The values of all of the components are now known and can be combined and divided into the net operating income to provide an indication of the appropriate overall rate, which is really a weighted average of the returns required to satisfy the investments in the components. Exhibit 36.6 summarizes the steps for each of the residual methods including the variables that must be known in order to apply a land, building, mortgage, or equity residual method. The residual methods are based on the theory that the overall rate was the weighted average of the returns required to satisfy the investment in the components, in particular land and building. Mortgage-equity analysis and discounted cash flow analysis permit a sophisticated analysis of the various financial components in a transaction.
DISCOUNTED CASH FLOW METHOD The overall value of the property is equal to the present value of the income stream plus the present value of the reversion of the property at the end of the projection period, which is shown in Formula 36.8:
574
Cost of Capital Exhibit 36.6
Residual Methods
Land Residual
Estimate net operating income Estimate building value Derive building capitalization rate Calculation of building income Deduct income to the building Equals residual income to the land Derive land capitalization rate Estimate land value Plus: building value Equals property value Calculate overall rate
(NOI, Ip) (MB) (cB) (cBMB = IB) (IpIB = IL) (IL) (cL) (IL=cL = ML) (ML + MB=PVp) (PVp) (Ip=PVp=cp)
Building Residual
Estimate net operating income Estimate land value Derive land capitalization rate Calculation of land income Minus: income to the land Equals: residual income to the building Derive building capitalization rate Estimate building value Plus: land value Equals: property value Calculate overall rate
(NOI, Ip) (ML) (cL) (cL ML=IL) (Ip IL=IB) (IB) (cB) (IB=cB = MB) (MB + ML = PVp) (PVp) (Ip=PVp = cp)
Mortgage Residual Estimate net operating income Estimate equity value Derive equity capitalization rate Calculation of equity income Minus: income to the equity Equals: residual income to the mortgage Derive mortgage capitalization rate Estimate mortgage value Plus: equity value Equals: property value Calculate overall rate
(NOI, Ip) (Me) (ce) (ce Me = Ie) (Ip Ie = Im) (Im) (cm) (Im=cm = Mm) (Mm + Me = PVp) (PVp) (Ip=PVp = cp)
Equity Residual
(NOI, Ip) (Mm) (cm) (cm Mm = Im) (Ip Im = Ie) (Ie) (ce) (Im=cm = Mm) (Me + Mm = PVp) (PVp) (Ip=PVp = cp)
Estimate net operating income Estimate mortgage value Derive mortgage capitalization rate Calculation of mortgage income Minus: income to the mortgage Equals: residual income to the equity Derive equity capitalization rate Estimate equity value Plus: mortgage value Equals: property value Calculate overall rate
(Formula 36.8) PVp ¼
CF1 CF2 CF3 CFN þ þ þ 2 3 ð1 þ kp Þ ð1 þ kp Þ ð1 þ kp Þn ð1 þ kp Þ þ
fðNOInþ1 =cn Þ ½ðNOInþ1 =cn Þ SC%g ð1 þ kp Þn
Estimating the Property Discount Rate
575
where: CF ¼ Cash flow for a specific period kp ¼ Overall rate of return or discount rate for property (property yield rate) NOIn+1 ¼ Net operating income in the year following the projection term cn ¼ Terminal or residual or going-out capitalization rate in final year n used to capitalize NOIn+1 SC% ¼ Cost of sale The last term is the reversion from the sale of the property. The net operating income is capitalized by the terminal capitalization rate or ‘‘going-out’’ capitalization rate. The terminal capitalization rate is usually, but not always, higher than the ‘‘going-in’’ capitalization rate. It is reasonable to assume that this rate will be higher because the improvements are older and the economic life may be reduced accordingly. In addition, there is more risk in forecasting the net operating income in the future. Ideally, the building is stabilized at that point in time. If not, adjustments may be required. The costs associated with selling the property must be deducted from the proceeds of sale at the end of the projection period. The cash flow and the reversion from the sale of the property are developed before deduction for interest, taxes, depreciation, and amortization. These items are considered if the analyst’s function is to estimate investment value, not market value. Semiannual, quarterly, or monthly discounting and capitalization are generally not used in estimating the market value of real property. Application of different time periods can affect the analysis. These conventions were used during the late 1970s when the inflation rate and the returns on money market accounts were quite high in comparison to historical averages. The proper approach would be market oriented, in which case most real property investors expect to receive the cash flows annually. For development properties, a shorter time period often is used. Different discount rates may be applied to the cash flows and the property reversion. If the real property is leased on a long-term basis to a creditworthy tenant, the risks associated with collecting the cash flow may be low and warrant a discount rate that might be comparable to the yield on the bonds that are available for a similar time period. The future sale price of the property may be quite speculative and will warrant a substantially higher discount rate to reflect the risk differential. The discount rate is also the weighted average of the yields associated with both components of the cash flow, from operations and the sale of the property.
ESTIMATING THE PROPERTY DISCOUNT RATE The property (overall) rate of return or discount rate (sometimes called property yield rate) is defined as the rate of return on the total capital invested, including both debt and equity. Generally, if the objective is to estimate market value, the real property is analyzed on a before-tax basis. The overall yield rate takes into consideration changes in net income over the investment period and net reversion at the end of the holding period. It is applied to cash flow before debt service.8
The property discount rate is forward looking and thereby cannot be abstracted from current comparable sales information without confirmation of the assumptions employed by the buyer to determine the price that was paid for an asset. The discount rate incorporates the investor’s compensation for the apparent risks, discussed previously, associated with that investment.
8
Ibid.
576
Cost of Capital
Not only do potential investors look at the risks previously mentioned, but they will also be cognizant of the yields on alternative investments and historical returns produced by similar investments. Investors often set a ‘‘target’’ or ‘‘hurdle’’ rate representing the minimum acceptable return. Investors are well aware of the cost of debt, which is influenced by inflation expectations and fluctuations in general in the capital markets as well as the supply and demand for debt. The expected property yield rate normally should exceed the weighted average cost of debt. In theory, the property discount rate should be the sum of its parts: the safe rate plus the expected inflation rate plus the risk premium (known as the build-up or summation method). The risk premium adjustment includes many previously mentioned factors that are difficult to quantify. Many consider it almost impossible to ‘‘build up’’ a discount rate by measuring the risks of each component. The property yield rate can be developed by the band of investment method provided that the assumptions used are market supported. The discount rate is the weighted average return on the financial components, equity and debt. The basic formula is: (Formula 36.9) kp ¼ ½ðFd =PVp Þ km Þ þ ½ð1 ðFd =PVp Þ ke where: km ¼ Mortgage interest rate ke ¼ Rate of Return on equity investment and all other variables as defined in Formulas 36.3 and 36.5. Based on the information provided earlier, the property discount rate can be estimated by applying Formula 31.8: Typical Mortgage Terms Loan-to-value ratio Interest rate Amortization period Payments Balloon payment Equity yield rate
70% 5.70% 30 years Monthly 10 years 14%
The formula is as follows: Equity Component ¼ ½ð1 ðFd =PVp Þ ke Plus : Debt Component ¼ ðFd =PVp Þ km Equals : Property Yield Discount Rate ¼ kp Inserting the example date; we get : Equity Component ¼ 30% 14:0% ¼ 4:20% Plus : Debt Component ¼ 70% 5:7% ¼ 3:99% Equals : Property Discount Rate ¼ 8:19% Formula 36.9 can be modified to include multiple equity investments and mortgages, such as mezzanine loans. The total weights must equal 100%. The typical real property investment includes debt, which provides support for this approach to develop the discount rate. The property discount rate provides for the required return on the mortgage and the expected return on the equity invested.
Estimating the Property Discount Rate
577
This method provides only an indication of the property discount rate during the first period. During subsequent periods, the equity component is increasing as the mortgage is amortized. The equity investor is seeking the same yield on the additional equity each year. This approach is widely used despite its shortcomings which become obvious when interest rates are increasing or decreasing and the terms of any refinancing assumptions are changed. The property discount rate can be estimated from overall capitalization rates if the anticipated changes in income and property value are known. Overall rates can be obtained from recent transactions. If the buyers are interviewed, the assumptions concerning the future changes in value and income can be established. If the income and value are expected to increase at a constant compound rate of growth, the formula to estimate the discount rate is derived from Formula 36.3: (Formula 36.10) kp ¼ cp þ A where all variables are as defined in Formula 36.3. The comparable sales indicated a range in capitalization rates between 6.31% and 6.78%, with average of 6.50%. If it is assumed that market participants expect value and income to increase at a compound rate of growth of 2.00% per year, the indicated discount rate from applying Formula 36.10 is: kp ¼ c p þ A ¼ 6:50% þ 2:0% ¼ 8:50% Formula 36.10 can be altered to accommodate level, increasing, or decreasing annuities. The property discount rates and the equity dividend capitalization rates can be extracted from comparable sales if the assumptions developed by the purchaser to prepare the expected cash flows prior to acquisition have been verified. Exhibit 36.7 summarizes the calculations for the comparables provided based on the assumptions developed by the purchasers. Based on the information obtained from the market, the indicated range in property discount rates is between 8.06% and 8.67%. Discount rates can also be estimated by surveying market participants. Published surveys are available summarizing the expectations and experience of investors. For example, Exhibit 36.8 explains information obtained from Korpacz Real Estate Investor Survey1. Exhibit 36.7
Example Derivation of Property Discount Rates from Comparable Sales for Apartments
Sale Number
1
2
3
4
5
Date of Sale Sale Price Net Operating Income Growth in Income Per Year Increase in Value in Five Years
10/1/2005 $3,350,000 $216,653 2.00% 2.00%
12/14/2005 $3,300,000 $223,644 1.50% 1.50%
10/25/2005 $4,100,000 $270,564 1.75% 1.75%
1/24/2006 $4,275,000 $269,714 1.75% 1.75%
2/25/2006 $3,750,000 $240,692 2.25% 2.25%
Cash Flow Per Year 0 (Purchase Price) 1 2 3 4 5 (Includes Reversion)
$3,350,000 $216,653 $220,986 $225,405 $229,913 $3,933,182
$3,300,000 $223,644 $226,999 $230,404 $233,860 $3,792,405
$4,100,000 $270,564 $275,299 $280,117 $285,019 $4,761,534
$4,275,000 $269,714 $274,434 $279,237 $284,123 $4,951,481
$3,750,000 $240,692 $246,108 $251,645 $257,307 $4,454,388
Inferred Property Discount Rate kp
8.47%
8.28%
8.35%
8.06%
8.67%
578 Exhibit 36.8
Cost of Capital Discount Rate Survey Data
National Central Business District Office Market Fourth Quarter 2006 Current Quarter
Last Quarter
Year Ago
6.00%–10.00% 8.11% —
6.25%–10.00% 8.34% 23
7.00%–10.00% 8.65% 54
4.50%–9.00% 6.94% —
4.50%–9.50% 7.07% 13
4.50%–9.50% 7.35% 41
6.00%–10.00% 7.78% —
6.75%–10.00% 7.98% 20
7.00%–10.00% 8.23% 45
0.00%–7.00% 3.25% —
0.00%–7.00% 3.04% +21
–3.00%–5.00% 2.10% +115
1.50%–4.00% 2.98% —
1.50%–4.00% 2.98% 0
1.50%–3.00% 2.85% +13
a
DISCOUNT RATE (IRR) Range Average Change (Basis Points) OVERALL CAP RATE (OAR)a Range Average Change (Basis Points) RESIDUAL CAP RATE Range Average Change (Basis Points) MARKET RENT CHANGE RATEb Range Average Change (Basis Points) EXPENSE CHANGE RATEb Range Average Change (Basis Points) a b
Rate on unleveraged, all-cash transactions. Initial rate of change.
This survey provides benchmarks that can be used along with other market information to support the discount rate. The discount rates reported can be compared to 10-year Treasury bonds over time to provide an indication of the risk premium associated with a real estate investment in a central business district (CBD). Clearly, a wide range is indicated, and further research is required to support the final selection of an appropriate discount rate. Tests of reasonableness should be performed. Yields on alternative investments can be analyzed and compared to the expected yields forecasted over time to indicate the trends that have occurred and test the expected yield. Exhibit 36.9 displays a comparison of 10-year Treasuries and Moody’s Baa yields to the expected yields on real estate. Exhibit 36.9
Comparison of Bond Yields to Real Estate Discount Rates In Percent
Survey—Real Estate Discount Rate Federal Funds Rate Bank Prime Loan Treasury Constant Maturities Conventional Mortgages Moody’s Seasoned Baa Real Estate vs. Moody’s Baa Spread Real Estate vs. Treasury Spread
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
11.20 5.46 8.44 6.35 7.60 7.87 3.33 4.85
11.36 5.35 8.35 5.26 6.94 7.22 4.14 6.10
11.52 4.97 8.00 5.65 7.43 7.88 3.64 5.87
11.41 6.24 9.23 6.03 8.06 8.37 3.04 5.38
11.49 3.89 6.91 5.02 6.97 7.95 3.54 6.47
11.90 1.67 4.67 4.61 6.54 7.80 4.10 7.29
10.22 1.13 4.12 4.01 5.82 6.76 3.46 6.21
9.56 1.35 4.34 4.27 5.84 6.39 3.17 5.29
8.97 3.22 6.19 4.29 5.86 6.06 2.91 4.68
8.30 5.24 8.25 4.63 6.13 6.30 2.00 3.67
Summary
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The indicated trend for the expected property discount rates was downward beginning in 2003 through 2006. Likely this trend will reverse itself as the market changes in late 2007 and early 2008. The spreads between Moody’s Baa and the 10-year constant maturity bonds was relatively constant until 2003, at which time the spreads began to narrow. There appears to be very little correlation with the federal funds rate and the bank prime rate. There is always a risk forecasting into the future based on the historical trends, but the basic parameters are established for supporting a discount rate or a range for the expected property discount rate. Other tests of reasonableness may include:
In theory, the going-in capitalization rate plus the annual compound rate of change in income over the projection period should be quite comparable to the property discount rate. Generally, the rate of return on equity or equity yield rate should be higher than the property discount rate and the mortgage interest rate. The equity yield rate should be higher than the equity dividend rate if it is anticipated that income and value will increase over time.
SUMMARY This chapter introduced the methods and applications utilized to develop the appropriate returns on individual, income-producing, real property investments. The basic concepts are quite similar to business valuation concepts, but additional factors must be considered in the analysis of incomeproducing real estate.
Appendix 36A
Valuing Real Property James MacCrate, MAI, CRE, ASA Introduction Steps in Estimating Real Property Value Determining the Projection (Capital Recovery or Holding) Period Measuring Income Projecting Cash Flows Summary
INTRODUCTION This appendix focuses on the income associated with the ownership of real property rights. This is different from the income and cost of capital that might be earned by a business enterprise operating on the property, such as a marina, hotel, fitness club, or restaurant. The value of real estate is the value of the real property or the rights inherent in the ownership of real estate or realty and is based on its capacity to support and house economic activities. In essence, real property value is a function of its physical attributes, rights inherent in the ownership of real estate or realty, and its economic location. The property’s comparative ability to generate income becomes its basis of value. Definitions of terms such as net income and cash flow differ from those used previously in this text. Chapter 36 and this appendix defines these terms for real estate valuation; they should not be confused with the terms as defined in financial textbooks.
STEPS IN ESTIMATING REAL PROPERTY VALUE Value is the present worth of future benefits. The future benefits derived from the ownership of real estate include the cash flow from the real estate plus the proceeds of the resale of the real property, which is often referred to as the reversion or ‘‘residual.’’ The reversion is defined as ‘‘a lump-sum benefit that an investor receives or expects to receive at the termination of an investment which is often called reversionary benefit.’’1 Five basic steps are required to estimate value by the income approach: 1. 2. 3. 4. 5.
1
Determine the projection (holding or capital recovery) period. Estimate the future cash flows over the projection (holding or capital recovery) period. Estimate the reversionary or residual value of the property. Select an appropriate yield or discount rate. Discount the expected cash flows including the reversionary or residual interest to present value.
Appraisal Institute, The Dictionary of Real Estate Appraisal, 4th ed. (Chicago: Appraisal Institute, 2002).
580
Steps in Estimating Real Property Value
581
DETERMINING THE PROJECTION (CAPITAL RECOVERY OR HOLDING) PERIOD Real property generally is not held indefinitely. Historically, the projection (often called holding or capital recovery period) was tied to the economic life or useful life of the property. Real estate was used in the operation of a business, such as a manufacturing operation. The improvements were considered to be a wasting asset and the investment in the improvements had to be recovered over its useful life and replaced. Subsequently, the income tax laws influenced the maximum holding period due to depreciation benefits. The typical holding period was between 7 and 10 years. The Tax Reform Act of 1986 reduced the tax-sheltered benefits associated with owning real estate, which has affected the holding period. The most typical projection period applied in the discounted cash flow analysis is 10 years. A different holding period may be justified when it is supported by the actions of market participants. A knowledgeable investor must take into consideration a number of factors in determining the projection or holding period. These factors include, but are not limited to:
Type of property Tax considerations, such as depreciation benefits
Mortgage rollovers
Lease rollovers Required capital investment
Changes in the conditions of the real estate market Leverage
Risk management
Portfolio management Changes in corporate strategy
Typical investors want to maximize their return. Investors may consider selling when the after-tax marginal rate of return falls below the after-tax marginal rate of return that can be achieved on alternative investments.2 However, if the after-tax marginal rate of return on the investment can be improved by refinancing and/or remodeling, the decision to sell might be postponed. It is also extremely important to consider the level of occupancy at the expiration of the projection period, which can impact the return on the investment, because occupancy will impact the resale price of the property. Ideally, the projected cash flow that provides the basis for the calculation of the resale proceeds should be at or near stabilized occupancy levels. If a projection period other than 10 years is used, the property yield rates may be affected by the shortening or lengthening of the holding period because the market expectations vary with the time period. Regardless, the projection period selected should always be market oriented and reflect the actions of informed buyers and sellers. MEASURING INCOME In the valuation of a real estate investment, it is important to develop a reconstructed income and expense statement at stabilized occupancy. The net operating income (NOI, Ip) is defined as ‘‘the actual or anticipated net income that remains after all operating expenses are deducted from effective gross income, but before mortgage 2
William B. Brueggeman and Jeffrey D. Fisher, Real Estate Finance and Investment, 13th ed. (New York: McGraw-Hill, 2006), 420.
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Cost of Capital
debt service and book depreciation are deducted; may be calculated before or after deducting replacement reserves.’’3 It is imperative to develop or reconstruct the operating statement based on the methodology utilized by the most probable purchasers. The analysis may be based on one of these:
Projected income during the first year of ownership
Trailing 12 months’ income Actual income at the time of the analysis
Projected income over the holding or projection period
Stabilized income
The income estimate must reflect the interest being analyzed. If the analyst is estimating the market value of the leased fee interest, the landlord/owner’s position, the contract income should be analyzed. This would be the income based on the actual leases in effect as of the date of the analysis and typically reflects the projected income to be received. If the fee simple interest is being analyzed, the appropriate market rents should be considered. Most often, typical investors forecast the stabilized income that is expected to be received over the next year. The stabilized income is achieved when the real property is at its long-term stabilized occupancy. Stabilized occupancy is defined as occupancy at that point in time when abnormalities in supply and demand or any additional transitory conditions cease to exist and the existing conditions are those expected to continue over the economic life of the property; the average long-term occupancy that an income-producing real estate project is expected to achieve under competent management after exposure for leasing in the open market for a reasonable period of time at terms and conditions comparable to competitive offerings.4
The degree to which the actual net operating income is above or below the stabilized net operating income is one factor that affects the risk associated with a particular real estate investment, and also provides the basis for analyzing comparable sales.5 This reconstructed operating statement generally differs from pro forma cash accounting income statement developed by accountants but is consistent with the accrual accounting procedures they use when annualizing multiperiod capital expenditures and longer-term outlays within a cash flow projection. Potential gross income includes all income from contractual obligations associated with leases, estimated market rent from vacant space, escalation income, and reimbursements for operating expenses and from services provided to the tenants. A market-derived potential gross income multiplier can be applied to the potential gross income to provide an indication of value. Effective gross income is defined as the potential gross income minus vacancy and credit loss. Vacancy and credit loss must be market oriented and can be obtained from published surveys, comparable properties, and/or interviews with market participants. Vacancy should include frictional (temporary) vacancy due to lease rollovers, structural (permanent) vacancy, and income loss until stabilized occupancy is achieved. Credit loss is the risk of default by the tenant. Lease concessions must also be considered. A market-derived effective gross income multiplier can be applied to the effective gross income to provide an indication of value. 3 4 5
Appraisal Institute, Dictionary of Real Estate Appraisal. Ibid. Richard D. Wincott, ‘‘A Primer on Comparable Sale Confirmation,’’ Appraisal Journal (July 2002): 274–282.
Projecting Cash Flows
583
Operating expenses must be deducted from the effective gross income to estimate the net operating income before capital expenses, such as tenant improvement costs and leasing commissions, annual debt service including interest and amortization, and income taxes. Operating expenses may be classified as fixed, variable, and reserves for replacement. Fixed expenses, such as real estate taxes, do not vary with occupancy. Variable expenses change with occupancy and must be adjusted to reflect actual occupancy over the projection period. Reserves for replacement or a reserve allowance may be necessary in order to replace items that may wear out and are estimated based on the useful life of the item. Building items that may require replacement include carpeting, painting, appliances, roof covering, and parking areas. The reconstructed income and expense statement should conform to the standard chart of accounts for that particular asset and be based on an analysis of historical income and expenses at the property, a review of comparable properties, and industry standards. Because the valuation must require a focus on the valuation of real estate as a function of its performance capacity, items that are commonly considered in the valuation of a business or an operating enterprise are excluded in the calculation of net operating income. Examples would include book depreciation, income taxes, capital contributions, mortgage interest and amortization, leasing commissions, tenant improvement costs, and major capital expenditures that are nonrecurring. The total operating expenses are deducted from the effective gross income to indicate the net operating income. As noted with the exclusions just discussed, only property-related expenses are included. A market-derived net income multiplier can be applied to the net operating income to provide an indication of value. Sample Reconstructed Operating Statement Exhibit 36A.1 provides an example of a typical reconstructed operating income and expense statement for a project at stabilized occupancy. The exhibit provides the basis for analyzing the costs and risks associated with an investment in the real property. The net operating income can be capitalized into value to provide an indication of value at stabilized occupancy by direct capitalization. If the property is not operating at stabilized occupancy, adjustments might be required to provide an indication of value ‘‘as is.’’ Adjustments for near-term capital expenditures, such as tenant improvement costs, leasing commissions, and other capital costs, can affect market value. Other adjustments may include the present value of tenant concessions,6 present value of rent loss until stabilization, present value of below-market rents, and present value of excess rents. In addition, the property discount rate has to reflect the market perceived risks. The annual debt service must be deducted to provide the pretax cash flow to the equity position. Usually, a pretax cash flow projection is developed. Pretax cash flow (CFpt) is defined as ‘‘the portion of net operating income that remains after total mortgage debt service is paid but before ordinary income tax on operations is deducted; also called before-tax cash flow or equity dividend.’’7
PROJECTING CASH FLOWS The overall value of the property is equal to the present value of the income stream plus the present value of the reversion of the property at the end of the projection period, as shown in Formula 36.10: 6
7
Tenant concessions are defined as an inducement for a tenant to lease space, usually in the form of free rent, additional tenant improvements, moving costs, and so on. Appraisal Institute, Dictionary of Real Estate Appraisal.
584
Cost of Capital
Exhibit 36A.1
Example Reconstructed Operating Income and Expense Statement
Potential Gross Income Leased Units Vacant Units Expense Reimbursements Concession Income Other Revenue Total Potential Gross Revenue Less Vacancy and Credit Loss Vacancy & Turnover (5%) Credit Loss (1.00%) Total Vacancy and Credit Loss Effective Gross Income Operating Expenses Fixed Expenses Real Estate Taxes Insurance Total Fixed Expenses Variable Expenses General & Administrative Management Fees Repairs and Maintenance Utilities Trash Removal Security Total Variable Expenses Replacement Allowance Carpeting Roof Cover Total Replacement Allowance Total Operating Expenses Stabilized Net Operating Income
$890,500 71,000 48,000 19,000 10,000 $1,038,500 $51,925 $10,385 $62,310 $976,190
$195,238 20,000 $215,238 $78,000 $49,000 44,000 34,000 4,000 5,900 $214,900 $7,000 15,000 $22,000 $452,138 $524,052
Source: MacCrate Associates LLC.
(Formula 36.10) PVp ¼ þ
CF1 CF2 CF3 CFn þ þ þ ð1 þ kpÞ ð1 þ kp Þ2 ð1 þ kp Þ3 ð1 þ kp Þn fðNOInþ1 =Cn Þ ½ðNOInþ1 =cn Þ SC%g ð1 þ kp Þn
where: CF ¼ Cash flow for a specific period kp ¼ Property discount rate or overall rate of return on property NOIn+1 ¼ Net operating income in the year following the projection term cn ¼ Terminal or residual or going-out capitalization rate SC% ¼ Cost of sale The actual cash flows, including the first year’s cash flow, may differ from the stabilized reconstructed income and expense statement presented previously. Investors usually acquire title to real property subject to the existing leases and other contractual obligations. The projected cash flow takes into consideration the actual contractual obligations specified in the leases. The lease obligations may
Projecting Cash Flows
585
differ substantially from the market standards that were used to reconstruct the income and operating expense statement. Projected vacancy is based on lease rollovers and structural vacancy. It will differ from the longterm equilibrium or stabilized vacancy and may vary over the projection period. Credit loss will be based on the creditworthiness of the tenants in place. The operating expenses must take into account the changes in occupancy over the projection period. Certain expenses are sensitive to changes in occupancy. Other expenses may have to be adjusted to reflect the expected inflation over the projection period. Certain expenditures are deducted from the net operating income to estimate the cash flow to the property before debt service and income taxes. The cash flow is the actual cash flow to the investors after deducting tenant improvement costs, leasing commissions, capital expenditures, and other nonrecurring anticipated expenses from the net operating income. These deductions may vary over the projection period. Typically, real estate investors prepare a cash flow including the resale of the property, which usually provides for the recapture of the investment plus a return on the investment if there is an increase in value. The resale price is referred to as the reversion or residual. The future sale price generally is based on capitalizing the income in the first year following the projection period. The rationale is that, at the end of the projection period, the typical buyer will estimate the future benefits that will be received after that point in time. The net operating income is capitalized by the terminal capitalization rate or ‘‘going-out’’ capitalization rate. The terminal capitalization rate is usually, but not always, higher than the ‘‘going-in’’ capitalization rate. It is reasonable to assume that this rate will be higher because the improvements are older and the economic life may be reduced accordingly. In addition, there is more risk in forecasting the net operating income in the future. Ideally, the building is stabilized at that point in time. If not, adjustments may be required. The costs associated with selling the property must be deducted from the proceeds of sale at the end of the projection period. The cash flow and the reversion from the sale of the property are developed before deduction for interest, taxes, depreciation, and amortization. These items are considered if the analysts’ function is to estimate investment value, not market value. The preceding can be summarized into seven steps: Step 1. Analyze and compare the historical and current income and expenses with competing properties and published industry sources to establish the basis for the forecast going forward. Step 2. Estimate market rent and the typical lease terms for the different types of tenant spaces, including the probability of lease renewal and downtime between leases. Step 3. Forecast the potential income over the projection period from all sources, including leased space, vacant space, lease escalations, and expense reimbursements, with a proper allowance for vacancy and credit loss. Step 4. Forecast and deduct the projected property operating expenses, tenant improvement costs, leasing commissions, and other anticipated capital expenditures from the projected income. Step 5. Determine the most probable projection period. Step 6. Estimate the terminal capitalization rate and calculate the projected property reversion. Step 7. Select the appropriate discount rate and discount the cash flows including the reversion to present value. The analysis must reflect the expected benefits that would be anticipated by market participants. The most common error is to utilize assumptions to forecast the income and expenses that do not reflect the actions of informed buyers and sellers. The values produced by direct capitalization and the discounted cash flow analysis should be identical with perfect information.
Chapter 37
Cost of Capital of Real Estate Entities James MacCrate Introduction Definition of a Real Estate Entity Structure of Real Estate Entities Capital Structure Real Estate Cycles Measuring Net Cash Flow for Real Estate Entities Valuation of Real Estate Entities Underlying Assets Approach Income Capitalization Approach Overall Direct Capitalization Estimating the Capitalization Rate Discounted Cash Flow Method Computing the Weighted Average or Overall Cost of Capital Estimating the Cost of Equity Capital ‘‘As If Publicly Traded’’ Implied FFO Yield Dividends Applying the Build-up Method Applying the Capital Asset Pricing Model Analysis of Long-term Dividend and Total Return Summary Additional Reading Appendix 37A
INTRODUCTION In Chapter 36 we discussed the development of the cost of capital for direct real property investments. An equity investment in real estate can also be made indirectly by purchasing shares of a company or partnership holding real property interests. In this chapter we discuss the development and application of the cost of capital for real estate entities that own real property interests to produce income. This chapter is an introduction to the subject; it is not intended to cover all the issues that an analyst might encounter in the process of estimating the cost of capital for real estate entities. This chapter focuses on real estate business enterprises that derive a large percentage of their income from tangible, real property interests, such as equity real estate investment trusts (REITs), partnerships, and real estate operating and/or investment companies. A business enterprise is defined
I would like to thank Ronald Donohue, PhD, The Hoyt Advisory Group, and Patricia Bellack for assistance with this chapter.
587
588
Cost of Capital
as ‘‘any commercial, industrial, service, or investment entity pursuing an economic activity.’’1 Since real estate entities are going concerns, or businesses that manage, buy, and sell real estate assets, an investment in this type of company is very different from a single direct investment in real property. Real estate entities can be very complex enterprises that require a thorough knowledge of the various factors that can impact the cost of capital. The cost of capital can vary substantially based on the characteristics of the entity that owns and controls the real property interest. REITs represent a large portion of the real estate market for which public information is available that can be analyzed. Therefore, we concentrate on REITs in this chapter.
DEFINITION OF A REAL ESTATE ENTITY A real estate entity can be defined as any person including, but not limited to, any partnership, corporation, limited liability company, trust, other entity, or multitiered entity that exists or acts substantially for the purpose of holding, directly or indirectly, title to or beneficial interest in real property. The value of a real estate entity includes many components, such as land, buildings, personal property, intangible assets, and the business operation. Real properties can be owned by individuals, partnerships, corporations, or trusts. These investment vehicles may take many different forms, such as REITs. A REIT is defined as ‘‘a company dedicated to owning, and in most cases, operating incomeproducing real estate, such as apartments, shopping centers, offices, and warehouses. Some REITs also engage in financing real estate.’’2 REITs can be publicly traded REITs, non–exchange-traded REITs, or private REITs. The characteristics of each type of entity are different with regard to regulatory oversight, liquidity, transaction costs, management, investor control, corporate governance, and taxation. Real estate entities are extremely diverse, but can be described in general as being engaged in the ownership, acquisition, redevelopment, investment in, and management of income-producing real property. As mentioned, ownership interests may be held in direct investments or indirect investments in joint ventures, syndications, and partnerships. These entities may own real properties that are operated as an ongoing business or held for investment or development or used in various activities. Property interests may be owned through controlled or noncontrolled investments and business enterprises. Many real estate entities specialize in a specific line of business, such as development of new properties, redevelopment of existing properties, or the operation of existing properties. They may concentrate on buying and selling properties or focus on operating properties, or some combination thereof. Some real estate entities are highly specialized in certain areas, such as developing singlefamily residential communities, marinas, cell towers, prisons, golf courses, timberland, restaurants, theaters, or automobile dealerships, while other real estate entities engage in a broader range of real estate activities. It is quite common for real estate entities to specialize by property type, such as industrial, office, multifamily residential, hotel, and health care facilities. Other entities diversify across property types or engage in mixed use development. Real estate entities may also choose to concentrate their investments and activities in specific markets or geographic regions. As a general rule, they acquire and/or
1
2
International Valuation Standards Committee, International Valuation Standards, 7th ed. (London: International Valuation Standards Committee, 2005), 60. National Association of Real Estate Investment Trusts, Glossary, www.investinreits.com/learn/glossary.cfm.
Definition of a Real Estate Entity
589
develop real property assets to operate as part of a business enterprise that generates income to distribute to shareholders or partners. The extent to which real estate entities are concentrated in a specific property type or geography can impact their cost of capital as concentration results in nonsystematic risk and can impact credit ratings and required yield spreads. Real estate entities typically are categorized in the investment community by asset class, type of business, property type, and/or geographical location. These categorizations are useful in helping to identify peer group for analytic and valuation purposes. For example, the National Association of Real Estate Investment Trusts (NAREIT) categorizes REITs as equity REITs, mortgage REITs, and hybrid equity-mortgage REITs. Equity REITs generally own and operate income-producing real estate. Mortgage REITs invest in loans secured by residential or commercial real estate or in residential or commercial mortgage-backed securities. Hybrid REITs typically own some combination of equity and debt interest in real estate. Equity REITs represent the majority of the REIT market, as measured by number of companies and market capitalization. Equity REITs can be further segmented into specific real estate subsectors, such as:
Residential properties
Office properties
Shopping centers and malls Storage centers
Industrial parks and warehouses Lodging facilities, including hotels, motels, and resorts
Health care facilities
Special use properties
Real estate companies are going-concern businesses that produce income and may be involved in many different activities, including asset or portfolio management, leasing, property development, and tenant services. Like other types of businesses, real estate entities may be able to create intangible value or franchise value. Franchise value pertains to the ability of management to create value over and above the current value of the existing real property portfolio.3 Conversely, it is possible to have negative franchise value, in which a collection of assets under management’s control is less valuable than current value of the existing real estate portfolio. The type of properties, the geographical location of the assets, and the business enterprise may influence the cost of capital because the perceived risks vary. The total return on an investment in a real estate entity comes from the distribution of income from the operation of the real property portfolio or development through dividend payments plus long-term appreciation if the real property assets or the entity is sold. Return of capital from depreciation, which is not consistent with accounting standards, represents a significant portion of the distributions from any REIT and other real estate entities. Real estate entities are operating businesses that include tangible assets (i.e., real estate) as well as intangible assets, such as the quality and expertise of management and tenant relationships. As a result, the value of a real estate entity can be more or less than the value of the underlying real estate owned by the entity. Equity shares in real estate entities that trade at a premium above the net value
3
Mike Kirby, Warner Griswold, and Jon Fosheim, ‘‘Pricing REIT Stocks,’’ REIT University, April 4, 2007.
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Cost of Capital
of the real estate may have a franchise value. The structure of the entity may create intangible value. While the net value of the real estate assets is important, other factors influence share price as well.4 STRUCTURE OF REAL ESTATE ENTITIES The legal structure of the entity may have an impact on its value and cost of capital. The entity may be a special-purpose entity,5 sole proprietorship, corporation, partnership, S corporation, or a limited liability company. Pass-through entities that can pass the earnings through to the investors may have certain tax advantages. For example, REITs and real estate limited partnerships/master limited partnerships make direct investments in real property assets. These entities are pass-through entities. And the legal requirements for these entities are quite specific. REITs are required by law to distribute at least 90% of their taxable income to their shareholders each year. REITs are not taxed at the entity level; rather the tax obligation is passed-through to the individual investors. REIT dividend distributions typically are derived from various sources. For tax purposes, distributions usually are allocated to ordinary income, capital gains, and return of capital. The return of capital distribution is not currently taxed, but the investor’s cost basis in the investment is reduced by the amount of the distribution. The reduced tax basis affects the capital gain for tax purposes at the time that the investment is sold. In a partnership, the partnership agreements dictate the timing, character, and amount of distributions to the various partnership interests. Often, distributions and their timing are controlled by the general partner. A real estate partnership may pass through gains, profits, and losses to different investors. Partnerships also have a limited life, whereas corporations generally have an unlimited life. Many real estate operating companies, public and closely held companies, are not structured as REITs or partnerships and are taxed at the entity level. But they do not face the distribution requirement of a REIT and may have greater opportunity to reinvest earnings. They also do not face the same restrictions on the type of real estate business it conducts.6 Other factors to consider in analyzing different ownership structures include different income tax rates, cost of management, diversification, and availability of financing as well as control and marketability issues. These factors may also have a direct impact on the cost of capital. CAPITAL STRUCTURE The real estate capital markets are considered to be segmented into four quadrants: 1. 2. 3. 4.
Private equity Public equity Private debt Public debt
The public markets have grown in importance throughout the 1990s into the 2000s through the availability of funds from commercial mortgage-backed securities market, mutual funds, growth in 4
5
6
Richard Marchitelli and James R. MacCrate, ‘‘REITs and the Private Market: Are Comparisons Meaningful?’’ Real Estate Issues (August 1996): 7–10. Jalal Soroosh and Jack T. Ciesielski, ‘‘Accounting for Special Purpose Entities Revised: FASB Interpretation 46(R),’’ CPA Journal Online, April 5, 2007, describes a special-purpose entity ‘‘as an off–balance-sheet entity that is created by a party (the transferor or the sponsor) by transferring assets to another party (the SPE) to carry out a specific purpose, activity, or series of transactions. Such entities have no purpose other than the transactions for which they are created. The legal form for these entities may be a limited partnership, a limited liability company, a trust, or a corporation.’’ Barron’s refers to a publicly traded real estate company that has opted out of the tax status afforded REITs as a real estate operating company (REOC). Dictionary of Real Estate Terms (Barron’s Educational Series, 2004).
Definition of a Real Estate Entity Exhibit 37.1
591
Percentage of Debt and Equity for Public REITs
Second Quarter 2006 Total Liabilities plus Shareholder Equity Secured Debt Unsecured Debt Other Liabilities Total Liabilities Total Mezzanine Financing Preferred Equity Common Equity Total Liabilities plus Shareholder Equity
29.1% 25.3% 14.0% 61.5% 4.5% 4.9% 29.2% 100.0%
Source: SNL Securities, NAREIT.
real estate investment trusts, and other investment vehicles. The private and public markets offer alternative investment opportunities to investors in both the debt and equity markets. Diversified capital instruments are available to provide debt and equity. For example, Exhibit 37.1 summarizes the total percentages of debt and equity for public REITs as of the second quarter of 2006. During the last few years, capital has been readily available for debt and equity positions in real estate entities and the cost has been relatively inexpensive in comparison to the long-term average cost of capital for real estate investors. Declines in interest rates will, ceteris paribus, lower the overall weighted average cost of capital. Increases in interest rates can have the reverse impact.7 The capital may include equity in the form of common stock or preferred stock, partnership interests, convertible debt, secured or unsecured debt, participation loans, and so on. The debt component may be short, intermediate, or long term, secured or unsecured, fixed or variable rate with different ratings, all of which impacts the cost of debt and the perceived risk of the equity and debt components. In many cases, real estate entities have substantial lines of credit, which typically are used as short-term sources of floating rate debt capital until they can be replaced with longer-term debt or equity capital. Other forms of short-term debt may include mezzanine or bridge loans, construction loans, and revolving credit. Debt may or may not be secured. When it is secured, it may be secured by one property or cross-collateralized with multiple properties. The amount of leverage is extremely important. The greater the leverage, the greater the risk to the equity and debt positions, raising required rates of return and the resulting cost of capital. Interest rate swaps have become more common to protect against changing interest rates. Interest rate risk is extremely important for a long-term investor in real property interests when debt is placed for shorter periods at variable rates. Some other factors that may affect the cost of debt include:
Position in the real estate and economic cycle Quality and credit rating of tenants
Property types and quality held by the entity
Total leverage Debt coverage ratio and individual property loan-to-value ratios
Bond rating Loan terms
Amount of variable rate debt
7
Pacific Security Capital, ‘‘The Impact of Rising Interest Rates on Commercial Real Estate,’’ Oregon: Pacific Security Capital, IRETO Report (May/June 2005).
592
Cost of Capital
Maturity date of the debt Management reputation and track record
Public REITs generally have a lower percentage of debt relative to real estate asset value compared to the private property markets, which can have debt to real estate asset value ratios in excess of 70%. This reduced leverage in the public markets lowers the cost of equity capital in comparison to the private markets because of reduced risk. During periods of rising interest rates, property values may decline, and this can negatively impact the value of real estate entities. During periods of declining interest rates, similar to the years 2003 to 2006, property values often rise, which generally increases the value of real estate entities. REAL ESTATE CYCLES The availability and cost of capital for real estate entities varies substantially over time. The variance may be the result of capital market factors or space market factors. On the space market side, the availability and cost of capital varies during the real estate cycle. When the supply of space exceeds the demand, the availability of capital decreases and the cost of capital may increase. Exhibits 37.2 and 37.3 show the changes that take place during the typical real estate market cycle for real estate investments.8 As the real estate market cycle changes, real estate investment companies may have an opportunity to increase earnings and improve their financial ratios as rents increase. When earnings increase, financial ratios improve and capital flow increases into real estate investments, which generally lowers the cost of capital. It is also possible for economic cyclical factors to lead to reduced earnings, negatively impacting financial ratios. When the market deteriorates rents decline, the cost of capital for a real estate entity may increase as it becomes more difficult to attract equity and debt investors. Market cycles impact capital flows because of their impact on perception of risk in the marketplace and the premium that investors demand for investing in real estate, which can increase or decline depending on supply and demand for space.
Market Cycle Quadrants Phase II—Expansion Declining Vacancy New Construction Long-Term Occupancy Average
Declining Vacancy No New Construction Phase I—Recovery
Exhibit 37.2 8
Phase III—Hypersupply Intreasing Vacancy New Construction
Increasing Vacancy More Completions
Phase IV—Recession
Changes in Real Property Supply during Typical Real Estate Market Cycle
Glenn Mueller, PhD, Dividend Capital Research.
Valuation of Real Estate Entities
593
Demand/Supply Equilibrium Point High Rent Rent Growth Growth in Rents Rise Positive but Tight Market Rapidly Declining toward New Construction Levels Cost-Feasible New Long-Term Construction Rents Occupancy Average Below Inflation and Negative Below Rent Inflation Growth Physical Rental Negative Market Cycle Growth Rental Characteristics Growth
Exhibit 37.3
Changes that May Occur in Rental Growth during the Real Estate Market Cycle
Source: Glenn Mueller, ‘‘Real Estate Market Cycle Moniter,’’ Dividend Capital Research, February 2007.
MEASURING NET CASH FLOW FOR REAL ESTATE ENTITIES The estimated net cash flow projection must be matched to the economic income or benefit received. The cash flow may represent net earnings, funds from operations (FFO), adjusted funds from operations (AFFO), or dividends. The typical equity investor is primarily concerned with the current dividend, the expected future growth in dividends, and expectations with regard to changes in FFO that impact the price capitalization rate accorded to the entity. FFO or AFFO represent a starting point in the analysis because these estimates are not always developed consistently. An economic unit of comparison similar to FFO or AFFO provides a common point of reference for analyzing guideline companies. The ratio of FFO or AFFO to price is a very common ratio that security analysts use to compare alternative REIT investment opportunities. The dividend yield is also an important consideration. This is discussed in more detail in Appendix 37A. The cash flow may be affected by other investments, refinancing, and properties developed, renovated, or sold. A land residual analysis may be required to estimate the market value of excess land that has been acquired for development. In the analysis of real estate entities, the prospective cash flow estimate is extremely complicated but is critical to the analysis.
VALUATION OF REAL ESTATE ENTITIES Even though International Financial Reporting Standards (IFRS) require fair value accounting for income-producing investment property, companies in the United States do not need to comply with these standards at this time. Most real estate entities do not routinely report estimates for real estate asset values, making it necessary for investors and analysts to develop their own estimates. The two primary approaches to value a real estate entity are the underlying asset approach and the capitalization of income.
594
Cost of Capital
Net income in accordance with generally accepted accounting principles (GAAP), net cash flow, FFO, AFFO, and other economic benefits that can be capitalized into value are not always consistently developed by Wall Street analysts and brokers, accountants, appraisers, and other financial professionals for publicly traded companies. Further complicating the analysis of publicly traded companies is the fact that these same professionals do not apply the same valuation methods or techniques. Many buy-side and sell-side analysts disagree on the proper methodology.9 Many of the firms and individuals who provide information to assist in the valuation of real estate entities do not have sufficient information to properly develop the economic benefits that are derived from the ownership of equity interests in real estate operating companies. Many also have biases that are created by conflicts of interest with regard to the net cash flow projections. The market value of invested capital developed by either approach may have to be adjusted for other assets that might include development projects, land held for future development or sale, other investments in unconsolidated subsidiaries, cash and cash equivalents, and miscellaneous items. The value of properties under development typically reflects the historical cost as opposed to market value and must be adjusted to reflect potential increases or decreases in value. The value of land held for development or being developed may be estimated based on projected net cash flows and current investor yield requirements for the related assets. Land that is held for development or sale may be similarly valued based on a land residual technique. Any remaining assets, as well as liabilities and preferred stock, usually are included in net asset value (NAV) at historical cost net book value but should be valued separately. UNDERLYING ASSETS APPROACH The underlying assets approach can be summarized as shown in Exhibit 37.4. Applying this approach to real estate companies requires a very thorough description of all of the real property assets, liabilities, other investments, equity, service activities, and any unrelated businesses because each asset requires a separate valuation. The real property interests would be valued based on the methodology indicated in Chapter 36. Real estate companies often own a collection of real property interests that can be valued separately based on private market transactions. The steps applied to estimate the net asset value vary from firm to firm, which makes a direct comparison of information difficult. The assets should be ‘‘marked-to-market’’ value by independent analysis. The net operating income developed by each asset can be estimated and divided by a market-derived capitalization rate to provide an indication of Exhibit 37.4 þ þ þ
Underlying Assets Approach Net Working Capital (typically at book value) Fair Market Value of Fixed Assets (as appraised) Other Assets (typically at book value) Intangible Asset Value (as appraised) Indicated Value of Assets
9
Long-term Debt (at market value, though book value is often used as a proxy) Preferred Capital (at market value or redemption value, if redeemable) Other Liabilities Indicated Value of 100% of Common Stock
Ross Nussbaum, ‘‘Cash Flow Matters—DCF Analysis Suggests REITs Are Fairly Valued. . .For Now,’’ New York University REIT Center, February 21, 2006 .
Valuation of Real Estate Entities
595
the value of each asset as if it was not part of the entity. In addition, a discounted cash flow analysis can be prepared on each asset. The indicated values can be reconciled to estimate the value of the asset. Some analysts apply one capitalization rate to the entire portfolio and/or roll up and discount the cash flows of all the properties. The indicated asset values by the income approach can be compared to the estimated depreciated cost net of the improvements plus the site value and comparable sales in the competitive markets. The property debt should be marked-to-market and can be deducted to provide an indication of the individual net asset value. The net asset values are added to provide an indication of the net asset value contributed by the real property interest. Adjustments are required for other business investments, such as management contracts, joint ventures, partnership investments, cash and cash equivalents, land held for development, and existing developments. Other liabilities must be marked to market and deducted to provide an indication of the net asset value. Wall Street analysts estimate net asset value in order to determine the premium or discount paid for an equity interest for comparison purposes. One of the major problems associated with this approach is that the net asset values are not readily available. As stated, REITs and other publicly traded companies are not required to provide the net asset values. Most analysts do not have access to the required property level detail to estimate value. Because it is extremely time consuming and difficult to secure individual property data on hundreds of assets, some analysts have chosen to develop a weighted average capitalization rate for all of an entity’s assets and business operations and apply it to net operating income to estimate value. In addition, some firms take shortcuts and do it incorrectly.
Example of Underlying Assets Approach For example, one Wall Street firm stated: NAV is an estimate of the private market value of a company’s assets. We first calculate a forward 12-month cash net operating income (NOI) based on annualized GAAP net operating income (real estate NOI plus joint venture NOI, adjusted for partial contributions, less lease termination fees where included in rental revenue), multiplied by an appropriate growth rate for the next 12 months, minus annualized straight-line rents. In cases in which joint-venture NOI was not available, we used the equity in unconsolidated subsidiaries reported on the company’s income statement. (Please note that, for malls and outlets, a rolling four quarters of NOI is used to account for the quarterly fluctuations in revenue driven by percentage rents.)The resultant cash NOI is then capitalized at an appropriate cap rate (adjusted for the quality of a company’s assets) to determine the implied value of owned properties. We next add capitalized management fee/service income (using a 20% cap rate, in most cases), cash and cash equivalents, construction in progress at 110% of cost, any land being held for development, other assets, and, in some cases, the value of tax-exempt debt in order to arrive at the gross market value of a company’s assets. To determine the net market value of assets, we then subtract all of the company’s liabilities and obligations, including preferred stock at liquidation value and the REIT’s share of joint venture debt. Our NAV estimates make no adjustment for any mark-to-market on company debt.
The forward-looking cash flow should take into consideration numerous factors, such as lease rollovers, rent escalations, expense escalations, and more, all of which impact the expected growth rate. In addition, the firm stated that ‘‘construction in progress at 110% of cost, any land being held for development’’ was added. The value of construction projects fluctuates during the real estate cycle, and it varies in each real estate market based on demand and supply factors. The value can easily be less than or more than its cost. This makes it difficult to compare the net asset value of
596
Cost of Capital
different companies. The net asset values are reliable only if they are properly developed. The firm stated that the net asset value represented the private market valuation. It may or may not. This analysis does not properly address any gains or losses on sales that may have occurred. During the regular course of business, the portfolio of assets may be continuously adjusted for acquisitions, dispositions, and development of properties. Gains on sale may be normal for some entities that are properly managed to create and maintain value over time through increasing the net cash flow. In addition, there are instances, due to poor management and other factors, where the value of the equity is less than the net asset value. Investors may be willing to pay a price for the equity in excess of its net asset value for the intangible value created by good management, access to capital markets, and the ability of management to increase earnings, FFO, and AFFO through internal or external growth.10 This must be captured in a proper analysis. INCOME CAPITALIZATION APPROACH The income capitalization approach can be implemented through either a direct capitalization or a discounted cash flow method. This approach tends to best reflect the actions of investors when analyzing a real estate entity. Most investors are interested in a company’s cash flow and the company’s ability to increase cash flow and distribute it to the investors through dividends. OVERALL DIRECT CAPITALIZATION In Chapter 4, the direct capitalization formula for business valuation was presented. We repeat it here as Formula 37.1: (Formula 37.1) PV ¼
NCF1 c
where: PV ¼ Present value NCF1 ¼ Net cash flow expected in the first period immediately following the valuation date c ¼ Capitalization rate The value of a real estate entity can be estimated using the same formula, but it is extremely important to correctly estimate the net cash flow. If we are valuing equity cash flows, the debt servicing and preferred capital servicing must be deducted from the net cash flow before debt and adjusted for any tax implications. In Chapter 36, direct capitalization of individual real property assets was accomplished through the basic formula net, operating income divided by an appropriate capitalization rate equals value. The basic valuation formula is similar, but the income to be capitalized is not the income to the real property but the income to the real estate entity. It is possible to separate income stream from owning and operating real estate and other types of income and capitalize each at different rates that are appropriate for the risks inherent in each type of income stream. These values can then be added together to estimate total entity value. If you choose to develop an overall capitalization rate and apply it to the entity’s total net income, that overall capitalization rate must reflect the risks
10
Ralph L. Block, Investing in REITs—Real Estate Investment Trusts (New York: Bloomberg Press, 2002).
Valuation of Real Estate Entities
597
associated with investing in the entity, a business enterprise. It must be based on the weighted average returns required by the market to satisfy the debt and equity capital providers to the real estate entity.
ESTIMATING THE CAPITALIZATION RATE Capitalization rates can be developed for any of these economic measures of ‘‘income’’:
Gross or net revenues Gross income
Net operating income
Net income before tax Net income after tax
Operating cash flow Net cash flows to equity or invested capital11
Funds from operations
Adjusted funds from operations Earnings before interest and taxes
Earnings before depreciation, amortization, interest, and taxes Dividends
Net cash flow, FFO, AFFO, and dividends are the typical measures of economic income that are utilized to develop an indication of value. The overall capitalization rate must be developed in a consistent manner to be relevant and produce a supportable and defensible indication of value. The most appropriate income measure is the net cash flow available to satisfy equity and debt investors through the payment of dividends, interest, and amortization. An implied capitalization rate can be estimated by dividing a real estate company’s net operating income (NOI) by its total market capitalization. Adjustments may be required for non–real estate assets and liabilities and other factors. Capitalization rates developed by dividing the FFO, AFFO, or dividend by the equity or shareholder value provide a better measure of economic performance for real estate entities than a similar ratio using GAAP income. The reciprocal of the FFO or AFFO multiple can provide an indication of the equity capitalization rate based on that measure of economic income of the entity. Observed market capitalization rates can be analyzed based on market capitalization (market value of equity), property type, projected growth in net cash flow, geographical location, leverage, and other factors that may impact investor expectations developed from guideline companies. The indicated FFO capitalization rate can then be applied to the subject company to provide an indication of the value of the equity. A similar procedure can be used by substituting the actual dividend payment made to the equity investors. The inferred yield will be higher because the dividend payment would likely be lower than FFO. You must be careful using capitalization rates developed from REITs or publicly traded real estate entities as a proxy for closely held corporations. The daily share price of REITs may reflect various 11
Shannon Pratt, Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed. (New York: McGraw-Hill, 2008).
598
Cost of Capital
stock market factors, such as short-term traders entering or exiting a sector or company in response to economic factors, as compared to investments made by long term-investors. In addition, the desire to achieve high growth in earnings by publicly traded companies may not match up well with the longterm buy-and-hold strategy employed by private, closely held real estate entities. Long-term investors are interested in the long-term net asset value because the real property interests generally represent a large percentage of the company’s assets. However, long-term investors also consider:
Quality of management Quality of assets
Quality of tenants
Entity structure Potential growth in earnings
Anticipated total return: net cash flow plus capital appreciation Potential growth in dividend
Current dividend yield
Dividend-paying capacity Debt coverage ratios
Leverage ratios Current real estate market cycle
Corporate governance
Capitalization rates similar to earnings-to-price ratio can be developed from guideline companies. However, earnings-to-price ratios are based on earnings after deducting depreciation and other items, while FFO and AFFO are calculated prior to deducting for depreciation and adjusted for other items. For publicly traded REITs, it is quite common for analysts to compare the share price to the dividend yield, FFO, or AFFO per share. It is preferable to use AFFO if the information is readily available and has been developed correctly. Many security firms have developed an estimate for AFFO based on their individual adjusted cash flows and models. As a result, inconsistencies exist in the calculation of AFFO and the respective capitalization rates. Public financial information and ratios can be obtained from several companies, such as Green Street Advisors, SNL Financial, and Standard & Poor’s (S&P) CapitalIQ. Many brokerage companies and stock analysts rely on these databases for real estate company information. The financial information in this chapter is based on CapitalIQ. The information can be exported to a spreadsheet for additional analysis. Market data, including guideline companies, can also be assembled quickly into a spreadsheet. This basic direct capitalization formula can be modified to analyze the financial or economic interest in the entity if the appropriate income streams can be estimated, as previously discussed. The analysis can be based on comparable or guideline companies.The chart in Exhibit 37.5 summarizes the value measures of several guideline companies that can provide an indication of capitalization rates and other information that can be used for comparative purposes. The items included are not all inclusive, but provide the basis for evaluating a public or private entity with additional information that may be deemed appropriate by the analyst. Exhibit 37.5 displays an example of a comparative ratio analysis based on guideline companies.12 12
Thank you to Nicholas Arens of Duff & Phelps for assistance in assembling information and calculations.
Valuation of Real Estate Entities Exhibit 37.5
599
Comparative Ratio Analysis for Guideline REITs
Company
1
2
3
4
5
Market Capitalization of Equity (in millions) Premium/Discount to Net Asset Value Dividend Payout/FFO
$1,420 $1,734 114% 111% 89.60% 83.70%
$1,974 106% 96.30%
$3,096 114% 67.10%
$3,166 117% 76.80%
FFO/Share Growth 2005 to 2006 Same Property NOI Change 2005 to 2006* Historical Five Year Average Dividend Yield Current Dividend Yield Forward Annual Dividend Yield Historical Five Year Average Total Return
4.10% 8.10% 4.10% 7.20% 6.80% 6.00% 6.20% 5.90% 6.90% 4.30% 5.00% 4.00% 4.50% 5.00% 5.00% 24.80% 19.69% 15.30%
11.80% 8.00% 4.10% 2.90% 3.50% 29.65%
24% 5.9% 4.90% 3.50% 4.00% 23.44%
34.18% 65.82% 5.57%
29.76% 70.24% 5.36%
33.81% 66.19% 4.81%
3.36% 2.75% 2.14% 5.14% 4.18% 3.14%
1.32% 2.75% 2.73% 2.03% 4.32% 3.41%
2.44% 2.87% 2.27% 3.80% 4.32% 3.41%
Total Debt at Book Value/Total Capitalization (Debt þ Equity) 45.17% 51.30% Total Equity at Market Value/Total Capitalization (Debt þ Equity) 54.83% 48.70% Weighted Average Cost of Debt 5.48% 5.03% GAAP Income/Total Capitalization (Debt þ Equity) FFO/Total Capitalization (Debt þ Equity) AFFO/Total Capitalization (Debt þ Equity) GAAP Income/Market Capitalization (Equity) FFO/Market Capitalization (Equity) AFFO/Market Capitalization (Equity)
0.79% 3.29% 3.89% 1.48% 6.22% 4.35%
2.67% 3.55% 2.73% 6.37% 7.53% 4.46%
*Same Property NOI Change refers to the change in net operating income at the property level. Wall Street analysts refer to this item as same store NOI, which is somewhat misleading for real property.
Exhibit 37.5 could be expanded, if need be, to include an analysis on a per-share basis and various statistical measures, such as measures of central tendency and dispersion. The information clearly indicates a wide range in the historical earnings-to-price ratios between the companies. The historical FFO and AFFO to price ranges narrow, as would be expected from the adjustments required to the earnings to properly reflect the economic benefits derived from the investments. Observed capitalization rates (FFO to price, AFFO to price, net cash flow to price, etc.) are influenced by risk and the expected growth in the respective FFO, AFFO, net cash flow, or dividend. Judgment is required to assess the relative risks between different entities. Some factors that might be considered include size, property sector, and geographical distribution of the assets, type of structure and management, share liquidity, corporate overhead, leverage, and future trends in the real estate markets. In addition to analyzing the comparative ratios, it is important to consider the potential growth from investments and from internal operations. The impact of floating rate debt and maturing debt should be considered. During periods of increasing interest rates, the net cash flow can be affected negatively. It is also important to consider the cash retention by the firm and the recovery of capital, which affects the investor’s cost basis.13 The typical time periods utilized to develop the economic benefits are:
Trailing 12 months Last fiscal year
Straight average for some number of years
Trend over some number of years Weighted average for some number of years
13
William B. Brueggeman and Jeffrey D. Fisher, Real Estate Finance and Investment, 13th ed. (New York: McGraw-Hill, 2006), 642–643.
600
Cost of Capital
Projected estimate for next fiscal year Projected estimate for next 12 months
Projected estimate for some number of years
DISCOUNTED CASH FLOW METHOD The value of a real estate entity also can be estimated using a discounted cash flow method based on the expected returns required by investors. The formula for the discounted cash flow method is: (Formula 37.2) PV ¼
NCF1 NCF2 NCFn þ þ þ ð1 þ kÞ ð1 þ kÞ2 ð1 þ kÞn
where: PV ¼ Present value NCF1. . .NCFn ¼ Net cash flow expected in each of the periods 1 through n, n being the last period of the discrete cash flow projections k ¼ Discount rate (cost of capital) If the expected net cash flows over the projection period to the entity or equity can be estimated and the price or value of the entity or equity is known, the discount rate or cost of capital can be estimated through an iterative calculation. The future net cash flows must be projected in order to develop a reliable estimate of the cost of capital for equity. This is not always feasible. If the cash flows grow evenly in perpetuity from the valuation date, the Constant Dividend or Gordon Growth Model can be employed. This is also referred to as a single-stage growth model. The formula is: (Formula 37.3) PV ¼
NCF1 kg
where: PV ¼ Present value NCF1 ¼ Net cash flow expected in period 1, the period immediately following the valuation date k ¼ Discount rate (cost of capital) g ¼ Expected long-term sustainable growth rate in net cash flow to investor If solving for k, the formula is revised to be: (Formula 37.4) k¼
NCF1 þg PV
where the definitions of the variables are the same as in Formula 37.3.
Valuation of Real Estate Entities
601
COMPUTING THE WEIGHTED AVERAGE OR OVERALL COST OF CAPITAL The weighted average cost of capital can be estimated for public companies from component costs derived from market information. For example:
Common stock Preferred stock Debt
No. of Shares or Face Value
Price/Share or % of Face Value
Component Value
Component Weight
15,500,000 1,500,000 $237,500,000 Market Value of Invested Capital
$26.71 $25.00 100%
$414,005,000 $37,500,000 $237,500,000 $689,005,000
60.1% 5.4% 34.5% 100.0%
Assume that cost of the common equity is estimated at 10%. The preferred stock’s cost is estimated at 8.5%. The bonds pay 7.00% on their face value. No discount has been applied. In this example, it is further assumed that all the debt is similar, but in actuality it may include convertible debt, variable rate debt, and mezzanine debt with various maturities. The combined rate for state and federal income taxes is estimated at 40%. The preceding information can be substituted into Formula 17.1 to compute the weighted average cost of capital: (Formula 37.5) WACC ¼ ðke We Þ þ ðk p W p Þ þ ½kdð ptÞ ð1 tÞ Wd ¼ ð10% 60:1%Þ þ ð5:4% 8:5%Þ þ ½7%ð1 0:40Þ 34:5% ¼ 6:01% þ 0:46% þ 1:45% ¼ 7:92% A closely held real estate company may be highly leveraged in comparison to publicly traded companies. Also it may be a pass-through entity. These factors would impact the cost of capital. An iterative process also is required to estimate the weighted average cost of capital for closely held companies or partnerships. The procedures outlined Chapters 17A and 17B previously can be applied for real estate entities as well. The cost of capital may be different for the entity than the cost of capital for an individual property owned by the entity. For example, if a real estate investment trust specializing in hotels sold one asset, the capitalization and/or discount rate applicable to estimate the market value of that asset may be different from the rates applied to a pool of assets that are part of an entity. Torto Wheaton Research reported that REITs may have an ‘‘accretion edge—selling their public equity capital at a low cap rate and buying private equity at higher cap rates.’’14 ESTIMATING THE COST OF EQUITY CAPITAL ‘‘AS IF PUBLICLY TRADED’’ The information on rates of return of publicly traded investment in real estate operating companies is limited. The best information currently available is based on REITs, which have certain special characteristics that can impact the expected or forward-looking returns. According to Morningstar, the available information dates back to 1972. Exhibit 37.6 summarizes the annual total returns on equity in equity REITs in comparison to other investments from 1972 through 2005. 14
‘‘Wall Street vs. Main Street, Real Estate Pricing and New Development,’’ Market Watch 9, no. 1 CB Commercial/Torto Wheaton Research, (Spring 1997): 3.
602 Exhibit 37.6
Cost of Capital Returns on Equity Capital, 1972–2005
Small Company Equity REITS Large Company Long-Term Corp. Long-Term Govt. Inter-Term Govt. Treasury Bills Inflation
Arithmetic Mean
Geometric Mean
Standard Deviation
17.20% 14.70% 12.60% 9.50% 9.50% 8.20% 6.10% 4.80%
14.90% 13.40% 11.20% 9.00% 8.90% 8.00% 6.10% 4.70%
22.80% 16.70% 17.50% 10.90% 11.70% 6.70% 3.00% 3.20%
Source: Calculated (or derived) based on CRSP1 data, # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago. Calculations performed by Doff & Phelps, LLC. Used with Permission. All rights reserved.
The historical returns are based on the dividends paid plus capital appreciation. It may not accurately reflect the expected returns required by equity investors going forward. The historical returns from REITs do form the basis for estimating the equity returns that are expected on other real estate operating companies. Exhibit 37.7 summarizes the total equity returns from REITs for the last 5, 10, 15, 20, 25, and 30 years and the moving average for each period from 1972. The 5- to 10-year averages are affected by the high returns experienced during the last five years. It is preferable to look at longer returns, which would approximate a long-term investor’s position. The data could be further segregated by property type. Exhibit 37.8, based on FFO (not dividends) and ranked by market capitalization, summarizes the estimated growth rate in FFO inferred FFO capitalization rate and FFO yield to the equity position by property type based on the formula that the FFO yield rate is equal to the capitalization rate plus the long-term average rate of growth (k ¼ c þ g) and assuming that the growth rate is into perpetuity. IMPLIED FFO YIELD The expected long-term growth rates in income and value are more likely to follow changes in inflation over a long period of time. The inferred ex ante FFO yield can be calculated based on solving for k utilizing a discounted cash flow model: (Formula 37.6) PV ¼
Exhibit 37.7
5 Year 10 Year 15 Year 20 Year 25 Year 30 Year Average
NCF1 NCF2 NCFn þ þ ... þ þ 2 ð1 þ kÞ ð1 þ kÞ ð1 þ kÞn
NCFn ð1 þ gÞ kg
ð1 þ kÞn
Total Equity REIT Returns for Various Periods Arithmetic Average
Geometric Average
Moving Average
19.72% 15.84% 16.45% 13.46% 14.70% 16.94% 16.19%
19.07% 14.50% 15.40% 12.36% 13.73% 15.92% 15.16%
15.39% 15.30% 14.92% 14.92% 15.30% 15.39% 15.21%
Source: Calculated (or derived) based on CRSP1 data, # 2006 Center for Research in Security Prices (CRSP1), Graduate School of Business, The University of Chicago. Calculations performed by Doff & Phelps, LLC. Used with Permission. All rights reserved.
Valuation of Real Estate Entities Exhibit 37.8
603
Inferred FFO Cost of Equity Capital Market Capitalization (000s)
Growth Rate
Inferred FFO Capitalization Rate
Inferred FFO Cost of Capital
Median High Low
$2,329 $3,282 $1,402
5.9% 6.6% 5.1%
5.32% 4.18% 7.53%
11.25% 10.77% 12.59%
Median High Low
$7,180 $15,038 $1,268
7.6% 8.3% 6.8%
5.62% 5.03% 6.29%
13.24% 13.36% 13.12%
Median High Low
$4,844 $16,963 $265
6.9% 12.0% 4.2%
4.42% 3.07% 6.36%
11.32% 15.07% 10.53%
Median High Low
$2,757 $7,591 $505
6.2% 8.1% 4.0%
5.64% 3.77% 7.05%
11.80% 11.91% 11.05%
Median High Low
$8,037 $22,414 $1,452
7.1% 8.9% 5.0%
6.83% 5.08% 10.21%
13.93% 14.02% 15.21%
Property Type Apartments
Industrial Buildings
Office Buildings
Shopping Centers
Regional Malls
Source: MacCrate Associates.
where: PV ¼ Present value NCF1. . .NCFn ¼ Net cash flow expected in each of the periods 1 through n, n being the last period of the discrete cash flow projections k ¼ Discount rate (cost of capital) g ¼ Expected long-term sustainable growth rate in net cash flow, starting with the last period of the discrete projections as the base year Exhibit 37.9, ranked by market capitalization, summarizes the expected FFO equity yield rate if it is assumed that the projected growth is for five years and, thereafter, in perpetuity is lowered to 2.5%, the expected long-term inflation rate. Based on the assumed 2.5% growth rate in perpetuity after five years, the implied FFO yield rate or cost of equity capital has declined. The terminal capitalization rate is higher, which would be anticipated because the assets are older and forecasting into the future is more speculative or uncertain. DIVIDENDS Historical information regarding AFFO is not easily obtainable. Many analysts rely on FFO and/or the actual dividend yield because historical information is available that provides support for the analysis. Historical dividend growth per share is readily available, which permits an analysis by either a discounted cash flow analysis or dividend growth models. Dividends are useful because they
604
Cost of Capital
Exhibit 37.9
Implied ex ante FFO Yield
Property Type
Market Capitalization
Five-Year Growth Rate
Inferred Capitalization Rate
Terminal Capitalization Rate
Inferred FFO Equity Yield
$2,329 $3,282 $1,402
5.9% 6.6% 5.1%
5.32% 4.18% 7.53%
5.64% 4.81% 8.18%
9.50% 7.31% 10.68%
$7,180 $15,038 $1,268
7.6% 8.3% 6.8%
5.62% 5.03% 6.29%
6.66% 6.11% 7.24%
9.15% 8.60% 9.74%
$4,844 $16,963 $265
6.9% 12.0% 4.2%
4.42% 3.07% 6.36%
5.13% 4.25% 6.72%
7.63% 6.75% 9.22%
$2,757 $7,591 $505
6.2% 8.1% 4.0%
5.64% 3.77% 7.05%
6.37% 4.58% 7.41%
8.87% 7.07% 9.90%
$8,037 $22,414 $1,452
7.1% 8.9% 5.0%
6.83% 5.08% 10.21%
7.92% 6.29% 11.01%
10.42% 8.78% 13.51%
Apartments Median High Low Industrial Buildings Median High Low Office Buildings Median High Low Shopping Centers Median High Low Regional Malls Median High Low Source: MacCrate Associates.
Dividend per Share Growth (Annual year-over-year growth, 1987–2006 9.00 7.97
8.00
7.46
7.39
7.09
7.02
7.00
6.76
6.76 5.98
6.00
5.80
5.41
5.38 Percent
7.65
5.17
4.88
5.00
5.37
5.54
3.80
4.00 3.00 2.40
2.62 1.85
2.00 1.00 0.00
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Exhibit 37.10
Dividend Growth per Share, 1987–2006
Source: National Association of Real Estate Investment Trusts 1, SNL Financial.
Valuation of Real Estate Entities Exhibit 37.11
605
Average Dividend Yield per Share Dividend Yield Arithmetic Average
Geometric Average
5.79% 6.42% 6.73% 7.22%
5.78% 6.41% 6.72% 7.22%
5 Year 10 Year 15 Year 20 Year Source: MacCrate Associates.
represent the net cash flow to investors. As long as the dividend does not exceed the FFO or AFFO, it might be the most appropriate measure of the economic return to consider for analyzing shareholder value. The analyst must be cognizant of the dividend payout ratio. Exhibit 37.10 shows the historical per share growth in dividends from 1987 through 2006 for REITs. Exhibit 37.11 is a summary of the average dividend yield per year plus the compounded change per year for the last 20 years through 2005 based on publicly traded equity REITs. The dividend yield has been falling while the total dividends paid have been increasing. If an analyst was estimating the cost of equity for a publicly traded REIT that has a share price of $34.00 that was expected to pay a $2.00 dividend per year and it was expected to grow in perpetuity at 3%, the cost of equity would be estimated using Formula 37.4: k¼
NCF1 þg PV
where: NCF1 ¼ $2.00 per share PV ¼ $34.00 per share g ¼ 2.0% per year
k
¼
$2:00 þ2:00% $34:00
¼ 5:88% þ 2:00% ¼ 7:88%
The indicated cost of equity would be 7.88%. It is extremely important that the forecasted expected growth rate is correct. It is quite common for REITs and other entities to pay dividends from other sources, such as reserve funds, the sale of assets, refinancing of assets, and/or one-time earnings from a large-scale development project. The dividend-paying ability is critical along with the forecasted compound change in the dividend over the projection period. This model does not permit the growth rate to exceed the cost of equity or capital. Some investment analysts apply a two- or three-stage growth model to estimate the value of real estate entities. The basic two-stage growth model from Formula 4.8 is:
606
Cost of Capital
(Formula 37.7) PV ¼
NCF1 NCF2 NCFn þ þ ... þ þ ð1 þ kÞ ð1 þ kÞ2 ð1 þ kÞn
NCFn ð1 þ gÞ kg
ð1 þ kÞn
where: PV ¼ Present value NCF1. . .NCFn ¼ Net cash flow expected in each of the periods 1 through n, n being the last period of the discrete cash flow projections k ¼ Discount rate (cost of capital) g ¼ Expected long-term sustainable growth rate in net cash flow, starting with the last period of the discrete projections as the base year The projection period should be reasonable and based on the time period for which reasonable forecasts can be made. It generally ranges from 3 to 10 years. The net cash flow, which is often assumed to be the dividend, should be projected for each year in the projection period. The net cash flow may be based on earnings per share, adjusted funds from operations, or dividends. Consistent application in the development of the information is most important. The last part of the equation provides an indication of the residual or terminal value based on capitalizing the income into perpetuity. No deduction for transaction costs is included as it is assumed that the entity is not being sold but held indefinitely.
Projection Period 1 2 3 4 5 Terminal Value Future Growth
Annual Dividend $2.00 $2.06 $2.14 $2.25 $2.29 $37.81 2.00%
Current Share Price
$34.00
The long-term growth rate in perpetuity should be supportable and defensible. The last part of the formula represents the constant growth or Gordon Growth Model and is used to estimate the terminal or residual value at the end of the projection period. Each year’s net cash flow is discounted back to present value, including the terminal value that is assumed to be received in the last year of the projection period. For illustration purposes, assume that the chart summarizes the information that has been developed from analyzing a real estate company and the general market information. Through the iterative process, the inferred discount rate or equity cost of capital is approximately 8.19% based on a current share price of $34.00. The next chart shows the calculation. The analyst must be cognizant of the relationships that develop based on the assumptions that are made concerning the cash flows. The current capitalization rate is 5.88% while the terminal capitalization increased to 6.19%, reflecting the lower forecasted growth in the net cash flows. The terminal value discounted represents approximately 75% of the present value of $34.00.
Valuation of Real Estate Entities
607
Projection Period
Annual Dividend
1 2 3 4 5 6 Terminal Value Terminal Capitalization Rate Future Growth Current Share Price Inferred Yield
$2.00 $2.06 $2.14 $2.25 $2.29 $2.34 $37.81 6.19% 2.00% $34.00 8.19%
Projection Period
Annual Dividend
1 2 3 4 5 6 Terminal Value Terminal Capitalization Rate Future Growth Current Share Price Inferred Yield
$2.00 $2.06 $2.14 $2.25 $2.29 $2.34 $39.79 5.88% 2.00% $34.00 9.12%
Growth
Net Cash Flow
3.00% 4.00% 5.00% 2.00% 2.00%
$2.00 $2.06 $2.14 $2.25 $40.10 Thereafter Total Present Value
Growth 3.00% 4.00% 5.00% 2.00% 2.00%
Present Value Factor@ 8.19%
Present Value
0.9243 0.8543 0.7897 0.7299 0.6746
$1.85 $1.76 $1.69 $1.64 $27.06 $34.00
Net Cash Flow
Present Value Factor@ 9.12%
Present Value
$2.00 $2.06 $2.14 $2.25 $42.08
0.9164 0.8398 0.7697 0.7053 0.6464
$1.83 $1.73 $1.65 $1.59 $27.20
Total Present Value
$34.00
If it was assumed that the current capitalization rate and the terminal rate were the same (5.88%), the indicated discount rate or equity cost of capital would be increased to 9.12%. The next chart provides proof of the calculations. The preceding examples were based on annual payments of dividends. Usually dividends are paid quarterly, and the cash flows should reflect quarterly discounting. The five apartment guideline companies selected (data displayed in Exhibit 37.5) can be analyzed based on the expected dividends to be paid in the future. The true return to the equity investors is the dividend yield and expected long-term growth rate in dividends. Using the same two-stage model formula, but applying it to the dividends expected to be paid over the long term, the next chart indicates the implied equity yield based on the assumption that the long-term growth expected after five years is 2.5% for each company. Company Forward Dividend Yield Expected Dividend Growth Long term Growth Implied Equity Yield
1
2
4.30% 4.50% 2.50% 7.11%
5.00% 5.00% 2.50% 7.94%
3 4.00% 5.00% 2.50% 6.86%
4
5
2.90% 5.00% 2.50% 5.62%
3.50% 2.50% 2.50% 6.19%
608
Cost of Capital
The chart provides a better indication of the cost of equity capital because it is based on the actual earnings received by the equity investor. APPLYING THE BUILD-UP METHOD Two major components comprise the cost of capital: a risk-free rate and an equity risk premium. The equity risk premium was further divided into a general risk premium, a size premium, and a company or industry-specific risk premium. The formula provided in Chapter 7 and repeated here is: (Formula 37.8) EðRi Þ ¼ R f þ RPm þ RPs þ RPi þ RPu where: E(Ri) ¼ Expected (market required) rate of return on security i Rf ¼ Rate of return available on a risk-free security as of the valuation date RPm ¼ General equity risk premium RPs ¼ Risk premium for small size RPi ¼ Risk premium for industry RPu ¼ Risk premium attributable to the specific company or to the industry
Risk-free Rate Generally, investments in real estate entities require a long-term commitment to realize the anticipated benefits from the investments that would justify utilizing the 5-, 10-, 20-, or 30-year bond as a proxy for the risk-free rate. Some analysts prefer the 10-year bond because the size and frequency of long-term bond issues declined during the 1990s and early 2000s. The 10-year Treasury bond is one of the most-followed investment instruments in the U.S. bond market and has become a proxy for long-term interest rates. It is often used in financing commercial properties as the current reference rate to which spreads are added to determine total interest rate on mortgage debt. Ten years is a fairly common holding period assumption in the real estate market. Stocks, Bonds, Bills and Inflation Valuation Edition 2006 Yearbook recommends that the 20-year Treasury bond be the basis for the long-term risk-free rate.15 Partnership Profiles, Inc., which provides information on partnership sales and discounts, recommends that the historical rates of return on longterm government bonds should correspond to the same time period analyzed for developing the industry returns, such as REITs.16 Alternate yields on treasuries with different maturities may be selected. In valuing real estate companies, similar to REITs, many analysts utilize the 10-year Treasury bond because it has the longest continuity in the public markets. The yield on 10-year Treasury bonds provides a reasonable estimate for the risk-free rate if a 10-year cash flow has been used to prepare the discounted cash flow model. Most analysts analyze real estate holdings over 10 years, and the termination value is based on the reversionary net asset value to be received at the end of 10 years. Generally, the real property assets owned by a real estate operating entity have been individually analyzed and real property cash flows for 10 years or longer have been prepared. Therefore, the 10year Treasury bond more closely matches the projection period. In addition, the longer time period reflects the longer investment horizon associated with investments in similar companies. The investment instrument that is selected as the basis to estimate the risk-free rate should take into consideration: 15 16
SBBI Valuation Edition 2006 Yearbook, 59. Partnership Profiles, 2007 Rate of Return Study (Fort Worth, TX: Partnership Profiles, 2007), 10.
Valuation of Real Estate Entities
609
Investment holding period Net cash flow projection period
Availability of equity risk premium data
Investors’ expectations
The next chart summarizes the average yield on various financial instruments based on information from the Federal Reserve Bank as of the end of 2005:
Type 30-year average 25-year average 20-year average 15-year average 10-year average 5-Year average
U.S. Treasury, Constant Maturities Treasury Bills 5 Year 10 Year 6.09% 7.48% 7.79% 5.75% 7.24% 7.58% 4.62% 6.02% 6.41% 3.87% 5.32% 5.76% 3.66% 4.81% 5.19% 2.12% 3.77% 4.44%
U.S. Treasury, Constant Maturities Type 1 year 2 year 3 year 5 year 7 year 10 year 20 year 30 year
2005 3.62% 3.85% 3.93% 4.05% 4.15% 4.29% 4.64% 4.66%
Yields on actively traded, non–inflation-indexed issues adjusted to constant maturities. Data from U.S. Treasury. Source: Board of Governors of the Federal Reserve System, Statistical Supplement to the Federal Reserve Bulletin, monthly. www.federalreserve.gov/rnd.htm.
Based on the preceding chart, it can be seen that the risk-free rate has been moving lower. The next table shows the projected yields for several different time horizons as of December 31, 2005. The average yields for 10-year Treasury bonds over 10- and 20-year periods are slightly higher than the yield on a similar investment at year-end 2005. If we assume that an investor expects to make an investment at year-end for 10 years, a reasonable risk-free rate would be between 4.3% and 5.0%. Therefore, in the remainder of this chapter we utilize a risk-free rate of 4.3%. Equity Risk Premium The equity risk premium (ERP) is that rate that compensates an investor for the additional risks associated with an equity investment. It is the expected risk differential between a fully diversified portfolio of equity securities and the rate of return expected on a risk-free security. The ERP should reflect the risk that investors place on an equity investment. Please see Chapter 9 for a discussion of the ERP. In this chapter, the ERP that will be used in the examples is 5.00%.
610
Cost of Capital
Size Premium An adjustment for size may be required based on studies completed by Morningstar,17 Duff & Phelps,18 and a study by Brent W. Ambrose, Michael J. Highfield, and Peter D. Linneman.19 The total return indicated by REITs indicates that REITs act like small stocks; however, a large percentage of the return comes from dividends, which is more comparable to a high-yielding investment than to small stocks. Additional risk is inherent in small-company stocks in comparison to larger stocks. The SBBI Yearbook segregates stocks strictly on market capitalization. See Chapter 12 for a discussion of the size premium. Industry Premia The SBBI Yearbook displays an industry premium for real estate investment trusts. In 2005, the adjustment was 4.56%. Example of Applying the Build-up Method Combining the risk-free rate, equity risk premium, size premium, and industry premium to provide an indication of the cost of equity for a mid-cap real estate investment trust, the formula would be: (Formula 37.9) EðRi Þ ¼ R f þ RPm þ RPs þ RPu where the definitions of the variables are the same as in Formula 37.8. Substituting into the formula the estimated cost of equity is: EðRi Þ
¼ R f þ RPm þ RPs þ RPu ¼ 4:3% þ 5% þ 1% þ ð4:56%Þ ¼ 5:74%
APPLYING THE CAPITAL ASSET PRICING MODEL The basic Capital Asset Pricing Model (CAPM) model can be utilized to estimate cost of equity capital. This formula was provided in Chapter 8 and repeated here: (Formula 37.10) EðRi Þ ¼ R f þ BðRPm Þ where E(Ri) ¼ Expected (market required) rate of return on security i Rf ¼ Rate of return available on a risk-free security as of the valuation date B ¼ Beta of the stock or industry RPm ¼ General equity risk premium 17 18 19
SBBI Valuation Edition 2006 Yearbook. Roger J. Grabowski and David King, Risk Premium Report 2006 (Duff & Phelps, Inc., 2006). Brent W. Ambrose, Michael J. Highfield and Peter D. Linneman, ‘‘Real Estate and Economies of Scale: The Case of REITs,’’ Real Estate Economics 33 (2005): 323–350.
Valuation of Real Estate Entities
611
Beta Betas are estimated for specific companies and industries. Beta estimates are available in Morningstar’s Beta Book, which is published every year. Other sources include S&P Company Profiles, S&P Stock Reports, Reuters’ Investor Stock Overview, Yahoo! Finance Key Statistics, and Value Line. Sources of beta estimates are discussed in Chapter 10. If a company is not publicly traded, analysts rely on guideline publicly traded companies and/or the industry beta as a proxy for the company being analyzed. It is assumed that the systematic risk exposures are the same throughout the industry. Example of Applying CAPM For illustration purposes, if we assume that you have been asked to analyze a closely held real estate investment trust, the cost of equity can be estimated based on these variables and no size premium: Risk-free rate 4.3% Expected equity premium 5.0% Industry beta (REITs) .63 EðRi Þ ¼ R f þ BðRPm Þ ¼ 4:3% þ 0:63ð5%Þ ¼ 7:45% The expected return is based on the assumption that the total capitalization and the capital structure of the company being analyzed are comparable to the industry average. If the actual financial leverage at the company is substantially different, the beta would be calculated based on unlevered betas (discussed previously) and relevered to reflect the actual risks based on the capital structure of the firm. See Appendix 10A for a discussion of formulas to unlever betas and Chapter 11 on beta estimation issues. Size Premium Published research indicates the size of a company is an influence on risk. Smaller companies have a greater risk than larger companies. Previously it was indicated that the beta-adjusted size premia was 1.00% for this example. The formula would be adjusted to incorporate a size premia: (Formula 37.11) EðRi Þ ¼ R f þ BðRPm Þ þ RPs where the definitions of the variables are the same as in Formulas 37.8 and 37.10. Substituting the risk-free rate, beta, the equity premium, and size premia indicated previously, the estimated cost of equity would be:
EðRi Þ ¼ R f þ BðRPm Þ þ RPs ¼ 4:3% þ 0:63ð5%Þ þ 1% ¼ 8:45%
612
Cost of Capital
Adjusting Beta for Closely Held REIT Aswath Damodaran states that if the owner has all of his or her wealth invested in the private business and is completely undiversified, that owner is exposed to all risk in the firm and it is not just the market risk (which is what the beta measures).20
He has defined total beta as: betas adjusted to reflect a firm’s total exposure to risk rather than just the market risk component. It is a function of the market beta and the portion of the total risk that is market risk. These betas might provide better estimates of costs of equity for undiversified owners of businesses.
The formula for total beta is Total Beta ¼ Market Beta=Correlation between stock and market 21 See Chapter 14 for a discussion of Total Beta. For illustration purposes, if an analyst is developing the cost of equity of an undiversified, closely held company that is similar to a REIT and it is assumed that the equity risk premium for the S&P 500 is reported to be 5.00%, the calculated betas (according to ‘‘Damodaran Online—Betas by Sector)’’22 for REITs are: Average 0.67 Unleveraged 0.63 Total Beta 2.40 If the numbers that are derived from market information are inserted into the formula to reflect the firm’s total exposure to risk rather than just the market risk component, the indicated cost of capital is: EðRi Þ ¼ R f þ BðRPm Þ ¼ 4:39% þ 2:40ð5%Þ ¼ 16:39% Adjustments for differences in leverage, size, and other factors may be considered. For example, if the company was a diversified real estate company, similar to the overall market, the estimated equity cost of capital would be: EðRi Þ ¼ R f þ BðRPm Þ ¼ 4:39% þ 0:63ð5%Þ ¼ 7:54%
20 21 22
Aswath Damodaran, Betas by Sector (New York: Damodaran Online, 2007). Ibid. Ibid.
Valuation of Real Estate Entities
613
ANALYSIS OF LONG-TERM DIVIDEND AND TOTAL RETURN Many investors and analysts compare the total return on REITs to the 10-year bond return to capture the risks associated with real estate companies in the public market. Real property is frequently analyzed using a 10-year discounted cash flow analysis. The 10-year bond approximates the risk-free investment of a similar investment period. Exhibit 37.12 summarizes the 10- to 30-year total return to the same return on the 10-year bond for a similar time frame. The exhibit indicates that the risk premium over the 10-year bond for an investment in a publicly traded real estate company is approximately 8.93% over a long investment horizon. The risk premium has been declining in the short term, which may indicate that the market has a greater understanding of REIT returns and risks. The long-term risk premium could be added to the current 10year bond yield to provide an indication of the equity cost of capital. Exhibit 37.13 displays a comparison between the 10-year bond and the average dividend yield for REITs. The trend for both is downward and the spread historically is quite narrow. Based on the preceding analysis, the majority of the risk associated with REITs appears to be in the long-term appreciation in value. Discount rates can also be estimated by analyzing publicly held real estate limited partnerships, which sell in the informal secondary markets.23 This method is similar to the build-up method based on REIT total returns. Partnership Profiles’ Rate of Return Study analyzes the sale of publicly held limited partnership interests. Additional adjustments may be required based on the type of entity being analyzed, leverage, and other factors.
Exhibit 37.12
Comparison of REIT and 10-Year Treasury Bond Returns
Total Return
REIT
10-Year Treasury
Difference
10 Year 15 Year 20 Year 25 Year 30 Year Average
15.84% 16.45% 13.46% 14.70% 16.94% 15.48%
5.19% 5.76% 6.41% 7.58% 7.79% 6.55%
10.65% 10.70% 7.05% 7.13% 9.15% 8.93%
Source: MacCrate Associates.
Exhibit 37.13
23
Returns on 10-Year Treasury Bonds versus REIT Dividend Yields
Average for
10-Year Treasury Bond
Dividend Yield
5 Year 10 Year 15 Year 20 Year 25 Year 30 Year Average
4.44% 5.19% 5.76% 6.41% 7.58% 7.79% 6.19%
5.79% 6.42% 6.73% 7.22% 7.32% 7.38% 6.81%
Difference 1.35% 1.22% 0.98% 0.81% 0.25% 0.41% 0.62%
Bruce A. Johnson, Spencer J. Jefferies, and James R. Park, Comprehensive Guide for the Valuation of Family Limited Partnerships, 3rd ed. (Fort Worth, TX: Partnership Profiles, Inc., 2006), 45.
614
Cost of Capital
The example provided in this chapter was based on a REIT that is required to distribute 90% of its income to equity investors. This is not always the case. The dividends that are paid may be lower or nonexistent, as with nondistributing partnerships. REITs also have relatively low debt in comparison to private companies and partnerships that use leverage to maximize the return to equity investors. REIT shares are relatively liquid in comparison to investments in restricted stock, partnership interests, and closely held corporations. An adjustment for liquidity may be required and is addressed in Chapter 25.
SUMMARY This chapter introduced the methods and applications utilized to develop the appropriate returns on real estate entities, such as REITs. The basic concepts are quite similar to business valuation concepts, but additional factors must be considered in the analysis of real estate entities.
ADDITIONAL READING Block, Ralph L., Investing in REITS: Real Estate Investment Trusts. (New York: Bloomberg Press, 2006). Erickson, John, Su Han Chan, and Ko Wang. Real Estate Investment Trusts: Structure, Performance, and Investment Opportunities, Financial Management Association Survey and Synthesis Series. (England: Oxford University Press 2002). Fass, Peter M., Michael E.Shaff, and Donald B. Zief. Real Estate Investment Trusts Handbook, 2005 ed. Securities Law Handbook Series, 2005). Lee, Ming-Long, Ming-Te Lee, and Kevin C.H. Chiang, ‘‘Real Estate Risk Exposure of Equity Real Estate Investment Trusts,’’ Working paper, July 6, 2006. Parsons, John, Richard T. Garrigan, and John F. C. Parsons, Real Estate Investment Trusts: Structure, Analysis and Strategy. (New York: McGraw-Hill, 1997).
Appendix 37A
Valuing Real Estate Entities James MacCrate, MAI, CRE, ASA Introduction Measuring Net Cash Flow for Real Estate Entities Projected Cash Flow from Real Estate Operations Projected Net Cash Flow for Real Estate Entity Funds from Operations and Adjusted Funds from Operations
INTRODUCTION Estimating the net cash flow associated with real estate entities is the focus of this appendix. Some real estate entities use their own set of definitions that parallel those used in business valuation. This appendix introduces the reader to the accounting measures that may be encountered in real estate entity valuations.
MEASURING NET CASH FLOW FOR REAL ESTATE ENTITIES The anticipated financial benefits that come from investing in a real estate entity are no different from any other enterprise. The three sources of these benefits are: 1. Earnings or cash flow From operations From investments 2. Liquidation or hypothecation of assets 3. Sale of the interest1 Real estate entities are going concerns engaged in a business enterprise. Generally, the value of a going-concern has been defined as
1
Shannon P. Pratt, Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed. (New York: McGraw-Hill, 2007), chap. 3.
615
616
Cost of Capital
the value of a business enterprise that is expected to continue to operate into the future. The intangible elements of going concern value result from factors such as having a trained work force, an operational plant, and the necessary licenses, systems, and procedures in place.2
The value of a going concern includes the tangible assets as well as the intangible assets. Most real estate entities prepare consolidated financial statements, which have been prepared in accordance with generally accepted accounting principles (GAAP). Income statements and cash flow statements prepared in accordance with GAAP must be adjusted by the analyst to provide a basis for forecasting future cash flows from operations and other investments as well as the potential residual or terminal interest if the entity is sold. Taxable income does not indicate the dividend-paying ability of real estate entities. The projected net cash flow that can be distributed to shareholders or partners is most important to investors. In addition, the book value of the real property assets does not generally reflect the actual net asset value of the assets. Since most real estate entities have a large percentage of fixed assets that are depreciated, the accounting statements may not properly reflect the actual operating results of a real estate entity.
PROJECTED CASH FLOW FROM REAL ESTATE OPERATIONS The projected operating income and expenses for each asset must be estimated in order to produce the total cash flows from the real property interests. The items considered in the analysis of individual assets in Chapter 37 must be considered for all the assets to produce a consolidated reconstructed income and operating expense statement. Projected capital expenditures such as nonrecurring expenditures, leasing commissions, and tenant improvement costs must be deducted. The annual debt service must be deducted for each asset to provide an indication of the cash flow to the entity before depreciation and taxes. Exhibit 37A.1 provides a sample projected cash flow statement from the real property operations of an entity prior to depreciation and taxes. The estimated total projected cash flow from real property operations before interest, taxes, depreciation, and amortization must take into consideration the potential changes in income and expenses at the property level and dispositions, acquisitions, exchanges, or refinancings that may have occurred at the property level or are expected over the projection period. Further adjustments are required for debt service, depreciation, interest, and taxes at the property level, if any. Exhibit 37A.2 provides a basic summary of the adjustments to provide an indication of the total projected after-tax cash flow from the real property operations. Additional items that must be modeled at the property level over the projection period may include:
Projected releasing assumptions upon lease expiration including leasing costs Capital expenditures
Tenant improvement costs
Redevelopment costs
This type of an analysis provides a good indication of the contribution made by the tangible assets to the projected before- and after-tax cash flows to the entity, which has a direct bearing on the cost of capital. Cash flows for other types of properties, such as development properties or assets held for 2
American Society of Appraisers, Business Valuation Standards-Glossary (Herndon, VA: American Society of Appraisers, 2006), 5.
Projected Cash Flow from Real Estate Operations
Exhibit 37A.1
Sample Projected Cash Flow Statement from Real Estate Operations
Projected Gross Revenue Potential Rental Revenue Loss Due to Absorption and Turnover Vacancy Base Rent Abatements ¼Projected Scheduled Base Rental Revenue þExpense Reimbursement Revenue þOther Income ¼Projected Total Gross Revenue General Vacancy Collection Loss ¼Projected Effective Gross Revenue Operating Expenses Real Estate Taxes Insurance Utilities Cleaning Repairs and Maintenance Management Fee Payroll and Benefits Ground Rent Recurring Capital Expenditures for Replacement Total Operating Expenses ¼Projected Net Operating Income from Real Property Operations Leasing and Replacement Capital Expenditures Tenant Improvements Leasing Commissions Nonrecurring Capital Expenditures for Replacement Total Leasing and Replacement Capital Expenditures ¼Total Projected Cash Flow from Real Property Operations before Debt Service, Depreciation, and Taxes Debt Service (principle plus interest payments) ¼Total Projected Net Cash Flow from Real Property Operations before Depreciation and Taxes
Exhibit 37A.2
Calculating After-Tax Cash Flow from Real Property Operations
Net Cash Flow Income from Real Property Operations before Depreciation and Taxes Interest Other Taxes Depreciation and Amortization Taxable Income Total Net Cash Flow from Real Property Operations before Depreciation and Taxes Taxable Income Tax Rate (if applicable)1 Total After-Tax Cash Flow from Real Property Operations before Depreciation and Taxes 1
There would not be federal taxes at the entity level for real property interests owned by pass-through entities.
617
618 Exhibit 37A.3
Cost of Capital Calculating Net Cash Flow
Total After-Tax Cash Flow (Real Property Operations before Depreciation and Taxes) þNet income from other sources ¼Net income to common stock or partnership (after tax, if any) þNoncash charges at the entity level (depreciation, amortization, and deferred taxes) Capital expenditures at the entity level to support projected operations Required additions to net working capital or retained earnings to support projected operations at the entity level þInterest expense at the entity level (net of the tax deduction, if any) þDividends on preferred stocks Net cash flow to invested capital
sale, can be developed separately or combined. Assets held in joint ventures may also be accounted for separately. Additional risks are associated with real property developments; these risks can impact the cost of capital as well as the expected net cash flow growth.
PROJECTED NET CASH FLOW FOR REAL ESTATE ENTITY Additional adjustments are required for corporate or partnership expenses, depreciation, and amortization that are not allocated to a specific real property asset. There may also be additional income from other investments, such as a minority interest in other partnerships. Additional income may be generated by providing management or development services or other property services to related or unrelated entities. A real estate entity may incur another layer of expenses, such as management and advisory fees, that are not incurred by an individual property owner. Other adjustments that may be required to provide the total projected net cash flow to the entity may include:
Projected net proceeds from the sale of assets Projected net proceeds from refinancing
Income from unconsolidated entities
Other nonoperating income Other nonoperating expenses
Adjustments for asset dispositions Adjustments for new asset acquisitions
Adjustments for new or completed real property developments.
Exhibit 37A.3 provides a basic formula to estimate the net cash flow to a real estate entity. If it is a pass-through entity, there would not be any adjustment for federal taxes at the entity level.
FUNDS FROM OPERATIONS AND ADJUSTED FUNDS FROM OPERATIONS Currently there is disagreement within the real estate community concerning the analysis of financial statements prepared in accordance with generally accepted accounting principles (GAAP) for real estate entities. Analysts must be keenly aware that real estate companies report earnings differently.
Funds from Operations and Adjusted Funds from Operations Exhibit 37A.4
619
Calculating FFO
Gross Revenues Operating Expenses Depreciation and Amortization Interest Expense General and Administration Expenses of the Entity Net Income Net Proceeds on Sale of Assets þDepreciation and Amortization Associated with Real Estate Assets Funds from Operations
Terminology in the industry also differs from Wall Street to Main Street. The calculation of the projected net cash flow is critical and must be clearly defined. It provides the basis for consistent comparative analysis. In order to promote an industry-wide standard measure of operating performance, the National Association for Real Estate Investment Trusts (NAREIT) adopted additional measures that analysts may consider for comparative purposes for real estate investment trusts (REITs).3 One measure is known as funds from operations (FFO). FFO is defined as net income (computed in accordance with generally accepted accounting principles), excluding gains (or losses) from sales of property, plus depreciation and amortization, and after adjustments for unconsolidated partnerships and joint ventures. Adjustments for unconsolidated partnerships and joint ventures will be calculated to reflect funds from operations on the same basis.4
Depreciation and amortization should reflect the amounts that are associated with the real estate assets. Exhibit 37A.4 summarizes the formula developed by NAREIT for the calculation of FFO. In a study completed by Desmond Tsang and Steve Fortin, the authors concluded that the GAAP earnings per share (EPS) measures have higher absolute forecast errors than the non-GAAP funds from operations measures. According to the study, EPS measures have higher forecast errors than FFO because:
Managers are more likely to manipulate EPS.
Analysts exert larger positive biases on EPS forecasts. The number of analysts following analysis of the EPS measure for REITs is less than that for other types of companies, making EPS forecasts less accurate.5
A study completed by David H. Downs and Z. Nuray Guner provides additional support for the conclusions developed by Tsang and Fortin. The study indicated that a very high percentage of income on real estate is contractually obligated through lease obligations and known to REIT management and analysts. The article went on to say that the income and expense streams are less volatile and income streams are more predictable than for many other types of businesses.6 3 4 5
6
NAREIT, ‘‘Funds from Operations,’’ National Association of Real Estate Investment Trusts, Inc., White Paper (April 2002): 2. Ibid. Desmond Tsang and Steve Fortin, ‘‘Analyst Forecast Accuracy on GAAP vs. Non-GAAP Financial Measures: Case of Real Estate Investment Trust,’’ Working paper (November 2005). David H. Downs and Z. Nuray Guner, ‘‘On the Quality of FFO Forecasts,’’ Journal of Real Estate Research 28, no. 3 (2006): 257– 274.
620
Cost of Capital Exhibit 37A.5
Calculating AFFO
Funds from Operations Recurring Capital Expenditures þOther Noncash Items Adjustment for Rent Straight-lining Adjusted Funds from Operations
Many analysts use funds from operations to estimate the equity or shareholder value of REITs. Some critics maintain that FFO may not be representative of the true operating profitability of an entity because the entity may not properly account for leasing commissions, tenant improvements, recurring capital expenditures, and other items.7 If proper adjustments are made to FFO, cash flow estimates, such as adjusted funds from operations (AFFO), also known as cash or funds available for distribution (CAD or FAD), can be developed for valuation purposes. These measures are used as benchmarks for valuing the equity interest in REITS. AFFO is usually calculated by subtracting from funds from operations (FFO):
Normalized recurring expenditures that are capitalized by the REIT and then amortized, but which are necessary to maintain a REIT’s properties and its prospective cash flow ‘‘Straight-lining’’ of rents
Other noncash items
The basic formula would be as shown in Exhibit 37A.5. Straight-line rent is the average rental revenue received over the life of the lease, not the actual rent received in a particular year.8
Adjustments may be required when rents have been straight-lined in accordance with GAAP because this adjustment may result in the reported income being overstated in the early years of the actual lease term. FFO or AFFO can provide analysts with a starting point in their analysis, but this information should be used with caution because companies may use different methods to estimate these measurements. It is important to develop a common point of reference to make comparisons by the type of entity or across the different types of entities. Many analysts use FFO or AFFO as a measure of the real estate company’s ability to pay dividends. Other analysts rely solely on the historic dividend payment and trend. The ratio of price to FFO or AFFO is a very common ratio that security analysts use to compare alternative REIT investment opportunities, in a manner that is similar to how price/earnings ratios are used in the broader equity market. Some analysts also use the dividend yield as a basis for estimating equity value. Regardless, the net cash flow projections must be indicative of the future operating performance for the entity and must take into consideration all recurring charges against gross revenues. The cost of capital developed must be matched conceptually and empirically to the definition of the economic income or benefit that will be capitalized or discounted.9 In the case of REITs, the cost of equity
7
8 9
Richard Marchitelli and James R. MacCrate, ‘‘REITs and the Private Market: Are Comparisons Meaningful?’’ Real Estate Issues (August 1996): 7–10. Jonathan Litt, ‘‘Gaming FFO,’’ Property (Fall 2001). Pratt, Valuing a Business, chap. 9.
Funds from Operations and Adjusted Funds from Operations
621
capital is generally a function of the current dividend return, the expected future growth in dividends, and expectations with regard to changing FFO multiples accorded to the entity. Real estate entities often create or have an interest in subsidiaries that can provide additional services to tenants or own or have an interest in development or other real estate companies and/or partnerships that may have a positive or negative influence on the entity’s net cash flow. During the real estate cycle, properties can be refinanced, renovated, or sold during the normal course of business, which will affect the net cash flow that should be considered. In some cases, excess land is purchased as part of the development process and held until developed or sold, often resulting in gains. Although this potential source of income typically is excluded from FFO, it should not be ignored. The analyst must develop a consistent framework to analyze real estate entities. In the normal course of valuation, the prospective free cash flow or net cash flow is critical.
Chapter 38
Cost of Capital in Ad Valorem Taxation
Introduction Assessed Value versus Fair Market Value General Categories of Legislative Constraints that Necessitate Adjustments to the Cost of Capital Tangible Assets Including Assemblage or Enhancement Operating Property in Existence on a Lien Date Capital Structure Weighted Average Cost of Capital Cost of Equity Cost of Preferred Stock Cost of Debt Ad Valorem Tax Adder Flotation Costs WACC versus WARA Summary
INTRODUCTION Ad valorem taxation is a process by which government entities assess a tax, or levy, on the value of property. Of the three basic types of taxes—on wealth, on income, and on transactions (or excise taxes)—the tax on wealth or property is the oldest and provides the revenue foundation for local governments. This tax is assessed per value, thus the Latin term ad valorem. Property value is determined by the taxing jurisdiction, and a rate, or levy, is applied to the value for assessment. Proceeds are collected and used to fund services to the population of the taxing entity. These services may include police and fire protection, school funding, road funding, governmental administration, and others. Many states have constitutional and statutory provisions that establish terms to define the value to be used by the assessor for tax purposes. The terms full cash value, actual cash value, fair cash value, fair value in exchange, value in exchange, and true and fair value are among the most commonly used in these provisions. The courts have consistently interpreted these terms as indicating the same kind of value, which is value in exchange or value in the marketplace, normally termed market value. Therefore, we may consider that the basis of assessment is market value and that the assessor’s task is to estimate the fair market value of property—yet with some limitations. For this reason, there is a need to estimate accurately the value of property so that it can be fairly applied within this context. The process of valuation has been described as an art rather than a science. The appraiser’s judgment must be used to reach a final conclusion of value. The assessment of value therefore is limited 623
624
Cost of Capital
by its tendency to be somewhat subjective; thus governmental authorities have attempted to make the process of assessment more objective through policymaking. Some of the policies that have been created to simplify and standardize the application of variables to value have served only to increase the complexity in the way cost of capital should be measured. There are three generally accepted approaches to value: 1. Income approach 2. Cost approach 3. Market approach Properties that are not frequently sold in the markets but have determinable income streams are the best candidates for the income approach to value. The income approach is a useful, though sensitive, appraisal tool. It is useful because, for most types of property, it is the most valid approach to value; it is sensitive, and therefore must be used with care, because any small error will be compounded. One parameter of concern in applying the income approach is the cost of capital. A basic assumption of the income approach is that investors purchase property for the income it will yield. A different way of stating this assumption is that the value of the property depends on the income it produces. In valuing income-producing property, the valuation of an income stream is a function of the level of income being measured. The level of income corresponds to the ownership rights to the cash flows. The preferred measure of return is net cash flow. There is certainly much discussion and many theories on this measure, as previous chapters illustrate. Using this return designates that the income to discount is the net cash flow income. Both creditors and shareholders expect to be compensated for the opportunity cost of investing their funds in one particular business instead of in others with equivalent risk. In ad valorem taxation, the level of income to be discounted depends on the limitations placed by statutory requirements. Because of legislative constraints on the definition of income, adjustments must be made to the net cash flow return to render it comparable with the measure of income to discount. In past years many of the methods for valuing income-producing properties had not changed but the entities being valued by these approaches had. In recent years, just as changes have occurred in financial reporting, similar changes have occurred in assessment methodologies. Many state assessment authorities still normalize net operating income (NOI) by averaging historic returns and dividing the normalized NOI by a weighted average cost of capital (WACC). This approach certainly had economic substance with rate-base regulated entities. Recently many assessing authorities have made modifications to this approach; these modifications (more specifically, modifications to the WACC) are the focus of this chapter. Many assessors have made these modifications because some companies, such as pipeline, telecommunications, and electric companies, have been subjected to deregulation. Governmental mandates and law changes—such as the Telecommunications Act of 1996,1 pipeline deregulation from Federal Communications Commission (FERC) orders 6362 and 637,3 electric deregulation from FERC orders 888, 889 and 890,4 and moves to break up electric companies into competitive segments, such as the repeal of the 1935 Public Utility Holding Company Act, through the passage of 1 2 3 4
Federal Communications Commission, ‘‘Telecommunications Act of 1996’’ www.fcc.gov/telecom.html. Federal Energy Regulatory Commission (FERC), ‘‘Order No. 636,’’ www.ferc.gov/legal/maj-ord-reg/land-docs/restruct.asp. FERC, ‘‘Order No. 637,’’ www.ferc.gov/legal/maj-ord-reg/land-docs/RM98-10-005.asp. FERC, ‘‘Order No. 890,’’ www.ferc.gov/whats-new/comm-meet/2007/021507/E-1.pdf.
Assessed Value versus Fair Market Value
625
the Energy Policy Act of 2005—have resulted in deregulation. Furthermore, competitive segments, such as wireless and unregulated electric generation, have grown into enterprises of significant size and now make up hundreds of billions of dollars in market capitalization. In many states these companies remain state assessed and are subject to derivatives of former rate-base regulated methodologies. Accordingly, to recognize the change that occurred in formerly regulated companies, many property tax assessors began modifying the traditional income approach to value (i.e., NOI/WACC). Primary modifications have centered on changes to the WACC by incorporating growth adjustments (i.e., WACC – g). Sometimes further adjustments to the correlated values have been incorporated in order to remove certain nontaxable components.
ASSESSED VALUE VERSUS FAIR MARKET VALUE Before diving directly in changes to WACC, it is helpful to get a sense of the difference between assessed value and fair market value. This understanding will provide context on the cost of capital. In many instances, limits or standards have promulgated the measure of income. For instance, if a governing body limits the definition of income to be measured as NOI, then the analyst must recognize these barriers and make appropriate adjustments in the cost of capital to compensate for the recognition of different levels of taxes and capital expenditures that would have been measured in a traditional free cash flow measurement. Statutory requirements can therefore demand that the standard net cash flow cost of capital be adjusted. It is essential that the analyst fully understand the cost of capital and its basis, then make adjustments that make the cost of capital comparable to the income being discounted. A reviewer of property tax assessments should recognize that certain complexities must be understood prior to making conclusions about a proper assessment. Generally these complexities fall within four categories: 1. 2. 3. 4.
Standard of value Discrimination and equalization Statutory guidelines and rules Taxable assets
Each of these categories has an indirect implication on the cost of capital and justification of its use. The governing standard of value differs from state to state. For example, in North Carolina, the standard of value is value-in-use5 while in Texas the standard of value is value-in-exchange. These two standards generally present different valuation results. In fair market value determinations, the governing principle is highest and best use. In financial reporting, the current standard of value is value-in-use for assets that will continue the same use after the transaction and value-in-exchange for assets that will change use or be held for sale. In the future, although these financial standards are being tweaked, SFAS No. 157, Fair Value Measurement,6 will likely govern toward a standard of value based on highest and best use. 5
6
Charles Neely Jr. and Nancy S. Rendleman, ‘‘Toward a Better Understanding of Value-In-Use in Property Tax Appraisals,’’ Journal of Property Tax Management (Winter 1997). Financial Accounting Standards Board, FAS No. 157, Fair Value Measurements, September 2006.
626
Cost of Capital
Discrimination and equalization in assessed values also play an important part in property tax value determination. Section 306 of the Railroad Revitalization and Regulatory Reform Act of 1976, 49 USC Section 11503 (4R Act): [. . .] forbids states or their subdivisions to assess such property at a higher fraction of fair market value than they assess other commercial and industrial property; to levy or collect a tax based on such an assessment; to tax rail transportation property at a higher rate than other commercial and industrial property; or—the specific provision involved in this case—to ‘‘impose another tax that discriminates against a rail carrier .’’7
Other taxpayers, most notably the large telecommunication companies, use discrimination as a means to keep value in reasonable check to competitive providers.
GENERAL CATEGORIES OF LEGISLATIVE CONSTRAINTS THAT NECESSITATE ADJUSTMENTS TO THE COST OF CAPITAL A good rule to use in making these adjustments is that any change made to the return on net cash flow ultimately should result in a value that would have been calculated by measuring the present value of the net cash flow under no constraints. A few situations in which adjustments to the cost of capital may be necessary are listed next:
Cost of capital is used as a capitalization rate
NOI is used as a proxy for free cash flow Before-tax cash flow is used as the proxy for income
Flotation costs Book value capital structure
To assist the assessor and to provide certain standards, handbooks and rules are created. For example, the California Assessors’ Handbook8 provides both tax assessors and property tax appraisers with proper methods and procedures for use in determining value. One such rule is Utah Rule 62, which outlines methods that are appropriate and acceptable for value determination.9 Certain interesting elements of the rule are:
Assemblage or enhanced value attributable to the tangible property should be included in the assessed value.
Yield capitalization is preferred where the yield capitalization formula is CF=(k g), where CF is a single year’s normalized cash flow; k is the nominal, risk-adjusted discount or yield rate; and g is the expected growth rate of the cash flow. Cash flow is restricted to the operating property in existence on the lien date, together with any replacements intended to maintain, but not expand or modify, existing capacity or function. Cash flow is calculated as NOI plus noncash charges (e.g., depreciation and deferred income taxes),
7 8 9
Burlington Northern Railroad Company v. Oklahoma Tax Commission, et al., No.86-337 (October term, 1986). California State Board of Equalization, Assessors’ Handbook, (State of California, 2006). State of Utah, ‘‘Tax Commission, Property Tax, R884-24P-62,’’ http://tax.utah.gov/research/effective/r884-24p-062.htm.
General Categories of Legislative Constraints
627
less capital expenditures and additions to working capital necessary to achieve the expected growth g. The risk premium shall be the arithmetic average of the spread between the return on stocks and the income return on long-term bonds for the entire historical period contained in the SBBI Yearbook published immediately following the lien date.10
TANGIBLE ASSETS INCLUDING ASSEMBLAGE OR ENHANCEMENT Similar to Utah’s Rule 62, many states also exempt intangibles but have clauses to include assemblage or enhancement. Case law in Utah provides this clarification to the definition: [. . .] fair market value reflects the benefit stream created by unitary operation of tangible property . If the legislature had desire to limit assessed value to the materials and installation cost of tangible assets, it could easily have done so. Since it did not do so, we conclude that the statutory and constitutional fair market value requirements recognize some element of value that is not attributable to either intangibles or simple cost and that this enhanced value is taxable.11
Therefore, it is clear that the courts in Utah believe that enhancement is taxable. What is not so clear is the definition of enhancement. If this concept was referring to assets that are valued for financial reporting and one were to look on the balance sheet for assets that were neither tangible nor intangible, no remaining taxable assets would be found (assuming goodwill is considered an intangible asset). The case law seems confusing because the example that it uses misclassifies the allocation of value that should simply be land or soft-cost elements, such as permits, engineering, or architectural design: The counties and the Commission view the enhancement as a taxable attribute of tangible property. The Commission used as an example a hillside home with a value-enhancing view, and proposed that the view is an inherent feature of a tangible asset. Although the view is more ephemeral than bricks and mortar, it is a part of the assessed value of the property for tax purposes. Location is another such element of value. ‘‘Location is the time-distance relationships, or linkages, between a property or neighborhood and all possible origins and destinations of residents coming to or going from the property or neighborhood.’’ The Appraisal of Real Estate (Appraisal Institute 10th ed. 1992). In other words, the augmentation in value results from property and market components, however incorporeal, that are not separately quantifiable as tax-exempt intangibles.12
Location, location, location are the three most important attributes in real estate, both improved and unimproved. All of these attributes relating to view, location, and neighborhood, as mentioned, equate to higher land value. Scarce attributes increase value. It is also true that certain intangible elements, such as permits, could be creating this value. For example, when two pieces of property are identical in every way except one has a permit and the other does not, the difference in value is due to the permit. One method to value this permit is to calculate the present value of the incremental income potential. This permit is an identifiable intangible asset. An experienced real estate appraiser responsible for valuing the hillside home in the earlier example would not place a value on a phantom asset and call it ‘‘enhancement.’’ The appraiser would value the land under the premise of a highest and best use approach, add the cost of the improvements, and correlate this result with comparable sales in the area. To the extent that comparable sales existed (on both vacant land parcels and 10 11 12
SBBI Yearbook Valuation Edition, Chicago: Morningstar. Beaver County v. WilTel, Inc., 995 P.2d 602 (Utah 2000). Ibid.
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Cost of Capital
improved parcels) and that the improved comparable values were far in excess of the subject value, the appraiser would first review the results of the improvement to verify all costs were included (i.e., architectural costs, increased labor and transportation associated with the unique site, validation of similar utility services, permits, etc.). If all costs (both hard and soft) were taken into account and it was deemed that there was an adequate supply of locations, the appraiser would be reticent to place any additional value on the property because of the limitations placed on the appraiser by the principle of substitution: The principle of substitution states that when several similar or commensurate commodities, goods, or services are available, the one with the lowest price attracts the greatest demand and widest distribution. This principle assumes rational, prudent market behavior with no undue cost to delay. According to the principle of substitution, a buyer will not pay more for one property than for another that is equally desirable. Property values tend to be set by the price of acquiring an equally desirable substitute property. The principle of substitution recognizes that buyers and sellers of real property have options, i.e. other properties are available for similar uses. The substitution of one property for another may be considered in terms of use, structural design, or earnings. The cost of acquisition may be the cost to purchase a similar site and construct a building of equivalent utility, assuming no undue cost due to delay; this is the basis of the cost approach. On the other hand, the cost of acquisition may be the price of acquiring an existing property of equal utility, again assuming no undue cost due to delay; this is the basis of the sales comparison approach.13
Where enhancement may come into play is when nonreplicable scarcity, which cannot be assigned to an asset, becomes a factor. Examples include a house that has historic significance or attributes that cannot be replicated, such as being designed by a famous deceased architect or artist. In the same vein, horrible events, such as a death or crime (specific to the property, not the neighborhood), can impact a specific property value negatively. When valuing an asset that can be replicated (i.e., reasonably readily available assets including equipment and land), the upper limit to its value is the replacement cost. While you may be asking yourself how all of this has any relevance to the cost of capital, many assessors use the concept of enhancement to reconcile the income approach of a business to the cost (book value or replacement value) of the tangible assets and assume that the difference of the two must be enhancement. However, many times the difference is simply attributed to intangible assets that have not been valued or are not listed on the balance sheet. Once proper identification and valuation of the intangible assets are performed, then, and only then, can you begin to make decisions about the applicability or existence of enhancement. OPERATING PROPERTY IN EXISTENCE ON A LIEN DATE When valuing property for taxation purposes, it is generally accepted that the taxable value is only the value of the assets that exist on the lien date. Utah Rule 62 provides this guidance on how to measure cash flow: Cash flow is restricted to the operating property in existence on the lien date, together with any replacements intended to maintain, but not expand or modify, existing capacity or function. [Furthermore,] capital expenditures should include only those necessary to replace or maintain existing plant and should not include any expenditure intended primarily for expansion or productivity and capacity enhancements.
13
The Appraisal Institute, The Appraisal of Real Estate, 12th ed. (Chicago: Appraisal Institute, 2001).
Capital Structure
629
In addition to placing parameters on cash flow, Utah Rule 62 provides specific guidance on the capitalization rate when determining the appropriate g in kg: [. . .] growth rate ‘g’ is the expected future growth of the cash flow attributable to assets in place on the lien date, and any future replacement assets, furthermore where [. . .] ‘g’ will be the expected inflationary rate in the Gross Domestic Product Price Deflator .
CAPITAL STRUCTURE In past years, many property tax assessors used book value capital structures as the appropriate measure of the employment of capital. Again, this was the result of regulatory influence. Regulators defined the allowed earnings as a return on the original investment. A utility company would receive both a return on its investment and a return of its investment. Depreciation serves as a return of the investment, and net book value (otherwise termed rate base) is identified as the basis for the return on the investment. Therefore, the utility company would be limited to a return on the net book value, not on the fair market value, of the assets. With the near cessation of regulated telecommunication and limited regulation on certain electric utility assets (as seen in state and federal deregulation advances), book value capital structures are no longer appropriate. Investors now look at the returns on the market value of the assets. Therefore, certainly for companies whose assets are not rate-base regulated, the cost of capital should be subject to a market-weighted capital structure. Today most assessors have modified the capital structure to a market basis accordingly. To determine the proportion for each form of capital, a target capital structure must be developed. A target capital structure is the level of leverage a company is trying to achieve. The company believes that this target capital structure will maximize its value. This target capital structure is also called the optimum capital structure. The optimum capital structure provides for the lowest overall WACC. The weighting between debt and equity is a balancing act. The higher the debt leverage, the higher the returns equity and debt investors require. The opposite is true for lower leverage. Some financial theorists claim that the weighted average is saucer shaped; others claim it is flat and not dependent on weighting. This author tends to believe that it is more saucer shaped than flat. In other words, there is a sweet spot in the balance of equity and debt that provides for the lowest cost of capital.14 The traditional method of calculating the proper capital structure is to measure typical capital structures from guideline companies. Chapter 17 contains a discussion of WACC and the change of capital structure on the WACC. On occasion assessors include deferred taxes in the capital structure. The history behind this also stems back to rate-base regulation. Many regulators, when determining the allowed rate of returns for companies that are rate-base regulated, would calculate the cost of capital by including deferred taxes in the capital structure. The goal of this calculation was to ensure that the company was properly compensated over time. However, a deferred tax balance would develop because tax depreciation would not match book depreciation. Tax depreciation is typically shorter and front end–weighted while book depreciation assumes that deterioration occurs over a longer period of time and follows a balanced and straight-line method. Consequently, as the deferred tax balance grew, the regulator would not allow a return on this beneficial tax depreciation. When using market capital structures, any value associated with tax benefits is captured in the market value of equity. Therefore, if deferred taxes were to be added to a market capital structure, deferred taxes would be double-counted.
14
See, e.g., http://pages.stern.nyu.edu/adamodar/pc/capstru.xls.
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Cost of Capital
WEIGHTED AVERAGE COST OF CAPITAL The resulting capital structure is then used to weight the cost of capital components: equity, preferred stock, and debt. COST OF EQUITY The method assessors commonly use for determining the cost of equity is the Capital Asset Pricing Method (CAPM) approach. Assessors use common data sources:
SBBI historical market risk premium
ValueLine beta for guideline public companies 20-year U.S. government bond yield
Some states also utilize variations of these metrics to adjust or determine the cost of equity:
Flotation costs. Costs associated with the issuance of new securities, including underwriting spread and the costs incurred by the issuing company from the offering. These are used as a proxy for differences in cost of capital between liquid publicly traded stocks and illiquid real property. Ex ante risk premiums. Forward-looking risk premiums. Geometric risk premium. Derived from historical risk premiums instead of the arithmetic average of historical risk premium. Size premium. Additional equity premiums required due to a higher amount of risk associated with a smaller company. Bloomberg betas. Beta estimates from a regression analysis of historical trading prices of the stock against the Standard & Poor’s (S&P) 500, using weekly data over a two-year period to develop a beta, which is used to determine the cost of equity. S&P’s Compustat beta. Beta estimates based on 60 month-end prices. The S&P 500 is used as a proxy for the market beta.
Risk Premiums For property tax appraisals, the proper risk premium to utilize may already be statutorily outlined and is the result of previous litigation efforts. For example, Utah’s Rule 62 states that: [. . .] the risk premium shall be the arithmetic average of the spread between the return on stocks and the income return on long term bonds for the entire historical period contained in the Ibbotson Yearbook published immediately following the lien date .
Equalization may dictate your ability to determine the general market risk premium, but nothing should get in the way of determining certain adjustments that should be taken when comparing differences to a specific company or to the industry. Next we examine potential uses of the Duff & Phelps Size and Risk Studies to account for company specific premiums. Subsidiary Risk Premium Delta In many cases, a subsidiary or operating segment is the property subject to assessment. The challenge to the assessor/appraiser is to determine the appropriate cost of capital for the operating segment. The
Weighted Average Cost of Capital Exhibit 38.1
631
Risk Premiums over Riskless Rate: For the Parent Company
Measurement
Company Size
Market Value of Equity Book Value of Equity 5-year Average Net Income Market Value of Invested Capital Total Assets 5-year Average EBITDA Sales Number of Employees
$1,200 mil. $1,000 mil. $100 mil. $1,800 mil. $3,000 mil. $300 mil. $2,500 mil. 2,000
Mean premium over riskless rate Median premium over riskless rate
Premium over Riskless 9.1% 8.2% 8.5% 8.8% 8.2% 8.6% 8.8% 10.1% 8.7% 8.8%
For a complete discussion of the size study and the eight size measures, see Chapter 12.
typical approach utilized by assessors is to calculate the CAPM for the publicly traded parent company and assume that it is appropriately applied to the subsidiary. The assumption is that size and risk between publicly traded parent and subsidiary are neutral. In reality, however, subsidiary risk premiums, due to size and greater risk, are typically higher. To solve this dilemma, the assessor could use a comparison of results as determined by Duff & Phelps’ Size Study (based on eight size measurements)15 and Risk Study (based on a three-factor risk measurement) to estimate the equity risk premium. By comparing the subsidiary’s and parent company’s results, a subsidiary risk premium delta (SRPD) can be developed. The following is an example result of the risk premium over riskless rate for a simulated company using the eight size measurements. Exhibit 38.1 shows the risk premiums over the risk-free rate for the parent company. Exhibit 38.2 shows the risk premiums over the risk-free rate as estimated for the subsidiary based on the size of the nonpublic subsidiary. Exhibit 38.3 shows the resulting SRPD. There are several benefits of this approach:
Since the premiums calculated are already in the form of equity risk premiums, the dependence on statistically insignificant betas is eliminated. Exhibit 38.2
Risk Premiums over Riskless Rate: For Subsidiary
Measurements Market Value of Equity Book Value of Equity 5-year Average Net Income Market Value of Invested Capital Total Assets 5-year Average EBITDA Sales Number of Employees
Company Size N/A $100 mil. $10 mil. N/A $300 mil. $30 mil. $250 mil. 200
Mean premium over riskless rate Median premium over riskless rate
15
For a complete discussion of the Size Study and the eight size measures, see Chapter 12.
Premium over Riskless N/A 11.1% 11.3% N/A 11.1% 11.7% 11.0% 12.6% 11.5% 11.2%
632 Exhibit 38.3
Cost of Capital Subsidiary Risk Premium Delta
Measurements
Parent
Subsidiary
SRPD
Market Value of Equity Book Value of Equity 5-year Average Net Income Market Value of Invested Capital Total Assets 5-year Average EBITDA Sales Number of Employees
9.1% 8.2% 8.5% 8.8% 8.2% 8.6% 8.8% 10.1%
N/A 11.1% 11.3% N/A 11.1% 11.7% 11.0% 12.6%
N/A 2.9% 2.8% N/A 2.9% 3.1% 2.2% 2.5%
8.8% 8.7%
11.6% 11.5%
2.7% 2.8%
Mean premium over riskless rate Median premium over riskless rate
Since this universe far outreaches any traditional measure of ‘‘pure play’’ comparable companies, the focus here is based strictly on the factors in question, and reliance on pure-play companies is avoided.
The use of eight size measures helps to broaden the scope of focus and mitigates the potential skewing of results that can stem from a more narrowly focused measure. The flexibility of using six size metrics not dependent on market capitalization to determine results helps to capture some of the historically unaccounted for factors that can have an effect on the true equity risk premium.
In addition to the eight size measures, three risk measures also can be quantified if the subsidiary and parent have at least five years of income statistics. Exhibit 38.4 shows the use of the Risk Study in estimating the SRPD.16 If a subsidiary valuation is desired, this SRPD approach may be helpful. If the assessor prefers statutory or legacy methods to determine risk premiums (e.g., SBBI full history arithmetic risk premium multiplied by the ValueLine beta), then the above SRPD approach provides directionally correct indications of the magnitude of the SRPD. COST OF PREFERRED STOCK Preferred stock is a capital source that is common in public utilities. However, it typically accounts for less than 5% of the total capital structure. The measurement of the cost of preferred stock is typically oversimplified and underestimated. The reason is that, due to its convertible nature, the preferred dividend yield (which typically is considered the total return) does not fully account for the total rate of return expected by its investors. Preferred stock in many cases can be converted into common stock. Because of this conversion right, which provides the holder of preferred stock a probabilistic incremental return, preferred stock can carry a dividend yield less than the required total return required by its investors. As such, the yield can be viewed as a hybrid between an equity stock dividend and the cost of debt. In order to properly quantify the required rate of return for preferred stock, the analyst can perform complex option pricing calculations. Because of its relatively small weight (even smaller when calculating industry capital structures), an analyst can either ignore this capital component or simply determine the cost of preferred stock to be a midpoint of the cost of debt (pretax) and equity. 16
See Chapter 14 for a complete discussion of the Risk Study and the three risk measures.
Weighted Average Cost of Capital
Exhibit 38.4
633
Estimating the SRPD Using Three Risk Measures
Table 1. Parent Income Measures Coefficient of Variation of Operating Margin: (Standard Deviation of Operating Margin)/(Average Operating Margin)
Net Sales Operating Income Operating Margin Median Operating Margin Standard Deviation of Op. Margin Average Operating Margin Coefficient of Variation
2005
2004
2003
2002
2001
$9,000 $1,205 13.39%
$8,000 $1,091 13.64%
$8,500 $1,011 11.89%
$7,500 $919 12.26%
$7,100 $864 12.17%
12.26% 0.79% 12.67% 6.22%
Coefficient of Variation of Return on Book Value of Equity: (Standard Deviation of ROE)/(Average of ROE)
Book Value Net Income before Extraordinary Items Return on Book Equity (ROE) Standard Deviation of ROE Average ROE Coefficient of Variation
2005
2004
2003
2002
2001
$8,200 $1,100 13.41%
$7,100 $1,000 14.08%
$6,300 $930 14.76%
$5,400 $850 15.74%
$5,000 $800 16.00%
1.09% 14.80% 7.37%
Table 2. Subsidiary Income Measures Coefficient of Variation of Operating Margin: (Standard Deviation of Operating Margin)/(Average Operating Margin)
Net Sales Operating Income Operating Margin Median Operating Margin Standard Deviation of Op. Margin Average Operating Margin Coefficient of Variation
2005
2004
2003
2002
2001
$900 $150 16.7%
$800 $120 15.0%
$850 $130 15.3%
$750 $80 10.7%
$900 $140 15.6%
15.30% 2.3% 14.6% 15.8%
Coefficient of Variation of Return on Book Value of Equity: (Standard Deviation of ROE)/(Average of ROE)
Book Value Net Income before Extraordinary Items Return on Book Equity (ROE) Standard Deviation of ROE Average ROE Coefficient of Variation
2005
2004
2003
2002
2001
$820 $110 13.4%
$710 $80 11.3%
$630 $90 14.3%
$540 $40 7.4%
$500 $100 20.0%
4.6% 13.3% 34.7% (continued )
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Cost of Capital
Exhibit 38.4 (Continued) The following results are calculated for the Parent Company: Table 3. Parent Company Risk Premiums Measurements
Result
Median Operating Margin CV (Operating Income %) CV (Return on Equity)
12.26% 6.22% 7.37%
Premium over Riskless 9.09% 7.67% 7.23%
Mean premium over riskless rate Median premium over riskless rate
8.00% 7.67%
When comparing the subsidiary’s results to the parent company’s results, the subsidiary risk premium delta emerges: Table 4. Subsidiary Risk Premiums Measurements
Result
Median Operating Margin CV (Operating Income %) CV (Return on Equity)
15.30% 15.8% 34.7%
Premium over Riskless 8.39% 9.50% 8.60%
Mean premium over riskless rate Median premium over riskless rate
8.83% 8.60%
Correlating both size premium and risk premium differentials using the mean provides a balanced approach for the subsidiary premium: Table 5. Subsidiary Risk Premiums Delta Parent
Subsidiary
SRPD
Median Operating Margin CV (Operating Income %) CV (Return on Equity)
9.09% 7.67% 7.23%
8.39% 9.50% 8.60%
0.70% 1.83% 1.37%
Mean premium over riskless rate Median premium over riskless rate
8.00% 7.67%
8.83% 8.60%
0.83% 1.37%
COST OF DEBT In order to determine the cost of debt, the appraiser should consider several factors. In general, the tasks are to determine the market cost of debt for each of the guideline companies and compare the results with certain financial and operating metrics of the subject. The cost of debt for the subject can be measured by determining an estimate of the yield-to-maturity (YTM) of the debt holdings of the guideline public companies. The YTM is the function of two items: 1. The coupon payment promised to the bond holder, assuming the bond is held to maturity and all payments are reinvested at the same rate 2. The price in which the bond trades The YTM for the guideline companies will produce a range of results. If the YTM is not readily observable through active bond trading, the next best alternative is to analyze the ratings of the
Weighted Average Cost of Capital
635
guideline companies. The ratings can then be compared with typical YTM of companies that have more active bond trading. If the results of this analysis of the guideline companies’ YTM or ratings are a small range, then an average is generally acceptable. If the range is wide, then additional research may be required. The primary approach utilized to determine an appropriate rate of debt is to evaluate certain trends that may be evident within the guideline companies. One trend is the ratings or cost of debt capital compared with leverage, both financial and operational. The cost of debt increases as a firm is more leveraged, and vice versa. Financial leverage can be measured by determining the proportion of debt in the capital structure. Another measure of financial leverage is the debt service coverage ratio (DSCR). The DSCR is a measure of the amount of cash flow available to cover annual interest and principal payments on debt. A ratio of less than 1 indicates negative cash flow and insufficient funds to cover debt service. See Chapter 36 for a discussion of DSCR. In determining operational leverage, a relatively easy measurement is the coefficient of variation of operating margins (CV-OM). The CV-OM is calculated by determining the standard deviation of the fiveyear historical operating margins and dividing it by the average of the five-year historical operating margins. See Chapter 6 for a discussion of credit ratings and estimating cost of debt capital using credit ratings. AD VALOREM TAX ADDER The most common multiplicative value adjustment in ad valorem assessment is a calculation to add back estimated ad valorem taxes. Many assessors want to remove the historical bias resulting from prior assessments of tax. Therefore, they may prefer to account for property tax within the discount rate. They do so by adding back the percent relationship of tax to market value to the discount rate. Property is generally deductible for income tax purposes; therefore, the property tax rate must be tax effected. An ad valorem tax adder (a) can be added directly to the overall property discount rate (k0) to determine the proper discount rate (ka) to use to calculate the assessed value by discounting cash flows that do not take into account property taxes. The formula is: (Formula 38.1) a ¼ rCð1 tÞ where: a ¼ Effective annual tax levied versus the fair market value of the entity r ¼ Property tax rate (expressed as a percentage of total fair market value) C ¼ Proportion of the entity that is assessed property tax t ¼ Income tax rate For example, assume that the market capitalization for the subject property equals 10%. The market value of the property can be estimated using Formula 36.1 as follows: (Formula 38.2) Ip PVp ¼ cp Where: PVp ¼ Overall value or present value of the property Ip ¼ Overall income of the property cp ¼ Overall property capitalization rate
636
Cost of Capital
Assume that 0 ¼ zero, so that kp ¼ cp ¼ 10%, the property tax rate (r) ¼ 2%, the mean tax rate t ¼ 4% and C ¼ 100%. ka ¼ kp þ rð1 tÞ ka ¼ :10 þ :02ð1 :4Þ ka ¼ :112 Assume that I0 before property tax equals $1,000. Capitalizing I0 by ka, we get an assessed value equal to $8,928 (¼$1,000/.112). Multiply by the property tax rate, we get the tax effected net operating income after property taxes equals $892 ($1,000 [$8,928 .012]). Capitalizing using k0, we get a market value equal to $8920 (¼$892 .10). This shows that formula 38.1 correctly adjusts the discount rate. FLOTATION COSTS Another type of adjustment that is applied in certain states is a flotation cost adjustment. This adjustment is recognition that the cost of capital for an illiquid project being assessed is greater than the cost of capital for publicly traded companies. Flotation costs occur when new issues of stock or debt are sold to the public. The firm usually incurs several kinds of flotation or transaction costs, which reduce the actual proceeds received by the firm. Some of these are direct out-of-pocket outlays, such as fees paid to underwriters, legal expenses, and prospectus preparation costs. Because of this reduction in proceeds, the firm’s required returns must be higher to compensate for the additional costs. Flotation costs can be accounted for either by amortizing the cost, thus reducing the cash flow to discount, or by incorporating the cost into the cost of capital. Since flotation costs typically are not applied to operating cash flow, they must be incorporated into the cost of capital. The cost of flotation is a function of size and risk. The larger the issuance, the lower the flotation cost relative to the size of the offering. Exhibit 38.5 shows examples of the relation of flotation cost to size of an issuance of stock that occurred during 2006 and 2007. Flotation costs are the greatest for equity issuances and the least for debt issuances. Preferred stock flotation costs tend to be somewhere in between the two.
Exhibit 38.5
Relation of Flotation Cost to Size of an Issuance of Stock
Company
Total Issuance
Total Flotation %
Gate House Media ITC Holdings Fortress Investment Group RSC Holdings KBR MetroPCS Communications BlackRock Citigroup SAIC Ford Motor Credit
200,000,000 218,500,000 750,000,000 458,330,000 550,000,000 1,225,000,000 1,175,000,000 1,500,000,000 1,725,000,000 2,956,200,000
10.2% 8.2% 7.9% 6.1% 5.7% 5.0% 4.8% 3.2% 2.7% 1.0%
WACC versus WARA
637
WACC VERSUS WARA Most business enterprises are comprised of various types of tangible and intangible assets. For example, a company in the business of owning, managing, and developing power plants would have a collection of various assets (i.e,. contracts, generation plants, permits, trained workforce, etc.). Each of these assets requires different rates of return based. Think of it as if each asset were owned separately. The cash flow for each asset would depend on its own economic characteristics. The rate of return would be subject to the asset’s operational risk and the asset’s ability to attract debt and equity capital. In order to fully understand and completely analyze a business, the appraiser can develop reconciliation of the weighted average return on assets (WARA) and the weighted average cost of capital (WACC). This method is utilized in the development of rates of return for contributing assets in purchase price allocations under SFAS No. 141, Business Combinations. See Chapter 21 for a discussion of reconciling rates of return for companies and reporting units to the rates of return on underlying assets. This analysis breaks apart each asset class and assigns a rate of return applicable to each, then weights the rates according to the percent of value that each class occupies and averages these weighted returns. The WARA should reconcile to the WACC. Exhibit 38.6 is an example of a WACC versus WARA analysis. In general, intangible assets (i.e., goodwill and brand value) required returns are the highest because of the inability to attract debt capital and high volatility while tangible assets tend to be lower because of the ability to attract debt capital and more stable earnings. The other use of this method is that it can assist in the allocation of the cash flow. For example, if the total enterprise value for a company that owns assets that require rates of return and are proportionally weighted as in the table in Exhibit 38.6, then the analyst can determine an allocation of cash flow to a certain asset. If the total enterprise value of this company was $1 million and the analyst needs to determine an appropriate return for property, plant, and equipment (PP&E), this calculation can be performed: Section
Measurements
Formula
A. B. C. D. E. F. G.
Required return of company (in $s) Required return of company (in %) Total enterprise value Allocation of value to PP&E Value of PP&E Required return on PP&E (in %) Required return on PP&E (in $s)
CA
$97,600
CD EG
$1,000,000 55% $550,000 8% $44,000
Exhibit 38.6
Results
Example of WACC versus WARA Analysis
Asset Type
Return
Percent of Value
Weighted WARA
Working Capital Property, Plant, & Equipment Customer Base Brand Value Goodwill WARA WACC
4.00% 8.00% 10.00% 12.00% 15.00%
5.00% 55.00% 15.00% 3.00% 22.00%
0.20% 4.40% 1.50% 0.36% 3.30% 9.76% 9.76%
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Cost of Capital
The allocation can be useful to demonstrate to assessors for purposes of determining the appropriate allocation of income to the taxable assets only. For example, if only PP&E was taxable, then the proper level of income to discount or capitalize is $44,000.
SUMMARY The cost of capital in an ad valorem taxation process is a function of market value principles, legislation, statutory rules, and assessor practices. Unless all of these drivers are taken into account, an analyst’s estimated cost of capital may be flawed. Prior to performing any valuation for ad valorem tax purposes, detailed research of the tax code and legislative history and discussions with taxing officials should be completed. These variables will add a layer of complexity to an appraisal report.
Part 7
Advice to Practitioners
Chapter 39
Dealing with Cost of Capital Issues
Introduction Practical Issues and Advice Equity Risk Premium Beta Estimates Reporting Unit Cost of Equity Capital Size Premiums for Reporting Unit Cost of Equity Capital Cost of Debt Capital Off-Balance Sheet Financing Subject Company Industry Risk Premium Cost of Capital of Proposed Acquisition Summary
INTRODUCTION The authors get asked many questions about cost of capital issues. We thought we would share our experiences and views with the users of this book. While many sources deal theoretically with cost of capital issues, there is not as much information available for resolving related issues on client engagements. Sometimes doing this requires compromise between the theoretical and the practical.
PRACTICAL ISSUES AND ADVICE EQUITY RISK PREMIUM Question: It has been my practice to use the realized risk premium data from the back page of the SBBI Valuation Edition Yearbook in developing the cost of equity capital. After reading the summary of the research presented in Chapter 9, I have come to the conclusion that an equity risk premium for 2007 is lower than the realized risk premium data from 1926 to 2006. I have concluded that an equity risk premium in the 5% range is more appropriate. How do I reconcile my conclusion this year with my past practices? Advice: The guiding principle in conducting valuations is that you should incorporate what is known or knowable at the time of the valuation date. While the evidence that the realized risk premiums since 1926 has overstated the forward-looking expected equity risk premium of today has been building over the past several years, only recently is the consensus of academics and researchers being made widely known to valuation practitioners. You should not continue using past practices just for consistency now that past practices have been found to be deficient. We as practitioners adopt new methodologies when they become regularly accepted into our practices. For example, 641
642
Cost of Capital
many people use the Capital Asset Pricing Model today to estimate the cost of equity capital. That method did not become widely used until the 1970s. Did introducing a new method invalidate prior valuations? In the years ahead we will be adopting newer and improved methods, and that will not invalidate the valuations we perform today. BETA ESTIMATES Question: After gathering data on guideline public companies, I unlever the betas using the Hamada formula. I find that the betas for the smallest guideline public companies are less than the betas for the larger guideline public companies. This indicates to me that the business risk of these smaller companies is less than the business risk of the larger companies. Are these beta estimates useful? Advice: Determining meaningful beta estimates using smaller guideline public companies is always problematic. ‘‘Forward beta’’ estimates from one data provider consistently underestimate the betas for smaller guideline public companies. You need first to determine if there is sufficient trading volume to make any estimate using realized returns meaningful. Some smaller guideline public companies trade so infrequently that no data source adequately corrects for this problem. Assuming that thin trading is not the issue, you should investigate calculating your own sum betas for all of the guideline public companies. Our experience is that sum beta estimates are significantly greater than other beta estimates (including so-called forward beta estimates provided by the data source mentioned earlier) for smaller public companies. You should also look at the industry beta estimates provided by Morningstar as a substitute or confirmation of your own beta estimates. Also consider using a fundamental beta (see Chapter 11). The goal is not to blindly use a beta estimate just because it came from a well-known data source. The mass data providers cannot analyze the actual underlying data to ensure that their mass-produced estimate is meaningful. Do not assume that the adjustments made by Bloomberg and Morningstar compensate for poor underlying data. Those adjustments are, for the most part, mechanical averaging toward a beta of 1. They are not based on an analysis of the underlying data. You may need to use data from fewer than 60 months to get a meaningful beta estimate if the company went through an acquisition. You may need to ignore completely a published beta as it is simply unrepresentative of the company’s risk. You may also want to make sure that you are unlevering the beta estimates using the appropriate formula. Are the smaller companies small because they are troubled and their equity prices trade at such low levels that they are trading like options? These companies cannot expect to utilize the tax deductions on interest payments as paid. Further, the Hamada formula, though used extensively, is appropriate only where the amount of debt is assumed constant (in dollars). It is not consistent with the theory that debt will increase/decrease as the net cash flows (and overall value) of the firm increase or decrease. Refer to the discussion in Appendix 10A for a full discussion. Ultimately, the goal is to conclude on a beta estimate that makes economic sense. Correct valuation requires applying value drivers reflected in today’s market pricing. The entire valuation process is based on applying reasoned judgment to the evidence derived from economic, financial, and other information and arriving at a well-reasoned opinion of value. It is not an exercise in mechanical application of formulas. Estimating the beta is no different. REPORTING UNIT COST OF EQUITY CAPITAL Question: In developing the cost of equity capital for a reporting unit for test for goodwill impairment, I have been told that all of the competitors of the reporting unit are either the segments of large,
Practical Issues and Advice
643
multisegment public companies or closely held companies. How can I develop the cost of equity capital using the Capital Asset Pricing Model? Advice: If you believe you must use the CAPM, then the full-information beta method will provide beta estimates for businesses with Standard Industrial Classification codes that are segments of larger companies. You should look at the Cost of Capital Yearbook published by Morningstar, but also consider using the Duff & Phelps Risk Premium Report—Risk Study to develop a cost of equity capital estimate using the build-up method. That study provides risk premium returns for fundamental risk measures. Exhibits D-1, D-2, and D-3 of the Risk Study present levered risk premiums. You can unlever the realized risk premiums displayed in those exhibits if you desire, using the same relationship between levered risk premiums and unlevered risk premiums in, say, Exhibits C-3 (risk premiums by size measured by net income) or Exhibit C-6 (risk premiums by size measured by earnings before interest, taxes, depreciation, and amortization [EBITDA]) of the Risk Premium Report. SIZE PREMIUMS FOR REPORTING UNIT COST OF EQUITY CAPITAL Question: In developing the cost of equity capital for a reporting unit, I am unsure if a size premium is appropriate. The company itself is of such a size that no size premium is appropriate. The segment within which the reporting unit resides is also large enough that no size premium is appropriate. What should I do? Advice: The size premium may or may not be appropriate. The data on size premiums are derived on averages across many firms, not by industry. You must determine fair values of reporting units based on the hypothetical price that market participant acquirers would pay assuming you were selling the reporting unit. This does not mean that reporting units must be looked at individually. SFAS 157, Fair Value Measurements, provides that you can look at groupings of assets (and reporting units) that will maximize value to the hypothetical seller and consider the fair value of that grouping. For example, perhaps the reporting units for a company represent individual European country businesses but the sale that would maximize value to the hypothetical seller (the ‘‘highest and best use’’ of the assets comprising the reporting units) would include all European reporting units. Risk (e.g., size) should be measured assuming such consolidation. If you are measuring risk using beta, compare the unlevered betas and size of the guideline public companies. There may be little evidence that the market believes that underlying business risk changes as size changes. Some industries have that pattern. Remember, size can be a proxy (on the average) for risk. Research has shown that variability of cash flows is correlated with size; small-size companies on the average exhibit greater variability of cash flows (and greater variability of returns not explained by beta). You should also consider using the Duff & Phelps Risk Premium Report—–Risk Study to develop a cost of equity capital estimate using the build-up method. That study provides risk premium returns for fundamental risk measures without regard to size. The subject reporting unit may exhibit less than or more than the average risk for companies of comparable size. The risk of the reporting unit, regardless of its size, is the most appropriate determinant of the appropriate discount rate. Exhibits D-1, D-2, and D-3 of the Risk Study present levered risk premiums based on the fundamental risk measures. You can unlever the realized risk premiums displayed in those exhibits if you desire, using the same relationship between levered risk premiums and unlevered risk premiums in, say, Exhibits C-3 (risk premiums by size measured by net income) or Exhibit C-6 (risk premiums by size
644
Cost of Capital
measured by EBITDA) of the Risk Premium Report. Then you can compare the fundamental risk of the reporting unit to the risk of the average of companies of comparable size. COST OF DEBT CAPITAL Question: The subject company has borrowed short term over the past few years at almost a constant level such that it appears to be permanent financing. (The company has no long-term debt.) The borrowing rate has been at 2 points over prime. Should that debt be counted in the capital structure of the subject business? Advice: If the short-term borrowings are providing working capital financing (e.g., floor plan financing of automobiles by an auto dealer), you may want to charge the interest expense as an operating expense. But many companies have taken advantage of low short-term interest rates and have borrowed short term for long periods of time. The cost of debt capital should reflect the expected average of interest rates over a long period of time. If the current yield curve is upward sloping (after removing the effect of the horizon premium), that indicates that future interest rates are expected to be higher than current short-term rates. You should consider using the long-term equivalent interest rate for bonds that would be comparably rated to the subject company (if it went for a debt rating). You also need to determine if the borrowing rate is low because the owners have provided personal guarantees. Depending on the purpose of the valuation and the standard of value, you may need to determine the cost of borrowing based on the nonguaranteed debt rating of the company, separating the credit rating of the owner from the credit rating of the company. We discuss estimating a credit ratio for the company in Chapter 6. OFF-BALANCE SHEET FINANCING Question: When should I consider going through the effort of considering off–balance sheet financing of the guideline public companies in unlevering beta estimates? Advice: You always want to compare the off–balance sheet financing (e.g., operating leases) used by the guideline public companies and compare that to the off–balance sheet financing used by the subject company. If the amount of off–balance sheet financing is small for all of the companies, there is likely no need to capitalize the operating leases and include them in the capital structures. But if the differences in financing are significant (e.g., the guideline public companies tend to lease most of their fixed assets and the subject company owns most of its fixed assets), then the effect of ignoring the off–balance sheet financing can be significant as well. If someone will be putting investment dollars at risk because of your work or if you may be challenged (e.g., by auditors or in litigation), then you likely do not want to ignore the off–balance sheet liabilities. The first time you do the adjustment it will take considerable time. But once you develop a methodology and work plan, the calculations can be done in a day or two. SUBJECT COMPANY Question: In valuing a subject company that has an environmental cleanup issue, how much do I add to the company discount rate? Advice: The expert should make adjustment at the end of the valuation. As one author says in Business Valuation Discounts and Premiums, extreme cases of environmental cleanup issues do not lend very well to factoring into the discount rate. Another concern is that most financial institutions will not accept as collateral any property with environmental issues. This fact typically reduces the collateral available and lending capacity of the subject company. The appropriate discount rate should likely
Summary
645
only include the long-term debt capacity ascribed to using working capital as collateral. The remaining capital (and discount rate) will likely be equity capital. This will reduce the debt-to-equity ratio for the subject company. INDUSTRY RISK PREMIUM Question: I am using a build-up method for a subject company and the industry risk premium adjustment in SBBI is –4.5%. Can I ignore it in developing the equity cost of capital? Advice: In some cases the segment used to develop the industry risk premium is not comparable with the subject company and further research must be conducted before ignoring the industry risk premium. You must download the SBBI list of companies and assess how big the segment is. The industry risk premium is developed using segment reporting data of the industry companies based on revenue. For each company, you must download the 10-k forms that were used to develop the industry risk premium and assess whether the companies are truly comparable to the subject company. If the companies are not comparable, you must be able to explain why you chose to ignore the company and the industry risk premium. If the companies are comparable, then the industry risk premium adjustment is appropriate. Simply ignoring the industry risk premium is not acceptable without research and justification. COST OF CAPITAL OF PROPOSED ACQUISITION Question: In valuing a proposed acquisition of a new business to my company, what factors should I consider in estimating the appropriate cost of capital? Advice: As we discussed in Chapter 22, the appropriate cost of capital matches the risk of the investment with the expected return. This includes both the cost of equity capital and the cost of debt capital based on the debt capacity and borrowing costs of the business to be acquired. This point has been reiterated by Aswath Damodaran in a recent talk titled the ‘‘Acquirers Anonymous: Seven Steps Back to Sobriety’’ He reminds potential acquirers that the appropriate cost of equity used for an investment should reflect the risk of the investment, not the risk characteristics of the investor who raised the funds, and that the cost of debt should reflect the debt capacity and cost of debt of the target. In his view, too many acquiring firms build their lower cost of equity and lower borrowing costs into the valuation of a target firm, essentially transferring wealth from the acquiring firm’s shareholders to the target firm’s shareholders. This also applies to the hypothetical discount rate in testing for goodwill impairment under SFAS 142, Goodwill and Other Intangible Assets. Based on the guidance contained in SFAS No. 157, Fair Value Measurements, you should estimate the discount rate appropriate for the reporting unit. That discount rate, both equity and debt components, should reflect the risk of the reporting unit, not the risk of the hypothetical market participants that comprise the pool of likely buyers for the reporting unit.
SUMMARY Putting this book together has been a challenge. Our aim has been to provide the practitioner with a guide and a reference resource. We hope this chapter has helped the reader synthesize the materials in this book to answer everyday problems.
Chapter 40
Questions to Ask Business Valuation Experts
Introduction Examination Outline Questions on Admissibility and Impact of Expert Questions on Overview of the Assignment Questions on the Income Approach: General Questions for Discounting Method Questions on Capitalization Method (Chapter 4) Questions on Cost of Capital (Chapter 6) Questions on the Build-up Method (Chapter 7) Questions on Capital Asset Pricing Model and Modified CAPM (Chapter 8) Questions on Debt Capital of Subject Company (Chapter 6) Questions on Marketability of Interest If Closely Held Entity Being Valued (Chapter 25 for Minority Interest; Chapter 26 for Controlling Interest) Questions on Estimating Net Cash Flows (Chapter 33)
INTRODUCTION Examining experts on cost of capital issues may at first seem like a daunting task for many attorneys. This outline of questions has been prepared to assist attorneys. Cross-references to the relevant chapters of this book and notes to examiners provide further information. The content of the book should be understandable to attorneys who deal even only occasionally with valuation issues. Attorneys also may wish to provide these questions to their financial expert to assist in developing an outline for questioning.
EXAMINATION OUTLINE QUESTIONS ON ADMISSIBILITY AND IMPACT OF EXPERT 1. What is your academic background? 2. To what extent did your academic background include courses in finance? 3. What professional designation(s) in business valuation do you hold? (For each such designation:) When did you achieve that designation, and what did you have to do to achieve it? 647
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Cost of Capital
4. To what professional business valuation organizations do you belong other than those in which you hold a professional designation? 5. What educational training have you availed yourself of in those organizations? 6. What other courses and/or seminars in business valuation (BV) have you attended? 7. Have you done any teaching in BV? If so, describe. 8. Have you done any writing in the field of BV? If so, describe. 9. Have you held any officer or committee positions in professional organizations dealing with BV? If so, describe. 10. Have either you or your organization done any work for the company being appraised or its affiliates, officers, directors, or owners in the past? If so, describe. 11. Have you worked with Lawyer ______ or others in his (her) firm in the past? If so, describe. 12. Describe the details of the development of your engagement (initial contact, description, and time of initial and subsequent assignments, produce engagement letter(s)). 13. What experience do you have in the industry in which the subject company operates? (Examiner: Keep in mind that, in most cases, prior industry knowledge is helpful but not essential. A good appraiser can develop the necessary industry knowledge during the course of the engagement.) 14. Did you comply with the Uniform Standards of Professional Appraisal Practice (USPAP)? Why or why not?
QUESTIONS ON OVERVIEW OF THE ASSIGNMENT 1. What standard of value did you use for this appraisal assignment (e.g., fair market value, defined as ‘‘. . .’’)? 2. What is the source of that definition? 3. Why is that standard of value appropriate for this valuation assignment (e.g., statutory definition, definition from precedential case(s) [which should be cited if relied on as authority], definition from binding contractual agreement)? 4. Is your appraisal based on a going-concern premise, a liquidation premise, or some combination of going concern and liquidation? Why? 5. What approach(es) did you rely on? Why? 6. What method(s) within the approach(es) did you rely on? Why? 7. Why did you not use the ______ approach? 8. Why did you not use the ______ method with the ______ approach? 9. Were there any past transactions in the company or its securities? Were there any offers to buy the company? Did the company itself make any acquisitions? 10. Does the company have any assets that are excess in nature—that is, not needed to support its normal operations as a going concern? If so, how did you treat those in the valuation? 11. Are there any buy-sell agreements and/or restrictions or obligations regarding transfer of ownership interests? If so, how did you treat them in your valuation?
QUESTIONS ON THE INCOME APPROACH: GENERAL 1. Within the income approach, what method or methods did you use? Why is this (are these) better than any other alternative method(s) for the purpose of this valuation? 2. Did you conduct your income approach on an equity basis or an invested capital basis? Why is that basis more appropriate for this assignment? (If on an invested capital basis:) What components did you include in your capital structure? Why?
Examination Outline
649
3. Did you use a discounting method or a capitalization method? Why? (Chapter 4) 4. What income variable did you choose to discount or capitalize? Why is this variable better in this case than some other measure of income? (Chapter 3)
QUESTIONS FOR DISCOUNTING METHOD 1. Will you please define in simple terms exactly what a discount rate is? (Examiner: This question tests the analyst’s knowledge and understanding of what the discounting method is all about and whether the analyst thinks that he or she has captured what is necessary in the rate—that is, the total rate of return that the market would demand to place money in this investment, apart from liquidity considerations.) (Chapter 4) 2. What is the source of your projection? Why did you use this source? What steps did you take to verify or analyze the reasonableness of these projections? 3. What procedure did you use to estimate your terminal value? (Examiner: This usually will be a capitalization of constant income, a constant growth model, or a market multiple of some income variable.) (If a market multiple:) Why is that procedure better than a capitalized income model? (If the terminal value is a large part of the value, using a market multiple likely changes the approach from an income approach to a market approach.) (If a capitalized income procedure:) Why is that procedure better than a market multiple model and what was the growth rate used in the terminal value? How did you derive this growth rate? 4. What percentage of your total present value is attributable to your terminal value? 5. (If an invested capital procedure was used) Please explain exactly how you computed your weighted average cost of capital (WACC). What percentage weight was assigned to each component of your capital structure? How did you arrive at these weights? Are the weights based on book value of equity or market value of equity? (Examiner: If book value, the WACC is virtually meaningless, but this is a common error.) (Chapter 17) 6. What sources did you use to derive the weights you used for each component of the capital structure? (Examiner: If the analyst used some comparative financial statement source, such as RMAs’Financial Statement Studies or the Almanac of Business and Industrial Financial Ratios, and said that the equity percentage was at market value, the analyst will have a problem, because those sources are at book value.) 7. Why are these weights appropriate to use in this particular valuation assignment? (Examiner: If an analyst is valuing a minority interest and uses some weights other than the company’s own actual weights—for example, some industry average weights—he or she has injected an element of control into the valuation, because the minority stockholder cannot cause a change in the company’s capital structure. If valuing a minority interest, weights other than actual company weights generally would not be appropriate under the standard of fair market value, and may or may not be appropriate under other standards of value.)
QUESTIONS ON CAPITALIZATION METHOD (CHAPTER 4) 1. Please explain in simple terms what a capitalization rate is. How does a capitalization rate relate to a discount rate? (Examiner: This is a perception check on the witness’s basic understanding. Often those not schooled in valuation are confused about the distinction between capitalization rates and discount rates.) 2. What is the definition of the income variable that you capitalized? Why was this a better variable to capitalize than some other measure of income that you might have chosen?
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Cost of Capital
3. What source did you use to determine the amount of the income variable that you capitalized? What steps did you take to determine that this was a reasonable, normalized level of income to capitalize? 4. How did you calculate your capitalization rate? What sources did you use?
QUESTIONS ON COST OF CAPITAL (CHAPTER 6) 1. What method did you use to develop your cost of equity capital? 2. What are the components that make up that method? 3. What risk-free instrument (Treasury bill, long-term government bond) did you use in developing the cost of equity capital? What was the yield of that instrument? Why did you use that instrument for your risk-free rate? As of what date did you observe the risk-free rate? 4. What equity risk premium did you use? (Chapter 9) What was the source of the equity risk premium you used? Why did you conclude on that equity risk premium? Why did you reject other risk premiums?
QUESTIONS ON THE BUILD-UP METHOD (CHAPTER 7) 1. Did you use a size premium? (Chapters 12 and 13) (Examiner: The two primary sources of size premium data are the SBBI Valuation Edition Yearbook and the Duff & Phelps Risk Premium Report.) 2. (If size premium added:) What factors did you consider in determining that size premium was appropriate? How did you measure the size of the subject company? What was the source of the size premium data? Why did you use that source? Why did you reject other data sources? 3. Did you add an industry risk premium adjustment? (Examiner: Industry risk premium adjustments come from SBBI Valuation Edition Yearbook and are based on the Standard Industrial Classification [SIC] code of subject company.) (If industry risk premium adjustment added:) What was the source of the adjustment? What companies are included in the industry risk adjustment? Why are these companies appropriate for making the industry risk adjustment for the subject company? (If industry risk premium adjustment not added:) What steps did you take to determine you should not apply an industry risk premium? 4. Did you add a company-specific risk adjustment? (Examiner: Be alert to double counting risk factors that are incorporated in the size premium or industry risk premium factors.) (If companyspecific risk adjustment added:) What company-specific risk adjustment did you add? Please list the risk factors that caused you to apply a company-specific risk adjustment. How did you arrive at your overall company-specific risk adjustment? (If expert weighted the risk factors:) What was the source of the weights you used?
QUESTIONS ON CAPITAL ASSET PRICING MODEL AND MODIFIED CAPM (CHAPTER 8) 1. What beta estimate did you use in applying the CAPM? (Chapters 10 and 11) (If subject company is publicly held:) What was the source of your beta estimate? Why did you choose that source? (If subject company is closely held:) What guideline public companies or other source did you use in determining your beta estimate? 2. What source or sources did you use for your betas in the CAPM? (Examiner: In Chapter 10 we said that, because different sources compute betas differently, all betas should come from the same source; otherwise the beta used will be bogus.)
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3. How did you determine to consider each guideline public company? How did you arrive at the concluded beta estimate for the subject company? (Examiner: Average, weighted or unweighted, median, etc.) 4. Why did you choose that method? What guideline public companies are most comparable to the subject company? Why? 5. Did you unlever the guideline public company betas? Why or why not? (Examiner: In Chapter 10 we discuss that unlevering removes the financing risk differences.) What formula did you use to unlever the guideline public company betas? Why? (The commonly used Hamada formula is typically not the best formula; see Chapter 10A.) 6. Did any of the guideline public companies you used in developing the beta estimate have off– balance sheet liabilities? If so, which ones and what are their liabilities? How did you handle those liabilities? 7. Did you relever the calculated beta? Why or why not? (If yes:) How did you relever the beta for the subject company? Why did you use that formula? How did you arrive at the appropriate capital structure to use in relevering the beta? (Examiner: The analyst should have used iterative method if using subject company capital structure or industry average capital structure of most comparable guideline public companies.) (Examiner: For size premium and company-specific risk adjustment, see Chapter 7. Industry risk premium adjustment is applicable only to the build-up method.) 8. (If market approach rejected:) Why did you use guideline public companies in your beta calculation but reject the guideline public company method? QUESTIONS ON DEBT CAPITAL OF SUBJECT COMPANY (CHAPTER 6) 1. What discount rate did you use for the cost of debt capital? 2. What was the source of the cost of debt capital? 3. How did you determine that interest rate was the appropriate cost of debt capital? (Examiner: Many closely held businesses borrow money on the cosignature of the owner(s). The cost of debt capital for the subject company should generally be determined without effect of the guarantee. Doing this requires an analysis of the debt rating of the subject company.) 4. Is the interest rate a short-term borrowing rate or long-term borrowing rate? Why is that rate appropriate? 5. Does the subject company have off–balance sheet liabilities (e.g., operating leases)? (If yes:) How did you consider them in developing the amount and cost of debt capital for the subject company? 6. Is the debt capital guaranteed? (Examiner: common for a closely held business). If yes, how did you handle the guarantee? (A common error is to estimate the cost of debt capital with the guarantee continuing.) If one is valuing the business intermingling the value of the business and the value of the guarantors personal assets. This may lead to a double counting. QUESTIONS ON MARKETABILITY OF INTEREST IF CLOSELY HELD ENTITY BEING VALUED (CHAPTER 25 FOR MINORITY INTEREST; CHAPTER 26 FOR CONTROLLING INTEREST) 1. How did you consider the marketability of the subject interest? What was the source of your adjustment? (Examiner: A frequent error is to cite studies applicable for minority interests and apply them to controlling interests.)
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QUESTIONS ON ESTIMATING NET CASH FLOWS (CHAPTER 33) 1. What are the subject company’s growth expectations? Why? 2. How do those growth expectations compare to the historical company growth? 3. How do these growth expectations compare to industry expectations? (If different:) Why are they different? 4. How did you estimate the added investments in net working capital required given the growth expectations? 5. How did you estimate the added investments in capital expenditures required given the growth expectations? 6. How did you estimate expected depreciation? 7. (If capital expenditures equal to depreciation in terminal value net cash flow:) How did you estimate long-term growth in capital expenditures and depreciation in the net cash flow you capitalized for the terminal value? (Examiner: Market evidence is that long-term capital expenditures should exceed long-term depreciation.) 8. Is growth expected to be the same or different for net income? Net cash flow? EBITDA? Why or why not?
Appendices
Appendix I
Bibliography This bibliography is separated into two sections, books and other publications and articles.
BOOKS AND OTHER PUBLICATIONS Abrams, Jay B. How to Value Your Business and Increase Its Potential. New York: McGraw–Hill, 2005. ———. Quantitative Business Valuation: A Mathematical Approach for Today’s Professionals. New York: McGraw–Hill, 2000. Akerson, Charles B. Capitalization Theory and Techniques Study Guide. Chicago: Appraisal Institute, 1984. Brealey, Richard A., Stewart C. Myers, and Franklin Allen. Principles of Corporate Finance, 8th ed. Boston: Irwin McGraw–Hill, 2006. American Institute of Certified Public Accountants. IPR&D Practice Aid. Jersey City, NJ: AICPA, 2001. American Society of Appraisers, Business Valuation Standards–Glossary. Herndon, VA: American Society of Appraisers, revised 2005. The Appraisal Foundation. Uniform Standards of Professional Appraisal Practice. Washington, DC: The Appraisal Foundation, 2006. Appraisal Institute. Advanced Income Capitalization. Chicago: Appraisal Institute, 2001. ———. The Appraisal of Real Estate, 12th ed. Chicago: Appraisal Institute, April 2001. ———. The Dictionary of Real Estate Appraisal, 4th ed. Chicago: Appraisal Institute, 2002. Armitage, Seth. The Cost of Capital: Intermediate Theory. New York: Cambridge University Press, 2005. Benninga, Simon. Financial Modeling, 2nd ed. Cambridge, MA: The MIT Press, 2000. Bernstein, Richard. Style Investing: Unique Insights into Equity Management. Hoboken, NJ: John Wiley & Sons, 1995. Best, Joel. Damned Lies and Statistics, Untangling Numbers from the Media, Politicians, and Activists. Los Angeles: University of California Press, 2001. ———. More Damned Lies and Statistics, How Numbers Confuse Public Issues. Los Angeles: University of California Press, 2004. Bierman, Harold Jr., and Seymour Smidt. The Capital Budgeting Decision: Economic Analysis of Investment Projects, 9th ed. London: Routledge, 2006. Black, Ken, and David L. Eldredge. Business & Economic Statistics Using Microsoft1 Excel. Stamford, CT: Thomson, South–Western, 2001. Block, Ralph L. Investing in REITs—Real Estate Investment Trusts. New York: Bloomberg Press, 2002. Brealey, Richard A., and Stewart C. Myers. Financial Management for Decision Making. Knoxville, TN: Beard Books, 2003. Bodie, Zvi, Alex Kane, and Alan J. Marcus. Capital Investment and Valuation. New York: McGraw Hill, 2002. ———. Investments, 6th ed. Boston: Irwin McGraw–Hill, 2004. Brigham, Eugene, and Louis Gapenski. Financial Management: Theory and Practice, 5th ed. Dryden Press, 1988. Brueggeman William B., and Jeffrey D. Fisher. Real Estate Finance and Investment, 13th ed. New York: McGraw– Hill, 2006. 655
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CFA Institute. Currency Risk in Investment Portfolios. Charlottesville, VA: CFA Institute (AIMR), 1999. Cornell, Bradford. Corporate Valuation: Tools for Effective Appraisal and Decision Making. New York: McGraw– Hill, 1993. ———. The Equity Risk Premium: The Long-Run Future of the Stock Market. Hoboken, NJ: John Wiley & Sons, 1999. Cottle, Sidney, Roger F. Murray, and Frank E. Block. Graham & Dodd’s Security Analysis, 5th ed. New York: McGraw–Hill, 1988. Damodaran, Aswath. Damodaran on Valuation: Security Analysis for Investment and Corporate Finance, 2nd ed. Hoboken, NJ: John Wiley & Sons, 2006. ———. Investment Valuation: Tools and Techniques for Determining the Value of Any Asset, 2nd ed. Hoboken, NJ: John Wiley & Sons, 2002. DeVisscher, Francois M., Craig E. Aronoff, and John L. Ward. Managing Capital and Liquidity in the Family Business. Marietta, GA: Family Enterprise Publisher, 1995. Dimson, Elroy, Paul Marsh, and Mike Staunton. The Global Investment Returns Yearbook 2007. Amsterdam: ABNAMRO, and London: London Business School, February, 2007. ———. Triumph of the Optimists: 101 Years of Global Investment Returns. Princeton, NJ: Princeton University Press, 2002. Duff & Phelps. Risk Premium Report. Chicago: Duff & Phelps, 2007 (updated annually). Ehrhardt, Michael C. The Search for Value: Measuring the Company’s Cost of Capital. Boston: Harvard Business School Press, 1994. Estrada, Javier. Finance in a Nutshell: A No-Nonsense Companion to the Tools and Techniques of Finance. New York: Financial Times Prentice-Hall, 2005. Fishman, Jay E., Shannon P. Pratt, and J. Clifford Griffith. PPC’s Guide to Business Valuations, 17th ed. Fort Worth, TX: Practitioners Publishing, 2007 (updated annually). Fishman, Jay E., Shannon P. Pratt, and William J. Morrison. Standards of Value: Theory and Application. Hoboken, NJ: John Wiley & Sons, 2007. Fredrikson, E. Bruce. Frontiers of Investment Analysis, 2nd ed. Scranton, PA: Intext Educational Publishers, 1971. See especially Chapter 17, ‘‘Relationship between Variability of Past Returns and Levels of Future Returns for Common Stocks, 1926–1960,’’ by Shannon P. Pratt. Gonick, Larry, and Woollcott Smith. The Cartoon Guide to Statistics. New York: HarperCollins, 1994. Hitchner, James R. Financial Valuation: Applications and Models, 2nd ed. Hoboken, NJ: John Wiley & Sons, 2006. Homer, Sidney, and Richard Sylla. A History of Interest Rates, 4th ed. Hoboken, NJ: John Wiley & Sons, 2005. Hull, John C. Options, Futures and Other Derivative Securities, 6th ed. Englewood Cliffs, NJ: Prentice-Hall, 2005. Ibbotson, Roger G., and Gary P. Brinson. Global Investing: The Professional’s Guide to the World Capital Markets. New York: McGraw-Hill, 1993. ———. Investment Markets. New York: McGraw-Hill, 1987. Ibbotson, Roger G., and Rex Sinquefield. Stocks, Bonds, Bills and Inflation: Historical Returns (1926–1987). Chicago: Irwin Professional Publishing, 1989. Internal Revenue Service. IRS Valuation Training for Appeals Officers, Coursebook. Chicago: CCH Incorporated, 1998. International Valuation Standards Committee. International Valuation Standards, 7th ed. London: International Valuation Standards Committee, 2005. Johnson, Bruce A., Spencer J. Jefferies, and James R. Park. Comprehensive Guide for the Valuation of Family Limited Partnerships, 3rd ed. Fort Worth, TX: Partnership Profiles, 2006.
Books and Other Publications
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Jones, Gerald Everett. How to Lie with Charts, 2nd ed. Charleston, SC: BookSurge Publishing, 2006. Kaufman, Mike. Handbook of Budgeting, 4th ed. Hoboken, NJ: John Wiley & Sons, 1999. Kinnard, William N. Jr. Income Property Valuation. Lexington, MA: Heath-Lexington Books, 1971. Koller, Tim, Marc Goedhart, and David Wessels. Valuation: Measuring and Managing the Value of Companies, 4th ed. Hoboken, NJ: John Wiley & Sons, 2005. Koosis, Donald J. Statistics—A Self-Teaching Guide, 4th ed. Hoboken, NJ: John Wiley & Sons, 1997. Kvanli, Alan H., Robert J. Pavour, and Kellie B. Keeling. Introduction to Business Statistics, A Microsoft1 Excel Integrated Approach. Stamford, CT: Thomson, South-Western, 2002. Lalli, William R. Handbook of Budgeting, 5th ed. Hoboken, NJ: John Wiley & Sons, 2003. Laro, David, and Shannon P. Pratt. Business Valuation and Taxes: Procedure, Law, and Perspective. Hoboken, NJ: John Wiley & Sons, 2005. Liu, Lon-Mu. Time Series Analysis and Forecasting, 2nd ed. Villa Park, IL: Scientific Computing Associates, 2006. Mendenhall, William, Robert J. Beaver, and Barbara M. Beaver. Introduction to Probability & Statistics, 11th ed. Belmont, CA: Thomson, Brooks/Cole, 2003. Mercer, Z. Christopher. Quantifying Marketability Discounts—Developing and Supporting Marketability Discounts in the Appraisal of Closely Held Business Interests. Memphis, TN: Peabody Publishing, 1997. ———. Valuing Enterprise and Shareholder Cash Flows: The Integrated Theory of Business Valuation. Memphis, TN: Peabody Publishing, 2004. ———. Valuing Financial Institutions. Homewood, IL: Business One Irwin, 1992. Morningstar. Beta Book, First 2007 ed. Chicago: Morningstar, 2007 (updated biannually). ———. Cost of Capital Resources. Chicago: Morningstar, 2007. ———. Cost of Capital Yearbook. Chicago: Morningstar, 2007 (updated annually). ———. Stocks, Bonds, Bills and Inflation Valuation Edition 2007 Yearbook. Chicago: Morningstar, 2007 (updated annually). Ogier, Tim, John Rugman, and Lucinda Spicer. The Real Cost of Capital. New York: Financial Times Prentice-Hall, 2004. Partnership Profiles. 2007 Rate of Return Study. Fort Worth, TX: Partnership Profiles, 2007. Penman, Stephen H. Financial Statement Analysis and Security Valuation, 3rd ed. New York: McGraw-Hill, 2007. Pereiro, Luis E. Valuation of Companies in Emerging Markets: A Practical Approach. Hoboken, NJ: John Wiley & Sons, 2002. Pradhuman, Satya Dev. Small-Cap Dynamics: Insights, Analysis, and Models. New York: Bloomberg Press, 2000. Pratt, Shannon P. Business Valuation Discounts and Premiums. Hoboken, NJ: John Wiley & Sons, 2001. ———. Valuing a Business: The Analysis and Appraisal of Closely Held Companies, 5th ed. New York: McGrawHill, 2007. Pratt, Shannon P., Robert F. Reilly, and Robert P. Schweihs. Valuing Small Businesses and Professional Practices, 3rd ed. New York: McGraw-Hill, 1998. Rachlin, Robert, and H. W. Allend Sweeny. Handbook of Budgeting, 4th ed. Hoboken, NJ: John Wiley & Sons, 1994. See especially Chapter 8, ‘‘Profitability and the Cost of Capital,’’ by Mike Kaufman. Ragsdale, Cliff T. Spreadsheet Modeling & Decision Analysis, 4th ed. Stamford, CT: Thomson, South-Western, 2004. Rappaport, Alfred. Creating Shareholder Value: A Guide for Managers and Investors, revised ed. New York: The Free Press, 1997. Reilly, Frank K., and Keith C. Brown. Investment Analysis and Portfolio Management, 8th ed. Stamford, CT: Thomson, South-Western, 2005.
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Reilly, Robert, and Robert P. Schweihs, eds. The Handbook of Business Valuation and Intellectual Property Analysis. New York: McGraw-Hill, 2004. Rosenburg, Michael R. Currency Forecasting: A Guide to Fundamental and Technical Models of Exchange Rate Determination. Chicago: Irwin Professional Publishing, 1996. Ross, Stephen A., Randolph W. Westerfield, and Jeffrey F. Jaffe. Corporate Finance, 8th ed. Burr Ridge, IL: McGraw-Hill, 2006. Sabal, Jaime. Financial Decisions in Emerging Markets. Oxford: Oxford University Press, 2002. Savage, Sam L. Decision Making with Insight, 2nd ed. Belmont, CA: Thomson, Brooks/Cole, 2003. Scherlis, Daniel R., and William A. Sahlman. A Method for Valuing High-Risk, Long Term, Investments: The Venture Capital Method. Boston: Harvard Business School Press, 1987. Schroeder, Larry D., David L. Sjoquist, and Paula E. Stephan. Understanding Regression Analysis—An Introductory Guide. Newbury Park, CA: Sage Publications, 1986. Shim, Jae K. U.S. Master Finance Guide, 2nd ed. Chicago: CCH, Incorporated, 2005. Siegel, Jeremy J. Stocks for the Long Run, 2nd ed. New York: McGraw-Hill, 1998. Sirower, Mark L. The Synergy Trap: How Companies Lose the Acquisition Game. New York: The Free Press, 1997. Smith, Richard L., and Janet Kiholm Smith. Entrepreneurial Finance, 2nd ed. Hoboken, NJ: John Wiley & Sons, 2003. Stewart, G. Bennett. The Quest for Value. New York: HarperCollins, 1991. Swensen, David F. Pioneering Portfolio Management: An Unconventional Approach to Institutional Investment. New York: The Free Press, 2000. Thomson Financial. FactSet’s I/B/E/S Detail Application. Norwalk, CT: FactSet Research Systems, updated daily. Trugman, Gary R. Understanding Business Valuation: A Practical Guide to Valuing Small to Medium-Sized Businesses. New York: American Institute of Certified Public Accountants, 1998. White, Gerald, Ashwinpaul C. Sondi, and Haim D. Fried. The Analysis and Use of Financial Statements, 3rd ed. Hoboken, NJ: John Wiley & Sons, 2003. Williams, John Burr. The Theory of Investment Value. Cambridge, MA: Harvard University Press, 1938.
ARTICLES To locate a working paper, search online using any major search engine (i.e., Google or Yahoo) by author and title. An example: the first link provided using the Google search engine when a search for ‘‘Adrian, Tobias, and Francesco Franzoni. Learning About Beta: an Explanation of the Value Premium’’ will be ‘‘SSRN–Learning About Beta: An Explanation of the Value Premium by . . . ’’ This link will direct you to the Social Science Research Network, where the article is downloadable. Abbott, Ashok. ‘‘Discount for Lack of Marketability: An Empirical Analysis.’’ Business Valuation Review (December 2003): 172–179. Abrams, Jay B. ‘‘A Breakthrough in Calculating Reliable Discount Rates.’’ ASA Valuation (August 1994): 8–24. Abrams, Jay B., and Hiatt, R. K. ‘‘The Bias in Annual (Versus Monthly) Discounting is Immaterial,’’ Business Valuation Review (September 2003): 127–135. Adhikari, Mike. ‘‘WACC as Used in Capitalization Formula Causes Overvaluation.’’ Business Valuation Update (October 2003): 1–4. Adrian, Tobias, and Francesco Franzoni. ‘‘Learning About Beta: Time-varying Factor Loadings, Expected Returns, and the Conditional CAPM.’’ Working paper, May 2005.
Articles
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Ahmed, Anwer S., and Lale Guler. ‘‘Evidence on the Effects of SFAS 142 on the Reliability of Goodwill Writeoffs.’’ Working paper, May 25, 2007. Alamar, Benjamin C. ‘‘Monte Carlo Simulation in the Valuation of High Risk Businesses.’’ Business Valuation Review (December 2002): 186–189. Ambrose, Brent W., Michael J. Highfield, and Peter D. Linneman. ‘‘Real Estate and Economies of Scale: The Case of REITs.’’ Real Estate Economics 33 (2005): 323–350. Amihud, Yakov, and Haim Mendelson. ‘‘Asset Pricing and the Bid-Ask Spread.’’ Journal of Financial Economics 17 (1986): 223–249. Ammann, Manual, and Michael Verhofen. ‘‘The Conglomerate Discount: A New Explanation Based on Credit Risk.’’ International Journal of Theoretical and Applied Finance, 9 No. 8, (2006): 1201–1214. Ammer, John, and Jon Wongswan. ‘‘Cash Flows and Discount Rates, Industry and Country Effects and CoMovement in Stock Returns.’’ Financial Review (May 2007). Anderson, Evan W., Eric Ghysels, and Jennifer L. Juergens. ‘‘The Impact of Risk and Uncertainty on Expected Returns.’’ Working paper, April 11, 2007. Ang, Andrew, and Joseph Chen. ‘‘CAPM over the Long Run: 1926–2001.’’ Journal of Empirical Finance (January 2007): 1–40. Ang, Andrew, Joseph Chen, and Yuhang Xing. ‘‘Downside Risk.’’ Review of Financial Studies, March 2, 2006, online. Ang, James S., Gregory Leo Nagel, and Jun Yang. ‘‘A Critical Long View of Capital Markets and Institutions: Realized Returns from Corporate Assets, 1950–2003.’’ Working paper, March 13, 2006. Angelidis, Timotheos, and Nikolaos Tessaromatis. ‘‘Equity Returns and Idiosyncratic Volatility: UK Evidence.’’ Working paper, June 2, 2005. Annin, Michael. ‘‘Fama-French and Small Company Cost of Equity Calculations.’’ Business Valuation Review (March 1997): 3–13. ———. ‘‘Using Ibbotson Associates’ Data to Develop Minority Discount Rates.’’ CPA Expert (Winter 1997): 1–4. Annin, Michael E., and Dominic A. Falaschetti. ‘‘Equity Risk Premium Still Produces Debate.’’ Valuation Strategies (January/February 1998): 17–23, 44. ———. ‘‘Is There Still a Size Premium?’’ CPA Expert (Winter 1998): 7–9. Arditti, Fred. ‘‘Risk and the Required Return on Equity.’’ Journal of Finance (March 1967): 19–36. Armentrout, Brant H. ‘‘A Sanity Test When Estimating Capital Expenditures in Excess of Depreciation.’’ Business Valuation Review (September 2003): 136–141. Arnott, Robert D. ‘‘Historical Results.’’ Equity Risk Premium Forum, CFA Institute (AIMR) (November 8, 2001): 27. Arnott, Robert D., and Peter L. Bernstein. ‘‘What Risk Premium Is Normal?’’ Financial Analysts Journal (March/ April 2002): 64–85. Arshanapalli, Bala, Daniel T. Coggin, John Doukas, and H. David Shea. ‘‘The Dimensions of International Equity Style.’’ Journal of Investing (Spring 1998). Arzac, Enrique R., and Lawrence R. Glosten. ‘‘A Reconsideration of Tax Shield Valuation.’’ European Financial Management (September 2005): 453–461. Asbra, Marc. ‘‘Contributory Asset Charges in the Excess Earnings Method.’’ Valuation Strategies (March/April 2007): 4–17. Ashton, D. J. ‘‘The Cost of Equity Capital and a Generalization of the Dividend Growth Model.’’ Accounting & Business Research (Winter 1995): 3–17. Asness, Clifford S. ‘‘Stocks versus Bonds: Explaining the Equity Risk Premium.’’ Financial Analysts Journal (April/May 2000): 96–113. Baca, Sean P., Brian L. Garbe, and Richard A. Weiss. ‘‘The Rise of Sector Effects in Major Equity Markets.’’ Financial Analysts Journal (September 2000): 34–40.
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Bajaj, Mukesh, and Scott Hakala. ‘‘The Valuation of Small Capitalization Companies.’’ In Financial Valuation: Business and Business Interests, ed. Hanan and Sheeler, Chapter 12A (1998). Bali, Turan G., and Nusret Cakici. ‘‘Idiosyncratic Volatility and the Cross-Section of Expected Returns.’’ Working paper, July 2006. Banz, Rolf W. ‘‘The Relationship between Return and Market Value of Common Stocks.’’ Journal of Financial Economics (March 1981): 3–18. Baptiste, Laurent, Gregory Borges, and Gary Carr. ‘‘Utility Bond Ratings and the Cost of Capital.’’ Public Utilities Fortnightly (October 27, 1988). Barad, Michael. ‘‘Beta Computations and Adjustments.’’ The 2003 Cost of Capital Workshop. University of Chicago, June 20, 2003. Available at www.BVLibrary.com. ———. ‘‘Ibbotson Clarifies Controversies on How to Estimate Size Premium; Prefers Return in Excess of CAPM for Both Build-Up and CAPM Models.’’ Business Valuation Update (July 2002): 1–4. Barber, Gregory A. ‘‘Valuation of Pass-Through Entities.’’ Valuation Strategies (March/April 2001): 4–11, 44–45. Bargeron, Leonce, Frederik P. Schlingemann, Rene´ M. Stulz, and Chad J. Zutter. ‘‘Why Do Private Acquirers Pay So Little Compared to Public Acquirers?’’ Charles A. Dice Center Working Paper No. 2007–8 and Fisher College of Business Working Paper No. 2007–03–011, April 2007. Bar-Hava, Keren, Roni Ofer, and Oded Sarig. ‘‘New Tests of Market Efficiency Using Fully Identifiable Equity Cash Flows.’’ Working paper, February 2007. Barnes, Mark A., Anthony Bercel, and Steven H.Rothmann. ‘‘Global Equities: Do Countries Still Matter?’’ Journal of Investing (Fall 2001): 43–48. Basu, Sanjay. ‘‘Investment Performance of Common Stocks in Relation to Their Price-Earnings Ratios: ATest of the Efficient Market Hypothesis.’’ Journal of Finance (June 1977): 129–156. Bauman W. Scott, Mitchell C. Conover, and Robert E. Miller. ‘‘Growth versus Value and Large-Cap versus SmallCap Stocks in International Markets.’’ Financial Analysts Journal (March/April 1998): 75–89. Bechard, M. ‘‘Weighing Public and Private Real Estate.’’ Real Estate Portfolio, National Real Estate Investment Trusts (November/December 2003). Becker, Brian, and Ian Gray. ‘‘Does a Small Firm Effect Exist When Using the CAPM? Not Since 1980 and When Using Geometric Means of Historical Returns.’’ Business Valuation Review (September 1999): 104–111. ———. ‘‘Using Average Historical Data for Risk Premium Estimates: Arithmetic Mean, Geometric Mean or Something Else?’’ Business Valuation Review (December 1998): 136–140. Bendixen, Christian L. ‘‘Improved Estimation of Equity Risk Premiums.’’ Business Valuation Review (March 1994): 22–32. Bennett, James A., and Richard W. Sias. ‘‘How Diversifiable Is Firm-Specific Risk?’’ Working paper, February 2007. Berges, Angel, John J. McConnell, and Gary G. Schlarbaum. ‘‘The Turn of the Year in Canada.’’ Journal of Finance (March 1984): 185–192. Berk, Jonathan B. ‘‘A Critique of Size Related Anomalies.’’ Review of Financial Studies (Summer 1995): 275–286. ———. ‘‘Does Size Really Matter?’’ Financial Analyst Journal (September/October 1997): 12–18. Bhamra, Harjoat, Lars-Alexander Kuehn, and Ilya Strebulaev. ‘‘The Levered Equity Risk Premium and Credit Spreads: A Unified Framework.’’ Working paper, July 18, 2007. Bhandari, Laxmi Chand. ‘‘Debt/Equity Ratio and Expected Common Stock Returns: Empirical Evidence.’’ Journal of Finance (June 1988): 507–528. Bhanot, K. ‘‘What Causes Mean Reversion in Corporate Bond Index Spreads? The Impact of Survival.’’ Journal of Banking and Finance (June 2005): 1385–1403. Bianchini, Roberto, Stefano Bonini, and Laura Zanetti. ‘‘Target Price Accuracy in Equity Research.’’ Working paper, June 25, 2007. Bishop, David M., and Frank C. Evans. ‘‘Avoiding a Common Error in Calculating the Weighted Average Cost of Capital.’’ CPA Expert (Fall 1997).
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Bishop, David M., and John P. White. ‘‘Overview of the Multiple Period Discounting Method: Practical Considerations for Application in the Valuation of Businesses.’’ ASA International Conference 2001, Pittsburgh, PA, July 23–25, 2001. Available at www.BVLibrary.com. Black, Fisher. ‘‘Beta and Return.’’ Journal of Finance Portfolio Management (Fall 1993): 8–18. ———. ‘‘Estimating Experted Return.’’ Financial Analysts Journal (September/October 1993): 36–38. Black, Fischer, and Myron Scholes. ‘‘The Pricing of Options and Corporate Liabilities.’’ Journal of Political Economy (May 1973): 637–654. Blume, Marshall E. ‘‘On the Assessment of Risk.’’ Journal of Finance (March 1971): 1–11. ———. ‘‘Unbiased Estimators of Long-Run Expected Growth Rates.’’ Journal of the American Statistical Association (September 1974): 634–638. Booth, Laurence. ‘‘The Capital Asset Pricing Model: Equity Risk Premiums and the Privately-Held Business.’’1998 CICBV/ASA Conference (September 1998): 23. ———. ‘‘Capital Cash Flows, APV and Valuation.’’ European Financial Management (January 2007): 29–48. ———. ‘‘Estimating the Equity Risk Premium and Equity Costs: New Ways of Looking at Old Data.’’ Journal of Applied Corporate Finance (Spring 1999): 100–112. ———. ‘‘Finding Value Where None Exists: Pitfalls in Using Adjusted Present Value.’’ Journal of Applied Corporate Finance (Spring 2002): 8–17. Booth, Laurence, and Cleveland S. Patterson. ‘‘Estimating the Cost of Equity Capital of a Non-Traded Unique Canadian Entity: Reply.’’ Canadian Journal of Administrative Sciences (June 1993): 122–133. Bordi, Lorena, and Daniel L. McConaughy. ‘‘The Long-Term Relationships between Capital Expenditures and Depreciation across Industries: Important Data for Capitalized Income-Based Valuations.’’ Business Valuation Review (March 2004): 14–18. Botosan, Christine A. ‘‘Disclosure Level and the Cost of Equity Capital.’’ Accounting Review (July 1997): 323–349. Boudoukh, Jacob, Matthew Richardson, and Robert F. Whitelaw. ‘‘Nonlinearities in the Relation between the Equity Risk Premium and the Term Structure.’’ Management Science (March 1997): 371–385. Bowers, Helen, and Tara Stephenson. ‘‘Determinants of the Discount for Lack of Marketability.’’ The Woodward Group and Lerner College of Business and Economics, University of Delaware (May 2004). Brav, Alon, Reuven Lehavy, and Roni Michaely. ‘‘Using Expectations to Test Asset Pricing Models.’’ Financial Management (Autumn 2005): 5–37. Brief, Richard P. ‘‘Accounting Valuation Models: A Short Primer.’’ Abacus 43 no. 4 (2007): 429–437. Bruno, Solnik, Robert D. Arnott, Mark P. Kritzman, and Richard M. Levich. ‘‘Currency Risk in Investment Portfolios.’’ CFA Institute (AIMR) (June 1999). Brown, David P., and Miguel A. Ferreira. ‘‘Idiosyncratic Volatility of Small Public Firms and Entrepreneurial Risk.’’ Working paper, December 2005. Budyak, James T. ‘‘Developing Discount Rates in a Global Environment.’’ Valuation Strategies (May/June 2001): 28–35. ———. ‘‘Getting a Grip on Foreign Discount Rates.’’ Business Valuation Update (January 2000): 8–10. ———. ‘‘Getting Your Head Out of the Model: Due Diligence and Developing International Cost of Capital.’’ Business Valuation Update (May 2006): 5–8. ———.‘‘Developing Discount Rates in a Global Environment.’’ Proceedings from the Sixth Joint Business Valuation Conference of the CICBVand the ASA, Toronto October 19–20, 2006; The Journal of Business Valuation (2007): 361–393. Burke, Brian H. ‘‘The Impact of S Corporation Status.’’ Business Valuation Review (June 2001): 15–24. Burns, Richard M. ‘‘Using DCF Analysis.’’ 1999 IBA National Conference—Business Valuations. Orlando, FL. Available at: www.BVLibrary.com. Burmeister, Edwin. ‘‘Using Macroeconomic Factors to Control Portfolio Risk.’’ Working paper, Duke University, March 9, 2003.
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Butler, Peter, and Keith Pinkerton. ‘‘Company-Specific Risk—A Different Paradigm: A New Benchmark.’’ Business Valuation Review (Spring 2006): 22–28. ———. ‘‘Quantifying Company-Specific Risk: A New, Empirical Framework with Practical Applications.’’ Business Valuation Update (February 2007): 1–11. ———. ‘‘Quantifying Company-Specific Risk: The Authors Answer Your Questions.’’ Business Valuation Resources (August 2007): 9–14. ———. ‘‘Comparing the Butler-Pinkerton Model to Traditional Methods Under Four Daubert Criteria.’’ Business Valuation Update (November 2007): 1, 4–7. Callahan, Carolyn M., and Rosanne M. Mohr. ‘‘The Determinants of Systematic Risk: A Synthesis.’’ Financial Review (May 1989): 157–181. Camera, Antonio, San-Lin Chung, and Yaw-Huei Wang. ‘‘The Cost of Equity Capital Implied by Option Market Prices.’’ Working paper, June 19, 2007. Campello, Murillo, Long Chen, and Lu Zhang. ‘‘Expected Returns, Yield Spreads, and Asset Pricing Tests.’’ Working paper, January 2006. Campbell, John Y., Martin Lettau, Burton G. Malkiel, and Yexiao Xu. ‘‘Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk.’’ Journal of Finance (February 2001): 1–43. Campbell, John Y., and Jianping Mei. ‘‘Where Do Betas Come From? Asset Price Dynamics and the Sources of Systematic Risk.’’ The Review of Financial Studies 6 No. 3 (1993): 567–592. Campbell, John Y., and Robert J. Shiller. ‘‘The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors.’’ Review of Financial Studies (May 1989): 195–228. Campbell, John Y., and Samuel B. Thompson. ‘‘Predicting the Equity Premium Out of Sample: Can Anything Beat the Historical Average?’’ Harvard Institute of Economic Research Discussion Paper No. 2084, July 2005. Cantor, Richard, and Frank Packer. ‘‘Determinants and Impacts of Sovereign Credit Ratings.’’ Economic and Policy Review (October 1996): 37–53. Carleton, Willard T., and Josef Lakonishok. ‘‘Risk and Returns on Equity: the Use and Misuse of Historical Estimates.’’ Financial Analysts Journal (January/February 1985): 38–47. Carrieri, Francesca, Vihang Errunza, and Basma Majerbi. ‘‘Does Emerging Market Exchange Risk Affect Global Equity Prices?’’ Journal of Financial Quantitative Analysis (September 2006): 511–540. Cassiere, George G. ‘‘Geometric Mean Return Premium versus the Arithmetic Mean Return Premium—Expanding on the SBBI 1995 Yearbook Examples.’’ Business Valuation Review (March 1996): 20–23. Cavaglia, Stefano, Chris Brightman, and Michael Aked. ‘‘The Increasing Importance of Industry Factors.’’ Financial Analysts Journal (September/October 2000): 41–54. Chan, Louis, Jason Karceski, and Joseph Lakonishok. ‘‘The Level and Persistence of Earnings Growth.’’ Journal of Finance (April 2003): 634–684. Chan, Louis, and Joseph Lakonishok. ‘‘Are the Reports of Beta’s Death Premature?’’ Journal of Portfolio Management (Summer 1993): 51–62. Chandler, William F. ‘‘Business Valuation Recent Cases, Rulings and Interpretations.’’ New York State Society of CPA’s Business Valuation Conference, May 17, 2004: 56. Chatfield, Robert E., R. Charles Moyers, and Phillip M. Sisneros. ‘‘The Accuracy of Long-Term Earnings Forecasts for Industrial Firms.’’ Quarterly Journal of Business and Economics (June 22, 1989). Chen, Nai-Fu. ‘‘Some Empirical Tests of Arbitrage Pricing.’’ Journal of Finance (December 1983): 1393– 1414. Chen, Nai-Fu, Richard Roll, and Stephen A. Ross. ‘‘Economic Forces and the Stock Market: Testing the APT and Alternative Pricing Theories.’’ Journal of Business 59 (1986): 383–403. Chen, Peng, Gary T. Bariel, and Paul D. Kaplan. ‘‘Venture Capital and Its Role in Strategic Asset Allocation.’’ Journal of Portfolio Management (Winter 2002): 83–89.
Articles
663
Chen, Peter F., and Guochang Zhang. ‘‘How Do Accounting Variables Explain Stock Price Movements? Theory and Evidence.’’ Journal of Accounting and Economics (July 2007): 219–244. Chen, Yueyun, Iskandar S. Hamwi, and Tim Hudson. ‘‘Capital Asset Pricing Model with Default Risk: Theory and Application in Insurance.’’ Atlantic Economic Society: International Advances in Economic Research 9, no. 1 (February 2003): 20. Chiugn-Min, Tsai. ‘‘Alternative Dynamic Capital Asset Pricing Models: Theories and Empirical Results.’’ Ph.D. diss. Rutgers, State University of New Jersey, November 2005. Christoffersen, Peter, Kris Jacobs, and Gregory Vainberg. ‘‘Forward-Looking Betas.’’ Working paper, August 4, 2006, rev. March 16, 2007. Chua, Jess, Philip C. Chang, and Zhenyu Wu. ‘‘The Full-Information Approach for Estimating Divisional Betas: Implementation Issues and Tests.’’ Journal of Applied Corporate Finance (Spring/Summer 2006): 53–61. Chung, Kee H. ‘‘The Impact of Demand Volatility and Leverage on the Systematic Risk of Common Stocks.’’ Journal of Business Finance and Accounting (June 1989): 343–360. Cimasi, Robert, and Charles Wilhoite. ‘‘Fair Market Value.’’ BV Q&A Newsletter (October 2005). Claus, James, and Jacob Thomas. ‘‘The Equity Premia as Low as Three Percent? Evidence from Analysts’ Earnings Forecasts for Domestic and International Stock Markets.’’ Journal of Finance (October 2001): 1629–1666. Clineball, John M., Douglas R. Kahl, and Jerry L. Stevens. ‘‘Time–Series Properties of the Equity Risk Premium.’’ Journal of Financial Research (Spring 1994): 105–116. Clubb, Colin D. B. and Paul Doran. ‘‘On the Weighted Average Cost of Capital with Personal Taxes.’’ Accounting & Business Research (Winter 1992): 44–48. Cochrane, John H. ‘‘The Dog That Did Not Bark: A Defense of Return Predictability.’’ Working paper, January 30, 2006. ———. ‘‘The Risk and Return of Venture Capital.’’ Journal of Financial Economics (January 2005): 3–52. Revision of NBER Working Paper 8066. Conine, Thomas E. Jr., and Maurry Tamarkin. ‘‘Divisional Cost of Capital Estimation: Adjusting for Leverage.’’ Financial Management (Spring 1985): 54–58. Conroy, Robert M., and Robert S. Harris. ‘‘How Good Are Private Equity Returns?’’ Journal of Applied Corporate Finance (Summer 2007): 96–108. Cooper, Ian. ‘‘Arithmetic versus Geometric Mean Estimators: Setting Discount Rates for Capital Budgeting.’’ European Financial Management (July 2001): 157–167. Cooper, Ian, and Sergei Davydenko. ‘‘Using Yield Spreads to Estimate Expected Returns on Debt and Equity.’’ London Business School IFA Working Paper and EFA 2003 Annual Conference Paper No. 901, December 2003. ———. ‘‘Estimating the Cost of Risky Debt.’’ Journal of Applied Corporate Finance (Summer 2007): 90–94. Cooper, Ian, and Kjell G. Nyborg. ‘‘Valuing the Debt Tax Shield.’’ Journal of Applied Corporate Finance (Spring 2007): 50–59. Copeland, Tom. ‘‘Seminar on Frontiers in Corporate Valuation.’’ New York University Leonard N. Stern School of Business, November 6–7, 1997. Cornell, Bradford. ‘‘Historical Results.’’ Equity Risk Premium Forum, CFA Institute (AIMR) (November 8, 2001): 38–41. ———. ‘‘Estimating the Cost of Equity Capital.’’ Proceedings of the 27th Annual Wichita Program: Appraisal for Ad Valorem Taxation, Wichita State University, August 3–7, 1997. Cummins, J. David, and Joan Lamm-Tennant. ‘‘Capital Structure and the Cost of Equity Capital in the Property– Liability Insurance Industry.’’ Insurance: Mathematics & Economics (December 1994): 187–201. Cvitanic´, Jaksˇa, Zvi Wiener, and Fernando Zapatero. ‘‘Analytic Pricing of Employee Stock Options.’’ Working paper, July 19, 2006.
664
Cost of Capital
Damodaran, Aswath. ‘‘Estimating Equity Risk Premiums.’’ Stern School of Business Working Paper No. FIN–99– 021 (1999). Can be downloaded without charge at www.stern.nyu.edu/fin. ———. ‘‘Marketability and Value: Measuring the Illiquidity Discount.’’ Working paper, July 30, 2005. ———. ‘‘Value and Risk: Beyond Betas.’’ Financial Analyst Journal (March/April 2005): 38–43. ———. ‘‘Betas by Sector.’’ New York: Damodaran Online, 2007. ———. ‘‘Acquirers Anonymous: Seven Steps Back to Sobriety.’’ Presentation at Duff & Phelps Seminar, Paris France, November 15, 2007. Dangl, Thomas, Michael Halling, and Otto Randl. ‘‘Equity Return Prediction: Are Coefficients Time Varying?’’ Working paper, April 2006. Daniel, Kent, and Sheridan Titman. ‘‘Evidence on the Characteristics of Cross–Sectional Variation in Stock Returns.’’ Journal of Finance (March 1997): 1–33. Daouk, Hazem, and David Ng. ‘‘Is Unlevered Firm Volatility Asymmetric?’’ AFA 2007 Chicago Meetings, January 11, 2007. Daves, Phillip R., and Michael C. Ehrhardt. ‘‘Convertible Securities, Employee Stock Options, and the Cost of Equity.’’ Working paper, June 7, 2004. Day, Theodore, Yi Wang, and Yexiao Xu. ‘‘Investigating Underperformance by Mutual Fund Portfolios.’’ Working paper, May 2001. Dechow, Patricia M., Amy P. Hutton, and Richard G. Sloan. ‘‘An Empirical Assessment of the Residual Income Valuation Model.’’ Journal of Accounting and Economics (January 1999): 1–34. Dechow, Patricia M., and Richard G. Sloan. ‘‘Returns to Contrarian Investment Strategies: Tests of Naive Expectations Hypotheses.’’ Journal of Financial Economics (January 1997): 3–27. Dechow, Patricia M., Richard G. Sloan, and Mark T. Soliman. ‘‘Implied Equity Duration: A New Measure of Equity Risk.’’ Review of Accounting Studies (June 2004): 197–228. De Franco, Gus, Ilanit Gavious, Justin Yiqiang Jin, and Gordon D. Richardson. ‘‘The Existence and Explanations for the Private Company Discount.’’ AAA 2007 Financial Accounting & Reporting Section Meeting Papers, September 15, 2006. DeMario, Marianne, and Anthony Fazzone. ‘‘The Adjusted Present Value: An Alternative Approach to the Effect of Debt on Business Value.’’ Business Valuation Update (December 2006): 1–4. Diavatopoulos, Dean, James S. Doran, and David R. Peterson. ‘‘Implied Idiosyncratic Volatility and the Cross– Section of Stock Returns.’’ Working paper, April 8, 2007. Dickerson, Gregg. ‘‘Estimating the Cost of Equity or They Ripped Out My CAPM and Stomped That Sucker Flat.’’ Proceedings of the 27th Annual Wichita Program: Appraisal for Ad Valorem Taxation, Wichita State University, August 3–7, 1997. Dickinson, Victoria. ‘‘Future Profitability and the Role of Firm Life Cycle.’’ Working paper, September 2006. Dickson, Lisa, Shannon P. Pratt, and Gary Trugman. ‘‘Fair Market Value on a Control Basis.’’ BV Q&A Newsletter (August 2004). Dietrich, Mark O. ‘‘Computing Premium for S Status Based on Buyer’s Benefit.’’ Valuation Strategies (May/June 2003). Dimson, Elroy, Paul Marsh, and Mike Staunton. ‘‘Global Evidence on the Equity Risk Premium.’’ Journal of Applied Corporate Finance (Summer 2003): 27–38. ———. ‘‘The Worldwide Equity Premium: A Smaller Puzzle.’’ EFA 2006 Zurich Meetings Paper, University of Zurich—Swiss Banking Institute, April 7, 2006. Dobbs, Richard, Billy Nand, and Werner Rehm. ‘‘Merger Valuation: Time to Jettison EPS.’’ McKinsey Quarterly (Spring 2005): 17–20. Dobner, Michael. ‘‘Mid-Year Discounting and Seasonality Factors.’’ Business Valuation Review (March 2002): 16–18.
Articles
665
Doherty, Neil A. ‘‘Risk Management, Risk Capital, and the Cost of Capital.’’ Journal of Applied Corporate Finance (Summer 2005): 119–123. Domian, Dale L., David A. Louton, and Marie D. Racine. ‘‘Diversification in Portfolios of Individual Stocks: 100 Stocks Are Not Enough.’’ Working paper, April 4, 2006. In press, The Financial Review. Donaldson, R. Glen, Mark J. Kamstra, and Lisa A. Kramer. ‘‘Estimating the Ex Ante Equity Premium.’’ Working paper, November 2006. ———. ‘‘Stare Down the Barrel and Center the Crosshairs: Targeting the Ex Ante Equity Premium.’’ Federal Reserve Bank of Atlanta Working paper, January 2003. Doran, David T. ‘‘Forecasting Error of Value Line Weekly Forecasts.’’ Journal of Business Forecasting (Winter 1993–94): 22–26. Dorrell, Darrell D. ‘‘Discount Rate Comparisons.’’ National Litigation Consultants’ Review (July 2002): 8–11. Downs, David H., and Nuray Z. Guner. ‘‘On the Quality of FFO Forecasts.’’ Journal of Real Estate Research 28, no. 3 (2006): 257–274. Downs, Thomas W., and Robert W. Ingram. ‘‘Beta, Size, Risk, and Return.’’ Journal of Financial Research (Fall 2000): 245–260. Durham, Gary. ‘‘Valuing a Seasonal Business to Assess Solvency.’’ National Litigation Consultants’ Review (April 2005): 5–8. Duvall, Richard M. ‘‘Capitalization of Earnings with Temporary Rapid Growth.’’ Business Valuation Review (June 2001): 3–4. ———. ‘‘Mid-year or End-of-year Discounting.’’ Business Valuation Review (December 2000): 208–211. Earles, Melanie J., and Edwin H. Duett. ‘‘Use of the Capital Asset Pricing Model for Valuing Closely Held Companies.’’ Valuation Strategies (July/August 2002): 12–17. Easterday, Kathryn E., Pradyot K. Sen, and Jens A. Stephan. ‘‘The Small Firm/January Effect: Is it Disappearing in US Market Because of Investor Learning?’’ Working paper, June 2007. Easton, Peter. ‘‘PE Ratios, PEG Ratios, and Estimating the Implied Expected Rate of Return on Equity Capital.’’ Accounting Review (January 2004): 73–95. ———. ‘‘Use of Forecasts of Earnings to Estimate and Compare Cost of Capital across Regimes.’’ Journal of Business Finance & Accounting (April/May 2006): 374–394. Easton, Peter, Gary Taylor, Pervin Schroff, and Theodore Sougiannis. ‘‘Using Forecasts of Earnings to Simultaneously Estimate Growth and the Rate of Return on Equity Investment.’’ Journal of Accounting Research (June 2002): 657–676. Eccles, Robert G., Kersten L. Lanes, and Thomas C. Wilson. ‘‘Are You Paying Too Much for That Acquisition?’’ Harvard Business Review (July/August 1999): 136–146. Elfakhani, Said, Larry J. Lockwood, and Tarek S. Zaher. ‘‘Small Firm and Value Effects in the Canadian Market.’’ Journal of Financial Research (Fall 1998): 277–291. Ely, Kirsten M. ‘‘Operating Lease Accounting and the Market’s Assessment of Equity Risk.’’ Journal of Accounting Research (Autumn 1995): 397–415. Equity Valuations, Inc. ‘‘Guide to Valuation of Preferred Stock. Revenue Ruling 83–120.’’ 2000. Available at: www.equityvaluations.com/pubs/revenueruling83–120.html. Erb, Claude, Harvey Campbell, and Viskanta Tadas. ‘‘Country Risk in Global Financial Management.’’ CFA Institute (AIMR) (March 1997). ———.‘‘Expected Returns and Volatility in 135 Countries.’’ Journal of Portfolio Management (Spring 1996): 46–58. ———. ‘‘The Influence of Political, Economic and Financial Risk on Expected Fixed-Income Returns.’’ Journal of Fixed Income (June 1996): 7–31
666
Cost of Capital
———. ‘‘The Risk and Expected Returns of African Equity Investments.’’ In Investment and Risk in Africa, ed. Paul Collier and Cathy Pattillo (New York: Macmillan 2000): 122–145 and Duke Finance Research. Erickson, Merle, and Shiing-wu Wang. ‘‘The Effect of Organizational Form on Acquisition Price.’’ Working paper, May 16, 2002. Estrada, Javier. ‘‘Discount Rates in Emerging Markets: Four Models and an Application.’’ Journal of Applied Corporate Finance (Spring 2007): 72–77. Estrada, Javier. ‘‘Downside Risk in Practice.’’ Journal of Applied Corporate Finance (Winter 2006): 117–125. Estrada, Javier, and Ana Paula Serra. ‘‘Risk and Return in Emerging Markets: Family Matters.’’ EFMA 2004 Basel Meetings Paper, 2004. Estridge, Juliet, and Babara Lougee. ‘‘Measuring Free Cash Flows for Equity Valuation: Pitfalls and Possible Solutions.’’ Journal of Applied Corporate Finance (Spring 2007): 60–71. Evans, Frank C. ‘‘Making Sense of Rates of Return and Multiples.’’ Business Valuation Review (June 1999): 51–57. ———. Practice Development/Business Valuation: Tips for the Valuator.’’ Journal of Accountancy (March 2000): 5–42. Evans, Frank C., and Kelly L. Strimbu. ‘‘Debt and Equity Weightings in WACC.’’ CPA Expert (Fall 1998): 4–5. Fama, Eugene F., and Kenneth R. French. ‘‘The CAPM: Theory and Evidence.’’ Journal of Economic Perspective (January 2004): 25–46. ———. ‘‘Common Risk Factors in the Returns on Stocks and Bonds.’’ University of Chicago Working Paper No. 360, November 1992. ———. ‘‘Dividend Yields and Expected Stock Returns.’’ Journal of Financial Economics (October 1988): 3–25. ———. ‘‘The Cross-Section of Expected Stock Returns.’’ Journal of Finance (June 1992): 427–486. ———. ‘‘The Equity Premium.’’ Journal of Finance (April 2002): 637–659. ———. ‘‘Forecasting Profitability and Earnings.’’ Journal of Business (April 2000): 161–175. ———. ‘‘Industry Cost of Equity.’’ Journal of Financial Economics (July 1997): 153–193. ———. ‘‘Migration.’’ Financial Analysts Journal (May/June 2007): 48–58. ———. ‘‘Taxes, Financing Decisions, and Firm Value.’’ Journal of Finance (June 1998): 819–843. ———. ‘‘Value versus Growth: The International Evidence.’’ Journal of Finance (December 1998): 427–465. Fang, Hsing, and Tsong-Yue Lai. ‘‘Co-kurtosis and Capital Asset Pricing.’’ Financial Review (May 1997): 293–307. Fannon, Nancy, and Heidi Walker. ‘‘Rates of Return: Don’t Ignore Public Market or Transactional Data.’’ Business Valuation Update (September 2007): 1, 4–6. Farber, Andre, Roland Gillet, and Ariane Szafarz. ‘‘A General Formula for the WACC.’’ International Journal of Business (Spring 2006): 211–218. Fauge`re, Christophe, and Julian Van Erlach. ‘‘The Equity Premium: Consistent with GDP Growth and Portfolio Insurance.’’ Financial Review (November 2006): 547–564. Feltham, J., and J. Ohlson. ‘‘Valuation and Clean Surplus Accounting for Operating and Financing Activities.’’ Contemporary Accounting Research 11, no. 2 (Spring 1995): 689–731. Ferguson, Richard. ‘‘The ‘Dirty Dozen’ Mistakes When Using a Valuation Expert.’’ American Journal of Family Law (Summer 2005): 266–275. Fernandez, Pablo. ‘‘APV and WACC with Constant Book Leverage Ratio.’’ IESE Business School Working paper, April 19, 2007. ———. ‘‘Equivalence If Ten Different Methods for Valuing Companies by Cash Flow Discounting.’’ International Journal of Finance Education 1, no.1 (2005): 141–168. ———. ‘‘Equity Premium: Historical, Expected, Required and Implied.’’ Working paper, February 18, 2007. ———. ‘‘Levered and Unlevered Beta.’’ Working paper, April 20, 2006. ———. ‘‘A General Formula for the WACC: A Comment.’’ International Journal of Business 12 No. 3 (2007).
Articles
667
Ferson, Wayne, and Dennis Locke. ‘‘Estimating the Cost of Capital through Time: An Analysis of the Sources of Error.’’ Management Science (April 1998): 485–500. Finnerty, John D. ‘‘Adjusting the Comparable Company Method for Tax Differences when Valuing Privately Held ‘S’ Corporations and LLCs.’’ Journal of Applied Finance (Fall/Winter 2002): 7–22. Finkel, Sidney R. ‘‘Is There an S Corporation Premium?’’ Valuation Strategies (July/August 2001): 14–27. Fiore, Owen, Jay Fishman, and Kevin Hines. ‘‘Discounts for Minority Interest and Lack of Marketability.’’ BV Q&A Newsletter (June 2004). Fischel, Daniel R. ‘‘The Law and Economics of Dividend Policy.’’ Virginia Law Review (May 1981): 699– 726. Fisher, Lawrence, and James H. Lorie. ‘‘Rates of Return on Investments in Common Stocks.’’ Journal of Business (January 1964): 1–21. Flannery, Sean P. ‘‘EMU and the Bond Markets of Western Europe.’’ Credit Analysis Around the World, CFA Institute (AIMR) (June 1998): 10–17. Formica, John. ‘‘Thinking of a Deal? New Accounting, New Strategies.’’ Accounting Policy & Practice Report (October 19, 2007). Fornari, Fabio. ‘‘The Size of the Equity Premium.’’ Working paper, January 2002. Fortuna, Philip S. ‘‘Old and New Perspectives on Equity Risk.’’ Practical Issues in Equity Analysis, CFA Institute (AIMR) (February 2000): 37–45. ———. ‘‘POP Goes the Market—A Historical Guide to Bubbles.’’ CFA Institute (AIMR) San Francisco Conference, March 18, 2004. Frankel, Richard, and Charles M. C. Lee. ‘‘Accounting Valuation, Market Expectation, and Cross-Sectional Stock Returns.’’ Journal of Accounting and Economics (June 1998): 283–319. Franklin, Steven M., and Kimberly M. Alvarado. ‘‘Building a Discount Rate.’’ National Litigation Consultants Review (February 2003): 1–5. Frazier, William H. ‘‘Nonmarketable Investment Company Evaluation.’’ Valuation Strategies (November/ December 2006). ———. ‘‘Quantitative Analysis of the Fair Market Value of an Interest in a Family Limited Partnership.’’ Valuation Strategies (January/February 2005). ———. ‘‘Valuing Minority Interests in Tiered Entities: Its Turtles All the Way Down.’’ ASA 23rd Annual Advanced Business Valuation Conference, October 8, 2004. Freeman, Neal L. ‘‘Cost of Capital Establishes a Benchmark for Evaluation of Investments: Common Equity, Debt, and Preferred Stock All Play Important Roles.’’ Ophthalmology Times (April 2004): 77. ———. ‘‘Economic Value Added Reflects Long-Term Benefits of Investments, Projects.’’ Ophthalmology Times (July 2004). Furfine, Craig H., and Richard J. Rosen. ‘‘Mergers and Risk.’’ Federal Reserve Bank of Chicago Working Paper, September 2006. Gaffen, Gregg S. ‘‘The Willamette Management Associates Failed IPO Study: Does a DLOM Apply to Controlling Ownership Interests?’’ Insights (Autumn 2004): 52–54. Garlappi, Lorenzo, and Hong Yan. ‘‘Financial Distress and the Cross Section of Equity Returns.’’ Working paper, April 2007. Garvey, Gerald T. ‘‘What Is an Acceptable Rate of Return for an Undiversified Investor?’’ Working paper, September 2001. Gebhardt, William, Charles Lee, and Bhaskaran Swaminathan. ‘‘Toward an Implied Cost of Capital.’’ Journal of Accounting Research (June 2001): 135–176. Gendreau, Brian, and Leila Heckman. ‘‘Estimating the Equity Premium across Countries.’’ Salomon Smith Barney, 2002.
668
Cost of Capital
Giaccotto, Carmelo. ‘‘Discounting Mean Reverting Cash Flows with the Capital Asset Pricing Model.’’ The Financial Review (May 2007): 247–265. Gilson, Stuart C., Edith S. Hotchkiss, and Richard S. Ruback. ‘‘Valuation of Bankrupt Firms.’’ Review of Financial Studies (Spring 2000): 43–74. Givoly, D., and Lakonishok, J. ‘‘The Quality of Analysts’ Forecasts of Earnings.’’ Financial Analysts Journal (September/October 1984): 40–47. Glaser, Jeffrey S. ‘‘The Capital Asset Pricing Model: Risk, Valuation, Judicial Interpretation, and Market Bias.’’ Business Law (February 1995): 687. Gode, Dan, and Partha Mohanram. ‘‘Inferring the Cost of Capital Using the Ohlson-Juettner Model.’’ Review of Accounting Studies (December 2003): 399–431. Godfrey, Stephen, and Ramon Espinoza. ‘‘A Practical Approach to Calculating Costs of Equity for Investments in Emerging Markets.’’ Journal of Applied Corporate Finance (Fall 1996): 80–89. Goetzmann, William N., and Roger G. Ibbotson. ‘‘History and the Equity Risk Premium.’’ Yale ICF Working paper No. 05–04, April 6, 2005. Goetzmann, William N., Roger Ibbotson, and Liang Peng. ‘‘A New Historical Database for NYSE 1915 to 1925: Performance and Predictability.’’ Journal of Financial Markets 4, no. 1 (2001): 1–32. Goetzmann, William N., and Philippe Jorion. ‘‘A Century of Global Stock Markets.’’ Journal of Finance (June 1999): 953–980. Goetzmann, William N., and Alok Kumar. ‘‘Why Do Individual Investors Hold Under-diversified Portfolios?’’ Working paper, November 2004. Goldenberg, David H., and Ashok J. Robin. ‘‘The Arbitrage Pricing Theory and Cost-of-Capital Estimation: The Case of Electric Utilities.’’ Journal of Financial Research (Fall 1991): 181–196. Gompers, Paul A., Joy L. Ishii, and Andrew Metrick. ‘‘Corporate Governance and Equity Prices.’’ Quarterly Journal of Economics (February 2003): 107–155. Gooch, Lawrence B. ‘‘Capital Charges and the Valuation of Intangible Assets.’’ Business Valuation Review (March 1992): 5–21. Good, Walter R. ‘‘Yes, Virginia, There Is a Risk Premium, But . . . ’’ Financial Analysts Journal (January/February 1994): 11–12. Goodwin, Thomas H., and Leola B. Ross. ‘‘Has Europe Outgrown Its Countries?’’ Old Dominion University & European Financial Management Association, February 2001. Gopinath, D. ‘‘Taking the Road Less Traveled.’’ Institutional Investor (March 1988): 173–174. Gordon, M. J., and Gould, L. I. ‘‘The Cost of Equity Capital: A Reconsideration.’’ Journal of Finance (June 1978): 849–861. Goyal, Amit, and Pedro Santa-Clara. ‘‘Idiosyncratic Risk Matters!’’ Journal of Finance (June 2003): 975– 1008. Goyal, Amit, and Ivo Welch. ‘‘A Comprehensive Look at the Empirical Performance of Equity Premium Prediction.’’ Working paper, January 11, 2006. Grabowski, Roger. ‘‘Equity Risk Premium: What Is the Current Evidence?’’ Business Valuation Update (November 2005): 1–7. ———. ‘‘Equity Risk Premiums.’’ 2003 ASA International Appraisal Conference. Tampa, FL, July 14–16, 2003. Available at: www.BVLibrary.com. ———. ‘‘S Corp Valuations in the Post-Gross World—Updated.’’ Business Valuation Review (September 2004): 139–166. ———. ‘‘Standard & Poor’s CVC Risk Premium report.’’ 2003 Cost of Capital Workshop, University of Chicago, June 20, 2003. Available at: www.BVLibrary.com.
Articles
669
Grabowski, Roger, and Michael W. Barad. ‘‘Equity Risk Premium: What Valuation Analysts Need to Know about Recent Research.’’ AICPA’s 2004 National Business Conference. Orlando, FL, November 2004. Available at: www.BVLibrary.com. Grabowski, Roger, and David King. ‘‘New Evidence on Equity Returns and Company Risk.’’ Business Valuation Review (September 1999): 112–130. ———. ‘‘New Evidence on Equity Returns and Company Risk: A Revision.’’ Business Valuation Review (March 2000): 32. ———. ‘‘New Evidence on Size Effects and Rates of Return.’’ Business Valuation Review (September 1996): 103– 115. ———. ‘‘Size Effects and Equity Returns: An Update.’’ Business Valuation Review (March 1997): 22–26. Graham, John R. ‘‘Debt and the Marginal Tax Rate.’’ Journal of Finance Economics (May 1996): 41–73. ———. ‘‘Proxies for the Corporate Marginal Tax Rate.’’ Journal of Financial Economics (October 1996): 187–221. Graham, John R., and Campbell R. Harvey. ‘‘The Equity Risk Premium in January 2007: Evidence from the Global CFO Outlook Survey.’’ Working paper, January 25, 2007. ———. ‘‘Expectations of Equity Risk Premia, Volatility and Asymmetry from a Corporate Finance Perspective.’’ Working paper, July 2003. Updated quarterly by Duke CFO Outlook Survey (www.cfosurvey.org). ———. ‘‘The Theory and Practice of Corporate Finance.’’ Journal of Financial Economics (May 2001): 187–243. Graham, John R., and Michael Lemmon. ‘‘Measuring Corporate Tax Rate and Tax Incentives: A New Approach.’’ Journal of Applied Corporate Finance (Spring 1998): 54–65. Graham, John R., Michael Lemon, and James Schallheim. ‘‘Debt, Leases, Taxes and the Endogeneity of Corporate Tax Status.’’ Journal of Finance (February 1998): 131–161. Graham, John R., and Lillian F. Mills. ‘‘Using Tax Return Data to Simulate Corporate Marginal Tax Rates.’’ Working paper, January 24, 2007. Greene, Martin. ‘‘Systemic Methodology Calculates Size Premiums.’’ Business Valuation Update (April 2006): 1–8. Greer, Willis R. ‘‘The Growth Rate Term in the Capitalization Model.’’ Business Valuation Review (June 1996): 72–79. Griffin, John M. ‘‘Are the Fama and French Factors Global or Country-Specific?’’ Review of Financial Studies (Summer 2002): 783–803. Gutner, Todi. ‘‘Who’s Afraid of Real Estate?’’ Business Week (December 30, 1996). Hall, Lance, Z. Christopher Mercer, Robert Oliver, and Shannon P. Pratt. ‘‘Applying the Discounted Cash Flow without Accounting for Dilution.’’ BV Q&A Newsletter (October 2004). Available at: www.BVLibrary.com. Hall, Lance, Z. Christopher Mercer, and Shannon P. Pratt. ‘‘Using the Term Marketability and Liquidity Interchangeably.’’ BV Q&A Newsletter (October 2004). Available at: www.BVLibrary.com. Halsey, Robert F. ‘‘Stationary Components of Earnings and Stock Prices.’’ AFA 2001 New Orleans, October 2000. Hanley, Frank J., and A. Gerald Harris. ‘‘Does Diversification Increase the Cost of Equity Capital?’’ Public Utilities Fortnightly (July 15, 1991): 26–30. Hamada, Robert S. ‘‘The Effect of the Firm’s Capital Structure on the Systematic Risk of Common Stocks.’’ Journal of Finance (May 1972): 435–452. Hardouvelis, Gikas, Dimitrious Malliartopulos, and Richard Priestly. ‘‘The Impact of Globalization on the Equity Cost of Capital.’’ Working paper, May 9, 2004. Hargis, Kent, and Jianping Mei. ‘‘Is Country Diversification Better than Industry Diversification?’’ European Financial Management 12, no. 3 (June 2006): 319–340. Harms, Travis W. ‘‘Another Nail in the Coffin of Benchmark Analysis.’’ E-Law Business Valuation Perspective (December 2002): 1–3.
670
Cost of Capital
Harris, Robert S., and Felicia Marston. ‘‘Estimating Shareholder Risk Premia Using Analysts’ Growth Forecasts.’’ Financial Management (Summer 1992): 63–70. Harris, Robert S., and John Pringle. ‘‘A Note on the Implications of Miller’s Argument for Capital Budgeting.’’ Journal of Financial Research (Spring 1983). Harris, Robert S., Felicia C. Marston, Dev R. Mishra, and Thomas J. O’Brien. ‘‘Ex Ante Cost of Equity Estimates of S&P 500 Firms: The Choice Between Global and Domestic CAPM,’’ Financial Management (Autumn 2003): 51–66. Harvey, Campbell R. ‘‘Country Risk Components, the Cost of Capital, and Returns in Emerging Markets.’’ Fuqua School of Business NBER Working paper, November 2004. ———. ‘‘The International Cost of Capital and Risk Calculator.’’ Fuqua School of Business, Duke University, Durham, NC, July 25, 2001. ———. ‘‘Predictable Risk and Return in Emerging Markets.’’ Review of Financial Studies (Fall 1995): 773– 816. ———. ‘‘Risk Analysis and Project Evaluation.’’ Duke Center for International Development at the Sanford Institute, May 27–28, 2002. Harvey, Campbell R., and Geert Bekaert. ‘‘Emerging Markets Finance.’’ Journal of Empirical Finance (December 2003): 3–56. Hatch, John. ‘‘Discount for Lack of Marketability: Do IPO Studies Tell Us Anything?’’ Business Valuation Review (March 2004): 10–24. ———. ‘‘Restricted Stock Studies and Discounts for Lack of Marketability.’’ Business Valuation Review (June 2004): 74–77. Hawkins, George B. ‘‘Active versus Passive Appreciation—The Same Old Inflation Argument—But Is It Valid?’’ Business Valuation Alert (April 2004): 9–10. ———. ‘‘Critically Assessing a Business Valuation: Is the Capitalization Rate Used Reasonable?’’ Fair Value (Spring 1996): 1–6. ———. ‘‘A Gross Result in the Gross Case Calls into Question Circumstances in Which Tax Affecting Is Valid.’’ Shannon Pratt’s Business Valuation Update (January 2002): 5–7. ———. ‘‘Why Time Travel in Business Valuation Is Wrong.’’ Business Valuation Review (September 2002): 120– 127. Hilscher, Jens. ‘‘Is The Corporate Bond Market Forward Looking?’’ European Central Bank Working Paper Series No 800, August 2007. Hitchner, James R. ‘‘About When to Use the Mean, Median, or Both.’’ CPA Expert (Winter 2005): 10. Hitchner, James, and Katherine Morris. ‘‘Cost of Capital Controversies: It’s Time to Look behind the Curtain (Parts 1 and 2 of 3).’’ Shannon Pratt’s Business Valuation Update (October 2004): 19–21, and (January 2005): 1–5. Hitchner, James, and Paul Vogt. ‘‘Cost of Capital Controversies: It’s Time to Look behind the Curtain (Part 3 of 3).’’ Shannon Pratt’s Business Valuation Update (May 2005): 1, 3–5. Hong Teoh, Siew, Yong Yang, and Yinglei Zhang. ‘‘R-square: Noise or Firm-specific Information?’’ Working paper, October 2, 2006. Honnold, Keith L. ‘‘The Link between Discount Rates and Capitalization Rates: Revisited.’’ Appraisal Journal (April 1990): 190–195. Horowitz, Joel L., Tim Loughran, and N. E. Savin. ‘‘A Spline Analysis of the Small Firm Effect: Does Size Really Matter?’’ Working paper, March 1997. Hughson, Eric, Michael Stutzer, and Chris Yung. ‘‘The Misuse of Expected Returns.’’ Financial Analysts Journal (November/December 2006): 88–96. Hur, Jungshik, and Vivek Sharma, ‘‘Stock Market Returns and Size Premium,’’ Working paper, March 2007.
Articles
671
Hyde, Paul R. ‘‘Forecasting Net Cash Flow.’’ 2004 Institute of Business Appraisers Conference. Las Vegas, NV, June 2004. Available at: www.BVLibrary.com. Ibbotson Associates (now Morningstar). ‘‘Cost of Capital Workshop.’’ Chicago: Ibbotson Associates, 1999. Ibbotson, Roger G. ‘‘Equity Risk Premium: Where We Stand Today.’’ Proceedings of the Equity Risk Premium Conference, University of Chicago, June 6, 1996. ———. ‘‘Supply-Side Equity Risk Premium.’’ 2003 Cost of Capital Workshop, University of Chicago, June 20, 2003. Available at: www.BVLibrary.com. Ibbotson, Roger G., and Peng Chen. ‘‘Long-Run Stock Returns: Participating in the Real Economy.’’ Financial Analysts Journal (January/February 2003): 88–98. ———. ‘‘The Supply of Stock Market Returns.’’ Working paper, March 2002. Ibbotson, Roger G., Paul D. Kaplan, and James D. Peterson. ‘‘Estimates of Small Stock Betas Are Much Too Low.’’ Journal of Portfolio Management (Summer 1997): 104–111. Ickert, Donald W. ‘‘Unsystematic Risk & Size Effects on Valuation.’’ ASA 2001 International Appraisal Conference. Pittsburgh, PA, July 23–25, 2001. Available at: www.BVLibrary.com. ———. ‘‘Unsystematic Risk & Size Effects on Valuations.’’ American Society of Appraisers, October 2001. Available at: www.BVLibrary.com. Imhoff, Eugene A. Jr., Robert C. Lipe, and David W. Wright. ‘‘Operating Leases: Income Effects of Constructive Capitalization.’’ Accounting Horizons (June 1997): 12–32. Indro, Daniel C., and Wayne Y. Lee. ‘‘Biases in Arithmetic and Geometric Averages as Estimates of Long-Run Expected Returns and Risk Premia.’’ Financial Management (Winter 1997): 81–90. Irvine, Paul, and Jeffrey Pontiff. ‘‘Idiosyncratic Return, Cash Flows, and Product Market Competition.’’ Working paper, April 2005. Jackson, Marcus. ‘‘The Gordon Growth Model and the Income Approach to Value.’’ Appraisal Journal (January 1994): 124–128. Jacob, John, Steve K. Rock, and David P. Weber. ‘‘Do Analysts at Independent Research Firms Make Better Earnings Forecasts?’’ Working paper, July 2003. Jacquier, Eric, Alex Kane, and Alan J. Marcus. ‘‘Optimal Forecasts of Long-Term Returns and Asset Allocations: Geometric, Arithmetic, or Other Means?’’ Working paper, October 31, 2002. Jagannathan, Ravi, and Zhenyu Wang. ‘‘The Conditional CAPM and the Cross-Section of Expected Returns.’’ Journal of Finance (August 1996): 3–53. Jegadeesh, Narasimhan, and Sheridan Titman. ‘‘Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.’’ Journal of Finance (March 1993): 65–91. Jensen, Michael C., and Eugene F. Fama ‘‘Separation of Ownership and Control.’’ In Foundations of Organizational Strategy, ed. Michael C. Jensen (Boston: Harvard University Press, 1998); and Journal of Law and Economics (June 1983): 301–350. Jensen, Michael C., and William H. Meckling. ‘‘Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure.’’ In A Theory of the Firm: Governance, Residual Claims and Organizational Forms, ed. Michael C. Jensen (Boston: Harvard University Press, 2000); and Journal of Financial Economics (October 1976): 305–360. Jiang, George J., and Yisong S. Tian. ‘‘Volatility Forecasting and the Expensing of Stock Options.’’ Working paper, November 21, 2005. Jones, Charles P., and Jack W. Wilson. ‘‘An Analysis of the S&P 500 Index and Cowles’s Extensions: Price Indexes and Stock Returns, 1870–1999.’’ Journal of Business (July 2002): 505–533. ———. ‘‘A Comparison of Annual Stock Market Returns: 1871–1925 with 1926–1985.’’ Journal of Business 60, no. 2 (1987): 239–258. ———. ‘‘Using the Supply Side Approach to Understand and Estimate Stock Returns.’’ Working paper, June 6, 2006.
672
Cost of Capital
Jong, Abe de, Rezaul Kabir, and Thuy Thu Nguyen. ‘‘Capital Structure Around the World: The Roles of Firm and Country-Specific Determinants.’’ ERIM Report Series Research in Management, September 2007. Julius, J. Michael. ‘‘Converting Distributions from S Corporations and Partnerships to a C Corporation Dividend Equivalent Basis.’’ Business Valuation Review (June 1997): 65–67. ———. ‘‘Market Returns in Rolling Multi-Year Holding Periods: An Alternative Interpretation to Ibbotson Data.’’ Business Valuation Review (June 1996): 57–63. Kairys, Joseph P. Jr. ‘‘Predicting Sign Changes in the Equity Risk Premium Using Commercial Paper Rates.’’ Journal of Portfolio Management (Fall 1993): 41–51. Kaltman, Todd A. ‘‘Capitalization Using a Mid-Year Convention.’’ Business Valuation Review (December 1995): 178–182. Kaplan, Paul D. ‘‘Why the Expected Rate of Return Is an Arithmetic Mean.’’ Business Valuation Review (September 1995): 126–129. Kaplan, Paul D., and James D. Peterson. ‘‘Full-Information Industry Betas.’’ Financial Management (Summer 1998): 85–93. Kaplan, Steven J., and Richard S. Ruback. ‘‘The Valuation of Cash Flow Forecasts: An Empirical Analysis.’’ Journal of Finance (September 1995): 1059–1093. Keck, Tom, Eric Levengood, and Al Longfield. ‘‘Using Discounted Cash Flow Analysis in an International Setting: A Survey of Issues in Modeling the Cost of Capital.’’ Journal of Applied Corporate Finance (Fall 1998): 82– 99. Kempf, Alexander, and Marliese Uhrig-Homburg. ‘‘Liquidity and Its Impact on Bond Prices.’’ Schmalenbach Business Review (January 2000): 26–44. Kenny, Thomas J. ‘‘Closely Held Corporation Valuation: Determining a Proper Discount Rate.’’ Business Valuation Review (March 1992): 22–30. Kholdy, Shady, and Ahmad Sohrabian. ‘‘Internal Finance and Corporate Investment.’’ Financial Review (May 2001): 97–114. Kihm, Steven G. ‘‘The Superiority of Spot Yields in Estimating Cost of Capital.’’ Public Utilities Fortnightly (February 1, 1996): 42–45. Kim, Chang-Jin, James C. Morley, and Charles R. Nelson. ‘‘The Structural Break in the Equity Premium.’’ Journal of Business & Economic Statistics (April 2005): 181–191. Kincheloe, Stephen C. ‘‘The Weighted Average Cost of Capital—The Correct Discount Rate.’’ Appraisal Journal (January 1990): 88–95. King, David W. ‘‘Do Data Biases Cause the Small Stock Premiums?’’ Business Valuation Review (June 2003): 56–61. ———. ‘‘The Equity Risk Premium for Cost of Capital Studies: Alternatives to Ibbotson.’’ Business Valuation Review (September 1994): 123–129. ———. ‘‘Recent Evidence on Discount Rates.’’ Proceedings of the AICPA 1995 National Business Valuation Conference, New Orleans, LA (December 1995): 12–13. Available at: BVLibrary.com. King, Tao-Hsien Dolly, and Kenneth Khang. ‘‘On the Importance of Systematic Risk Factors in Explaining the Cross-Section of Corporate Bond Yield Spreads.’’ Journal of Banking & Finance (December 2005): 3141–3158. Kirby, Mike, Warner Griswold, and Jon Fosheim. ‘‘Pricing REIT Stocks.’’ REIT University: Core Curriculum, April 4, 2007. Kisgen, Darren. ‘‘The Influence of Credit Ratings on Corporate Capital Structure Decisions.’’ Journal of Applied Corporate Finance (Summer 2007): 65–73. Klassen, Kenneth J., and Devan Mescall. ‘‘Valuation of Income Trusts: An Exploration of Clienteles and Implicit Taxes.’’ Working paper, April 2006.
Articles
673
Koedijk, Kees G., Clemens J. M. Kool, Peter C. Schotman, and Mathijs A. van Dijk. ‘‘The Cost of Capital in International Financial Markets: Local or Global?’’ Journal of International Money and Finance 21 (2002): 905– 929. Korteweg, Arthur. ‘‘The Costs of Financial Distress across Industries.’’ Working paper, January 15, 2007. Kothari S. P., Jay Shanken, and Richard G. Sloan. ‘‘Another Look at the Cross-Section of Expected Returns.’’Journal of Finance (March 1995): 185–224. Kritzman, Mark. ‘‘What Practitioners Need to Know about Future Value.’’ Financial Analysts Journal (May/June 1994): 12–15. Krueger, Mark K., and Charles M. Linke. ‘‘A Spanning Approach for Estimating Divisional Cost of Capital.’’ Financial Management (Spring 1994): 64–70. Kwan, Simon H. ‘‘Firm-specific Information and the Correlation between Individual Stocks and Bonds.’’ Journal of Financial Economics (January 1996): 63–80. Lally, Martin. ‘‘The Accuracy of CAPM Proxies for Estimating a Firm’s Cost of Equity.’’ Accounting & Finance (May 1995): 63–72. Lamdin, Douglas J. ‘‘New Estimates of the Equity Risk Premiums and Why Business Economists Need Them.’’ University of Maryland Working paper, January 2002. Lang, Mark H. ‘‘Employee Stock Options and Equity Valuation.’’ Research Foundation of CFA Monograph, July 2, 2004. Lanstein, Ronald, Kenneth Reid, and Barr Rosenberg. ‘‘Persuasive Evidence of Market Inefficiency.’’ Journal of Portfolio Management 11, no. 3 (Spring 1985): 9–17. LaPorta, Rafael. ‘‘Expectations and the Cross-Section of Stock Returns.’’ Journal of Finance (December 1996): 1715–1742. Larson, David. ‘‘Africa and the Middle East.’’ Credit Analysis Around the World, CFA Institute (AIMR) (June 1998): 26–37. Lavely, Joe, and Frank Bacon. ‘‘Risk and Rate of Return for Electric Utilities.’’ Public Utilities Fortnightly (September 1, 1993): 18–20. Lee, Ming-Long, Ming-Te Lee and Kevin C. H. Chiang. ‘‘Real Estate Risk Exposure of Equity Real Estate Investment Trusts.’’ Working paper, July 6, 2006. Leibowitz, Martin L. ‘‘Introduction’’ Equity Risk Premium Forum, AIMR, November 8, 2001. ———. ‘‘Spread-Driven Dividend Discount Models.’’ Financial Analysts Journal (November/December 2000): 64–77. Lerch, Mary Ann. ‘‘Are We Capitalizing the Right Measure of Cash Flow?’’ Business Valuation Review (September 2001): 32–34. ———. ‘‘Pretax/Aftertax Conversion Formula for Capitalization Rates and Cash Flow Discount Rates.’’ Business Valuation Review (March 1990): 18–22. Lessard, Donald R. ‘‘Incorporating Country Risk in the Valuation of Offshore Projects.’’ Journal of Applied Corporate Finance (Fall 1996): 52–63. Leuhrman, Timothy A. ‘‘Using APV: A Better Tool for Valuing Operations.’’ Harvard Business Review (May/June 1997): 145. Levy, Haim. ‘‘Equilibrium in an Imperfect Market: A Constraint on the Number of Securities in a Portfolio.’’ American Economic Review (September 1978): 643–658. Levy, Moshe, and Haim Levy. ‘‘The Danger of Assuming Homogeneous Expectations.’’ Financial Analysts Journal (May/June 1996): 65–70. L’Her, Jean-Francois, Tarek Masmoudi, and Jean-Marc Suret. ‘‘Evidence to Support the Four-Factor Pricing Model from the Canadian Stock Market.’’ Working paper, July 2003.
674
Cost of Capital
Li, Kevin, and Geoff Meeks. ‘‘The Impairment of Purchased Goodwill: Effects on Market Value.’’ Working paper, November 28, 2006. Li, Qing, Maria Vassalou, and Yuhang Xing. ‘‘An Investment-Growth Asset Pricing Model.’’ AFA 2002 Atlanta Meetings, March 7, 2001. Li, Xiafei, Chris Brooks, and Joelle Miffre. ‘‘The Value Premium and Time-Varying Unsystematic Risk.’’ Working paper, April 2007. Liew, Jimmy, and Maria Vassalou. ‘‘Can Book-to-Market, Size and Momentum Be Risk Factors that Predict Economic Growth?’’ Journal of Financial Economics (August 2000): 221–245. Lintner, John. ‘‘The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.’’ Review of Economics and Statistics (February 1965): 13–37. Lippitt, Jeffrey W., and Nicholas J. Mastriacchio. ‘‘Developing Capitalization Rates for Valuing a Business.’’ CPA Journal (November 1995): 24–28. Litt, Jonathan. ‘‘Gaming FFO.’’ Property (Fall 2001). Liu, Jing, Doron Nissim, and Jacob Thomas. ‘‘Equity Valuation Using Multiples.’’ Journal of Accounting Research (March 2002): 135–172. ———. ‘‘Is Cash Flow King in Valuations?’’ Financial Analysts Journal 63, no. 2 (March/April 2007): 56–68. Ljungqvist, Alexander, and Matthew P. Richardson. ‘‘The Cash Flow, Return and Risk Characteristics of Private Equity.’’ New York University, Finance Working Paper No. 03–001, January 9, 2003. Ljungqvist, Alexander, Matthew Richardson, and Daniel Wolfenzon. ‘‘The Investment Behavior of Buyout Funds: Theory and Evidence.’’ ECGI Working paper, June 2007. Lo, Andrew W., and A. Craig McKinlay. ‘‘Stock Market Prices Do Not Follow Random Walks.’’ Review of Financial Studies 1, no. 1 (Spring 1988): 41–46. Loncarski, Igor, Jenke ter Horst, and Chris Veld. ‘‘Why Do Companies Issue Convertible Bonds? A Review of Theory and Empirical Evidence.’’ In Advances in Corporate Finance and Asset Pricing, ed. L. Renneboog (Amsterdam: Elsevier, 2006): 311–339. Long, Michael S., and Jing Feng Zhang. ‘‘Growth Options, Unwritten Call Discounts and Valuing Small Firms.’’ EFA 2004 Maastricht Meetings Paper No. 4057, March 2004. Longhofer, Ronald S. ‘‘The Residual Income Method of Business Valuation.’’ Business Valuation Review (June 2005): 65–70. Longstaff, Francis A. ‘‘How Much Can Marketability Effect Security Values?’’ Journal of Finance (December 1995): 1767–1774. Lvov, Dmitri, Ali Bora Yigitbasioglu, and Naoufel El Bachir. ‘‘Pricing Convertible Bonds by Simulation.’’ Working paper, December 2004. MacKay, Peter, and Gordon M. Phillips. ‘‘Is There an Optimal Industry Financial Structure?’’ NBER Working Paper 9032, June 2002. ———. ‘‘How Does Industry Affect Firm Financial Structure?’’ The Review of Financial Studies 18 Issue 4 (2005): 1433–1465. Madden, Bartley J. ‘‘The CFROI Valuation Model.’’ Journal of Investing (Spring 1998): 31–44. Malkiel, Burton G., and Yexiao Xu. ‘‘Idiosyncratic Risk and Security Returns.’’ Working paper, July 2000. ———. ‘‘Investigating the Behavior of Idiosyncratic Volatility.’’ Journal of Business (October 2003): 613–644. ———. ‘‘Risk and Return Revisited.’’ Journal of Portfolio Management (Spring 1997): 9–14. Mandron, Alix. ‘‘DCF Valuation Should Be Improved: Challenges to Conventional Wisdom.’’ Business Valuation Update (January 2001): 1–4. Mangiero, Susan M. ‘‘Model Risk and Valuation.’’ Valuation Strategies (March/April 2003): 34–39. Marchitelli, Richard, and James R. MacCrate. ‘‘REITs and the Private Market: Are Comparisons Meaningful?’’ Real Estate Issues (August 1996): 7–10.
Articles
675
Mard, Michael J., and James S. Rigby. ‘‘New Research to Estimate Cost of Capital.’’ CPA Expert (Fall 1995): 9– 12. Margulis, Marc S., Jeremy Krasner, and Mark J. Melancon. ‘‘Size-Adjusting Beta.’’ Valuation Strategies (March/ April 2005): 4–9, 47. Maris, Brian A., and Fayez A. Elayan. ‘‘Capital Structure and the Cost of Capital for Untaxed Firms: The Case of REITs.’’ Journal of the American Real Estate & Urban Economics Association (Spring 1990): 22–39. Mariscal, Jorge O., and E. Dutra. ‘‘The Valuation of Latin American Stocks: Part III.’’ Goldman Sachs, New York (November 1995). Mariscal, Jorge O., and Rafaelina M. Lee. ‘‘The Valuation of Latin American Stocks: Part II.’’ Goldman Sachs, New York (May 1994). ———. ‘‘The Valuation of Mexican Stocks: An Extension of the Capital Asset Pricing Model.’’ Goldman Sachs, New York (June 1993). Markowitz, Harry M. ‘‘Portfolio Selection.’’ Journal of Finance (March 1952): 77–91. Martin, Harold G. Jr. ‘‘Cost of Capital.’’ Joint presentation made with Ronald L. Seigneur at the AICPA National Business Valuation Conference. Las Vegas, NV, December 4, 2001. Martin, R. D., and Simin, T. T. ‘‘Outlier-Resistant Estimates of Beta.’’ Financial Analysts Journal (September/ October 2003): 56–69. Mastriacchio, Nicholas J., and Jeffrey W. Lippitt. ‘‘A Comparison of the Earnings Capitalization and the Excess Earnings Models in the Valuation of Closely Held Businesses.’’ Journal of Small Business Management (January 1996): 1–12. Massari, M., F. Rocaglio, and L. Zanetti. ‘‘On the Equivalence between the APV and the WACC Approach in a Growing Leveraged Firm.’’ European Financial Management (in press, January 2007). Matthews, Gilbert E. ‘‘Cap X ¼ Depreciation Is Unrealistic Assumption for Most Terminal Values.’’ Business Valuation Update (March 2002): 1–3. ———. ‘‘When Averaging Multiples, Apply the Harmonic Mean.’’ Business Valuation Update (June 2006): 1–4. ———. ‘‘Errors and Omissions in DCF Calculations: A Critique of Delaware’s Dr. Pepper Appraisal.’’ Business Value Update (October 2007): 9. Mattson, Michael J., Donald S. Shannon, and David E. Upton. ‘‘Empirical Research Concludes S Corporation Values Same as C Corporations, Part 1–2.’’ Shannon Pratt’s Business Valuation Update (November 2002): 1–5 (December 2002): 1–4. Mayfield, Scott E. ‘‘Estimating the Market Risk Premium.’’ Working paper, October 1999. McConaughy, Daniel L. ‘‘Negative Takeover Premia and Stock Price Levels in Internet Stocks.’’ Valuation Strategies (March/April 2002): 20–29. ———. ‘‘Is the Cost of Capital Different for Family Firms?’’ Family Business Review (December 1999): 353–359. McGrattan, Ellen R. and Edward C. Prescott. ‘‘Is the Market Overvalued?’’ Federal Reserve Bank of Minneapolis Quarterly Review (Fall 2000): 20–24. ———. ‘‘Taxes, Regulations and Asset Prices.’’ Federal Reserve Bank of Minneapolis Working paper, July 2001. McKinsey & Company. ‘‘How Companies Spend Their Money: A McKinsey Global Survey.’’ McKinsey Quarterly (June 2, 2007). McNulty, James M., Tony D. Yeh, William S. Schulze, and Michael H. Lubatkin. ‘‘What’s Your Real Cost of Capital?’’ Harvard Business Review (October 2002): 114. Mello-e-Souza, Carlos A. ‘‘Bankruptcy Happens: A Study of the Mechanics of Distress-driven CAPM Anomalies.’’ Working paper, January 25, 2002. ———. ‘‘Limited Liability, the CAPM and Speculative Grade Firms: A Monte Carlo Experiment.’’ Working paper, August 18, 2004.
676
Cost of Capital
Mercer, Christopher Z. ‘‘The Adjusted Capital Asset Pricing Model for Developing Capitalization Rates: An Extension of Previous ‘Build-Up’ Methodologies Based upon the Capital Asset Pricing Model.’’ Business Valuation Review (December 1989): 147–156. Merton, Robert C. ‘‘An Intertemporal Capital Asset Pricing Model.’’ Econometrica (September 1973): 867– 887. ———. ‘‘A Simple Model of Capital Market Equilibrium with Incomplete Information.’’ Journal of Finance (July 1987): 483–510. Meyer, James E., Patrick Fitzgerald, and Mostafa Moini, ‘‘Loss of Business Profits, Risk, and the Appropriate Discount Rate.’’ Journal of Legal Economics (Winter 1994): 27–42. Miles, James A., and John R. Ezzell. ‘‘The Weighted Average Cost of Capital, Perfect Capital Markets and Project Life: A Clarification.’’ Journal of Financial and Quantitative Analysis (September 1980): 719–730. Miller, Warren D. ‘‘Assessing Unsystematic Risk.’’ CPA Expert (Summer 1999): 1–5. ———. ‘‘Assessing Unsystematic Risk: Part II—The Macroenvironment.’’ CPA Expert (Winter 2000): 1–5. ———. ‘‘An Overview of the Analysis and Interpretation of Investment-Specific Risk.’’ Business Valuation Review (June 2003): 62–65. Mishra, Dev R., and Thomas J. O’Brien. ‘‘A Comparison of Cost of Equity Estimates of Local and Global CAPMs.’’ The Financial Review 36 (2001): 27–48. ———. ‘‘Risk and Ex Ante Cost of Equity Estimates of Emerging Market Firms.’’ Emerging Market Review 6 (2005): 107–120. Mohanty, Pitabas. ‘‘Solving the Circularity Problem in Estimating the Cost of Capital: A Practical Approach.’’ The Icfai Journal of Applied Finance (2007): 29–38. Morris, James. ‘‘Reconciling the Equity and Invested Capital Methods of Valuation When the Capital Structure Is Changing.’’ Business Valuation Review (March 2004): 36–46. Moskowitz, Tobias J., and Annette Vissing-Jorgensen. ‘‘The Private Equity Premium Puzzle.’’ Working paper, November 2000. Moyer, Charles R., and Ajay Patel. ‘‘The Equity Risk Premium: A Critical Look at Alternative Ex Ante Estimates.’’ Working paper, February 2000. Proceedings of the Ibbotson Equity Risk Premium Conference, University of Chicago, June 6, 1996. Abstracted in Shannon Pratt’s Business Valuation Update (August 1996): 1–2. ‘‘New Studies Quantifying Size Premiums Offer Strong Cost of Capital Support.’’ Shannon Pratt’s Business Valuation Update (August 1997): 1, 3. Murphy, Austin. ‘‘An Analysis of Preferred Stock.’’ Financial Engineering News (January/February 2004). Myers, Randy. ‘‘GM Remeasures the Bar in Latin America.’’ CFO Magazine (May 1998). National Association of Real Estate Investment Trusts, Inc. ‘‘Funds from Operations.’’ NAREIT White Paper (April 2002): 2. Neely, Charles Jr., and Nancy S. Rendleman. ‘‘Toward a Better Understanding of Value-in-Use in Property Tax Appraisals.’’ Journal of Property Tax Management (August 1998). Nekrasov, Alexander, and Pervin K. Shroff. ‘‘Fundamentals-Based Risk Measurement in Valuation.’’ Working paper, January 2007. Nussbaum, Ross. ‘‘Cash Flow Matters—– DCF Analysis Suggests REITs Are Fairly Valued . . . For Now.’’ New York University, The REIT Center, February 21, 2006. O’Brien, Thomas J. ‘‘The Global CAPM and a Firm’s Cost of Capital in Different Currencies.’’ Journal of Applied Corporate Finance (Fall 1999): 73–79. ———. ‘‘Risk Management and the Cost of Capital for Operating Assets.’’ Journal of Applied Corporate Finance (Fall 2006): 105–109. ———. ‘‘Foreign Exchange and Cross-Border Valuation.’’ Journal of Applied Corporate Finance (Spring/Summer 2004): 147–154.
Articles
677
Ohlson, James A., and Beate E. Juettner-Nauroth. ‘‘Expected EPS and EPS Growth as Determinants of Value.’’ Working paper, 2003. Olsen, Robert, and George Troughton. ‘‘Are Risk Premium Anomalies Caused by Ambiguity?’’ Financial Analysts Journal (March/April 2000): 24–31. Pacific Security Capital. ‘‘The Impact of Rising Interest Rates on Commercial Real Estate.’’ Oregon: Pacific Security Capital, IRETO Report (May/June 2005). Paolo, Stanley B. S. ‘‘The Weighted Average Cost of Capital: A Caveat.’’ Engineering Economist (Winter 1992): 178–183. Paschall, Michael A. ‘‘The 35% ‘Standard’ Marketability Discount: R.I.P.’’ Fair ValueTM (Winter/Spring 2005): 1, 12–17. Paschall, Michael A., and George B. Hawkins. ‘‘Are Smaller Companies More Risky?’’ Fair Value (Fall 1999): 1, 5–12. Pastor, Lubos, and Robert F. Stambaugh. ‘‘Cost of Equity Capital and Model Mispricing.’’ Journal of Finance (February 1999): 67–114. ———. ‘‘The Equity Premium and Structural Breaks.’’ Journal of Finance (August 2001): 1207–1239. Patterson, Cleveland S. ‘‘The Cost of Equity Capital of a Non-Traded Unique Entity: A Canadian Study.’’ Canadian Journal of Administrative Sciences (June 1993): 115–121. Penman, Stephen H. ‘‘Handling Valuation Models.’’ Journal of Applied Corporate Finance (Spring 2006): 48–55. Pettit, Justin, Mack Ferguson, and Robert Gluck. ‘‘A Method for Estimating Global Costs: The Case of Bestfoods.’’ Journal of Applied Corporate Finance (Fall 1999): 80–90. Phillips, John. ‘‘S-Corp or C-Corp? M&A Deal Prices Look Alike.’’ Shannon Pratt’s Business Valuation Update (March 2004): 1–6. Phylaktis, Kate, and Lichuan Xia. ‘‘Sources of Firms’ Industry and Country Effects in Emerging Markets.’’ Journal of International Money and Finance (April 2006): 459–475. Pinkowitz, Lee and Rohan Williamson. ‘‘What Is the Market Value of a Dollar of Corporate Cash?’’ Journal of Applied Corporate Finance (Summer 2007): 74–81. Piotroski, Joseph D. ‘‘Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers.’’ Journal of Accounting Research 38 (supplement 2000): 1–41. Plummer, James L. ‘‘QED Report on Venture Capital Financial Analysis.’’ QED Research, Inc., Palo Alto, CA (1987). Post, Thierry, and Pim VanVliet. ‘‘Conditional Downside Risk and the CAPM.’’ Working paper, June 2004. Poterba, James M., and Lawrence H. Summers. ‘‘Mean Reversion in Stock Prices: Evidence and Implications.’’ Journal of Financial Economics (October 1988): 27–59. Pratt, Shannon P. ‘‘Alternative Equity Risk Premium Measures Unstable; Lack Robust Predictive Power.’’ Shannon Pratt’s Business Valuation Update (August 1996): 1–2. ———. ‘‘Building Better Betas Is Ibbotson’s Answer to Beta Controversy.’’ Shannon Pratt’s Business Valuation Update (August 1997): 1–2. ———. ‘‘Calculating Fair Market Value of Corporation Shares.’’ BV Q&A Newsletter (March 2005). ———. ‘‘Discount Rates Based on CAPM Don’t Always Lead to Minority Value.’’ Shannon Pratt’s Business Valuation Update (March 2001): 1–3. ———. ‘‘Evidence Suggests Equity Risk Premium Lower Than Conventional Wisdom Thinks.’’ Shannon Pratt’s Business Valuation Update (July 1996): 1–5. ———. ‘‘New Measures of Risk That Really Work.’’ Shannon Pratt’s Business Valuation Update (December 1999): 1–4. ———. ‘‘One Key Distinction between Market and Income Approaches Is Use of Net Cash Flow.’’ Business Valuation Update (June 2003): 1–2.
678
Cost of Capital
———. ‘‘Practitioners Disagree Strongly on Excess Earnings Methodology.’’ Shannon Pratt’s Business Valuation Update (April 1997): 1–3. Qin, Yan, and Sitikantha Pattanaik, ‘‘Measuring Cost of Capital—Credit Rating vs Global CAPM.’’ Economic and Political Weekly (September 2000): 3325–3334. Raabe, William A., and Gerald E. Whittenburg. ‘‘Is the Capital Asset Pricing Model Appropriate in Tax Litigation?’’ Valuation Strategies (January/February 1998): 10–15, 36–37. Ramnath, Sundaresh, Steve Rock, and Philip Shane. ‘‘Value Line and I/B/E/S Earnings Forecast.’’ International Journal of Forecasting (January 2005): 185–198. Reto, James, and Gary Trugman. ‘‘Avoiding Valuation Traps in Court: Lessons Learned the Hard Way.’’ Business Valuation Update (May 2006): 1–3. Reynolds, Kevin B. ‘‘Reconciling the Single Period Capitalization Method with the Discounted Future Earnings Method.’’ Business Appraisal Practice (Spring 2000): 16–27. Rigby, Jim, and Michael J. Mattson. ‘‘Capitalization and Discount Rates: Mathematically Related, but Conceptually Different.’’ CPA Expert (Fall 1996): 1–3. Robak, Espen. ‘‘Discounts for Illiquid Shares and Warrants: The LiquiStatTM Database of Transactions on the Restricted Securities Trading Network.’’ Pluris Valuation Advisors White Paper, September 19, 2006. ———. ‘‘Introducing a Completely New Way of Determining DLOM.’’ Business Valuation Update (January 2007): 24–26. Robb, Russell, and Tom West. ‘‘Non-financial Factors in Valuations.’’ M&A Today (May 2003): 6–7, 11. Roll, Richard, and Stephen A. Ross. ‘‘An Empirical Investigation of Arbitrage Pricing Theory.’’ Journal of Finance (December 1980): 1073–1103. ———. ‘‘On the Cross-sectional Relation between Expected Returns and Betas.’’ Journal of Finance (March 1994): 101–121. Ross, Franz. ‘‘‘‘Just One Thing’’: The Most Reliable Variable for Use in the Market Approach.’’ Business Valuation Update (September 2004): 1, 3–7. Ross, Stephen A. ‘‘The Arbitrage Theory of Capital Asset Pricing.’’ Journal of Economic Theory (December 1976): 241–260. ———. ‘‘Return, Risk, and Arbitrage.’’ In Risk and Return in Finance, ed. Irwin I. Friend and I. Bisksler (Cambridge, MA: Ballinger, 1977): 189–218. Ruback, Richard S. ‘‘Capital Cash Flows: A Simple Approach to Valuing Risky Cash Flows.’’ Financial Management (Summer 2002): 85–103. Sack, Brian P. ‘‘Using Treasury STRIPS to Measure the Yield Curve.’’ FEDS Working Paper No. 2000–42, October 2000. Samuel, Marc. ‘‘The Applicability of a Market Approach Valuation Analysis That Employs Only a Single Comparable: Heck v. Commissioner,’’ Tax Lawyer (Winter 2003): 475–483. Sarin, Atulya, and David J. Denis. ‘‘Taxes and the Relative Valuation of S Corporations and C Corporations.’’ Working paper, March 2002. Sarin, Atulya, Sanjiv Ranjan Das, and Murali Jagannathan. ‘‘The Private Equity Discount: An Empirical Examination of the Exit of Venture Backed Companies.’’ Working paper, January 22, 2002. ———. ‘‘The Private Equity Returns: An Empirical Examination of the Exit of Venture Backed Companies.’’ Journal of Investment Management (First Quarter 2003): 152–177. Sarin, Atulya, John Koeplin, and Alan C. Shapiro. ‘‘The Private Company Discount.’’ Journal of Applied Corporate Finance (Winter 2000): 94–101. Sarkar, Sudipto. ‘‘Expansion Financing and Capital Structure.’’ Working paper, January 2007. Savage, Sam L. ‘‘The Flaw of Averages.’’ Harvard Business Review (November 2002): 20–21. Schilt, James, ‘‘CAPM and Business Valuation.’’ Business Valuation Review (June 2004): 60–62.
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Schmid, Markus M., and Ingo Walter. ‘‘Do Financial Conglomerates Create or Destroy Economic Value?’’ Working paper, August 28, 2007. Scholtens, Bert. ‘‘On the Comovement of Bond Yield Spreads and Country Risk Ratings.’’ Journal of Fixed Income (March 1999): 99–103. Schramm, Ronald M., and Henry M. Wang. ‘‘Measuring the Cost of Capital in an International CAPM Framework.’’ Journal of Applied Corporate Finance (Fall 1999): 63–72. Schwert, G. William. ‘‘Indexes of Common Stock Returns from 1802 to 1987.’’ Journal of Business (July 1990): 399–425. Schwinn, Carl R. ‘‘The Predictable and Misleading Consequences When Using Periodic Returns in Traditional Tests of the Capital Asset Pricing Model.’’ Working paper, December 2006. Scott, M. F. G. ‘‘The Cost of Equity Capital and the Risk Premium on Equities.’’ Applied Financial Economics (March 1992): 21–32. Sharpe, Steven A. ‘‘How Does the Market Interpret Analysts’ Long-term Growth Forecasts?’’ Federal Reserve Board, Finance and Economics Discussion Series Paper 2002–7, September 2002. Sharpe, William F. ‘‘Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.’’ Journal of Finance (September 1964): 425–442. ———. ‘‘Capital Asset Prices with and without Negative Holdings.’’ Nobel Lecture: The Nobel Foundation, Royal Swedish Academy of Sciences, December 1990. ———. ‘‘Factor Models, CAPMs, and the ABT.’’ Journal of Portfolio Management (Fall 1984): 21–25. Shumway, Tyler. ‘‘The Delisting Bias in CRSP Data.’’ Journal of Finance (March 1997): 327–340. Siegel, Jeremy J. ‘‘Historical Results.’’ Equity Risk Premium Forum, CFA Institute (AIMR) (November 8, 2001): 30–34. ———. ‘‘Perspectives on the Equity Risk Premium.’’ Financial Analysts Journal (November/December 2005): 61–73. Siegel, Jeremy, and Richard Thaler. ‘‘The Equity Risk Premium Puzzle.’’ Journal of Economic Perspectives 11, no. 1 (Winter 1997): 191–200. Silber, William L. ‘‘Discounts on Restricted Stock: The Impact of Illiquidity on Stock Prices.’’ Financial Analysts Journal (July/August 1991): 64. Sirower, Mark L., and Sumit Sahni. ‘‘Avoiding the ‘Synergy Trap’: Practical Guidance on M&A Decisions for CEOs and Boards.’’ Journal of Applied Corporate Finance (Summer 2006): 83–95. Soliman, Mark T. ‘‘Using Industry-Adjusted DuPont Analysis to Predict Future Profitability.’’ Working paper, February 2004. Soroosh, Jalal, and Jack T. Ciesielski. ‘‘Accounting for Special Purpose Entities Revised: FASB Interpretation 46(R).’’ CPA Journal Online (April 5, 2007). Stanton, Thomas C. ‘‘The Anatomy of Beta: Getting Down to Basics.’’ Business Appraisal Practice (Fall 1999): 34– 38. Available at: www.BVLibrary.com. Starr, Samuel P., John G. Schmatz, Daniel G. Baucum, and Robert J. Crnkovich. ‘‘Limited Liability Companies.’’ Tax Management (1998). Statman, Meir. ‘‘How Much Diversification Is Enough?’’ Working paper, October 2002. Stattman, Dennis W. ‘‘Book Values and Stock Returns.’’ Chicago MBA: A Journal of Selected Papers 4 (1980): 25–45. Stegink, Rudolf, Marc Schauten, and Gijs de Graaff. ‘‘The Discount Rate for Discounted Cash Flow Valuations of Intangible Assets.’’ Working paper, March 2007. ‘‘Stock Recipients Liable for Fraudulent Transfer Underpayment.’’ Shannon Pratt’s Business Valuation Update (January 1999): 10. Stulz, Rene´ M. ‘‘Globalization, Corporate Finance, and the Cost of Capital.’’ Journal of Applied Corporate Finance (Fall 1999): 8–25.
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———. ‘‘Globalization of Capital Markets and the Cost of Capital: The Case of Nestle´.’’ Journal of Applied Corporate Finance (Fall 1995): 30–39. ———. ‘‘The Limits of Financial Globalization.’’ Journal of Finance, American Finance Association (August 2005): 1595–1638. Suvas, Arto. ‘‘Cost of Equity Capital Redefined.’’ Quarterly Journal of Business & Economics (Spring 1992): 53– 71. Sweeney, Richard J., Arthur D. Warga, and Drew Winters. ‘‘The Market Value of Debt, Market versus Book Value of Debt, and Returns to Assets.’’ Financial Management (Spring 1997): 5–21. Sziklay, Barry S. ‘‘Discounts & Premiums Core.’’ AICPA National Business Valuation Conference, November 2004. Available at: www.BVLibrary.com. Tabak, David. ‘‘A CAPM-Based Approach to Calculating Illiquidity Discounts.’’ NERA Economic Consulting. Working paper, November 11, 2002. Tan, Zhiguo, and Yiping Cai. ‘‘Risk Equilibrium Binomial Model for Convertible Bonds Pricing.’’ South West University of Finance and Economics Working paper, January 28, 2007. Tarbell, Jeffrey S. ‘‘The Small Company Risk Premium: Does It Really Exist?’’ ASA 18th Annual Advanced Business Valuation Conference. New Orleans, LA, October 29, 1999. Available at: www.BVLibrary.com. Taylor, Alex P. ‘‘Conditional Factor Models and Return Predictability.’’ AFA 2006 Boston Meetings Paper, February 2005. Tham, Joseph, and Ignacio Velez-Pareja. ‘‘Top 9 (Unnecessary and Avoidable) Mistakes in Cash Flow Valuation.’’ Working paper, January 29, 2004. Thompson, Howard E., and Wing K. Wong. ‘‘On the Unavoidability of ‘Unscientific’ Judgment in Estimating the Cost of Capital.’’ Managerial & Decision Economics (February 1991): 27–42. Thompson, Samuel C. Jr. ‘‘Demystifying the Use of Beta in the Determination of the Cost of Capital and an Illustration of Its Use in Lazard’s Valuation of Conrail.’’ Journal of Corporation Law (Winter 2000): 241–306. Treharne, Chris, Nancy J. Fannon, and Jim Hitchner. ‘‘Valuation of Pass-Through Entities.’’ ASA 23rd Annual Advanced Business Valuation Conference, October 8, 2004. Trout, Robert R. ‘‘Mid-year Discounting without Bias.’’ Business Valuation Review (December 2001): 39–41. ———. ‘‘Minimum Marketability Discounts.’’ Business Valuation Review (September 2003): 124–126. Trugman, Gary. ‘‘Guideline Public Company Method – Control or Minority Value?’’ Business Valuation Update (December 2003): 1–5. Tsang, Desmond, and Steve Fortin. ‘‘Analyst Forecast Accuracy on GAAP vs. Non-GAAP Financial Measures: Case of Real Estate Investment Trust.’’ Working paper, November 2005. Ukren, Perry. ‘‘Estimating Discount Rates– An Alternative to CAPM.’’ Valuation Strategies (March/April 2005). Van Binsbergen, Jules, John Graham, and Jie Yang. ‘‘The Cost of Debt.’’ Working paper, September 2007. Vander Linden, Eric. ‘‘Cost of Capital Derived from Ibbotson Data Equals Minority Value?’’ Business Valuation Review (December 1998): 123–127. VanderWeide, J., and W. T. Carleton, ‘‘Investor Growth Expectations: Analysts vs. History.’’ Journal of Portfolio Management (Spring 1988): 78–82. Van Dijk, Mathijs. ‘‘Is Size Dead? A Review of the Size Effect in Equity Returns.’’ Working paper, February 2007. Vasan, Ashwin, ‘‘Eastern Europe.’’ Credit Analysis Around the World, CFA Institute (AIMR) (June 1998): 18–25. Vasicek, Oldrich A. ‘‘A Note on Using Cross-Sectional Information in Bayesian Estimation of Security Betas.’’ Journal of Finance (1973): 1233–1239. Vassalou, Maria, Jing Chen, and Lihong Zhou. ‘‘The Relation Between Liquidity Risk and Default Risk in Equity Returns.’’ EFA 2006 Zurich Meetings, July 16, 2006. Vassalou, Maria, and Yuhang Xing. ‘‘Default Risk in Equity Returns.’’ Journal of Finance (in press).
Articles
681
Velez,-Pareja, Ignacio, Rauf Ibragimov, and Joseph Tham. ‘‘Constant Leverage and Constant Cost of Capital: A Common Knowledge Half-Truth.’’ Working paper, June 29, 2007. Vulpiani, Marco. ‘‘Cost of Capital and Valuation of Merging and Acquisition Operations.’’ Business Valuation Review (January 2006): 157–165. Vuolteenaho, Tuomo. ‘‘What Drives Firm Level Stock Returns.’’ Journal of Finance (February 2002): 233–264. Watanabe, Akiko, and Masahiro Watanabe. ‘‘Time-Varying Liquidity Risk and the Cross Section of Stock Returns.’’ 8th Annual Texas Finance Festival, January 9, 2007. Weidig, Tom, Andreas Kemmerer, and Bjorn Born. ‘‘The Risk Profile of Private Equity Fund-of-Funds.’’ Working paper, March 2004. Welch, Ivo. ‘‘The Equity Premium Consensus Forecast Revisited.’’ Yale University, Cowles Foundation Discussion Paper No. 1325, September 2001. Available at: http://papers.ssrn.com/abstract=285169. Wincott, Richard D. ‘‘A Primer on Comparable Sale Confirmation.’’ Appraisal Journal (July 2002): 274–282. Wise, Richard. ‘‘Closely Held Preferred Stock. A Review of the Common Value Drivers.’’ Business Valuation Review (September 2003): 149–154. Wright, Stephen H. ‘‘Measures of Stock Market Value and Returns for the US Nonfinancial Corporate Sector, 1900– 2000.’’ Birkbeck College, Economics, Working paper, February 1, 2002. Yamaguchi, Katsunari. ‘‘Estimating the Equity Risk Premium from Downside Probability.’’ Journal of Portfolio Management (Summer 1994): 17–27. Yang, Yunguang Mike. ‘‘Corporate Governance, Agency Conflicts, and Equity Returns along Business Cycles.’’ Working paper, October 20, 2005. Young, David S. ‘‘Some Reflections on Accounting Adjustments and Economic Value Added.’’ Journal of Financial Statement Analysis (Winter 1999): 7–19. Zabolotnyuk, Yuriy, Robert Jones, and Chris Veld. ‘‘An Empirical Comparison of Convertible Bond Valuation Models.’’ Working paper, June 18, 2007. Zellweger, Thomas. ‘‘Time Horizon, Costs of Equity Capital, and Generic Investment Strategies of Firms.’’ Family Business Review 20 No.1 (March 2007): 1–15. Zyla, Mark. ‘‘Valuing Companies with Changing Debt Levels: Is the APV Method Better than the DCF?’’ Business Valuation Update (June 2005): 1–5.
Appendix II
Data Resources Morningstar Cost of Capital Data Duff & Phelps, LLC, Risk Premium Report Betas Earnings Forecasts and Related Data First Call and I/B/E/S Databases (Thomson Financial) Integra 5-Year Industry Data Reports First Research Industry Profiles Reuters Estimates (formerly Multex Estimates) Value Line Publishing, Inc. Zacks Investment Research, Inc. Arbitrage Pricing Model Data BIRR Portfolio Analysis, Inc. Publicly Traded Stock Data 10k Wizard EDGAR Online Inc. Electronic Data Gathering, Analysis, and Retrieval (EDGAR) Service Mergent, Inc. (formerly Moody’s) Standard & Poor’s, a Division of McGraw-Hill Larger Company Merger and Acquisition Transaction Sources Financial Post Crosbie: Mergers & Acquisitions in Canada FactSet Flashwire Mergerstat Custom Research Service Mergerstat M& A Decade Library Mergerstat Online Transaction Roster Mergerstat Review Mergerstat/BVR Control Premium StudyTM Public StatsTM Private Company Sale Transaction Data BIZCOMPS1 BIZCOMPS1 Special Food Service Edition DoneDeals1 IBA Market Database Pratt’s StatsTM Partnership Transaction Data Minority Interest Discount Database Package Lack of Marketability Emory Pre-IPO Discount Studies, the Discounts for Lack of Marketability The FMV Restricted Stock StudyTM Valuation Advisors’ Lack of Marketability Discount StudyTM International Risk BondsOnline Group, Inc The PRS Group, Inc Periodicals Business Valuation Library 683
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Business Valuation Review Business Valuation UpdateTM Financial Valuation and Litigation Expert
MORNINGSTAR COST OF CAPITAL DATA Morningstar, Product sales and support (312) 384-4000, Global Headquarters 225 West Wacker Drive, Chicago, IL 60606; (312) 696-6000. www.morningstar.com. Morningstar acquired Ibbotson Associates in 2006. Stocks, Bonds, Bills and Inflation1 Classic Edition Yearbook is published annually in March. Available in print. Provides historical data on U.S. asset classes. Gives a comprehensive, historical view of the performance of capital markets dating back to 1926. Contains total returns and index values for large- and small-company stocks, long-term corporate bonds, long- and intermediate-term government bonds, Treasury bills, and inflation. Optional reports supplement the yearbook on a monthly, quarterly, or semiannual basis. Stocks, Bonds, Bills and Inflation1 Valuation Edition Yearbook is published annually in March. Available in print. Complete with real-world examples and useful graphs to illustrate the analyses to help readers make decisions in cost-of-capital estimates. Contains an overview and comparison of the build-up method, Capital Asset Pricing Model, Fama-French 3-factor model, and discounted cash flow approach. Quarterly subscribers receive the yearbook plus three quarterly reports featuring updated industry risk premia for use in the build-up method. Cost of Capital Yearbook is published annually in June plus three quarterly updates in print. Contains valuable information and data on over 300 different industries based on Standard Industrial Classification (SIC) code. Four separate company size designations based on equity capitalization are used. Detailed statistics for sales, profitability, capitalization, beta, multiples, ratios, equity returns, capital structure, and five separate measures of cost of equity and weighted average cost of capital. Beta Book is published semiannually in February and July. Available in print. Includes statistics on more than 5,000 companies that are essential for calculating cost of equity with the Capital Asset Pricing Model and Fama-French 3-factor model. Traditional 60-month levered and unlevered beta calculations using CAPM regressions are presented. Cost of Capital Resources (formerly Cost of Capital Center) is available online at www.morningstar.com. Users may download analysis of more than 300 industries and 5,000 companies based in the United States, plus 170 other countries. The International Cost of Capital Report is updated annually; it estimates the cost of equity for more than 170 countries from the perspective of U.S.-based investors with investments in other countries around the world. The International Cost of Capital Perspectives Report estimates the cost of equity for more than 170 countries from the perspectives of investors based in Australia, Canada, France, Germany, Japan, and the United Kingdom. The International Equity Risk Premia Report provides historical equity risk premia for 16 countries, including data back to 1970 for most of the countries covered. The Canadian Risk Premia over Time Report features historical long-horizon equity risk premia beginning in 1936 (Canadian-dollar-denominated) or 1939 (U.S.-dollar-denominated). The United Kingdom Risk Premia over Time Report includes historical long-horizon equity risk premia beginning in 1919 (British-pound-denominated) or 1920 (U.S.-dollar-denominated). The Risk Premia over Time Report contains long-, intermediate-, and short-term equity risk premia and mid-, low-, and micro-cap size premia. The Duff & Phelps, LLC Risk Premium Report estimates risk premia for companies broken into 25 different size groups correlated with different risk groups. Individual Industry Reports help in performing discounted cash flow analysis. The
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reports by SIC code feature industry betas, multiples, cost of equity estimates, weighted average cost of capital, and more.
DUFF & PHELPS, LLC, RISK PREMIUM REPORT Duff & Phelps, LLC, Risk Premium Report can be a useful tool for estimating the cost of equity capital. One data set allows the user to estimate the cost of equity using a build-up method. Another data set provides corrections to the textbook CAPM estimate of cost of equity capital for the size effect. Available through Morningstar (www.morningstar.com) and Business Valuation Resources (www.BVResources.com). For more information contact Roger Grabowski, Managing Director, Duff & Phelps, LLC, at (312) 697-4720.
BETAS Bloomberg, (212) 318-2000, fax: (917) 369-5000. www.bloomberg.com. Merrill Lynch, Merrill Lynch Research, Global Equity Research and Global Strategy and Economics, 4 World Financial Center, 250 Vesey Street, New York, NY 10080; (212) 449-1000. www.ml.com. Morningstar (formerly Ibbotson Associates), Product sales and support (312) 384-4000, Global Headquarters 225 West Wacker Drive, Chicago, IL 60606; (312) 696-6000. www.morningstar.com. Beta Book: individual company betas; Cost of Capital Yearbook: industry betas. MSCI Barra, 2100 Milvia Street, Berkeley, CA 94704-1113; (510) 548–5442, fax: 510.548.4374. Client Support, U.S.: (888) 588-4567. www.barra.com. Standard & Poor’s, 55 Water Street, New York, NY 10041; (800) 523-4534. www.standardandpoors.com, www.compustat.com. Standard & Poor’s Compustat and Standard & Poor’s Stock Reports. Value Line Publishing, Inc., 220 East 42nd Street, 6th Floor, New York, NY 10017; (800) 6343583; www.valueline.com.
EARNINGS FORECASTS AND RELATED DATA The information offered by providers listed here goes well beyond just earnings forecasts, because providers compile almost intimidating vast amounts of other data and opinions about stocks, industries, and markets that can be helpful in estimating cost of capital. (The use of earnings forecasts in estimating cost of capital by the discounted cash flow method is the subject of Chapter 12.) First Call and I/B/E/S Databases (Thomson Financial) is an industry standard for real-time broker-sourced research, earnings estimates, equity and fixed-income ownership information, insider-trading information, and corporate news releases. The Thomson First Call content set features: Thomson First Call Notes, Thomson First Call Research Direct, I/B/E/S Earnings Estimates, Thomson StreetEvents, and Thomson Worldscope Fundamentals. It can be accessed via Thomson ONE and IRChannel. I/B/E/S Aggregated Forecasts provides objective, aggregated quantitative information to make profitable asset allocation and global valuation decisions consistent with your investment style. Use the three databases to access forecasted data at the aggregate level. I/B/E/S Global Aggregates allows the user to access aggregated information for 56 countries, dating back to 1987. I/B/E/S Sector & Industry Aggregates provides access to sectorand industry-level aggregates by country and by region. I/B/E/S S&P 5001 Aggregates provides sector- and industry-level aggregates for the U.S. market from as far back as 1985. The product
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begins by aggregating analysts’ expectations for all the stocks in the index and then building forecasted earnings, price/earnings ratios, growth rates, and revisions data for the index. Available from Thomson Financial at 195 Broadway, New York, NY 10007; (646) 822-2000; www.thomson.com/solutions/financial. Integra 5-Year Industry Data Reports, through the use of 33 different data sources, has compiled financial performance data on over 4.5 million privately held businesses. These reports provide industry financial benchmarks of companies in over 900 industries and 13 sales size ranges. Integra Information, the leader in providing business valuation and analysis data, offers a number of products. Available from Integra Information, a Division of MicroBilt Corporation, 1640 Airport Road Suite 115, Kennesaw, GA 30144; (800) 780-2660, www.integrainfo.com. Also available from Business Valuation Resources, LLC, 1000 SW Broadway Suite 1200, Portland, OR 97205; (888) BUSVALU [287-8258], fax: (503) 291-7955; www.BVResources.com. First Research Industry Profiles cover over 200 industries and are updated every 90 days. They provide detailed information by SIC code and include critical issues, quarterly industry updates, an industry overview, credit and business risk issues, business trends, and industry forecasts. Available from First Research, 4321 Lassiter at North Hills Avenue, Suite 200, Raleigh, NC 27609; (919) 7889387, toll free: (866) 788-9389, fax: (919) 788–9397. Also available from Business Valuation Resources, LLC, 1000 SW Broadway Suite 1200, Portland, OR 97205; (888) BUS-VALU [287-8258], fax: (503) 291-7955; www.BVResources.com. Reuters Estimates (formerly Multex Estimates) is a global provider of quality real-time forecast information. Reuters collects forecast data from over 600 brokers around the world. Consensus and detailed estimates and company-reported actuals are provided for over 18,000 active companies and 10,000 inactive companies in more than 70 countries. Comprehensive annual and interim data is available for over 25 financial measures including revenue; profit; earnings before interest, taxes, depreciation, and amortization; cash flow; and three flavors of earnings per share. Available from Reuters, 1-800-REUTERS, (800) 738-8377; www.reuters.com. Value Line Publishing, Inc., employs a staff of more than 70 independent professional security analysts and statisticians. The Value Line Investment Survey is a comprehensive source of information and advice on approximately 1,700 stocks, more than 90 industries, the stock market, and the economy. Every week, the Value Line Ranking System screens millions of data items and, using a proprietary series of calculations, ranks each of the approximately 1,700 stocks for probable performance relative to each other during the next 6 to 12 months. This organization has several other print services, including The Value Line Mutual Fund Survey, The Value Line No-Load Fund Advisor, The Value Line Special Situations Service, The Value Line Options Survey, and The Value Line Convertibles Survey. Value Line also has an array of electronic publications, starting with Value Line Investment analyzer. The software includes over 350 search fields on each stock, more than 60 charting and graphing variables for comparative research, and 10 years of historical financial data for scrutinizing performance, risk, and yield. In addition, there are several other electronic products. There is a Value Line DataFile with fundamental data on more than 8,000 companies. It has annual data since 1955, quarterly since 1963, and full 10-Q data since 1985. It includes balance sheet and income data, risk measures, rates of return, and analytic ratios. Value Line is at 220 East 42nd Street, 6th Floor, New York, NY 10017; customer service: (800) 634-3583, fax: (201) 939-9079; www .valueline.com. Zacks Investment Research, Inc., offers many products including the Zacks Rank and Zacks Equity Research, which combines the best of quantitative and qualitative analysis. Zacks material is also distributed electronically through several vendors. Zacks is at 111 N. Canal Street, Suite 1101, Chicago, IL 60606; (800) 767-3771; (312) 630-9880; fax: (312) 630-9898; www.zacks.com.
Larger Company Merger and Acquisition Transaction Sources
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ARBITRAGE PRICING MODEL DATA Only one firm still offers data to implement the arbitrage pricing model (APT) cost of capital estimation. BIRR Portfolio Analysis, Inc., has a software system called BIRR Risks and Returns Analyzer1. BIRR is an acronym for Burmeister (Edwin), Ibbotson (Roger), Roll (Richard), and Ross (Stephen). It provides APT multiregression factor inputs for companies and industries for five macroeconomic risk factors: confidence risk, time horizon risk, inflation risk, business cycle risk, and market timing risk. (Each of these factors is described in Exhibit 15.1 in the chapter on alternative cost of equity models.) BIRR is at 2200 West Main Street, Suite 210, Durham, NC 27705; (919) 687-7053. www.birr.com.
PUBLICLY TRADED STOCK DATA 10k Wizard is an SEC EDGAR search and retrieval service for company, industry, and financial or accounting research. It provides the user the ability to search through the myriad of information available to the public via the Security and Exchange Commission’s EDGAR (Electronic Data Gathering, Analysis and Retrieval) system. EDGAR Online Inc. provides interactive business and financial data on global companies to financial, corporate, and advisory professionals. The company makes its information and a variety of analytical tools available via online subscriptions and licensing agreements. The company provides a broad spectrum of data including SEC filings, fundamental data, institutional holdings, insider trades, initial public offerings/SPO registrations, and access to global annual reports and conference call transcripts. Available from the EDGAR Online New York sales office, 122 East 42nd Street, 24th Floor, New York, NY 10168; (888) 870-2316 or (212) 457-8200, fax: (212) 457-8222; www.edgar-online.com. Electronic Data Gathering, Analysis, and Retrieval (EDGAR) Service provides access to Securities and Exchange Commission filings for more than 15,000 companies through the Securities and Exchange Commission at www.sec.gov/edgar.shtml. There is no charge for access. Mergent, Inc. (formerly Moody’s) provides a wide variety of publications on publicly traded companies, including Mergent Industrial Manual, Mergent Bank & Financial Manual, Mergent OTC Industrial Manual, Mergent OTC Unlisted Manual, Mergent Public Utilities Manual, Mergent Transportation Manual, Mergent U.S. Company Archives Manual, Mergent International Company Archives Manual, and Mergent Industry Review. These publications are available from 525077 Center Drive, Suite 150, Charlotte, NC 28217; (800) 342-5647; (704) 559-7601; fax: (704) 559-6945; www.mergent.com. Standard & Poor’s, a Division of McGraw-Hill, provides a wide variety of publications, both print and electronic, on publicly traded companies, including Capital IQ, Compustat, Standard & Poor’s Industry Survey, and Standard & Poor’s Stock Reports. These publications are available from Standard & Poor’s, 55 Water Street, New York, NY 10041; (800) 523-4534; www.standardandpoors .com, www.compustat.com.
LARGER COMPANY MERGER AND ACQUISITION TRANSACTION SOURCES Financial Post Crosbie: Mergers & Acquisitions in Canada is a database of record for the Canadian mergers and acquisitions (M&A) market. CanWest Interactive Inc. acquired this database in April 2005 from Crosbie. To subscribe contact CanWest Interactive Inc., (416) 442-2121, Toll free:
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(800) 661-7678. Crosbie continues to produce a quarterly report on Canadian M&A activity based on data compiled from the database. To subscribe contact Crosbie, 150 King Street West, 15th Floor, PO Box 95, Toronto, ON, M5H 1J9; (416) 362-7726; fax: (416) 362-3447. www.crosbieco.com. FactSet Flashwire is available monthly and weekly. It contains analyses and graphics that cover the world of mergers and acquisitions (M&A), giving readers an understanding of the latest trends. Each issue of the Flashwire Monthly analyzes the M&A world and contains aggregate statistics from the FactSet Mergerstat database. Both publications are published electronically and delivered in PDF format via e-mail. Available from FactSet Mergerstat LLC, 2150 Colorado Avenue, Suite 150, Santa Monica, CA 90404; (310) 315-3100; fax: (310) 829-4855. www.mergerstat.com. Mergerstat Custom Research Service provides access to Mergerstat’s global mergers and acquisitions (M&A) data in custom-tailored reports. Custom reports address occasional information needs and limited budgets providing an easy and cost-effective way to get specific, premium M&A data on an as-needed basis. Available from FactSet Mergerstat, LLC. For a free quote call (800) 455-8871 or (310) 315-3100. www.mergerstat.com. Mergerstat M&A Decade Library is available on CD-ROM and provides 10 editions of the annual Mergerstat Review, spanning 1990 to 2000. Each edition contains in-depth statistical, industry, geographic, and historical analysis of mergers and acquisitions activity plus multiyear trend analysis. Available from FactSet Mergerstat LLC, 2150 Colorado Avenue, Suite 150, Santa Monica, CA 90404; (310) 315-3100; fax: (310) 829-4855. www.mergerstat.com. Mergerstat Online Transaction Roster provides unlimited access to comparable transaction data (where available) for each transaction tracked by FactSet Mergerstat. Includes seller and buyer Standard Industrial Classification codes, location, description, announced date, closed date, base price, price/earnings ratio, payment method, and an insightful synopsis of the transaction. Available online through an easy-to-use interface with quick and flexible custom search capability by seller industry, broken down into 49 categories. Available from FactSet Mergerstat LLC, 2950 31st Street, Suite 130, Santa Monica, CA 90405; (310) 315-3100; fax: (310) 8294855. www.mergerstat.com. Mergerstat Review, published annually in April, with optional monthly updates, tracks mergers and acquisitions involving U.S. companies, including privately held, publicly traded, and foreign companies. It also analyzes unit divestitures, management buyouts, and certain asset sales. Includes industry analysis by size, premium, and transaction multiples. It also provides trend analysis by seller, type, deal size, and industry as well as offering 25 years of summary merger and acquisition statistics, including average premium and price/earnings ratio. Available from FactSet Mergerstat LLC, 2950 31st Street, Suite 130, Santa Monica, CA 90405; (310) 315-3100; fax: (310) 829-4855. www.mergerstat.com. Mergerstat/BVR Control Premium StudyTM is a Web-based tool used to quantify minority discounts and control premiums used in the business valuation, business appraisal, venture capital, and merger and acquisition (M&A) professions. Subscribers are granted access to all of the details in the database, including the control premium, five valuation multiples, and the available information to calculate the ROE (Net Income/[BV per share number of shares outstanding]). Approximately 58% of the Mergerstat1/BVR Control Premium StudyTM represents U.S.-based companies, with the remainder being international companies. Subscribers gain access to eight-plus years of valuable back data (1998–present). The database has been enhanced with the transaction purpose code, classifying each transaction into a horizontal, vertical, conglomerate, or financial transaction. As of July 2007, the Mergerstat1/BVR Control Premium StudyTM contained 5,590 total transactions; with over 770 deals in business services, over 690 deals on depository institutions, and 195 deals in the communications industry. Of the deals in the database, 52% have net sales less than $100 million; the remainder have net sales greater than $100 million. Available from Business Valuation Resources,
Private Company Sale Transaction Data
689
LLC, 1000 SW Broadway, Suite 1200, Portland, OR 97205; (888) BUS-VALU [287-8258]; fax: (503) 291-7955. www.BVResources.com. Public StatsTM compiles and reports information on 63 data points, highlighting the financial and transactional details of the sales of publicly held companies. As of February 2007, Public StatsTM had compiled details on approximately 2,010 public company business sales from 1995 to present, ranging in deal price from under $1 million to $114.070 billion. The industries represented in Public StatsTM are no less diverse, as evidenced by the roughly 380 unique Standard Industrial Classification (SIC) codes and 440 unique North American Industry Classification System (NAICS) codes. Additionally, Public StatsTM has approximately 80 SIC and 70 NAICS codes with five or more transactions reported. Available from Business Valuation Resources, LLC, 1000 SW Broadway, Suite 1200, Portland, OR 97205; (888) BUS-VALU [287-8258]; fax: (503) 2917955. www.BVResources.com.
PRIVATE COMPANY SALE TRANSACTION DATA Several databases cover private company transactions. Jack Sanders is the author of BIZCOMPS1 and Managing Director of Spectrum Corporate Resources, LLC, PO Box 97757, Las Vegas, NV 89193; (702) 454-0072. www.bizcomps.com. BIZCOMPS1 provides deals that are sorted by industry and contain revenue and discretionary earnings multiples. It is published in four editions: Western (over 2,950 transactions), Central (over 1,500 transactions), Eastern (over 3,060 transactions), and National Industrial (over 1,250 larger transactions). Data for each sale includes Standard Industrial Classification code, type of business, ask price, sale price, annual sales, seller’s discretionary cash flow, percent down, terms, inventory, fixtures and equipment, rent percent of sales, general location, ratio of sale price to gross sales, and sale price to seller’s discretionary cash flow. A variety of summaries and averages are presented for various subgroups of companies. The annual publications are available online through www.bizcomps.com and through Business Valuation Resources, LLC at www.BVMarketData.com. BIZCOMPS1 Special Food Service Edition includes restaurants, fast food, delicatessens, catering, coffee houses, and cocktail lounges. It is a study of over 1,500 actual food-service businesses sold totaling over $200 million. The sold businesses are compared by: sales price to gross sales, sales price to seller’s earnings, actual down payment versus all cash, rent as a percent of gross sales, the value of furniture, fixtures and equipment, and the value of inventory at time of sale. The publication is available online through www.bizcomps.com and through Business Valuation Resources, LLC at www.BVMarketData.com. DoneDeals1 provides hard-to-obtain corporate transaction details for private and public midmarket companies sold for purchase prices between $1 million and $1 billion. It is a comprehensive source of midmarket transaction data, with approximately half of the deals under $15 million and half over $15 million. Approximately 79% of the selling companies are privately owned. Data can be searched by Standard Industrial Classification code, price, buyer or seller, private or public company, location, and key word. Available from Thomson PPC, PO Box 966, Fort Worth, TX 76101; (800) 323-8724. www.DoneDeals.com. IBA Market Database is the largest database of guideline transactions for valuing midsize and smaller businesses. The database includes information on over 30,300 sales of closely held businesses in more than 725 Standard Industrial Classification codes. Access to the database is free to members. Institute of Business Appraisers, PO Box 17410, Plantation, FL 33318; (954) 584-1144; fax: (954) 584-1184; www.go-iba.org.
690
Cost of Capital
Pratt’s StatsTM provides detailed information on the sales of privately and closely held businesses. Pratt’s Stats1 compiles and reports information on up to 81 data points highlighting the financial and transactional details of the sales of privately and closely held companies. Primarily, the data found in Pratt’s Stats1 are used to conduct the market approach to valuing a business in an effort to determine a business’s fair market value or to perform financial research on the pricing of similar companies. Additionally, Pratt’s Stats1 data are used in price discovery by entrepreneurs, investors, advisors and business owners that are considering a business purchase or sale. A significant benefit of the data found in Pratt’s Stats1 is their ability to remove marketplace uncertainty and provide detailed, meaningful financial and transactional information about ‘‘real-world’’ business sales. As of February 2007, Pratt’s Stats1 contained details on approximately 9,420 private and closely held business sales from 1990 to present, ranging in deal price from under $1 million to $14.435 billion. The industries represented in Pratt’s Stats1 are no less diverse, as evidenced by the roughly 700 unique Standard Industrial Classification (SIC) codes and 840 unique North American Industry Classification System (NAICS) codes. Additionally, Pratt’s Stats1 has approximately 210 SIC and 230 NAICS codes with 10 or more transactions reported. Available from Business Valuation Resources, LLC, 1000 SW Broadway, Suite 1200, Portland, OR 97205; (888) BUS-VALU [2878258], fax: (503) 291-7955, www.BVResources.com.
PARTNERSHIP TRANSACTION DATA Minority Interest Discount Database Package provides access to the Minority Interest Discount Database, an interactive database that supplies access to market data compiled from 1994 to 2006 in connection with Partnership Profiles’ annual Partnership Re-Sale Discount Surveys. The package also provides the Executive Summary Report on Partnership Re-Sale Discounts, Detailed Partnership Data, and PartnerDisc. Partnership Profiles, Inc. publishes the Direct Investments Spectrum Newsletter (formerly the Partnership Spectrum). Available from Partnership Profiles, Inc.; (800) 634-4614; www.partnershipprofiles.com.
LACK OF MARKETABILITY Emory Pre-IPO Discount Studies, the Discounts for Lack of Marketability, by John D. Emory Sr., F. R. Dengel III, and John D. Emory Jr., provide data to help quantify discounts for lack of marketability. The studies were conducted from 1980 through 2000. The studies compare the prices of stock transactions occurring within five months prior to an initial public offering to the subsequent initial public offering price. Available from Emory & Co., 611 N. Broadway, Suite 210, Milwaukee, WI 53202; (800) 252-5984; online at www.emorybizval.com/valuation-studies.shtml. The FMV Restricted Stock StudyTM contains detailed information used to quantify marketability discounts in the business valuation, business appraisal, venture capital, and the merger and acquisition professions. It contains 55 data fields for each of its 475 transactions. Available from Business Valuation Resources, LLC, 1000 SW Broadway, Suite 1200, Portland, OR 97205; (888) BUS-VALU [287-8258], fax: (503) 291-7955. www.BVResources.com. Valuation Advisors’ Lack of Marketability Discount StudyTM contains details on pre-IPO transactions with 15 data points for each. This database currently contains details on 3,290 transactions. Available from Business Valuation Resources, LLC, 1000 SW Broadway, Suite 1200, Portland, OR 97205; (888) BUS-VALU [287-8258], fax: (503) 291-7955. www.BVResources.com.
Periodicals
691
INTERNATIONAL RISK BondsOnline Group, Inc. provides instant data on current and historic prices and descriptive information for all current or past stocks, preferred stocks, bonds, indices, and other securities from around the world, and yield spreads for US Corporate and Agency Debt securities on a pay as you need basis. Available at BondsOnline Group, Inc., 9311 SE 36th Street, Suite 201, Mercer Island, WA 98040; (800) 883-1808. www.bondsonline.com. The PRS Group, Inc. Web site combines data, publications, and online accessibility for international risk data. The Political Risk Services publishes 100 Country Reports that monitor the risks to international business over the next five years, using the Coplin-O’Leary methodology. The International Country Risk Guide (ICRG) and related publications monitor 161 countries, rating a wide range of risks to international businesses and financial institutions. CountryData.com is designed to allow you to pick only the data, forecasts, or risk ratings needed from both ICRG and Political Risk Services data. Available at the PRS Group, Inc., 6320 Fly Road, East Syracuse, NY 13057. www.prsgroup.com.
PERIODICALS Business Valuation Library is an online database that allows the user to build a custom library of resources by selecting from BVUpdate, Deluxe BVUpdate, BVLaw, Economic Outlook Update, BVPapers, and Business Valuation Data Directory. Available from Business Valuation Resources, LLC, 1000 SW Broadway, Suite 1200, Portland, OR 97205; (888) BUS-VALU [287-8258], fax: (503) 291-7955. www.BVResources.com. Business Valuation Review is a quarterly professional journal focusing on business valuation topics authored by leaders in the profession. Available in print and online, its goal is to advance knowledge and understanding of the professional practice of appraising various business interests through the publication of high-quality, practitioner-relevant research. Available from the Committee of the American Society of Appraisers, www.bvappraisers.org/IssueStore/. Business Valuation UpdateTM is a monthly newsletter available in print and online. It focuses on news, views, and resources for business valuation professionals. Monthly features include guest articles and interviews, legal and court case updates, cost of capital, data and publications updates, special reports, reader/editor exchange, news updates, and calendar updates. Available from Business Valuation Resources, LLC, 1000 SW Broadway, Suite 1200, Portland, OR 97205; (888) BUS-VALU [287-8258], fax: (503) 291-7955. www.BVResources.com. Financial Valuation and Litigation Expert is a bimonthly journal presenting views and tools from many of the leading experts in financial valuation, forensics/fraud, and litigation services. Some features include summaries of current court cases, expert resources and data sources, association news, industry-specific updates, valuation methods and applications, discounts and premiums, intellectual property infringement, expert witness suggestions, forensic/fraud examples, and damage calculation illustrations. Available from Valuation Products & Services, LC, 3340 Peachtree Road NE, Suite 1785 Tower Place, Atlanta, GA 30326; (404) 814-3731. www.valuationproducts.com.
Appendix III
International Glossary of Business Valuation Terms To enhance and sustain the quality of business valuations for the benefit of the profession and its clientele, the listed societies and organizations have adopted the definitions for the terms included in this glossary. The performance of business valuation services requires a high degree of skill and imposes on valuation professionals a duty to communicate the valuation process and conclusion in a manner that is clear and not misleading. This duty is advanced through the use of terms whose meanings are clearly established and consistently applied throughout the profession. If, in the opinion of the business valuation professional, one or more of these terms needs to be used in a manner that materially departs from the enclosed definitions, it is recommended that the term be defined as used within that valuation engagement. This glossary has been developed to provide guidance to business valuation practitioners by further memorializing the body of knowledge that constitutes the competent and careful determination of value and, more particularly, the communication of how that value was determined. Departure from this glossary is not intended to provide a basis for civil liability and should not be presumed to create evidence that any duty has been breached. American Institute of Certified Public Accountants American Society of Appraisers Canadian Institute of Chartered Business Valuators The Institute of Business Appraisers National Association of Certified Valuation Analysts Definitions defined exclusively by the American Society of Appraisers are marked with an asterisk (*). Definitions defined exclusively by The Appraisal Institute, The Dictionary of Real Estate Appraisal, 4th ed. (Chicago: Appraisal Institute, 2002) are marked with two asterisks (**). Definitions defined exclusively for this book are marked with three asterisks (***). Adjusted Book Value*—the book value that results after asset or liability amounts are added, deleted, or changed from their respective book amounts. Adjusted Book Value Method—a method within the asset approach whereby all assets and liabilities (including off–balance sheet, intangible, and contingent) are adjusted to their fair market values. [NOTE: In Canada on a going-concern basis.] Adjusted Net Asset Method—see Adjusted Book Value Method. Appraisal—see Valuation. Appraisal Approach—see Valuation Approach. Appraisal Date—see Valuation Date. Appraisal Method—see Valuation Method. Appraisal Procedure—see Valuation Procedure.
693
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Cost of Capital
Appraised Value*—the appraiser’s opinion or conclusion of value. Arbitrage Pricing Theory—a multivariate model for estimating the cost of equity capital, which incorporates several systematic risk factors. Arithmetic Mean***—the sum of all the numbers of a list divided by the number of items in the list. Asset (Asset-Based) Approach—a general way of determining a value indication of a business, business ownership interest, or security using one or more methods based on the value of the assets net of liabilities. Beta—a measure of systematic risk of a stock; the tendency of a stock’s price to correlate with changes in a specific index. Blockage Discount—an amount or percentage deducted from the current market price of a publicly traded stock to reflect the decrease in the per-share value of a block of stock that is of a size that could not be sold in a reasonable period of time given normal trading volume. Book Value—see Net Book Value. Business—see Business Enterprise. Business Appraiser*—a person who, by education, training, and experience, is qualified to develop an appraisal of a business, business ownership interest, security, or intangible asset. Business Enterprise—a commercial, industrial, service, or investment entity (or a combination thereof) pursuing an economic activity. Business Risk—the degree of uncertainty of realizing expected future returns of the business resulting from factors other than financial leverage. See Financial Risk. Business Valuation—the act or process of determining the value of a business enterprise or ownership interest therein. Capital Asset Pricing Model (CAPM)—a model in which the cost of capital for any stock or portfolio of stocks equals a risk-free rate plus a risk premium that is proportionate to the systematic risk of the stock or portfolio. Capitalization—a conversion of a single period of economic benefits into value. Capitalization Factor—any multiple or divisor used to convert anticipated economic benefits of a single period into value. Capitalization of Earnings Method—a method within the income approach whereby economic benefits for a representative single period are converted to value through division by a capitalization rate. Capitalization Rate—any divisor (usually expressed as a percentage) used to convert anticipated economic benefits of a single period into value. Capital Structure—the composition of the invested capital of a business enterprise; the mix of debt and equity financing. Cash Equivalent Price**—a price expressed in terms of cash, as distinguished from a price expressed totally or partly in terms of the face amounts of notes or other securities that cannot be sold at their face amounts. Calculating the cash-equivalent price requires an appraiser to compare transactions involving a typical financing to transactions involving comparable properties financed at typical market terms. Cash Flow—cash that is generated over a period of time by an asset, group of assets, or business enterprise. The term may be used in a general sense to encompass various levels of specifically defined cash flows. When the term is used, it should be supplemented by a qualifier (e.g., ‘‘discretionary’’ or ‘‘operating’’) and a specific definition in the given valuation context.
International Glossary of Business Valuation Terms
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Common Size Statements—financial statements in which each line is expressed as a percentage of the total. On the balance sheet, each line item is shown as a percentage of total assets, and on the income statement, each item is expressed as a percentage of sales. Control—the power to direct the management and policies of a business enterprise. Control Premium—an amount or a percentage by which the pro rata value of a controlling interest exceeds the pro rata value of a noncontrolling interest in a business enterprise, to reflect the power of control. Cost Approach—a general way of determining a value indication of an individual asset by quantifying the amount of money required to replace the future service capability of that asset. Cost of Capital—the expected rate of return that the market requires in order to attract funds to a particular investment. Debt-Free—we discourage the use of this term. See Invested Capital. Direct Capitalization**—a method used to convert an estimate of a single year’s income expectancy into an indication of value in one direct step, either by dividing the income estimate by an appropriate rate or by multiplying the income estimate by an appropriate factor. Or a capitalization technique that employs capitalization rates and multipliers extracted from sales. Only the first year’s income is considered. Yield and value change are implied but not identified. Discount for Lack of Control—an amount or percentage deducted from the pro rata share of value of 100% of an equity interest in a business to reflect the absence of some or all of the powers of control. Discount for Lack of Liquidity*—an amount or percentage deducted from the value of an ownership interest to reflect the relative inability to quickly convert property to cash. Discount for Lack of Marketability—an amount or percentage deducted from the value of an ownership interest to reflect the relative absence of marketability. Discount for Lack of Voting Rights—an amount or percentage deducted from the per share value of a minority interest voting share to reflect the absence of voting rights. Discount Rate—a rate of return used to convert a future monetary sum into present value. Discounted Cash Flow Method—a method within the income approach whereby the present value of future expected net cash flows is calculated using a discount rate. Discounted Future Earnings Method—a method within the income approach whereby the present value of future expected economic benefits is calculated using a discount rate. Discretionary Earnings*—earnings that may be defined, in certain applications, to reflect earnings of a business enterprise prior to the following items: Income taxes Nonoperating income & expenses Nonrecurring income & expenses Depreciation and amortization Interest expense or income Owner’s total compensation for those services, which could be provided by sole owner/manager. Duration***—the average number of years to an asset’s discounted cash flow. It is a common gauge of the price sensitivity of a fixed income asset or portfolio to a change in interest rates.
696
Cost of Capital
Economic Benefits—inflows such as revenues, net income, net cash flows, etc. Economic Life—the period of time over which property may generate economic benefits. Effective Date—see Valuation Date. Enterprise—see Business Enterprise. Equity—the owner’s interest in property after deduction of all liabilities. Equity Net Cash Flows—those cash flows available to pay out to equity holders (in the form of dividends) after funding operations of the business enterprise, making necessary capital investments, and increasing or decreasing debt financing. Equity Risk Premium—a rate of return added to a risk-free rate to reflect the additional risk of equity instruments over risk free instruments (a component of the cost of equity capital or equity discount rate). Ex Ante***—a Latin phrase meaning ‘‘before the event.’’ Calculation performed on future returns to give projections before an event occurs. Excess Earnings—that amount of anticipated economic benefits that exceeds an appropriate rate of return on the value of a selected asset base (often net tangible assets) used to generate those anticipated economic benefits. Excess Earnings Method—a specific way of determining a value indication of a business, business ownership interest, or security determined as the sum of (a) the value of the assets derived by capitalizing excess earnings and (b) the value of the selected asset base. Also frequently used to value intangible assets. See Excess Earnings. Ex Post***—A Latin phrase meaning ‘‘after the event.’’ Calculations performed on future returns to give projections after an event occurs. Fair Market Value—the price, expressed in terms of cash equivalents, at which property would change hands between a hypothetical willing and able buyer and a hypothetical willing and able seller, acting at arms length in an open and unrestricted market, when neither is under compulsion to buy or sell and when both have reasonable knowledge of the relevant facts. [NOTE: In Canada, the term price should be replaced with the term highest price.] Fairness Opinion—an opinion as to whether the consideration in a transaction is fair from a financial point of view. Financial Risk—the degree of uncertainty of realizing expected future returns of the business resulting from financial leverage. See Business Risk. Forced Liquidation Value—liquidation value at which the asset or assets are sold as quickly as possible, such as at an auction. Free Cash Flow—we discourage the use of this term. See Net Cash Flow. Geometric Mean***—a collection of positive data to the nth root of the product of all the members of the data set, where n is the number of members. Going Concern—an ongoing operating business enterprise. Going Concern Value—the value of a business enterprise that is expected to continue to operate into the future. The intangible elements of going concern value result from factors such as having a trained workforce, an operational plant, and the necessary licenses, systems, and procedures in place. Goodwill—that intangible asset arising as a result of name, reputation, customer loyalty, location, products, and similar factors not separately identified.
International Glossary of Business Valuation Terms
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Goodwill Value—the value attributable to goodwill. Goodwill Value*—the value attributable to the elements of intangible assets above the identifiable tangible and intangible assets employed in a business. Guideline Public Company Method—a method within the market approach whereby market multiples are derived from market prices of stocks of companies that are engaged in the same or similar lines of business, and that are actively traded on a free and open market. Holding Company*—an entity that derives its return from investments rather than from the sale of products or services. Horizon Premium***—the long-term premium of government bond returns in excess of Treasury bill returns. Hypothetical Condition*—that which is contrary to what exists but is supposed for the purpose of analysis. Income (Income-Based) Approach—a general way of determining a value indication of a business, business ownership interest, security, or intangible asset using one or more methods that convert anticipated economic benefits into a present single amount. Intangible Assets—nonphysical assets, such as franchises, trademarks, patents, copyrights, goodwill, equities, mineral rights, securities, and contracts, as distinguished from physical assets, that grant rights and privileges, and have value for the owner. Internal Rate of Return—a discount rate at which the present value of the future cash flows of the investment equals the cost of the investment. Intertemporal***—occurring across time, or across different periods of time. Intrinsic Value—the value that an investor considers, on the basis of an evaluation or available facts, to be the ‘‘true’’ or ‘‘real’’ value that will become the market value when other investors reach the same conclusion. When the term applies to options, it is the difference between the exercise price or strike price of an option and the market value of the underlying security. Invested Capital—the sum of equity and debt in a business enterprise. Debt is typically (a) all interest-bearing debt or (b) long-term interest-bearing debt. When the term is used, it should be supplemented by a specific definition in the given valuation context. Invested Capital Net Cash Flows—those cash flows available to pay out to equity holders (in the form of dividends) and debt investors (in the form of principal and interest) after funding operations of the business enterprise and making necessary capital investments. Investment Horizon***—the length of time a sum of money is expected to be invested. Investment Risk—the degree of uncertainty as to the realization of expected returns. Investment Value—the value to a particular investor based on individual investment requirements and expectations. [NOTE: in Canada, the term used is ‘‘Value to the Owner’’.] Key Person Discount—an amount or percentage deducted from the value of an ownership interest to reflect the reduction in value resulting from the actual or potential loss of a key person in a business enterprise. Levered Beta—the beta reflecting a capital structure that includes debt. Limited Appraisal—the act or process of determining the value of a business, business ownership interest, security, or intangible asset with limitations in analyses, procedures, or scope. Liquidity—the ability to quickly convert property to cash or pay a liability.
698
Cost of Capital
Liquidity*—the ability to readily convert an asset, business, business ownership interest, or security into cash without significant loss of principal. Liquidation Value—the net amount that would be realized if the business is terminated and the assets are sold piecemeal. Liquidation can be either ‘‘orderly’’ or ‘‘forced.’’ Majority Control—the degree of control provided by a majority position. Majority Interest—an ownership interest greater than 50% of the voting interest in a business enterprise. Market (Market-Based) Approach—a general way of determining a value indication of a business, business ownership interest, security, or intangible asset by using one or more methods that compare the subject to similar businesses, business ownership interests, securities, or intangible assets that have been sold. Market Capitalization of Equity—the share price of a publicly traded stock multiplied by the number of shares outstanding. Market Capitalization of Invested Capital—the market capitalization of equity plus the market value of the debt component of invested capital. Market Multiple—the market value of a company’s stock or invested capital divided by a company measure (such as economic benefits, number of customers). Marketability—the ability to quickly convert property to cash at minimal cost. Marketability*—the capability and ease of transfer or salability of an asset, business, business ownership interest, or security. Marketability Discount—see Discount for Lack of Marketability. Merger and Acquisition Method—a method within the market approach whereby pricing multiples are derived from transactions of significant interests in companies engaged in the same or similar lines of business. Mid-Year Discounting—a convention used in the Discounted Future Earnings Method that reflects economic benefits being generated at midyear, approximating the effect of economic benefits being generated evenly throughout the year. Minority Discount—a discount for lack of control applicable to a minority interest. Minority Interest—an ownership interest less than 50% of the voting interest in a business enterprise. Multiple—the inverse of the capitalization rate. Net Assets*—total assets less total liabilities. Net Book Value—with respect to a business enterprise, the difference between total assets (net of accumulated depreciation, depletion, and amortization) and total liabilities as they appear on the balance sheet (synonymous with shareholder’s equity). With respect to a specific asset, the capitalized cost less accumulated amortization or depreciation as it appears on the books of account of the business enterprise. Net Cash Flow—when the term is used, it should be supplemented by a qualifier. See Equity Net Cash Flows and Invested Capital Net Cash Flows. Net Income*—revenue less expenses and taxes. Net Operating Income (NOI, IO) **—the actual or anticipated net income that remains after all operating expenses are deducted from effective gross income but before mortgage debt service
International Glossary of Business Valuation Terms
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and book depreciation are deducted; may be calculated before or after deducting replacement reserves. Net Present Value—the value, as of a specified date, of future cash inflows less all cash outflows (including the cost of investment) calculated using an appropriate discount rate. Net Tangible Asset Value—the value of the business enterprise’s tangible assets (excluding excess assets and nonoperating assets) minus the value of its liabilities. Nonoperating Assets—assets not necessary to ongoing operations of the business enterprise. [NOTE: in Canada, the term used is ‘‘Redundant Assets’’.] Normalized Earnings—economic benefits adjusted for nonrecurring, noneconomic, or other unusual items to eliminate anomalies and/or facilitate comparisons. Normalized Financial Statements—financial statements adjusted for nonoperating assets and liabilities and/or for nonrecurring, noneconomic, or other unusual items to eliminate anomalies and/or facilitate comparisons. Operating Company*—a business that conducts an economic activity by generating and selling, or trading in a product or service. Orderly Liquidation Value—liquidation value at which the asset or assets are sold over a reasonable period of time to maximize proceeds received. Planning Horizon***—the length of time a plan extends into the future. Premise of Value—an assumption regarding the most likely set of transactional circumstances that may be applicable to the subject valuation; for example, going concern, liquidation. Present Value—the value, as of a specified date, of future economic benefits and/or proceeds from sale, calculated using an appropriate discount rate. Pretax Cash Flow (PTCF)**—the portion of net operating income that remains after total mortgage debt service is paid but before ordinary income tax on operations is deducted; also called before-tax cash flow or equity dividend. Portfolio Discount—an amount or percentage deducted from the value of a business enterprise to reflect the fact that it owns dissimilar operations or assets that do not fit well together. Price/Earnings Multiple—the price of a share of stock divided by its earnings per share. Rate of Return—an amount of income (loss) and/or change in value realized or anticipated on an investment, expressed as a percentage of that investment. Redundant Assets—see Nonoperating Assets. Report Date—the date conclusions are transmitted to the client. Replacement Cost New—the current cost of a similar new property having the nearest equivalent utility to the property being valued. Reproduction Cost New—the current cost of an identical new property. Required Rate of Return—the minimum rate of return acceptable by investors before they will commit money to an investment at a given level of risk. Residual Value—the value as of the end of the discrete projection period in a discounted future earnings model. Return on Equity—the amount, expressed as a percentage, earned on a company’s common equity for a given period. Return on Investment—see Return on Invested Capital and Return on Equity.
700
Cost of Capital
Return on Invested Capital—the amount, expressed as a percentage, earned on a company’s total capital for a given period. Reversion**—a lump-sum benefit that an investor receives or expects to receive at the termination of an investment, which is often called reversionary benefit. Risk-free Rate—the rate of return available in the market on an investment free of default risk. Risk Premium—a rate of return added to a risk-free rate to reflect risk. Rule of Thumb—a mathematical formula developed from the relationship between price and certain variables based on experience, observation, hearsay, or a combination of these; usually industryspecific. Special Interest Purchasers—acquirers who believe they can enjoy postacquisition economies of scale, synergies, or strategic advantages by combining the acquired business interest with their own. Stabilized Occupancy**—occupancy at that point in time when abnormalities in supply and demand or any additional transitory conditions cease to exist and the existing conditions are those expected to continue over the economic life of the property; the average long-term occupancy that an incomeproducing real estate project is expected to achieve under competent management after exposure for leasing in the open market for a reasonable period of time at terms and conditions comparable to competitive offerings. Standard of Value—the identification of the type of value being utilized in a specific engagement; for example, fair market value, fair value, investment value. Stochastic***—of or pertaining to a process involving a randomly determined sequence of observations each of which is considered as a sample of one element from a probability distribution. Sustaining Capital Reinvestment—the periodic capital outlay required to maintain operations at existing levels, net of the tax shield available from such outlays. Systematic Risk—the risk that is common to all risky securities and cannot be eliminated through diversification. The measure of systematic risk in stocks is the beta coefficient. Tangible Assets—physical assets (such as cash, accounts receivable, inventory, property, plant and equipment, etc.). Terminal Value—see Residual Value. Transaction Method—see Merger and Acquisition Method. Unlevered Beta—the beta reflecting a capital structure without debt. Unsystematic Risk—the portion of total risk specific to an individual security that can be avoided through diversification. Valuation—the act or process of determining the value of a business, business ownership interest, security, or intangible asset. Valuation Approach—a general way of determining a value indication of a business, business ownership interest, security, or intangible asset using one or more valuation methods. Valuation Date—the specific point in time as of which the valuator’s opinion of value applies (also referred to as ‘‘Effective Date’’ or ‘‘Appraisal Date’’). Valuation Method—within approaches, a specific way to determine value. Valuation Procedure—the act, manner, and technique of performing the steps of an appraisal method.
International Glossary of Business Valuation Terms
701
Valuation Ratio—a fraction in which a value or price serves as the numerator and financial, operating, or physical data serve as the denominator. Value to the Owner—[NOTE: in Canada, see Investment Value.] Voting Control—de jure control of a business enterprise. Weighted Average Cost of Capital (WACC)—the cost of capital (discount rate) determined by the weighted average, at market value, of the cost of all financing sources in the business enterprise’s capital structure. Working Capital*—the amount by which current assets exceed current liabilities.
Appendix IV
Sample Report Submitted to U.S. Tax Court by Roger J. Grabowski Introduction Required Rates of Return on Equity and Invested Capital Capital Asset Pricing Model Guideline Company Capital Structures Size/Return Study Risk/Return Study Fama-French Three Factor Model Duration Adjusted CAPM Concluded Rates of Return
INTRODUCTION This appendix is an excerpt from the report submitted to the U.S. Tax Court by Roger J. Grabowski, ASA, in the matter of Herbert V. Kohler, Jr., et al., Petitioners v. Commissioner of Internal Revenue. It is included to demonstrate the explanations of various cost of capital methodologies.
REQUIRED RATES OF RETURN ON EQUITY AND INVESTED CAPITAL I considered four methods for estimating a required rate of return on the equity component of the capital structure:
Capital Asset Pricing Model (CAPM) Size/Return Study Risk/Return Study Fama-French Three Factor Model (the Fama-French Model)
The CAPM is the most widely used method for calculating the rate of return on equity. However, researchers have pointed out that CAPM often misprices risk for certain investments.1 In particular, researchers have observed that commonly used methods of measuring risk used in the CAPM, ‘‘beta,’’ often understate the correct risk, and thus understate the required return, for small company stocks. Beta is defined as a risk measure that reflects the sensitivity of a company’s stock return to the 1
A sample of academic research articles include: Rolf Banz, ‘‘The Relationship Between Return and Market Value of Common Stocks,’’ Journal of Financial Economics (March 1981): 3–18; Eugene Fama and Kenneth French, ‘‘The Cross Section of Expected Stock Returns,’’ Journal of Finance (June 1992): 427–486; Kent Daniel and Sheridan Titman, ‘‘Evidence on the Characteristics of Cross Sectional Variation in Stock Returns,’’ Journal of Finance (March 1997): 1–33.
703
704
Cost of Capital
movements of return of the stock market as a whole. In an attempt to correct for the problems with CAPM, I have: (a) adjusted the CAPM rate of return on equity by a size premium consistent with research; and (b) applied alternative methods for calculating the rate of return on equity, such as the Size/Return Study, the Risk/Return Study, and the Fama-French Model. These methods resulted in fairly consistent indicated rates of return on equity, as described below. I also calculated a required rate of return on equity that reflects a premium for the illiquidity of an investment in Kohler. This point is supported by William Silber in his article, ‘‘Discounts on Restricted Stock: The Impact of Illiquidity on Stock Prices,’’ referring to the results of his restricted stock study: ‘‘The results indicate that marketing a large block of illiquid securities requires significant price concessions, even from firms with substantial credit-worthiness. Liquidity clearly has a significant impact on the cost of equity capital.’’2 As discussed in Section V of the report, the general formula for calculating the WACC is: WACC ¼ Kd ðd%Þ þ Ke ðe%Þ where: WACC ¼ Weighted average rate of return on invested capital Kd ¼ After-tax rate of return on debt capital d% ¼ Debt capital as a percentage of the sum of the debt, preferred and common equity capital (‘‘Total Invested Capital’’) Ke ¼ Rate of return on common equity capital e% ¼ Common equity capital as a percentage of the Total Invested Capital
CAPITAL ASSET PRICING MODEL Rate of Return on Equity The rate of return on equity capital is often estimated using the CAPM.3 CAPM estimates the rate of return on common equity of U.S. companies as the current risk-free rate of return on U.S. Treasury bonds, plus a market risk premium expected over the risk-free rate of return, multiplied by the beta for the stock. The CAPM rate of return on equity capital is calculated using the formula: ke ¼ R f þ ðb ðRm R f ÞÞ þ SSP where:
RM
2
3
KE ¼ Rate of return on equity capital RF ¼ Risk-free rate of return b ¼ Beta or systematic risk for this type of equity investment RF ¼ Market risk premium; the expected return on a broad portfolio of stocks in the market (RM) less the risk-free rate (RF) SSP ¼ Small Stock Premium
William L. Silber, ‘‘Discounts on Restricted Stock: The Impact of Illiquidity on Stock Prices,’’ Financial Analysts Journal (July– August 1991): 64. Richard A. Brealey and Stewart C. Myers, Principles of Corporate Finance, 4th edition (New York: McGraw-Hill, 1991), 166.
Required Rates of Return on Equity and Invested Capital
705
a) Risk-free Rate The 20-year U.S. Treasury bond was utilized to measure the risk-free rate of return. The general preference for the 20-year rate is because the 20-year Treasury security matches the typical long-term horizon of equity investments, and is subject to less volatility than short-term rates.4 The most recent available 20-year rate, as of the Valuation Date, was approximately 5.4 percent. b) Beta Practical application of the CAPM relies upon the ability to identify publicly traded companies that have similar risk characteristics as the subject company in order to derive meaningful measures of the company beta and a normalized industry capital structure. Beta is a measure of how a company’s stock return moves relative to overall returns of the market. The market return is often measured by an index such as the Dow Jones Industrial Average, the S&P 500, or the New York Stock Exchange Index. The S&P 500 is the most commonly used measure of market returns in estimating betas. An ‘‘average risk’’ stock is defined as one whose returns tend to move up and down in step with the general market. Such a stock will, by definition, have a beta, b, of 1.0, which indicates that, in general, if the market return moves up by 10 percent, the stock’s return would be expected to move up by 10 percent, while if the market return falls by 10 percent, the stock’s return would be expected to likewise fall by 10 percent. If b ¼ 0.5, the stock’s return is expected to rise and fall only half as much as the return on the market. Conversely, if b ¼ 2.0, the stock’s return is expected to rise and fall twice the market percentage. I considered several alternate methods in deriving an estimate of beta. A traditional approach is to use statistical regression analysis, also known as Ordinary Least Squares (‘‘OLS’’). The OLS approach regresses the returns on a company’s common stock against the returns on the S&P 500 index over a period of time. A commonly accepted approach is to use 60 months of data. The estimate of a company’s beta is the slope coefficient from this regression. I did not rely on the OLS approach, as the OLS approach tends to understate the true beta of companies that exhibit cross-autocorrelation with the market portfolio.5 Autocorrelation is the process whereby a company’s current stock movements appear to be influenced not only by current movements in the S&P 500 index, but also by prior movements in the index.6 The effects can be especially pronounced for stocks with relatively low trading volume, but it can also be observed for some larger companies. In order to correct for the problem of autocorrelation in the OLS approach, I relied on a method of estimating beta that captures this effect, developed by the financial economist Elroy Dimson (called ‘‘SumBeta’’ or ‘‘Dimson’’ beta). This differs from the OLS approach in that a multiple regression analysis is used with both a current market return and a lagged market return as explanatory variables. SumBeta is the sum of the coefficients on the current and lagged market terms.7 In my analysis I used current market returns and one-month lagged market returns to calculate SumBeta of the selected publicly traded guideline companies, as displayed below:
ðrs r f Þ ¼ as þ bs0 ðrm0 r f 0 Þ þ bs1 ðrm1 r f 1 Þ þ et where: (rs rf) ¼ Excess return of a security over the risk-free rate as ¼ Regression constant bs0 ¼ Beta coefficient for realized market excess returns (rm0 rf0) ¼ Realized market excess return 4 5
6 7
Robert F. Reilly and Robert P. Schweihs, The Handbook of Advanced Business Valuation (New York: McGraw-Hill, 2000), 12. Roger G. Ibbotson, Paul D. Kaplan, and James D. Peterson, ‘‘Estimates of Small-Stock Betas Are Much Too Low,’’ Journal of Portfolio Management (Summer 1997): 104–111. Ibid. Ibbotson Associates, Stocks, Bonds, Bills, and Inflation 2003 Yearbook, 130.
706
Cost of Capital
bs1 ¼ Beta coefficient for lagged realized market excess returns (rm1 rf1) ¼ Lagged realized market excess return et ¼ The error term of the regression SumBeta ¼ bs0 + bs1 I calculated SumBetas of the selected publicly traded guideline companies as of the Valuation Date using 60 months of historical stock returns, where available. Only 42 months’ historical stock return data were available for American Standard, a guideline company of the Kitchen & Bath Group. After analyzing the data, I determined that this was sufficient to provide a reliable indication of beta. Betas estimated directly from company stock prices are ‘‘levered,’’ i.e., they incorporate the added risk to a stockholder due to the debt financing of the specific company. To remove the effects of differing capital structures, the levered betas of the guideline companies is first ‘‘unlevered.’’ The unlevering is accomplished by employing the following equation8: Unlevered Beta ¼
Levered Beta 1 þ ½ð1 Tax RateÞ Debt=Equity
I calculated unlevered beta of the guideline companies considered in the Market Approach in order to remove the effects of the specific capital structure of the guideline companies. Companies with abnormally high leverage ratios and/or negative SumBeta indications were excluded from the analysis, as they did not provide reliable indications of relative risk. GUIDELINE COMPANY CAPITAL STRUCTURES In the course of my analysis, I made several adjustments to the book value of debt and equity for the guideline companies in order to more accurately reflect Fair Market Value. Debt In estimating the Fair Market Value of debt for the guideline companies, I used fair value disclosures included in the footnotes to the audited financial statements included in the 10-K filing for each of the guideline companies, and assumed that fair value reflected Fair Market Value.9 For each of the companies analyzed, the footnotes included either a representation of fair value of debt, or a statement that the carrying value of debt approximates fair value. The fair value disclosures for debt were only provided in the year-end 10-K financial statements. More current balance sheet information was obtainable for each of the guideline companies from the 10-Q filings released for the second quarter of 1998. For each of the guideline companies, I adjusted the fair value indicated in the 10-K filings using data from the most recent 10-Q filings in order to determine an estimate of fair value of debt as of the Valuation Date. I calculated the change in book value of long-term debt from the year-end 1997 filing to the second quarter 1998 filing and applied this change as a market value adjustment to the year-end 1997 fair value of long-term debt. Typically, corporations issuing new debt do so at or near Fair Market Value, i.e., little to no premium (discount)
8 9
Reilly and Schweihs, The Handbook of Advanced Business Valuation, 13. Fair value defined in FAS 141 as ‘‘The amount at which an asset (or liability) could be bought (or incurred) or sold (or settled) in a current transaction between willing parties, that is, other than in a forced or liquidation sale’’ (p. 106) for the relevant balance sheet items should be consistent with Fair Market Value.
Required Rates of Return on Equity and Invested Capital
707
to par value. Therefore, any new long-term debt issued during 1998 would most likely be issued at or very near book value. I also included in my adjustments any publicly traded debt that was issued after the issuance of 10-Q filings for the second quarter and prior to the Valuation Date. None of the guideline companies included in our conclusions had such issuances. Any non-public transactions in debt that occurred for the guideline companies after the issuance of second quarter 10-Q filings but prior to the Valuation Date could not be included in my adjustments, as this information was not made public. Finally, I added the fair value of debt due after one year and the adjustment for debt issued during 1998 to the book value of total short-term debt from the 10-Q filing. As with new issuances of longterm debt, book value of short-term debt was used to approximate fair value since (1) short-term debt is typically issued at floating interest rates, in which case no adjustment to fair value would be necessary, or because (2) the period between the issuance of the debt and the Valuation Date is short enough that fluctuations in market interest rates during that period would not be large enough to cause changes in the fair value of the debt that would be material to my analysis. Adding the fair value of long-term debt due after one year from the 10-K filings to the change in long-term debt during the first two quarters of 1998 and total short-term debt from the most recent quarter ended as of the Valuation Date resulted in an indication of fair value of total debt for each of the guideline companies analyzed. Debt—Adjustment for Capitalized Operating Lease Obligations Many of the guideline companies analyzed lease certain amounts of their assets. These operating leases can be used in place of issuing debt to purchase the assets. For each guideline company selected, I considered the hypothetical capitalized value of these operating lease agreements that, if the associated assets were financed through debt rather than leased, would cause the company to have higher than reported debt levels. Forecasted payments for the next five years and thereafter for lease commitments are disclosed in the footnotes to financial statements in each company’s 10-K filing. For the payments forecasted after five years, I estimated annual payments, dividing the total amount expected after five years by the expected payment in the fifth year and applying this average remaining payment in each year until the total amount has been paid. I discounted these payments to present value using a 10 percent rate of return as described in ‘‘Operating Lease Analytical Model’’ by Paul Harvey. This standard rate of return is used because implicit lease rates are rarely disclosed in financial statements.10 The resulting value is the indicated value of operating lease agreements and was added to the Fair Market Value of debt for each guideline company. For each company selected, these adjustments had a minimal impact on value. Debt—Adjustment for Preferred Stock Only two of the guideline companies considered had preferred stock listed on their most recently available financial statements as of the Valuation Date. Each of these companies was considered comparable to the Hospitality Group. I estimated Fair Market Value for the preferred equity using methodologies dependent on the amount of information available in the financial statements. For one company, the preferred stock was publicly traded as of the Valuation Date.11 Therefore, I calculated the Fair Market Value by simply multiplying the observed market price per share of the preferred stock by the number of shares of preferred stock outstanding. 10
11
Paul B. Harvey, ‘‘Operating Lease Analytical Model,’’ Standard & Poor’s Ratings Direct (June 21, 1999), http:// www.ratingsdirect.com/Apps/RD/controller/Article?id=108707. This text refers to Felcor Lodging Trust Incorporated.
708
Cost of Capital
For the other company, the fair value disclosure in the audited financials indicated that the fair value of long-term debt approximated the carrying amount based on current rates offered to the company for similar debt,12 and I therefore used book value as an approximation for fair value based on this disclosure. Preferred stock, while usually classified as equity on financial statements, is in some ways more similar to debt. The dividends payable to the preferred stockholders represent a fixed obligation that the company must make before any distributions to common shareholders. Also, dividend rates on preferred stock typically represent a rate of return more consistent with interest rates on debt than with rates of return on equity required by investors. For this reason, I have added the value of preferred stock to the value of debt, rather than equity, for each of the guideline companies. Equity All of the guideline companies were publicly traded as of the Valuation Date. Thus, I calculated the Fair Market Value of the common stock of each of the guideline companies simply by multiplying the number of common shares outstanding as indicated in the company’s most recent 10-Q SEC filing by the observed closing market price for the common shares as of the Valuation Date. There were no significant secondary offerings for any of the guideline companies between the issuance of the 10-Q filings and the Valuation Date.
Equity—Adjustment for Employee Stock Options I also considered the value of outstanding stock options as an adjustment to equity value for each guideline company. Outstanding stock options, while not reflected in published figures for shares outstanding in a company, reflect an equity interest in a company that could be created at the discretion of the owner. Generally speaking, the value of an option reflects the amount by which the current stock price exceeds (if at all) the stated exercise price of the option (price at which the option holder owns a right to purchase shares), as well as the expected likelihood and degree by which the stock price may exceed the exercise price over the life of the option, as measured by the volatility of the underlying stock. I valued the employee stock options using the widely accepted Black-Scholes13 option pricing formula and several variables disclosed in the notes to the audited financial statements. The BlackScholes option pricing formula for a call option is as follows: C ¼ SNðd1 Þ Xert Nðd2 Þ where: C ¼ call option price S ¼ current stock price X ¼ exercise price r ¼ short-term risk-free interest rate e ¼ 2.718 t ¼ time remaining to expiration date 12 13
Innkeepers USA Trust 10-K filing for fiscal year 1997, footnote 1. Fischer Black and Myron Scholes, ‘‘The Pricing of Options and Corporate Liabilities,’’ Journal of Political Economy (May 1973): 637–654.
Required Rates of Return on Equity and Invested Capital
709
s ¼ standard deviation of the stock price N( ) ¼ the cumulative normal probability d1 ¼ (ln(S/X) + (r + 0.5s2)t)/(sHt) d2 ¼ d1 (sHt) Disclosures in the financial statements for each guideline company provide average exercise price, number of options outstanding, weighted average contractual life remaining and volatility information. Standard deviation of the stock price is the square root of the volatility. For the risk-free rate, I used a seven-year zero coupon government bond, a term which represents the average remaining contractual life for the options of each of the guideline companies. Multiplying the calculated Fair Market Value of one option by the number of options outstanding for each company results in the total value of outstanding options for each company, which was added to the value of common stock outstanding. Minority Interests In calculating capital structures for each of the guideline companies for the CAPM calculation, I have not included the book value of minority interests. Minority interests are funded through whatever combination of debt and equity the holders of the interests choose. Analysis of a required return on minority interests is not possible without information about the debt and equity funding, which is not provided in the audited financial statements of the guideline companies. I have therefore not considered minority interest in my calculation of guideline company capital structures. Summary—Guideline Company Capital Structures In summary, the Fair Market Value of total debt used in calculating the capital structure of each of the guideline companies includes Fair Market Value of balance sheet debt, value of operating leases as if capitalized, and preferred stock. The fair value of equity used in calculating the capital structure of each of the guideline companies included market value of common shares outstanding and the value of outstanding employee stock options. Unlevered Beta Calculation Using the adjusted capital structures described above, I concluded on the following as reasonable estimates of unlevered beta for the Kitchen & Bath Group, the Power Systems Group, the Interiors Group, and the Hospitality Group: Business Unit Kitchen & Bath Group Power Systems Group Interiors Group Hospitality Group
Unlevered Beta 0.95 0.46 1.11 0.51
To arrive at the unlevered beta of Kohler on a consolidated basis, I weighted each business unit’s unlevered beta by the business unit’s EBITDA as a percent of overall Kohler EBITDA during the twelve months ended August 31, 1998. I estimated the weighted unlevered beta to be 0.87.
710
Cost of Capital
To derive a beta applicable to Kohler, the unlevered betas must be relevered to reflect Kohler’s assumed capital structure. Relevering the betas to Kohler’s capital structure that includes debt reflects the additional risk that the Estate Stock assumes relative to an investment with a capital structure with no debt. The relevering is accomplished by employing the following equation14: Relevered Beta ¼ Unlevered Beta [(1 Tax Rate) Debt/Equity] Kohler Company Capital Structure Capital structure refers to the proportions of debt and equity capital with which a company is financed. The theory of WACC requires that the proportion of debt and equity in the capital structure be based upon the market value of debt and the market value of equity. In determining the capital structure to assume in valuing a company, appraisers frequently consider the average or median capital structure of guideline companies in the subject company’s industry, since the market value of equity is easy to observe for publicly traded guideline companies. This method assumes that if markets are efficient, mature companies in a particular industry will generally operate over the long term with a capital structure that optimizes the benefits of financial leverage (i.e., tax deductibility and a source of growth capital without ceding control of a company), while minimizing the risks of financial leverage (i.e., financial distress and bankruptcy). This optimal capital structure may be different for different industries, based on volatility of cash flows, relative attractiveness to equity investors, industry practice, etc. Thus, in a willing buyer/willing seller situation, this method assumes that the willing buyer would finance its acquisition of a company based on the typical industry capital structure. In the general case, therefore, where control of a private business is being valued, the target capital structure selected is that of public comparable companies where the Fair Market Value of debt and equity are available from market quotes. Accordingly, the WACC is determined directly based on the weighting of the debt and equity components using their observed industry proportions. This approach also involves the use of two critical assumptions: 1. The assumption that the optimal capital structure for the subject company is equal to the average capital structure of the industry as described; and 2. The assumption that the holder of the subject interest in the subject company is willing and able (through the exercise of management control) to change the capital structure to match the ‘‘optimal’’ industry average. As discussed in Section V of the report, Management has represented to me that it views its capital structure as of the Valuation Date as optimal for the objectives of the Company (and that an industry average capital structure based on public companies is not optimal in their opinion for Kohler, a private company), so the first assumption does not apply. Since the collection of business units that Kohler comprises is a unique business mix for which there is not a perfectly comparable company, I consider Management’s representation to be a more accurate indication of the optimal capital structure for Kohler than the average of observed comparable companies. Also, even if the Estate, as a minority shareholder, desired to change the capital structure of Kohler, the 14.45 percent interest in the equity that it held was not sufficient to force such a management policy change, so the second assumption does not apply.
14
Ibid, p. 14.
Required Rates of Return on Equity and Invested Capital
711
Since neither assumption applies, it is not appropriate to use a simple observed industry average capital structure for the expected capital structure of Kohler going forward, but rather the existing capital structure of the Company. Where the target capital structure is assumed to be different than that of the public comparable companies, as has been determined by Management, an alternate approach is required to select the proper capital structure weightings. Unfortunately, while the Fair Market Value of equity for publicly traded companies is directly observable, the Fair Market Value of equity for Kohler, as a private business, is not directly observable from public market transactions. Accordingly, I used an alternative approach in order to develop an appropriate capital structure to use for calculating the WACC, referred to as an iterative process by which the Fair Market Value capital structure indicated by the results of the discounted cash flow analysis is made to reconcile with the capital structure used to calculate the WACC. Management has provided me with a reasonable estimate of the optimal capital structure for Kohler based on book value, but a WACC is based on a market value capital structure. For the market value of Kohler debt, I used book value as an approximation of market value based on disclosures in the financial statements that indicated the debt was carried at fair value.15 As a private company, Kohler’s market value of equity cannot be directly observed; however, the value indicated by a discounted cash flow model represents the Fair Market Value of equity (after subtracting debt). Therefore, I used the results of the Discounted Available Cash Flow Method to estimate the market value of equity for Kohler for the purpose of calculating the WACC. This methodology presents a contradiction, however, since the value indicated by the discounted cash flow model is itself dependent on the WACC that is used. This circular relationship can be solved by stepping through several iterations of the calculation until equilibrium is reached where the capital structure indicated by the discounted cash flow model matches the capital structure used to calculate the WACC (which is then used in the discounted cash flow model, and so on). These calculations can be performed quickly with commonly available spreadsheet software. Please see Appendix IV for a simplified example of this ‘‘iterative process.’’ This methodology is supported by published valuation literature, including Cost of Capital by Shannon Pratt and Corporate Valuation by Bradford Cornell, for cases in which the appraiser is calculating a minority interest in a privately held company. According to Cornell, One simple and popular procedure for estimating the target weights is to assume that they equal the company’s current market value weights. . .In most cases, a company is being appraised because the market value of its securities is unknown and, therefore, cannot be used to calculate the weights . . . . The estimated value of the equity depends on the WACC, which, in turn, depends on the value of the equity . In light of the circularity, an iterative procedure must be employed to solve simultaneously for the value of the equity and for the WACC.16
Pratt also advocates this methodology: In computing WACC for a closely held company. . . because there is no [public] market for the securities, we have to estimate market values in order to compute the capital structure weightings . . . the estimated weightings for each component of the capital structure becomes an iterative process .17
15 16
17
Kohler Company Annual Report 1997. Footnote 5 discusses the company’s long-term debt. Bradford Cornell, Corporate Valuation: Tools for Effective Appraisal and Decision Making (New York: McGraw-Hill, 1993), 224. Shannon Pratt, Cost of Capital: Estimation and Applications (Hoboken NJ: John Wiley & Sons, 2002), 48.
712
Cost of Capital
Analysts often assume a capital structure in the process of estimating a market value of equity, and the resulting estimated market value of equity makes the capital structure, at the estimated market value, different from that which was assumed. In such cases, the projected capital structure has to be adjusted and the process iterated until the estimated market value of equity results in a capital structure consistent with that which is projected in estimating the cost of capital.18
The steps in the iterative process for estimating capital structure component weights for a closely held company can be summarized as follows: Step 1. Estimate the market value of debt as of the Valuation Date. Step 2. Using a capital structure based on the estimate of market value of debt and an estimate of the market value of equity, make a first approximation computation of the WACC. Step 3. Project (a) the net cash flows available to all invested capital, and (b) the projected growth rate necessary for either a discounting valuation model or a capitalizing valuation model. Step 4. Using the first approximation WACC from Step 2 and the projected cash flows from Step 3, compute a first approximation market value of invested capital (‘‘MVIC’’). Step 5. Subtract the market value of the debt (Step 1) from the MVIC (Step 4). This gives the first approximation market value of the common equity. Step 6. Compute the capital structure weights using the market value of equity from Step 5. Step 7. Repeat the process, starting with Step 4, until the computed market value weights come reasonably close to the weights used in computing the WACC. Through this iterative process, I determined that the capital structure of Kohler was 28.4 percent debt to total capital ($258.3/$909.6 ¼ 28.4%), or 39.7 percent debt to equity ($258.3/$651.2 ¼ 39.7 percent), where debt and equity are measured on a market value basis. Beta—Conclusion Based on Kohler’s implied market value capital structure of 28.4 percent debt capital and 71.6 percent equity capital, I concluded on a levered beta of 1.08. c) Market Equity Risk Premium19
I estimated the market equity risk premium (Rp) using two different methods of analysis. The first method looks at the long-term historical returns to a portfolio of publicly traded common stocks, compared to long-term historical returns of ‘‘risk-free’’ investments (i.e., U.S. Government Treasury Bonds). The historical method is sensitive to the time period chosen for the analysis. The highest quality information for U.S. equity markets is available from 1926 onwards, but good information is available back to about 1870 while less reliable information is available back to the 1790s. Below are historical equity premiums relative to returns on U.S. Treasury bonds for alternative time periods. Geometric averages are derived from the compound rates of return over the sample period. Arithmetic averages are derived from the means of the annual premiums over the sample period20:
18 19 20
Ibid., page 154. Reilly and Schweihs, The Handbook of Advanced Business Valuation, 56–58, 64–67. Compiled from equity and bond data from various sources. Data since 1926 is taken from Ibbotson Associates’ Stock, Bonds, Bills and Inflation database; equity data before 1926 is taken from 1) Global Investing, Roger Ibbotson and Gary Brinson (McGraw-Hill, 1993), and 2) the database compiled by Dr. William Schwert as described in ‘‘Indexes of U.S. Stock Prices from 1802–1987,’’ William Schwert, Journal of Business, July 1990; bond data before 1926 is taken from A History of Interest Rates (3rd Edition), Sidney Homer and Richard Sylla (Rutgers University Press, 1991).
Required Rates of Return on Equity and Invested Capital
Geometric Arithmetic 20 years (1978–1997) 30 years (1968–1997) 40 years (1958–1997) 72 years (1926–1997) 200 years (1798–1997)
713
7.8% 4.0% 5.2% 5.8% 3.8%
8.5% 5.2% 6.3% 7.8% 5.2%
The second method is based on forecasts of long-term equity premiums prepared by securities analysts. Below are forecasts from three sources using data available near the beginning of 1998:21
Merrill Lynch publishes forecasts of equity returns based on the results of a Dividend Discount Model, whereby the rate of return on the S&P 500 is estimated from the internal rates of return for the component companies in the S&P 500, which equate observed market prices for individual companies with forecasts of dividends over an infinite horizon.
Value Line, an independent equity research firm, publishes projected rates of return for several hundred companies over a 3- to 5-year horizon, based on the return implied by current market prices and analysts’ projections of future prices and dividends.
Greenwich Associates, a financial research firm, conducted an annual survey of pension plan officers regarding their expected return on the S&P 500 portfolio over a 5-year horizon.
When considering the results of forward-looking returns, it is helpful to compare the most recent evidence with estimates over several recent years. This long-term perspective may give a better indication of current expectations if projections made at a particular time are distorted by recent movements in stock prices that indicate information that may not be fully reflected in analysts’ estimates of future dividends or future prices. Average
Merrill Lynch (infinite horizon) Value Line (3–5 year horizon) Greenwich Survey (5-year horizon)
1994–1998
1998
4.7% 4.0% 2.7%
4.9% 1.8% 3.9%
The historical evidence tends to support an equity market risk premium in a range of 4.0 percent to 9.0 percent as of early 1998. The forward-looking sources tend to support a premium in a range of 2.0 percent to 5.0 percent as of early 1998. After consideration of all of the data, I used a 5.0 percent equity risk premium, which I judged to be a reasonable estimate of the expected premium over the risk-free rate of return for U.S. equities as represented by the S&P 500 portfolio.22
21
22
Merrill Lynch: Implied returns from the Dividend Discount Model as reported in Merrill Lynch Quantitative Profiles, various dates; Value Line: Compiled by Standard & Poor’s using capitalization-weighted averages of expected returns reported in Value Line’s Value Screen database, various dates; Greenwich Survey: Expected returns obtained by Standard & Poor’s from survey data reported by Greenwich Associates, various dates. For all three of the above sources, premiums over Treasury bonds were calculated by subtracting long-run bond yields as reported in Ibbotson’s Stock, Bonds, Bills and Inflation Yearbook, various dates. Reilly and Schweihs, The Handbook of Advanced Business Valuation, Chapter 3.
714
Cost of Capital
An incremental risk premium is appropriate when a company has a small capitalization relative to the companies in the market-weighted S&P 500 index. Market evidence shows that smaller companies have, on average, earned rates of return in excess of returns predicted by the CAPM.23 The size premium is a correction to the standard CAPM as risk is measured by betas for smaller companies, even Sum Betas, is underestimated. The size effect is not just evident for the smallest companies in the marketplace, but becomes evident for all but the largest groups of companies, including companies with a market capitalization in excess of $1 billion. A common practice is to incorporate this evidence by adding a ‘‘small stock premium’’ to the CAPM formula when valuing companies that are comparatively small. I derive a size premium for Kohler using the results of the Size/Return Study.24 This study calculates historical returns on size-ranked portfolios of companies, using eight alternate measures of size. For each portfolio, I calculated a ‘‘size premium’’ using the methodology developed by Ibbotson Associates for estimating historical returns in excess of CAPM, as described in Ibbotson Associates’ Stock, Bonds, Bills and Inflation 1998 Yearbook. The formula for this adjustment is: d) Size Premium
Size Premium ¼ Portfolio Premium (Portfolio Beta Historical Market Premium) In this formula:
‘‘Portfolio Premium’’ is the actual return over the riskless rate earned by a given portfolio between 1963 and 1997;
‘‘Portfolio Beta’’ is the beta estimated relative to the S&P 500 market portfolio using annual returns between 1963 and 1997; and ‘‘Historical Market Premium’’ is 5.69 percent, or the average return on the S&P 500 universe between 1963 and 1997.
The portfolio beta times the historical market premium gives an indication of the return that would be expected over this period according to the CAPM. For example, Kohler had a five-year average EBITDA of approximately $213 million as of the Valuation Date, putting it into the 10th largest portfolio (out of 25 total portfolios) of companies ranked by average EBITDA in my study. The average premium over the riskless rate for this portfolio from 1963 through 1997 was 7.77 percent, while the beta for this portfolio was 1.06. The Size Premium therefore becomes: Size Premium ¼ 7:77% ð1:06 5:69%Þ ¼ 1:74% I made an adjustment to ‘‘smooth’’ the relationship between size and return using a method similar to that used in calculating premiums over the riskless rate.25 I calculated a ‘‘smoothed premium’’ using regression analysis, which gives a linear relationship between company size (converted into a base-10 logarithm) and the historical size premium in excess of CAPM. In the case of ranking by average EBITDA, this indicates the following relationship: Smoothed Size Premium ¼ 5:668% ð1:383% logðEBITDAÞÞ 23
24 25
A sample of academic research articles include: Rolf Banz, ‘‘The Relationship Between Return and Market Value of Common Stocks,’’ Journal of Financial Economics 9 (1981): 3–18; Fama and French, ‘‘The Cross Section of Expected Stock Returns’’; Kent Daniel and Sheridan Titman, ‘‘Evidence on the Characteristics of Cross Sectional Variation in Stock Returns,’’ Journal of Finance (March 1997). Refer to Section VI, B of this report for a detailed discussion of this study. Ibid.
Required Rates of Return on Equity and Invested Capital
715
The average EBITDA for the 10th portfolio is $237 million, indicating a smoothed premium for Portfolio 10 of 2.38% ¼ 5.668% (1.383% log($237)). In this case, the smoothed premium is similar to the unadjusted premium calculated above. The Size Return/Return Study uses eight criteria to estimate the return of a subject company. I excluded two measures of size that were based on market value, since this would involve circularity in applying the results to the valuation of Kohler. The public equity markets price securities based on earnings, and therefore, I excluded an additional measure, Number of Employees, that is not based on earnings. The measures used included Book Value, Net Income, Total Assets, EBITDA, and Sales. The following chart itemizes the premiums indicated for Kohler according to each of my five measures of size. Based on the above data and analysis, the average small stock premium was calculated to be 2.2 percent.
Book Value of Equity 5-Year Average Net Income Total Assets 5-Year Average EBITDA Sales Average Excess Return Over CAPM—Small Stock Premium
Kohler Result
Applied Portfolio
Excess Return over CAPM
$ 724 69 1,485 213 2,333
10 10 11 10 8
1.81% 2.21% 2.27% 2.38% 2.28% 2.2%
e) Rate of Return on Equity – Indicated Summary Based on the inputs discussed above, the
indicated rate of return on equity for Kohler was computed, as of the Valuation Date, as follows: Rate of Return on Equity ¼ 5.4% þ [5.0% 1.08] þ 2.2% ¼ 13.0%
Rate of Return on Debt The rate of return on debt for Kohler’s business would most likely approximate that for Standard & Poor’s A-rated corporate bonds, which was 6.8 percent as of the Valuation Date. I performed a hypothetical credit analysis for Kohler as of the Valuation Date using calculated ratios based on the historical results of Kohler and benchmarks published in Standard & Poor’s Creditstats. This analysis indicated a hypothetical ‘‘A’’ rating for Kohler. As a result, the expected pre-tax rate of return on debt capital was estimated using S&P’s A-rated corporate bond index yield as a measure of the long-term debt rate for a company similar to Kohler. The after-tax rate of return on debt was estimated by assuming a 40.0 percent blended tax rate. The tax rate was derived based on the Wisconsin state income tax rate of 7.9 percent, adjusted for federal deductibility, and the federal marginal income tax rate of 35.0 percent. Although Kohler operates in other countries and jurisdictions with differing tax rates, Kohler management believed that a long-term blended tax rate of approximately 40.0 percent is a reasonable assumption for the Company. Based on the inputs discussed above, the after-tax rate of return on debt for Kohler was computed, as of the Valuation Date, as follows: After-Tax Rate of Return on Debt Capital ¼ 6.8% (1 40.0%) ¼ 4.1%
716
Cost of Capital
Indicated Rates of Return Based on CAPM Therefore, based on an indicated required return on equity of 13.1 percent, an indicated cost of debt of 4.1 percent, and Kohler’s implied capital structure discussed above, the WACC for Kohler computed by the CAPM was: WACC ¼ ð13:0% 71:6%Þ þ ð41% 28:4%Þ ¼ 9:3% þ 1:2% ¼ 10:5% Based on the CAPM method, the indicated rate of return on equity for Kohler was 13.1 percent as if Kohler stock were publicly traded and the indicated rate of return on invested capital for Kohler was 10.5 percent as of the Valuation Date. SIZE/RETURN STUDY The size of a company is one of the most important risk elements for an investment in a small firm. We conducted a study of the relation between firm size and investor returns using the database of the Center for Research in Securities Prices (‘‘CRSP’’) at the University of Chicago and Standard & Poor’s Compustat Database. The Size/Return Study was initially published in 1996 and has been updated annually since then.26 For this analysis, I used the procedures found in the 1999 study, with data through December 31, 1997. I used the aforementioned Size/Return Study to conduct an analysis of the rate of return on equity for Kohler. In the Size/Return Study, companies were ranked at the beginning of each year (going back to 1963) into 25 groupings (portfolios) based on size. Size breakpoints were established by ranking companies trading on the NYSE. I added American Stock Exchange and NASDAQ companies depending on where they fell in relation to the New York Stock Exchange breakpoints. For each year of my study, I filtered the data to exclude companies that lacked a five-year trading history, that were not profitable over the previous five years, that were highly leveraged, or that had certain other characteristics of poor financial performance in the years prior to forming portfolios. The exclusion of companies based on historical financial performance does not imply any unusual foresight on the part of hypothetical investors in these portfolios. In forming portfolios for a given year, I exclude companies on the basis of performance during previous years, rather than current or future years. For instance, to form portfolios for 1963, I take into account the average net income for the five fiscal years preceding September 1962. I repeat this procedure for each year from 1963 through the latest available year. Traditionally, researchers have used market value of equity as a measure of ‘‘size’’ in conducting historical rate of return research. A company’s market capitalization may be affected by characteristics of the company other than size (for instance, a company with a large asset base may have low market capitalization as a result of high leverage or depressed earnings). I therefore, considered eight alternate additional measures of size in conducting my analyses of the rate of return on equity. The measures include Market Value of Equity, Book Value of Equity, 5-Year Average Net Income, Market Value of Invested Capital, Total Assets, 5-Year Average EBITDA, Net Sales, and Number of Employees.
26
Roger Grabowski and David King, ‘‘New Evidence on Size Effects and Equity Returns,’’ Business Valuation Review (September 1996).
Required Rates of Return on Equity and Invested Capital
717
We calculated an average premium from 1963 through 1997 for each portfolio by subtracting average income returns on long-term U.S. Treasury notes (using data from Ibbotson’s SBBI Yearbook) from the average portfolio return. The result was a clear inverse relationship between size and premium over long-term bond yields. I made an adjustment to ‘‘smooth’’ irregularities in the relationship between size and return using a method similar to that used in calculating premiums over CAPM described earlier in this report. I calculated a ‘‘smoothed premium’’ using regression analysis, which gives a linear relationship between company size (converted into a base-10 logarithm) and the historical arithmetic average premium over the income return on Treasury bonds. In the case to ranking by average EBITDA, this indicates the following relationship: Smoothed Premium ¼ 15:051% ð2:720% logðEBITDAÞÞ For example, Kohler has a 5-year average EBITDA of $213 million, making it most similar to the 10th largest portfolio (out of 25 total portfolios) of companies ranked by average EBITDA in my study. The average EBITDA for the 10th portfolio is $237 million, indicating a smoothed premium for Portfolio 10 of 8.6% ¼ 15.051% (2.720% log($237)). The Size Return/Return Study uses eight criteria to estimate the return of a subject company. I excluded two measures of size that were based on market value, since this would involve circularity in applying the results to the valuation of Kohler. The public equity markets price securities based on earnings, and therefore, I excluded an additional measure, Number of Employees, that is not based on earnings. The measures used included Book Value, Net Income, Total Assets, EBITDA, and Sales. I used the data calculated above to estimate the required return on equity. I identified the portfolio that contained companies whose average size, based upon available data, was most similar to Kohler. An average of the risk premium was calculated. The following chart summarizes the smoothed premiums calculated for Kohler, using the study discussed above, and the resulting average risk premium:
Book Value of Equity 5-Year Average Net Income Total Assets 5-Year Average EBITDA Sales Average Excess Return Over CAPM—Small Stock Premium
Kohler Result
Applied Portfolio
Excess Return over CAPM
$724 69 1,485 213 2,333
10 10 11 10 8
1.81% 2.21% 2.27% 2.38% 2.28% 2.2%
I make a further adjustment to the average premium in order to reconcile the historical data with the forward-looking equity risk premium that I use in the application of the CAPM analysis described above. The average premium relative to Treasury bonds on the S&P 500 portfolio was 5.69 percent during the period covered by the Size/Return Study (1963–1997). However, as discussed above, I estimate a forward-looking premium for U.S. equities to have been approximately 5.0 percent as of early 1998. This means that on a forward-looking basis, investors expected to earn 0.69 percent less than they realized on average over the period 1963–1997. I reduce the indicated equity risk premium to 7.8 percent (that is, the 8.5 percent average less 0.69 percent). The required return was estimated by adding the risk premium for this portfolio to the market yield on long-term Treasury notes as of the Valuation Date. The market yield for long-term Treasury notes, as of the Valuation Date, was 5.4 percent.
718
Cost of Capital
Based on the inputs discussed above, the required return on equity for Kohler, on a stand-alone basis, as indicated by the Size/Return Study, as of the Valuation Date, was calculated as follows: Required Rate of Return on Equity ¼ 5.4% þ 7.8% ¼ 13.2% After determining the appropriate required return on equity based on the size study, as described above, I applied the same after-tax cost of debt and capital structure that was used in the CAPM method to estimate a WACC. I calculated the weighted average cost of capital for Kohler, based on the application of the size study, as follows: WACC ¼ ð13:2% 71:6%Þ þ ð41% 28:4%Þ ¼ 9:5% þ 1:2% ¼ 10:6% Based on the Size/Return Study, the indicated required rate of return on equity for Kohler was 13.2 percent as if Kohler stock were publicly traded and the indicated rate of return on invested capital for Kohler was 10.6 percent as of the Valuation Date. RISK/RETURN STUDY The Risk/Return Study is based on an extension of the Size/Return Study. Instead of ranking companies into portfolios by size, I ranked companies into 25 portfolios based on three alternate measures of financial risk. These measures included the Five-Year Operating Income Margin, the Coefficient of Variation in Operating Income Margin, and the Coefficient of Variation in Return on Book Equity, where Coefficient of Variation is defined as the standard deviation divided by the mean. All three measures used average financial data for the five years preceding the formation of annual portfolios. The first statistic measures profitability and the other two statistics measure the volatility of earnings. The result of the study was a clear relationship between risk and return, whereby higher returns were associated with low profitability and high volatility of earnings. As I did with the Size/Return Study, I used regression analysis to smooth irregularities in the data, creating a linear relationship between average premium and the logarithm (base 10) of the risk statistic for the portfolio. I have used this data to estimate the required return on equity. The following chart summarizes the smoothed premiums calculated for Kohler, using the study discussed above, and the resulting average risk premium: Financial Criteria 5-Year Average Operating Margin Coefficient of Variation – Operating Margin Coefficient of Variation – Return on Equity Calculation of Equity Risk Premium (Average of Smoothed Premiums)
Smoothed Premium 11.1% 9.4% 8.2% 9.6%
As discussed above, the historical return on equities over the period 1963–1997 covered by the Risk/Return Study was about 0.69 percent higher than the expected return as of early 1998. Accordingly, I adjusted the equity risk premium indicated by the Risk/Return Study to 8.9 percent (that is, the 9.6 percent average premium less 0.69 percent, rounded). The required return was estimated by adding the average risk premium calculated above to the market yield on long-term Treasury notes as of the Valuation Date. The market yield for long-term Treasury notes, as of the Valuation Date, was 5.4 percent.
Required Rates of Return on Equity and Invested Capital
719
Based on the inputs discussed above, the required rate of return on equity for Kohler, as indicated by the Risk/Return Study, was calculated as follows: Required Rate of Return on Equity ¼ 5:4% þ 8:9% ¼ 14:3% After determining the appropriate required return on equity based on the Risk/Return Study, as described above, I applied the same after-tax cost of debt and capital structure that was used in the CAPM method to estimate a WACC. I calculated the weighted average cost of capital for Kohler, based on the application of the Risk/Return Study, as follows: WACC ¼ ð14:3% 71:6%Þ þ ð4:1% 28:4%Þ ¼ 10:2% þ 1:2% ¼ 11:4% Based on the Risk/Return Study, the indicated required rate of return on equity for Kohler was 14.3 percent as if Kohler stock were publicly traded and the indicated rate of return on invested capital for Kohler was 11.4 percent as of the Valuation Date. FAMA-FRENCH THREE FACTOR MODEL I also estimated the required rate of return on equity and the WACC for Kohler using an alternative method, the Fama-French Three Factor Model (the ‘‘Fama-French Model’’).27 The Fama-French model was developed in response to the empirical failure of CAPM to fully account for the high returns observed for certain types of companies. These include two types of companies in particular. As mentioned in my discussion of the CAPM, small companies have historically earned higher rates of return than would be predicted by the CAPM (the size effect). Also, companies with a high ratio of book value of equity to market value of equity (sometimes called ‘‘value’’ stocks) have historically earned higher returns than the CAPM would predict. The Fama-French model tries to capture these effects by measuring the sensitivity of a company’s returns to movements in the prices of small companies and ‘‘value’’ companies. The Fama-French Model estimates returns according to the following formula: Ri ¼ RF þ bi ðRM RF Þ þ ðsi SMBÞ þ ðhi HMLÞ where: Ri ¼ expected return on company i Rf ¼ risk-free rate RmRf ¼ expected return on the overall market in excess of the risk-free rate SMB ¼ expected return on a portfolio of small stock relative to a portfolio of big company stocks (‘‘Small minus Big’’) HML ¼ expected return on a portfolio of high book-to-market stocks relative to a portfolio of low book-to-market stocks (‘‘High minus Low’’) bi ¼ measure of the sensitivity of the returns on company i to movements in the overall market 27
Eugene Fama and Kenneth French, ‘‘Common Risk Factors in the Returns on Stocks and Bonds,’’ Journal of Financial Economics (February 1993): 3–56.
720
Cost of Capital
si ¼ measure of the sensitivity of returns on company i stock to movements in the returns of high book-to-market stocks relative to low book-to-market stocks. hi ¼ measure of the sensitivity of returns on company i stock to movements in the returns of high book-to-market stocks relative to low book-to-market stocks. Thus, according to the Fama-French Model, the expected returns consist of a risk-free rate plus three premiums for risk. The first premium reflects sensitivity to movements in the overall stock market. The second premium reflects sensitivity to movements in the prices of small companies relative to big companies, and the third premium reflects sensitivity to movement in the prices of ‘‘value’’ stocks relative to low book-to-market stocks. Thus, it is not a company’s size or ‘‘value’’ status per se that determines whether it has a high or low expected rate of return; rather, a company has a high or low return according to the degree of its sensitivity to movements in the prices of small company stocks (relative to big company stocks) and ‘‘value’’ stocks (relative to low book-to-market stocks), in addition to its sensitivity to the overall market. A source for empirical measures of the Fama-French factors is Ibbotson Associates. Ibbotson Associates estimates the three Fama-French Model coefficients by running a time series multiple regression for comparable companies. The dependent variable is the company’s monthly excess stock returns over Treasury bill returns. The independent variables are 1) the monthly excess return on the S&P 500 index over Treasury Bills; 2) the difference between the monthly return on small-cap stocks and large-cap stocks; and 3) the difference between monthly returns on high book-to-market stocks and low book-to-market stocks. The three coefficients (or ‘‘slope’’ terms) of this regression give empirical estimates of the bi, si, and hi terms in the model. Similar to the CAPM as discussed above, the bi or beta term measures the sensitivity of a stock to movements in the market. The RM RF term is the same Market Risk Premium as I described above when discussing the CAPM, or 5%. The si term measures a company’s sensitivity to the movements in a portfolio of small company stocks relative to a portfolio of big company stocks. The SMB term is the expected premium on a portfolio of small stocks in excess of a portfolio of big stocks. It is measured as the historical rate of return on a portfolio of companies with market capitalization below the median of companies on the NYSE (when ranked by market capitalization) less the historical rate of return earned by a portfolio of companies with above-median market capitalization. The difference between the historical average returns on the small-cap and large-cap portfolios was 3.23% as of the valuation date.28 The SMB premium is computed by multiplying this historical difference by the sensitivity term si, as estimated in the multiple regression. The hi term measures a company’s sensitivity to the movements in a portfolio of high book-tomarket stocks relative to a portfolio of low book-to-market stocks. The HML term is the expected premium on a portfolio of high book-to-market stocks in excess of low book-to-market stocks. It is measured as the historical rate of return on a portfolio of companies whose book-to-market ratio falls above the 70th percentile of companies on the NYSE (when ranked by book-to-market ratio) less the historical rate of return earned by a portfolio of companies whose book-to-market ratios fall below the 30th percentile. The difference between the historical average returns on the high book-to-market and low book-to-market portfolios was 4.98% as of the valuation date valuation date.29 The HML premium is computed by multiplying this historical difference by the sensitivity term hi, as estimated in the multiple regression.
28 29
Ibbotson Associates, Beta Book, Second Edition 1998. Ibid.
Required Rates of Return on Equity and Invested Capital
721
I compiled the betas, SMB Premium (si * SMB), and HML (hi * HML) Premium from Ibbotson Associates’ Beta Book, Second Edition 1998, for each comparable company considered in the Market Approach. Betas, SMB Premiums, and HML Premiums compiled from Ibbotson Associates are ‘‘levered,’’ i.e., they incorporate the added risk to a stockholder due to the debt financing of the specific company. To remove the effects of differing capital structures, the beta, SMB Premium, and HML Premium of the guideline companies must first be unlevered. The unlevering and relevering is accomplished by employing the following equations: Unlevered Beta ¼
Levered Beta 1 þ ½ð1 Tax RateÞ Debt=Equity
Unlevered SMB Premium ¼
Levered SMB Premium 1 þ ½ð1 Tax RateÞ Debt=Equity
Unlevered HML Premium ¼
Levered HML Premium 1 þ ½ð1 Tax RateÞ Debt=Equity
I calculated unlevered betas, unlevered SMB premiums, and unlevered HML premiums of the comparable companies considered in the Market Approach. I excluded from the analysis companies for which this data was unavailable. I concluded on the following estimates:
Business Unit Kitchen & Bath Group Power Systems Group Interiors Group Hospitality Group
Unlevered Beta
Unlevered SMB Premium
Unlevered HML Premium
0.65 0.63 0.99 0.44
0.60% 1.67% 1.79% 1.41%
1.76% 1.03% 0.81% 1.95%
To arrive at the unlevered beta, SMB Premium, and HML Premium for Kohler on a consolidated basis, I weighted the indicated factors for each business unit (as displayed above) by the business unit’s EBITDA as a percent of overall Kohler EBITDA during the twelve months ended August 31, 1998. I estimated the weighted unlevered beta, SMB Premium, and HML Premium to be 0.66, 0.86%, and 1.60%, respectively. To derive a beta, SMB Premium, and HML Premium applicable to Kohler, this unlevered data must be relevered to reflect Kohler’s implied capital structure, as explained above in the discussion of CAPM. The relevering is accomplished by employing the following equations: Relevered Beta ¼ Unlevered Beta ½ð1 Tax RateÞ Debt=Equity Relevered SMB Premium ¼ Unlevered SMB Premium ½ð1 Tax RateÞ Debt=Equity Relevered HML Premium ¼ Unlevered HML Premium ½ð1 Tax RateÞ Debt=Equity My estimate of the typical capital structure was based on Kohler’s implied proportions of interestbearing debt and common equity value, as discussed above in the discussion of CAPM. Based on Kohler’s implied capital structure of 28.4 percent debt capital and 71.6 percent equity capital, I have concluded on a levered beta, levered SMB Premium, and levered HML Premium of 0.82, 1.06%, and 1.98%, respectively.
722
Cost of Capital
The Fama-French rate of return on equity is calculated as follows: KE ¼ RF þ b ðRM RF Þ þ SMB Premium þ HML Premium where: KE ¼ Rate of return on equity capital RF ¼ Risk-free rate of return b ¼ Beta or systematic risk for this type of equity investment RMRF ¼ Market risk premium; the expected return on a broad portfolio of stocks in the market (RM) less the risk-free rate (RF) SMB Premium ¼ The return premium that companies with small market capitalization experience relative to large capitalization companies HML Premium ¼ The return that investors expect from high book equity to market equity ratio companies. Based on the inputs discussed above, the required return on equity for Kohler was computed, as follows: Required Rate of Return on Equity ¼ 5:4% þ ½ð0:82 5:0%Þ þ 1:06% þ 1:98% ¼ 12:6% After determining the appropriate required return on equity based on the Fama-French Model, as described above, I applied the same after-tax rate of return on debt and capital structure that was used in the CAPM method to estimate a WACC. I calculated the WACC for Kohler, based on the application of the Fama-French Model, as follows: WACC ¼ ð12:6% 71:6%Þ þ ð4:1% 28:4%Þ ¼ 9:0% þ 1:2% ¼ 10:2% Based on the Fama-French Model, the indicated rate of return on equity for Kohler was 12.6 percent as if Kohler stock were publicly traded and the indicated rate of return on invested capital was 10.2 percent as of the Valuation Date.
DURATION ADJUSTED CAPM The required rates of return discussed above are derived from returns to publicly traded stock and are the appropriate required returns for an investment on an as-if publicly traded basis. But Kohler stock is not publicly traded. I therefore adjusted the concluded required rate of return on equity to incorporate a discount for lack of marketability appropriate for the Estate Stock. I performed an analysis of an additional premium to the rate of return based on the duration of an investment in Kohler relative to the average duration of public equity markets. Duration represents an investor’s expectation of the average amount of time that will pass before receiving the cash flows from the investment. It is defined as the sum of present value, time weighted cash flows divided by the total present value of cash flows. The larger the duration, the longer the investor expects to wait for payment of cash flows on average. When the investment is illiquid during this waiting period, the investor will require an additional return on the investment for this added risk. Amihud and
Required Rates of Return on Equity and Invested Capital
723
Mendelson confirm this principle in their article, ‘‘Liquidity, Asset Prices and Financial Policy’’: ‘‘Liquidity is an important factor in asset pricing. For both stocks and bonds, the lower the liquidity of an asset (that is, the higher the cost of trading it), the higher the return it is expected to yield.’’30 I examined the duration of an investment in Kohler under two scenarios—a scenario under which an investor expects to receive only dividends, and a scenario under which the investor takes into consideration the possibility of an IPO or private sale of Kohler. The cash flows analyzed under these scenarios correspond with the Discounted Dividend Method and Adjusted Discounted Dividend Method. I applied the results of a study that attempts to quantify the additional required return related to increased duration in an equity investment to determine required rates of return based on the duration of an investment in Kohler under these two scenarios.31 The resulting required rates of return were 18.0 percent and 14.0 percent for the Discounted Dividend Method and the Adjusted Discounted Dividend Method, respectively. Since I consider the Adjusted Discounted Dividend Method to be the most accurate representation of the value of an investment in Kohler, I concluded that the corresponding rate of return of 14.0 percent was the most appropriate in estimating a required rate of return for Kohler that reflects a lack of marketability. The increase in required rate of return from 13.0 percent to 14.0 percent causes a decrease of approximately 35 percent in the value indicated by the Adjusted Dividend Discount Model. The size of this discount is due to the relatively long duration of an investment in Kohler. The higher the duration of an investment, the longer the investor expects to wait to receive cash flows. When the discount rate is increased, the value of an investment with a long duration will decrease at a faster rate than one with a shorter duration. For example, assume an investor holds two investments; one will pay a return of $1000 ten years in the future, and the other will pay a return of $1000 thirty years in the future. The first investment has a duration of ten years and the second has a duration of thirty years. At a 10% required rate of return, the first investment has a value of [$1000=(1 þ 10%)^10] ¼ $386, and the second investment has a value of [$1000/(1 þ 10%)^30] ¼ $57. Increasing this required rate of return to 15% results in a decrease in value of the first investment to [$1000/ (1 þ 15%)^10] ¼ $247 and a decrease in value of the second investment to [$1000/ (1 þ 15%)^30] ¼ $15. Note that this represents a discount of [($386 $247)/$386] ¼ 36 percent for the first investment, but a discount of [($57 $15)/$57] ¼ 74 percent for the second investment. The second investment, with a higher duration, is much more sensitive to an increase in discount rate than the first investment. This explains why an investment in Kohler, with a relatively high duration, is sensitive to an increase in the discount rate (required rate of return). CONCLUDED RATES OF RETURN In concluding on the appropriate required rate of return on equity and WACC to apply in my analysis, I considered each methodology to be relevant methodologies to indicate rates of return for Kohler as of the Valuation Date. Refer to Exhibit D.1 for details leading to my concluded rates of return. The indicated required return on equity and WACC from the application of the methodologies discussed above resulted in similar indications in a tight range. Therefore, I equally weighted each 30
31
Yakov Amihud and Haim Mendelson, ‘‘Liquidity, Asset Prices and Financial Policy,’’ Financial Analysts Journal (November– December 1991): 56. Patricia M. Dechow, Richard G. Sloan, and Mark T. Soliman, ‘‘Implied Equity Duration: A New Measure of Equity Risk,’’ Social Science Research Network Electronic Paper Collection (June 2001).
724 Exhibit IV.1
Cost of Capital Concluded Discount Rates
Methodology
Indicated Rate of Return on Equity
Kohler Company Capital Structure Capital Asset Pricing Model CVC Size/Return Study CVC Risk/Return Study Fama-French Model Projected Returns Average Conclusion—As if Publicly Traded
13.0% 13.2% 14.3% 12.6% 13.3% 13.0%
Discount Rate with Illiquidity Adjustment Conclusion—Adjusted for Lack of Ready Marketability
14.0% to 18.0% 14.0%
Indicated WACC 10.5% 10.6% 11.4% 10.2% 10.7% 10.7%
methodology and concluded on a required return on equity and a WACC by taking the average of the indicated required rates of return on equity and WACCs from each methodology. As discussed above, I also calculated a required rate of return on the equity of Kohler that incorporated an additional discount for lack of marketability and illiquidity. Per William Silber, ‘‘That credit-worthy companies must offer price discounts of more than 30 percent to sell a significant block of restricted stock illustrate the importance of liquidity to the valuation of common stock.’’32 Based on the above analyses, the estimated required rate of return on equity and WACC for Kohler as if Kohler stock were publicly traded, as of the Valuation Date, were calculated as in exhibit IV.1.
32
Silber, ‘‘Discounts on Restricted Stock,’’ 60.
Appendix V
Developing Cost of Capital (Capitalization Rates and Discount Rates) Using ValuSource Valuation Software Z. Christopher Mercer Edited by David Fein Introduction Cost of Capital, Discount Rates, and Capitalization Rates Data for the (Adjusted) Capital Asset Pricing Model Earnings Stream to Be Capitalized Application of Marketability Discounts
INTRODUCTION ValuSource’s current line of valuation applications, including ValuSource PRO, BVM Pro, and Express Business Valuation, were introduced in their current form in late 1996. This appendix should be helpful to users of ValuSource PRO, BVM Pro, and Express Business Valuation software. The discussion is framed in the context of the development of capitalization rates in the ‘‘Appraisal’’ section of the software package.
COST OF CAPITAL, DISCOUNT RATES, AND CAPITALIZATION RATES This book has discussed several sources of cost of capital data:
Morningstar publishes the Stocks, Bonds, Bills and Inflation (SBBI) Classic Edition and Valuation Edition Yearbooks annually as well as the other publications, including the Cost of Capital Yearbook and the Beta Book.1
Roger Grabowski and David King also have done interesting work on the impact of size on historical rates of return in the public stock markets. This work has been published partially in Business Valuation Review and has been discussed in Business Valuation Update1.2 Their work is updated annually and is currently published as the Duff & Phelps Risk Premium Report.
1
Stocks, Bonds, Bills and Inflation, Classic Edition and Valuation Edition, published annually; Cost of Capital Yearbook, published annually with quarterly updates; and Beta Book, published semiannually. Chicago: Morningstar. Roger Grabowski and David King, ‘‘Size Effects and Equity Returns, An Update,’’ Business Valuation Review (March 1997): 22–26. Discussed in Shannon Pratt’s Business Valuation Update1 (August 1997): 1.
2
725
726
Cost of Capital
Others, such as Michael Julius, have analyzed the Morningstar historical data to address the question of whether the arithmetic mean, the geometric mean, or some other statistic should be used as the basis for equity premia.3 Please refer to Chapter 9 for a complete discussion of the current research on the equity risk premia.
There is nothing magical about any of these studies. All are attempting to measure the historical returns generated in the public stock markets for differing groups of stocks. The SBBI Yearbooks, portions of the Cost of Capital Yearbook, and the Duff & Phelps Risk Premium Report focus on market returns and stratify the public markets by various measures of size (sales, market capitalization, etc.). The major portion of the Cost of Capital Yearbook focuses on stratifying the public markets by Standard Industrial Classification (SIC) codes. Given the background of this book, we can focus briefly on the Capital Asset Pricing Model (CAPM) to derive some guidance on how to develop capitalization rates (i.e., cost of capital) using ValuSource valuation software.
DATA FOR THE (ADJUSTED) CAPITAL ASSET PRICING MODEL A number of chapters have discussed the so-called build-up method for developing capitalization rates and CAPM. In my opinion, the basic build-up method is simply a variation of CAPM under the assumption that beta is equal to 1.0. In the absence of market evidence to the contrary, business appraisers sometimes assume that the appropriate assumption for beta is 1.0, or the expected volatility of the broader stock market, which forms the first building block of the ‘‘build-up’’ of an equity discount rate and reflects the long-run historical premium in returns of the broader market over longterm Treasuries. In years prior to 1994, this premium was referred to in the Morningstar SBBI Yearbooks as the common stock premium. Since then it has been renamed the large company stock premium. Too often, some appraisers and writers try to make an arbitrary distinction between the build-up method and the CAPM. But, clearly, the former is a special instance of the latter with beta equal to 1.0. Users of ValuSource software have to be aware of this assumption each time they decide to use the build-up method. Many business appraisers and other financial analysts have used the historical premium return analysis presented in each year’s SBBI Yearbook. In recent years, that information has come from Table 2.1 in each SBBI Yearbook. Appraisers typically have used the current year’s analysis (e.g., the SBBI 2001 Yearbook, which covers Morningstar’s analysis of historical return information from 1926 to 2000). Historical appraisals typically reference the cumulative premium data from the then-current 3
J. Michael Julius, ‘‘Market Returns in Rolling Multi-Year Holding Periods: An Alternative Interpretation of the Ibbotson Data,’’ Business Valuation Review (June 1996): 57–71. There has been something of a controversy over whether the more appropriate average statistics from Morningstar’s SBBI Yearbook is the arithmetic mean or the geometric mean. At its simplest, the Julius analysis recognizes that the arithmetic mean of the Morningstar return data from 1926 to 1997 is the arithmetic mean (average) of 71 annual returns. The annual returns are the geometric means of the annual observations. So the arithmetic mean advanced by Morningstar is the arithmetic mean of 71 annual (geometric) returns, reflecting 71 one-year holding periods. The geometric mean advanced by others is simply the compound growth rate in total return from 1926 to 1997, or the geometric mean return for the period, which represents a single, 71-year holding period. From a practical viewpoint, neither extreme makes logical sense (and I am oversimplifying complex logical arguments to be practical). The Julius analysis examines the arithmetic mean of geometric returns for multiyear holding periods that have occurred from 1926 to 1995 (in the cited article). The effect of this averaging process over many multiyear holding periods is to develop a series of average returns for more reasonable holding periods such as, say, five or 10 years. The result, incidentally, is effectively to split the difference between the arithmetic mean and the geometric mean as calculated by Morningstar. We have used this analysis for years as a basis for determining the appropriate common stock and small stock premium return measures.
Data for the (Adjusted) Capital Asset Pricing Model Exhibit E.1
727
Calculating Build-up or CAPM Discount and Capitalization Rates Appraiser Decision Letters
Appraiser Decision Numbers 1 2 3 Calc 4 Calc 5 6 Calc 7 Calc Calc Calc
ACAPM Component Risk-free rate of return Equity risk premium Industry beta ¼ Beta-adjusted common stock premium þ Risk adjustment for size ¼ Base equity discount rate þ Company-specific premium þ Cash flow to earning conversion ¼ Net earnings discount rate (cost of equity capital) Sustainable growth ¼ Base capitalization rate for next year* Base capitalization rate for current year* Base capitalization factor*
A SBBI 1997 Yearbook Arithmetic Mean
B SBBI 1997 Yearbook Geometric Mean
C Julius Multi-year Holding Period Analysis
6.5% 7.3% 1.0
6.5% 5.6% 1.0
6.5% 6.5% 1.0
7.3% 5.0% 18.8% 3.0% 0.0%
5.6% 1.9% 14.0% 3.0% 0.0%
6.5% 3.5% 16.5% 3.0% 0.0%
21.8% 5.0%
17.0% 5.0%
19.5% 5.0%
17.0%
12.0%
15.0%
16.2% 5.88
11.4% 8.33
14.3% 6.67
Note: Boldfaced items require market evidence and appraiser judgments, italicized items require specific appraiser judgments Calc ¼ calculated by software. *User options. User selects desired factor. Source: Data compiled from Michael J. Julius, ‘‘Market Returns in Rolling Multi-Year Holding Periods, An Alternative Interpretation of the Ibbotson Data,’’ Business Valuation Review (June 1996): 57–71, published by the Business Valuation Committee of the American Society of Appraisers. Reprinted with permission.
SBBI Yearbook. The actual historical geometric and arithmetic mean returns for the cumulative periods are provided for large-company stocks, small-company stocks, and long-term government bonds, and the actual premiums are calculated:
Large-company stock premium returns in excess of long-term government bond returns
Small-company stock premium returns in excess of large-company stock returns Small-company stock premium in excess of long-term government bond returns
Appraisers often use the current numbers for the appropriate premia in building up discount rates. Users selecting the Capital Asset Pricing Model in ValuSource software will find a screen providing the various components of a capitalization rate (or factor). An illustrative example is shown in Exhibit E.1. The figures for the arithmetic mean and the geometric mean returns come from the SBBI 1997 Yearbook, and the figures labeled ‘‘Julius Multi-Year Holding Period Analysis’’ are derived from the article referenced in note 5. The CAPM components in the exhibit are called ACAPM components, for the Adjusted Capital Asset Pricing Model. I have referred to this model as the adjusted CAPM because the basic CAPM
728
Cost of Capital
stops at the net cash flow or net earnings discount rate and, in the process, assumes that companyspecific (nonsystematic) factors are ‘‘diversified away.’’ The ACAPM incorporates company-specific risk factors. Any user of ValuSource software should recognize from Exhibit E.1 that neither software nor any single publication will enable the appraiser to develop an appropriate net equity discount rate or capitalization rate without the exercise of considerable judgment and the review and understanding of numerous sources of direct or indirect market evidence. With all assumptions remaining the same in Exhibit E.1 except the selection of the arithmetic mean or geometric mean returns, a spread in implied base capitalization rates (CR) is developed, ranging from 12.0% to 17.0%. To put this in perspective by converting these capitalization rates into price/earnings multiples (P/E ¼ 1/CR), the arithmetic mean selection developed a net earnings multiple of 5.88 and the geometric mean selection developed a multiple of 8.33, or some 42% greater. The use of the Julius multiyear holding period analysis produces a price/earnings multiple of 6.67, which is higher than that developed using the arithmetic mean but closer to that result than to the multiple derived using the geometric mean. My best advice to any appraiser, whether using ValuSource valuation software or not, is to be very clear at each of the numbered decision points (noted in Exhibit E.1) about what market data are being used and why. Furthermore, appraisers should be clear about the assumptions made regarding the lettered decision points in the exhibit as well. Appraisers referring to the SBBI Yearbooks will develop components for the common stock equity premium, the appropriate beta, if applicable, and the small-stock premium. Those referring to the Duff & Phelps Risk Premium Report analyses may have to calculate the implied size premium in relationship to the base equity premiums initially used. The point is that at numbered decision 4, the net size adjustment is developed by subtracting a total premium over Treasuries implied by Risk Premium Report from the common stock premium used in the analysis. In addition, appraisers may make a judgmental adjustment for size in addition to any developed using the SBBI Yearbook, Risk Premium Report, or anyone else—if their subject companies are substantially smaller than the public companies used as reference points. In the ValuSource valuation software, size premia are best considered in the ‘‘Risk Adjustment for Size’’ line. Appraisers using other than a so-called standard small-stock premium from Morningstar should explain in their reports exactly how their size premia were developed. Note that some appraisers have considered very small size as a company-specific risk factor. There is nothing conceptually wrong with this treatment; however, before doing so, they should be familiar with current research on size premia or run the possible risk of being viewed as arbitrary. The company-specific premium is an integral part of the development of the cost of equity capital. A breakout of several possible factors to consider in developing this premium is provided in the software. There is no market evidence to help the appraiser deal with most of these factors, and judgment must be carefully exercised.4 ValuSource valuation software provides a line called ‘‘Cash Flow to Earnings Conversion.’’ Shannon Pratt has indicated that he believes that the CAPM (or ACAPM) discount rate is applicable to the net cash flow of a business enterprise. I have suggested that it may be applicable to the net income of the enterprise. In Valuing Financial Institutions, I prepared an analysis indicating a methodology for developing a conversion of a net cash flow discount rate to a net income discount rate and suggested that for many private companies, the differential might not be large.5 This analysis was also turned 4
5
As the appraisal profession matures, various appraisers are creatively examining the public stock markets for guidance on fundamental issues like developing company-specific risk premiums. An article typifies these efforts: Steven Bolten and Yan Wang, ‘‘The Impact of Management Depth on Valuation,’’ Business Valuation Review (September 1997): 143–146. See Mercer, Valuing Financial Institutions, Exhibit 14.7, 262–266.
Earnings Stream to Be Capitalized
729
into an article that was published in the Business Valuation Review.6 Certainly in the very long run, the net cash flow of an enterprise will approximate its net income. In any event, appraisers should be clear in their own minds what they believe on this issue and why, and then develop their remaining judgments consistently from this vantage point. At this point, we have conceptually developed a net cash flow or net earnings discount rate. This discount rate is the equity cost of capital. This discount rate would be applicable to projected net earnings in a discounted future earnings analysis (or, properly styled or adjusted, to the projected net cash flows in a discounted cash flow analysis). However, many appraisals are prepared without specific projections. To develop a single-period capitalization rate, expected future earnings growth must be subtracted from the discount rate (for all the reasons explained earlier in this book).
EARNINGS STREAM TO BE CAPITALIZED It should be fairly obvious that the discount rate or capitalization rate applied to any measure of earnings should be appropriately developed for that measure, whether net income, pretax income, debtfree pretax income, or another level of the income statement. The CAPM discount rate discussed here and elsewhere in this book is generally considered applicable to either the net income or the net cash flow of a business enterprise. In application in actual appraisals, however, a legitimate question can be raised: To what net income or cash flow does the discount rate apply? There has been considerable discussion in recent years regarding whether discounted future earnings (DFE) or discounted cash flow (DCF) valuation methods develop minority interest or controlling interest indications of value. A detailed discussion of the concept of levels of value is discussed elsewhere in this book; however, the question deserves some treatment.7 The two major trains of thought are: 1. Since the CAPM discount rate is applicable to the net income of a business enterprise, and since this discount rate generally is believed to develop value indications at the marketable minority interest level of value, the value indication from a discounted future cash flow or earnings valuation is a minority interest (marketable) conclusion. As a result, it would be proper to apply a control premium to this value indication if a controlling interest conclusion is called for in the appraisal.8 2. Since appraisers make so-called control adjustments in developing their projections for DFE or DCF methods, the income stream is said to be control-adjusted, and the resulting valuation indication is at the controlling interest level.9 According to the first argument, buyers of companies might appear to have different discount rates than hypothetical investors at the marketable minority interest level. According to the second argument, there is only one discount rate, and it is the same for appraisers at the marketable minority interest level and for acquirers at the controlling interest level.
6
7 8 9
Z. Christopher Mercer, ‘‘Adjusted Capitalization Rates for the Difference between Net Income and Net Free Cash Flow,’’ Business Valuation Review (December 1992): 201–207. See Mercer, Quantifying Marketability Discounts, Revised Reprint, Chapter 1. See Estate of Jung v. Commissioner for a discussion of this argument, 101 T.C. 412 (U.S. Tax Ct. 1993). See Chapter 19 of this book, written by Michael W. Barad and Tara McDowell and edited by James Harrington of Morningstar, for elements of this argument.
730
Cost of Capital
According to the first argument, one would add an appropriate control premium to a DCF/DFE valuation method to arrive at a controlling interest level of value. According to the second argument, a control premium might not be appropriate. As is often the case, the truth may lie somewhere in between. To begin to resolve the controversy, we can divide the so-called control adjustments into their two primary component parts: 1. Normalizing adjustments. In developing capitalization rates using data from SBBI Yearbook, Risk Premium Report, or any other source of market return information, there are implicit ‘‘market baskets’’ of publicly traded companies that constitute the basis of comparison with subject private companies. We know that the typical public company in a group is larger than many of the closely held businesses that appraisers value, and this size differential gives rise to premium required returns. We also know, generally, that public companies must pay competitive salaries to senior management or else run the risk of being penalized in their market capitalizations. Likewise, related party transactions, to the extent that they exist, must be conducted at arm’s length, and nonworking members of the president’s family are not normally found on the payroll of public companies. The point is that a significant portion of the control adjustments made in many appraisals are, in reality, adjustments to normalize the earnings of the subject company with the group of public companies with which it is implicitly being compared. 2. Acquirer’s potential economic (control) adjustments. Logically, an acquirer would make the normalizing adjustments noted earlier in the context of an acquisition of a private company. Clearly, an owner is not going to be paid for the capitalized value of excess salary and then continue to receive that salary. However, acquirers look at acquisition prospects differently from public market securities investors. Acquirers often have an opportunity to generate economic benefits from acquisitions that go beyond the normalizing adjustments noted earlier. For example, an acquirer in a similar business may be able to generate significant economies by stripping out general and administrative or selling expenses from the acquired entity. Alternatively, an acquirer may be able to generate economic benefits that are not readily visible on a private company’s financial statements. For example, an acquirer may be willing to pay a premium for a business because of planned increased sales of existing products through the acquired company’s sales force. These types of potential economic benefits (adjustments) may generate the willingness to pay an apparent control premium for a company that otherwise might not be immediately justified. The example in Exhibit E.2 illustrates a delineation of potential valuation adjustments into those categorized as normalizing (Line 2) and those noted as economic (control) adjustments made by a potential acquirer of control (Line 3). In most appraisals, the adjustments made normally fall into the category of normalizing adjustments. The analysis in Exhibit E.2 indicates that it is not at all inconsistent to suggest that the discount rates are the same for the potential buyer of a company as for the hypothetical willing buyer of a marketable minority interest. (See Line 7, where the same price/earnings multiple and, implicitly, discount rate, is applied to differing perceptions of a subject company’s earnings.) This would suggest, however, that the economic benefits of control have not yet been factored into the appraisal process at the marketable minority interest level, and that a control premium may be necessary to reach a proper conclusion of value on a controlling interest basis (see Line 10, where the implied control premium is 20%). In the alternative, the appraiser would estimate these economic benefits specifically and capitalize them to develop a controlling interest conclusion. In the example in Exhibit E.2, the control premium provides a vehicle to estimate the magnitude of the benefit of potential economic (control) adjustments and to reflect them in the appraisal.
Application of Marketability Discounts Exhibit E.2
731
Calculating Indicated Values
Line
Item
As Reported
1 2 3 4 5 6 7 8 9
Reported pretax earnings þ Normalized adjustment (owner compensation) þ Acquirer’s economic adjustments ¼ Adjusted pretax income Taxes@ assumed rate of 40% ¼ Adjusted net income Net income capitalization factor (1/cap rate ¼ P/E) ¼ Indicated value Indicated level of value
$1,000 – – 1,000 (400) 600
10
Implied control premium over marketable minority value indication Apparent net multiple without economic adjustments
11
Appraiser’s Normalizing Adjustments $1,000 200 – 1,200 (480) 720 6.67 $4,802 Marketable, minority
Acquirer’s Economic (Control) Adjustments $1,000 200 240 1,440 (576) 864 6.67 $5,763 Control 20% 8
For users of ValuSource valuation software, the message is clear. Be sure to understand what adjustments have been made in an appraisal. To the extent that the normalizing adjustments of an appraisal do not consider the potential economic benefits available to potential acquirers, a judgmental control premium may be appropriate. The software makes this option readily available. That control premium, however, should be justified by a separate analysis or discussion of the potential factors leading to the apparent additional value attributable to control relative to the initially derived discount rate.
APPLICATION OF MARKETABILITY DISCOUNTS Earlier in this book it was suggested that the marketability discount can be considered a premium to the equity cost of capital. Conceptually, this is correct; however, such a consideration would make the implicit assumption that the cash flows from which the initial marketable minority interest value indication is derived are the same as those available to the prospective holder of nonmarketable minority interests of private companies, which is clearly not the case in many closely held businesses. For this reason, among others, we have developed a Quantitative Marketability Discount Model (QMDM), which develops appropriate marketability discounts based on the facts and circumstances facing hypothetical willing buyers of a company’s minority interests.10 Unless the expected cash flows available to a hypothetical minority investor are the same as those that formed the basis for developing the marketable minority interest value indication (a very rare circumstance), it is preferable to develop a marketability discount analysis separate from the initial development of the equity cost of capital (i.e., the capitalization factor). ValuSource offers the QMDM in a CD-ROM format. The resultant discounts from this CD-ROM product can be incorporated into all of ValuSource valuation software.11
10 11
See Mercer, Quantifying Marketability Discount, Revised Reprint, Chapter 8. Z. Christopher Mercer, ‘‘Quantifying Marketability Discount Modeling,’’ Wiley ValuSource (software), 1-800-825-8763.
Appendix VI
Review of Statistical Analysis Mark W. Shirley Introduction Population and Sample Distributions Symmetrical Distribution Bimodal Distribution Skewed (Asymmetrical Unimodal) Distribution Measures of Central Tendency Mean Davies’ Coefficient of Skewness Median Mode Measures of Variability (Dispersion) Deviation about the Mean Variance Standard Deviation Logarithmic Standard Deviation Percentiles Quintiles and Deciles Interquartile Range Range Normal Probability Distribution Properties of Continuous Distribution Tabulating Areas of the Normal Probability Distribution Interpreting Individual Measurements z-score Requirements to Use z Distribution Tables Using z Distribution Tables Student’s t-Test Applying t Distribution Tables Relationship between Two Sets of Measures Regression Correlation Coefficients Coefficient of Determination Event Relationships Presentation of Event Relationships Conditional Probability Bayes’ Theorem Laws of Probability Proportionate Law Law of Averages Addition Law Multiplication Law
733
734
Cost of Capital
Sampling Random Sampling Sample Size Stratified Random Sampling Other Sampling Methods Data Acquisition Errors Elimination of Outlier Values Random and Systematic Error Sampling Distribution Sampling Variability Central Limit Theorem Summary Statistical Terms Summary of Microsoft Excel Statistical Formulas Measure of Central Tendency Measure of Population Variability Measure of Sample Variability Binomial Probabilities Normal Probabilities Critical Values of z and t Critical Values for Binomial Functions t Test Functions Critical Values of F F Test Function Correlation Functions Critical Values of X2 (Chi Square) X2 Test Function Excel Analysis Toolpak Solver Add-In Additional Reading
INTRODUCTION The discipline of business valuation has historically been represented as more art than science. If the art of business valuation is rooted in professional judgment and deductive reasoning, then the science of business valuation is statistics. Because this book discusses statistical concepts, we thought it would be useful to include a source for a review of statistical methods and terminology. To understand the appropriate uses and limitations of numeric data, we must first define the term statistics. According to W. Allan Wallis—economist, statistician, past dean of the University of Chicago School of Business, under-secretary of state for economic affairs, and former president and chancellor of the University of Rochester: Statistics may be defined as a body of methods for making wise decisions in the face of uncertainty.
The discipline of business valuation is characterized by the quantification of uncertainty. Statistics is a branch of mathematics concerned with the collection of data involving the number of occurrences, the analysis of the data, and the presentation of conclusions based on the analysis. Descriptive statistics consists of procedures used to summarize and describe the important characteristics of a set of measurements. . . . Inferential statistics consists of procedures used to make
Population and Sample Distribution
735
inferences about population characteristics from information contained in a sample drawn from that population.1
An inference is a statistical estimate used to solve a particular problem and relates to the degree of probability of a thing being true or that a particular event will occur. Statistics provides a logical framework from which to make relevant and reliable inferences about groups based on incomplete or limited information.
POPULATION AND SAMPLE DISTRIBUTION According to Raymond C. Miles, technical director of the Institute of Business Appraisers: [V]alue is a range or even a probability distribution.
Assembled numeric data from a variety of sources is integral to the discipline of business valuation. The number of surveys, studies, and samples increases annually. These assemblages of data share a single and fundamental characteristic: Each represents a distribution of a population or sample. It is essential for the practitioner to understand the nature of data distributions to provide a foundation for interpreting the assembled data. This review of statistics begins with a discussion of the characteristics of numeric data. In the nomenclature of statistics, data are classified by the numeric descriptions of distributions and their geometric shape. Statistical data are generally classified as either parameter or statistic. Parameter refers to the population, the collection of all elements of interest in a particular study. The fundamental numeric descriptions of population data includes:
Population mean
Population deviation
Population variance Population standard deviation
Statistic is a numeric characteristic of a random sample of the population data and includes:
Sample mean
Sample deviation Sample variance
Sample standard deviation Generally, three basic geometric shapes characterize distributions of numeric data:
1. Symmetrical distribution 2. Bimodal distribution 3. Skewed distribution SYMMETRICAL DISTRIBUTION The most commonly used symmetrical distribution is the normal distribution (or bell curve), a unimodal distribution consisting of a mound shape with mirror-image halves. This is the 1
William Mendenhall, Robert J. Beaver, and Barbara M. Beaver. Introduction to Probability & Statistics, 11th ed. (Belmont, CA: Thomson, Brooks/Cole, 2003), 3.
736
Exhibit VI.1
Cost of Capital
Normal Distribution
fundamental distribution for deriving statistical inferences. The symmetrical construct provides for predictable relationships between the data points and areas under the curve. The location of the measures of central tendency, in a normal distribution, are approximately equal (e.g., mean ¼ mode ¼ median). The mean is the average value of the distribution, the mode is the value which occurs with greatest frequency, and the median is the value which is the middle value in the distribution. The convergence of the measures of central tendency provides a curve with a symmetrical shape. Half of the values of the distribution occur above and half below the mean, as shown in Exhibit VI.1.
BIMODAL DISTRIBUTION A bimodal distribution is characterized by two ‘‘modes,’’ or mounds, as shown in Exhibit VI.2. Distributions of data are not always symmetrical or unimodal (as is the normal distribution). SKEWED (ASYMMETRICAL UNIMODAL) DISTRIBUTION When the measures of central tendency do not converge on a single value, the distribution is asymmetrical. Asymmetrical distributions are defined by the direction of the skewness and generally are classified as either negatively or positively skewed. Positively skewed distributions (see Exhibit VI.3) are characterized by values of greatest frequency occurring to the left. The geometric shape of a positively skewed distribution is referred to as skewed to the right.
Exhibit VI.2
Bimodal Distribution
Population and Sample Distribution
737
Mean Median Mode
Exhibit VI.3 Positively Skewed Distribution
Negatively skewed distributions (see Exhibit VI.4) are characterized by values of greatest frequency occurring to the right. The geometric shape of a negatively skewed distribution is referred to as skewed to the left. The location of the measures of central tendencies determines the geometric shape, symmetrical or asymmetrical, of a distribution. The relative asymmetry (skew) of a distribution is indicated by the interval between the measures of central tendency.
Mode Median Mean
Exhibit VI.4 Negatively Skewed Distribution
738
Cost of Capital
Location of Measures of Central Tendency Normal distribution: Mean ¼ Median ¼ Mode Negatively skewed distribution: Mode > Median > Mean Positively skewed distribution: Mean > Median > Mode
MEASURES OF CENTRAL TENDENCY In any group, population, or sample, the measurements of individual items will vary through the range. A single numeric reference is required that fairly represents the entire group. There is a distinct difference between a value that fairly represents a data set and a value that is a reliable predictor of an uncertain value. Measures of central tendency are generally classified as the mean, median, or mode. Each expression of central tendency has a specific function within applied statistics. MEAN There are four methods of summarizing the data and quantifying the mean of the distribution: arithmetic mean, harmonic mean, logarithmic mean, and geometric mean. Arithmetic Mean The arithmetic mean is the best estimate for making inferences about the parent group from a sample when the distribution is approximately symmetrical or moderately asymmetrical and where the data is in units of an equi-intervaled scale. Data characterized as equi-intervaled scales refers to data that are measured in increasing numerical values (e.g., quantitative data). The arithmetic mean is the least accurate indicator of central tendency when the distribution is extremely asymmetrical and consists of units or measures (scales) that are not equi-intervaled. Examples of unequi-intervaled are qualitative data. Arithmetic mean (M, m, m, x): X xi =n Arithmetic mean ¼ ðx1 þ x2 þ x3 þ xn Þ=n ¼ Analysts traditionally use the arithmetic mean as a ‘‘conservative’’ predictor or benchmark absent consideration of the variability of the data and the location of the subject company data in the distribution. This assertion is fundamentally flawed and produces a relevant and reliable inference only by random chance. [W]henever an average is used to represent an uncertain quantity, it ends up distorting the results because it ignores the impact of the inevitable variations.2
This is true whether using average historic sales, average discount rates, or averages of studies forming the basis for buildup methods. Simply stated, ‘‘Decisions based on average numbers are usually wrong.’’3 Harmonic Mean The harmonic mean is appropriate when data consists of ratios (e.g., miles per hour, price/earnings ratio and other market value multiples). 2 3
Sam L. Savage, ‘‘The Flaw of Averages,’’ Harvard Business Review (November 2002): 20–21. Ibid., 1
Measures of Central Tendency
739
2 1.5
Mean of Log Values 1.34
1 0.5 0 1
2
3
4
5
6
7
Exhibit VI.5 Logarithmic Scale
Harmonic mean (H): Hðx1 ; ; xn Þ of n numbers xi ; where i ¼ 1; 2; . . . ; n n X 1=H 1=n 1=xi i¼1
Logarithmic Mean The logarithmic mean is calculated as the arithmetic mean of the logarithmic values. If data are plotted on a logarithmic scale, the curve becomes a straight line. Because the curve is a straight line, the arithmetic mean of the logarithmic values will represent the average of the data (see Exhibit VI.5). Logarithmic mean ¼ ðlog x1 þ log x2 þ ::: þ log xi Þ=n The logarithmic mean is the correct measure of central tendency when averaging rates of change and data having a logarithmic pattern. A logarithm is not a useful descriptive measure and must be converted to the normal scale by determining its antilogarithm (i.e. the geometric mean). Since the demise of the slide ruler, many practitioners have not received instruction in logarithms. A refresher of logarithm (base 10) conversion follows: Log 1 ¼ Log 10 ¼ Log 100 ¼ Log 0.1 ¼
0 1 2 1
Geometric Mean The geometric mean is appropriate for data characterized by geometric progression. A geometric progression is a series of numbers, each of which is formed by multiplying the previous one by a constant number; geometric means are used for compound interest, growing populations, increasing revenues, and expenses. A geometric progression also is characterized as a series of numbers, each of which is formed by dividing the previous one by a constant number; geometric progressions are seen in depreciation, deteriorations, and decay rates over time (see Exhibit VI.6). Decay curves have been adopted by the insurance industry, petroleum industry (valuation of reservoir yield), and the business valuation profession (valuation of client/customer base based on attrition).
740
Cost of Capital
70 60 50 40 Arithmetic Mean 27.97 Geometric Mean 21.95
30 20 10 0 1
Exhibit VI.6
2
3
4
5
6
7
Curve of Geometric Depreciation
A geometric progression is characterized by data with a logarithmic distribution. The arithmetic mean is not equal to the geometric mean. Q Geometric mean ( ; xg ): The nth root of the product of the absolute values of the observations taken with the proper sign Q Geometric mean xg ¼ ð jxi jÞ1=n Q Geometric mean ¼ Antilog ½ðlog x1 þ log x2 þ þ log xi Þ=n ! n Y Gða1 ; . . . ; an Þ ai thus; Gða1 ; a2 ; a3 Þ ¼ ða1 ; a2 ; a3 Þ1=3 i¼1
Geometric mean ¼ Antilog ½Logarithmic mean
DAVIES’ COEFFICIENT OF SKEWNESS Davies’ coefficient of skewness is a test for logarithmic distribution (asymmetry). The formula determines the appropriate measure of central tendency: geometric or arithmetic. An arithmetic mean is the appropriate measure for symmetrical distributions and when the data have a moderate degree of asymmetry. The geometric mean is the appropriate measure for asymmetrical distributions. If the test indicates asymmetry, data have a logarithmic distribution. A normal logarithmic curve is an asymmetrical, positively skewed distribution. Stock return data often can best be described as log-normally distributed. Davies’ coefficient of skewness: ½ðlog Q1 þ log Q3 Þ ð2 log Q2 Þ=ðlog Q3 log Q1 Þ If the calculated coefficient is greater than þ0.20, the data are symmetrical and the arithmetic mean is appropriate. If the calculated coefficient is less than or equal to þ0.20, the data are asymmetrical and the geometric mean is appropriate. The accuracy of Davies’ coefficient depends on several factors:
The data are definitely asymmetrical in their distribution, not roughly symmetrical (logarithmic distribution).
Measures of Variability (Dispersion)
Asymmetry is defined as a positively skewed distribution. The results are meaningless if distribution is negatively skewed.
The sample contains at least 50 observations.
Quartile values are unreliable with small samples.
741
MEDIAN The median is the point that divides the distribution into two equal parts and is not sensitive to any values in the distribution, only the number of elements. The median is not a substitute for the mean in statistical formulas. The median is preferable when:
The mean is biased and inappropriate.
The distribution of quantitative data is extremely asymmetrical. The precise location of the bisected halves of the distribution is material.
The data are ordered but not precisely quantitative. The median is calculated in two steps:
1. Sort the observations in ascending order. 2. Locate the middle observation. For odd-number distributions, the median is the middle observation. For even-number distributions, the median is the midpoint between the two middle observations. MODE The mode is the point or value of greatest frequency in the distribution and is not sensitive to any values, only to the frequency of specific elements.
MEASURES OF VARIABILITY (DISPERSION) DEVIATION ABOUT THE MEAN The deviation is the fundamental equation that forms an integral expression in statistical formulas quantifying areas under the curve. The deviation is the difference between a data value x and the mean. Deviation about the mean: Population deviation ¼ ðxi mÞ Sample deviation ¼ ðxi xÞ VARIANCE The variance is the average of the squared deviations. Squared units restrict an intuitive understanding and interpretation of the numeric value of the variance. The variance is useful only in comparing the amount of variance in two data sets (ANOVA). Certain statistical formulas use the variance to calculate variability: F test and Chi squared. The application of these formulas is beyond the scope of this chapter; however, they are included in the glossary of terms and addressed in several of the academic texts listed in the Additional Reading section.
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Population variance (s2): s2 ¼
P ðxi mÞ2 =N
where x ¼ Value of an observation in the population m ¼ Arithmetic mean of the population N ¼ Total number of observations in the population Sample variance (s2): s2 ¼
P
ðxi xÞ2 =ðn 1Þ
where xi ¼ Value of an observation in the sample x ¼ Arithmetic mean of the sample n ¼ Total number of observations in the sample The expression (n1) is referred to as the degree of freedom (df) and is used to counter the tendency of the statistic to understate the population mean by reducing the sample size n by the value of one (1) in the denominator of the sample variance formulas: df ¼ (n 1).
STANDARD DEVIATION The standard deviation is a numerical index of variability of the dispersion of data around the mean and is the prevalent measure of variability. The standard deviation is the square root of the variance. Population standard deviation (s): s¼
pffiffiffiffiffi s2
s¼
pffiffiffiffi s2
Sample standard deviation (s):
LOGARITHMIC STANDARD DEVIATION Certain significance tests need the standard deviation of logarithmically distributed measurements. When the logarithmic mean is used, the standard deviation must also be logarithmic. It is calculated like an ordinary standard deviation, except all measurements must be first converted to logarithms. PERCENTILES Percentiles are measures that locate values in the data set that are not necessarily central locations. Percentiles provide information regarding how the data are dispersed over the interval from the smallest to the largest value. The pth percentile is the value such that at least p% of the items are equal to this value and at least 100 – p% are greater than or equal to () this value. Follow these two steps to calculate the pth percentile:
Measures of Variability (Dispersion)
743
Step 1. Arrange the data in ascending order. Step 2. Compute an index i. where I ¼ ( p=100)n p ¼ Percentile of interest n ¼ Number of observations If i is an integer, the pth percentile is the average of the data values in positions i and i þ 1. If i is not an integer, the next integer greater than i denotes the position of the pth percentile.
QUINTILES AND DECILES A quartile is the number of quarters of a distribution that are located above or below the score/measure being reported. A decile is the number of tenths of a distribution that are located below the score/measure being reported.
INTERQUARTILE RANGE The interquartile range (IQR) is the set of measurements lying between the upper and lower quartiles, the middle 50%. The IQR does not facilitate further mathematical exploration. The IQR is a companion measure to the median. Division points:
Q1 ¼ First Quartile ¼ 25th percentile 75% of the values or measures are located above the first quartile, Q1 ¼ ðn þ 2Þ=4, provided the set of measurements is arranged in ascending order. Q2 ¼ Second Quartile ¼ 50th percentile 50% of the values are located above the second quartile, Q2 ¼ ðn þ 1Þ=2, provided the set of measurements is arranged in ascending order. Q3 ¼ Third Quartile ¼ 75th percentile 25% of the values or measures are located above the third quartile, Q3 ¼ ð3n þ 2Þ=4 alternative. 75(n þ 1), provided the set of measurements is arranged in ascending order. IQR ¼ Q3 Q1 defines the interval containing the median, the middle 50% of values or measures. In a normal distribution, one standard deviation equals approximately 0.741 times IRQ. One standard deviation equals 0.741 of the interquartile range.
RANGE The range is a measurement of the differences between the extreme values in a distribution. The range is a poor measurement of central tendency and disregards all observations except the two extremes. The range increases with the dispersion of the data and the number of observations.
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NORMAL PROBABILITY DISTRIBUTION The normal or symmetrical distribution is the fundamental distribution from which statistical inferences are derived. The term bell curve is also a descriptive reference to the normal probability curve. Specific characteristics common to all data exhibiting a normal probability distribution are as follows:
The observations involve a process of measurement. The normal probability distribution is a continuous scale of values beginning at zero and extending to infinity. The frequency with which a particular value of x occurs is given by the height y of the curve at that point. The normal distribution describes with fair accuracy the pattern of variations from the average in binomial situations. The normal distribution provides for the calculation of the probability of any particular deviation from the average. All data exhibiting a normal distribution are subject to elements of random chance and experimental error are always present.
Data are often depicted as histograms but analyzed by continuous probability distributions such as the normal distribution. The probability distribution for a continuous random variable can be thought of as the limiting histogram for a very large set of measurements utilizing the smallest possible interval width. Therefore, the outline of the histogram appears as a continuous line. PROPERTIES OF CONTINUOUS DISTRIBUTION Mathematical function f(x) traces the curve for varying values of x. This function is referred to as a probability distribution or the probability density for the random variable x. Mathematical models merely provide approximations of reality, which require further verification through experimental processes. pffiffiffiffiffiffi f ðxÞ ¼ 1=s 2p e1=2 ððx mÞ=s Þ2 ;
1 < X < 1
where x s p e m
¼ ¼ ¼ ¼ ¼
Random variable Measures the spread or dispersion of the distribution Mathematical constant ¼ 3.14159 Base of the natural log ¼ 2.7183 Center of the symmetrical distribution
Almost all values in a distribution of a normally distributed random variable lie within the interval m 3s. The curve is merely a model that approximates an actual distribution of measurements. However, it can be used as an effective model for many types of measurements. When s is small, the distribution is peaked and tightly dispersed about the mean. When s is large, the distribution is less
Normal Probability Distribution
745
peaked and loosely dispersed about the mean. The vertical height of the curve is referred to as the kurtosis of the curve. The area under the relative frequency histogram (probability distribution) is equal to 1. The probability that x is included in the interval from a to b is determined by summing the probabilities from a to b. The area under the curve over the interval from a to b exhibits the following relationships: Pða < x < bÞ;
and
Pðx ¼ aÞ ¼ 0
Therefore, P(x a) ¼ P(x > a) and P(x a) ¼ P(x < a). This is not generally true for discrete random variables.
TABULATING AREAS OF THE NORMAL PROBABILITY DISTRIBUTION The probability that a continuous random variable lies between a and b is measured by the area under the probability density function between the values a and b. Although areas under a continuous curve are computed using calculus, most probability and statistics texts include tables for calculating areas under the curve. Areas under the normal curve can be found either by numerical methods (calculus) or by published tables. Because assembling different tables for each normal distribution with a given mean and standard deviation is tedious, a standardized procedure was developed by which a single table can be used for all normal distributions. The standardized procedure (z-score) expresses the value x as the number of standard deviations to the left or right of the mean. z ¼ x m=s therefore; x ¼ m þ zs: If x lies to right of the mean: z < 0: If x lies to left of the mean: z > 0: When x ¼ m: z > 0 The standard normal random variable z has a mean equal to 0. Since x represents the distance from the mean, in units equal to standard deviations, the standard deviation of z is equal to 1. Tabulated areas are those less than a given number, z0. The area to the left of z0 is expressed as A(z,0). The total area under the curve is equal to 1; therefore, Pðz > z0 Þ ¼ 1 Pðz < z0 Þ. Determining the probabilities of any normal random variable x that has a mean m and standard deviation s requires only basic mathematic skills. First, convert the random variable x to the standard normal random variable z, and work problem in terms of z. Since probability statements are written in the form of inequalities, the integrity of the equations is maintained if:
The same number is subtracted from each member of the inequality and/or Each member of the inequality is divided by the same positive number.
Standard deviations divide the normal curve into predictable proportions, from which statistical inferences can be made.
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–3σ
–2σ
–1σ
–0σ +1σ Mean .6826
+2σ
+3σ
.9544 .9972 Area under the Curve
Exhibit VI.7
Theoretical Proportions of a Normal Distribution
Theoretical proportions of a normal distribution are detailed in the next and in Exhibit VI.7. 1s < m < 1s contains 68.26% of the distribution elements. 2s < m < 2s contains 95.44% of the distribution elements. 3s < m < 3s contains 99.72% of the distribution elements.
INTERPRETING INDIVIDUAL MEASUREMENTS The properties of the normal curve provide a foundation for calculating estimates of the probable occurrence of measures in a normal distribution.
Z-SCORE The z-score is the standard scale used in predicting occurrences in a normal distribution. The z-score expresses a measure in terms of the number of standard deviations the measure is from the mean. Location can reference positions above or below the mean. A z table provides the probability of a sample mean between and (m þ z). Tables of z values accompany most texts on applied statistics.
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REQUIREMENTS TO USE Z DISTRIBUTION TABLES
The distribution must be approximately symmetrical (normal).
The sample must be random. The sample size must be greater than or equal to () 30.
The formula applies to populations, samples, and grouped data. The mean and standard deviation of the population must be known.
The z-score of the mean is equal to 0 and the total of all probabilities is equal to 1.
z-score: z ¼ ðx mÞ=s Published tables reference tabular probabilities, areas under the curve, for specific z-scores. The z tables are based on standard binomial probabilities. Published z tables are not uniform. Tables may present interval probabilities for z-scores or may present cumulative probabilities for z-scores. Tables can be used inversely to find the z-score corresponding to a desired probability.
USING Z DISTRIBUTION TABLES 1. Identify the first two digits of the z-score on the left header column. 2. Identify the second two digits of the z-score on the horizontal header. 3. Intersection is the probability associated with the z-score. STUDENT’S t-TEST The student’s t-test compares a random sample consisting of three or more measurements with a large parent group whose mean is known but whose standard deviation is unknown. This measure is a modification of the z-test (where the standard deviation is known and presumed normal). The standard deviation of the sample is used as an estimate of the population standard deviation. Standard deviations from the same population will vary between samples. The t-test considers the sample size as a variable. Requirements to use the t distribution tables:
The distribution must be approximately symmetrical (normal).
The sample must be random. The sample cannot be a stratified random sample.
The sample size is less than 30.
t distributions are essentially the same as z distributions. The t test is preferred for the value of testing for distributions that change shape. When n is very large, the difference between z and t is negligible. When n is as large as the population, z ¼ t. Applying the t-test to samples greater than or equal to 30 produces values similar to the z test. The t-test is used almost universally in place of z whenever inferences must be made from accessible samples to inaccessible populations. Knowledge of the formula is not critical. Published tables are used in lieu of calculating t manually.
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Student’s t-test: t ¼ ðx mÞ=s
pffiffiffi where s ¼ s= n
APPLYING t DISTRIBUTION TABLES The critical values of t vary with the number of measurements n in the sample. The left column in published tables corresponds to the sample size. Each line in the table represents the distribution of t for a particular sample size. Degrees of freedom (df) are represented by the left vertical header column, df ¼ (n 1). The horizontal row header provides the probability that the mean is outside the upper or lower limit set by the indicated value of t. Probability ¼ ð1 confidence intervalÞ 0:5 For a confidence interval level of 95%, the horizontal value for the probability is 0.025 or 2.5%. The intersection of the horizontal and vertical values provides the value of t.
RELATIONSHIP BETWEEN TWO SETS OF MEASURES A scatterplot is used to display graphically the relationship between two different measures in a sample. It is possible to summarize the relationship between two measures quantitatively using a correlation coefficient. It is possible to test the significance of a correlation coefficient by referring to a sampling distribution. If two measures are related, it is possible to use one measure to predict the other (see Exhibit VI.9). Scatterplot construction is represented by an x-y graph. When one measure may be used to predict another, predictor is represented by the x-axis. Data point distributions illustrate the relationship graphically. The stronger the relationship, the closer the data points.
Linear
Curvilinear
Random data points indicate an absence of a relationship
REGRESSION Regression analysis is the method utilized to understand the relationship between two variables. The regression line of y on x indicates the best prediction of y for every value of x on the basis of the sample data. The absence of a relationship invalidates the calculation. If there is no relationship between x and y (r ¼ 0.0), the best prediction of y is always y regardless of the value of x. A visual representation (scatterplot) should always be prepared to insure the relationship between x and y is linear. The formula provides the best prediction of y for any given value of x. Regression line of y on x: b ¼ rsy =sx
y ¼ y þ bðx xÞ P P P P P or ½n ðxyÞ ð xÞð yÞ ½n x2 ð x2 Þ
Relationship between Two Sets of Measures
749
Exhibit VI.8 Scatter Plot
Unless all of the observations fall on the straight line, there are ‘‘errors’’ in fitting the data values. The error is measured by the distance the data values are from their projected values on the regression line. If a point is on the regression line, the error of that observation equals zero. Regression analysis performed on business data inevitably involves sample data, not population data. Since population data (parameters) are unknown, they must be estimated by using the sample statistics, b0 and b1. y ¼ b0 þ b1 x where: b0 ¼ Sample intercept b1 ¼ Sample slope
To determine the equation of the regression line for a sample of data, the values for b0 and b1 must be determined. Least squares analysis is used to estimate these values. In a least squares analysis, a regression model is developed by producing the minimum sum of the squared values. The plotted line does not pass through any of the points. The vertical distance from each point to the line is the error of the prediction. Theoretically, an infinite number of lines could be constructed to pass through the points. The least squares regression line yields a line representing smallest sum of errors squared. Regressions are linear, fitting data to a straight line, or nonlinear, fitting data to a curve. The scatter plot illustrates that as the distances between the data values and the regression line decrease, the more accurate the regression. Conversely, as those distances increase, the less accurate the regression line. Interpreting a regression line requires the interpretation of numerous statistics. There are three techniques for testing the fit of the regression line to the data: residual analysis, standard error of the estimate (Se), and coefficient of determination (r2).
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Cost of Capital
Residual Analysis The fit of a regression line can be tested against the historic data used to construct the equation of the line. Actual y values correspond to the x values used in constructing the regression line. Substituting the historic X values in the regression line equation yields the predicted y values (yˆ). The predicted value (yˆ) is referred to as ‘‘hat’’ yˆ. The error of the regression line equation is quantified by comparison of predicted values to actual y values. This difference is the error (residual) of the regression line at a given point, y yˆ. The least squares line is the minimization of the sum of the residuals. Except for rounding errors, the sum of the residuals is always zero. The equations used to solve for the slope and intercept locate the regression line geometrically in the middle of the points. Consequently, the sum of the vertical distances will always equal zero. By examining the residuals, you can determine how well the regression line fits the historical data points. Analysis of residuals is also used to locate outliers. Outliers are data points with values at the extreme ends of the distribution. Outliers can produce residuals with large magnitudes; however, they are easily identified by inspecting the scatter plot. Outliers may result from misrecorded data, miscoded data, or data that does not conform to the general trend. The equation of the regression line is influenced by every data point used in its calculation, similar to the arithmetic mean. Therefore, outliers can adversely influence the regression line by ‘‘pulling’’ the line toward the outlier values. The outlier values must be investigated to determine if they should be retained or eliminated. Outliers frequently are eliminated arbitrarily or because they compromise the intended outcome. Residual values are plotted against the x-axis to provide a reference as the values of x increases. Using Residuals to Test the Assumptions of the Regression Model The analysis of residuals is used to test assumption of simple regression analysis:
The model is linear. The error terms have constant variations. The error terms are independent. The error terms are normally distributed.
The behavior of residuals can be investigated by constructing a residual plot, a graph that plots the residuals for the particular regression model and their associated value of x as an ordered pair (x, x-y). The graph assists in determining how well the regression model meets regression assumptions. As the sample size increases, residual plots become more meaningful. With small sample sizes, residual plot analysis becomes problematic due to increased reliance on interpretation rather than data-driven inferences. A horseshoe-shaped residual plot indicates that the assumption of linearity is invalid. The horseshoe shape illustrates that the residuals are negative for low and high values of x and are positive for middle values of x. The pattern illustrated by the graph is parabolic, not linear. The residual plot does not have to reflect this shape for a nonlinear relationship to exist. Any significant deviation from the approximate linear residual plot may indicate nonlinear relationships between the two variables. The assumption of a constant error variance is referred to as homoscedasticity. If the error variances are not constant (heteroscedasticity), the residual plots patterns will resemble shapes similar to the symbols for ‘‘greater than’’ (>) or ‘‘less than’’ (<). The pattern illustrated by a greater than (>) symbol indicates error variance greater for small values of x and smaller for larger values of x. The corollary is true for shapes similar to a less than (<) symbol. If the error terms are not independent, the residual plots will resemble a downward or upward curve. For nonindependent relationships, the value of the residual is a function of the residual value
Relationship between Two Sets of Measures
751
next to it; that is, a large positive residual is next to a large positive residual and a small negative residual is next to a small negative residual. A graph of the residuals from a regression analysis that meets the assumptions might reflect a horizontal shape or straight line across the x axis. The pattern illustrates a relatively linear relationship; the variance of the errors is about equal for each value of x, and the error terms are not related to adjacent terms. Standard Error of the Estimate Residuals represent errors of estimation for individual points. The computation of residual values for large data samples is laborious, even with computer assistance. The volume of data inhibits the review and interpretation of the residual errors generated by the regression model. An alternative is the standard error of the estimate, which provides a single measure of the regression error. Since the sum of the residuals is zero, determining the total amount of error by summing the residuals is a pointless exercise. The sum-zero characteristic of residuals is avoided by squaring the residuals before summing them. The total of the residuals squared is referred to as the sum of the squares of error (SSE). X SSE ¼ ðy ^yÞ2 Theoretically, an infinite number of lines can be fitted to a data set. The equation for the slope of the regression line produces a best fit by minimizing the SSE. The equation for the slope of the regression line is derived from calculus for this purpose. Consequently, the regression process discussed herein is commonly referred to as the least squares regression. The computation formula for the SSE is: X X X 2 ðyÞ b1 ðxyÞ SSE ¼ ðyÞ b0 The sum of the squared error is in part a function of the number of pairs of data being used to compute the sum, which lessens the value of the SSE as a measurement of error. A more useful measurement of error is the standard error of the estimate. The standard error of the estimate (Se) is a standard deviation of the error of the regression model and has more practical use than SSE. The formula for Se is: rffiffiffiffiffiffiffiffiffiffiffi SSE Se ¼ n2 If data are normally distributed, the empirical rule states that about 68% of all values will be located within m 1s and about 95% of all values will be located within m 2s. A fundamental assumption for regression is that for a given x, the error terms are normally distributed. Because the error terms are normally distributed, Se is the standard deviation of the error, the average error is zero, approximately 68% of the error values (residuals) should be within 0 1Se, and 95% of the error values (residuals) should be located within 0 2Se. Based on knowledge of the variables being studied and examination of the value of Se, an inference can be made about the fit of the regression model to the data by using Se. The standard error of the estimate provides a single measure of error, which can be used to understand the magnitude of the errors in the model. The standard error of the estimate can be used to identify outliers, data outside 2Se or 3Se.
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CORRELATION COEFFICIENTS If two measures have a linear relationship, it is possible to describe the strength of the relationship with a correlation coefficient. The population parameter is represented by r (uppercase rho). The sample statistic is represented by r (lowercase rho). Correlation coefficients: P
ðx mx Þ=s x ðy my Þ=s y P r ¼ 1=ðn 1Þ ðx xÞsx ðy ^yÞ=sy
r ¼ 1=N
Interpretation:
r ¼ þ1.0
All scores are exactly on the line; high scores on each measure correspond to the other, indicating that the relationship is perfect. One measure will predict the other measure. Every pair of observations ðx xÞ=sx is exactly equal to ðy yÞsy .
þ1.0 r .0.0
High scores on one measure correspond to low scores on the other, indicating that the relationship is not perfect.
r ¼ 0.0 No relationship exists between the ðx xÞ=sx and ðy yÞ=sy data points.
1.0 r .0.0
High scores of one measure correspond to low scores on the other, indicating that the relationship is not perfect.
r ¼ 1.0
All scores are exactly on the line; high scores of one measure correspond to low scores on the other, indicating that the relationship is perfect. One measure will predict the other measure. Every pair of observations ðx xÞ=sx is exactly equal to ðy yÞ=sy . Correlations are perhaps the most widely known and most consistently abused measure in inferential statistics. A correlation coefficient is not a proportion or percentage. A coefficient of 0.75 is not equivalent to 75% nor does it imply a percentage relationship to values in the population. Correlations are simply a measure of the relationships between variables, not an indication or measurement of causation. Descriptive statistics are developed first, to define the characteristics of the data. Correlations assist in focusing the statistical tests on relevant data by providing information regarding the existence and strength of relationships. However, correlations do but reveal anything about the nature of the relationship. Although the correlation coefficient, r, is not a proportion, r-squared (r2) is the percentage of variation in one variable that is accounted for by the variation in the other variable. A correlation coefficient of .75 yields an r2 of .5625, indicating that 56.25% of the variation in y is accounted for by variation in x. It is important to understand that correlation is not directional.
Relationship between Two Sets of Measures
753
There are two predominant correlation tests, Pearson and Spearman. As with measures of central tendency, the nature of the data determines which measure is appropriate. There are true values (test scores) and ranked values (values assigned to represent unknown values). If one or both of the variables are ranked scores, the Spearman correlation should be used. The Pearson correlation will return an artificially low coefficient for nonlinear relationships. The initial calculation should be Pearson, since a Spearman calculation will indicate a nonlinear relationship. The two calculations should be compared to determine linear or nonlinear relationships. Pearson is a parametric statistic and Spearman is a nonparametric statistic. Parametric tests are designed for normal distributions of data, and therefore rely on means. Nonparametric tests are designed for asymmetrically distributed data. ANOVA is a parametric test while chi2 is a nonparametric test. The term parametric refer to the design of the test, not data characteristics. Parametric tests can be used on nonnormally distributed data, and nonparametric tests can be used on data with normal distributions, provided the samples are relatively large (greater than 25). A parametric test will yield more accurate P values as a general rule, but nonparametric tests may reveal additional information. Although correlation and regression are related tests, each has a specific purpose and situation to which it applies. Correlation measures the strength of a relationship between variables, while regression determines the functional relationship. However, both correlation and regression tests should be performed. The preliminary test of data is correlation, which identifies which variables show an association. If two variables are not correlated, further testing of relationships and attributes is unwarranted, unless the absence of a relationship is an anomaly (a relationship should exist but does not). COEFFICIENT OF DETERMINATION The square of the correlation coefficient describes exactly what percentage of the variance of y is explained by x. The variance is not a cause-and-effect relationship; it only describes how one variable can be used to predict the other. Coefficient of determination: r2 ¼ coefficient of determination Values for r2 range from 0 to 1. A value of zero indicates that the predictor accounts for none of the variability of the dependent variable and that no regression prediction of y by x is possible. A value of 1 indicates a perfect prediction of y by x and that 100% of the variability of y is accounted for by x. Since r2 values will be between these two extremes, an interpretation regarding a particular r2 (whether high or low) depends on the intended use of the model and the context within which the model was developed. The dependent variable (y) being predicted has a variation measured by the sum of squares of y(SSyy) and is the sum of the squared deviations of the y values from the mean value of y: P X X ð yÞ2 ðy ^yÞ2 ¼ y2 ¼ SSyy ¼ y The equation is disassembled into the explained variation, measured by the sum of squares of regression (SSR), and the unexplained variations, measured by the sum of squares of error (SSE), to show the relationship between the individual components: SSyy ¼ SSR þ SSE
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Dividing each term in the equation by SSyy produces this equation: 1¼
SSR SSE þ SSyy SSyy
The term r2 is the proportion of the y variability that is explained by the regression model and equals one component in the formula: r2 ¼
SSR SSyy
Substituting the formula for r2, the formula is restated as: r2 ¼ 1
SSE ¼1 SSyy
SSE Sy2
ð SyÞ2 n
Absent an analysis of the residuals, a regression line is no more than a straight line drawn between data points. Whereas r is a coefficient of correlation between an independent variable and a dependent variable, r2 is the coefficient of correlation between the actual value (score) and the value (score) predicted by the regression. The square of the correlation coefficient, r2, is the percentage of the variability in the predicted score explained by the variability in the score. Excel frequently departs from standard statistical terms in the description of statistical tests. The Standard Error identified as a regression statistic in Excel regression VBA is the standard error of the estimate (SSE). The SSE identifies the average magnitude, in one direction or another, the predicted score is off. ANOVA indicates whether the difference between two or more population means is statistically significant or not. The t-test compares population means to an expected value. The test determines whether the difference between two means is significantly greater or less than an expected difference (one-tailed tests determine whether the difference is less than, and two-tailed tests determine both). There are several problems with using the t-test as an ANOVA substitute. First, no more than two variables can be compared with any one test. Second, each time a sequential test is run, the probability of an error is compounded. Like the t-test, chi2 is used to compare a value to an expected value and determine if the difference is statistically significant or not. The two tests are not the same. The t-test is used to compare a mean to an expected value. Chi2 is used to analyze variance, not a mean. Predicting values by regression analysis is subject to errors due to the relationship resulting entirely from chance.
EVENT RELATIONSHIPS Lattice option models are based on event relationships. The union of events A and B is the event that either A or B or both occur. Events consisting of those simple events that are in either A or B or both A and B are denoted as A B. The intersection of events A and B is the event that both A and B occur or the event of those simple events that are in both A and B and is denoted as A \ B. \
Event Relationships
755
The complement of an event A is the event that occurs when A does not occur. The event consisting of all those events in sample space S that are not in event A is denoted as AC. Complement: PðAc Þ ¼ 1 PðAÞ PðAÞ þ PðAc Þ ¼ 1 Two events are mutually exclusive (disjointed) if when one event occurs the other can not. Mutually exclusive: PðA \ BÞ ¼ 0 A [ Ac ¼ S Pð A [ B Þ ¼ P ð A Þ þ P ð B Þ Two events are independent if and only if:
P(A) ¼ P(AjB) when P(B) > 0 or,
P(B) ¼ P(BjA) when P(A) > 0.
A vertical bar j is read ‘‘given,’’ and the events appearing to the right of the bar are those that have occurred. If two events A and B are independent, then: Pð A \ BÞ ¼ PðAÞPðBÞ If two events A and B are dependent, then: PðAjBÞ 6¼ PðAÞ
PRESENTATION OF EVENT RELATIONSHIPS Two graphic methods are used to represent visually the relationship between two or more events: Venn and tree diagrams. A Venn diagram consists of an outer box represents the sample space containing all sample events Ei. Circles within the sample space indicate the relationship between two or more sample events. A tree diagram is integral to queuing models and is similar to a ‘‘bracket’’ diagram used in sporting tournaments (i.e., basketball regional playoffs). Each successive level of branching corresponds to a step required to generate final outcome. CONDITIONAL PROBABILITY Two events A and B are independent if and only if the probability of event B is not influenced or changed by the occurrence of event A. The events A and B are not independent if probability that event A will occur is influenced given that event B has occurred and the proportion of P(B) that will give rise to event A.
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Conditional probability of B, given that A has occurred: PðAjBÞ ¼ PðA \ BÞ=PðBÞ If PðBÞ 6¼ 0: Conditional probability of B, given that A has occurred: PðBjAÞ ¼ PðB \ AÞ=PðAÞ If PðAÞ 6¼ 0:
BAYES’ THEOREM Bayes’ theorem is an approach to conditional probability based on deductive reasoning in lieu of inductive reasoning. The theorem is useful when a problem requires reasoning from the effect (a defective is observed) to the cause (the population producing the defective). Conditions: Sample space S can be partitioned into k mutually exclusive events (subpopulation) S1 ; S2 ; . . . ; Sk , so that S ¼ S1 [ S2 [ S3 [ . . . [ Sk .
A single repetition of experiment results in event A, with P(A) > 0. Probabilities PðS1 Þ; PðS2 Þ; . . . ; PðSk Þ must be known (referred to as prior probabilities). If prior probabilities are unknown, it is commonly assumed that all subpopulations are equally probable: PðS1 Þ ¼ . . . ¼ PðSk Þ ¼ 1=k. Conditional probability PðSi jAÞ is the posterior probabilities, resulting subsequently and taking account of the sample information in event A. Query is an inference regarding which event (subpopulation) probably resulted in event A.
Probability that Si was sampled given that A occurred:
X k P S j P AjS j PðSi jAÞ ¼ Pð Si \ AÞ=Pð AÞ ¼ PðSi ÞPð AjSi Þ j¼1
LAWS OF PROBABILITY The probability of each element in a build-up calculation and the sum of the probabilities can be calculated. PROPORTIONATE LAW Theory Whenever something can have more than one result, if all the possible results have an equal chance of occurring, the probability of any one of them occurring in a single trial will be the proportion which that particular result bears to all the possible results.
Laws of Probability
757
Explanation The technical definition of probability is the frequency or proportion of times a certain result is to be expected. The probability of a specific result can be foretold from the nature of the procedure, if the tests or occurrences are unbiased. Probability refers to the ‘‘relative frequency’’ or proportion of times a certain event is expected to occur over long-term trials. Relative frequency of event: A ¼ Frequency=n where: Frequency ¼ Number of times event A occurred n ¼ Number of repetitions of the experiment P(A) ¼ lim Frequency=n n1
As n increases (n ! 1), the entire population eventually will be generated. Precision increases as the number of trials or samples increase, assuming the trials are unbiased and the samples are properly drawn.
LAW OF AVERAGES Theory Whenever something can have more than one result, if all the possible results have an equal chance of occurring, the results that will be observed in a number of trials generally will vary to some extent from the inherent proportions, but the extent of the variation will become progressively less as the number of trials increase.
Explanation The proportionate law provides the expected occurrence of a specific event in a finite number of trials. The observed outcomes will approach the expected rate of occurrence as the number of trials increase. It is the observed proportions that approach the theoretical expectation. The difference between the observed and the expected number actually increases as the number of trials increases. The tendency to vary from the exact proportions applies to sampling from existing groups. The tendency for any particular set of observations to vary from the exact proportions is attributable to chance. The observed outcomes (proportionate law) will approach the theoretical probability (expected rate of occurrence) as the number of trials increase. The observed proportions will approach the theoretical expectation over long-term trials. The numeric difference between the observed and the expected number actually increases as the number of trials increases. A test of 50 tosses may not yield 25 heads and 25 tails; however, as the number of tests increases, the observed proportions will converge on the theoretical proportions. The tendency to vary from the exact proportions applies to sampling from existing groups. The tendency for any particular set of observations to vary from the exact proportions is attributable to chance.
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ADDITION LAW Theory Whenever something can have more than one result, if all the possible results have an equal chance of occurring, the probability of alternate results occurring in a single trial will be the sum of their individual probabilities. Explanation The probability of two distinct occurrences from a specific population is the sum of their respective probabilities. Given two events A and B, the probability of A union B is equal to the probability of A plus the probability of B less the probability of A intersecting B: Pð A [ BÞ ¼ Pð AÞ þ PðBÞ Pð A \ BÞ The probability of A union B is equal to the probability of A plus the probability of B where the events are mutually exclusive: Pð A [ BÞ ¼ Pð AÞ þ PðBÞ If event A is contained in event B: Pð A [ BÞ ¼ PðBÞ MULTIPLICATION LAW Theory Whenever something can have more than one result, if all the possible results have an equal chance of occurring, the probability of getting any particular combination of results in two or more independent trials (whether consecutively or simultaneously) will be the product of their individual probabilities. Explanation It makes no difference whether the events occur one after the other or at the same time as long as they are independent. The result of each event exerts no influence on the outcome of the other. The probability of a combination of two distinct occurrences from a specific population is the product of their respective probabilities. A vertical bar j is read ‘‘given,’’ and the events appearing to the right of the bar are those that have occurred. The ordering, sequence, or simultaneous occurrence of the events is immaterial as long as the events are independent. The result of each event exerts no influence on the outcome of the other. The probability of a combination of two distinct occurrences from a specific population is the product of their respective probabilities. The probability of A intersect B is equal to the product of the probability of B and the probability of A given B. Given two events A and B, the probability of A intersect B: PðA \ BÞ ¼ PðBÞPðAjBÞ or
Sampling
759
The probability of A intersect B is equal to the product of the probability of A and the probability of B given A. PðA \ BÞ ¼ PðAÞPðBjAÞ The probability of A intersecting B is equal to the probability of A plus the probability of B where the events are mutually exclusive. Given two independent events A and B, the probability of A intersecting B: PðA \ BÞ ¼ PðAÞPðBÞ Given three mutually independent events A, B and C, the probability that A, B and C will occur: PðA \ B \ C \ Þ ¼ PðAÞPðBÞPðCÞ
SAMPLING Sampling consists of examining a small portion (sample) of a group (parent) in order to draw conclusions about the parent group. The proper selection of samples is one of the most difficult areas in applied statistics. A properly selected sample substitutes for a complete count of the parent group. Absent a properly selected sample, the resultant statistical inferences are misleading, biased, and unreliable. Estimation is a common application of sampling. Often in business valuation, our ‘‘sample’’ consists of the entire available selection of data (e.g., all guideline public companies comparable to the subject company). In these situations, there may be great controversy as to whether the data selection is representative of the population. RANDOM SAMPLING A sample is reliable (within calculated limits) provided every member in the parent group has an equal probability of selection in the sample. Reliability is a function of the sampling procedure, not the proportion that the sample bears to the parent group. Samples consisting of 20% or more of the parent become less susceptible to random selection requirements. Size is not a singular indicator of a properly selected sample. The Laws of Probability apply only when the sample is random. Random does not mean the sample is haphazard or aimless; rather the sample is a cross-section or proportionate representation of the elements in the parent group. Statistical reliability is undermined by manipulation to achieve predetermined population proportions within the samples. In such cases, the samples are not random and the laws of probability have been vacated. There are two ways to insure random selection of a sample from a population: table of random numbers and random-number generators. SAMPLE SIZE Precision is a function of the size pffiffiof ffi a properly drawn sample. Precision of a sample increases by the square root of the sample size ( n). It is important to understand that sample size is not a substitute for proper selection procedures, but a complement. The most difficult area of applied statistics is designing and executing sampling procedures, particularly the calculation sample size. If the sample is improperly selected, any inferences from that
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data will be compromised and the inferred probabilities will not apply. Sample size is dependent on the degree of precision required and the amount of variability in the parent group. za=2
pffiffiffi ðs= nÞ ¼ B
where: zp a/2 ffiffiffi ¼ Value of z having an area s=2 to its right s= n ¼ Standard Error (SE) of the sample mean B ¼ Bound on the error of the estimate and a confidence coefficient (1 – a) If s is unknown, then s Range=4. A preliminary assessment or pilot study is often completed to determine the sample size required for the requisite degree of precision. STRATIFIED RANDOM SAMPLING Random samples suffer from a single major drawback, cost. Cost constraints become acute when significant variations exist between the members of the parent group and a lack of consistency in characteristics among members. Sampling of different strata or subgroups of the parent is referred to as stratified random sampling. Each stratum should be as homogeneous as possible. Random sampling requires data regarding the relative numbers within each strata. Pilot surveys are used to define the various strata and are the preferred method for market research and opinion polls. OTHER SAMPLING METHODS If the parent group is volatile or moving, systematic sampling may be utilized. A systemic sampling program selects individual items at regular specified intervals along the time line. If the parent group varies in a regular cyclical manner, then samples must be selected at regular intervals. The presenting sample is commonly used in medical research and consists of a consecutive series of patients presenting themselves for treatment for a specific condition.
DATA ACQUISITION ERRORS Business analysts and valuators must be cognizant of possible and probable data errors in published compendiums, summaries, and studies. Data errors are common in the published studies and numeric information business analysts and valuators customarily rely on without critical examination. These include: industry and economic studies, comparable company financial compendiums, sales and acquisition summaries, traded company statistics, marketability studies, and control premium and minority discount studies.
ELIMINATION OF OUTLIER VALUES Data mining is a common technique used by analysts to validate predetermined outcomes. The most common form of data mining is the subjective elimination of outlier values from a sample. When combined with improper sampling methods, the results are typically unreliable and precise by random chance.
Data Acquisition Errors
761
Outliers must not be arbitrarily eliminated as they may represent specific elements and characteristics of the population. The evaluation of outliers requires a systematic approach to minimize the elimination of data characteristic of the population. Each outlier must be reviewed carefully to determine if the item or value has been:
Incorrectly recorded and should be corrected before proceeding;
Incorrectly included in the data set and should be removed before proceeding, or Correctly included in the data set, although unusual, and should not be removed.
A predetermined outcome eventually can be confirmed if the size of the sample group is reduced methodically. Standardized scores (z-scores) can be used to identify outliers. Generally scores greater than 3 standard deviations should be investigated. This is not an incontrovertible test leading to automatic exclusion.
RANDOM AND SYSTEMATIC ERROR Random errors occur as a result of sampling variability and relate to random chance occurrences. They are minimized (not eliminated) by selecting larger samples or a larger number of samples. Systematic errors (bias) refers to the tendency to consistently under- or overstate a true value (i.e., the sample is biased or not random or the population is limited or exclusive).
SAMPLING DISTRIBUTION A sampling distribution refers to the distribution of data obtained by computing the statistic for a large number of samples drawn from the same population. Sampling distributions are fundamental to statistical inference.
SAMPLING VARIABILITY Sampling variability is the tendency of the same statistic computed from a number of random samples drawn from the same population to differ. This variability reinforces the basic theories of sampling precision. Precision of a statistic is directly related to:
Randomness of the sample Size of the sample
Number of samples
CENTRAL LIMIT THEOREM The more sample means that are included in the sampling distribution, the more accurate the sampling distribution becomes as an estimate of the population mean. The larger the sample, the less variability of sample means. Even for a population that is strongly asymmetrical, the sampling distribution of means will be approximately normal when the sample sizes 30.
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The Central Limit Theory assumes that the sample mean is a proxy for the population mean: (mx) ¼ m. The standard deviation of the sampling pffiffiffi mean, a measure of the statistics random variability, is referred to as standard error: s x ¼ s= n .
SUMMARY When evaluating numeric data, it is imperative to recognize the propensity of statistics to be subject to manipulation and misinterpretation. Numeric (statistical) information must be evaluated carefully before it is used as a foundation for an opinion. Statistical analysis is not a substitute for common sense and logical reasoning.
STATISTICAL TERMS Alternate hypothesis—a research hypothesis. The hypothesis concluded to be true if the null hypothesis is rejected. Bar chart—a graphical device for depicting the information presented in a frequency distribution or a relative frequency distribution of qualitative data, displaying how data is classified into various categories or groupings. Bell curve—a symmetrical, single mode frequency distribution. Bias—the consistent understating or overstating of a true value. Bimodal—a curve with two scores of highest frequency, a curve with two modes. Binomial—an event with only two outcomes or probabilities. Bivariate—an equation or study involving two variables. Central Limit Theorem—a theorem which states that a sampling distribution of means from either symmetrical or asymmetrical populations will produce a normal distribution when the sample sizes are greater than or equal to thirty. Chebyshev’s Theorem—a theorem applying to any data set that can be used to make statements about the percentage of items that must be within a specified number of standard deviations of the mean. Chi square—a probability distribution used to test the independence of two nominal variables. Class frequency—the number of observations that are included in each class interval. Class interval—the categories or groupings illustrated by frequency graphics. Coefficient of Determination—a measure of the population of variablities of shared by two variables. Coefficient of Variation—a descriptive statistic of the relationship between the standard deviation and the mean measuring the relative kurtosis of a distribution. Confidence interval—the estimated range of values of a population parameter at a specified level of confidence. Confidence level—the confidence associated with an interval estimate; the probability of obtaining a given result or outcome by chance. Continuous variable—a variable y that can be measured with whole and fractional numbers. Correlation coefficient—a measure of the degree to which two variables are linearly related.
Statistical Terms
763
Critical value—the value of a calculated statistic compared with the test statistic to determine whether or not to reject the null hypothesis. Cumulative Frequency Distribution—a tabular summary of a set of quantitative data showing the number of items having values less than or equal to the upper class limit of each class. Cumulative Relative Frequency Distribution—a tabular summary of a set of quantitative data showing the fraction or proportion of the items having values less than or equal to the upper class limit of each class. Data—the facts and figures (numeric and non-numeric) that are collected, analyzed, presented, and interpreted. Data set—all data collected in a particular study. Degrees of Freedom—a parameter of the t-distribution. When the t-distribution is used in the computation of an interval estimate of a population mean, the appropriate t distribution has n – 1 degrees of freedom, where n is the size of the random sample. Used to account for the tendency of a statistic to understate the parameter of a population. Dependent events—events that are related in that the outcome of one affects the probability of the outcome of the other. Dependent variable—a variable that is caused or influenced by another. Descriptive statistic—numerical data that describe an observed phenomena; tabular, graphical, and numerical methods used to summarize data. Directional test—a test of the prediction that one value is higher than another. Distribution—a collection of measurements indicating the dispersion of the elements about the measurement scale. Dot plot—a graphic that displays the variability in a small set of measures. Elements—the entities on which data are collected. Empirical rule—a rule that states the percentages of items that are within one, two, and three standard deviations from the mean for normal distributions. Frequency distribution—a tabular summary of a set of data showing the frequency (or number) of items in each of several nonoverlapping classes. Frequency histogram—a graphic that displays the number of measures contained within different classes. Frequency polygon—a graphic presentation of frequency of a phenomenon using straight lines and points. Grouped data—data arranged in class intervals as summarized in a frequency; individual values of the original data are not identified. Histogram—a graphical presentation of a frequency distribution or relative frequency distribution of qualitative data constructed by placing the class intervals on the horizontal axis and the frequencies or relative frequencies on the vertical axis. Independent events—events that are unrelated in that the outcome of one is unaffected by the outcome of the other. Independent variable—a variable that causes or influences another variable. Inference—a conclusion regarding the characteristic of a population parameter based upon an analysis of a sample statistic.
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Cost of Capital
Intercept—the value or measure on the y-axis where a line crosses the vertical axis. Interquartile range (IQR)—a measure of dispersion, defined as the difference between the third (upper, 75th percentile) and the first (lower, 25th percentile) quartiles. Interval—a scale using numbers to rank order in equal intervals with an arbitrary 0 value or point. Interval scale—a scale of measurement (numeric only) that has the properties of an ordinal scale and where the interval between the data values is expressed in terms of a fixed unit of measure. Joint occurrence—an event where two outcomes occur simultaneously, P(AB). Least squares—any line or curve fitting model that minimizes the squared distance of data points to the line. Level of Significance—the maximum probability of a Type I error. Lower quartile (Q1) —the 25th percentile of a set of measures. Mean—a measure of central tendency or location for a data set, calculated by summing all the data values and dividing by the number of items. Measures of Central Tendency—a descriptive measure indicating the center of a set of values or measures. Measures of Variation—descriptive measures indicating the dispersion of a set of values. Median—a measure of central tendency or location for a data set. The value that splits the data into two equal groups, one with values greater than or equal to the median and the other with values less than or equal to the median. Middle quartile (Q2)—the 50th percentile of a set of measures; the median. Mode—a measure of central tendency or location for a data set defined as the most frequently occurring data value. Mutually exclusive—events such that the occurrence of one precludes the occurrence of the other. Nominal—a scale using numbers, symbols, or labels to designate different subclasses. Nominal scale—a scale of measurement (numeric or nonnumeric) that uses labels or categories to define an attribute of an element. Normal distribution—a smooth bell-shaped curve symmetrical about the mean providing for the application of the empirical rule. Null hypothesis—the converse of the research hypothesis; the hypothesis tentatively assumed true in the hypothesis-testing procedure. Ogive—a graphic that displays a running total. One-tailed test—a hypothetical test in which rejection of the null hypothesis occurs for values of the test statistic in one tail of the sampling distribution. Observation—the set of measurements or data obtained for a single element. Ordinal scale—a scale of measurement (numeric and nonnumeric) that has the properties of a nominal scale and can be used to rank or order the data. Outlier—a data point, value, or measure that is significantly divergent from the other measures in the set. Percentile—a value such that at least p percent of the items are less than or equal to this value and at least (100 p) percent of the items are greater than or equal to this value. The 50th percentile is the mean.
Statistical Terms
765
Population—the collection of all elements of interest in a particular study. Population parameter—a numeric value used as a summary measure for a population of data (e.g., population mean, population variance, population standard deviation). p-value—the probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as the observation, often referred as the observed level of significance. Percentile—the value in an ordered set of measures such that P% of the measures lie below that value. Pie chart—a graphical device for presenting qualitative data summaries based on subdividing a circle into sections that correspond to the relative frequency of each class. Power—the probability of correctly rejecting the null hypothesis when it is false. Precision—a probability statement about the sampling error. Probability—a quantitative measure of the chances for a particular outcome or outcomes. Probability distribution—a description of how the probabilities are distributed over the values the random variable can take. Qualitative data—data (numeric and nonnumeric) obtained with a nominal or ordinal scale of measurement. Data that provide labels or names for categories of like items. Quantitative data—data (numeric only) obtained with an interval or ratio scale of measurement. Data that indicate ‘‘how much’’ or ‘‘how many’’ for the variable of interest. Quartiles—the 25th, 50th, and 75th percentiles referred to as the first quartile, second quartile (median) and the third quartile, respectively. The quartiles can be used to divide the data set into four equal parts, each containing approximately 25% of the data. Random error—an error occurring as a result of sampling variability. Range—a measure of dispersion, defined as the difference between the largest and smallest data values in a set. Ratio—a scale using numbers to rank order; its intervals are equal and the scale has an absolute 0 point. Region of Acceptance—the area of a probability curve in which a computed test statistic will lead to acceptance of the null hypothesis. Region of Rejection—the area of a probability curve in which a computed test statistic will lead to rejection of the null hypothesis. Regression—a statistical procedure used to estimate the linear dependence of one or more independent variables on a dependent variable. Relative frequency distribution—a tabular summary of a set of data showing the relative frequency (fraction or proportion) of the total number of items in each of several nonoverlapping classes. Sample—a group of members of a population selected to represent that population. Sampling distribution—a probability distribution consisting of all possible values of a sample statistic; a distribution obtained by computing a statistic for a large number of samples drawn from the same population. Sampling error—the absolute value of the difference between the value of an unbiased point estimator. Sample statistic—a numeric value used as a summary measure for a sample (e.g., sample mean, sample variance, sample standard deviation).
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Sampling variability—the tendency of the same statistic computed from a number of random samples drawn from the same population to differ. Scatter plot—a graphic display used to illustrate degree of correlation between two variables. Skewed—a distribution displaced at one end of the scale and a tail strung out at the other end. Slope—a measure of a line’s inclination. Standard deviation—a measure of dispersion for a data set, measured as the positive square root of the variance. Standard error—a measure of the random variability of a statistic. Statistic—a characteristic of a sample. Statistical inference—the process of using data obtained from a sample to make estimates or test claims about the characteristics of a population. Statistical significance—the probability of obtaining a given result by chance. Statistics—a branch of mathematics that describes and reasons from numerical observations or descriptive measures of a sample. Symmetry—a shape such that one side is the exact mirror image of the other. Systematic error—the consistent underestimation or overestimation of a true value. t-Distribution—a family of probability distributions often used to develop interval estimates of a population mean whenever the population standard deviation is unknown and the population has an approximately normal probability distribution or when the sample is small. Test statistic—a computed quantity used to decide hypothesis tests. Trimmed mean—the mean of the data remaining after a percent of the smallest and a percent of the largest have been removed. The purpose of a trimmed mean is to provide a measure of central tendency that has eliminated the effect of extremely large and small data values. Two-tailed test—a hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in either tail of the sampling distribution. Type I error—the error of rejecting a null hypothesis when it is true. Type II error—the error of accepting the null hypothesis when it is false. Upper quartile (Q3)—the 75th percentile of a set of measures. Variable—a characteristic of interest for the elements. Variance—a measure of dispersion for a data set based on the squared deviations about the mean of a distribution. z-score—a standardized value denoting the number of standard deviations a data value is from the mean, calculated by dividing the deviation about the mean by the standard deviation.
SUMMARY OF MICROSOFT EXCEL STATISTICAL FORMULAS MEASURE OF CENTRAL TENDENCY Mean ¼ AVERAGE(range) Median ¼ MEDIAN(range) Mode ¼ MODE(range)
Critical Values for Binomial Functions
767
MEASURE OF POPULATION VARIABILITY Standard Deviation (s) ¼ STDEVP(range) Variance (s2) ¼ VARP(range) Maximum ¼ MAX(range) Minimum ¼ MIN(range) Range ¼ MAX(range)-MIN(range)
MEASURE OF SAMPLE VARIABILITY Standard Deviation (s) ¼ STDEV(range) Variance(s2) ¼ VAR(range)
BINOMIAL PROBABILITIES Exactly x successes or at most x successes Binomial Distribution ¼ BINOMDIST(x,n,P,type) type FALSE: exactly x successes type TRUE: at most x successes
NORMAL PROBABILITIES Results are the proportion under the entire curve that is less than the given value of z. Areas between z ¼ 0 and the given value are obtained by subtracting. Cumulative probability ¼ NORMDIST(x, mx,sx,TRUE) Cumulative probability (z-score) ¼ NORMSDIST(z) z-score ¼ STANDARDIZE(x, mx,sx) CRITICAL VALUES OF z AND t Functions return the value of z and t for a given probability level. An inverse function is used to derive a value of z from a given probability. ‘‘conf’’ is expressed as (1 – confidence level) * .5. The chance of error is the reciprocal of the confidence level (e.g. a confidence level of 95% is equivalent to a 5% chance of error). For z-scores, ‘‘sd’’ represents standard deviation. For t scores, ‘‘df’’ represents degrees of freedom. z-score ¼ NORMINV(conf,mean,sd) t score ¼ TINV(conf,df)
CRITICAL VALUES FOR BINOMIAL FUNCTIONS Function returns the number of successes required to at least equal the cumulative sampling probability (p). Formula requires the number of trials (n), the null hypothesis probability (P), and the cumulative sample probability (p). Binomial ¼ CRITBINOM(n,P.p)
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Cost of Capital
t TEST FUNCTIONS Function returns the probability of the sample result against the null hypothesis. Formula requires identification of the ranges containing the two sets of sample data, the type of desired test and whether a one-tailed (1) or two-tailed (2) test is desired. t test ¼ t TEST(range1,range2,tails,type) Type 1: paired data Type 2: Independent samples with approximately equal variance CRITICAL VALUES OF F Function returns the one-tailed test probability of F greater than or equal to ‘‘ ’’ the given value. The inverse function returns the critical value of F corresponding to a given significance level. Formula requires the ‘‘degrees of freedom’’ (df) for both the numerator and the denominator. F probability ¼ FDIST(F,dfnum,dfdenom) F critical value ¼ Finv(p,dfnum,dfdenom) F TEST FUNCTION Function returns the one-tailed probability of the sample result. Formula requires identification of the two ranges of data for comparison. F test ¼ FTEST(range1,range2) @ftest(range1,range2) CORRELATION FUNCTIONS Function returns the population parameter r, not the sample correlation r. Population correlation ¼ CORREL(rangex,rangey) Population covariance ¼ COV(rangex,rangey) Sample correlation ¼ PEARSON(rangex,rangey) Sample covariance ¼ RSQ(rangex, rangey) The critical values for r are derived from the t distribution. Spreadsheet functions do not provide a separate function for computing the probability of a given value of r or an inverse function for deriving the value of r corresponding to a given probability level. A combination of functions must be utilized. tn2 ¼ (r*SQRT(n-2))/SQRT(1-(r*r)) Two-tailed probability ¼ T DIST(t,n-2,2) CRITICAL VALUES OF X 2 (CHI SQUARE) Function returns the one-sided test probability greater than or equal to the given value. Inverse functions return the critical value of X2 corresponding to the given significance level. Chi square probability ¼ CHIDIST(x2,df) Chi square critical value ¼ CHINV(p,df)
Critical Values for Binomial Functions
769
X 2 TEST FUNCTION Function returns a one-tailed probability of the comparison of actual data to predicted data. Predicted frequencies must be computed manually. X2 Test ¼ CHITEST(range1, range2) EXCEL ANALYSIS TOOLPAK Provides functions and interfaces for financial, statistical, and engineering analysis. The various analysis tools apply the appropriate statistical or engineering macro function and display the results in an output table. Some tools generate charts in addition to tables. ANOVA—single factor. Performs a simple analysis of variance, testing the hypothesis that means from two or more samples are drawn from populations with the same mean. ANOVA—two factors with replication. Performs an extension of the single-factor ANOVA that includes more than one sample for each group of data. ANOVA—two factors without replication. Performs a two-factor ANOVA that does not include more than one sampling per group, testing the hypothesis that means from two or more samples are drawn from populations with the same mean. Correlation—measures the relationship between two data sets that are scaled to be independent of the unit of measure. The population correlation calculation returns the covariance of the two data sets divided by the product of their standard deviations. Determines whether two ranges of data move together, whether small values of one set are associated with large values of the other, or whether values in both sets are unrelated. To return the correlation coefficient for two cell ranges, use CORREL worksheet function. Covariance—the measure of the relationship between two ranges of data. The tool returns the average of the product of deviations of data points from their respective means. Determines whether two ranges of data move together, whether small values of one set are associated with large values of the other, or whether values in both sets are unrelated. Descriptive statistics—generates a report on unvariate statistics for data in the input range, providing information about the central tendency and variability of the data. Exponential smoothing—predicts a value based on the forecast for the prior period, adjusted for the error in that forecast. The tool uses the smoothing constant @, the magnitude of which determines how strongly the forecasts respond to errors in the prior forecast. F-test—two-sample variables. Performs a two-sample F-test to compare two population variances. Fourier analysis—solves problems in linear systems and analyzes periodic data by using the Fast Fourier Transform (FFT) method to transform data. This tool also supports inverse transformation, in which the inverse of transformed data returns the original data. Histogram—calculates individual and cumulative frequencies for a cell range and data bins. The tool generates data for the number of occurrences of a value in a data set. Moving average—projects values in the forecast period, based on the average value of the variable over a specific number of preceding periods. A moving average provides trend information that is a simple average of all historic data would mast. Random number generation—tool fills a range with independent random numbers drawn from one of several distributions.
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Cost of Capital
Rank and percentile—produces a table containing the ordinal and percentage rank of each value in a data set. Regression—performs linear regression analysis by using least squares method to fit a line through a set of observations. Sampling—creates a sample from a population by treating the input range as a population. t-test—two-sample variables assuming equal variances. Performs a two-sample t-test. This test form assumes that the means of both data sets are equal; it is referred to as a homoscedastic t-test. t-test—two-sample variables assuming unequal variances. Performs a two-sample student t-test. The test form assumes that the variances of both ranges of data are unequal; it is referred to as a heteroscedastic t-test. t-test—two-sample variables for means. Performs a paired two-sample student’s t-test to determine whether a sample’s means are distinct. This test does not assume that the variances of both populations are equal. z-test—performs a two-sample z-test for means with unknown variances. This tool is used to test hypotheses about differences between two population means.
SOLVER ADD-IN The Solver Add-in contains tools for optimization and equation solving. They calculate solutions to what-if scenarios based on adjustable cells and constraint cells. What-if is a process of changing the values in cells to evaluate how those changes affect the outcome of formulas in the worksheet.
ADDITIONAL READING Best, Joel. Damned Lies and Statistics, Untangling Numbers from the Media, Politicians, and Activists. Los Angeles: University of California Press, 2001. ———. More Damned Lies and Statistics, How Numbers Confuse Public Issues. Los Angeles: University of California Press, 2004. Black, Ken, and David L. Eldredge. Business & Economic Statistics Using Microsoft1 Excel. Stamford, CT: Thomson, South-Western, 2001. Gonick, Larry, and Woollcott Smith. The Cartoon Guide to Statistics. New York: HarperCollins, 1994. Jones, Gerald Everett. How to Lie with Charts, 2nd ed. Booksurge Publishing, 2006. Koosis, Donald J. Statistics—A Self-Teaching Guide, 4th ed. New York: John Wiley & Sons, 1997. Kvanli, Alan H., Robert J., Pavour and Kellie B. Keeling. Introduction to Business Statistics, A Microsoft1 Excel Integrated Approach. Stamford, CT: Thomson, South-Western, 2002. Mendenhall, William, Robert J. Beaver, and Barbara M. Beaver. Introduction to Probability & Statistics, 11th ed. Belmont, CA: Thomson, Brooks/Cole 2003. Ragsdale, Cliff T. Spreadsheet Modeling & Decision Analysis, 4th ed. Stamford, CT: Thomson, South-Western, 2004. Savage, Sam L. Decision Making with Insight, 2nd ed. Belmont, CA: Thomson, Brooks/Cole, 2003. Schroeder, Larry D., David L. Sjoquist, and Paula E. Stephan. Understanding Regression Analysis—An Introductory Guide. Newbury Park, CA: Sage Publications, 1986. White, Gerald, Ashwinpaul C. Sondi, and Haim D. Fried. The Analysis and Use of Financial Statements, 3rd ed. Hoboken, NJ: John Wiley & Sons, 2003.
Index A Abbreviations, xxxvii–xxxviii Abnormal earnings growth (AEG), 19–20 for implied cost of equity capital, 259–260 valuation using, 35, 37 Acquisitions: evaluating, 383–389, 528 practical issues related to, 643 Adding back tax, 633–634 Adjusted betas: in Beta Book, 351–352 for excess cash and investments, 128, 130 for operating leverage differences, 128, 129 for size risk, 172 Adjusted funds from operations (AFFO), 591, 596, 597, 616–619 Adjusted present value (APV), 279–280, 364–365, 505–506 Ad valorem taxation, 621–636 adjustment to cost of capital, 624–627 assessed value vs. fair market value, 623–624 capital structure, 627 cost of capital in, 554 generally accepted approaches to, 622 and reconciliation of WACC and WARA, 635–636 weighted average cost of capital, 628–634 AEG, see Abnormal earnings growth AFFO, see Adjusted funds from operations After-tax capitalization rate, 500–502 After-tax weighted average cost of capital, 264–278 actual vs. hypothetical capital structure for, 272–275 for closely held company/reporting unit/project, 270–272 constant vs. variable capital structure for, 275–277 fixed book-value leverage ratio, 275, 277–278 and income tax rates, 266–270 market value of debt, 270 optimal capital structure, 266 for public company, 267–268 Agency costs, 453 APT, see Arbitrage pricing theory APV, see Adjusted present value Arbitrage pricing theory (APT), 241–246
Assets: competition of real property with other classes, 561–562 contributory, 378–379 cost of capital for, 398–404 differentiating risks among, 375–376, 397 enhancement of, 625–626 estimating risk of, 42–44 fixed, 376–377, 509–510 intangible, 377, 379–381, 391–392, 404, 406 of real estate entities, 587–588 tangible, 625 underlying, 373–375, 592–594 Asset turnovers, 510 B Band of investment method, 566–567 Bankruptcy reorganizations, 546–552 setting interest rates, 546–549 valuation of stock by income approach, 549–552 Beta, 117–118 alternatives to, 321–322 bottom-up estimates for, 140 company-specific risk adjustment, 172 in court deliberations, 542–543 criticisms of, 161 of debt capital, 139–140 downside, 176–177 for emerging markets, 321–322 equity, see Equity beta evaluating quality of, 529 excess cash and investments adjustment, 128, 130 full-information, 135, 154–159 for multifactor models, 529–530 operating leverage differences adjustment, 128, 129 ordinary least squares regression for, 151–154 practical issues related to, 640 problems with measuring, 207–208 reliability of, 163–166 as risk measure, 45, 162–163 size risk adjustment, 172 sum, 131–135, 151–154 top-down estimates for, 140 total, 232–234 Beta Book (Morningstar), 348–352, 682 Bias: bid/ask bounce bias, 219 in compounding, 114–115 delisting, 188–193, 219–220
in discounting, 115 in ERP estimation, 100–101 BIRR Portfolio Analysis, Inc., 245, 685 BIZCOMPS1, 687 BIZCOMPS1 Special Food Service Edition, 687 Bloomberg, 683 Bonds: calculating duration of, 54–55 as ERP benchmark, 91–92 historical returns on, 94 maturity dates for, 71–72 valuing, 11–12 yield of, 70–71 BondsOnline Group, Inc., 689 Bonus plans, 411–412 Book value, 6, 627 Bottom-up approach: beta, 140 estimated risk premium, 106–108 Budgeting decisions, evaluating, 12 Build-up method, 69–78 Capital Asset Pricing Model vs., 79 capitalization rate, 495–496 company-specific risk premium in, 73–75 cost of equity capital by, 70 in court deliberations, 543 equity risk premium in, 72–73 questioning business valuation experts about, 648 for real estate entities, 606–608 risk-free rate in, 70–72 small-company premium in, 73 using Duff & Phelps data, 76–78, 189–199, 228–232 using Morningstar data, 75–76, 182–184 Business combinations, new rules of accounting for, 381, 388 Business cycle risk, 243 Business enterprises, 585–586 Business outlook risk, 242 Business risk, 42–44, 561 Business Valuation Library, 689 Business Valuation Review, 689 Business Valuation UpdateTM, 689 Buy-in payments, 404 Buyout investments, realized returns on, 474–475 C Call option pricing, 520–521 Capital Asset Pricing Model (CAPM), 79–87 adjusting, 169–170
771
772 Capital Asset Pricing Model (CAPM) (continued) assumptions underlying, 86–87, 162–163 in Beta Book, 351 beta for expected rate of return, 81–83 build-up model vs., 79 company-specific risk factor in, 84 in Cost of Capital Yearbook, 345, 347 in court deliberations, 539–543 criticisms of, 161–166 expanded cost of capital formula, 84 firm size phenomenon in, 83–84 globally nested, 318 global version of, 316–318 inappropriate beta in, 529 local, single-country version of, 312–313 questioning business valuation experts about, 648–649 for real estate entities, 608–610 risk premium as function of market risk, 80–81 using Duff & Phelps data, 85–86, 199–206 using Morningstar data, 84–85, 184–185 for WACC when capital structure is changing, 295–306 for WACC when capital structure is constant, 281–294 Capital budgeting, 362–365 Capital cash flow (CCF), 278–279, 364 Capitalization, 23 combining discounting and, 27–29 discounting vs., 26 equivalency of discounting and, 29–30 formula for, 24 midyear convention, 31 questioning business valuation experts about, 647–648 of residual earnings, 34–36 Capitalization rates, 23 converting from after-tax to pretax, 500–502 converting to discount rates, 531 in court deliberations, 543, 545 discount rates vs., 7, 527–528 functional relation of discount rate and, 24–26 for real estate entities, 595–596 for real property, 569–571 Capital market risk, 561 Capital market theory (CMT), 46, 80 Capital structure, 51–65 across countries, 325 actual vs. hypothetical, 272–275 common equity, 64–65 complex, 51 components of, 4 constant, cost of equity in WACC for, 281–294 constant vs. variable, 275–277
Index convertible debt, 63–64 debt capital, 52–63 employee stock options, 64 internally inconsistent, 533 in merger/acquisition evaluations, 387–388 optimal, 266 preferred equity, 63–64 of real estate entities, 588–589 variable, cost of equity for WACC for, 295–306 CAPM, see Capital Asset Pricing Model Cash flow: capital, 364 discounted, see Discounted cash flow expected, 17–18, 92–93 free, 9, 15 net, see Net cash flows net free, 16 real vs. nominal, 324–325 Cash risk premium, 49–50 CCF, see Capital cash flow Center for Research in Security Prices (CRSP) database, 219, 220 Certainty-equivalent approach, 49–50 Classic Edition Yearbook, see Stocks, Bonds, Bills and Inflation Yearbook Closely held companies: lack of marketability discount, 417–427 pass-through entities, 435–445 private company discount, 427–433 private investment companies, 447–465 venture capital investments, 467–475 weighted average cost of capital, 270–272 CMT, see Capital market theory Cochrane study, 470–472 Common equity capital, 64–65 Company-specific risk, 46, 223–239. See also Unique risk in build-up method, 73–75 in Capital Asset Pricing Model, 84 cost to cure, 234 in court deliberations, 544, 550 distress, 234–238 in Duff & Phelps study, 224–232, 683 in global cost of capital models, 323–324 inadequate support for premium, 534–535 total beta, 232–234 Comparable uncontrolled transactions (CUT) method, 397 Compounding, bias in, 114–115 Conditional ERP, 91, 112 Confidence risk, 243 Constant growth model, 26–27 Contributory assets, 378–379 Controlling ownership interests, 479–483 lack of marketability discount, 427 in Morningstar data, 343
Control premium, 483–490 in court deliberations, 540–541 factors affecting, 484 Mergerstat/Shannon Pratt’s study of, 486–489, 686–687 and takeovers below public market trading prices, 490 Convertible debt, 63–64 Convertible preferred equity, 63–64 Corporate reward system, 411–413 Cost of capital, 3–7. See also specific topics from after-tax vs. pretax returns, 530–531 base value for, 6 basic factors for, 39–40 court deliberations on, see Legal rulings on cost of capital debt, see Cost of debt capital as discount rate, 10. See also Discount rates equity, see Cost of equity capital global models for, see Global cost of capital models impact of risk on, 40–44 key characteristics of, 7 notation system for variables, xxvii–xxxiii questioning business valuation experts about, 648 real vs. nominal, 324–325 reasonableness check for, 495–496 use of term, 6 weighted average, see Weighted average cost of capital Cost of Capital Resources Web site, 352–357, 682 Cost of Capital Yearbook, 343–348, 682 Capital Asset Pricing Model, 345, 347 cost of equity models, 345, 346 Fama-French 3-factor model, 347 implied or discounted cash flow models, 347–348 organization of data, 344–345 Cost of debt capital, 52–63 ad valorem taxation, 632–633 current market yields on debt, 52–55 default loss in, 62–63 employee stock options, 64 personal guarantees, 59–61 postretirement obligations, 61–62 practical issues related to, 642 preferred equity, 63–64 tax effect on, 55–56 Cost of equity capital, 46 ad valorem taxation, 628–630 arbitrage pricing theory, 241–246 ‘‘as if publicly traded,’’ 599–600 by build-up method, 70 Capital Asset Pricing Model, 79–87 in Cost of Capital Yearbook, 345, 346 in court deliberations, 542 for distressed firms, 236–238
Index Fama-French 3-factor model, 246–249 global models for, see Global cost of capital models implied, see Implied cost of equity capital incorrect/inadequately-supported data used for, 534–535 Market-Derived Capital Pricing Model, 249–250 for reporting units, 640–642 risk premiums, 628–630 in SBBI Yearbooks, 330–331 yield spread model, 250–251 Cost of invested capital, 46. See also Weighted average cost of capital Cost to cure, 234 Countries, sources of information on, 311 Country credit rating method, 319 Country risks, 309–311, 319–320 CRSP database, see Center for Research in Security Prices database Currency risk, 308–309 CUT (comparable uncontrolled transactions) method, 397 D Damages, cost of capital included in, 552 Das, Jagannathan, and Sarin study, 472–474 Data resources, 681–689. See also specific resources arbitrage pricing model, 685 betas, 683 Duff & Phelps Risk Premium Report, 683 earnings forecasts and related data, 683–64 equity risk premium, 110–112 global cost of capital models, 311, 320–321 implied cost of equity capital, 261 international risk, 689 lack of marketability, 688 larger company mergers and acquisitions, 685–687 Morningstar cost of capital data, 682 partnership transactions, 688 periodicals, 689 private company sale transactions, 687–688 publicly traded stock, 685 DCF, see Discounted cash flow DCR, see Debt service coverage ratio DDM, see Dividend discount model Debt capital: in acquisitions, 387–388 beta of, 139–140 cost of, see Cost of debt capital leases as, 56–59 market value of, 270 questioning business valuation experts about, 649
773 Debt ratings, 52 Debt service coverage ratio (DSCR, DCR), 568–569 Default loss, 62–63 Delisting bias, 188–193, 219–220 Depreciation, 509, 627 Direct capitalization, 562–571 band of investment method, 566–567 Elwood formula, 567–569 estimating capitalization rate, 569–571 overall, 562–566 residual methods, 571, 572 Discounted cash flow (DCF), 253–259 as best corporate decision model, 362–364 in Cost of Capital Yearbook, 347–348 in court deliberations, 538–542, 545, 550–551 for FMV of distressed firms, 521–522 for implied cost of equity capital, 253–259 for individual real property investments, 571–573 in merger/acquisition decisions, 385 multistage model of, 254, 258–259 for potential future value of distressed firm, 517–519 projecting net cash flows, 503–506 for real estate entities, 598 single-stage model of, 254–256 Discounting, 23 bias in, 115 capitalizing vs., 26 combining capitalization and, 27–29 equivalency of capitalizing and, 29–30 midyear convention, 30 questioning business valuation experts about, 647 Discount rates, 6. See also Cost of capital adjusting to alternative economic measures, 499–502 building lack of marketability discount into, 425–426 capitalization rate derived from, 23 capitalization rates vs., 7, 527–528 converting to capitalization rates, 531 cost of capital as, 10 in court deliberations, 540, 544 defined, 6 functional relation of capitalization rate and, 24–26 mismatching economic income measure and, 530–531 for net cash flow vs. net income, 531 real vs. nominal, 530 Distressed firms, 235–238 cost of equity capital of, 236–238 valuing, 235–236 Diversified companies, valuing businesses of, 534 Dividends:
long-term, 611–612 for real estate entities, 601–605 Dividend discount model (DDM), 106–107 Divisional costs of capital, 367–369 divisional size as risk measure, 369 estimating, 368–369 DoneDeals1, 687 Downside beta, 176–177 Downside risk, 170–171 DSCR, see Debt service coverage ratio Duff & Phelps data: build-up method using, 76–78, 189–199 Capital Asset Pricing Model using, 85–86, 199–206 company-specific risk in, 224–232, 683 correcting for ‘‘delisting bias,’’ 188–193 description of data, 186–188 divisional cost of equity capital, 367 practical application of data, 195–199 ranking of companies, 188 size effect in, 185–206 E Economic income: mismatching discount rate and, 530–531 net cash flow as measure of, 9–10, 18–19 total expected benefits as, 6 Economic value added (EVA), 407–414 as basis of financial management system, 409–410 in capital budgeting and feasibility analysis, 361, 383 and corporate reward system, 411–413 increasing shareholder value with, 408 standard accounting treatments vs., 408–409 Economic value added method, 506 EDGAR Online Inc., 685 EDGAR service, 685 Effective gross income, 580 Elwood formula, 567–569 Emory Pre-IPS Discount Studies, 688 Employee stock options, 64, 544–545 Enhancement of assets, 625–626 Enterprise value, 533 Environmental issues: cleanup, 642–643 for real property, 562 Equity. See also Equity capital employee stock options as, 64 net cash flow to, 16, 504 valuation of, 12 Equity beta, 117–139 adjusted, 131 choice of market index, 122 choice of risk-free rate, 122
774 Equity beta (continued) differences in estimation of, 121–122 estimation of, 118–121 estimation research, 138 frequency of return measurement, 122 full-information, 135 fundamental, 136–138 and length of sample/look-back period, 121–122 levered and unlevered, 123–130, 143–150 modified, 130, 131 peer group, 135–136 smoothed, 131 sum beta, 131–135 Equity capital: common, 64–65 cost of, see Cost of equity capital preferred, 63–64 Equity cash flow method, 504 Equity risk premium (ERP), 89–113 in build-up method, 72–73 choice of risk-free rate for, 91–93 defining, 90–91 for developed economies, 312–313 estimating, 91–93 Morningstar’s long-term average as, 529 practical issues related to, 639–640 realized risk premium approach, 93–105 risk-free rate for, 528 in SBBI Yearbooks, 330–331 sources of estimates, 110–112 unconditional vs. conditional, 112 Erb-Harvey-Viskanta country credit rating method, 319 ERP, see Equity risk premium Estate of Adams v. Commissioner, 544 Estate of Heck v. Commissioner, 544 EVA, see Economic value added Examination of experts on cost of capital, 645–650 Ex ante approach, 91. See also Forward-looking approaches Excess earnings method, 491–497 conceptual basis for, 493 in cost of capital reasonableness check, 495–496 Revenue Ruling 68-609, 492 sanity check on valuations with, 531–532 steps in applying, 493–494 vagaries of, 497 Expanded beta, 172 Expected cash flows: measuring average period of, 92–93 probability-weighted, 17–18 Expected rates of return, 6. See also Cost of capital cost of capital as representation of, 5–6 discount rate as, 6
Index historical rates of return vs., 528–529 total, 10 Expected value method, 48 Ex post approach, 91. See also Realized risk premium F FactSet Mergerstat LLC data, 686 Fair market value, 449, 483, 521–525, 623–624 Fair value, future earnings in, 537 Fama-French (FF) 3-factor model, 246–249, 347 Family law, cost of capital in, 545–546 FASB Concepts Statement No. 7 (Con 7), 48–50 Feasibility studies, 362–365 Fernandez formulas, 127, 150 FF model, see Fama-French 3-factor model FFO, see Funds from operations Financially distressed firms, 516–525 and FMV exceeding face value of debt, 521–525 potential future value of, 517–521 Financial management system, 409–410 Financial Post Crosbie, 685–686 Financial risk, 43 Financial Valuation and Litigation Expert, 689 First Call database, 683 First Research industry profiles, 684 Fiscal years, matching projection periods and, 32–34 Fixed assets, 376–377, 509–510 Fixed book-value leverage ratio, 150, 275, 277–278 Flotation costs, 634 The FMV Restricted Stock StudyTM, 418–420, 688 Forecasting, 260–261 Forward-looking approaches (to ERP), 106–110 bottom-up, 106–108 surveys, 109–110 top-down, 108–109 Free cash flow, 9, 15. See also Net cash flows Full-information beta, 135, 154–159 Functions: cost of capital for, 398–404 differentiating risks of, 395–397 Funds from operations (FFO), 591, 596, 597, 600–602, 616–619 Fundamental risk, 174–175 G Generally accepted accounting principles (GAAP), 408 Global cost of capital models, 307–325 adjusting for local country risk exposure, 319–320 alternative risk measures to beta, 321–322
capital structure, 325 choosing, 311–312 company-specific risk factor in, 323–324 country credit rating method, 319 country risks, 309–311 currency risk, 308–309 expanded formula, 324 global version of CAPM, 316–318 local, single-country version of CAPM, 312–313 nominal vs. real cash flows and cost of capital, 324–325 risks in, 308–311 size premium in, 322 sources of information for, 311, 320–321 U.S. cost of equity capital adjusted for country yield spreads, 313–314 U.S. cost of equity capital adjusted for non-U.S. volatility spreads, 314–316 Goodwill impairment, 370–371 Gordon Growth Model, 26–27, 254 Gross v. Commissioner, 435–440, 544 Growth, notation system for, xxxvi Growth rates: perpetual annual, 256–258 projected beyond value of capital, 532–533 sustainability of, 531 unattainable, 535 Growth stocks, 246 H Hamada formulas, 127, 143–144 Hardzog, In re, 547–548 Harris-Pringle formulas, 127, 147–148 Herbert V. Kohler, Jr., et al., Petitioners v. Commissioner of Internal Revenue report, 701–722 Historical returns: on company and market index, 152–153 expected rates of return vs., 528–529 financial analysis of, 506–510 on stocks and bonds, 94–95 Hyperinflation, 6 I I/B/E/S/ database, 683–684 IBS market database, 687 Implied cost of equity capital, 253–260 in Cost of Capital Yearbook, 347–348 discounted cash flow method, 253–259 residual earnings method, 250–260 sources of information for, 261 Implied FFO yields, 600–602 Incentive compensation, 411 Income approach: questioning business valuation experts about, 646–647
Index valuation of bankruptcy stock by, 549–552 valuation of real property, 578–581 Income capitalization valuation approach, 594 Income tax: and transfer pricing, 391 and WACC, 266–270 Income variables, notation system for, xxxiv Individual real property investments, 559–577 band of investment method, 566–567 capitalization rate estimation, 569–571 competition of real property with other asset classes, 561–562 direct capitalization method, 562–571 discounted cash flow method, 571–573 Elwood formula, 567–569 overall direct capitalization, 562–566 property discount rate estimation, 573–577 residual capitalization methods, 571, 572 typical structure of transactions, 560–561 Industry beta, 352 Industry risk premium, 74, 337–342, 643 Inflation risk, 242, 243, 562 Initial public offering (IPO), 419. See also Pre-initial public offering studies Intangible assets: categories of, 392–394 identifiable, 377 implied overall rate of return for, 379–381 SFAS No. 141 and valuation of, 404, 406 value of, 391–392 Integra 5-year industry data reports, 684 Intellectual property, 392–394. See also Intangible assets Interest rates, in bankruptcy reorganizations, 546–549 Interest rate risk, 242 International Cost of Capital Perspectives Report, 353–357 International differences between markets, see Global cost of capital models Invested capital, 504–505 net cash flow to, 16, 504–505 valuation of, 12 Investments: cost of capital as function of, 5 liquidity of, 449–450, 454 Investment risk, for real property, 561 Investment value, 483 Investor expectations, comparing realized risk premium to, 101–105 IRS regulations, Section 482, 404, 405
775 Iterative process for cost of equity, 270, 271 with changing capital structure, 295–306 with constant capital structure, 281–294 steps in, 272–274 using financial spreadsheet model, 285–293, 297–305 J January effect, 218 L Lack of marketability discounts, 417–427 built into discount rate, 425–426 for controlling ownership interests, 423–425, 427–433 discrete percentage discount, 418–425 for minority ownership interests, 418–423 private company discount, 427–433 private investment companies, 454–455 and venture capital returns, 431–432 Lag effect (beta), 131–135 Leases, as debt, 56–59 Legal rulings on cost of capital, 537–555 adjustments based on, 624–625 for ad valorem taxation, 54 after-tax vs. pretax returns, 531 for bankruptcy reorganizations, 546–552 cash flow measurement, 626–627 for ESOP stock valuation, 544–545 for fair value, 440–441 for family law, 545–546 included in damages, 552 for pass-through entities, 436–440 for prior trading prices, 484 for S corporation value, 444 for shareholder disputes, 537–541 in tax courts, 541–544 for taxicab lease rates, 553–554 for utility rate-setting, 552–553 Legislative risk, for real property, 562 Leverage, 75 Leveraged stock options (LSOs), 412–413 Levered equity beta, 123–130 in Beta Book, 351 capital structure weights in, 150 choosing unlevered beta vs., 125–128 for distressed companies, 237–238 excess cash and investments adjustment, 128, 130 Fernandez formulas for, 150 formulas for, 123–125 Hamada formulas for, 143–144 Harris-Pringle formulas for, 147–148 Miles-Ezzell formulas for, 144–147 operating leverage differences
adjustment, 128–130 practitioners’ method for, 148–149 Levered firms, valuing, 264 Liquidity of investments, 46, 449–450, 454 Local country risk, 319–320 LSOs, see Leveraged stock options M McCord v. Commissioner, 457–464 Marketability of interest, questioning business valuation experts about, 649. See also Lack of marketability discounts Market-Derived Capital Pricing Model, 249–250 Market inefficiency, 46 Market risk, 45, 79–81, 308, 398, 561 Market risk premium, 89, 117. See also Equity risk premium Market timing risk, 243–244 Market value: in ad valorem taxation, 621 book value vs., 6 of debt capital, 270 and discount rate, 216 and size of company, 186 Mathematical functions, notation system for, xxxvi Maturity risk, 45, 398 Mergent, Inc., 685 Mergers, evaluating, 383–389 Mergerstat/Shannon Pratt’s Control Premium Study, 486–489, 686–687 Merrill Lynch, 683 Midyear convention, 30–32 Miles-Ezzell formulas, 127, 144–147 Minority Interest Discount Database Package, 688 Minority ownership interests, 479–483 lack of marketability discount, 427 in Morningstar data, 343 Mismatching error, 530–531 Modified CAPM, questioning business valuation experts about, 648–649 Morningstar, Inc., 329, 682, 683 Morningstar data, 179–185 Beta Book, 348–352, 682 build-up method using, 75–76, 182–184 Capital Asset Pricing Model using, 84–85, 184–185 Cost of Capital Resources, 352–357, 682 Cost of Capital Yearbook, 343–348, 682 long-term average, 529 and minority vs. controlling interest, 343 size effect in, 179–185 Stocks, Bonds, Bills and Inflation Yearbook, 330–343, 682 and taxes, 337, 342–343
776 MSCI Barra, 683 Multifactor models, inappropriate beta in, 529–530 Multistage DCF model, 254, 258–259 N Net cash flows, 9–10, 15–19, 21 adjusted present value method, 505–506 alternative, 514–515 applying discount rate for net income to, 531 in capital budgeting and feasibility studies, 362–364 common errors in estimating, 515 converting to other economic income variables, 499–502 defining, 15–16 economic value added method, 506 to equity, 16, 504 equity cash flow method, 504 estimating, 503–506 to invested capital, 16, 504–505 invested capital method, 504–505 in merger/acquisition evaluations, 385–386 as preferred measure of economic income, 18–19 as probability-weighted expected values, 17–18 projecting, 506–510 questioning business valuation experts about, 649–650 for real estate entities, 591, 613–614 residual income method, 505 risky, 41–42 testing estimates of, 511–514 Net free cash flow, 16 Net income, applying discount rate for net cash flow to, 531 Net operating income (NOI), 579–580, 622 Net present value (NPV), 361–362 Net working capital, 376–377, 510 NOI, see Net operating income Noncash charges, 509–510 Nonmarketable investment company evaluation (NICE), 448, 450–451, 457, 464–465 NPV, see Net present value O Off-balance sheet financing, 642 OLS regression, see Ordinary least squares regression Operating expenses, 581 Operating statement, reconstructed, 581, 582 Operations: estimating risk of, 42–44 of real estate entities, 614–619 Optimal capital structure, 266 Option pricing model: for FMV of distressed firms, 522–525
Index for potential future value of distressed firm, 520 Ordinary least squares (OLS) regression, 151–154 beta, 131–138 size premiums, 207–209 Overall cost of capital, 46. See also Weighted average cost of capital Overall direct capitalization: for individual real property, 562–566 for real estate entities, 594–595 Ownership interest, 411–413 controlling, 343, 423–425, 427–433, 479–483 minority, 343, 418–423, 479–483 P Pass-through entities, 435–445 characteristics of, 436 Delaware court adjustment for tax difference, 440–441 and Gross decision, 436–440 market evidence of value of interests in, 441–444 risks of investments in, 444–445 Peer group beta, 135–136, 352 PEG ratio, 260 Periods: investment, value and, 449–452 look-back, 121–122 projection, matching fiscal years and, 32–34 sample, 98–100, 121–122 in a series, notation system for, xxxiv used in measurements, 96–100 Perpetual growth rate, 256–258 Personal guarantees, 59–61 PICs, see Private investment companies Postretirement obligations, 61–62 Potential future value (distressed firms), 517–521 Potential gross income, 580 Practitioners’ method (beta), 148–149 Pratt’s StatsTM, 688 Preferred equity (stock): ad valorem taxation, 630–632 convertible, 63–64 valuing, 24 Pre-initial public offering studies, 419–423 Present value: formula for, 11 traditional vs. expected cash flow approaches to, 48 Pretax capitalization rate, 500–502 Pretax weighted average cost of capital, 278–280 Private company discount, 427–433 discrete percentage for, 427–428 quantifying, 428–431 reasons for, 432 and venture capital returns, 431–432 Private investment companies (PICs), 447–465
characteristics of, 448–449 investment period and value in, 449–452 lack of control with, 452–453 lack of marketability or illiquidity with, 454–456 McCord v. Commissioner example of, 457–464 Probability-weighted expected values, 17–18 Profitability estimates, 508–510 Profit split methods, 397–398 Projects: after-tax WACC for, 270–272 cost of capital for, 362 realized returns on, 470–474 selection of, 9–13 weighted average cost of capital for, 270–272 Projected cash flow, 614–616 Projected net cash flow, 616 Projection periods, matching financial statement fiscal years and, 32–34 Property discount rate, 573–577 The PRS Group, Inc., 689 R Rates of return: historical vs. expected, 528–529 notation system for variables, xxvii–xxxiii total expected, 10 Real estate cycles, 590–591 Real estate entities, 585–612 adjusted funds from operations, 616–619 assets of, 587–588 build-up method, 606–608 Capital Asset Pricing Model, 608–610 capitalization rate estimation, 595–596 capital structure of, 588–589 categorization of, 587 cost of equity capital ‘‘as if publicly traded,’’ 599–600 and cycles in real estate, 590–591 definition of, 586–587 discounted cash flow valuation of, 598 dividends, 601–605 funds from operations, 616–619 implied FFO yield, 600–602 income capitalization valuation approach, 594 legal structure of, 588 long-term dividend and total return analysis, 611–612 measuring net cash flow for, 591, 613–614 overall direct capitalization, 594–595 projected cash flow from real property operations, 614–616 projected net cash flow for, 616 underlying assets valuation approach, 592–594
Index valuation considerations for, 591–592 weighted average cost of capital, 599 Real estate investment trusts (REITs), 585, 586. See also Real estate entities Realized risk premium, 93–105 bias in, 100–101 comparing investor expectations to, 101–105 historical stock and bond returns, 94–95 measuring, 93–94 periodicity of past measurement, 96–97 selecting sample period, 98–100 summarizing data, 95–96 unexpectedly large, 105 Real property valuation, 578–583 individual, see Individual real property investments notation system for, xxxvi–xxxvii projecting cash flows, 581–583 steps in, 578–581 Reconstructed operating statement, 581, 582 Reporting unit cost of capital, 367, 370–381 after-tax WACC, 270–272 contributory assets, 378–379 differentiating risks among assets, 375–376 fair value of units, 371–372 identifiable intangible assets, 377 implied overall rate of return for intangible assets, 379–381 measuring, 372 net working capital and fixed assets, 376–377 practical issues related to, 640–642 size premiums for, 641–642 testing for impairment of goodwill, 370–371 underlying assets of units, 373–375 unit size as risk measure, 372–373 weighted average, 270–272 Required rate of return, 6. See also Cost of capital Residual earnings (RE), 19–20 capitalization of, 34–36 for implied cost of equity capital, 250–260 Residual income method, 505 Residual risk, 46 Restricted stock studies, 418–420 Retirement benefits, 61–62 Reuters estimates, 684 Revenue estimates, 508–509 Revenue Ruling 608–609, 491–492 Reward systems, 411–413 Risk, 39–47. See also Risk measures; specific types of risk in APT model, 242–246 defining, 40 in discount rate, 6
777 impact on cost of capital, 40–44 pricing of, 41–42 Risk-adjusted discount rate, 48–49 Risk-free rate, 39, 45 in build-up method, 70–72 for equity beta, 122 in ERP estimation, 91–93 for estimated equity risk premium, 528 Risk measures, 161–174 beta, 162–166, 172. See also Beta divisional size as, 369 downside risk, 170–171 duration, 173–174 fundamental risk, 174–175 total risk, 167–169 unique risk, 166–167 value at risk, 171–172 variance, 162 Risk premium, 39 cash, 49–50 company-specific, 73–75 compared to investor expectations, 101–105 Duff & Phelps data, 224–232, 683 equity, see Equity risk premium estimated market, 117 as function of market risk, 80–81 for individual real property, 561 industry, 74, 337–342, 643 market, 89, 117 realized, see Realized risk premium S SBBI Yearbook, see Stocks, Bonds, Bills and Inflation Yearbook Seasonal businesses, midyear conventions for, 32 Seasonality, size effect and, 218–219 Shareholder disputes, cost of capital in, 537–541 Shareholder value, increasing, 408 Shareholder value added (SVA), 361, 383 Single-stage DCF model, 254–256 Size effect, 179–206 and accuracy of beta, 207–208 and bid/ask bounce bias, 219 and composition of smallest decile, 209–212 data issues with, 212–214 and delisting bias, 219–220 in Duff & Phelps studies, 185–206 and measures of size, 186 in Morningstar studies, 179–185 in non-U.S. markets, 322 relationship of risk effect and, 216–217 and risks of small companies, 214–216. See also Small-company premium and seasonality, 218–219 and time-varying risk factors, 221 and transaction costs, 220
Size premium, 46, 83–84 with annual vs. monthly betas, 182 with CAPM model, 184–185 in global cost of capital models, 322 in reporting unit cost of equity capital, 641–642 in SBBI Yearbooks, 333–336 Small-company premium, 73, 182–184 Smoothed beta, 131 Standard of value: assumptions affecting, 534 impact of, 483 state differences in, 623 Standard & Poor’s, 52, 63, 683, 685 Statistical analysis, 731–768 data acquisition errors, 758–760 event relationships, 752–754 interpreting individual measurements, 744–746 laws of probability, 754–757 measures of central tendency, 735–739 measures of variability (dispersion), 739–741 with Microsoft Excel, 764–768 normal probability distribution, 742–744 population and sample distribution, 732–735 relation between two sets of measures, 746–752 sampling, 757–758 terms used in, 760–765 Stocks: equity estimates for, 246 The FMV Restricted Stock StudyTM, 688
historical returns on, 94–95 Morningstar data on, 330–343, 682 preferred, 24, 63–64 publicly traded, 685 restricted, 418 Stocks, Bonds, Bills and Inflation (SBBI) Yearbook, 330–343, 682 Classic and Valuation Editions, 330 cost of equity models, 330–331 equity risk premium, 331–333 firm size premium, 333–336 industry risk premium, 337–342 and minority vs. controlling interest, 343 and taxes, 337, 342–343 Stock options: employee, 64, 544–545 leveraged, 412–413 Sum beta, 131–135, 151–154 Sustainable growth method, 260–261 SVA, see Shareholder value added Systematic risk, 45. See also Market risk T Takeovers, prices of, 490 Target capital structure, 627
778 Target cost of capital, 365 Taxes. See also After-tax weighted average cost of capital ad valorem, see Ad valorem taxation converting from after-tax to pretax rate, 500–502 and cost of debt, 55–56 court deliberations, 541–544 double taxation, 436 and Morningstar data, 337, 342–343 property, 624 and transfer pricing, 391 Taxicab lease rates, 553–554 10K Wizard, 685 Terminal value, 535 Time horizon risk, 243 ‘‘Time to a liquidity event,’’ 449–450 Time value of money, 6 Time-varying risk factors, 221 Top-down approach: beta, 140 estimated risk premium, 108–109 Total beta, 232–234 Total expected rate of return, 10 Total return analysis, 611–612 Total risk, 167–169 Traditional method (Con 7), 48 Transfer pricing, 391–406 comparable uncontrolled transactions method, 397 cost of capital for functions and assets, 398–404 differentiating risks among company assets, 397 differentiating risks of company functions, 395–397 differentiating types of risks, 398 functional analysis, 392–395 IRS regulations, 404, 405 profit split method, 397–398 relating valuation of intangible assets to SFAS No. 141, 404, 406 value of intangible assets, 391–392 Trend and cycle analysis, 260 Two-stage model, 27–29 midyear convention in, 31–32 steps in, 28 U Uncertainty, 40, 394 Unconditional ERP, 91, 112 Underlying assets, 373–375 Undiversifiable risk, see Market risk
Index Unique risk, 46, 80, 166–167, 308, 398. See also Companyspecific risk U.S. cost of equity capital adjustments: for country yield spreads in dollardenominated debt issued by local country governments, 313–314 for non-U.S. volatility spreads, 314–317 Unlevered equity beta, 123–130 in Beta Book, 351 choosing levered beta vs., 125–128 excess cash and investments adjustment, 128, 130 Fernandez formulas for, 150 formulas for, 123–125 Hamada formulas for, 143–144 Harris-Pringle formulas for, 147–148 Miles-Ezzell formulas for, 144–147 operating leverage differences adjustment, 128–130 practitioners’ method for, 148–149 Unsystematic risk, 46. See also Unique risk Utility rate-setting, cost of capital in, 552–553 V Valuation, 9–13. See also specific topics Valuation Advisors’ Lack of Marketability Discount StudyTM, 688 Valuation date, 32 Value at risk (VaR), 171–172 Value Line Publishing, Inc., 683, 684 Value stocks, 246 ValuSource valuation software, 723–729 Variables in a series, notation system for, xxxiv Variance, 162 Vasicek shrinkage, 131 Venture capital investments, 467–475 benchmark data on, 467–468 benchmark returns on, 468–470 lack of marketability and returns on, 431–432 realized returns on buyouts, 474–475 realized returns on projects, 470–474 Volatility, 74–75 in international markets, 311 non-U.S. volatility spreads, 314–317 and size of realized risk premiums, 105
W WACC, see Weighted average cost of capital WARA, see Weighted average return on assets Weighted average capitalization rate, 495 Weighted average cost of capital (WACC), 263–280 actual vs. hypothetical capital structure for, 272–275 adjusted, 364–365 after-tax, see After-tax weighted average cost of capital assumptions inherent in, 296 for businesses of diversified companies, 534 with changing capital structure, 295–306 for closely held companies/reporting units/projects, 270–272 with constant capital structure, 281–294 constant vs. variable capital structure for, 275–277 fixed book-value leverage ratio, 275, 277–278 and income tax rates, 268–270 market value of debt, 270 optimal capital structure, 266 pretax, 278–280 for public companies, 267–268 for real estate entities, 599 for reporting units, 372–373, 375 valuing levered firms, 264 with varying capital structures, 533–534 weighted average return on assets vs., 635–636 when to use, 263–264 Weighted average return on assets (WARA), 635–636 Weightings, notation system for, xxxiv–xxxv Y Yield curve, 52, 54 Yield spreads, 174, 242 Yield spread model, 250–251 Yield-to-call date, 54 Yield to maturity, 54 Z Zacks Investment Research, Inc., 684
