LSBF class notes ACCA F2

ACCA Paper F2

Management Accounting Class Notes June 2011

© The Accountancy College Ltd January 2011 All rights reserved. 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 or otherwise, without the prior written permission of The Accountancy College Ltd.

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Contents PAGE INTRODUCTION TO THE PAPER

5

FORMULAE PROVIDED IN THE EXAMINATION PAPER

9

CHAPTER 1:

INTRODUCTION TO COST ACCOUNTING

11

CHAPTER 2:

COST CLASSIFICATION AND BEHAVIOUR

19

CHAPTER 3:

BUSINESS MATHS

29

CHAPTER 4:

MATERIALS, LABOUR, STOCK CONTROL

39

CHAPTER 5:

OVERHEADS AND ABSORPTION COSTING

53

CHAPTER 6:

COST BOOKKEEPING

65

CHAPTER 7:

MARGINAL COSTING AND CONTRIBUTION THEORY

71

CHAPTER 8:

COSTING FOR JOBS, BATCHES, AND SERVICES

79

CHAPTER 9:

PROCESS COSTING, JOINT AND BY-PRODUCTS

91

CHAPTER 10: BUDGETS

113

CHAPTER 11: STANDARD COSTING AND VARIANCE ANALYSIS

123

CHAPTER 12: CVP ANALYSIS

139

CHAPTER 13: LIMITING FACTORS, LINEAR PROGRAMMING, RELEVANT COSTS 149 SOLUTIONS TO EXERCISES

161

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Introduction to the paper

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IN T R O D U C T I O N T O T H E P A P E R

AIM OF THE PAPER The aim of the paper is to develop knowledge and understanding of how to prepare and process basic cost and quantitative information to support management in planning and decision-making in a variety of business contexts.

MAIN CAPABILITIES On successful completion of this paper candidates should be able to: A

Explain the nature and purpose of cost and management accounting

B

Describe costs by classification, behaviour and purpose

C

Apply essential business mathematics and use computer spreadsheets

D

Explain and apply cost accounting techniques

E

Prepare and coordinate budgets and standard costing for planning, feedback and control

F

Use management accounting techniques to make and support decisionmaking.

Within these main capabilities, ACCA provides a more detailed guidance on the syllabus. This can be found on pages 3 – 8 of your textbook. RELATIONAL DIAGRAM OF MAIN CAPABILITIES The nature and purpose of cost and management accounting (A)

Cost classification, behaviour and purpose (B)

Cost accounting techniques (D)

Budgeting and standard costing (E)

Business Mathematics and computer spreadsheets (C)

Short-term decisionmaking techniques (F)

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IN T R O D U C T I O N T O T H E P A P E R

EXAMINER The paper F2 examiner is David Forster, who previously examined paper 1.2. David also wrote the F2 pilot paper, which gives us a good indication of how the syllabus areas will be examined under F2. David has made notable changes to the paper, both in format and syllabus content.

FORMAT OF THE EXAM PAPER Paper F2 can be sat as a written or a computer based paper. 2 hour paper. Both computational and non-computational questions. 90 marks in total. 40 two mark questions and 10 one mark questions. Mix of MCQ and true or false. In the CBE equivalent, other question forms may be used, such as multiple response, multiple-response matching, or number entry.

ALL QUESTIONS ARE COMPULSORY

ARTICLES Five steps to multiple-choice success 17 May 2007 Steve Widberg describes a five-step approach to answering multiple-choice questions. Building knowledge 03 Nov 2006 Bob Souster, David Forster and Nicola Ventress guide students through the new ACCA Qualification Knowledge Module papers / RELEVANT TO NEW ACCA QUALIFICATION PAPERS F1, F2, AND F3.

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IN T R O D U C T I O N T O T H E P A P E R

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Formulae provided in the examination paper

Regression analysis

∑ y b∑ x − n n

a=

n∑ xy − ∑ x ∑ y

b=

r =

2

n∑ x 2 − (∑ x )

n∑ xy − ∑ x ∑ y

[(n∑ x

2

2

− (∑ x )

)(n∑ y

2

2

− (∑ y )

)]

Economic order quantity

=

2C 0D Ch

Economic batch quantity

=

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2C 0D D  C h 1 −  R 

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F O R M U L A E P R O V ID E D IN T H E E X A M I N A T IO N P A P E R

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Chapter 1

Introduction to cost accounting

CHAPTER COVERAGE 1.

What are the main differences between financial accounting and management accounting?

2.

What is the difference between data and information?

3.

What are the different levels of management within and organisation?

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C H A P T E R 1 – I N T R O D U C T I O N T O C O S T A C C O U N T IN G

CHAPTER CONTENTS INTRODUCTION ---------------------------------------------------------- 13 DATA AND INFORMATION ---------------------------------------------- 14 MANAGEMENT ACTIVITIES --------------------------------------------- 15 LEVELS OF MANAGEMENT ----------------------------------------------- 16 ORGANISATIONS -------------------------------------------------------- 17

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C H A P T E R 1 – I N T R O D U C T I O N T O C O S T A C C O U N T IN G

INTRODUCTION Accounting is divided into two main areas – financial accounting and management accounting. Whereas financial accounting looks at the performance of the organisation (in the past), management accounting looks at past performance as well as providing information which is used for decision making within the organisation (for the future).

Financial Accounting ●

External use

●

Strict rules format

●

●

Management Accounting ●

Internal use

●

Content and format adopted to company needs

Primarily financial information

●

Both financial information

Prepared annually

●

Prepared as often as necessary

for

content

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and

and

non-financial

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C H A P T E R 1 – I N T R O D U C T I O N T O C O S T A C C O U N T IN G

DATA AND INFORMATION Many people assume that data and information are the same. They are not. Data is raw, unprocessed information. Information is processed data. meaningful to the user.

It must be processed in a way that makes it

Examples:

For data to be meaningful it must have certain characteristics or attributes. These are many but can be summarised by the acronym – ACCURATE. Can you identify what you think would be an attribute for each of the letters of accurate?

A C C U R A T E What do we use information for?

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C H A P T E R 1 – I N T R O D U C T I O N T O C O S T A C C O U N T IN G

MANAGEMENT ACTIVITIES In organisations information is used for management activities such as planning, decision making and control. Each of these three uses will be highlighted throughout this subject. Before that, how would you describe each of these techniques?

Planning:

Decision making:

Control:

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C H A P T E R 1 – I N T R O D U C T I O N T O C O S T A C C O U N T IN G

LEVELS OF MANAGEMENT Management may be on either an operational, tactical or strategic level within the organisation. How can we differentiate between these?

Strategic

Tactical

Operational

16

Long-term

0

0

0

Medium-term

Short-term

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C H A P T E R 1 – I N T R O D U C T I O N T O C O S T A C C O U N T IN G

ORGANISATIONS No organisation will operate as a single entity. Each organisation would be divided up into various departments. Some of these departments would be dealing with producing our products while others would be providing a service, both to our customers and to our production departments. These will be highlighted later in the course.

Cost centre – is defined as a production or service location, a function, an activity or an item of equipment for which costs can be ascertained. Revenue centre – a centre devoted to raising revenue only. Profit centre – a centre accountable for costs and revenues. Investment centre – a centre which has its performance evaluated by its return on capital employed. Cost unit – a unit of product or services for which costs can be ascertained. These are usually classed in relation to the unit the product is sold in. Examples: Petrol

- per litre

Paint

- per tin

Bread

- per loaf

Using these cost units assist us being able to cost the products made. We also need to identify service units. These will be discussed in the session on service costing.

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C H A P T E R 1 – I N T R O D U C T I O N T O C O S T A C C O U N T IN G

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Chapter 2

Cost classification and behaviour

CHAPTER COVERAGE 1.

What are different classifications of costs within an organisation?

2.

Which costs are involved directly in the production of goods and services?

3.

What are the different cost behaviours?

4.

What methods are used to separate fixed and variable costs and use this information for forecasting?

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C H A P T E R 2 – C O S T C L A S S IF I C A T IO N A N D B E H A V IO U R

CHAPTER CONTENTS COST CLASSIFICATIONS ------------------------------------------------ 21 DIRECT AND INDIRECT COSTS

21

PRODUCTION AND NON-PRODUCTION COSTS

21

COST BEHAVIOUR ------------------------------------------------------- 22 FIXED COSTS

22

VARIABLE COSTS

22

STEP COSTS

23

SEMI-VARIABLE COSTS

23

HIGH-LOW METHOD ----------------------------------------------------- 25

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C H A P T E R 2 – C O S T C L A S S IF I C A T IO N A N D B E H A V IO U R

COST CLASSIFICATIONS Costs in any organisation come in many forms and relate to many different things. In order to properly control the costs of a business, management must understand the nature of the costs that it faces and how they behave. We can divide or classify these costs into 3 main areas: ●

Materials

●

Labour

●

Other expenses

Materials and labour costs speak for themselves, however other expenses cover many different expenses within the business – rent, administration, heating and lighting, motoring – the list is endless.

Direct and indirect costs ●

Direct costs are those which are directly involved with the making of a product or service. The sum of the direct costs is equal to the Prime Cost

●

Indirect costs are those which are incurred for other reasons. For instance, the wages of a production worker is said to be a direct cost whilst the wages (salary) of a supervisor would be considered as an indirect cost. The sum of the indirect costs is equal to the Overheads

We will deal with these classifications in more detail in future sessions.

Production and non-production costs Production costs relate to costs that are incurred in the manufacture of goods or the delivery of a service. They are incurred as a result of manufacture and therefore should be included in the cost of sales in the income statement and should also be included as part of the inventory valuation. Non-production costs are incurred by the business in order to operate as a successful entity (other than production costs). The main categories of nonproduction costs are: Distribution costs Selling costs Finance costs Administrative costs.

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C H A P T E R 2 – C O S T C L A S S IF I C A T IO N A N D B E H A V IO U R

COST BEHAVIOUR As well as dividing the costs into the above classifications each cost can be further classified into fixed, variable, stepped and semi-variable. This classification depends upon the behaviour of the cost. Cost behaviour looks at whether or not a cost will change when the company’s level of activity changes. Level of activity = number of units produced and sold

Fixed costs A fixed cost is a cost which remains constant in total terms when level of activity changes. An example of a fixed cost would be the rent of a building. A fixed sum we pay each period. A fixed cost can be represented in a graph as: Total cost

Level of activity

These costs, although fixed in total, do reduce on a per unit basis as the level of activity rises. For example is company has fixed costs of $5,000 and plans to produce and sell 1,000 units, then the fixed cost per unit can be calculated as: $5,000 / 1,000 = $5 /unit If the company increased the level of activity to 2,500 units then the fixed cost per unit would be $5,000 / 2,500 = $2 /unit

Variable costs Variable costs vary in proportion to the level of activity. For example if it costs £5 to make 1 unit we assume that it costs £10 to make 2, £50 to make 10 and so on. A variable cost can be represented in a graph as:

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C H A P T E R 2 – C O S T C L A S S IF I C A T IO N A N D B E H A V IO U R

Total cost

Level of activity As activity increases, total variable cost will increase. Variable cost per unit usually remains constant.

Step costs Stepped costs are fixed costs over a wider activity range. Some fixed costs will increase once the level of activity goes above a certain threshold. An example of this might be a supervisor in a factory on a salary. Each supervisor is in charge of 20 workers. As soon as we employ more than 20 workers we need to employ another supervisor. A stepped cost may be represented in a graph as: Total cost

Level of activity

Semi-variable costs A semi-variable cost contains a fixed and a variable element. An example of this would be an electricity bill where we pay a fixed charge per period plus a variable charge for each unit of electricity consumed. A semi-variable cost can be represented in a graph as:

Total cost

Level of activity

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C H A P T E R 2 – C O S T C L A S S IF I C A T IO N A N D B E H A V IO U R

We assume that all these relationships are linear, ie, the act is a straight line. Unfortunately in practice this does not happen due to economies of scale (discounts for quantity purchases or sales). For the purposes of our studies we will assume that costs react to each other in a linear (straight line) relationship.

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C H A P T E R 2 – C O S T C L A S S IF I C A T IO N A N D B E H A V IO U R

HIGH-LOW METHOD If we have a semi variable cost we need to calculate the fixed and variable elements of the cost. The method we use is called the HIGH-LOW method. It is based upon the equation of a straight line: y = a + bx This can also be represented as: Total cost = fixed cost + (variable cost x no of units) Once the fixed and variable cost elements have been calculated, this information can be used to forecast what Total Costs will be at different levels of activity.

Exercise 1 The following cost information is available. Output

65,000 units

105,000 units

Cost

£133,000

£210,000

Required Using the above data, calculate the fixed and variable costs for the business and the total cost for 165,000 units.

Solution: Variable cost per unit

=£

Total fixed cost

=£

Total cost for 165.000 units

=£

+ (£

x 165,000 units) = £

It is essential to master this technique as it is a common examination question and you will be required to use this technique many times during your management accounting studies. When there are more than two pairs of data given we will always use the highest and lowest for this technique.

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C H A P T E R 2 – C O S T C L A S S IF I C A T IO N A N D B E H A V IO U R

Class exercises 1.

A manufacturing company has four types of cost (identified as T1, T2, T3 and T4). The total cost for each type at two different production levels is: Cost type T1 T2 T3 T4

Total cost for 125 units £ 1,000 1,750 2,475 3,225

Total cost for 180 units £ 1,260 2,520 2,826 4,644

Required: Which two cost types would be classified as being semi-variable?

2.

A

T1 and T3.

B

T1 and T4.

C

T2 and T3.

D

T2 and T4.

The following diagram represents the behaviour of one element of cost: Total cost

Volume of activity

Required: Which of the following descriptions is consistent with the above diagram?

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A

Annual total cost of factory power where the supplier sets a tariff based on a fixed charge plus a constant unit cost for consumption which is subject to a maximum annual charge.

B

Total annual direct material cost where the supplier charges a constant amount per unit which then reduces to a lower amount per unit after a certain level of purchases.

C

Total annual direct material cost where the supplier charges a constant amount per unit but when purchases exceed a certain level a lower amount per unit applies to all purchases in the year.

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C H A P T E R 2 – C O S T C L A S S IF I C A T IO N A N D B E H A V IO U R

D

3.

Annual total cost of telephone services where the supplier makes a fixed charge and then a constant unit rate for calls up to a certain level. This rate then reduces for all calls above this level.

An organisation has the following total costs at two activity levels: Activity level (units) Total costs (£)

17,000 140,000

22,000 170,000

Variable cost per unit is constant in this range of activity and there is a step up of £5,000 in the total fixed costs when activity exceeds 18,000 units.

Required: What is the total cost at an activity level of 20,000 units?

A

£155,000

B

£158,000

C

£160,000

D

£163,000

Before answering this question, think carefully about the information given relating to the step cost. How should we use it?

4.

An organisation has the following total costs at two activity levels: Activity level (units) Total costs (£)

8,000 22,000

13,000 31,000

Fixed costs are constant in this range of activity and variable cost per unit decreases by £1.5 per unit when activity exceeds 12,000 units

Required: What is the total cost at an activity level of 16,000 units?

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C H A P T E R 2 – C O S T C L A S S IF I C A T IO N A N D B E H A V IO U R

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Chapter 3

Business maths

CHAPTER COVERAGE 1.

How to draw a scatter-graph and use regression analysis for forecasting.

2.

Understanding and calculating the correlation coefficient

3.

The co-efficient of determination

4.

What are expected values and why do management accountants use them?

5.

Business spreadsheets

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C H A P T E R 3 – B U S IN E S S M A T H S

CHAPTER CONTENTS SCATTER GRAPHS ------------------------------------------------------- 31 REGRESSION ANALYSIS

31

CORRELATION ----------------------------------------------------------- 33 INTERPOLATION AND EXTRAPOLATION ------------------------------ 34 THE COEFFICIENT OF DETERMINATION------------------------------- 35 EXPECTED VALUES------------------------------------------------------- 36 BUSINESS SPREADSHEETS --------------------------------------------- 37

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C H A P T E R 2 – B U S IN E S S M A T H S

SCATTER GRAPHS A scatter-graph is a graph on which pairs of data, which have no direct relationship, are plotted. In order to estimate future costs for a given activity level, we must draw a line through these points. It is impossible to draw a straight line which will connect all points and so we draw what is known as a LINE OF BEST FIT. From this line we can estimate future costs. This line is very subjective. Everyone will draw it in a slightly different place and so our forecasts will also differ. To make a more accurate prediction of future costs we will use regression analysis.

Regression analysis This is also known as the least squares method. The formulae we will use is:

y = a + bx b=

n∑ xy − ∑ x ∑ y 2

n∑ x 2 − (∑ x )

We will also need to calculate the average of x and y. This is done by dividing the total of x (and y) by n as in the second equation.

a = y − bx

or

a=

∑ y b∑ x − n n

where n = number of items. In this method we are required to calculate totals of columns of figures. A total is represented by the sign Σ. This is pronounced sigma. The first column of figures x represents the units. The second column y represents the costs. Σx is the total of the column of x. We also need to calculate Σxy, Σx2.

Exercise 1 Month January February March April May June

Units 400 600 550 800 750 900

Cost (£) 1,050 1,700 1,600 2,100 2,000 2,300

Required: Using the following methods, calculate the fixed and variable cost elements and forecast the cost for an output of 850 units. 1.

High-low method

2.

Regression analysis

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C H A P T E R 3 – B U S IN E S S M A T H S

Solution: 1.

High-low method

2.

Regression Month January February March April May June

32

Units (x) 400 600 550 800 750 900

Costs (y) 1,050 1,700 1,600 2,100 2,000 2,300

Xy

X2

Y2

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C H A P T E R 2 – B U S IN E S S M A T H S

CORRELATION Regression analysis assumes a linear relationship. However, this does not measure the degree of correlation between the variables as it is unlikely that the true relationship is a straight line. To do this we need to calculate the correlation coefficient, r. (This is known as Pearson’s correlation coefficient.)

r =

n∑ xy − ∑ x ∑ y

[(n∑ x

2

2

)(

2

− (∑ x ) n∑ y 2 − (∑ y )

)]

r varies between +1 and –1. +1 means perfect linear correlation 0 means no correlation -1 means perfect negative linear correlation

Required: Using the information above in Exercise 1, calculate the correlation coefficient. What does this answer signify?

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C H A P T E R 3 – B U S IN E S S M A T H S

INTERPOLATION AND EXTRAPOLATION This is simply identifying values of x and y from the regression line plotted. Interpolation is where we interrogate the line within the known range. Extrapolation is where we interrogate the line outside of the known range where the accuracy/relationship is assumed to be still valid. In reality this is not always so.

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C H A P T E R 2 – B U S IN E S S M A T H S

THE COEFFICIENT OF DETERMINATION The coefficient of determination is represented by r2 – the square of r. This signifies how much of the variation in the dependent variable is because of the variation in the independent variable. The remaining variation is then assumed to be because of random fluctuations. To explain this in simple terms, it means that if r = 1 then r2 would also = 1 or 100%. This would assume that units and costs would be in perfect proportion, ie if units were doubled then costs would also double. If r2 is below 100%, part of the increase in costs would be for other reasons. It may be that a discount was obtained in the cost of material or that the labour cost was lower/higher because of different productivity/efficiency.

Required: What is the coefficient of determination from Exercise 1?

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C H A P T E R 3 – B U S IN E S S M A T H S

EXPECTED VALUES Expected values are based on weighted averages. What is a weighted average as opposed to a simple average? In order to calculate an expected value we multiply the probability of something happening (p) by the value of the outcome (x). The expected value is therefore px. To calculate the expected value of a series of things happening we simply add up the total of all the expected values. So the total expected value is equal to:

෍ px Expected values are also used in decision making situations. A series of expected value calculations can be made and the one with the best overall expected value would be chosen.

Exercise 2 A company has a choice of three alternative investments. If successful investment A gives a profit of £100,000, of which there is a 40% chance or probability, however if not it will yield loss of (£40,000). Investment B, if successful (60%), will yield a profit of £50,000; but if not, a loss of (£20,000). Investment C, if it is successful (80% chance), will yield profit of £40,000; however if not it will deliver loss of (£10,000). Required: Which investment should be considered?

Exercise 3 A company needs to decide between two projects – Project X and Project Y. The profits that may be generated from each project are as follows: Project Probability 0.4 0.6

X Profit £3,000 £1,500

Project Y Probability Profit 0.35 £10,000 0.65 £0

Required: Which project should be chosen? What is the expected value of the profit?

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C H A P T E R 2 – B U S IN E S S M A T H S

BUSINESS SPREADSHEETS A spreadsheet is a computerized tool for mathematical analysis and presentation of numerical data. It enables mathematical analysis and calculations to be performed quickly and efficiently. Spreadsheets are used in many areas of management accounting including: ●

Budgeting

●

Variance analysis

●

Forecasting & decision making. Spreadsheets could be set up to analyse different possible outcomes of a project.

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C H A P T E R 3 – B U S IN E S S M A T H S

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Chapter 4

Materials, labour, stock control

CHAPTER COVERAGE 1.

What are various procedures and documents required for ordering, receiving and issuing stocks of materials?

2.

Why do the companies hold additional inventories?

3.

What different types of mechanics are used to calculate and interpret optimal re-order levels, re-order quantities and minimum and maximum levels of stock to be held.

4.

How to minimise the total cost of holding and ordering stocks.

5.

What are different methods of remuneration for work done.

6.

What are direct and indirect labour costs.

7.

How do we account for overtime payments in an accounting system.

8.

How to measure labour turnover, efficiency and productivity.

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

CHAPTER CONTENTS MATERIALS --------------------------------------------------------------- 41 STOCK HOLDING COSTS AND ECONOMIC ORDERING QUANTITY -- 42 STOCK HOLDING COSTS

42

STOCK ORDERING COSTS

42

ECONOMIC ORDER QUANTITY

42

BULK DISCOUNTS

44

RE-ORDER LEVELS ------------------------------------------------------- 45 FREE STOCK -------------------------------------------------------------- 46 LABOUR COSTS ---------------------------------------------------------- 47

40

BONUS SCHEMES

49

DIRECT AND INDIRECT LABOUR COSTS

50

LABOUR RATIOS

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

MATERIALS Materials required for stock and later issue to production are subject to a set procedure: a.

A purchase requisition is raised and sent to the purchasing dept.

b.

A purchase order is sent to the supplier.

c.

A delivery note is received together with the goods (advice note). checked to the purchase order to ensure it is the same.

d.

A GRN (goods received note) records the details for entering into stock.

e.

A purchase invoice is sent to the company from the supplier to request payment.

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This is

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

STOCK HOLDING COSTS AND ECONOMIC ORDERING QUANTITY A company needs to consider two things in relation to stock management: ●

How many units of stock to purchase each time an order is placed with the supplier

●

How much stock the company should hold to ensure there are no shortages.

Stock holding costs The company needs to hold a certain amount of stock to ensure it can meet customer demand. This has a charge to it: ●

Warehouse space

●

Operatives

●

Insurance

●

Capital costs

●

Deterioration costs.

These costs vary according to the amount of stock held at any one time. The company must try to minimise these costs by holding as little stock as is possible. The annual cost of holding stock is calculated as:

Q × Ch 2 Where

Q

=

order quantity

Ch

=

cost of holding one item for a year.

Stock ordering costs It costs money to order stock. This may be in the form of: ●

Administrative costs

●

Delivery charges.

The greater the number of orders, the greater the charge incurred. This means that we need to have as few orders as possible to minimise the ordering costs. The annual cost of ordering stock is calculated as: D × C0 Q Where

C0

=

cost of placing each order

D

=

annual demand

Economic order quantity By looking at these two costs we can see that larger orders cost more to hold and less to order. Smaller orders cost less to hold and more to order. What we need to do is find a point where we are able to minimise the total cost of ordering and holding stock.

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

There are two ways of calculating this point. The first is by means of a tabular format whereby we calculate the cost of orders using various order quantities and the cost of holding those quantities to find the total cost. Example: The following information is available for a company: Ch

=

£1.5

Co

=

£10

Demand = 10,000 units Calculate the annual holding costs and annual ordering costs at the following different order quantities Order Quantity

Annual holding

cost

of

Annual cost ordering

of

Total annual stock cost

10 100 1000

Plotting this information on a graph: Annual Cost

Order Quantity The point where total annual costs are minimised is the economic order quantity. EOQ =

2C0D Ch

Exercise 1 Calculate the economic order quantity (EOQ) for the following item of inventory: ●

Quantity required per year 32,000 items;

●

Order costs are $15 per order;

●

Inventory holding costs are estimated at 3% of inventory value per year;

●

Each unit currently costs $40.

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

Bulk discounts Sometimes suppliers will give a discount for orders of large quantities. This quantity may not be the EOQ, but the discount given may make the higher order quantity worthwhile. So far we have ignored the purchase costs of the materials, because they were common to all order quantities. When bulk discounts are present we must calculate the total cost including the purchase price.

Exercise 2 BF manufactures a range of domestic appliances. Due to past delays in suppliers providing goods, BF has had to hold an inventory of raw materials, in order that the production could continue to operate smoothly. Due to recent improvements in supplier reliability, BF is re-examining its inventory holding policies and recalculating economic order quantities (EOQ). ●

Item “Z” costs BF £1000 per unit

●

Expected annual production usage is 65,000 units

●

Procurement costs (cost of placing and processing one order) are £2500

●

The cost of holding one unit for one year has been calculated as £300

The supplier of item “Z” has informed BF that if the order was 2,000 units or more at one time, a 2% discount would be given on the price of the goods.

Required: Calculate the EOQ for item “Z” before the quantity discount. Advise BF if it should increase the order size of item “Z” so as to qualify for the 2% discount.

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

RE-ORDER LEVELS It is essential we know when to re-order goods so that we do not run out of stock. This must take account of LEAD times – the time between placing the order and the goods arriving in the warehouse for use.

Re-order level = maximum demand x maximum lead time Minimum stock level = re-order level – (average demand x average lead time) Maximum stock level = re-order level + re-order quantity – (minimum demand x minimum lead time)

Exercise 3 Calculate the re-order level, minimum stock level and maximum stock level from the following data: Minimum lead time Average lead time Maximum lead time Maximum usage Minimum usage Re-order quantity

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4 days 5 days 7 days 500 per day 300 per day 5,400

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

FREE STOCK Free stock is that amount of stock which is left over after all commitments have been met. It can be calculated as: Physical stock + Stock on order – Stock for customers’ orders already committed.

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

LABOUR COSTS Employees may be paid a fixed salary per week/month or a wage based on the amount of hours worked or work done in a period. Basic rate is usually paid for each hour worked. Overtime premium is paid on top of basic rate for each hour worked over and above the normal working hours. Eg. An employee is paid £10 per hour for a 38 hour week and an overtime premium of 25% (time and a quarter). In a week in which he works 42 hours he is paid – 42 hours x £10 4 hours x £2.50 Total wage

= = =

£420 £ 10 £430

His normal wage would be £380

PLEASE NOTE –` for the purposes of accounting we show the TOTAL hours worked x basic rate and the OVERTIME hours worked x premium only. This is because the premium part is treated differently in the accounts. Employees may be paid a wage based on the work done by the employee (piecerate). Eg. An employee is paid £2.50 for each unit produced up to 150 units. The rate increases to £2.75 for each unit produced in excess of 150 units. If the employee produces 230 units in a week they will be paid: 150 units x £2.50

=

£375

80 units x £2.75

=

£220

Total

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£595

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

Method

Description

Graph

Hourly paid

Workers are paid for time spent at work and not output, possibly receiving an enhanced rate as the result of overtime

£ wages

hrs

In this case workers are paid by output rather than time spent. A rate per unit is used to calculate wages

Piecework

£ wages

In addition to being paid a single piecework rate they may be paid on a differential piecework scheme. This will mean that they are paid a lower rate for the first number of units produced and this will increase for further units.

Guaranteed wage

minimum

In order to give wage stability, many workers will be guaranteed a minimum wage. Once output or attendance time reaches a threshold level, workers will revert to a variable rate of pay.

units

£ wages

units

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

Exercise 4 A company employs 3 workers who are paid on a piece-work basis. The rate of pay is £2.25 for each unit produced in a week, up to 100 units, and a rate of £3 for each unit in excess of 100 units. There is a guaranteed minimum weekly wage of £180 for each employee. During one week, the output produced by each employee was: Employee A B C

Units produced 96 122 76

Required: What was their total pay for the week?

Bonus schemes In addition, both individuals and groups may be awarded bonus payments based upon their efficiency in getting the work done. Bonuses are usually calculated by comparing the standard hours of actual production to the actual time taken. This then gives us the amount of time saved. The time saved is multiplied by the given percentage and the rate to find the amount of bonus awarded. The standard hours of actual production is equal to: Standard labour hours per unit x actual units produced

Exercise 5 A jobbing company operates a premium bonus scheme for its employees of 75% of the time saved compared with the standard time allowed for a job, at the normal hourly rate. The data relating to job 1206 completed by an employee is as follows: Allowed time for job 1206 Time taken to complete Job 1206 Normal hourly rate of pay

4 hours 3 hours £8

What is the total pay of the employee for Job 1206?

A

£24

B

£30

C

£32

D

£38

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

Direct and indirect labour costs Direct Labour costs: ●

Basic Rate of pay on productive hours

●

Overtime premiums on work outside normal hours specifically requested by the customer.

Indirect Labour costs: ●

Overtime premiums to production staff except if specifically requested by the customer

●

Idle time of production staff at basic rate of pay

●

Bonus and incentive payments to staff

●

Wages paid to non production staff.

IDLE TIME is time spent doing nothing. It may be due to breaks, machine breakdowns, lack of orders etc. This time cannot be charged directly to jobs but must be costed and incorporated into indirect overheads.

Exercise 6 Johnson is paid by the hour. She gets paid £7.50 an hour basic plus an overtime premium of £2.50 for any hours over 40 in a week. Johnson assembles seed propagators. Each propagator should take 30 minutes to complete. Johnson is paid a bonus of 50% of time saved based on her standard hourly rate. Idle time is not included in the calculation of actual time taken. Last week Johnson was at work for 54 hours, though 4 of these were lost due to a machine breakdown. She assembled 124 propagators that week. Johnson's total wages are:

£

How much of Johnson’s wages should be treated as a direct cost and how much as an indirect cost?

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

Labour ratios Labour ratios are used to: ●

Measure turnover

●

Measure efficiency

●

Measure capacity

Labour turnover – Number of staff leaving and needing replacemen t × 100% Average number of employees This is the rate at which the employees leave an organisation and it should be kept as low as possible due to the costs involved and also to avoid harm to the organisation’s reputation. Turnover costs include the time spent finding a replacement and providing training to new members of staff.

Labour efficiency – Actual output in standard hours × 100% Actual hours The labour efficiency ratio measures whether it has taken production line workers more or less time than expected to produce the output units. 100% is average. Above that is good. working up to the required standard.

Below 100% and our workforce is not

Labour capacity – Actual hours worked × 100 % Budgeted hours The labour capacity ratio measures whether more or less hours than planned were worked.

Production Volume – Capacity ratio x Efficiency ratio = Production Volume ratio The production volume ratio measures whether more or less units have been produced than planned.

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CHAPTER 4 – MATERIALS, LABOUR, STOCK CONTROL

Exercise 7 A company has the following information for a period: Budgeted labour hours Actual labour hours Standard hours of actual production

10,000 9,000 9,800

There were 52 employees at the start of the period and 71 employees at the end of the period. 5 employees left and were replaced.

Required: Calculate the labour turnover, efficiency, capacity ratios and production volume ratios.

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Chapter 5

Overheads and absorption costing

CHAPTER COVERAGE 1.

What are overheads?

2.

What are the different types of overheads?

3.

What is a systematic approach in charging overheads to products and services?

4.

What is allocation and apportionment and how to apportion overheads to production and service cost centres using an appropriate basis?

5.

How to re-apportion service centre costs to production cost centres using: ●

Elimination method

●

Repeated distribution

●

Algebraic method (simultaneous equations).

6.

What is an Overhead Absorption Rate and how to calculate the appropriate overhead absorption rates for each cost centre.

7.

How to calculate and account for over or under absorbed overheads.

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C H A P T E R 5 – O V E R H E A D S A N D A B S O R P T IO N C O S T I N G

CHAPTER CONTENTS OVERHEADS -------------------------------------------------------------- 55 OVERHEAD ALLOCATION ----------------------------------------------- 56 OVERHEAD APPORTIONMENT ------------------------------------------ 57 SECONDARY APPORTIONMENT ---------------------------------------- 58 1.

ELIMINATION

58

2.

REPEATED DISTRIBUTION

59

3.

ALGEBRAIC

59

OVERHEAD ABSORPTION ----------------------------------------------- 60 OVER/UNDER ABSORPTION OF OVERHEADS ------------------------- 63

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C H A P T E R 5 – O V E R H E A D S A N D A B S O R P T IO N C O S T I N G

OVERHEADS Overheads are defined as expenditure on labour, materials or services that cannot be directly identified with a saleable cost unit. Overheads are divided into two main areas: ●

Production and

●

Non-production.

Production overheads are indirect costs that are directly related to the production. These include items such as: ●

Power

●

Maintenance of machinery.

Non-production overheads are necessary expenses of the business, which are not directly related to production. These can be classified into: ●

Administration overheads

●

Selling and distribution overheads

●

Finance overheads.

Absorption costing is used to calculate the production overhead cost per unit

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C H A P T E R 5 – O V E R H E A D S A N D A B S O R P T IO N C O S T I N G

OVERHEAD ALLOCATION Some costs can be easily identified with a unit or units of production such as labour and material costs. These are said to be ‘allocated to the product’. Often they are allocated to the cost centre or department before being shared among the units of production.

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C H A P T E R 5 – O V E R H E A D S A N D A B S O R P T IO N C O S T I N G

OVERHEAD APPORTIONMENT Some costs relate to the business as a whole. These costs then have to be shared between the various departments or cost centres. This is done by ‘apportioning the costs’. “The division of costs amongst two or more cost centres in proportion to the estimated benefit received, by using a proxy. Eg, area, headcount, capital value etc. These overheads then have to be included into the cost of the products which are produced in that department. It would be easy to just divide the cost by the number of units made. This would be fine if only one product was made or if all products took exactly the same time to be made. As this is not the case we have to find a way of sharing the overhead costs between the products.

Exercise 1 ABC is preparing its departmental budgets and product cost estimates for the year ended 31 December 19X5. The company has three manufacturing departments – Machining, Assembly, and Finishing – together with a production maintenance department. The following costs and related data have been estimated for the year to 31 December 19X5: Costs: Indirect wages Indirect materials Power Light and heat Depreciation Rent and rates Personnel Other data: Direct labour hours Machine hours Employees Floor area (m2) Net book value of fixed assets

Machining £’000 10 15

Assembly £’000 6 4

Finishing £’000 8 8

Maint £’000 30 20

Total £’000 54 47 102 10 7 25 63

12,000 40,000 6 1,000

8,000 5,000 4 400

16,000 6,000 8 300

6,000 3 300

42,000 51,000 21 2,000

20,000

8,000

3,000

4,000

35,000

The maintenance department is expected to spend 60% of its time working for the machining department with the remainder of its time being shared equally between assembly and finishing.

Required: Prepare an overhead analysis sheet for ABC Ltd for its year ended 31 December 19X5.

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C H A P T E R 5 – O V E R H E A D S A N D A B S O R P T IO N C O S T I N G

SECONDARY APPORTIONMENT Not all departments are production based. Some act as a service to the production departments. Eg, canteen, stores, maintenance. The costs of these have to be included into the total overheads of the production departments. Secondary apportionment is a means of apportioning overheads from service cost centres to production cost centres by means of relevant usage factors. ●

A canteen – on basis of number of employees

●

A stores – on the number of stores issues.

Sometimes both service cost centres provide services to each other (reciprocal servicing). This has to be taken into account before the final apportionments are made. There are three ways of secondary apportionment:

1.

Elimination

2.

Repeated distribution

3.

Algebraic.

1. Elimination This method is used where one service centre does not use the services of another. For instance it is unlikely that the stores would provide a service to the canteen while the canteen would provide a service to the stores. In this case the canteen costs would be apportioned first followed by the stores.

Exercise 2 Elimination Method The ABC washing machine Co. produces a standard washing machine in three production departments (Machining, Assembly, and Finishing) and two service departments (Materials handling and Production control). Costs for last year, when 2,000 machines were produced were as follows: Production departments Dept:

Machining

Assembly

Finishing

Indirect materials Indirect wage Other indirect costs

£41,920

£12,960

£7,920

% use of Materials handling

60%

30%

10%

% use of Production Control

40%

30%

20%

Service Materials Production Handling Control £4,000 £8,000 £8,000

£11,200 £2,400

10%

Required: Prepare a statement showing the overhead allocated and apportioned to each of the production departments.

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C H A P T E R 5 – O V E R H E A D S A N D A B S O R P T IO N C O S T I N G

2. Repeated distribution The costs are repeatedly shared on an equitable basis until they are all accounted for.

3. Algebraic By means of using simultaneous equations to arrive at the notional total used in the continuous allotment method.

Exercise 3 Repeated distribution and algebraic methods Dept: Costs % of P used % of Q used

Production departments A B C £3,000 £4,000 £2,000 20% 30% 25% 25% 25% 30%

Service P Q £2,500 £2,700 25% 20% -

Required: Reapportion the service centre costs to the production centres using:

(a)

Repeated distribution method.

(b)

Algebraic method.

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C H A P T E R 5 – O V E R H E A D S A N D A B S O R P T IO N C O S T I N G

OVERHEAD ABSORPTION An absorption rate can be thought of as a charge out rate for overheads. Absorption rates can be calculated in a number of ways but the most common ways for exam questions are: ●

A rate per unit

●

A rate per labour hour

●

A rate per machine hour.

It is worth remembering that absorption rates are always calculated using BUDGETED figures. Rates have to be available at the start of a period so it is possible to cost output as the period progresses. Actual figures are only available at the end of a period. Absorption rates are calculated as: Budgeted overheads / budgeted activity = OAR A single absorption rate can be calculated for a company as a whole, known as a blanket rate. Equally, separate absorption rates can be calculated for individual departments, known as departmental rates.

Exercise 4 Blanket rates Tulip Ltd makes a single product, the Bulb. Each Bulb has a prime cost of £20.00, takes 2 labour hours and 3 machine hours. The following budgeted information is available for the factory. Budgeted Budgeted Budgeted Budgeted

Overhead Output Labour Hours Machine Hours

£100,000 20,000 units 50,000 hours 100,000 hours

£ What is the absorption rate per unit?

What is the absorption rate per labour hour?

What is the absorption rate per machine hour?

What is the total production cost using the unit based absorption rate?

What is the total production cost using the labour hour absorption rate?

What is the total production cost using the machine hour absorption rate?

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C H A P T E R 5 – O V E R H E A D S A N D A B S O R P T IO N C O S T I N G

Exercise 5 Departmental rates It may be more accurate to calculate separate absorption rates for different departments. Would it be fair or meaningful to use labour hours, for instance, to charge out overheads in a machine intensive department? A company has the following information available:

Cutting

Finishing

Budgeted Overheads Machine Hours Labour Hours

£100,000 50,000 20,000

£50,000 3,000 12,500

Actual Overheads Machine Hours Labour Hours

£132,000 40,000 28,000

£38,000 4,200 12,000

The following information is also available about one of the company's products:

Machine Hours Labour Hours

Cutting hrs 6 2

Finishing hrs 1 4 £

What is an appropriate absorption rate for the Cutting Department?

What is an appropriate absorption rate for the Finishing Department?

What is the total overhead cost per unit of product?

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C H A P T E R 5 – O V E R H E A D S A N D A B S O R P T IO N C O S T I N G

Exercise 6 A company manufactures two products P1 and P2 in a factory divided into two cost centres, X and Y. The following budgeted data are available:

Cost Centre X Y Allocated and apportioned fixed overhead costs Direct labour hours per unit: Product P1 Product P2

$88,000

$96,000

3.0 2.5

1.0 2.0

Budgeted output is 8,000 units of each product. Fixed overhead costs are absorbed on a direct labour hour bases.

What is the budgeted fixed overhead cost per unit for Product P2? A

$10

B

$11

C

$12

D

$13

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C H A P T E R 5 – O V E R H E A D S A N D A B S O R P T IO N C O S T I N G

OVER/UNDER ABSORPTION OF OVERHEADS Calculation of the overhead absorption rate (OAR) is done by using budgeted figures. We cannot use actual figures because we do not know these until after the event. This means that for every item we make we absorb a certain amount of overheads into the unit. The total amount absorbed will depend upon the number of units made. It is highly unlikely that the budgeted production will agree exactly with the actual or that the budgeted overhead will agree with the actual spend. Because of this we need to calculate how much overhead has been absorbed into our production, compare this with the actual amount and make an adjustment to our P&L account. If we have absorbed too much (over absorption) we will have to add back the difference into our P&L. This will increase the reported profit. If we have not absorbed enough (under absorption) we will have to take more out of our P&L. This will decrease the reported profit. Under or over absorbed overhead is calculated using:

£ Absorbed overhead (actual activity x OAR)

Actual Overhead

Under/over absorption:

Exercise 7 Under/Over absorption Aurricula Ltd use absorption costing. production department is as follows:

The following information for its one

Shredding Budgeted Overhead Machine Hours Labour Hours

£200,000 100,000 30,000

Actual Overheads Machine Hours Labour Hours

£208,000 80,000 41,000

Required: Complete the following statement.

Overheads were

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by

£

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C H A P T E R 5 – O V E R H E A D S A N D A B S O R P T IO N C O S T I N G

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Chapter 6

Cost bookkeeping

CHAPTER COVERAGE 1.

Interpret the entries and balances in the material inventory account

2.

Interpret the entries in the labour account

3.

Interpret the entries in the production overhead account

4.

Adjust the production overhead under/over absorption of overheads

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and

income

statement

accounts

for

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CHAPTER 6 – COST BOOKKEEPING

CHAPTER CONTENTS COST ACCOUNTS --------------------------------------------------------- 67

66

STOCK CONTROL ACCOUNT

67

LABOUR CONTROL ACCOUNT

67

WORK IN PROGRESS ACCOUNT

67

PRODUCTION OVERHEAD CONTROL ACCOUNT

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CHAPTER 6 – COST BOOKKEEPING

COST ACCOUNTS A control account is a summary account. For F2, students need to understand the stock control, labour control, work in progress and overhead control accounts and how costs build up in these accounts. A flow into the account is shown on the debit side and a flow out of the account is shown on the credit side of the T account. The credit and debit sides of the T account must balance at the end of the period.

Stock control account Debit Entries The debit side shows the flow of materials into the company. direct and indirect materials purchases.

This will include

Opening stock balance will also be shown as a debit.

Credit Entries As materials are used in production, they will be shown as a credit entry in the stock control account. Direct materials are allocated to the WIP account. Indirect materials are allocated to the production overhead account. Closing stock value will be the balancing figure on the credit side of the T account.

Labour control account There is not opening or closing stock of labour. Instead, the labour control account shows the wages paid out to staff for the period.

Debit Entries The debit entries reflect the wages paid out to staff.

Credit Entries The credit side of the labour control account will split the wages paid out between direct and indirect costs to the company

Work in progress account The work in progress account is also called the cost unit account.

Debit Entries The costs associated with producing units of output are built up on the debit side. This will include direct materials, direct labour and production overhead absorbed

Credit Entries The total costs built up on the debit side is the value of the units produced. This is shown on the credit side as an output to finished goods.

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CHAPTER 6 – COST BOOKKEEPING

Production overhead control account The production overhead control account is used to build up the indirect costs incurred by each production cost centre.

Debit Entries Overhead costs are built up on the debit side as they are incurred during the period.

Credit Entries Overheads will be absorbed from the production overhead account to the WIP account based on the overhead absorption rate. The absorbed overhead is shown on the credit side as an allocation out of the production overhead account and into the WIP account. As we have seen in Chapter 3, there may be an under or over absorption of production overheads. This will be calculated at the end of the period. Under absorption is shown as a balancing figure on the credit side of the production overhead account. Over absorption is shown as a balancing figure on the debit side of the production overhead account. The other side of the under/over absorption adjustment is in the Income Statement account.

Exercise 1 A company had the following budgeting information: Production overheads

£90,000

Labour hours

4,500

Actual costs for the period were as follows: Direct materials

£40,000

Indirect materials

£20,000

Direct materials issued to production

£25,000

Indirect materials issued to production

£20,000

Indirect wages

£15,000

Direct wages for 3,900 hours

£30,000

Other indirect expenses

£45,000

Opening inventory value was £5,000. Write up the T accounts for the period

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CHAPTER 6 – COST BOOKKEEPING

Stock Control

Labour Control

WIP

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CHAPTER 6 – COST BOOKKEEPING

Production Overhead Control

Income Statement expense

Exercise 2 A company had the following budgeting information: Production overheads

£50,000

Labour hours

10,000

Actual costs for the period were as follows: Direct materials

£15,000

Indirect materials

£7,500

Direct materials issued to production

£11,000

Indirect materials issued to production

£4,300

Direct materials returned to supplier

£2,000

Indirect wages

£22,000

Direct wages for 10,500 hours

£32,000

Other indirect expenses

£21,000

Opening inventory value was £1,500

Write up the T accounts for the period.

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Chapter 7

Marginal costing and contribution theory

CHAPTER COVERAGE 1.

What is the concept of contribution and how it is calculated?

2.

What are differences between Absorption and Marginal costing?

3.

What is the impact of the difference on stock valuations of absorption and marginal costing?

4.

What is the impact on profit and loss accounts using absorption and marginal costing?

5.

Reconcile the profits achieved under each method.

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C H A P T E R 7 – M A R G IN A L C O S T IN G A N D C O N T R I B U T I O N T H E O R Y

CHAPTER CONTENTS ABSORPTION versus MARGINAL COSTING EXPLAINED ------------- 73 ABSORPTION COSTING

73

MARGINAL COSTING

73

PROFIT CALCULATIONS ------------------------------------------------- 74 ABSORPTION COSTING

74

MARGINAL COSTING

75

PROFIT RECONCILIATIONS -------------------------------------------- 77

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C H A P T E R 7 – M A R G IN A L C O S T IN G A N D C O N T R I B U T I O N T H E O R Y

ABSORPTION versus MARGINAL COSTING EXPLAINED There are two main methods of costing:

1.

Absorption costing – where the fixed production overhead costs are absorbed into the product cost by means of an overhead absorption rate (OAR).

2.

Marginal costing – where the total fixed costs are written off in full in the period in which they occur.

In order to correctly assess the full cost of production we need to have a portion of these overheads included in the cost of the item.

Absorption costing Sales – production costs = gross profit Gross profit – non-production costs = net profit

Marginal costing Sales – variable costs = contribution Contribution – fixed overheads = profit

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C H A P T E R 7 – M A R G IN A L C O S T IN G A N D C O N T R I B U T I O N T H E O R Y

PROFIT CALCULATIONS Absorption costing Absorption Costing profit is calculated using the following pro forma Sales revenue

X

Production Costs Opening inventory

X

Direct materials

X

Direct labour

X

Production absorbed

overheads

Under/over absorption Closing inventory Total Production Costs Gross Profit Non Production Costs Net Profit

X

X/(X) (X) (X) X (X) X

In an absorption costing system, inventory is valued at the production cost per unit. Under absorption increases costs and should be added to production costs. Over absorption decreases costs and should be subtracted from production costs.

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C H A P T E R 7 – M A R G IN A L C O S T IN G A N D C O N T R I B U T I O N T H E O R Y

Marginal costing Marginal Costing profit is calculated using the following pro forma Sales revenue

X

Variable Costs Opening inventory

X

Direct materials

X

Direct labour

X

Variable overheads

X

Closing inventory

(X)

Total Variable Costs

(X)

Contribution

X

Fixed Costs

(X)

Profit

X

In a marginal costing system, inventory is valued at the variable cost per unit

Exercise 1 A company makes and sells a single product. Details of this product are as follows:

Selling price Direct materials Direct labour Variable production overheads Fixed production overheads

Per unit £20 £6 £3 £4 £20,000 per month

The fixed overhead is absorbed on the basis of expected production of 20,000 units per month.

Required: If actual production and sales are 20,000 units in a month, calculate

(a)

The contribution per unit, the total contribution for the month and the total profit for the month, using marginal costing.

(b)

The profit for the month using absorption costing.

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C H A P T E R 7 – M A R G IN A L C O S T IN G A N D C O N T R I B U T I O N T H E O R Y

Exercise 2 A company produces a single product with the following budget: Selling price Direct materials Direct wages Variable production overheads Fixed production overheads Budgeted production

£10 £3 per unit £2 per unit £1 per unit £10,000 per month 5,000 units per month

Required: Show the operating statement for the month when 4,800 units were produced and sold using:

(a)

Absorption costing

(b)

Marginal costing

Assume that all costs were as budget. You will notice that in this question you will need to account for over or under absorption.

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C H A P T E R 7 – M A R G IN A L C O S T IN G A N D C O N T R I B U T I O N T H E O R Y

PROFIT RECONCILIATIONS In the two exercises just done the profits achieved under both methods are exactly the same. This is because opening inventory = closing inventory. If there is a movement in inventory, the profits will differ. We need to be able to reconcile these profits. This is a simple matter and very easy to do. It is also a common exam question.

Exercise 3 Using the above budget in Exercise 2, recalculate the operating statements assuming that production had been 6,000 units and sales 4,800 units.

Reconcile the profits. From the figures you have calculated you will see that there is a closing stock balance of 1,200 units. The value of these balances differ because of the amount of fixed overhead contained within the absorption costing stock. From this we can deduce that the difference in the profit figures is because of the change in the number of units of stock x fixed production overhead cost per unit. Try it:

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C H A P T E R 7 – M A R G IN A L C O S T IN G A N D C O N T R I B U T I O N T H E O R Y

IMPORTANT EXAM POINT Please remember: ●

If closing inventory > opening inventory, then absorption costing profit will be greater than marginal costing profit. This is because some of the fixed overhead for the period is contained in the closing stock.

●

If closing inventory < opening inventory, then absorption costing profit will be less than marginal costing profit. This is because some of the overhead from a prior period has been written off in the current period from the stock taken from the opening stock.

●

If closing inventory = opening inventory then absorption costing profit will be equal to marginal costing profit

●

Difference in profit = movement in inventory x fixed production overhead cost per unit

Exercise 4 A company has a profit of £75,000 using a marginal costing system. Budgeted fixed costs were £30,000 and budgeted activity was 10,000 units. The following information is also available: Opening inventory Production Sales

500 units 10,500 units 10,750 units

What would the profit be using absorption costing?

A

£72,750

B

£74,250

C

£75,750

D

£77,250

Exercise 5 Z Ltd produces a single product. The management currently uses marginal costing, but is considering using absorption costing in the future. The budgeted fixed production overheads for the period are £250,000. The budgeted output for the period is 1,000 units. There were 400 units of opening stock for the period and 250 units of closing stock.

Required: If absorption costing principles were applied, by how much would the profit for the period compared to marginal costing differ?

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Chapter 8

Costing for jobs, batches, and services

CHAPTER COVERAGE 1.

What are the various characteristics of specific order costing?

2.

In which situations would job, batch or service costing be appropriate?

3.

What are the treatments of direct and indirect costs?

4.

What are various cost records and accounts involved in job order costing?

5.

What is the difference between profit mark-up and profit margin?

6.

How profit mark-up and margin are used to establish selling prices.

7.

Analyse service costs.

8.

Identify suitable cost unit measures that may be used in a variety of different operations and services.

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C H A P T E R 8 – C O S T IN G F O R J O B S , B A T C H E S , A N D S E R V I C E S

CHAPTER CONTENTS INTRODUCTION TO JOB COSTING ------------------------------------- 81 COST ACCUMULATION FOR JOBS

81

COST ACCOUNTS

84

BATCH COSTING

86

PRICING

87

SERVICE COSTING ------------------------------------------------------- 88

80

CHARACTERISTICS

88

IDENTIFICATION OF COST UNITS

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C H A P T E R 8 – C O S T IN G F O R J O B S , B A T C H E S , A N D S E R V I C E S

INTRODUCTION TO JOB COSTING Jobbing production involves producing items to the specific order of a customer. As such, mass production of items does not occur and each job will have its own characteristics and hence costs. It is important, therefore, that costs due to an individual job are collected separately, and remain identifiable within the accounts. Job costs are normally collected on a job card that records specific costs incurred as part of the job. Once a job is completed overheads are added to work out the total cost of the job.

Cost accumulation for jobs In cost bookkeeping, a separate job account is maintained for each job. These are then consolidated into single work in progress account.

Exercise 1 A company makes three products, details of which are given below: A local jobbing company has just completed a one-off job which involved making a specialist iron frame. The item was given the job number 666. Materials issued were as follows: Steel grade A: Steel grade B:

400 metres at a cost of £5.00 per metre 800 metres at £6.00 per metre

Note 60 metres of grade B steel were unused and were returned to store. The iron frame involved two production departments: Welding: Finishing:

220 normal hours, 100 overtime hours 100 normal hours, 100 overtime hours

Hourly rate Welding: Finishing:

£4.00 per normal hour, £1.00 overtime premium £5.00 per normal hour, £1.50 overtime premium

Production overheads are absorbed at the rate of £3.00 per direct labour hour in each department. Note the company uses cost plus pricing of work and adds 40% to the cost of a job to determine price. The company is very busy and would not normally work overtime on a job of this nature

Required: You have been asked to complete the following cost summary:

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Job 666

£

£

Materials

Grade A Steel Grade B Steel Wages Wages Welding Wages Finishing Total Direct Cost Overheads Total Cost

Profit Selling Price

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C H A P T E R 8 – C O S T IN G F O R J O B S , B A T C H E S , A N D S E R V I C E S

Exercise 2 A company operates a job costing system to enable them to identify the costs incurred in carrying out works to customer specifications. Wherever possible, this system allocates costs directly to a job. Production overhead costs are absorbed into the cost of a job at the end of each month at an actual rate per direct labour hour for each of the two production departments. The following information has been collected relating specifically to one job which was carried out in the month just ended: ●

400 kgs of Material Y were issued from stores to Department A. Material Y is currently valued at £0.51 per kg.

●

76 direct labour hours were worked in Department A at a basic wage of £4.50 per hour. 6 of these hours were classed as overtime at a premium of 50%.

●

300 kgs of Material Z were issued from stores to Department B. Department B returned 35 kgs of Material Z to the storeroom as it was excess to requirements for the job. Material Z is currently valued at £1.45 per kg.

●

110 direct labour hours were worked in Department B at a basic wage of £4.00 per hour. 30 of these hours were classified as overtime at a premium of 50%. All overtime worked in Department B in the month is as a result of the request of a customer for early completion of another job that had originally been scheduled for completion in the month following.

Overhead costs incurred during the month on all jobs in the two production departments were as follows:

Indirect labour, at basic wage rate Overtime premium Lubricants and cleaning compounds Maintenance Other costs Total labour hours worked during the month

Dept A £ 2,510 450 520 720 1,200 2,000

Dept B £ 2,960 680 510 2,150 2,800

Prepare a list of the costs that should be assigned to the job.

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Cost accounts Exercise 3 The following information concerns Sunflower Ltd. At the end of last month, one job was uncompleted, and the costs to date were: JOB 6832 Direct Materials Direct Labour (120 hrs) Factory Overhead (£2 per hr) Factory cost to date

£ 630 960 240 1,830

At the start of the month two new jobs were started: JOB 6833, JOB 6834. By the end of the month jobs 6832, 6833 were competed. The following cost information is available: Direct Materials Issued to: Job 6832 Job 6833 Job 6834

£ 2,390 1,680 3,950

Materials Transfers: Job 6834 to Job 6833 Job 6832 to Job 6833

£ 250 620

Materials Returned to Store From Job 6832

£ 870

Direct Labour Hours Recorded Job 6832 Job 6833 Job 6834

430 hrs 650 hrs 280 hrs

Labour is charged at £8.00 per hour. Production overheads are absorbed at the rate of £2.00 per labour hour. The actual overheads incurred during the month were £3,800.

Required: Complete the following job accounts:

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C H A P T E R 8 – C O S T IN G F O R J O B S , B A T C H E S , A N D S E R V I C E S

Job 6832

Job 6833

Job 6834

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C H A P T E R 8 – C O S T IN G F O R J O B S , B A T C H E S , A N D S E R V I C E S

Batch costing Batch costing is similar to job costing in that each batch is separately identifiable. In batch costing, the cost per unit is calculated as: Total cost of the batch / Number of units in the batch

Exercise 4 A company operates a batch costing system. produced in a batch.

For a particular order, 5 units are

The following costs were incurred producing the batch: Direct materials £230 Direct labour £180 Direct labour is paid at £7.50 per hour. Production overheads are absorbed at a rate of £12 per direct labour hour and nonproduction overheads are absorbed at a rate of 30% of total production cost. What is the total cost per unit in this batch? A

£82

B

£139.60

C

£181.48

D

£235.92

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C H A P T E R 8 – C O S T IN G F O R J O B S , B A T C H E S , A N D S E R V I C E S

Pricing When determining a price, a company may use mark up or margin. ●

Mark up

- profit expressed as a percentage of cost

●

Margin

- profit expressed as percentage of price

Equally, a company may decide to use variable (marginal) cost of a unit or full cost when calculating a price. It is important to check questions that ask for prices carefully. Which cost is being used and is the question using mark up or margin?

Exercise 5 A company has the following cost card:

Direct Labour Direct Materials Prime cost Variable Production Overhead Fixed Production overhead Production cost Variable non-production cost Fixed non-production cost Total

£ 10 12 22 5 4 31 6 3 40

Required: £ Using a mark-up on marginal cost of sales of 80%, what is the price?

What is the resulting profit?

Using a margin of 80% on total production cost what is the price?

What is the resulting profit?

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C H A P T E R 8 – C O S T IN G F O R J O B S , B A T C H E S , A N D S E R V I C E S

SERVICE COSTING Characteristics Definition: “Cost accounting for services or functions, eg canteens, maintenance, personnel. These may be referred to as service centres, departments or functions. Service costing is also known as Operations Costing.” Service organisations do not make or sell tangible goods. Most, however, still seek to make a profit and in doing so are required to build up costs of their services for charging out. Examples: ●

Transport

●

Accountants

●

Hotels

●

Hospitals

●

Schools/colleges

●

Banks etc.

Recording costs for the organisations is very similar to other methods of costing, ie direct and indirect costs. ●

they tend to have a very low level of direct material costs

●

it is difficult to cost one unit of output as it is often intangible

●

as no two service industries are similar, costing methods will differ considerably.

Services have certain specific characteristics which have to be taken into account:

Intangibility – The performance of the service depends upon other factors rather than just the service. A bus service depends upon timing, reliability, comfort, cleanliness etc.

Simultaneity – The production and consumption of the service are done at the same time. The product cannot be inspected beforehand. The bus journey is provided and taken at the same time. It cannot be assessed before the journey takes place but comments can be made afterwards.

Perishability – The service is perishable. It cannot be provided in advance and stored.

Heterogeneity – The exact service provided will vary each time. The bus journey will vary as to the exact time it takes; the comfort of the passengers depends upon the number and type of people travelling at that particular time. 88

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Identification of cost units Some service units can be easily costed using an apt basis. For others there may be a choice of bases to be used. Eg:

Hotel – cost per guest day Transport service – cost per passenger mile

Each service organisation will therefore have to decide upon a basis to be used that is relevant to them. The cost per service unit is then calculated as: Total costs for the period / Number of service units provided in the period

Exercise 6 An accountant is setting up his own business. He will be working a 40 hour work for 48 weeks of the year. Expenses are expected to be £35,000 and a mark-up of 30% will be applied to cost to establish the charge per hour. 95% of his time will be chargeable to customers and the remainder will be spent reviewing changes to statutory requirements. What should he charge per hour for the accountancy services provided (to the nearest penny)?

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C H A P T E R 8 – C O S T IN G F O R J O B S , B A T C H E S , A N D S E R V I C E S

Exercise 7 Little Larson Ltd operates a small fleet of delivery vehicles. Standard costs have been established as follows: Loading Loading costs: Labour (casual) Equipment depreciation Supervision Drivers’ wages (fixed) Petrol Repairs Depreciation Supervision Other general expenses (fixed)

1 hour per tonne loaded £2 per hour £80 per week £80 per week £100 per man per week 10p per kilometre 5p per kilometre £80 per week per vehicle £120 per week £200 per week

There are two drivers and two vehicles in the fleet. During a quiet week, only six journeys were made. Journey 1 2 3 4 5 6

Tonnes carried (one way) 5 8 2 4 6 5

One-way distance of journey (km) 100 20 60 50 200 300

Required: Calculate: (a)

The total variable cost for the week.

(b)

The total fixed cost for the week.

(c)

The expected average full cost per tonne/kilometre for the week.

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Chapter 9

Process costing, joint and by-products

CHAPTER COVERAGE 1.

What is Process Costing and in which environment it is used for?

2.

What are normal and abnormal losses/gains in process costing?

3.

How to calculate the cost per unit of output.

4.

What are various accounts involved in process costing?

5.

What are equivalent units and how are they calculated?

6.

Account for opening and closing work-in-progress using FIFO and weighted average methods.

7.

What are joint and by-products?

8.

Value joint and by-products at the point of separation using physical units and sales value methods.

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CHAPTER 9 – PROCESS COSTING, JOINT AND BY-PRODUCTS

CHAPTER CONTENTS INTRODUCTION ---------------------------------------------------------- 93 LOSSES AND GAINS ----------------------------------------------------- 95 NORMAL LOSS

95

ABNORMAL LOSS

96

COST PER UNIT ---------------------------------------------------------- 98 ABNORMAL GAIN

99

COST ACCOUNTS -------------------------------------------------------- 103 WORK-IN-PROGRESS AND EQUIVALENT UNITS

103

OPENING WORK IN PROGRESS

105

AVCO VALUATION ------------------------------------------------------ 106 FIFO VALUATION ------------------------------------------------------- 107 JOINT AND BY-PRODUCTS --------------------------------------------- 109

92

INTRODUCTION

109

TREATMENT OF BY-PRODUCTS AND JOINT COSTS

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CHAPTER 9 – PROCESS COSTING, JOINT AND BY-PRODUCTS

INTRODUCTION In a significant number of manufacturing processes it is not possible to identify individual cost units because of the continuous nature of production, eg oil refining, paint production, chemical manufacture. Using process costing it becomes possible to derive a cost for both output and closing stocks. Process costing has a number of features that distinguish it from job, batch and service costing: ●

Under continuous production there is almost always work in progress to be valued.

●

Wastage during a continuous production process is common and has to be taken into account (see later).

Students often find process costing a difficult topic to understand. However, it is straightforward if the following points are kept in mind: 1.

Process accounts are simple control accounts that have debit and credit entries and are nothing more than work in progress accounts.

2.

Ledger accounts contain quantity columns that should be balanced off.

3.

A set of rules applies to each procedure - once learnt they always apply.

Exercise 1 Manufacturing a product involves two processes, cutting and forming. Units of material input Cutting Forming

Cutting Forming

1,000,000 500,000 Direct Labour Costs £ 200,000 150,000

Value £ 500,000 300,000 Production Overhead £ 200,000 150,000

Required: Given that output from Cutting is fed into Forming, write up the process accounts.

Debit

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PROCESS 1 (CUTTING)

Credit

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Debit

PROCESS 2 (FORMING)

Credit

Note that direct labour and production overheads are sometimes lumped together and termed conversion cost.

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LOSSES AND GAINS Most processes are not 100% efficient and involve some form of loss in weight or volume. This has to be accounted for. In process costing, an important division is made between NORMAL LOSS and ABNORMAL LOSS.

Normal loss These are losses that are expected as part of the production process. The cost of a normal loss is spread across the remaining good units. Any scrap revenue from a normal loss is used to reduce the cost of the main process. The cost per unit of good output is calculated as:

Total costs - value of normal loss Expected output units

Where Expected output = Input units – Normal loss units. The heart of getting the correct answer in questions involving abnormal losses and gains is to calculate the unit cost of output correctly.

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CHAPTER 9 – PROCESS COSTING, JOINT AND BY-PRODUCTS

Exercise 2 A process has a normal loss of 5%, which can be sold for £5 per tonne. In a period, materials used were 160 tonnes at £23 per tonne and labour and overheads amounted to £3,200. All losses were normal.

Required: What were the costs per tonne of good output? Process a/c

Normal loss a/c (scrap sales)

Abnormal loss Abnormal losses are unexpected losses. Unless told otherwise it is assumed that losses occur at the end of the process and are costed at the same rate as good units. An abnormal loss occurs when actual output is less than expected output. If there are abnormal loss units, these may also be sold for scrap. Accounting for abnormal losses: 1.

Credit the process account with good output and normal loss. Value the good output at the cost per unit value.

2.

Calculate the difference between actual good output and expected output and record the difference as abnormal loss on the credit side of the process account.

3.

Abnormal loss is valued at the cost per unit value in the process account.

4.

Record the abnormal loss as a debit in the abnormal losses/gains account.

5.

Increase the scrap sales by the abnormal loss.

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6.

The difference between the cost per unit value of abnormal loss and the scrap value is reported as a loss in the profit and loss account. This is calculated as: Abnormal loss units x Cost per unit – Scrap value of abnormal loss units

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CHAPTER 9 – PROCESS COSTING, JOINT AND BY-PRODUCTS

COST PER UNIT Exercise 3 Using the above information (Exercise 2), prepare the process accounts assuming that output was 150 tonnes.

Process a/c

Normal loss a/c (scrap sales)

Abnormal loss/gain a/c

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CHAPTER 9 – PROCESS COSTING, JOINT AND BY-PRODUCTS

Abnormal gain Abnormal gains occur when actual good output is greater than expected output. Abnormal gains represent extra good units so are costed at the same rate as other, expected, good units. By making more good units than expected a company will have lost out on scrap revenue. This is accounted for in the abnormal loss/gain account. Accounting for abnormal gains: 1.

Credit the process account with good output and normal loss. Value the good output at the cost per unit value

2.

Calculate the difference between actual good output and expected output and record the difference as abnormal gain on the debit side of the process account

3.

Abnormal gain is valued at the cost per unit value in the process account

4.

Record the abnormal gain as a credit in the abnormal losses/gains account

5.

Decrease the scrap sales by the abnormal gain

6.

The difference between the cost per unit value of abnormal gain and the scrap value is reported as a gain in the profit and loss account. This is calculated as: Abnormal gain units x Cost per unit – Scrap value of abnormal gain units.

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CHAPTER 9 – PROCESS COSTING, JOINT AND BY-PRODUCTS

Exercise 4 Using the above information (Exercise 2), prepare the process accounts assuming that output was 156 tonnes.

Process a/c

Normal loss a/c (scrap sales)

Abnormal loss/gain a/c

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CHAPTER 9 – PROCESS COSTING, JOINT AND BY-PRODUCTS

Exercise 5 In a local factory normal loss is 10% and each scrapped unit makes £0.50 from process 1 and £3.00 from process 2.

Required: Using the following information, prepare:

(a)

Process 1 Account;

(b)

Process 2 Account;

(c)

Abnormal Loss/Gain Account;

(d)

Scrap Account.

Direct materials added Direct materials cost Direct labour Production oh Output to process 2 Output to finished goods

Process 1 2,000 units £8,100 £4,000 150% direct labour 1,750

Process 2 1,250 units £1,900 £10,000 120% direct labour 2,800

Process 1 a/c

Process 2 a/c

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Normal loss a/c (scrap sales)

Abnormal loss/gain a/c

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CHAPTER 9 – PROCESS COSTING, JOINT AND BY-PRODUCTS

COST ACCOUNTS Work-in-progress and equivalent units At the end of the period there is likely to be some partly completed work (work-inprogress) and some of the costs of the period have to be attributed to it. The number of EQUIVALENT UNITS is calculated in order to spread the costs incurred over fully and partly completed units. If 2,000 units had been introduced into a process and only 1,500 had been completed it would be unfair to apportion costs in the ratio 3:1 between finished output and closing stock as the part-finished goods would not have 'received' their complete amount of labour and materials. This problem is overcome by converting part completed work into EQUIVALENT UNITS of finished output. For example, if 200 units were 70% completed, they would be charged with the cost of 140 completed units. Getting the right answer to a question involving closing work in progress is a threestage process. 1.

Convert physical outputs to equivalent statement of equivalent units.

units

by

constructing

2.

Calculate the cost per equivalent unit. This is equal to:

a

Total Costs / Total Equivalent Units 3.

Calculate the value of each output by multiplying the number of equivalent units by unit cost in a statement of valuation.

Exercise 6 In a period 1,000 fully completed and 200 partly completed units were produced. The partly completed units were 50% complete. Total costs for the period were £5,500.

Required: Calculate the cost per equivalent unit.

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CHAPTER 9 – PROCESS COSTING, JOINT AND BY-PRODUCTS

Exercise 7 The following information is available for Stinkwort Ltd.

Direct materials Direct Labour Production overhead

Units 5,000

£ 16,560 7,360 5,520 29,440

Of the 5,000 units, 4,000 were completed and 1,000 were 60% complete. £ The value of finished units is

The value of closing WIP is

Required: Complete the process account below for Stinkwort Ltd.

Process a/c

In this example it was assumed that unfinished work was completed to the same extent for labour and materials. In reality, however, it may be the case that all materials have been added but only a portion of the labour (or any variation on this theme). The next exercise illustrates how this might be accounted for.

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Exercise 8 In a given period the production data and costs for a process were: Production

2100 fully complete 700 partly complete

Degree of completion of the partly complete units was: Materials Labour Overheads

80% 60% 50%

The costs for the period were: Materials Labour Overheads

£24,800 £16,750 £36,200

Calculate the total equivalent production, the cost per complete unit and the value of the WIP.

Opening work in progress We have been able to calculate the value of the closing work-in-progress using the degree of completion. As this is at the end of the period, we can assume that it is therefore the opening work-in-progress at the beginning of the next period. There are two methods for doing this – weighted average and FIFO.

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AVCO VALUATION Weighted average method takes the total for each element of cost and this is divided by the equivalent units to find the cost per equivalent unit as previously calculated.

Statement of equivalent units Units of output x 100% +

closing work-in-progress x % completion

=

total equivalent units

Cost per equivalent unit When calculating the cost per equivalent unit, it is important to include the total cost of the work done. Total cost of work done = Current period costs + Opening value of OWIP Using the average method, all the work done on OWIP is included when calculating the equivalent units. It is important therefore to also include all the costs associated with OWIP when calculating the cost per equivalent unit.

Valuation Value each component – Output and CWIP. The value will be equal to: Number of equivalent units x Cost per equivalent unit

Exercise 9 A company operates a process costing system using the AVCO method of valuation. The following data relate to last month: Opening work in progress: Units: 3,000 100% complete for materials at a cost of £12,600 30% complete for conversion costs at a cost of £970 Closing work in progress: Units: 2,000 100% complete for materials 60% conversion costs Inputs for the period: Materials: 7,000units at a cost of £28,000. Conversion costs for the period were £17,430

Required: What is the cost per equivalent unit for materials and conversion costs? What was the total value of the units completed last month?

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FIFO VALUATION FIFO method assumes that we complete the opening work-in-progress prior to starting on any new production. This method is preferred by the examiner. For FIFO method we require that the degree of completion (%) for each element of cost in opening work-in-progress is given. For FIFO, we only look at the work done in the current period and associated costs.

Statement of equivalent units +

opening work-in-progress x % left to complete in period

+

goods started started and finished in period x 100%

=

equivalent units completed in period

+

closing work-in-progress x %

=

total equivalent units

Cost per equivalent unit Under the FIFO method, only the work done in the current period is included in the statement of equivalent units calculation Therefore, only the current period costs should be included when calculating the cost per equivalent unit.

Valuation Value each component as follows: OWIP: Opening value of OWIP + Number of equivalent units x cost per equivalent unit Goods started and finished in the period: Number of equivalent units x cost per equivalent unit CWIP: Number of equivalent units x cost per equivalent unit

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Exercise 10 A company operates a process costing system using the first in first out (FIFO) method of valuation. No losses occur in the process. The following data relate to last month:

Opening work in progress Completed during the month Closing work in progress

Units 100 900 150

Degree of completion 60%

Value £680

48%

Costs incurred in the period were £10,944 What was the value of the closing work in progress?

A

£816

B

£864

C

£936

D

£1,800

What was the total value of the units completed last month?

A

£10,080

B

£10,320

C

£10,760

D

£11,000

Exercise 11 Imagine the following information is available Opening WIP Added units Closing WIP Finished units

500 units (60% complete)

£2,325

1,000 units 300 units (50% complete) 1,200 units

£10,500

Required: Using the information above, write up the process account for the period using:

AVCO FIFO

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JOINT AND BY-PRODUCTS Introduction Quite often when materials are input into a process, more than one product emerges. These are then known as ‘joint products’. “Two or more products separated in processing, each having a sufficiently high saleable value to merit recognition as a main product.”

Product A joint costs

Process 1 Product B

Sometimes a product is made by accident or we discover we sell the wastage as a product. This is then known as a ’by-product’. “A product that is produced from a process, together with other products, that is either of insignificant quantity or insignificant sales value.” To distinguish between joint products and by-products: ●

A joint product is an important saleable item. producing it.

Production is geared to

●

A by-product is something produced which is a bonus to the company. would not be produced as a main product.

It

Sometimes we are in a situation where we can sell our output from a process or we can process it further and sell other products a later stage.

Product B joint costs

Process 1

Process 2

Product C Product D

Product A is sold after Process 1

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Treatment of by-products and joint costs Up to the ‘split-off’ point all costs are classed as common or joint. They have to be shared between all joint products. After this point the additional costs have to be allocated to the various products. The main problem is of the need to split the joint or common costs between the joint products to enable us to cost them efficiently. There are two main methods used to spit these costs:

1.

Physical quantities – the costs are apportioned in proportion to their physical weight or volume of production.

2.

Sales value – the costs are apportioned in proportion to the sales value of production or the final sales value after further processing costs have been removed.

Accounting for by-products is similar to accounting for normal losses; credit any income received to the process account and deduct this value form the total cost before apportioning the costs over the good production.

Exercise 12 A process produces the following products: Product Quantity (Kg) Selling price / kg X 100,000 £1 Y 20,000 £10 Z 80,000 £2.25 The costs incurred in the process prior to the separation point were £240,000.

Required: Apportion the joint costs to each product using:

(a)

Physical units basis

(b)

Sales value basis.

Exercise 13 Three joint products (A,B,C) and 1 by-product (D) arise from a process. Total joint costs are £16,500 and outputs and selling prices are as follows: A B C D

200 300 500 100

kgs kgs kgs kgs

@ @ @ @

£20 £14 £18 £5

Required: Apportion the joint costs using:

(a)

The physical units basis

(b)

The sales value basis.

When further processing has to be taken into account it is sometimes helpful to draw a small diagram and annotate the costs on to it.

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Exercise 14 PCC Ltd produces two joint products from a single process. Joint processing costs of £150,000 are incurred up to the split-off point, when 100,000 units of A and 50,000 units of C are produced. The selling prices at spilt-off point are £1.25 per unit for A and £2 per unit for C. The units of A could be processed further to produce 60,000 units of a new chemical Aplus, but at an extra fixed cost of £20,000 and variable cost of 30p per unit of input. The selling price of Aplus would be £3.25 per unit.

Required: Ascertain whether the company should sell A or Aplus.

Exercise 15 At the end of manufacturing in Process 1, Product K can be sold for £10 per litre. Alternatively product K could be further processed into product KK in Process 2 at an additional cost of £1 per litre input into this process. Process 2 is an existing process with spare capacity in which a loss of 10% of the input volume occurs. At the end of the further processing, product KK could be sold for £12 per litre. Which of the following statements is correct in respect of 9,000 litres of product K?

A

Further processing into product KK would increase profits by £9,000.

B

Further processing into product KK would increase profits by £8,100.

C

Further processing into product KK would decrease profits by £900.

D

Further processing into product KK would decrease profits by £1,800.

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CHAPTER 9 – PROCESS COSTING, JOINT AND BY-PRODUCTS

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Chapter 10

Budgets

CHAPTER COVERAGE 1.

What is a budget?

2.

What are objectives of budget preparation?

3.

What are different types of budgets and how are they prepared?

4.

What is the key or limiting factor for budgets?

5.

What is difference between fixed and flexible budgets?

6.

Prepare flexible budgets and identify variances between budget and actual costs and revenues.

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CHAPTER CONTENTS INTRODUCTION --------------------------------------------------------- 115 BUDGET PREPARATION ------------------------------------------------ 116 SALES BUDGETS -------------------------------------------------------- 117 PRODUCTION BUDGETS ------------------------------------------------ 118 MATERIAL USAGE AND PURCHASE BUDGETS ------------------------ 119 OTHER FUNCTIONAL BUDGETS---------------------------------------- 120 FLEXIBLE BUDGETS ---------------------------------------------------- 122

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INTRODUCTION A budget is defined as 'a quantitative statement, for a defined period of time, which may include planned revenues, expenses, assets, liabilities and cash flows for a forthcoming accounting period’. Budgets are prepared for a number of reasons: 1.

To set and communicate targets.

2.

To establish a standard against which actual performance can be compared.

3.

To co-ordinate inter and intra functional activities.

Both functional budgets and a master budget can be prepared. Typical functional budgets include: ●

Sales Budget

●

Sales Overhead Budget

●

Production Budget

●

Materials Usage Budget

●

Materials Purchase Budget

●

Labour Budget.

The master budget has three elements:

1.

Budgeted income statement

2.

Cash budget

3.

Budgeted balance sheet

Budget construction is commonly overseen by a BUDGET COMMITTEE who often produce a BUDGET MANUAL. This commonly contains information on the following: 1.

The objectives behind the budgeting process.

2.

A list of organisational structures, including the major budgets (and their interrelationships), together with those responsible for controlling them.

3.

Procedural and administrative information on budget preparation.

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CHAPTER 10 – BUDGETS

BUDGET PREPARATION Before the Master Budget can be prepared functional budgets have to be completed. Given that functional budgets are inter-related, changes in one budget can engender changes in several others. The process is iterative and can be very time consuming. The budgeting process begins with identifying the PRINCIPAL BUDGET factor ie, the factor limiting the activities of a company. The budget containing this limiting factor is the one to be constructed first as it controls all others. In most cases the principal budget factor is sales demand ie, levels of production /service provision are controlled by levels of demand. Equally, however, availability of cash, labour, machine time, and raw materials can all become the principal budget factor.

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SALES BUDGETS Sales budgets are relatively straightforward to construct.

Exercise 1 Creating a sales budget Dahlia Limited makes three products Collerette, Pompom, and Cacti. Budgeted Sales Collerette Pompom Cacti

2,000 @ £100 4,000 @ £130 3,000 @ £150

Required: Using the information above, complete the sales budget template: Collerette

Pompom

Cacti

Total

Sales Volume Unit price Total Value

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CHAPTER 10 – BUDGETS

PRODUCTION BUDGETS Production Budgets can only be constructed once sales budgets have been completed and decisions made over planned stocks of finished goods.

Exercise 2 Planning production In addition to the sales figures given in Exercise 1, Dahlia Ltd intends to have the following stocks of finished goods. Finished Stock Budget Opening Stock Units Closing Stock Units

Collerette 500 600

Pompom 800 1,000

Cacti 700 800

Required: Using this information, complete the production budget for Dahlia Ltd.

Collerette

Pompom

Cacti

Sales Units Closing stock Less Opening Stock Production Units

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CHAPTER 10 – BUDGETS

MATERIAL USAGE AND PURCHASE BUDGETS As this series of exercises based on Dahlia Ltd illustrates, functional budgets are interrelated to each other, and materials usage and purchase budgets are no different. A materials purchase budget can only be completed once a usage budget has been finalised, together with decisions regarding stocks of raw materials. In turn raw material usage cannot be completed until production figures are known.

Exercise 3 How much material do we need? In Exercise 2 you should have found that the company intends to manufacture the following number of each product.

Production Units

Collerette 2,100

Pompom 4,200

Cacti 3,100

The following information on materials is available: Raw Material Usage M1 Collerette Pompom Cacti

5 3 2

M2 kg/unit 2 2 1

M3

Cost per kg

£5

£3

£4

M1 kg 21,000 18,000

M2 kg 10,000 9,000

M3 kg 16,000 12,000

2 3

Raw Materials Stock

Opening stock Closing

kgs Usage of M1 Usage of M2 Usage of M3 kgs

Value (£)

Purchases of M1 Purchases of M2 Purchases of M3

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CHAPTER 10 – BUDGETS

OTHER FUNCTIONAL BUDGETS In addition to the functional budgets produced here it is possible to produce other functional budgets, including those for labour and overheads. As with other functional budgets there is a strong degree of inter-linkage.

Exercise 4 Labour budget Production figures for Dahlia Ltd's three products were as follows:

Production Units

Collerette 2,100

Pompom 4,200

Cacti 3,100

The following information on labour usage is also available:

Hours per unit Hourly rate

Collerette 4 £8.50

Pompom 6 £8.50

hrs

Cacti 8 £8.50

Value (£)

Labour usage for the Collerette

Labour usage for the Pompom

Labour usage for the Cacti

Exercise 5 Johnson Ltd manufactures two products, A and B, and is preparing its budget for 200X. Both products are made by the same grade of labour, grade Q. The company currently holds 800 units of A and 1,200 units of B in stock, but 250 of these units of B have just been discovered to have deteriorated in quality and must therefore be scrapped. Budgeted sales of A are 3,000 units and of B 4,000 units provided that the company maintains finished goods stocks at a level equal to 3 months’ sales. Grade Q labour was originally expected to produce one unit of A in two hours and one unit of B in three hours, at an hourly rate of £7.50 per hour. In discussions with trade union negotiators, however, it has been agreed that the hourly wage rate should be raised by 50p per hour provided that the times to produce A and B are reduced by 20%. Produce the production budget and direct labour budget for 19X9. Sometimes we have to take account of inefficiencies in production. We may lose some material or have a workforce which does not work at the required rate.

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Exercise 6 Truro Ltd manufactures a single product Q, with a single grade of labour. Its sales budget and finished goods stock budget for period 3 of 2010 are as follows: Sales Opening stocks, finished goods Closing stocks, finished goods

700 units 50 units 70 units

The goods are inspected only when production work is completed and it is budgeted that 10% of finished work will be scrapped. The standard direct labour hour content of product Q is 3 hours. The budgeted productivity ratio for direct labour is only 80% (which means that labour is only working at 80% efficiency). The company employs 18 direct operatives who are expected to average 144 working hours each in period 3.

Required: (a)

Prepare a production budget.

(b)

Prepare a direct labour budget.

(c)

Comment on the problem that your direct labour budget reveals, and suggest how this problem may be overcome.

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FLEXIBLE BUDGETS To this point the notes have examined the production of fixed budgets, ie no account is taken of possible variation in budgeted levels of activity. Flexible budgets take into account possible variation in levels of activity and costs. They are defined as ‘a budget which, by recognising different cost behaviour patterns, is designed to change as volume of activity changes’. Flexible budgets are relatively straightforward to produce as they use the principles of marginal costing. Calculating fixed costs and fully variable costs is straightforward. However, care must be taken when dealing with semi-variable costs, ie costs that have a fixed and a variable element. Remember that semi-variable costs can be broken down into their fixed and variable elements by using the High-Low method.

Exercise 7 Flexing a budget The following information for Artichoke Ltd is available. The company's directors are concerned by the large difference between budgeted and actual activity. They have asked you to produce a flexible budget and to present meaningful variances.

Sales Less Direct Materials Direct Labour Fixed Production overheads Gross Profit Less Variable Selling cost Fixed selling cost Profit

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Budget 3,000 units £ 90,000

Flexed 4,000 units

Actual 4,000 units £ 110,000

30,000 15,000 2,500

45,000 20,000 2,300

42,500

42,700

3,000 1,500 38,000

4,000 2,000 36,700

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Chapter 11

Standard costing and variance analysis

CHAPTER COVERAGE 1.

What is meant by a standard?

2.

What are the different types of standards?

3.

How to calculate the standard cost per unit of a product.

4.

What is a variance?

5.

How to calculate variances.

6.

How to reconcile the standard profits with the actual profits through the variances.

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CHAPTER 11 – STANDARD COSTING AND VARIANCE ANALYSIS

CHAPTER CONTENTS INTRODUCTION --------------------------------------------------------- 125 TYPES OF STANDARD -------------------------------------------------- 126 IDEAL STANDARD

126

ATTAINABLE STANDARD

126

CURRENT STANDARD

126

BASIC OR HISTORIC STANDARD

126

VARIANCES AND VARIANCE ANALYSIS ------------------------------ 128 MATERIAL VARIANCES

129

LABOUR VARIANCES

131

VARIABLE OVERHEAD VARIANCES

132

FIXED OVERHEAD VARIANCES

132

SALES VARIANCES

134

OPERATING STATEMENTS --------------------------------------------- 136

124

ABSORPTION COSTING OPERATING STATEMENT

136

MARGINAL COSTING OPERATING STATEMENT

137

CAUSES OF VARIANCES

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CHAPTER 11 – STANDARD COSTING AND VARIANCE ANALYSIS

INTRODUCTION A standard cost is a carefully predetermined unit cost that is calculated in advance of production taking place. As such it includes standard amounts of labour at standard cost, standard amounts of materials at standard cost, together with budgeted overheads absorbed at predetermined rates using budgeted levels of activity. Standard costing is often used to establish expected costs against which actual costs can be compared ie, a standard cost can be used to establish control over costs. Differences between standard and actual costs are known as variances. The process of analysing differences between actual and standard costs is known as variance analysis.

A typical standard cost card might be as follows:

£

£

Direct Material X (2 units) Y (3 units) Z (2 units)

7 8 9 24

Direct Labour Grade 1 (6 hrs) Grade 2 (5 hrs)

80 20

Standard Standard Standard Standard

Direct Cost Variable Cost of Production Fixed Cost Factory Cost

100 124 100 50 274

Standard Standard Standard Standard

Administration and Selling Overhead Cost of Sale Profit (50%) Sales Price

120 394 197 591

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CHAPTER 11 – STANDARD COSTING AND VARIANCE ANALYSIS

TYPES OF STANDARD Standard can be set on a number of bases.

Ideal standard This is the 'perfect' standard ie, what should be achieved if there is no wastage or loss and the whole production process functions perfectly. This type of standard can act as long-term aspirational target.

Attainable standard These are standards in advance of what is currently being achieved. However, the degree of improvement required to attain the standard is a practical proposition. This form of standard can be very motivational for staff.

Current standard This is the standard an organisation is currently achieving. It does not provide inspiration for improvement but it does provide a benchmark against which to measure day-to-day activity.

Basic or historic standard This is a standard that was set some time ago and has not been updated. It allows a company to measure its progress over time.

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Exercise 1 Standard cost card Using information in the paragraph below produce a standard cost card for product Callestemon. Each Callestemon uses 2kg of material Q at a standard cost of £30 per kg, 6 hours of labour at £10 per hour. Variable overheads have a standard cost of £15 per hour. The company has fixed production overheads of £20,000 and is budgeting to produce 500 units. A standard profit of £100 is added to cost to determine standard price.

£ Materials Labour Overheads Fixed Overheads Standard Cost Standard Profit Standard Price

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VARIANCES AND VARIANCE ANALYSIS Variances can be defined as the 'Difference between a planned, budgeted or standard cost and the actual cost incurred. The same comparisons can be made for revenues’. Analysis of the difference between standard and actual costs is known as VARIANCE ANALYSIS.

FAVOURABLE VARIANCES occur when actual results are better than expected, producing higher than expected profits. ADVERSE VARIANCES occur when actual results are worse than expected, producing lower than expected profits. Variances are calculated in total (as the variance in flexible budgets). then broken down into their constituent parts as per the diagram below.

They are

Price

Material Usage

Rate

Labour Efficiency Expenditure

Variable overheads Efficiency Expenditure

Fixed overheads

Capacity Volume Efficiency Price

Sales Volume profit

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CHAPTER 11 – STANDARD COSTING AND VARIANCE ANALYSIS

Example 1 Owen Owen Ltd uses a standard costing system. The standard cost card for one product is shown below: Direct Material Direct Labour Variable Overhead Total Variable Cost Fixed Overhead Total Product Cost Standard Selling Price Standard Profit Margin

4 kg at £5 per kg 2 hours at £8 per hour 2 hours at £3.5 per hour 2 hours at £7 per hour

£ 20 16 7 43 14 57 70 13

The budgeted output and sales was 1,000 units. Actual output for the period was 1,300 units and actual sales for the period was 1,250 units. Actual cost and revenue were as follows: Direct Material Direct Labour Variable Overhead Fixed Overhead Sales Revenue

5,000 kg, costing 2,850 hours, costing

1,250 units at £68 per unit

£ 22,700 21,500 7,800 14,600 85,000

Required: Calculate all possible variances.

Material variances Standard Cost Direct Material

4 kg at £5 per kg

Actual Results Actual output Materials Purchased and used

5,000 Kg, costing

1,300 units £22,700

Key pro forma

SQ x SP Usage AQ x SP Price AQ x AP

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CHAPTER 11 – STANDARD COSTING AND VARIANCE ANALYSIS

Possible reasons Price Variance

Usage Variance

1.

Wrong budgeting

1.

Wrong budgeting

2.

Lower/higher quality material

2.

Lower/higher quality of material

3.

Good/poor purchasing

3.

Lower/higher quality of labour

4.

External factors (inflation, exchange rates etc)

4.

Theft

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Labour variances Standard Cost Direct Labour

2 hours at £8 per hour

Actual Results Actual output Hours paid and worked Labour Cost

1,300 units 2,850 £21,500

Key pro forma

SH x SR Efficiency AH x SR Rate AH x AR

Possible reasons Rate Variance

Efficiency Variance

1.

Wrong budgeting

1.

Wrong budgeting

2.

Wage inflation

2.

Lower/higher morale

3.

Lower/higher skilled employees

3.

Lower/higher skilled employees

4.

Unplanned overtime or bonuses

4.

Lower/higher quality of material

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Variable overhead variances Standard Cost Variable overhead

2 hours at £3.5 per hour

Actual Results Actual output Hours worked (from above) Variable overhead cost

1,300 units 2,850 £7,800

Key pro forma

SH x SR Efficiency AH x SR Expenditure AH x AR Possible reasons Efficiency Variance As per labour efficiency.

Expenditure (rate) Variance Variable overheads are made up of many different overhead cost elements; to identify reasons for the variance we would need to analyse all elements separately.

Fixed overhead variances Fixed costs are a constant in total terms, hence total cost is our starting point. The analysis of variances will be dependent on the costing methodology. Do we use absorption costing or marginal costing? Either is potentially applicable.

Absorption costing principles Using absorption costing the fixed cost is charged or absorbed to the cost unit or product. The total fixed overhead variance will be similar to the under/ over absorption of overhead. The total variance may be sub-analysed into two:

1.

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Volume variance – if the company produces more or less units and hence absorb more or less overhead than budgeted.

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CHAPTER 11 – STANDARD COSTING AND VARIANCE ANALYSIS

2.

Expenditure variance – if the company spends more or less fixed overhead than budgeted.

Question extract Standard and Budgeted Cost The fixed cost is (£7/hour for 2 hours) £14 per unit The budgeted number of units is 1,000 Budgeted fixed overheads is therefore £14,000

Actual Results Actual output Hours worked (from above) Fixed overhead Cost

1,300 units 2,850 £14,600

Key pro forma

Std fixed o/h cost (of actual output) Volume variance Budgeted fixed o/h cost Expenditure variance Actual fixed o/h cost Further analysis of fixed overheads It is also possible to further analyse fixed overheads by considering actual hours in relation to the actual and budgeted units produced. To be comparable the output measures must be measures in terms of standard hours.

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Key pro forma

SH x SR Efficiency AH x SR Capacity BH x SR Expenditure AH x AR

Sales variances Standards budget

and

Total Product Cost Standard Selling Price Standard Profit Margin Budgeted sales

57 70 13 1,000

Actual Results Sales (units) Selling Price

1,250 £68

Production units

1,300

Key formulae

Volume variance (AS - BS) x SPM Price variance (AP - SP) x AS

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Changes to variances when using marginal costing Variances that remain the same

Variances that change

All variable cost variances Sales price variance

Sales volume variance now valued at standard contribution margin

Fixed overhead expenditure

Fixed overhead volume (and hence capacity and efficiency) disappear

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CHAPTER 11 – STANDARD COSTING AND VARIANCE ANALYSIS

OPERATING STATEMENTS Though individual variances provide useful information for management, they can be combined to produce an operating statement that can be used to reconcile budgeted and actual profit. Since an adverse variance brings down profit it is subtracted from budgeted profit in an operating statement. Conversely, each favourable variance puts up profit and should be added to budgeted profit.

Absorption costing operating statement Example 2 Owen Using information on variances, calculated in exercises above, complete the operating statement for Owen Ltd under absorption costing.

£ Budgeted Profit Sales Volume Variance Standard profit for actual sales volume Sales Price Variance

Cost Variances F

A

Materials Price Materials Usage Labour Rate Labour Efficiency Variable Overhead Expenditure Variable Overhead Efficiency Fixed Overhead Expenditure Fixed Overhead Capacity Fixed Overhead Volume Total Actual profit

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CHAPTER 11 – STANDARD COSTING AND VARIANCE ANALYSIS

Marginal costing operating statement When reconciling using marginal costing principles it is normal to reconcile from budgeted contribution.

Example 3 Owen Using information on variances, calculated in exercises above, complete the operating statement for Owen Ltd under absorption costing.

Budgeted Contribution Sales Volume Variance Standard contribution for actual sales volume Sales Price Variance Sub-total

Variable Cost Variances F

A

Materials Price Materials Usage Labour Rate Labour Efficiency Variable Overhead Expenditure Variable Overhead Efficiency Sub-total Actual contribution Less budgeted fixed cost Variance Sub-total Actual profit

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CHAPTER 11 – STANDARD COSTING AND VARIANCE ANALYSIS

Causes of variances Variances can arise for a number of reasons. table below.

Example reasons are given in the

Fill in the shaded boxes with further reasons. Variance Materials Price

Purchase of better quality materials

Material Usage

Use of different quality materials

Labour Rate

Workers claiming overtime

Labour Efficiency

Inexperienced workers used to complete work

Variable Overhead Expenditure Variable Overhead Efficiency Fixed Overhead Sales Price

Sales Promotion

Sales Volume

Competition

Variances can be inter-related. Buying high quality materials will lead to an adverse materials price variance. However, better quality material will improve labour efficiency, leading to a favourable labour efficiency variance.

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Chapter 12

CVP analysis

CHAPTER COVERAGE 1.

How to calculate the contribution per unit of a good or service.

2.

How to calculate the contribution to sales ratio (C/S).

3.

What is a break even point?

4.

How to draw a break-even chart and profit/volume chart.

5.

How to identify the break-even point by using:

6.

●

Break-even chart

●

Profit/volume chart

●

Mathematical technique.

What is the margin of safety and how it is calculated?

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CHAPTER CONTENTS BREAK-EVEN ANALYSIS (CVP ANALYSIS) --------------------------- 141 BREAK-EVEN POINT

141

TARGET PROFITS

141

MARGIN OF SAFETY

142

CONTRIBUTION / SALES RATIO -------------------------------------- 144

140

BREAK-EVEN CHART

146

PROFIT/VOLUME CHART

146

LIMITATIONS OF BREAK-EVEN ANALYSIS

147

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C H A P T E R 1 2 – C V P A N A L Y S IS

BREAK-EVEN ANALYSIS (CVP ANALYSIS) CVP analysis is a technique which uses cost behaviour to identify the level of activity at which we have no profit or loss (break-even point). It can also be used to predict the profits or losses to be earned at varying activity levels (using the assumed linearity of costs and revenues). CVP analysis assumes that selling prices and variable costs are constant per unit regardless of the level of activity and that fixed costs are just that – fixed. In order to calculate these levels we need to consider the contribution provided by each unit of production. Contribution is the term given to the difference between the selling price and the variable costs which contributes first towards paying the fixed costs and then towards providing profit. The price of each unit we sell consists of three (3) parts. 1.

the variable element which is incurred for each unit of production.

2.

the fixed element which varies according to the number of units made. If the units increase, the amount of fixed costs per unit required will decrease.

3.

the profit element.

Break-even point If we are to calculate the break-even point let us first imagine that the fixed costs are a large hole in the ground. What we need to find out is how many contributions it takes to fill that hole. Unit contribution

=

Selling price per unit – Variable cost per unit

Total contribution

=

Unit contribution x volume

At the break-even point, profit is 0: Total Contribution = Fixed Costs + 0 Break-even point (units)

=

Fixed costs Unit contribution

Exercise 1 Break-even point A company has a budgeted level of activity of 10,000 units with a budgeted total contribution of £90,000. Fixed costs are £45,000. Each unit is sold for £15. What is the breakeven point in units? What is the breakeven sales revenue?

Target profits Similarly the profit we require is the pile on top of the hole. contributions does it take to reach the required height? Contribution target

=

Fixed costs + Target profit

Volume target (units)

=

Contributi on target Unit contributi on

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How many

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C H A P T E R 1 2 – C V P A N A L Y S IS

Exercise 2 Breaking even and reaching a target profit A company makes the Daisy. Each Daisy has a variable cost of £4 and a selling price of £9. Fixed costs for the company are £35,000. Given that company wishes to make a profit of £15,000, how many units does it have to: Units Sell to breakeven?

Sell to reach its target profit?

Margin of safety The margin of safety is the area between the break-even point and the maximum sales. This is the area that the company can operate in and be certain of making a profit. It is usually classed as the amount of sales that a company can afford to lose before it gets into a loss making situation. Knowing that a product breaks even at a certain sales volume is helpful but it can be misleading in certain circumstances. A company makes two products, the breakeven volumes for which are shown below: Product A Product B

500 units 200 units

All other things being equal, which product is most likely to make a profit? It is tempting to state B as it has the lower breakeven point. You should reconsider this in the light of the budgeted sales figures below: Product A Product B

2,000 units 300 units

Breakeven sales are a smaller percentage of budgeted sales for Product A than they are for Product B and as such Product A is much more likely to make a profit. Margin of safety measures the difference between budgeted and breakeven sales and expresses it as a percentage of budgeted sales. It represents how far below budgeted sales actual sales can fall before a loss will be made. Margin of safety = (budgeted sales – breakeven sales / budgeted sales) x 100 Product A

(2,000 – 500 / 2,000 x 100 = 75%

Product B (300 – 200) / 300 x 100% = 33%

Exercise 3 Margin of Safety A company is budgeting to sell 150,000 units at £7. Each unit has a variable cost of £4 and the company’s fixed costs are £342,000. What is the margin of safety?

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Quick exercises 1.

Selling price Variable costs Fixed costs

£3 per unit £1 per unit £500

Calculate the break-even point.

2.

If the fixed costs increase by 10% and the company aims to make £200 profit, what output is required?

3.

Assuming the maximum output is 250 units, what selling price would achieve the required profit target of £200 assuming the increased fixed costs?

4.

Budgeted sales Selling price Variable costs Fixed costs

80,000 units £8 £4 per unit £200,000

What would be the break-even point and the margin of safety?

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CONTRIBUTION / SALES RATIO The above calculations are useful in calculating the break-even point of one unit of production. If a company makes more than one product it may be better to calculate the C/S ratio. C/S ratio

=

Unit contributi on Unit sales

or

Total contributi on Total sales

A product having a sales price of £10 and unit contribution of £4 would have a C/S ratio of: £4 = £10

0.4

This means that forty pence of every pound of sales revenue is contribution. Breakeven sales revenue can then be calculated as: Fixed Costs C/S ratio

Exercise 4 C/S Ratio Penstemon Ltd make a product, the Sepal. Each Sepal sells for £15 and has a variable cost of £6. Total fixed costs are £198,000. The company is budgeting to sell 66,000 units. Unit contribution is:

£

C/S Ratio is:

144

Breakeven revenue is:

£

Margin of safety is:

£

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C H A P T E R 1 2 – C V P A N A L Y S IS

Exercise 5 The following details relate to a shop which currently sells 25,000 pairs of shoes annually. Selling price per pair Purchase cost per pair Total annual fixed costs: Salaries Advertising Other fixed expenses

£40 £25

£100,000 £40,000 £100,000

Required: Answer each part independently of data contained in other parts of the requirement.

(a)

Calculate the break-even point and margin of safety in number of pairs of shoes sold.

(b)

Assuming that 20,000 pairs of shoes were sold in a year, estimate the shop’s net income or loss.

(c)

If a selling commission of £2 per pair of shoes sold was introduced, how many pairs of shoes would need to be sold in a year in order to earn a net income of £10,000?

(d)

Assume that for next year an additional advertising campaign costing £20,000 is proposed, whilst at the same time selling prices are to be increased by 12%, what would be the break-even point in number of pairs of shoes?

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C H A P T E R 1 2 – C V P A N A L Y S IS

Break-even chart Costs and revenues

Sales revenue

Total costs Profit

Fixed costs Margin of safety Sales activity Break-even point

Budgeted activity

Profit/volume chart A break-even chart shows the costs and revenues at a number of activity levels. It does not however, show the amount of profit or loss at these levels. This is shown on the profit/volume chart.

Profit

Total profit

Sales activity Break-even point

Loss Fixed costs (total loss)

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From this chart we can read off the amount of profit or loss for any level of activity. 1.

The x axis represents sales (units or values)

2.

The y axis shows profits above the x axis and losses below.

3.

When sales = zero, the net loss is equal to the fixed costs.

4.

If variable cost per unit and total fixed costs are constant throughout the relevant range, the profit/volume chart is shown as a straight line.

5.

If there are\changes in either of these costs at various levels of activity, it will be necessary to calculate the profit or loss at each point where the cost structure alters before plotting the points onto the chart.

Limitations of break-even analysis Once costs and revenues have been determined, it is usually assumed that they will have a linear relationship, ie ●

Fixed costs will be constant over the relevant range

●

Variable costs will vary in direct proportion to volume

●

Selling price will remain unchanged

●

The efficiency and productivity of the workforce remain constant.

The analysis covers either a single product or a mix of products at which it is assumed that the proportion of each product will remain the same as volume increases or decreases. In constructing a break-even chart, the sales and costs are likely to be valid only in a particular range of activity. This is referred to as THE RELEVANT RANGE. Outside this range the same cost and revenue relationships are unlikely to exist. Eg, an alteration in volume could affect the level of fixed costs (stepped) or the rate of variable costs or selling prices (economies of scale).

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Chapter 13

Limiting factors, linear programming, relevant costs

CHAPTER COVERAGE 1.

What is a limiting factor?

2.

How to find out any limitation in the production process.

3.

How to rank the products and work out the optimum production plan by using the limiting factor/resource.

4.

Why do management accountants have to use Linear programming technique in limiting factor analysis?

5.

What is relevant cost?

6.

Why is relevant cost study important in short term decision making?

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CHAPTER CONTENTS LIMITING FACTORS (SCARCE RESOURCES) ------------------------- 151 METHOD OF WORKING

152

LINEAR PROGRAMMING ----------------------------------------------- 155 RELEVANT COSTS AND REVENUES ------------------------------------ 157

150

RELEVANT CASH FLOWS ARE FUTURE CASH FLOWS

158

RELEVANT CASH FLOWS ARE INCREMENTAL CASH FLOWS

158

COMMITTED COSTS ARE NOT RELEVANT

158

RELEVANT COSTS CAN BE OPPORTUNITY COSTS

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LIMITING FACTORS (SCARCE RESOURCES) Within most business organisations there are not enough resources available to fulfil all the plans of the organisation. The factor which is in short supply is known as the ‘limiting factor’. When an organisation is short of a resource it has to make decisions regarding its production scheduling so as to make the best use of that resource. Typically the limiting factor is the forecast level of sales. In some circumstances, limited supply of labour or machine time could govern the level of output. Questions at this level, assume that a company wishes to maximise its return on the resources it has available. Limiting factor analysis is the technique used to calculate the mix of products that should be made to maximise return on a single limiting factor. Take the two products below. Which one should the company make to maximise its return on scarce machine hours?

Unit Sales Price Unit Variable Cost Contribution Unit Fixed cost Unit Profit

Red

Herring

£ 40 10 30 20 10

£ 80 20 60 20 40

It is tempting to state the Herring due to its higher unit profit. However, this could be the wrong suggestion for two reasons: 1.

Profit should not be used as its calculation includes fixed costs that do not change as the result of the decision.

2.

The apportioning of fixed cost between products could be quite arbitrary. Contribution should be used.

Even if contribution is used the wrong decision can still be made. Contribution per unit of product does not take into account the amount of scarce resource used to generate that contribution. Decisions on production priorities should be made using the contribution generated per unit of scarce resource used – in this case contribution per machine hour. Imagine if 1,000 machine hours are available and each Red takes 1 hour and each Herring 3 hours.

Unit Sales Price Unit Variable Cost Contribution Machine hrs Contribution per hour Total hours available Total contribution

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Red £ 40 10 30 1 30 1,000 £30,000

Herring £ 80 20 60 3 20 1,000 £20,000

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Method of working 1.

If not stated, calculate the limiting factor

2.

Find the contribution per unit of each product by deducting variable cost from selling price.

3.

Calculate the contribution per unit of limiting factor by dividing the contribution per unit by the units of limiting factor required to make each product.

4.

Rank these in order of priority.

5.

Prepare a production schedule showing how many units of each product you are going to make taking account of priorities and prior contracts etc.

6.

Calculate the total contribution earned by this production.

7.

If required, deduct fixed costs to find the profit achieved in the period.

Exercise 1 A company makes three products, details of which are given below:

Demand Unit price Variable cost Labour hours

Speedwell 1,000 units £ 50 10 4

Nettle 1,000 units £ 70 50 1

Liatris 1,000 units £ 50 25 2

Total fixed costs for the company are £7,500. There are 1,800 hours available.

Required: How much of each product should be made to maximise profit for the company? Units of Speedwell

Units of Nettle

Units of Liatris

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Exercise 2 X Ltd makes three products, A, B and C, of which unit costs, machine hours and selling prices are as follows: A

B

C

10

12

14

£

£

£

Direct materials @ 50p/kg

7

6

5

Direct wages @ 75p/hr

9

6

3

Variable overheads

3

3

3

Marginal cost

19

15

11

Selling price

25

20

15

6

5

4

4,000

6,000

6,000

Machine hours

Contribution per unit

Sales demand for the period is:

As a matter of company policy it is decided to produce a minimum of 1,000 units of Product A. The supply of materials in the period is unlimited but machine hours are limited to 200,000 and direct labour hours to 50,000.

Required: Indicate the production levels that should be adopted for the three products in order to maximise profitability, and state the maximum contribution that would be achieved.

Note: In this question we have a prior commitment that has to be honoured before we can proceed with our production scheduling.

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Exercise 3 X Ltd manufactures 4 liquids – A, B, C and D. The selling price and unit cost details for these products are as follows: A

B

C

D

£/litre

£/litre

£/litre

£/litre

100

110

120

120

Direct materials

24

30

16

21

Direct labour (£6/hr)

18

15

24

27

-

-

3

-

Variable overhead

12

10

16

18

Fixed overhead

24

20

32

36

Profit

22

35

29

18

Selling price

Direct expenses

Fixed overhead is absorbed on the basis of labour hours, based on a budget of 1,600 hours per quarter. During the next 3 months the number of direct labour hours is expected to be limited to 1,345. The same labour is used for all products. The marketing director has identified the maximum demand for each of the 4 products during the next 3 months as follows: A B C D

200 150 100 120

litres litres litres litres

These maximum demand levels include the effects of a contract already made between X Ltd and one of its customers, Y Ltd, to supply 20 litres each of A, B, C, and D during the next 3 months.

Required: (a)

Determine the number of litres of products A, B, C, and D to be produced/sold in the next 3 months in order to maximise profits.

(b)

Calculate the profit that this would yield.

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LINEAR PROGRAMMING Linear programming is a graphical technique used to identify the profit maximising production levels when there is more than one limiting factor (constraint). In order to be able to use this technique there must be a linear relationship between the variables. The best way of describing this technique is by means of an example.

Exercise 4 A company makes and sells two products X and Y. It has a shortage of labour which is limited to 20,000 hours per annum. This is insufficient to satisfy the full demand for both products. The unit costs, contributions and labour hours are as follows:

Labour hours per unit of output

Product X 5

Product Y 10

Selling price

£ 80

£ 100

Variable cost

50

50

Contribution

30

50

The company can sell any number of product Y but expects the maximum annual demand of X to be 3,000 units.

Method: 1.

Define the unknowns – the variables which must be considered. Let x = number of units of X produced and sold Let y = number of units of Y produced and sold

2.

Formulate the constraints – the limitations to be placed on the variables. This means expressing them as a mathematical equation. Labour hours

3.

≤ 20,000

Maximum sales

x

Non-negativity

x, y ≥ 0

≤ 3,000

Formulate the objective function (what we want to maximise). usually to maximise contribution. Maximise

4.

5x + 10y

This is

30x + 50y

Graph the constraints and objective function. We need to transfer these figures onto the graph by means of drawing straight lines which relate to the constraints already determined.

5.

Identify the “feasible region”. feasible option.

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This is the area where production is a

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6.

Establish the optimum point using the graph or simultaneous equations. To find the optimum point, place a clear ruler along the objective function. Slide the ruler outwards from the origin, staying parallel to the objective function. The last point in the feasible region to cross the leading edge of the ruler is the optimum point. 2500 2000 1500 Units of Y 1000 500 0 0

1000

2000

3000

4000

5000

Units of X

Exercise 5 JWW Ltd manufactures two products, X and Y, and any quantities produced can be sold for £60 per unit and £25 per unit respectively. Variable costs of the two products are:

Materials (at £5 per kg) Labour (at £6 per hour) Other variable costs Total

X £ per unit 15 24 6 45

Y £ per unit 5 3 5 13

Next month only 4,200 kg of material and 3,000 labour hours will be available. The company holds no stocks and aims to maximise total contribution each month.

Required: Write down the objective function. Write down the constraints of the problem. Graph these constraints and shade the feasible region. Determine the numbers of each product to be produced to achieve the objective of maximising contribution.

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RELEVANT COSTS AND REVENUES Relevant costing decisions are based on an analysis of what changes as the result of a decision – not total cost or total revenue but change in total cost and revenue.

Exercise 6 A company makes moulds and estimates that its standard product costs £1,500 to make. At present there is spare capacity in the factory and the owners are searching for additional business. A small local company has offered to buy 10 moulds for £900 each.

Required: Should the company accept the offer? On the face of it the answer is clear. If each pump costs £1,500 and they can only sell them for £900, there is little point in their manufacture. However, using relevant costing the problem would be approached from a different angle. 1.

How does total cost change if one more pump is built?

2.

How does total revenue change if one more pump is sold?

Imagine the following breakdown of mould cost is available.

Materials Labour Fixed Production Overheads Total

£ 500 300 700 1,500

Making one more mould will incur an additional £500 of materials and £300 of labour. However, factory overheads will not change, as they are all fixed costs. The relevant (extra) cost of making one more mould is therefore £800. If the mould is sold, the company will receive £900.

Relevant revenue Less: Materials Labour Contribution

£ 900 (500) (300) 100

Since sale of the mould makes a positive contribution the company should go ahead with the contract. This £100, although not profit, will contribute towards paying the company’s fixed costs. So what are relevant costs/revenues? Relevant costs and revenues are simply cash flows that arise as the result of a decision. If a cash flow if unaffected by a decision then it is not relevant.

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Relevant cash flows are future cash flows In the example of the mould, development costs for the product are not taken into account. They are sunk (historical costs) that will not be changed as a result of a decision.

Relevant cash flows are incremental cash flows The quarterly bill for materials used to make moulds could be £50,000. Increasing the number of moulds produced by one unit increases the bill to £50,500. The relevant cost of the extra mould is neither £50,000 nor £50,500. It is the change in total material costs triggered by the decision to make one more mould – £500.

Committed costs are not relevant Before the new contract for additional moulds arose the company was due to pay a labour bill of £7,000 at the end of the month. This is not a relevant cost as it will have to be paid regardless of the company’s decision regarding the extra moulds ie, the company is committed to paying the wages irrespective of the decision being made.

Relevant costs can be opportunity costs A company has a limited supply of materials. If it uses them to make moulds it cannot also make plastics. For every mould made the company loses contribution on plastics worth £200. This is a relevant cost ie, it is a cash inflow that does not arise as the result of a decision to manufacture moulds.

Exercise 7 A company has 600kgs of material in stock that cost £50/kg three years ago. To replace the material would cost the company £60/kg. Relevant Cost £ At present the company does not have a use for the materials. If it receives a one-off order that can use the material, what is the relevant cost per kg? At present the company does not have a use for the materials. However, it can sell the materials at £5/kg to a local scrap merchant. If it receives a one-off order that can use the material, what is the relevant cost per kg? The company currently uses the materials in all of its products. It can sell the materials for £5 per kg to a local scrap merchant. If the company uses a kg of the materials in a product, what is the relevant cost?

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Exercise 8 A company has just secured a new contract which requires 700 hours of labour. There are 200 hours of spare labour capacity. The remaining hours could be worked as overtime at time and a half or labour could be diverted from the production of Product P. Product P currently earns a contribution of $8 per labour hour and direct labour is currently paid at a rate of $9 per normal hour. What is the relevant cost of labour for the contract?

Exercise 9 A company has a machine it was planning to sell for proceeds of £15,000 as the machine is no longer in use by the company. The machine cost £70,000 5 years ago. A customer has requested a specific contract which the machine would be required for. The duration of the contract would be 1 year. At the end of the contract, the machine would have no sales value. The cost of disposing the machine would be £5,000. What is the relevant cost of the machine for this contract?

A

£70,000

B

£20,000

C

£15,000

D

£5,000

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Solutions to exercises

CHAPTER CONTENTS CHAPTER 2 -------------------------------------------------------------- 162 CHAPTER 3 -------------------------------------------------------------- 164 CHAPTER 4 -------------------------------------------------------------- 166 CHAPTER 5 -------------------------------------------------------------- 170 CHAPTER 6 -------------------------------------------------------------- 175 CHAPTER 7 -------------------------------------------------------------- 178 CHAPTER 8 -------------------------------------------------------------- 180 CHAPTER 9 -------------------------------------------------------------- 185 CHAPTER 10 ------------------------------------------------------------- 196 CHAPTER 11 ------------------------------------------------------------- 199 CHAPTER 12 ------------------------------------------------------------- 200 CHAPTER 13 ------------------------------------------------------------- 203

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CHAPTER 2 Exercise 1 Units 105,000 65,000 40,000

High Low

Cost £210,000 £133,000 £77,000

Variable cost = £77,000/40,000 = £1.925 per unit Fixed cost = £210,000 – (105,000 x £1.925) = £7,875 Forecast for 165,000 units = £7,7875 + (165,000 x £1.925) = £325,500

Class Exercises 1.

A A simple way to identify these would be to assess which are totally variable. T1 T2 T3 T4

2.

= = = =

1,000/125 1,750/125 2,475/125 3,225/125

x x x x

180 180 180 180

= = = =

1,440 2,520 3,564 4,644

Ans Ans Ans Ans

= = = =

Semi variable Variable Semi variable Variable

D This diagram shows a variable above a fixed cost. The variable cost decreases after a certain level of activity (slope is less steep).

3.

C From the information give we cannot use the high-low method in its normal form as the fixed cost increases by £5,000. We need to remove this stepped increase first and add it back in any forecasts we make above the limit of 18,000 units.

High Low

Units 22,000 17,000 5,000

Cost £165,000 £140,000 £5,000

Variable cost = £25,000/5,000 = £5 per unit Fixed cost = £140,000 – (17,000 x £5) = £55,000 Forecast for 20,000 units = £55,000 + (20,000 x £5) + 5,000 = £160,000

4.

£32,800 We need to remove the change in variable cost per unit before the high low method can be applied. Adjusted total costs at the high level of activity = £31,000 + £1.5 x 1,000 = £32,500

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Variable cost = (32,500 – 22,000)/(13,000 – 8,000) = £2.1 For the first 12,000 units produced, the variable cost per unit will be £2.1. For any additional units produced the variable cost per unit will be £2.1 - £1.5 = £0.6 Fixed costs = £22,000 - £2.1 x 8,000 = £5,200 Total cost for 16,000 units = £5,200 + £2.1 x 12,000 + £0.6 x 4,000 = £32,800

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CHAPTER 3 Exercise 1 1

High-low method

2,300 − 1,050 1,250 = 900 − 400 500 Variable cost = £2.50 Fixed cost = 2300 – (900 x £2.50) = £50 Forecast for 850 units = 50 + (850 x £2.50) = £2175

2

Regression

Month

x

y

xy

x2

y2

January

400

1,050

420,000

160,000

1,102,500

February

600

1,700

1,020,000

360,000

2,890,000

March

550

1,600

880,000

302,500

2,560,000

April

800

2,100

1,680,000

640,000

4,410,000

May

750

2,000

1,500,000

562,500

4,000,000

June

900 4,000

2,300 10,750

2,070,000 7,570,000

810,000 2,835,000

5,290,000 20,252,500

b=

(6 * 77,570,000) − (4,000 * 10,750) (6 * 2,835,000) − 4,0002

b =

45,420,000 − 43,000,000 17,010,000 − 16,000,000

a=

10,750  4,000  − * 2.396  = 194.33 6  6 

b = £2.396

For forecasting, our equation is y = 194.33 + 2.396x 850 units = 194.33 + (2.396 x 850) = £2,230.93

3

r =

r =

4

164

Correlation

(6 * 77,570,000) − (4,000 * 10,750)

[(6 * 2,835,000 − 4,000 )(6 * 20,252,500 − 10,750 )] 2

2,420,000 1,010,000 * 5,952,500

2

= 0.98697

Coefficient of determination = r2 = 0.974 = 97%

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S O L U T IO N S T O E X E R C I S E S

Exercise 2 A

=

(100,000 * 40%) + ( (40,000) * 60%)

=

£16,000

B

=

(50,000 * 60%) + ( (20,000) * 40%)

=

£22,000

C

=

(40,000 * 80%) + ( (10,000) * 20%)

=

£28,000

C is the best option.

Exercise 3 Project X: Expected value = 0.4 x £3,000 + 0.6 x £1,500 = £2,100 Project Y: Expected value = 0.35 x £10,000 + 0.65 x £0 = £3,500 Project Y is the best option

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CHAPTER 4 Exercise 1 EOQ =

2 * 15 * 32,000 = 894 (to nearest whole number) 40 * 3%

Exercise 2 EOQ =

2 * 2500 * 65,000 = 1,041 = 1,000 (nearest whole number) 300

Number of orders per year = 65,000/1,000 = 65 * £2,500 = £162,500 Cost of holding = 1,000/2 * £300 = £150,000 Total cost = £312,500 If we purchase 2,000 units per order Ordering cost = 32.5 * £2,500 = £81,250 Holding cost = 2,000/2 * £300 = £300,000 Total cost = £381,250 BUT we save 65,000 * £1,000 * 2% = £1.3 m Answer = Yes.

Exercise 3 ROL = 500 * 7 = 3,500 Minimum level = 3,500 – (5 * 400) = 1,500 Maximum level = 3,500 + 5,400 – (4 * 300) = 7,700.

Exercise 4 Employee A B

C Total

166

Produced 96

Rate 2.25

Earned 216.00

Received 216.00

100 22 122

2.25 3.00

225.00 66.00 291.00

291.00

76

2.25

171.00

180.00 687.00

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S O L U T IO N S T O E X E R C I S E S

Exercise 5 Expected hours to complete job: 4 hours Actual hours to complete job:

3 hours

Time saved:

1 hour

Bonus: 1 hr x £8 x 75% = £6 Total wage for job: £8 x 3 + £6 = £30

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Exercise 6 Hours Basic rate Overtime premium

Rate

Total

54

7.50

405.00

14

2.50

35.00

Bonus

45.00

Total pay

485.00

Bonus calculation: Should take

124 units * 0.5 hrs

62.00

Did take

50.00

Time saved

12.00

Bonus = 12 hrs * 50% * £7.50

= £45.00

Direct cost

Indirect cost

Worked hours @ basic rate

50

7.50

375.00

Idle time Overtime premium

4

7.50

30.00

14

2.50

35.00

Bonus 375.00

168

45.00 110.00

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S O L U T IO N S T O E X E R C I S E S

Exercise 7 Turnover Ratio = 5/61.5 x 100% = 8.13% Average staff = (52 + 71)/2 = 61.5 Efficiency Ratio = 9,800/9,000 x 100% = 108.89% Capacity Ratio = 9,000/10,000 x 100% = 90% Production Volume = 108.89% x 90% = 98%

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CHAPTER 5 Exercise 1 Solution – method of working (a): From the question we can see that the costs for indirect wages and materials have been allocated directly to the cost centres. This is because we can identify these costs directly to the cost centres concerned. The remainder of the costs must be shared over the cost centres in relation to the amount of usage of the cost. This can be established by looking at the additional information and deciding which piece of information relates to which cost. For example the power costs would be determined by the number of hours the machines had been working and the light and heat by the overall area of the building. To apportion costs we need to take the total of the overhead cost and divide it by the total of the basis used. The resulting figure can then be multiplied by the individual usage of the cost. Power (for machining dept)

£102,000 × 40,000 51,000 m/c hours

This process can then be repeated for each cost and cost centre. The figures can then be inserted into the table above and the columns totalled.

Costs

Basis

Machining

Assembly

Finishing

Maint

Total

Indirect wages Indirect materials

allocated

10.000

6.000

8.000

30.000

54.000

15.000

4.000

8.000

20.000

47.000

Power

allocated machine hours

80.000

10.000

12.000

Light & Heat

floor area

5.000

2.000

1.500

1.500

Depreciation

NBV

4.000

1.600

0.600

0.800

7.000

Rent & Rates

floor area

12.500

5.000

3.750

3.750

25.000

Personnel

employees

18.000

12.000

24.000

9.000

63.000

144.500

40.600

57.850

65.050

308.000

170

102.000 10.000

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S O L U T IO N S T O E X E R C I S E S

Exercise 2 Machine

Assembly

Finishing

Indirect materials

4000.00

Indirect wages

8000.00

Indirect expenses

Prod control

Handling

Total

11200.00

41920.00

12960.00

7920.00

8000.00

2400.00

41920.00

12960.00

7920.00

20000.00

Prod cont

5440.00

4080.00

2720.00

Handling

12816.00 60176.00

6408.00 23448.00

2136.00 12776.00

1360.00 21360.00 0.00

13600.00 13600.00

0.00

96400.00 0.00 0.00 96400.00

Exercise 3 (repeated distribution method) A

B

C

P

Q

Total costs

3000.00

4000.00

2000.00

2700.00

P costs * %

500.00

750.00

625.00

2500.00 2500.00

Q costs * %

831.25

831.25

997.50

665.00

-3325.00

P costs * %

133.00

199.50

166.25

-665.00

166.25

Q costs * %

41.56

41.56

49.88

33.25

-166.25

0.00

625.00 3325.00

P costs * %

6.65

9.98

8.31

-33.25

8.31

Q costs * %

2.08

2.08

2.49

1.66

-8.31

P costs * %

0.5 4515.04

-1.66 0.00

0.00

0.66 5835.03

0.5 3849.93

(algebraic method) P = 2500 + 20%Q Q = 2700 + 25%P Substituting Q into the first equation: P = 2500 + 20%(2700 + 25%P) P = 2500 + 540 + 5%P 0.95P = 3040 P = 3200 Q = 2700 + 25%(3200) Q = 3500 A

B

C

P

Q

Total costs

3000.00

4000.00

2000.00

2700.00

P costs * %

640.00

960.00

800.00

2500.00 3200.00

Q costs * %

875.00 4515.00

875.00 5835.00

1050.00 3850.00

700.00 0.00

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800.00 3500.00 0.00

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Exercise 4 Absorption rate per unit = £100,000/20,000 = £5 per unit Production cost = £20 + £5 = £25 Absorption rate per labour hour = £100,000/50,000 hours = £2 per lab hr Production cost = £20 + (2 x £2) = £24 Absorption rate per machine hour = £100,000/100,000 hours = £1 per mc hr Production cost = £20 + (3 x £1) = £23

Exercise 5 This question has two pitfalls. Firstly, the actual data for the cost centres are irrelevant as absorption rates are always calculated using budgeted data. Secondly, the question does not give guidance over whether labour or machine hours should be used to calculate rates. This is straightforward to solve. For each department use the higher of labour or machine hours.

Cutting: Use machine hours as budgeted machine hours higher than budgeted labour hours Finishing: Use labour hours as budgeted labour hours higher than budgeted machine hours. Absorption rates are calculated as: Budgeted Overhead / Budgeted Activity

Cutting: £100,000 / 50,000 = £2 per machine hour Finishing: £50,000 / 12,500 = £4 per labour hour

Product Costing

172

Cutting 6 x £2 = £12

Finishing 4 x £4 = £16

Total £28

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Exercise 6 The total budgeted fixed overhead cost for P2 will be the sum of: Fixed overhead cost per unit in Dept X + Fixed overhead cost per unit in Dept Y To calculate this, we first need to calculate the overhead absorption rate in each department The OAR for each department will be equal to: Budgeted overhead/budgeted activity Department X: Budgeted labour hours: Product

Labour hours per unit

Number of units

Total labour hours

P1

3

8,000

24,000

P2

2.5

8,000

20,000 44,000

OAR for Department X = $88,000 / 44,000 = $2/labour hour Department Y: Budgeted labour hours: Product

Labour hours per unit

Number of units

Total labour hours

P1

1

8,000

8,000

P2

2

8,000

16,000 24,000

OAR for Department X = $96,000 / 24,000 = $4/labour hour Total budgeted overhead for product P2 = 2.5 hrs x $2 + 2 hrs x $4 = $13/unit

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Exercise 7 Overhead absorption rates are calculated using budgeted figures. Further, machine hours should be used as this is the higher of the two measures of activity. Absorption rates are calculated as: Budgeted Overhead / Budgeted Activity £200,000 / 100,000 = £2 per unit

£ Absorbed overhead (actual activity x OAR) (80,000 x £2)

160,000

Actual Overhead

208,000

Under absorption:

174

48,000

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CHAPTER 6 Exercise 1 Stock Control Balance b/d Purchases Purchases

£5,000 £40,000 £20,000

WIP Production o/h Balance c/f

£65,000

£25,000 £20,000 £20,000 £65,000

Labour Control Wages paid

£45,000

WIP Production o/h

£45,000

£30,000 £15,000

£45,000

WIP

Direct materials Direct wages Production o/h

£25,000 £30,000 £78,000 £133,000

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Finished Goods

£133,000

£133,000

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Production Overhead Control Indirect materials Indirect wages Other expenses

£20,000 £15,000 £45,000

WIP Under absorption

£80,000

£78,000 £2,000

£80,000

Income Statement Expense Under absorption Production o/h

£2,000

Exercise 2 Stock Control Balance b/d Purchases Purchases

£1,500 £15,000 £7,500

WIP Production o/h Purchase returns Balance c/f

£11,000 £4,300 £2,000 £6,700

£24,000 £24,000

Labour Control Wages paid

£54,000

£54,000

176

WIP Production o/h

£32,000 £22,000

£54,000

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S O L U T IO N S T O E X E R C I S E S

WIP

Direct materials Direct wages Production o/h

£11,000 £32,000 £52,500

Finished Goods

£95,500

£95,500

£95,500

Production Overhead Control

Indirect materials Indirect wages Indirect expenses Over absorption

£4,300 £22,000 £21,000 £5,200

WIP

£52,500

£52,500

£52,500

Income Statement Expense

Over absorption Production o/h

£5,200

£5,200

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CHAPTER 7 Exercise 1 The contribution per unit = Selling price – variable cost. 20 – (6 + 3 + 4) = 7 Total contribution = 7 x 20,000 units = £140,000 Total profit = total contribution – total fixed costs £140,000 - £20,000 = £120,000 To calculate the profit using absorption costing, we first need to calculate the OAR. This is equal to £20,000 / 20,000 units = £1 per unit This means that the full production cost per unit is variable cost + fixed cost = 13 + 1 = 14 Total sales = Total production cost = Total profit =

20,000 x £20 = 20,000 x £14 =

£400,000 £280,000 £120,000

Exercise 2 Absorption costing: £

£

Sales (4,800 x £10)

48,000

Production cost (4,800 x £8)

38,400 9,600

Under absorption

400 9,200

OAR = £10,000/5,000 = £2 per unit Total production cost = 3 + 2 + 1+ 2 = £8 Absorbed = 4,800 x £2 Actual overhead cost Under absorption

9,600 10,000 400

Marginal costing: £ Sales (4,800 x £10) Production cost (4,800 x £6)

£ 48,000 28,800 19,200

Less fixed costs

178

10,000 9,200

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Exercise 3 Absorption costing: £ Sales (4,800 x £10) Production cost (6,000 x £8) Closing stock (1,200 x £8)

£ 48,000

48,000 9,600 38,400 9,600

Over absorption

2,000 11,600

Absorbed = 6,000 x £2

12,000

Actual overhead cost Over absorption

10,000 2,000

Marginal costing: £ Sales (4,800 x £10) Production cost (6,000 x £6) Closing stock (1,200 x £6)

£ 48,000

36,000 7,200 28,800 19,200

Fixed costs

10,000 9,200

Reconciliation: Difference in profits = £2,400 Change in stocks x OAR = 1,200 x £2 = £2,400.

Exercise 4 Closing inventory = 500 + 10,500 – 10,750 = 250 Inventory has decreased by 500 – 250 = 250units. As inventory has decreased, absorption costing profit will be less than marginal costing profit. Fixed cost per unit = £30,000 / 10,000 = £3 Absorption costing profit = £75,000 – 250 x £3 = £74,250

Exercise 5 OAR = £250,000/1,000 = £250 per unit Stock decreased by 150 units Profit for absorption costing will be lower by 150 x £250 = £37,500.

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CHAPTER 8 Exercise 1 Job 666 £

£

Materials *1

Grade A Steel

2,000

Grade B Steel

4,440

Wages *2 Wages Welding

1,280

Wages Finishing

1,000

Total Direct Cost Overheads *3

8,720 1,560

Total Cost

10,280

Profit

4,112

Selling Price *

1

14,392

Direct Material Costs

Steel Grade A (400m x £5.00) Steel Grade B (740m x £6.00)

£ 2,000 4,440

Note materials returned to store are not included in the cost of the job. *

2

Direct Labour Cost

Welding Department (320hrs x £4.00) Finishing Department (200hrs x £5.00)

£ 1,280 1,000 2,280

The question implies overtime is worked because the factory is generally busy. The overtime premium should not be charged to the customer and should, therefore, be charged to production overheads.

180

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S O L U T IO N S T O E X E R C I S E S *

3

Absorbed overheads £ 1,560

Absorbed overhead (520 x £3.00)

Price £10,280 x 1.40 = £14,392.

Exercise 2 Job 123

£ Materials*1 Material Y

204

Material Z

384.25

Wages* Dept A

2

Dept B

342 440

Total Direct Cost Overheads*3

1,368.25 452.70

Total Cost

*1

£

1820.95

Direct Material Costs £ 204 384.25

Material Y (400kg x £0.51) Material Z (265kg x £1.45)

Note materials returned to store are not included in the cost of the job.

*2

Direct Labour Cost £ 342 440

Dept A (76hrs x £4.50) Dept B (110hrs x £4.00)

The question implies overtime in Dept A is worked because the factory is generally busy. The overtime premium should not be charged to the customer and should, therefore, be charged to production overheads. In Dept B the overtime is worked at the request of a customer but not this one, so it will be charged to the other job. This overtime premium is not a production overhead.

*3

Absorbed overheads

Total overheads for the period Total hours OAR

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Dept A £ 5,400 2,000 £2.70 /hr

Dept B £ 6,300 2,800 £2.25 /hr

(ex premium)

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Exercise 3 Job 6832

Opening Balance Materials Control Labour (£8 x 430) Overhead (£2 x 430)

£ 1,830 2,390 3,440 860 8,520

Material returns Job 6833 Finished Goods (bal)

£ 870 620 7,030 8,520

Job 6833

Materials Control Labour (£8 x 650) Overhead (£2 x 650) Job 6834 Job 6832

£ 1,680 5,200 1,300 250 620 9,050

Finished Goods

£ 9,050

9,050

Job 6834

Materials control Labour (£8 x 280) Overheads (£2 X 280)

£ 3,950 2,240 560 6,750

Job 6833 Closing WIP

£ 250 6,500 6,750

Exercise 4 Total cost for the batch: Direct materials Direct labour Production o/h Total production cost Non Production cost Total cost

£230 £180 £288 £698 £209.4 £907.4

Cost per unit = 907.4 / 5 = £181.48 Production o/h: Labour hours for the batch = £180/£7.50 = 24 hours Production o/h cost = 24 hours x £12 = £288

182

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S O L U T IO N S T O E X E R C I S E S

Exercise 5

£ Using a mark up on marginal cost of sales of 80%, what is the price?

59.40

Marginal cost = £22 +£5 + £6 = £33 Mark up £33 x 1.8 = £59.40 What is the resulting profit?

19.40

(£59.40 - £40 = £19.40) Using a margin of 80% on total production cost what is the price?

155

Total production cost = £31 Price: £31 / 20 x 100 What is the resulting profit?

115

(£155 - £40)

Exercise 6 Service cost unit = Client hour Total service units provided in the period = 40 hours x 48 weeks x 95% = 1824 Cost per service unit = £35,000/1824 = £19.19 Charge per hour = £19.19 + 30% x £19.19 = £24.95

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Exercise 7

Loading costs

Labour (30 x 1 x 2)

1

Variable

Fixed

£

£

60

Depreciation

80

Supervision Other costs

80

Wages (£100 x 2) Petrol (10p x 730 x 2)

200 2

Repairs (5p x 730 x 2)

146 73

Depreciation (£80 x 2)

160

Supervision

120

General expenses

200 279

1

Total number of tonnes loaded = 30

2

Please note we have to make a trip back as well Tonnes

840

Kms

Total

5

100

500

8

20

160

2

60

120

4

50

200

6

200

1200

5

300

1500 3,680

Cost per tonne km =

1,119 3680

184

=

£ 0.30

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CHAPTER 9 Exercise 1 PROCESS 1 (CUTTING) Units Direct Materials 1,000,000 Direct Labour Production overheads 1,000,000

£ 500,000 200,000 200,000 900,000

Output to P2:

Units 1,000,000

£ 900,000

1,000,000

900,000

Units 1,500,000

£ 1,500,000

1,500,000

1,500,000

PROCESS 2 (FORMING) Units Materials from P1 1,000,000 Added materials 500,000 Direct Labour Production overheads 1,500,000

£ 900,000 300,000 150,000 150,000 1,500,000

Output to Finished Goods

Exercise 2 Process a/c Units Materials

160

Lab & ohds 160

Cost per tonne of good output =

£

Units

£

3,680

N. loss

8

40

3,200

Output

152

6,840

160

6,880

Units

£

8

40

6,880

6,880 − 40 = £45 160 − 8

Value of output = 152 x £45 = £6,840

Normal loss a/c (scrap sales) Units Process a/c

8

£ 40 40

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Bank/cash

40

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S O L U T IO N S T O E X E R C I S E S

Exercise 3 Process a/c Units Materials

£

160

Lab & ohds 160

Units

£

3,680

N. loss

8

40

3,200

Output

150

Ab loss

2

6,880

6,750 90

160

6,880

Normal loss a/c (scrap sales) Units

£

Process a/c

8

40

Ab loss a/c

2

10

Bank/cash

Units

£

10

50

50

50

Abnormal loss/gain a/c Units Process a/c

£

2

90

Scrap sales

Units

£

2

10

P&L a/c

80

90

90

Exercise 4 Process a/c Materials

Units

£

160

3,680

N. loss

8

40

3,200

Output

156

7,020

164

7,060

Lab & ohds Ab gain

4

180

164

7,060

Units

£

Normal loss a/c (scrap sales) Process a/c

Units

£

8

40 40

186

Units

£

Bank/cash

4

20

Ab gain

4

20 40

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S O L U T IO N S T O E X E R C I S E S

Abnormal loss/gain a/c Units Scrap sales

4

P&L a/c

£ 20

Units

£

4

180

160 180

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Process a/c

180

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S O L U T IO N S T O E X E R C I S E S

Exercise 5 Process 1 a/c Units

£

2,000

8,100

N. loss

200

Labour

4,000

Process 2

1,750

P Ohds

6,000

Ab loss

50

Materials

2,000

Units

18,100

2,000

£ 100 17,500 500 18,100

Cost of good output = (8,100 – 100) / (,000 – 200) = £10

Process 2 a/c Units

£

Process 1

1,750

17,500

N. loss

300

900

Materials

1,250

1,900

Output

2,800

42,000

3,100

42,900

Labour

10,000

P Ohds

12,000

Ab gain

100 3,100

Units

£

1,500 42,900

Cost of good output = (41,400 – 900) / (3,000 – 300) = £15.

Normal loss a/c (scrap sales) Units

£

Units

£

Process 1

200

100

Bank/cash

4

725

Process 2

300

900

Ab gain

100

300

50

25

550

1,025

104

1,025

Ab loss

Abnormal loss/gain a/c Units Process 1 Scrap sales

50 100

P&L a/c

Units

£

500

Scrap sales

50

25

300

Process 2

100

1,500

150

1,525

725 150

188

£

1,525

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S O L U T IO N S T O E X E R C I S E S

Exercise 6 Units

% completion

Equivalent units

1,000

100%

1,000

50%

100 1,100

200

Cost per equivalent unit = £5,500 / 1,100 = £5.

Exercise 7 Getting the right answer here is a three-stage process:

1.

Calculating the number of equivalent units.

2.

Calculating the cost the cost per equivalent unit.

3.

Combining the above to value each output from the process.

1.

Statement of Equivalent units

Output Finished goods Closing WIP

2.

Physical Units 4,000 1,000

Equivalent units 4,000 (100% complete) 600 (60% complete)

Statement of Unit Cost

ie, 9,440/4,600 = £6.40.

3.

Statement of Evaluation:

Finished goods: Closing WIP:

4,000 equivalent units x £6.40 =£25,600 600 equivalent units x £6.40 = £3,840

Process a/c Units

£

5,000

16,560

Labour

7,360

P Ohds

5,520

Materials

5,000

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29,440

Units

£

Output

4,000

25,600

Closing WIP

1,000

3,840

5,000

29,440

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Exercise 8 Process a/c Units

£

2,800

24,800

Output (1)

Labour

16,750

Closing WIP (2)

P Ohds

36,200

Materials

Units

£

2,100

64,575

700

13,185

2,800

-10 77,750

(rounding error) 2,800

77,750

Statement of Equivalent units Output WIP

Cost Cost/Eq unit

Units

%

Materials

Labour

Overheads

2100

100%

2100

2100

2100

700

80%

700

60%

700

50%

560 420 350 2660

2520

2450

£24,800 £9.32

£16,750 £6.65

£36,200 £14.78

Statement of Valuation 1.

Output = 2100 x (9.32 + 6.65 + 14.78) = £64,575

2.

WIP = (560 x 9.32) + (420 x 6.65) + (350 x 14.78) = £13,185.

190

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S O L U T IO N S T O E X E R C I S E S

Exercise 9 Statement of Equivalent units Conversion Units % Materials Costs Output

8000

100%

8000

WIP

2000

100%

2000

60%

1200 10,000

Cost Cost/Eq unit

8000

£40,600 £4.06

9,200 £18,400 £2.00

Value of units completed: 8,000 x £4.06 + 8,000 x £2.00 = £48,480

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Exercise 10 Statement of Equivalent units Equivalent Units % Units OWIP Goods Started & finished

100

40%

800

100%

CWIP

150

48%

40 800 72 912

Cost Cost/Eq unit

£10,944 £12

CWIP valuation: 72 x £12 = £864 Units completed: Goods started & finished: 800 x £12

£9,600

OWIP completed: 40 x £12

£480

OWIP value from prior period:

£680

Total value of goods completed:

£10,760

192

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S O L U T IO N S T O E X E R C I S E S

Exercise 11 Process a/c Op WIP Added units

Units

£

500

3,000

1,000

10,500

1,500

13,500

Closing WIP Finished units

W Ave

FIFO

Units

£

£

300

1,500

1,500

1,200

12,000

12,000

1,500

13,500

13,500

Statement of Equivalent units (W Average) Output WIP

Units

%

1,200

100%

300

50%

Costs 1,200 150 1,350

Cost

10,500 3,000

Cost/Eq unit

£13,500 £10.00

Valuation: WIP = 150 x £10 = £1,500 Finished units = 1,200 x £10 = £12,000.

Statement of Equivalent units (FIFO) Output - Op WIP

Units

%

1,200

100%

500

60%

Costs 1,200 300 900

+ WIP

300

50%

150 1,050

Cost

£10,500

Cost/Eq unit

£10.00

Valuation: WIP = 150 x £10 = £1,500 Finished units = 900 x £10 = + Op WIP b/f Total

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£9,000 £3,000 £12,000

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Exercise 12 Product

Quantity

S Price

Sales Value

X

100,000

£1

£100,000

Y

20,000

£10

£200,000

Z

80,000 200,000

£2

£180,000 £480,000

Physical units method –

£240,000 200,000

£240,000 480,000

Sales value method –

x

x

100,000

=

£120,000

20,000 80,000

= =

£24,000 £96,000

100,000

=

£50,000

200,000 180,000

= =

£100,000 £90,000

Exercise 13 The sales value of the by-product is deducted from joint costs. The remaining joint cost balance is then apportioned across the joint products. Joint costs = £16,500 – 100 x £5 = £16,000

Product

Quantity

S Price

Sales Value

A

200

£20

£4,000

B

300

£14

£4,200

C

500

£18

£9,000

1,000

Physical units method –

Sales value method –

194

£17,200

£16,000 1,000

£16,000 17,200

x

x

200

=

£3,200

300 500

= =

£4,800 £8,000

4,000

=

£3,721

4,200 9,000

= =

£3,907 £8,372

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Exercise 14 Option 1 – sell 100,000 units of A @ £1.25 = £125,000 Option 2 – sell 60,000 units of A+ @ £3.25 = £195,000. Increase in revenue of £70,000. Extra costs are (100,000 x £0.30) + £20,000 = £50,000. Therefore net gain of £70,000 - £50,000 = £20,000.

Exercise 15 Option 1 – sell 9,000 litres of K @ £10 = £90,000 Option 2 – sell (9,000 x 90%) litres of KK @ £12 = £97,200. Increase of £7,200. Extra costs are 9,000 x £1 = £9,000. Therefore loss of revenue (and therefore profits) of £1,800.

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CHAPTER 10 Exercise 1 Sales Volume Unit price Total Value

Collerette 2,000 £100 £200,000

Pompom 4,000 £130 £520,000

Cacti 3,000 £150 £450,000

Total

£1,170,000

Exercise 2 Production budgets can only be completed once sales budgets are known. Note too, how opening and closing stocks of finished goods have to be taken into account. Opening stocks are a subtraction from the production total and closing stocks an addition.

Sales Units Closing stock Less Opening Stock Production Units

Collerette 2,000 600 2,600 (500) 2,100

Pompom 4,000 1,000 5,000 (800)

Cacti 3,000 800 3,800 (700)

4,200

3,100

Exercise 3 Collerette Pompom Cacti Usage (kgs)

Production Units 2,100 4,200 3,100

M1 (kg) 10,500 12,600 6,200 29,300

M2 (kg) 4,200 8,400 3,100 15,700

M3 (kg) 8,400 9,300 17,700

When constructing the materials purchase budget, opening and closing stocks of material should be taken into account.

Materials Purchase Budget

Budgeted usage Closing stocks Opening stocks Budgeted purchases Unit cost Total

196

M1 kg

M2 kg

M3 kg

29,300 18,000 47,300 21,000 26,300

15,700 9,000 24,700 10,000 14,700

17,700 12,000 29,700 16,000 13,700

£5 £131,500

£3 £44,100

£4 £54,800

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Exercise 4 Labour budgets are relatively straightforward to construct. Multiply production figures by unit hours to get total hours consumed for each product. This can then be multiplied by hourly rates to get cost.

Production Units Hours per unit Total hours Hourly rate Cost

Collerette 2,100 4 8,400 hrs £8.50 £71,400

Pompom 4,200 6 25,200 £8.50 £214,200

Cacti 3,100 8 24,800 £8.50 £210,800

Exercise 5 A Budgeted sales

B

3,000

4,000

750

1,000

3,750

5,000

- Opening stock

800

950

Production units

2,950

4,050

Closing stock (1)

Labour hours (2) Total hours

1.6 4,720

9,720

£8

£8

£37,760

£77,760

Rate per hour Labour cost

2.4

(1)

– closing stock = (sales / 12) x 3

(2)

– Labour hours = original time x 80%

Exercise 6 Q Budgeted sales Closing stock

700 70 770

- Opening stock Required units Scrap Production units

50 720

= 90%

80

= 10%

800

Labour hours

= 100%

3.0

Total hours

2,400

= 80%

Paid hours

3,000

= 100%

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Exercise 7 Sales and variable costs are scaled up according to the difference in activity level. Examples: Sales: 4,000 / 3,000 x £90,000 = £120,000 Direct materials: 4,000 / 3,000 x £30,000 = £40,000 Fixed costs are simply copied across the budget as these items are not related to activity.

Sales Less Direct Materials Direct Labour Fixed Production overheads Gross Profit Less Variable Selling cost Fixed selling cost Profit

198

Original Budget 3,000 units £ 90,000

Flexed Budget 4,000 units £ 120,000

Actual

Variances

4,000 units £ 110,000

£ 10,000 (A)

30,000 15,000 2,500

40,000 20,000 2,500

45,000 20,000 2,300

42,500

57,500

42,700

3,000 1,500 38,000

4,000 1,500 52,000

4,000 2,000 36,700

5,000 (A) 0 200 (F)

0 500 (A) 15,300 (A)

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CHAPTER 11 Exercise 1 Standard cost card £ Materials

2kg x £30/kg

60

Labour

6hrs x £10/hr

60

Overheads

6hrs x £15/hr

90

Fixed Overheads

£20,000/500

40

Standard Cost

250

Standard Profit

100

Standard Price

350

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CHAPTER 12 Exercise 1 The first step is to calculate unit contribution: Contribution per unit: £90,000 / 10,000 = £9 Breakeven sales volume can be calculated as:

Fixed Costs Unit Contribution

= £45,000 / £9 = 5000 units Breakeven sales revenue = Breakeven units x Selling Price = 5000units x £15 = £75,000

Exercise 2 The first step is to calculate unit contribution: ie

£9 - £4 = £5.

Breakeven sales volume can be calculated as: ie

£35,000 = 7,000 units . £5

Target sales volume can be calculated as: ie

Fixed Costs Unit Contribution

Fixed Costs + Target Profit Unit Contribution

£35,000 + £15,000 = 10,000 units . £9 − £4 Units

Sell to breakeven?

Sell to reach its target profit?

200

7,000

10,000

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Exercise 3 Step 1: Calculate unit contribution: Unit sales price – unit variable cost: £7 - £4 = £3

Step 2: Calculate breakeven sales: Fixed cost / unit contribution = breakeven sales volume £342,000 / £3.00 = 114,000 units

Step 3: Calculate margin of safety: (Budgeted sales – breakeven sales / budgeted sales) x 100) 150,000 – (114,000 / 150,000) x 100% = 24% The margin of safety is 14.3%. This means that sales can fall 14.3% below budget before a loss is made.

Quick exercises 1.

500 / (3 – 1) = 250

2.

(550 + 200) / 2 = 375

3.

250 = 750 / cont/unit

cont/unit = 3

therefore s. price = 3 + 1 = 4

4.

BEP = 200,000 / (8 – 4) = 50,000 Margin of safety = (80,000 – 50,000) / 80,000 = 37.5%

Exercise 4 Unit contribution is (unit sales price – unit variable cost): £15 - £6 = £9 C/S Ratio (unit contribution / unit sales):

£9 / £15 = 0.6 or 60%

Breakeven revenue: Fixed costs / C/S Ratio = £192,000 / 0.6 = £320,000 Margin of safety: (Budgeted sales – breakeven sales / budgeted sales) x 100) Budgeted sales: 62,000 x £15 = £930,000 (£930,000 - £320,000 / £930,000) x 100 = 65.6%

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Exercise 5 (a)

Unit contribution = £40 - £25 = £15 Breakeven point: Fixed costs / Contribution = £240,000 / 15 = 16,000 Margin of safety = Budgeted sales – breakeven sales = 25,000 – 16,000 = 9,000 pairs

(b)

20,000 x £15 = £300,000 - £240,000 = £60,000

(c)

Unit contribution = £40 – (£25 + 2) = £13 Required = (£240,000 + £10,000) / 13 = 19,231

(d)

Unit contribution = (£40 + £4.80) – £25 = £19.8 Breakeven point: = (£240,000 + £20,000)/ 19.8 = 13,132

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CHAPTER 13 Exercise 1 Speedwell 1,000 units £ 50 10 40 4 £10 3rd

Demand Unit price Variable cost Unit contribution Labour hours Contribution per hr Priority Number of products made

0

Hours used

0

Nettle 1,000 units £ 70 50 20 1 £20 1st

Liatris 1,000 units £ 50 25 25 2 £12.50 2nd

1,000

400

(1,000 x 1hr) 1,000 hours

(400 x 2) 800 hours

Production Schedule Product

Units

Hrs/unit

Total hrs

Balance

Nettle

1,000

1

1,000

800

Liatris

*400

2

800

-

1,800

* Balancing figure

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Exercise 2 Machine hours required

Product

Demand 4,000

A

Hrs/unit 10

Total hours 40,000

B

6,000

12

72,000

C

6,000

14

84,000 196,000

Labour hours required

Product

Hrs/unit(1) 12

Demand 4,000

A

Total hours 48,000

B

6,000

8

48,000

C

6,000

4

24,000 120,000

As we have 200,000 machine hours available we have spare capacity. hours are limited to 50,000 – which means we are short by 70,000 hours.

Labour

Labour hours is our limiting factor. (1)

Product A = £9 paid at £0.75 / hr = 12 hours.

A

B

C

£

£

£

S Price

25

20

15

Variable cost

19

15

11

6

5

4

12

8

4

£0.50

0.625

£1

3

2

1

Cont / unit Labour hours

(1)

Cont / lab hr Ranking

Production Schedule Product

Units

Hrs/unit

Total hrs

Balance 50,000

A

1,000

12

12,000

38,000

C

6,000

4

24,000

14,000

B

*1,750

8

14,000

-

* Balancing figure

Contribution Schedule Product

Units

Cont / unit

Total cont

A

1,000

6

6,000

C

6,000

4

24,000

B

1,750

5

8,750 38,750

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Exercise 3

S Price

A

B

C

D

£

£

£

£

100

110

120

120

Variable cost

54

55

59

66

Cont / unit

46

55

61

54

Labour hours(1)

3

2.5

4

4.5

Cont / lab hr

£15.33

£22.00

£15.25

£12.00

Ranking

2

1

3

4

(1)

Product A = £18 paid at £6 / hr = 3 hours. Product

Units

Hrs/unit

Total hrs

Balance 1,345

A, B, C, D

20

14

280

1,065

B

130

2.5

325

740

A

180

3

540

200

C

*50

4

200

-

* Balancing figure

Profit statement: Product A

Units 200

Cont / unit 46

Total cont 9,200

B

150

55

8,250

C

70

61

4,270

D

20

54

1,080 22,800

Less Fixed cost

(2)

Profit (2)

12,800 10,000

Fixed overhead absorbed on basis of labour hours. Product A fixed overhead = £24, labour hours = 3, OAR = £8/lab hr. Budgeted fixed overheads = 1,600 hours x £8 = £12,800.

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Exercise 5 Let the number of product X = x and the number of product Y = y. Contribution per unit of X: £60 - £15 - £24 - £6 = £15 Contribution per unit of Y: £25 - £5 - £3 - £5 = £12 The objective is to maximise total contribution: Maximise 15x + 12y Constraint 1: Only 4,200kg of material is available

Material usage (per unit)

X

Y

3kg

1kg

Therefore, 3x + 1y ≤ 4,200 Constraint 2: Only 3,000 labour hours are available: X Labour usage (per unit)

Y

4hrs 0.5hrs

Therefore, 4x + 0.5y ≤ 3,000 Represented graphically:

7000 6000 5000 A 4000 No of Units of Y

B

3000

Feasible region

2000 1000 0 0

500

C

1000

1500

Number of Units of X The optimal production plan will be at one of the corner of the feasible region (points A, B and C): Point A is where the line 3x + y = 4,200 crosses the Y axis and so x = 0. If x = 0, then 3(0) + y = 4,200, so y = 4,200units Total contribution at point A: 15(0) + 12(4,200) = £50,400 Point B is there the lines 3x + y = 4,200 and 4x + 0.5y = 3,000 intersect. This point can be calculated using simultaneous equations: 3x + y = 4,200, so y = 4,200 – 3x 4x + 0.5y = 3,000

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Substituting the first equation for y gives: 4x + 0.5(4,200 – 3x) = 3,000 4x + 2,100 – 1.5x = 3,000 2.5x = 900 X = 360 units So y = 4,200 – 3(360) = 3,120 units Total contribution at point B: 15(360) + 12(3,120) = £42,840 Point C is there the line 4x + 0.5y = 3000 meets the X axis, so y = 0. If y = 0, then 4x + 0.5(0) = 3,000, so x = 750units Total contribution at point C: 15(750) + 12(0) = £11,250

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Exercise 7 A company has 600kgs of material in stock that cost £50/kg three years ago. To replace the material would cost the company £60/kg. Relevant Cost £ At present the company does not have a use for the materials. If it receives a one-off order that can use the material, what is the relevant cost per kg?

Nil

Reasoning. The company has no use for the material and the price paid for the material in stock is a sunk cost. At present the company does not have a use for the materials. However, it can sell the materials at £5/kg to a local scrap merchant. If it receives a one-off order that can use the material, what is the relevant cost per kg?

£5

Reasoning. The company has no use for the material. However, it could sell the material for scrap. This is the opportunity cost of accepting the one-off order. The company currently uses the materials in all of its products. It can sell the materials for £5 per kg to a local scrap merchant. If the company uses a kg of the materials in a product, what is the relevant cost?

£60

Reasoning. The company uses the materials in all products. Any materials used would have to be replaced so replacement cost is the relevant cost.

Exercise 8 Option 1: the hours could be worked as overtime Relevant cost = 500 x $9 x 1.5 = $6,750 Option 2: labour hours could be diverted from Product P Relevant cost = 500 x $9 + 500 x $8 = $8,500 The relevant cost is the lower of the 2 options, so $6,750.

Exercise 9 The £70,000 is a sunk cost. The £15,000 current sales value is relevant as it is an opportunity cost. The £5,000 is a relevant cost as it is a cost the company will incur in the future as a result of using the machine for the project. Total relevant cost = £5,000 + £15,000 = £20,000.

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