Kommentare zur 1. und 2. Auflage: „Als Professorin einer privaten Universität ist für mich außer den Inhalten gerade auch...
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Kommentare zur 1. und 2. Auflage: „Als Professorin einer privaten Universität ist für mich außer den Inhalten gerade auch die Didaktik der von mir verwendeten Lehrbücher wichtig. Der „Grundkurs Buchführung“ stellt dank seiner verständlichen Sprache, den zahlreichen Beispielen, Übungen und Online-Aufgaben eine ernsthafte Konkurrenz zu den etablierten Standardwerken dar.“ Prof. Dr. Luise Hölscher, Frankfurt School of Finance & Management
„Herr Auer schafft mit seinem Buch einen ebenso einfachen wie dennoch umfassenden Zugang zur Buchführung. Sein didaktischer Ansatz, seine klare Sprache und die Konzentration auf das Wesentliche vermitteln den Studierenden das für das Studium notwendige Grundwissen.“ Prof. Dr. Reiner Anselstetter, FH Amberg-Weiden
„Logisch aufgebaut und gespickt mit Beispielen enträtselt sich manche komplizierte Struktur. Pluspunkt ist ein ausführlicher Übungsteil, der fast ein Drittel des Seitenumfangs ausmacht.“ Wirtschaft – IHK Osnabrück-Emsland
Geleitwort der Herausgeberin Jede Einführung in die Wirtschaftswissenschaften, ob in der Schule, Berufs- oder Hochschule, beginnt mit einem Grundkurs in Buchführung. Leider beginnt sie dadurch auch oft mit Langeweile. Und intelligente Menschen mit Buchführung zu langweilen, ist nicht nur didaktisch ungeschickt, sondern auch Verschwendung von Zeit und Ressourcen. Allerdings ist die Doppik kein Inhalt, der auf Spaß ausgerichtet ist – das zeigt ein Blick in die Geschichte: Erste Dokumentationen einer doppelten Buchführung stammen aus dem 15. Jahrhundert, und das erste bekannte Lehrbuch datiert auf das Jahr 1592. Gut 200 Jahre später wurde die Bilanzierungspflicht in Preußen eingeführt, und ihre Vernachlässigung wurde 1884 deutschlandweit unter Strafe gestellt. Heute umfasst der Markt für Buchführungsbücher im Allgemeinen wie im Speziellen allein im deutschsprachigen Sektor über 250 Titel. Warum nun also noch ein Buch, warum gerade dieses Buch zur Buchführung? Als Herausgeberin der zweiten Auflage freue ich mich, mit dem „Grundkurs Buchführung“ von Benjamin Auer ein Lehrbuch zu betreuen, das in seinem Ansatz darauf ausgerichtet ist, „diesem Fach den Schrecken zu nehmen“ (so das Vorwort zur ersten Auflage). Es gelingt ihm mittels verständlicher Sprache, übersichtlicher Vorgehensweise, unterstützenden Grafiken, vielen Beispielen und Übungsaufgaben und nicht zuletzt der Hinterlegung mit Online-Aufgaben, den Leser in das Thema mitzunehmen und es ihm „learning by doing“ nahezubringen. Für den Dozenten ist es eine Erleichterung, da Textbausteine von den Lernenden vorbereitet und dann anhand von Aufgaben gemeinsam in die Praxis umgesetzt werden können. Gleichzeitig kann der engagierte Studierende sein Wissen überprüfen und durch Variationen vertiefen. Aus diesen Gründen wünsche ich dem „Grundkurs Buchführung“ eine zahlreiche Nutzer- und Leserschaft, die sich hiermit – ohne Langeweile – die Grundsätze kaufmännischer Rechnungslegung zugänglich machen kann. Luise Hölscher Frankfurt, im November 2007
Benjamin Auer
Grundkurs Buchführung Mit ergänzendem Übungsteil kostenlos im Internet Herausgegeben von Luise Hölscher 2., vollständig überarbeitete und erweiterte Auflage
Bibliografische Information Der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über abrufbar.
Verlagsseitiger Online-/Dozentenservice unter http://app.gwv-fachverlage.de/tu/99 oder autorenseitiger Online-/Dozentenservice unter www.buchhaltung-auer.de
1. Auflage April 2005 2., vollständig überarbeitete und erweiterte Auflage 2008 Alle Rechte vorbehalten © Betriebswirtschaftlicher Verlag Dr. Th. Gabler | GWV Fachverlage GmbH, Wiesbaden 2008 Lektorat: Dr. Riccardo Mosena Der Gabler Verlag ist ein Unternehmen von Springer Science+Business Media. www.gabler.de Das Werk einschließlich aller seiner Teile ist urheberrechtlich geschützt. Jede Verwertung außerhalb der engen Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung des Verlags unzulässig und strafbar. Das gilt insbesondere für Vervielfältigungen, Übersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen. Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw. in diesem Werk berechtigt auch ohne besondere Kennzeichnung nicht zu der Annahme, dass solche Namen im Sinne der Warenzeichen- und Markenschutz-Gesetzgebung als frei zu betrachten wären und daher von jedermann benutzt werden dürften. Umschlaggestaltung: Ulrike Weigel, www.CorporateDesignGroup.de Druck und buchbinderische Verarbeitung: Wilhelm & Adam, Heusenstamm Gedruckt auf säurefreiem und chlorfrei gebleichtem Papier Printed in Germany ISBN 978-3-8349-0486-7
Vorwort Vorwort zur zweiten Auflage Liebe Leserinnen und Leser, in dieser zweiten Auflage wurden die von aufmerksamen Lesern bemerkten Fehler, die sich in die erste Auflage eingeschlichen hatten, korrigiert, sowie das Layout und die Inhalte komplett überarbeitet. Nicht mehr zeitgemäße Themenbereiche (z.B. Wechsel) wurden entfernt und andere Themenbereiche im Hinblick auf Bilanzierung nach Handels- und Steuerrecht ergänzt. Der rechtliche Hintergrund von Buchungsaktivitäten ist also mehr in den Vordergrund gerückt. Außerdem wurden die Inhalte an die neue Rechtslage (z.B. neuer Umsatzsteuersatz) angepasst. Zudem sind nun im Online-Service neben den bekannten Übungsaufgaben, die ebenso aktualisiert und erweitert wurden, nützliche Excel-Tools verfügbar, die etwa bei Themen wie Abschreibung praktische Hilfestellung bieten. Der Online-Service auf www.buchhaltung-auer.de (Benutzername: Besucher, Passwort: Unterlagen) umfasst nun
ergänzende Übungsaufgaben und Lösungen,
alle im Buchtext zitierten Gesetzestexte,
einen Exkurs zum Thema Rechtsformen,
nützliche Excel-Tools zur Buchführung, T
Vertiefungen zu ausgewählten Themenbereichen, die im Buch keinen Platz mehr fanden, V
und vieles mehr.
Ich wünsche Ihnen auf diesem Wege viel Erfolg bei der Arbeit mit diesem Lehrbuch und dem Material des Online-Services. Über Anregungen zur Erweiterung oder Verbesserung des Online-Services würde ich mich sehr freuen. Außerdem möchte ich die Gelegenheit nutzen, meiner Herausgeberin Frau Prof. Dr. Luise Hölscher für die Mitarbeit an der 2. Auflage und den Herren Christian Wels und Tobias Müllner für ein Korrekurlesen des Materials im Online-Service besonderen Dank auszusprechen. Sie haben damit entscheidend zur Qualität dieses Lehrbuchs und seines Begleitmaterials beigetragen. Pleystein, im Oktober 2007
Benjamin Auer
VI
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dÉë~ãíòìë~ããÉåÜ~åÖ=_Éëí~åÇëJ=ìåÇ=bêÑçäÖëâçåíÉåKKKKKKKKKKKKKKKKKKKKKKKKK RU
Q=hçåíÉåê~ÜãÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RV _K=oÉÅÜíäáÅÜÉê=eáåíÉêÖêìåÇ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKSP N=oÉÅÜíëèìÉääÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SR NKN=^ääÖÉãÉáåÉë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SR NKO=dÉëÉíòäáÅÜÉ=_ÉëíáããìåÖÉå=áã=e~åÇÉäëêÉÅÜí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SS NKOKN
^ääÖÉãÉáåÖΩäíáÖÉ=sçêëÅÜêáÑíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ST
NKOKO
oÉÅÜíëÑçêãëéÉòáÑáëÅÜÉ=sçêëÅÜêáÑíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ST
NKOKP
dê∏≈Éå~ÄÜ®åÖáÖÉ=sçêëÅÜêáÑíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SU
NKOKQ
_ê~åÅÜÉå~ÄÜ®åÖáÖÉ=sçêëÅÜêáÑíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SV
NKP=dÉëÉíòäáÅÜÉ=_ÉëíáããìåÖÉå=áã=píÉìÉêêÉÅÜí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TM NKPKN
j~≈ÖÉÄäáÅÜâÉáí=ÇÉê=e~åÇÉäëÄáä~åò=ÑΩê=ÇáÉ=píÉìÉêÄáä~åò KKKKKKKKKKKKKKKKKKKKKK TM
NKPKO
rãÖÉâÉÜêíÉ=j~≈ÖÉÄäáÅÜâÉáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TN
NKPKP
aìêÅÜÄêÉÅÜìåÖ=ÇÉê=j~≈ÖÉÄäáÅÜâÉáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TN
O=_ìÅÜÑΩÜêìåÖëéÑäáÅÜíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TP OKN=_ìÅÜÑΩÜêìåÖëéÑäáÅÜí=å~ÅÜ=e~åÇÉäëêÉÅÜí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TP OKO=_ìÅÜÑΩÜêìåÖëéÑäáÅÜí=å~ÅÜ=píÉìÉêêÉÅÜíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TR P=dêìåÇë®íòÉ=çêÇåìåÖëã®≈áÖÉê=_ìÅÜÑΩÜêìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TT PKN=_ìÅÜÑΩÜêìåÖëÖêìåÇë®íòÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TU PKO=_áä~åòáÉêìåÖëÖêìåÇë®íòÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TV PKOKN
^ääÖÉãÉáåÉ=dêìåÇë®íòÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TV
PKOKO
_ÉïÉêíìåÖëÖêìåÇë®íòÉ=å~ÅÜ=¬=ORO=ed_ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UO
Q=pÅÜêáííÉ=ÇÉê=oÉÅÜåìåÖëäÉÖìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UV QKN=^ìÑëíÉääìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UV =
IX
QKO=mêΩÑìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVM QKP=cÉëíëíÉääìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVM QKQ=lÑÑÉåäÉÖìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVM R=sÉêëí∏≈É=ÖÉÖÉå=_ìÅÜÑΩÜêìåÖëéÑäáÅÜíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVP RKN=e~åÇÉäëêÉÅÜíäáÅÜÉ=p~åâíáçåÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVP RKO=píÉìÉêêÉÅÜíäáÅÜÉ=p~åâíáçåÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVQ `K=i~ìÑÉåÇÉ=_ìÅÜìåÖÉå=áå=fåÇìëíêáÉÄÉíêáÉÄÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VR N=_ÉëÅÜ~ÑÑìåÖ=îçå=tÉêâëíçÑÑÉå=ìåÇ=e~åÇÉäëï~êÉå=f KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVT NKN=mêçÇìâíáçåëÑ~âíçêÉå=ìåÇ=iÉáëíìåÖëÉêëíÉääìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVT NKO=^åÖÉÄçíëîÉêÖäÉáÅÜ=Eh~äâìä~íáçå=îçå=báåëí~åÇëéêÉáëÉåFKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVU NKP=sÉêÄìÅÜìåÖ=îçå=báåÖ~åÖëêÉÅÜåìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMM NKQ=kÉÄÉåâçëíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMO NKR=_ÉÜ~åÇäìåÖ=îçå=mêÉáëå~ÅÜä®ëëÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMR NKRKN
o~Ä~ííÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMS
NKRKO
k~ÅÜä®ëëÉ=~ìÑÖêìåÇ=îçå=j®åÖÉäêΩÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMT
NKRKP
_çåá KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMV
NKRKQ
pâçåíáKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNM
NKS=_ìÅÜìåÖ=îçå=oΩÅâëÉåÇìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNM NKT=_ìÅÜìåÖ=ÇÉê=_Éò~ÜäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNP NKU=^åò~ÜäìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNS NKV=hçåíÉå~ÄëÅÜäìëë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNV NKVKN
bêãáííäìåÖ=ìåÇ=_ìÅÜìåÖ=îçå=_Éëí~åÇëîÉê®åÇÉêìåÖÉå KKKKKKKKKKKKKKKKKKKKK NNV
NKVKO
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O=_ÉëÅÜ~ÑÑìåÖ=îçå=tÉêâëíçÑÑÉå=ìåÇ=e~åÇÉäëï~êÉå=ffKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOR P=sÉêÄìÅÜìåÖ=ïÉáíÉêÉê=mêçÇìâíáçåëÑ~âíçêÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPN PKN=_ÉíêáÉÄëãáííÉä=EjáÉíÉI=m~ÅÜíI=iÉ~ëáåÖF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPN PKO=^êÄÉáí=EiçÜåJ=ìåÇ=dÉÜ~äíë~ÄêÉÅÜåìåÖF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPP PKOKN
PKOKNKN=
píÉìÉêåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPP
PKOKNKO=
pçòá~äîÉêëáÅÜÉêìåÖëÄÉáíê®ÖÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPP
PKOKO
=
dêìåÇä~ÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPP
_ìÅÜìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPQ
PKOKOKN=
içÜåJ=ìåÇ=dÉÜ~äíëò~ÜäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPQ
PKOKOKO=
sçêëÅÜΩëëÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPS
PKOKOKP=
sÉêã∏ÖÉåëïáêâë~ãÉ=iÉáëíìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPU
PKOKOKQ=
dÉëÉíòäáÅÜÉ=råÑ~ääîÉêëáÅÜÉêìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQN
X
Q=sÉêâ~ìÑ=îçå=cÉêíáÖÉêòÉìÖåáëëÉå=ìåÇ=e~åÇÉäëï~êÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQP QKN=h~äâìä~íáçå=îçå=sÉêâ~ìÑëéêÉáëÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQP QKO=^ìëÖ~åÖëêÉÅÜåìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQR QKP=sÉêë~åÇâçëíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQS QKQ=k~ÅÜä®ëëÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQU QKQKN
pçÑçêíê~Ä~ííÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQU
QKQKO
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RKNKO
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dÉêáåÖÑΩÖáÖÉ=táêíëÅÜ~ÑíëÖΩíÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTR
SKNKO
dÉêáåÖïÉêíáÖÉ=táêíëÅÜ~ÑíëÖΩíÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTS
SKNKP
p~ÅÜ~åä~ÖÉÖΩíÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTT
SKO=^åëÅÜ~ÑÑìåÖëåÉÄÉåâçëíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTU SKP=mêÉáëå~ÅÜä®ëëÉ=ìåÇ=oΩÅâëÉåÇìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NUM SKQ=_Éò~ÜäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NUN SKR=wìë~ããÉåÑ~ëëÉåÇÉë=_ÉáëéáÉäKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NUP SKS=fåëí~åÇÜ~äíìåÖ=îçå=p~ÅÜ~åä~ÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NUR T=_ÉëÅÜ~ÑÑìåÖ=îçå=ìåÄÉïÉÖäáÅÜÉå=^åä~ÖÉÖΩíÉêå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NUV TKN=h~ìÑ=ìåÄÉÄ~ìíÉê=dêìåÇëíΩÅâÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NUV TKO=h~ìÑ=ÄÉÄ~ìíÉê=dêìåÇëíΩÅâÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NVN TKP=_~ì=îçå=dÉÄ®ìÇÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NVP U=sÉêâ~ìÑ=îçå=ÄÉïÉÖäáÅÜÉå=ìåÇ=ìåÄÉïÉÖäáÅÜÉå=^åä~ÖÉÖΩíÉêåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NVR UKN=^ìëïáêâìåÖ=~ìÑ=ÇÉå=råíÉêåÉÜãÉåëÉêÑçäÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NVR UKO=_ìÅÜìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NVS =
XI
UKOKN
s~êá~åíÉ=^=Eãáí=fåíÉêáãëâçåíçF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NVS
UKOKO
s~êá~åíÉ=_=EçÜåÉ=fåíÉêáãëâçåíçF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NVV
UKOKP
fåò~ÜäìåÖå~ÜãÉ=ÖÉÄê~ìÅÜíÉê=^åä~ÖÉÖΩíÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMM
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bÑÑÉâíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMV
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dêìåÇÄÉÖêáÑÑÉ=áã=^âíáÉåÜ~åÇÉä KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONM
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iáÉÑÉê~åíÉåâêÉÇáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOU
NOKOKO
hçåíçâçêêÉåíâêÉÇáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOU
NOKOKP
^åëÅÜ~ÑÑìåÖëÇ~êäÉÜÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPM
NOKOKQ
fåîÉëíáíáçåëÇ~êäÉÜÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPM
NOKOKR
iÉ~ëáåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPP
NOKP=sÉêÄìÅÜìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPR NOKPKN
hêÉÇáí~ìÑå~ÜãÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPR
NOKPKO
i~ìÑÉåÇÉ=_ìÅÜìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPS
NOKPKOKN
dÉÄΩÜêÉå=ìåÇ=wáåëÉå=EhêÉÇáíáåëíáíìíÉF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPS
NOKPKOKO=
dÉÄΩÜêÉå=ìåÇ=wáåëÉå=EìåíÉê=h~ìÑäÉìíÉåF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPU
NOKPKP
oΩÅâò~ÜäìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQM
NOKPKQ
iÉ~ëáåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQM
NP=mêáî~íâçåíç KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQN NPKN=tÉëÉå=ÇÉë=mêáî~íâçåíçëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQN NPKO=_ìÅÜìåÖÉå=ìåÇ=^ÄëÅÜäìëë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQO NPKOKN
mêáî~íÉ=båíå~ÜãÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQO
NPKOKO
mêáî~íÉ=báåä~ÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQR
NPKOKP
hçåíÉå~ÄëÅÜäìëë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQS
NPKP=bêïÉáíÉêíÉ=aáëí~åòêÉÅÜåìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQT =
XII
NQ=píÉìÉêå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQV NQKN=sÉêÄìÅÜìåÖ=å~ÅÜ=píÉìÉêâ~íÉÖçêáÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQV NQKNKN
^âíáîáÉêìåÖëéÑäáÅÜíáÖÉ=píÉìÉêå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQV
NQKNKO
_ÉíêáÉÄäáÅÜÉ=^ìÑï~åÇëíÉìÉêå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORM
NQKNKP
mêáî~íÉ=píÉìÉêå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORM
NQKNKQ
píÉìÉêå=~äë=ÇìêÅÜä~ìÑÉåÇÉ=mçëíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORN
NQKO=píÉìÉêêΩÅâÉêëí~ííìåÖÉå=ìåÇ=Jå~ÅÜò~ÜäìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORO aK=g~ÜêÉë~ÄëÅÜäìëë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKORR N=_ìÅÜìåÖëâêÉáëä~ìÑ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORT O=_ÉïÉêíìåÖ=ÇÉë=^åä~ÖÉîÉêã∏ÖÉåë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORV OKN=mä~åã®≈áÖÉ=^ÄëÅÜêÉáÄìåÖ=ÇÉë=^åä~ÖÉîÉêã∏ÖÉåë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORV OKNKN
^ÄëÅÜêÉáÄìåÖëÄ~ëáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSN
OKNKO
kìíòìåÖëÇ~ìÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSN
OKNKP
^ÄëÅÜêÉáÄìåÖëãÉíÜçÇÉ=EáåâäK=sÉêÄìÅÜìåÖF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSO
OKNKPKN=
iáåÉ~êÉ=^ÄëÅÜêÉáÄìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSP
OKNKPKO=
aÉÖêÉëëáîÉ=^ÄëÅÜêÉáÄìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSS
OKNKPKP=
mêçÖêÉëëáîÉ=^ÄëÅÜêÉáÄìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSV
OKNKPKQ=
iÉáëíìåÖë~ÄëÅÜêÉáÄìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSV
OKNKPKR=
^ÄëÉíòìåÖ=ÑΩê=pìÄëí~åòîÉêêáåÖÉêìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTM
OKNKQ
_ÉëçåÇÉêÜÉáíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTM
OKNKQKN=
^ÄëÅÜêÉáÄìåÖ=ÄÉá=wìÖ~åÖ=ï®ÜêÉåÇ=ÇÉë=dÉëÅÜ®Ñíëà~ÜêÉëà~ÜêÉë KKK OTM
OKNKQKO=
^ÄëÅÜêÉáÄìåÖ=ÄÉá=^ÄÖ~åÖ=ï®ÜêÉåÇ=ÇÉë=dÉëÅÜ®Ñíëà~ÜêÉëKKKKKKKKKKKKK OTN
OKNKQKP=
dÉêáåÖïÉêíáÖÉ=táêíëÅÜ~ÑíëÖΩíÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTP
OKNKQKQ=
tÉÅÜëÉä=ÇÉê=^ÄëÅÜêÉáÄìåÖëãÉíÜçÇÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTQ
OKNKQKR=
^ÄëÅÜêÉáÄìåÖ=îçå=dêìåÇëíΩÅâÉå=ìåÇ=dÉÄ®ìÇÉå KKKKKKKKKKKKKKKKKKKKKKKK OTS
OKO=^ì≈Éêéä~åã®≈áÖÉ=^ÄëÅÜêÉáÄìåÖ=ÇÉë=^åä~ÖÉîÉêã∏ÖÉåë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTS OKOKN
^åëÅÜ~ÑÑìåÖëâçëíÉåéêáåòáé KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTT
OKOKO
^ì≈Éêéä~åã®≈áÖÉ=^ÄëÅÜêÉáÄìåÖ=áå=ÇÉê=e~åÇÉäëÄáä~åò KKKKKKKKKKKKKKKKKKKKK OTT
OKOKOKN=
e~åÇÉäëêÉÅÜíäáÅÜÉê=q~ÖÉëïÉêí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTT
OKOKOKO=
káÉÇÉêëíïÉêíéêáåòáé=ìåÇ=~ì≈Éêéä~åã®≈áÖÉ=^ÄëÅÜêÉáÄìåÖKKKKKKKKKKK OTT
OKOKOKP=
tÉêí~ìÑÜçäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTU
OKOKP
^ì≈Éêéä~åã®≈áÖÉ=^ÄëÅÜêÉáÄìåÖ=áå=ÇÉê=píÉìÉêÄáä~åò KKKKKKKKKKKKKKKKKKKKKKKK OTV
OKOKPKN=
=
qÉáäïÉêí~ÄëÅÜêÉáÄìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTV
OKOKPKO=
píÉìÉêêÉÅÜíäáÅÜÉê=qÉáäïÉêíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTV
OKOKPKP=
tÉêí~ìÑÜçäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUM
XIII
OKOKQ
sÉêÄìÅÜìåÖ=ÇK=~ì≈Éêéä~åã®≈áÖÉå=^ÄëÅÜêÉáÄìåÖ=ÄK=p~ÅÜ~åä~ÖÉå KKK OUM
OKOKR
sÉêÄìÅÜìåÖ=ÇK=~ì≈Éêéä~åãK=^ÄëÅÜêÉáÄìåÖ=ÄK=tÉêíé~éáÉêÉåKKKKKKKKKKKK OUQ
P=_ÉïÉêíìåÖ=ÇÉë=rãä~ìÑîÉêã∏ÖÉåë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUT PKN=^ääÖÉãÉáåÉ=_ÉïÉêíìåÖëÖêìåÇë®íòÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUT PKNKN
^åëÅÜ~ÑÑìåÖëâçëíÉåéêáåòáé KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUT
PKNKO
píêÉåÖÉë=káÉÇÉêëíïÉêíéêáåòáéKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUT
PKO=_ÉïÉêíìåÖ=îçå=sçêê®íÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUU PKOKN
^ääÖÉãÉáåÉë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUU
PKOKO
^ìëÖÉï®ÜäíÉ=_ÉïÉêíìåÖëîÉêÉáåÑ~ÅÜìåÖëîÉêÑ~ÜêÉå=ÑΩê=píçÑÑÉ KKKKKKKKKKK OUV
PKOKOKN=
aìêÅÜëÅÜåáííëîÉêÑ~ÜêÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUV
PKOKOKO=
_ÉÜ~åÇäìåÖ=ÇÉê=sÉêÑ~ÜêÉåëÉêÖÉÄåáëëÉ=ÄÉáã=g~ÜêÉë~ÄëÅÜäìëëKKKKKK OVM
PKOKP
_ÉëçåÇÉêÜÉáíÉå=ÄÉá=ÑÉêíáÖÉå=ìåÇ=ìåÑÉêíáÖÉå=bêòÉìÖåáëëÉåKKKKKKKKKKKKKKKK OVN
PKP=_ÉïÉêíìåÖ=îçå=cçêÇÉêìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OVP PKPKN
^ääÖÉãÉáåÉë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OVP
PKPKO
^ÄëÅÜêÉáÄìåÖ=ìåÉáåÄêáåÖäáÅÜÉê=cçêÇÉêìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OVQ
PKPKP
w~ÜäìåÖëÉáåÖ®åÖÉ=~ìë=~ÄÖÉëÅÜêáÉÄÉåÉå=cçêÇÉêìåÖÉåKKKKKKKKKKKKKKKKKKKKKK OVT
PKPKQ
_ÉïÉêíìåÖ=òïÉáÑÉäÜ~ÑíÉê=cçêÇÉêìåÖÉå=Ebt_F KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OVU
PKPKR
_ÉïÉêíìåÖ=Éáåï~åÇÑêÉáÉê=cçêÇÉêìåÖÉå=Emt_FKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PMQ
PKQ=_ÉïÉêíìåÖ=îçå=tÉêíé~éáÉêÉå=ÇÉë=rãä~ìÑîÉêã∏ÖÉåë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PMU Q=oÉÅÜåìåÖë~ÄÖêÉåòìåÖëéçëíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PNP QKN=^ääÖÉãÉáåÉë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PNP QKO=^êíÉå=ÇÉê=oÉÅÜåìåÖë~ÄÖêÉåòìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PNQ QKOKN
^âíáîÉ=ìåÇ=é~ëëáîÉ=oÉÅÜåìåÖë~ÄÖêÉåòìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PNQ
QKOKO
pçåëíáÖÉ=cçêÇÉêìåÖÉå=ìåÇ=sÉêÄáåÇäáÅÜâÉáíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PNU
QKOKP
rãë~íòëíÉìÉêéÑäáÅÜíáÖÉ=^ÄÖêÉåòìåÖëÑ®ääÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PON
R=oÉÅÜëÑçêã~ÄÜ®åÖáÖÉ=báÖÉåâ~éáí~äÄáä~åòáÉêìåÖ=ìåÇ=bêÑçäÖëÄìÅÜìåÖ KKKKKKKKKKKKKKKKKKK POP RKN=báåòÉäìåíÉêåÉÜãÉå=ìåÇ=mÉêëçåÉåÖÉëÉääëÅÜ~ÑíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POP RKNKN
báåòÉäìåíÉêåÉÜãÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POP
RKNKO
lÑÑÉåÉ=e~åÇÉäëÖÉëÉääëÅÜ~Ñí=EledFKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POQ
RKNKP
hçãã~åÇáíÖÉëÉääëÅÜ~Ñí=EhdFKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POR
RKO=h~éáí~äÖÉëÉääëÅÜ~ÑíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POT RKOKN
dÉòÉáÅÜåÉíÉë=h~éáí~ä KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POU
RKOKNKN=
dêìåÇ=ìåÇ=pí~ããâ~éáí~ä KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POU
RKOKNKO=
^ìëëíÉÜÉåÇÉ=báåä~ÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POV
RKOKO
oΩÅâä~ÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PPM
RKOKOKN= =
h~éáí~äêΩÅâä~ÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PPN
XIV
RKOKOKO= RKOKP
dÉïáååêΩÅâä~ÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PPO
bêÖÉÄåáëîÉêïÉåÇìåÖ=ìåÇ=báÖÉåâ~éáí~ä~ìëïÉáëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PPP
RKOKPKN=
dêìåÇä~ÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PPP
RKOKPKO=
sÉêÄìÅÜìåÖ=ÇÉê=bêÖÉÄåáëîÉêïÉåÇìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PPS
S=oΩÅâëíÉääìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQN SKN=^ääÖÉãÉáåÉë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQN SKO=^åë~íòJ=ìåÇ=_ÉïÉêíìåÖëîçêëÅÜêáÑíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQO SKOKN
^åë~íòâêáíÉêáÉå=áå=e~åÇÉäëJ=ìåÇ=píÉìÉêÄáä~åò KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQO
SKOKO
^ìëÖÉï®ÜäíÉ=sçêëÅÜêáÑíÉå=ÇÉê=oΩÅâëíÉääìåÖëÄÉïÉêíìåÖKKKKKKKKKKKKKKKKKKKK PQP
SKOKOKN=
_ÉïÉêíìåÖ=å~ÅÜ=îÉêåΩåÑíáÖÉê=â~ìÑã®ååáëÅÜÉê=_ÉìêíÉáäìåÖKKKKKKKKK PQP
SKOKOKO=
dêìåÇë~íò=ÇÉê=sçêëáÅÜíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQP
SKP=sÉêÄìÅÜìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQP T=sÉêÄáåÇäáÅÜâÉáíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQT TKN=^ääÖÉãÉáåÉë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQT TKO=^åë~íò=ìåÇ=_ÉïÉêíìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQT TKOKN
^ääÖÉãÉáåÉëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQT
TKOKO
oΩÅâò~ÜäìåÖëÄÉíê~ÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQU
TKOKP
e~åÇÉäëêÉÅÜíäáÅÜÉë=e∏ÅÜëíïÉêíéêáåòáé KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQU
TKOKQ
_ÉïÉêíìåÖ=áå=e~åÇÉäëJ=ìåÇ=píÉìÉêÄáä~åò=áã=sÉêÖäÉáÅÜ KKKKKKKKKKKKKKKKKKKK PQU
TKP=sÉêÄìÅÜìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQV bK=^ìÑÖ~ÄÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKPRN N=^ìÑÖ~ÄÉåëíÉääìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PRP O=i∏ëìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PTR ^åÜ~åÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQNV §ÄìåÖëâçåíÉåéä~å=ÖÉã®≈=fho KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QON iáíÉê~íìêîÉêòÉáÅÜåáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QOV pÅÜä~ÖïçêíîÉêòÉáÅÜåáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QPN
= = =
=
Abkürzungsverzeichnis =
^KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ^âíáî~= ^_ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ^åÑ~åÖëÄÉëí~åÇ= ^Ñ^ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ^ÄëÉíòìåÖ=ÑΩê=^ÄåìíòìåÖ= ^d KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ^âíáÉåÖÉëÉääëÅÜ~Ñí= ^d^L=^k^ KKKKKKKKKKKKKKKKKKKKKK ^êÄÉáíÖÉÄÉê~åíÉáäL^êÄÉáíåÉÜãÉê~åíÉáä= ^eh KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ^åëÅÜ~ÑÑìåÖëJ=ìåÇ=eÉêëíÉääìåÖëâçëíÉå= ^h KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ^åëÅÜ~ÑÑìåÖëâçëíÉå= ^âídKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ^âíáÉåÖÉëÉíò= ^lKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ^ÄÖ~ÄÉåçêÇåìåÖ= ^mKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ^åÖÉÄçíëéêÉáë= ^s KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ^åä~ÖÉîÉêã∏ÖÉå= =
_afKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _ìåÇÉëîÉêÄ~åÇ=ÇÉê=ÇÉìíëÅÜÉå=fåÇìëíêáÉ= _bm KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _~êÉáåâ~ìÑëéêÉáë= _ce KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _ìåÇÉëÑáå~åòÜçÑ= _d^ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _ÉíêáÉÄëJ=ìåÇ=dÉëÅÜ®Ñíë~ìëëí~ííìåÖ= _d_ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _ΩêÖÉêäáÅÜÉë=dÉëÉíòÄìÅÜ= _de KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _ìåÇÉëÖÉêáÅÜíëÜçÑ= _pí_äK KKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _ìåÇÉëëíÉìÉêÄä~íí= _sL=_scbL=_srb KKKKKKKKKKK _Éëí~åÇëîÉê®åÇÉêìåÖÉåL=Á=~å=cbL=Á=~å=rb= _sm KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _~êîÉêâ~ìÑëéêÉáë= _wh KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK _ÉòìÖëâçëíÉå= =
b_h KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK bê∏ÑÑåìåÖëÄáä~åòâçåíç= bded_ KKKKKKKKKKKKKKKKKKKKKKKKKKK báåÑΩÜêìåÖëÖÉëÉíò=òìã=ed_= bhKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK báÖÉåâ~éáí~ä= bm KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK báåëí~åÇëéêÉáë= bpídL=bpíeL=bpíoKKKKKKKKKKKK báåâçããÉåëíÉìÉêÖÉëÉíòL=JÜáäÑÉåL=JêáÅÜíäáåáÉå= bt_ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK báåòÉäïÉêíÄÉêáÅÜíáÖìåÖ= =
cb KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK cÉêíáÖÉ=bêòÉìÖåáëëÉ= cdh KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK cÉêíáÖìåÖëÖÉãÉáåâçëíÉå= chKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK cêÉãÇâ~éáí~ä= ci KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK cÉêíáÖìåÖëä∏ÜåÉ= ciiKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK cçêÇÉêìåÖÉå=~ìë=iáÉÑÉêìåÖÉå=ìåÇ=iÉáëíìåÖÉå= cj KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK cÉêíáÖìåÖëã~íÉêá~ä= =
d^^m KKKKKKKKKKKKKKKKKKKKKKKKKKKKKK dÉåÉê~ääó=^ÅÅÉéíÉÇ=^ÅÅçìåíáåÖ=mêáåÅáéäÉë= dÉådKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK dÉåçëëÉåëÅÜ~ÑíëÖÉëÉíò= dÉïpíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK dÉïÉêÄÉëíÉìÉê= dhoKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK dÉãÉáåëÅÜ~ÑíëâçåíÉåê~ÜãÉå=ÇÉê=fåÇìëíêáÉ= dãÄe KKKKKKKKKKKKKKKKKKKKKKKKKKKKK dÉëÉääëÅÜ~Ñí=ãáí=ÄÉëÅÜê®åâíÉê=e~ÑíìåÖ= dãÄed KKKKKKKKKKKKKKKKKKKKKKKKKK dãÄeJdÉëÉíò= dç_L=dç_áäKKKKKKKKKKKKKKKKKKKKK dêìåÇë®íòÉ=çêÇåìåÖëã®≈áÖÉê=_ìÅÜÑΩÜêìåÖL=_áä~åòáÉêìåÖ= =
XVI
dìsKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK dÉïáååJ=ìåÇ=sÉêäìëíêÉÅÜåìåÖ= dìsJhçåíç KKKKKKKKKKKKKKKKKKKKK dÉïáååJ=ìåÇ=sÉêäìëíâçåíç= =
e KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK e~ÄÉåëÉáíÉ=ÉáåÉë=hçåíçë= ed_ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK e~åÇÉäëÖÉëÉíòÄìÅÜ= ehKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK eÉêëíÉääìåÖëâçëíÉå= =
fho KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK fåÇìëíêáÉâçåíÉåê~ÜãÉå= =
hdKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK hçãã~åÇáíÖÉëÉääëÅÜ~Ñí= htd KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK hêÉÇáíïÉëÉåÖÉëÉíò= =
ipías KKKKKKKKKKKKKKKKKKKKKKKKKKKKKK içÜåëíÉìÉêÇìêÅÜÑΩÜêìåÖëîÉêçêÇåìåÖ= =
jdhKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK j~íÉêá~äÖÉãÉáåâçëíÉå= jïpí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK jÉÜêïÉêíëíÉìÉê= =
led KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK lÑÑÉåÉ=e~åÇÉäëÖÉëÉääëÅÜ~Ñí= =
mKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK m~ëëáî~= éK~KL=éKãKKKKKKKKKKKKKKKKKKKKKKKKK à®ÜêäáÅÜ=Eéêç=~ååçFL=ãçå~íäáÅÜ= mìÄädKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK mìÄäáòáí®íëÖÉëÉíò= mt_ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK m~ìëÅÜ~äïÉêíÄÉêáÅÜíáÖìåÖ= =
o^m KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK oÉÅÜåìåÖë~ÄÖêÉåòìåÖëéçëíÉå= o_tKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK oÉëíÄìÅÜïÉêí= oe_JpíçÑÑÉ KKKKKKKKKKKKKKKKKKKKKK oçÜJI=eáäÑëJ=ìåÇ=_ÉíêáÉÄëëíçÑÑÉ= =
p KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK pçääëÉáíÉ=ÉáåÉë=hçåíçë= p^KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK p~ÅÜ~åä~ÖÉå= p_KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK pÅÜäìëëÄÉëí~åÇ= p_h KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK pÅÜäìëëÄáä~åòâçåíç= pbhcbL=pbhsq KKKKKKKKKKKKKKK pçåÇÉêÉáåòÉäâçëíÉå=ÇÉê=cÉêíáÖìåÖL=Á=ÇÉë=sÉêíêáÉÄë= phmKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK pÉäÄëíâçëíÉåéêÉáë= pçäwKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK pçäáÇ~êáí®íëòìëÅÜä~Ö= píd_KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK píê~ÑÖÉëÉíòÄìÅÜ= =
rb KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK råÑÉêíáÖÉ=bêòÉìÖåáëëÉ= rpíL=rpíd KKKKKKKKKKKKKKKKKKKKKKK rãë~íòëíÉìÉêL=JÖÉëÉíò= rpías KKKKKKKKKKKKKKKKKKKKKKKKKKKKK rãë~íòëíÉìÉêÇìêÅÜÑΩÜêìåÖëîÉêçêÇåìåÖ= rs KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK rãä~ìÑîÉêã∏ÖÉå= =
shm KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK sÉêâ~ìÑëéêÉáë= sii KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK sÉêÄáåÇäáÅÜâÉáíÉå=~ìë=iáÉÑÉêìåÖÉå=ìåÇ=iÉáëíìåÖÉå= spíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK sçêëíÉìÉê= sqdh KKKKKKKKKKKKKKKKKKKKKKKKKKKKKK sÉêíêáÉÄëÖÉãÉáåâçëíÉå= ssm KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK îçêä®ìÑáÖÉê=sÉêâ~ìÑëéêÉáë= stdhKKKKKKKKKKKKKKKKKKKKKKKKKKKKK sÉêï~äíìåÖëÖÉãÉáåâçëíÉå= =
wbm KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK wáÉäÉáåâ~ìÑëéêÉáë= wsm KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK wáÉäîÉêâ~ìÑëéêÉáë= =
Abbildungs- und Tabellenverzeichnis = ^ÄÄáäÇìåÖ=NW== qÉáäÄÉêÉáÅÜÉ=ÇÉë=áåíÉêåÉå=oÉÅÜåìåÖëïÉëÉåë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKP ^ÄÄáäÇìåÖ=OW== _ÉíêáÉÄäáÅÜÉë=oÉÅÜåìåÖëïÉëÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQ ^ÄÄáäÇìåÖ=QW== lêÖ~åáë~íáçå=ÇÉê=_ìÅÜÑΩÜêìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKR ^ÄÄáäÇìåÖ=RW== g~ÜêÉë~ÄëÅÜäìëë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKS ^ÄÄáäÇìåÖ=SW== _ÉáëéáÉäÜ~ÑíÉ=fåîÉåí~êÖäáÉÇÉêìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKU ^ÄÄáäÇìåÖ=TW== _áä~åò=Eãáí=éçëáíáîÉã=báÖÉåâ~éáí~äFKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NO ^ÄÄáäÇìåÖ=UW== _áä~åòÖäÉáÅÜìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NO ^ÄÄáäÇìåÖ=VW== _áä~åòÖäÉáÅÜÖÉïáÅÜíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NO ^ÄÄáäÇìåÖ=NMW=_áä~åòîÉê®åÇÉêåÇÉ=dÉëÅÜ®ÑíëîçêÑ®ääÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OP ^ÄÄáäÇìåÖ=NNW=^âíáîJ=ìåÇ=m~ëëáîâçåíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OU ^ÄÄáäÇìåÖ=NOW=_áä~åò=ãáí=åÉÖ~íáîÉã=báÖÉåâ~éáí~ä KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PR ^ÄÄáäÇìåÖ=NPW=bê∏ÑÑåìåÖëJ=ìåÇ=pÅÜäìëëÄáä~åòâçåíç KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PR ^ÄÄáäÇìåÖ=NQW=_ìÅÜìåÖë~Ää®ìÑÉ=îçå=bê∏ÑÑåìåÖëJ=òìê=pÅÜäìëëÄáä~åòKKKKKKKKKKKKKKKKKKKKKKKKKKKK PU ^ÄÄáäÇìåÖ=NRW=báåÑ~ÅÜÉ=aáëí~åòêÉÅÜåìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QS ^ÄÄáäÇìåÖ=NSW=dÉïáååJ=ìåÇ=sÉêäìëíêÉÅÜåìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QS ^ÄÄáäÇìåÖ=NTW=bêÑçäÖëâçåíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QT ^ÄÄáäÇìåÖ=NUW=^ÄëÅÜäìëë=ÇÉë=dìsJhçåíçë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QV ^ÄÄáäÇìåÖ=NVW=^ÄëÅÜäìëë=ÇÉë=dìsJhçåíçë=ÄÉá=sÉêäìëí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RM ^ÄÄáäÇìåÖ=OMW=^ÄëÅÜäìëë=ÇÉë=dìsJhçåíçë=ÄÉá=dÉïáåå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RM ^ÄÄáäÇìåÖ=ONW=wìë~ããÉåëÉíòìåÖ=ÇÉë=dÉë~ãíÉêÑçäÖÉë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RN ^ÄÄáäÇìåÖ=OOW=wìë~ããÉåëÉíòìåÖ=ÇÉë=dÉë~ãíÉêÑçäÖÉë=áã=dìsJhçåíç KKKKKKKKKKKKKKKKKKKKKKKK RO ^ÄÄáäÇìåÖ=OPW=dìs=å~ÅÜ=rãë~íòâçëíÉåîÉêÑ~ÜêÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RS ^ÄÄáäÇìåÖ=OQW=dìs=å~ÅÜ=dÉë~ãíâçëíÉåîÉêÑ~ÜêÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RS ^ÄÄáäÇìåÖ=ORW=dÉë~ãíòìë~ããÉåÜ~åÖ=hçåíÉå~êíÉå=ìåÇ=_áä~åòKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RU ^ÄÄáäÇìåÖ=OSW=^ìÑÄ~ì=ÇÉë=fåÇìëíêáÉâçåíÉåê~ÜãÉåëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SM ^ÄÄáäÇìåÖ=OTW=^ÄëÅÜäìëëÖäáÉÇÉêìåÖëéêáåòáéKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SN ^ÄÄáäÇìåÖ=OUW=^ìÑÄ~ì=dÉãÉáåëÅÜ~ÑíëâçåíÉåê~ÜãÉå=ÇÉê=fåÇìëíêáÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SO ^ÄÄáäÇìåÖ=OTW=dÉëÉíòäáÅÜÉ=oÉÅÜåìåÖëäÉÖìåÖëîçêëÅÜêáÑíÉå=Eeo=ìåÇ=poF KKKKKKKKKKKKKKKKKKKKK SR ^ÄÄáäÇìåÖ=OUW=dÉëÉíòäáÅÜÉ=oÉÅÜåìåÖëäÉÖìåÖëîçêëÅÜêáÑíÉå=EeoF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SS ^ÄÄáäÇìåÖ=OVW=j~≈ÖÉÄäáÅÜâÉáí=ìåÇ=_áä~åò~åë®íòÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TM ^ÄÄáäÇìåÖ=PMW=_ìÅÜÑΩÜêìåÖëéÑäáÅÜí=å~ÅÜ=e~åÇÉäëJ=ìåÇ=píÉìÉêêÉÅÜíKKKKKKKKKKKKKKKKKKKKKKKKKKKK TP ^ÄÄáäÇìåÖ=PNW=tÉêíÉêÜÉääÉåÇÉ=ìåÇ=JÄÉÖêΩåÇÉåÇÉ=q~íë~ÅÜÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TV ^ÄÄáäÇìåÖ=POW=fãé~êáí®íëéêáåòáéKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK US ^ÄÄáäÇìåÖ=PPW=káÉÇÉêëíJ=ìåÇ=e∏ÅÜëíïÉêíéêáåòáé KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UT ^ÄÄáäÇìåÖ=PQW=^ääÖÉãÉáåÉ=pÅÜêáííÉ=ÇÉê=oÉÅÜåìåÖëäÉÖìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UV ^ÄÄáäÇìåÖ=PRW=sÉêäÉíòìåÖ=ëíÉìÉêêÉÅÜíäáÅÜÉê=_ìÅÜÑΩÜêìåÖëîçêëÅÜêáÑíÉåKKKKKKKKKKKKKKKKKKKKKKKK VQ ^ÄÄáäÇìåÖ=PRW=_ÉíêáÉÄëïáêíëÅÜ~ÑíäáÅÜÉ=mêçÇìâíáçåëÑ~âíçêÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VT ^ÄÄáäÇìåÖ=PSW=mêçÇìâíáçåëéêçòÉëë=ìåÇ=j®êâíÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VU ^ÄÄáäÇìåÖ=PTW=báåâ~ìÑëâ~äâìä~íáçå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VV ^ÄÄáäÇìåÖ=PUW=iáÉÑÉêÄÉÇáåÖìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMR ^ÄÄáäÇìåÖ=PVW=^êíÉå=îçå=mêÉáëå~ÅÜä®ëëÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMS ^ÄÄáäÇìåÖ=QMW=pÅÜÉã~=pâçåíç=Ebáåâ~ìÑFKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNQ =
XVIII
^ÄÄáäÇìåÖ=QNW=_Éëí~åÇëîÉê®åÇÉêìåÖÉå=Esçêê®íÉFKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOM ^ÄÄáäÇìåÖ=QOW=tÉêâëíçÑÑîÉêÄê~ìÅÜLt~êÉåÉáåë~íò KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOO ^ÄÄáäÇìåÖ=QPW=jáÉíÉI=m~ÅÜíI=iÉ~ëáåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPN ^ÄÄáäÇìåÖ=QQW=içÜåJ=ìåÇ=dÉÜ~äíë~ÄêÉÅÜåìåÖ=EÖêçÄÉë=pÅÜÉã~F KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPP ^ÄÄáäÇìåÖ=QRW=_Éáíê~Öëë®íòÉ=ÖÉëÉíòäáÅÜÉ=pçòá~äîÉêëáÅÜÉêìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPQ ^ÄÄáäÇìåÖ=QSW=pÅÜÉã~=ÖÉë~ãíÉê=mÉêëçå~ä~ìÑï~åÇ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQO ^ÄÄáäÇìåÖ=QTW=sÉêâ~ìÑëâ~äâìä~íáçå=EëÉäÄëí=ÉêëíÉääíÉ=bêòÉìÖåáëëÉFKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQP ^ÄÄáäÇìåÖ=QUW=sÉêâ~ìÑëâ~äâìä~íáçå=Ee~åÇÉäëï~êÉåF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQQ ^ÄÄáäÇìåÖ=QVW=pÅÜÉã~=pâçåíç=EsÉêâ~ìÑF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRO ^ÄÄáäÇìåÖ=RMW=_Éëí~åÇëîÉê®åÇÉêìåÖÉå=EÑÉêíáÖÉ=ìåÇ=ìåÑÉêíáÖÉ=bêòÉìÖåáëëÉF KKKKKKKKKKKKK NRT ^ÄÄáäÇìåÖ=RNW=dÉë~ãíòìë~ããÉåÜ~åÖ=_Éëí~åÇëîÉê®åÇÉêìåÖÉå=EcbI=rbF KKKKKKKKKKKKKKKKK NSM ^ÄÄáäÇìåÖ=ROW=w~Üää~ëíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSO ^ÄÄáäÇìåÖ=RPW=_ÉëíáããìåÖ=ÇÉê=aÉòÉãÄÉêìãë~íòëíÉìÉêò~Üää~ëí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSV ^ÄÄáäÇìåÖ=RQW=^åëÅÜ~ÑÑìåÖëâçëíÉå=ÄÉïÉÖäáÅÜÉê=^åä~ÖÉÖΩíÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTP ^ÄÄáäÇìåÖ=RRW=tÉêíÉêÜ~äíÉåÇÉ=ìåÇ=JÉêÜ∏ÜÉåÇÉ=oÉé~ê~íìêÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NUR ^ÄÄáäÇìåÖ=RSW=dêΩåÇÉ=ÑΩê=ÇÉå=sÉêâ~ìÑ=îçå=^åä~ÖÉÖΩíÉêåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NVR ^ÄÄáäÇìåÖ=RTW=fåíÉêáãëâçåíç=EsÉêâ~ìÑ=^åä~ÖÉÖÉÖÉåëí®åÇÉåF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NVS ^ÄÄáäÇìåÖ=RUW=pÉäÄëíâçëíÉåÉêãáííäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMQ ^ÄÄáäÇìåÖ=RVW=pÉäÄëíâçëíÉåÉêãáííäìåÖ=å~ÅÜ=e~åÇÉäëJ=ìåÇ=píÉìÉêêÉÅÜíKKKKKKKKKKKKKKKKKKKKKK OMR ^ÄÄáäÇìåÖ=SMW=sÉêíêÉíÄ~êÉ=bÑÑÉâíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMV ^ÄÄáäÇìåÖ=SNW=^ìÑÄ~ì=ÖÉÇêìÅâíÉê=bÑÑÉâíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONM ^ÄÄáäÇìåÖ=SOW=h~ìÑ~ÄêÉÅÜåìåÖ=ÄÉá=^âíáÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONO ^ÄÄáäÇìåÖ=SPW=^âíáÉå=ÇÉë=^åä~ÖÉJ=ìåÇ=rãä~ìÑîÉêã∏ÖÉåë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONP ^ÄÄáäÇìåÖ=SQW=sÉêâ~ìÑë~ÄêÉÅÜåìåÖ=ÄÉá=^âíáÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONQ ^ÄÄáäÇìåÖ=SRW=h~ìÑ~ÄêÉÅÜåìåÖ=ÄÉá=ÑÉëíîÉêòáåëäáÅÜÉå=tÉêíé~éáÉêÉåKKKKKKKKKKKKKKKKKKKKKKKKKK ONV ^ÄÄáäÇìåÖ=SSW=sÉêâ~ìÑë~ÄêÉÅÜåìåÖ=ÄÉá=ÑÉëíîÉêòáåëäáÅÜÉå=tÉêíé~éáÉêÉå KKKKKKKKKKKKKKKKKKK OOO ^ÄÄáäÇìåÖ=STW=oΩÅâò~ÜäìåÖëÄÉíê~Ö=ÄÉá=hêÉÇáíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOR ^ÄÄáäÇìåÖ=SUW=hêÉÇáí~êíÉå=å~ÅÜ=cêáëíáÖâÉáíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOT ^ÄÄáäÇìåÖ=SVW=dáêçâçåíç=ìåÇ=hçåíçâçêêÉåíâêÉÇáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOV ^ÄÄáäÇìåÖ=TMW=fåîÉëíáíáçåëÇ~êäÉÜÉå=å~ÅÜ=^êí=ÇÉê=qáäÖìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPN ^ÄÄáäÇìåÖ=TNW=cáå~åòáÉêìåÖëJ=ìåÇ=léÉê~íáåÖJiÉ~ëáåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPQ ^ÄÄáäÇìåÖ=TOW=mêáî~íÉáåä~ÖÉåJ=ìåÇ=Éåíå~ÜãÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQN ^ÄÄáäÇìåÖ=TPW=mêáî~íâçåíç KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQN ^ÄÄáäÇìåÖ=TQW=rãë~íòëíÉìÉêéÑäáÅÜíáÖâÉáí=éêáî~íÉê=båíå~ÜãÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQO ^ÄÄáäÇìåÖ=TRW=mêáî~íâçåíç~ÄëÅÜäìëëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQT ^ÄÄáäÇìåÖ=TSW=bêïÉáíÉêíÉ=aáëí~åòêÉÅÜåìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQT ^ÄÄáäÇìåÖ=TTW=_ìÅÜÜ~äíÉêáëÅÜÉ=píÉìÉêÖêìééÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQV ^ÄÄáäÇìåÖ=TUW=_ìÅÜìåÖëâêÉáëä~ìÑ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORT ^ÄÄáäÇìåÖ=TVW=dêìåÇëíêìâíìê=ÇÉê=e~åÇÉäëÄáä~åò KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORU ^ÄÄáäÇìåÖ=UMW=sÉêÉáåÑ~ÅÜíÉ=báåíÉáäìåÖ=ÇÉê=dÉÖÉåëí®åÇÉ=ÇÉë=^åä~ÖÉîÉêã∏ÖÉåë KKKKKK ORV ^ÄÄáäÇìåÖ=UNW=^ÄëÅÜêÉáÄìåÖëJL^ÄëÉíòìåÖëãÉíÜçÇÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSO ^ÄÄáäÇìåÖ=UOW=oÉëíÄìÅÜïÉêí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSP ^ÄÄáäÇìåÖ=UPW=iáåÉ~êÉ=^ÄëÅÜêÉáÄìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSP ^ÄÄáäÇìåÖ=UQW=aÉÖêÉëëáîÉ=^ÄëÅÜêÉáÄìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSS ^ÄÄáäÇìåÖ=URW=^ì≈Éêéä~åã®≈áÖÉ=^ÄëÅÜêÉáÄìåÖÉå=E^åä~ÖÉîÉêã∏ÖÉåF KKKKKKKKKKKKKKKKKKKKKK OTU ^ÄÄáäÇìåÖ=USW=píÉìÉêäáÅÜÉë=wìëÅÜêÉáÄìåÖëÖÉÄçí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUQ ^ÄÄáäÇìåÖ=UTW=^ì≈Éêéä~åã®≈áÖÉ=^ÄëÅÜêÉáÄìåÖÉå=Erãä~ìÑîÉêã∏ÖÉåFKKKKKKKKKKKKKKKKKKKKKK OUT ^ÄÄáäÇìåÖ=UUW=_ÉïÉêíìåÖëîÉêÉáåÑ~ÅÜìåÖëîÉêÑ~ÜêÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUU =
XIX
^ÄÄáäÇìåÖ=UVW=cçêÇÉêìåÖëâä~ëëÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OVP ^ÄÄáäÇìåÖ=VMW=_ÉïÉêíìåÖ=îçå=tÉêíé~éáÉêÉå=ÇÉë=rs=Eh~éáí~äÖÉëÉääëÅÜ~ÑíÉåF KKKKKKKKKKK PMU ^ÄÄáäÇìåÖ=VNW=oÉÅÜåìåÖë~ÄÖêÉåòìåÖëéçëíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PNP ^ÄÄáäÇìåÖ=VOW=oΩÅâä~ÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PPN ^ÄÄáäÇìåÖ=VPW=dÉïáååîÉêïÉåÇìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PPP ^ÄÄáäÇìåÖ=VQW=^åë~íòîçêëÅÜêáÑíÉå=ÑΩê=oΩÅâëíÉääìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQO ^ÄÄáäÇìåÖ=VRW=^ìÑïÉêíìåÖÖÉÄçíÉ=ìåÇ=JîÉêÄçíÉ=ÄÉá=sÉêÄáåÇäáÅÜâÉáíÉåKKKKKKKKKKKKKKKKKKKKKK PQV = q~ÄÉääÉ=NW== sÉêÉáåÑ~ÅÜíÉ=_áä~åòKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NP q~ÄÉääÉ=OW== _ÉáëéáÉäÉ=òì=_áä~åòéçëíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NP q~ÄÉääÉ=PW== dìs=áå=pí~ÑÑÉäÑçêã=EdÉë~ãíâçëíÉåîÉêÑ~ÜêÉåF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NS q~ÄÉääÉ=QW== dìs=áå=qJhçåíÉåJcçêã KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NU q~ÄÉääÉ=RW== sçêJ=ìåÇ=k~ÅÜíÉáäÉ=îçå=aáëí~åòêÉÅÜåìåÖ=ìåÇ=dìsKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QS q~ÄÉääÉ=SW== bêÑçäÖëëé~äíìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RN q~ÄÉääÉ=TW== dê∏≈Éåâä~ëëÉå=ÄÉá=h~éáí~äÖÉëÉääëÅÜ~ÑíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SU q~ÄÉääÉ=UW== sçê~ìëëÉíòìåÖÉå=ÑΩê=ÇáÉ=^åïÉåÇìåÖ=ÇÉë=mìÄäd KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SV q~ÄÉääÉ=VW== _ÉãÉëëìåÖëÖêÉåòÉå=ÑΩê=_ìÅÜÑΩÜêìåÖëéÑäáÅÜí=å~ÅÜ=píÉìÉêêÉÅÜí KKKKKKKKKKKKKKKK TR q~ÄÉääÉ=NMW=_Éëí~åÇíÉáäÉ=ÇÉê=oÉÅÜåìåÖëäÉÖìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VO q~ÄÉääÉ=NNW=^ìÑëíÉääìåÖëJI=cÉëíëíÉääìåÖëJ=ìåÇ=lÑÑÉåäÉÖìåÖëÑêáëíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VO q~ÄÉääÉ=NOW=sÉêÄìÅÜìåÖ=îÉêã∏ÖÉåëïáêâë~ãÉê=iÉáëíìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPU q~ÄÉääÉ=NPW=içÜåòìë~íòâçëíÉå=E_ÉáëéáÉäÉF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQN q~ÄÉääÉ=NQW=rãë~íòëíÉìÉêâçåíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSR q~ÄÉääÉ=NRW=^åëÅÜ~ÑÑìåÖëåÉÄÉåâçëíÉå=ÄÉïÉÖäáÅÜÉê=p~ÅÜ~åä~ÖÉÖΩíÉê KKKKKKKKKKKKKKKKKKKKKKKK NTQ q~ÄÉääÉ=NSW=tÉêíÖêÉåòÉå=ÄÉá=^âíáîáÉêìåÖ=îçå=^åä~ÖÉÖΩíÉêåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTR q~ÄÉääÉ=NTW=kÉÄÉåâçëíÉå=ÄÉáã=dêìåÇëíΩÅâëâ~ìÑ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NUV q~ÄÉääÉ=NUW=^åëÅÜ~ÑÑìåÖëåÉÄÉåâçëíÉå=îçå=dÉÄ®ìÇÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NVN q~ÄÉääÉ=NVW=báåòÉäJ=ìåÇ=dÉãÉáåâçëíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMP q~ÄÉääÉ=OMW=_~ëÉå=ÑΩê=dÉãÉáåâçëíÉåòìëÅÜä~ÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMQ q~ÄÉääÉ=ONW=hìêëÖÉïáååJ=ìåÇ=JîÉêäìëíâçåíÉå=ÄÉáã=^âíáÉåîÉêâ~ìÑKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONS q~ÄÉääÉ=OOW=aáîáÇÉåÇÉåÉêíê~ÖëâçåíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONT q~ÄÉääÉ=OPW=_~åâîÉêÄáåÇäáÅÜâÉáíëâçåíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPR q~ÄÉääÉ=OQW=_ÉíêáÉÄäáÅÜÉ=^ìÑï~åÇëíÉìÉêå=EhçåíÉåF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORM q~ÄÉääÉ=ORW=píÉìÉêêΩÅâÉêëí~ííìåÖÉå=EhçåíÉåF KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORO q~ÄÉääÉ=OSW=^ìëÖÉï®ÜäíÉ=^ÄëÅÜêÉáÄìåÖëãÉíÜçÇÉå=áã=e~åÇÉäëJ=ìåÇ=píÉìÉêêÉÅÜí KKKKK OSO == == == == == ==
=
= = =
A. TECHNIK UND ERGEBNIS DER BUCHFÜHRUNG = In diesem Kapitel lernen Sie, wie die Buchführung in das industrielle Rechnungswesen einzuordnen ist, welcher Zweck mit ihr verfolgt und welches Ergebnis (Jahresabschluss: Bilanz, Gewinn- und Verlustrechnung, Anhang) sie liefert. Um genau zu erkennen, wie die einzelnen Komponenten des Jahresabschlusses entstehen, werden Sie in die allgemeine Buchführungstechnik eingeführt. Es werden unter anderem
die Grundzüge der doppelten Buchführung,
das Wesen verschiedener Kontenarten,
die Verbuchung von Geschäftsvorfällen,
der Kontenabschluss sowie
die buchhalterische Ermittlung des Unternehmenserfolges
vorgestellt, wobei zunächst allgemeine Kontenbezeichnungen verwendet werden. Zur Herstellung des Praxisbezuges wird dann der Industriekontenrahmen eingeführt, dessen Kontennummern in den Folgekapiteln Grundlage für die Verbuchung von Geschäftsvorfällen ist. Im Rahmen der Vorstellung dieser allgemeinen Buchführungstechnik, wird im Kapitel A aus didaktischen Gründen auf die Berücksichtigung der Umsatzsteuer verzichtet. Diese wird erst in Kapitel C eingeführt. = = = =
1.
Gliederung des betrieblichen Rechnungswesens
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4
A. Technik und Ergebnis der Buchführung
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2.1 Organisation táÉ= ÄÉêÉáíë= áã= îçêÜÉêÖÉÜÉåÇÉå= ^ÄëÅÜåáíí= Éêï®Üåí= ïìêÇÉI= ÇçâìãÉåíáÉêí= ÇáÉ= cáJ å~åòÄìÅÜÜ~äíìåÖ= áå= òïÉá= ÖÉíêÉååíÉå= _ΩÅÜÉêå= ~ääÉ= ïáêíëÅÜ~ÑíäáÅÜÉå= sçêÖ®åÖÉ= EëçÖK= dÉëÅÜ®ÑíëîçêÑ®ääÉFI= ÇáÉ= ÇÉå= _ÉíêáÉÄ= áååÉêÜ~äÄ= ÉáåÉê= ^ÄêÉÅÜåìåÖëéÉêáçÇÉ= ÄÉêΩÜJ êÉåK=aáÉëÉê=~ìÅÜ=~äë=dÉëÅÜ®Ñíëà~Üê=ÄÉòÉáÅÜåÉíÉ=wÉáíê~ìã=ìãÑ~ëëí=ã~ñáã~ä=NO=jçJ å~íÉI= ÄÉÖáååí= áå= ÇÉê= oÉÖÉä= ~ã= MNKMNK= ìåÇ= ÉåÇÉí= ~ã= PNKNOK= bê∏ÑÑåÉí= Éáå= dÉëÅÜ®ÑíëJ ã~åå=ëÉáå=råíÉêåÉÜãÉå=åìå=~ÄÉê=òK_K=áã=^ìÖìëíI=ëç=â~åå=Éê=~ìÅÜ=Éáå=îçã=h~äÉåJ ÇÉêà~Üê= ~ÄïÉáÅÜÉåÇÉë= dÉëÅÜ®Ñíëà~Üê= ï®ÜäÉåK= píÉääí= Éáå= dÉëÅÜ®Ñíëã~åå= ëÉáåÉå= dÉJ ëÅÜ®ÑíëÄÉíêáÉÄ= áã= ä~ìÑÉåÇÉå= dÉëÅÜ®Ñíëà~Üê= ÉáåI= ëç= â~åå= Ç~ë= dÉëÅÜ®Ñíëà~Üê= ~ìÅÜ= âΩêòÉê=~äë=NO=jçå~íÉ=ëÉáåK=bÖ~ä=ïáÉ=ä~åÖ=Ç~ë=dÉëÅÜ®Ñíëà~Üê=~ÄÉê=~ìÅÜ=ëÉáå=ã~ÖI=~ääÉ= ~ìÑíêÉíÉåÇÉå=dÉëÅÜ®ÑíëîçêÑ®ääÉ=ãΩëëÉå=äΩÅâÉåäçë=~ìÑÖÉòÉáÅÜåÉí=ïÉêÇÉåK= aáÉëÉ= ^ìÑòÉáÅÜåìåÖ= ~ääÉê= sçêÑ®ääÉ= EÄòïK= bê∏ÑÑåìåÖëÄìÅÜìåÖÉåI= ä~ìÑÉåÇÉ= _ìÅÜìåJ ÖÉåI= ^ÄëÅÜäìëëÄìÅÜìåÖÉåF= áå= ÅÜêçåçäçÖáëÅÜÉê= oÉáÜÉåÑçäÖÉ= áëí= dêìåÇä~ÖÉ= ÇÉê= ÖÉJ ë~ãíÉå= _ìÅÜÑΩÜêìåÖK= páÉ= ÉêÑçäÖí= ~ìÑÖêìåÇ= ÇÉê= îçêäáÉÖÉåÇÉå= _ÉäÉÖÉ= áã= dêìåÇJ ÄìÅÜK= _Éá= ÇÉê= ë~ÅÜäáÅÜÉå= ^ìÑÄÉêÉáíìåÖ= ïÉêÇÉå= ~ääÉ= ^ìÑòÉáÅÜåìåÖÉå= ~ìë= ÇÉã= dêìåÇÄìÅÜ= ~ìÑ= ÇáÉ= qJhçåíÉå= ÇÉë=e~ìéíÄìÅÜÉë= ΩÄÉêíê~ÖÉå= EòK_K= jÉÜêìåÖÉå= ìåÇ= jáåÇÉêìåÖÉå= ÇÉë= _~åâÖìíÜ~ÄÉåë= ~ìÑ= Ç~ë= hçåíç= _~åâFK= ^ìÅÜ= ÑΩê= ÇáÉ= _áä~åòÉå= áëí= áã=o~ÜãÉå=ÇÉê=lêÖ~åáë~íáçå=ÇÉê=_ìÅÜÑΩÜêìåÖ=Éáå=ÉáÖÉåÉë=_ìÅÜI=Ç~ë=ëçÖK=_áä~åòJ ÄìÅÜ=~åòìäÉÖÉåK=a~=ÇáÉëÉ=ÇêÉá=ëçÖK=póëíÉãÄΩÅÜÉê=åìê=ïÉêíã®≈áÖÉ=^ìÑòÉáÅÜåìåJ ÖÉå=ÇÉê=dÉëÅÜ®ÑíëîçêÖ®åÖÉ=ÉåíÜ~äíÉåI=ïÉêÇÉå=ëáÉ=ìã=ãÉåÖÉåã®≈áÖÉ=^ìÑòÉáÅÜåìåJ ÖÉå= áå= ÇÉå= ëçÖK= kÉÄÉåÄΩÅÜÉêå= EòK_K= hìåÇÉåÄìÅÜW= rãÑ~åÖ= ìåÇ= e®ìÑáÖâÉáí= îçå= _ÉëíÉääìåÖÉåF= ÉêÖ®åòíK= aÉå= wìë~ããÉåÜ~åÖ= ÇáÉëÉê= _ΩÅÜÉê= òÉáÖí= ÑçäÖÉåÇÉ= ^ÄÄáäJ ÇìåÖK= = =
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6
A. Technik und Ergebnis der Buchführung =
2.2 Ergebnis 2.2.1
Grundlegendes
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^ääÖÉãÉáå=ÉêÑΩääí=ÇÉê=g~ÜêÉë~ÄëÅÜäìëë=ÑçäÖÉåÇÉ=cìåâíáçåÉåW= açâìãÉåí~íáçåëÑìåâíáçåW= aìêÅÜ= p~ããäìåÖ= ìåÇ= ^ìÑÄÉêÉáíìåÖ= îçå= j~íÉêá~äI= ëóëíÉã~íáëÅÜÉ= ^ìÑòÉáÅÜåìåÖI= òìÖêáÑÑëÄÉêÉáíÉ= ^êÅÜáîáÉêìåÖ= ìåÇ= ^ìÑòÉáÅÜåìåÖ= ë®ãíäáÅÜÉê=dÉëÅÜ®ÑíëîçêÑ®ääÉ=E¬=OPU=f=pK=P=ed_W=dÉëÅÜ®ÑíëîçêÑ®ääÉ=ãΩëëÉå=ëáÅÜ= áå=áÜêÉê=båíëíÉÜìåÖ=ìåÇ=^ÄïáÅâäìåÖ=îÉêÑçäÖÉå=ä~ëëÉåF=ïáêÇ=ÉáåÉ=k~ÅÜéêΩÑÄ~êJ âÉáí= áã= eáåÄäáÅâ= ~ìÑ= í~íë®ÅÜäáÅÜÉ= çÇÉê= îÉêãÉáåíäáÅÜÉ= mÑäáÅÜíîÉêäÉíòìåÖÉå= ÇÉë= _áä~åòÉêëíÉääÉêë=ÖÉï®ÜêäÉáëíÉíK= fåÑçêã~íáçåëÑìåâíáçåW=dÉã®≈=¬=OPU=f=pK=O=ed_=ãìëë=_ìÅÜÑΩÜêìåÖ=ìåÇ=Ç~ãáí= ~ìÅÜ= ÇÉê= g~ÜêÉë~ÄëÅÜäìëë= ëç= ÄÉëÅÜ~ÑÑÉå= ëÉáåI= Ç~ëë= ëáÅÜ= Éáå= ë~ÅÜîÉêëí®åÇáÖÉê= aêáííÉê= àÉÇÉêòÉáí= Éáå= _áäÇ= ΩÄÉê= ÇáÉ= ïáêíëÅÜ~ÑíäáÅÜÉ= i~ÖÉ= ìåÇ= båíïáÅâäìåÖ= ÇÉë= råíÉêåÉÜãÉåë=ã~ÅÜÉå=â~ååK=_Éá=h~éáí~äÖÉëÉääëÅÜ~ÑíÉå=áëí=Ç~ÄÉá=ÄÉëçåÇÉêë=ÇáÉ= sÉêã∏ÖÉåëJI=cáå~åòJ=ìåÇ=bêíê~Öëä~ÖÉ=E¬=OPU=ff=ed_F=îçå=fåíÉêÉëëÉK= aáÉ=sÉêã∏ÖÉåëä~ÖÉ=ÖáÄí=^ìÑëÅÜäìëë=Ç~êΩÄÉêI=ïáÉ=îáÉä=sÉêã∏ÖÉå=òìê=pÅÜìäÇÉåJ ÇÉÅâìåÖ= îçêÜ~åÇÉå= áëíK= dÉê~ÇÉ= ÜáÉêÄÉá= áëí= ÇáÉ= _áä~åò= EîÖäK= ^= OKOKPF= îçå= ÄÉJ ëçåÇÉêÉê= _ÉÇÉìíìåÖK= páÉ= òÉáÖí= ÇáÉ= ÉáåòÉäåÉå= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ= EòK_K= =
2. Organisation und Ergebnis der Finanzbuchhaltung
7
dêìåÇëíΩÅâÉI=dÉÄ®ìÇÉI=j~ëÅÜáåÉåI=c~ÜêòÉìÖÉI=sçêê®íÉI=_~åâÖìíÜ~ÄÉåI=ìëïKF= ìåÇ= pÅÜìäÇÉå= EòK_K= a~êäÉÜÉåI= iáÉÑÉê~åíÉåîÉêÄáåÇäáÅÜâÉáíÉåI= ìëïKF= òì= ÉáåÉã= ÖÉïáëëÉå= wÉáíéìåâí= E_áä~åòëíáÅÜí~Ö= Z= áK= ÇK= oK= båÇÉ= ÇÉë= dÉëÅÜ®Ñíëà~ÜêÉëF= ~ìÑK= sÉêÑΩÖí= Éáå= råíÉêåÉÜãÉå= ~äëç= ÄÉáëéáÉäëïÉáëÉ= ΩÄÉê= ÉáåÉå= ÜçÜÉå= pÅÜìäJ ÇÉåëí~åÇ=ìåÇ=Éáå=ÖÉêáåÖÉë=sÉêã∏ÖÉåI=áëí=ëÉáåÉ=hêÉÇáíïΩêÇáÖâÉáí=ÖÉêáåÖK= _Éá= ÇÉê= _Éíê~ÅÜíìåÖ= ÇÉê= cáå~åòä~ÖÉ= ÄÉÑ~ëëí= ã~å= ëáÅÜ= Ü~ìéíë®ÅÜäáÅÜ= ãáí= ÇÉã= dê~Ç=ÇÉê=iáèìáÇáÉêÄ~êâÉáí=îçå=sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉåK=pç=ëáåÇ=ÄÉáëéáÉäëïÉáJ ëÉ=cçêÇÉêìåÖÉå=ãáí=ÉáåÉê=oÉëíä~ìÑòÉáí=îçå=ãÉÜê=~äë=ÉáåÉã=g~Üê=E¬=OSU=fs=ed_F= ìåÇ=sÉêÄáåÇäáÅÜâÉáíÉå=ãáí=ÉáåÉê=oÉëíä~ìÑòÉáí=îçå=ïÉåáÖÉê=~äë=ÉáåÉã=g~Üê=E¬=OSU= s=ed_F=ÖÉëçåÇÉêí=~ìëòìïÉáëÉåK= aáÉ=bêíê~Öëä~ÖÉ=ÖáÄí=ÄÉáëéáÉäëïÉáëÉ=^ìÑëÅÜäìëë=ΩÄÉê=ÇáÉ=sÉêòáåëìåÖ=ÇÉë=áåîÉëJ íáÉêíÉå=h~éáí~äë=EZ=dÉïáååFK=j~å=ëÅÜÉåâí=ÜáÉê=Ç~ÜÉê=ÇÉê=dÉïáååJ=ìåÇ=sÉêäìëíJ êÉÅÜåìåÖ= EdìsF= ÄÉëçåÇÉêÉ= ^ìÑãÉêâë~ãâÉáíK= rã= ÇáÉë= òì= Éêâä®êÉå= ãìëë= òìJ å®ÅÜëí= Éíï~ë= ~ìëÖÉÜçäí= ïÉêÇÉåK= aáÉ= aáÑÑÉêÉåò= ~ìë= sÉêã∏ÖÉå= ìåÇ= pÅÜìäÇÉå= ÄÉòÉáÅÜåÉí= ã~å= ~äë= oÉáåîÉêã∏ÖÉå= çÇÉê= báÖÉåâ~éáí~äK= aáÉ= sÉê®åÇÉêìåÖ= ÇÉë= báÖÉåâ~éáí~äë= áååÉêÜ~äÄ= ÉáåÉë= dÉëÅÜ®Ñíëà~ÜêÉë= ïáêÇ= áå= ÇÉê= dÉïáååJ= ìåÇ= sÉêJ äìëíêÉÅÜåìåÖ= Ç~êÖÉëíÉääíK= báåÉ= éçëáíáîÉ= sÉê®åÇÉêìåÖ= ÄòïK= ÉáåÉ= wìå~ÜãÉ= ÇÉë= báÖÉåâ~éáí~äë= ÄÉòÉáÅÜåÉí= ã~å= ~äë= dÉïáååI= ÉáåÉ= åÉÖ~íáîÉ= sÉê®åÇÉêìåÖ= ÄòïK= ^Äå~ÜãÉ= ~äë= sÉêäìëíK= báå= råíÉêåÉÜãÉåI= ïÉäÅÜÉë= ~äëç= ÄÉáëéáÉäëïÉáëÉ= ΩÄÉê= ãÉÜêÉêÉ=dÉëÅÜ®Ñíëà~ÜêÉ=ÜáåïÉÖ=ëíÉíë=åìê=dÉïáååÉ=ÉêòáÉäí=Ü~íI=îÉêÑΩÖí=ΩÄÉê=ÉáJ åÉ=ëÉÜê=éçëáíáîÉ=bêíê~Öëä~ÖÉ=ìåÇ=ëç=~ìÅÜ=ΩÄÉê=ÉáåÉ=ÜçÜÉ=hêÉÇáíïΩêÇáÖâÉáíK= ^ìëëÅÜΩííìåÖëÄÉãÉëëìåÖëÑìåâíáçåW= dêìåÇä~ÖÉ= ÑΩê= ÇáÉ=^ìëëÅÜΩííìåÖ= ÇÉê= aáîáJ ÇÉåÇÉ= ~å= ^âíáçå®êÉ= áëí= ÇÉê= g~ÜêÉë~ÄëÅÜäìëë= å~ÅÜ=e~åÇÉäëêÉÅÜíK= bê= áëí= ëçïçÜä= _~ëáë= ÑΩê= ÇáÉ= bêÑçäÖëÉêãáííäìåÖ= E_ÉëíáããìåÖ= ÇÉê= _ÉïÉêíìåÖëçÄÉêÖêÉåòÉå= ÑΩê= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ= ìåÇ= _ÉïÉêíìåÖëìåíÉêÖêÉåòÉå= ÑΩê= pÅÜìäÇÉåX= íÜÉã~íáJ ëáÉêí= áå= h~éáíÉä= aF= ~äë= ~ìÅÜ= ÇáÉ= bêÑçäÖëîÉêïÉåÇìåÖ= Ee∏ÅÜëí~ìëëÅÜΩííìåÖI= oΩÅâä~ÖÉåÄáäÇìåÖX=îÖäK=ÉÄÉåÑ~ääë=h~éáíÉä=aFK== píÉìÉêÄÉãÉëëìåÖëÖêìåÇä~ÖÉW= aÉê= g~ÜêÉë~ÄëÅÜäìëë= å~ÅÜ= píÉìÉêêÉÅÜí= áëí= ÇáÉ= dêìåÇä~ÖÉ=ÑΩê=ÇáÉ=bêãáííäìåÖ=ÇÉê=bêíê~ÖëëíÉìÉêåK= dä®ìÄáÖÉêëÅÜìíòW= aáÉ= Ü~åÇÉäëêÉÅÜíäáÅÜÉå= sçêëÅÜêáÑíÉå= îÉêÑçäÖÉå= ~äë= oÉÅÜJ åìåÖëäÉÖìåÖëòïÉÅâ=îçêê~åÖáÖ=ÇÉå=dä®ìÄáÖÉêëÅÜìíòK=aÉê=h~ìÑã~åå=Ç~êÑ=ëÉáåÉ= sÉêã∏ÖÉåëJ=ìåÇ=bêíê~Öëä~ÖÉ=åáÅÜí=ÖΩåëíáÖÉê=Ç~êëíÉääÉå=~äë=ëáÉ=ïáêâäáÅÜ=áëíK=
=
2.2.2
Inventur und Inventar
2.2.2.1
Inventar
gÉÇÉê=h~ìÑã~åå=Ü~í=òì=_ÉÖáåå=ìåÇ=båÇÉ=ëÉáåÉë=e~åÇÉäëÖÉïÉêÄÉë=ìåÇ=òìã=båÇÉ= àÉÇÉë= dÉëÅÜ®Ñíëà~ÜêÉë= E_áä~åòëíáÅÜí~ÖíáÅÜí~ÖF= ëÉáåÉ= ë®ãíäáÅÜÉå= sÉêã∏ÖÉåëÖÉÖÉåëJ í®åÇÉ=ìåÇ=pÅÜìäÇÉå=ÖÉå~ì=òì=îÉêòÉáÅÜåÉå=ìåÇ=ÇÉå=tÉêí=ÇÉê=ÉáåòÉäåÉå=mçëáíáçåÉå= ~åòìÖÉÄÉå= E¬= OQM= f= ed_I= ¬= NQN= ^lFK= báå= ëçäÅÜÉë= sÉêòÉáÅÜåáë= ÇÉê= sÉêã∏ÖÉåëJ ÖÉÖÉåëí®åÇÉ= ìåÇ= pÅÜìäÇÉå= å~ÅÜ= ^êí= Ej~êâÉI= qóéFI= jÉåÖÉ= EpíΩÅâI= âÖI= ãI= äF= ìåÇ= tÉêí= Eáå= bìêçF= ÄÉòÉáÅÜåÉí= ã~å= ~äë= fåîÉåí~êK= bë= ëáåÇ= ~ääÉ= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ= ìåÇ=pÅÜìäÇÉå=ÖêìåÇë®íòäáÅÜ=ÉáåòÉäå=~ìÑòìòÉáÅÜåÉåI=ëç=Ç~ëë=Éë=çÑí=ìãÑ~åÖêÉáÅÜ=ìåÇ= ìåΩÄÉêëáÅÜíäáÅÜ=ïáêÇK=a~ë=fåîÉåí~ê=áëí=NM=g~ÜêÉ=ä~åÖ=E~Ä=pÅÜäìëë=ÇÉë=^ìÑëíÉääìåÖëà~ÜJ êÉëF=~ìÑòìÄÉï~ÜêÉå=ìåÇ=ïáêÇ=Éíï~=ïáÉ=ÑçäÖí=ÖÉÖäáÉÇÉêíW= =
=
8
A. Technik und Ergebnis der Buchführung =
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_K= pÅÜìäÇÉå= fK= i~åÖÑêáëíáÖÉ=pÅÜìäÇÉå= i~åÖÑêáëíáÖÉ=_~åâîÉêÄáåÇäáÅÜâÉáíÉå= ffK= hìêòÑêáëíáÖÉ=pÅÜìäÇÉå= hìêòÑêáëíáÖÉ=_~åâîÉêÄáåÇäáÅÜâÉáíÉå= sÉêÄáåÇäáÅÜâÉáíÉå=~ìë=iáÉÑÉêìåÖÉå=ìåÇ=iÉáëíìåÖÉå= =
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a~ë= rãä~ìÑîÉêã∏ÖÉå= îÉê®åÇÉêí= ëáÅÜ= ëí®åÇáÖ= ìåÇ= ï~åÇÉäí= ëáÅÜ= áå= ~åÇÉêÉ= cçêãÉå= ìã= EòK_K= cçêÇÉêìåÖÉå= áå= _~åâÖìíÜ~ÄÉåFK= fÜã= ïÉêÇÉå= sÉêã∏ÖÉåëJ éçëíÉå= òìÖÉçêÇåÉíI= ÇáÉ= åìê= îçêΩÄÉêÖÉÜÉåÇ= áå= ÇÉê= råíÉêåÉÜãìåÖ= ÖÉÄìåÇÉå= ëáåÇ= ErãâÉÜêëÅÜäìëë= ~ìë= ¬= OQT= ff= ed_FK= aáÉ= ^åçêÇåìåÖ= ÇÉê= mçëíÉå= ÉêÑçäÖí= å~ÅÜ=ëíÉáÖÉåÇÉê=iáèìáÇáí®í=E_~êÖÉäÇå®ÜÉFK=
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2. Organisation und Ergebnis der Finanzbuchhaltung
9
a~ë= ëçÖK= oÉáåîÉêã∏ÖÉå= EbáÖÉåâ~éáí~äF= òÉáÖí= ~åI= áå= ïÉäÅÜÉê= e∏ÜÉ= ÇÉê= _ÉJ íêáÉÄëáåÜ~ÄÉê=EdÉëÉääëÅÜ~ÑíÉêF=ÉáÖÉåÉë=h~éáí~ä=áã=råíÉêåÉÜãÉå=ÉáåÖÉëÉíòí=Ü~íK= bë=Ü~åÇÉäí=ëáÅÜ=~äëç=ÜáÉê=ìã=dÉäÇãáííÉäI=ÇáÉ=ÇÉê=råíÉêåÉÜãìåÖ=ìåÄÉÑêáëíÉí=òìê= sÉêÑΩÖìåÖ=ëíÉÜÉåK= cΩê= ÇáÉ= ^ìÑÖäáÉÇÉêìåÖ= ÇÉë= sÉêã∏ÖÉåë= ìåÇ= ÇÉê= pÅÜìäÇÉå= áååÉêÜ~äÄ= ÇÉë= fåîÉåí~êë= ÖáÄí=Éë=âÉáåÉ=ÖÉëÉíòäáÅÜÉå=sçêëÅÜêáÑíÉåK=bë=ÉãéÑáÉÜäí=ëáÅÜ=~ÄÉêI=ëáÅÜ=~å=ÇáÉ=ÑΩê=h~éáJ í~äÖÉëÉääëÅÜ~ÑíÉå=îçêÖÉëÅÜêáÉÄÉåÉ=_áä~åòÖäáÉÇÉêìåÖ=å~ÅÜ=¬=OSS=ed_=òì=Ü~äíÉåK= ⌦= ^äë= _ÉáëéáÉä= ÑΩê= Éáå= íóéáëÅÜÉë= fåîÉåí~ê= ÉáåÉë= ãáííÉäëí®åÇáëÅÜÉå= råíÉêåÉÜãÉåë= òìã= wÉáíéìåâí=ÇÉê=dÉëÅÜ®ÑíëÖêΩåÇìåÖ=ÄÉíê~ÅÜíÉ=ã~å=cçäÖÉåÇÉëW= =
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10
A. Technik und Ergebnis der Buchführung
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= 2.2.2.2
Inventur
rã=~ääÉ=å∏íáÖÉå=a~íÉå=òìê=^ìÑëíÉääìåÖ=ÉáåÉë=fåîÉåí~êë=EìåÇ=ÇÉê=sÉêòÉáÅÜåáëëÉF=òì= ÉêÜ~äíÉåI= ëáåÇ= ~ääÉ= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ= ìåÇ= pÅÜìäÇÉå= áã= báåòÉäåÉå= ~ìÑòìåÉÜJ ãÉåK= aáÉëÉ= q®íáÖâÉáí= ÄÉòÉáÅÜåÉí= ã~å= ~äë= fåîÉåíìêK= bë= ëáåÇ= Ç~ÄÉá= ÑçäÖÉåÇÉ= _ÉJ ëí~åÇë~ìÑå~ÜãÉ~êíÉå=òì=ìåíÉêëÅÜÉáÇÉåW= =
2. Organisation und Ergebnis der Finanzbuchhaltung
11
báåÉ= â∏êéÉêäáÅÜÉ= _Éëí~åÇë~ìÑå~ÜãÉ= ÖÉëÅÜáÉÜí= ÄÉá= ã~íÉêáÉääÉå= dÉÖÉåëí®åJ ÇÉåI= ïáÉ= Éíï~= j~ëÅÜáåÉå= çÇÉê= oçÜëíçÑÑÉå= ÇìêÅÜ= jÉëëÉåI= táÉÖÉå= çÇÉê= w®ÜJ äÉåK= páÉ= â~åå= ~äë= sçääJ= E^ìÑå~ÜãÉ= ~ääÉê= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉF= çÇÉê= ~äë= píáÅÜéêçÄÉåáåîÉåíìê= EqÉáäÉêÜÉÄìåÖ= ìåÇ= eçÅÜêÉÅÜåìåÖ= ~ìÑ= ÇáÉ= àÉïÉáäáÖÉ= dêìåÇÖÉë~ãíÜÉáí=å~ÅÜ=¬=OQN=f=ed_F=ÇìêÅÜÖÉÑΩÜêí=ïÉêÇÉåK=_Éá=dΩíÉêå=ÖÉêáåJ ÖÉå= tÉêíÉëI= ÇáÉ= ëáÅÜ= åìê= ëÅÜïÉê= ~ìÑåÉÜãÉå= ä~ëëÉå= EpÅÜΩííÖΩíÉêI= òK_K= p~åÇFI= ëáåÇ=~ìÅÜ=pÅÜ®íòìåÖÉå=òìä®ëëáÖK=
báåÉ= ÄìÅÜã®≈áÖÉ= _Éëí~åÇë~ìÑå~ÜãÉ= E_ìÅÜJ= çÇÉê= _ÉäÉÖáåîÉåíìêF= áëí= ÄÉá= áãã~íÉêáÉääÉå= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉå= EòK_K= m~íÉåíÉFI= _~åâÖìíÜ~ÄÉåI= cçêÇÉJ êìåÖÉå= ìåÇ= pÅÜìäÇÉå= ÇìêÅÜ= _ìÅÜÑΩÜêìåÖëìåíÉêä~ÖÉåI= _ÉäÉÖÉ= ìåÇ= ^ìÑòÉáÅÜJ åìåÖÉå= EòK_K= oÉÅÜåìåÖÉåI= sÉêíê®ÖÉI= rêâìåÇÉåI= m~íÉåíÇçâìãÉåíÉF= ã∏ÖäáÅÜK= rã= ÇáÉ= _ÉïÉáëâê~Ñí= ÇÉê= _ÉäÉÖáåîÉåíìê= òì= ÉêÜ∏ÜÉåI= ïÉêÇÉå= Ü®ìÑáÖ= ÇáÉ= dÉJ ëÅÜ®Ñíëé~êíåÉê=EòK_K=_~åâF=~åÖÉëÅÜêáÉÄÉå=ìã=p~äÇÉåÄÉëí®íáÖìåÖÉå=ÉáåòìÜçäÉåK= _Éá= p~ÅÜ~åä~ÖÉîÉêã∏ÖÉå= áëí= ïÉÖÉå= ÇÉê= áKÇKoK= ÖìíÉå= §ÄÉêëÅÜ~ìÄ~êâÉáí= ÉáåÉ= à®ÜêäáÅÜÉ= â∏êéÉêäáÅÜÉ= bêÑ~ëëìåÖ= åáÅÜí= ÉêÑçêÇÉêäáÅÜI= ïÉåå= ÇÉê= _Éëí~åÇ= ~ã= _áJ ä~åòëíáÅÜí~Ö==~ìÑÖêìåÇ=ä~ìÑÉåÇÉê=_ÉêΩÅâëáÅÜíáÖìåÖ=~ääÉê=wìJ=ìåÇ=^ÄÖ®åÖÉ=ÇÉë= dÉëÅÜ®Ñíëà~ÜêÉë= ìåÇ= ÉáåÉê= tÉêíÑçêíëÅÜêÉáÄìåÖ= EwìJ= ìåÇ= ^ÄëÅÜêÉáÄìåÖÉåF= ~ìë= ÉáåÉã= ëçÖK= ä~ìÑÉåÇÉå= _Éëí~åÇëîÉêòÉáÅÜåáë= EfåÜ~äíW= ÖÉå~ìÉ= _ÉòÉáÅÜåìåÖ= ÇÉë= dÉÖÉåëí~åÇÉëI=q~Ö=ÇÉê=_ÉëÅÜ~ÑÑìåÖLeÉêëíÉääìåÖI=e∏ÜÉ=ÇÉê=^åëÅÜ~ÑÑìåÖëJ=ìåÇ= eÉêëíÉääìåÖëâçëíÉåI=tÉêí=~ã=_áä~åòëíáÅÜí~ÖI=q~Ö=ÇÉë=^ÄÖ~åÖëF=ÉêãáííÉäÄ~ê=áëíK= báå= ëçäÅÜÉë= sÉêòÉáÅÜåáë= ïáêÇ= ëíÉìÉêêÉÅÜíäáÅÜ= äÉÇáÖäáÅÜ= ÑΩê= ÄÉïÉÖäáÅÜÉ= ^åä~ÖÉJ ÖΩíÉê=îÉêä~åÖí=Eo=RKQ=f=bpíoFK=råÄÉïÉÖäáÅÜÉ=^åä~ÖÉÖΩíÉê=â∏ååÉå=~åÜ~åÇ=îçå= ^åä~ÖÉåâçåíÉåI=^åä~ÖÉâ~êíÉáÉå=ìåÇ=dêìåÇÄìÅÜ~ìëòΩÖÉå=ÉêÑ~ëëí=ïÉêÇÉåK=
aìêÅÜ=ÇáÉ=fåîÉåíìê=ÄòïK=Ç~ë=fåîÉåí~ê=ä~ëëÉå=ëáÅÜ=ÄÉáëéáÉäëïÉáëÉ=pÅÜïìåÇI=sÉêÇÉêJ ÄÉå= çÇÉê= aáÉÄëí~Üä= îçå= ÖÉä~ÖÉêíÉå= oçÜëíçÑÑJI= bêòÉìåÖáëJ= çÇÉê= t~êÉåîçêê®íÉå= ìåÇ= _áä~åòÑ®äëÅÜìåÖÉå= ÇìêÅÜ= Ç~ë= j~å~ÖÉãÉåí= ÄòïK= Ç~ë= _ÉíêáÉÄëéÉêëçå~ä= ~ìÑÇÉÅâÉå= ìåÇ=å~ÅÜïÉáëÉåK=fåîÉåíìê=ìåÇ=fåîÉåí~ê=ÉêÑΩääÉå=ÇÉãå~ÅÜ=ÉáåÉ=pÅÜìíòÑìåâíáçå=ÑΩê= dä®ìÄáÖÉê=ìåÇ=dÉëÉääëÅÜ~ÑíÉêK=tÉáÅÜÉå=ÇáÉ=í~íë®ÅÜäáÅÜÉå=fåîÉåíìêÄÉëí®åÇÉ=îçå=ÇÉå= áå= ÇÉå= _ΩÅÜÉêå= îÉêòÉáÅÜåÉíÉå= ~ÄI= ëç= ëáåÇ= ÇÉãÉåëéêÉÅÜÉåÇ= hçêêÉâíìêÉå= îçêòìJ åÉÜãÉå=Ełj~≈ÖÉÄäáÅÜâÉáí=ÇÉë=fåîÉåí~êë=ÑΩê=ÇÉå=g~ÜêÉë~ÄëÅÜäìëë FK= = = =
2.2.3
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2.2.3.1
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12
A. Technik und Ergebnis der Buchführung
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2. Organisation und Ergebnis der Finanzbuchhaltung
13
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14
A. Technik und Ergebnis der Buchführung
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2.2.3.2
Gesetzliche Gliederungsvorschriften
cΩê= ÇáÉ= píÉìÉêÄáä~åò= îçå= h~éáí~äÖÉëÉääëÅÜ~ÑíÉå= ÖáÄí= Éë= âÉáåÉ= däáÉÇÉêìåÖëîçêJ ëÅÜêáÑíÉåK= få= ÇÉê= mê~ñáë= ïáêÇ= àÉÇçÅÜ= áKÇKoK= ÇáÉ= däáÉÇÉêìåÖ= ÇÉê= e~åÇÉäëÄáä~åò=ΩÄÉêJ íê~ÖÉåK= dêç≈Éå= h~éáí~äÖÉëÉääëÅÜ~ÑíÉå= E¬= OST= ff= ed_F= áëí= ÉáåÉ= jáåÇÉëíÖäáÉÇÉêìåÖ= ÑΩê= ÇáÉ= e~åÇÉäëÄáä~åò= Eå~ÅÜ= ¬= OSS= ff= ìåÇ= fff= ed_F= îÉêÄáåÇäáÅÜ= îçêÖÉëÅÜêáÉÄÉåK= ^ìÅÜ= ÇáÉ= oÉáÜÉåÑçäÖÉ=ÇÉê=mçëáíáçåÉå=ãìëë=ÉáåÖÉÜ~äíÉå=ïÉêÇÉå=E¬=OSS=f=pK=O=ed_FK=däÉáÅÜÉë= Öáäí= ÑΩê= báåòÉäìåíÉêåÉÜãÉå= ìåÇ= mÉêëçåÉåÜ~åÇÉäëÖÉëÉääëÅÜ~ÑíÉåI= ÇáÉ= ìåíÉê= Ç~ë= mìÄäd=Ñ~ääÉå=E¬=R=f=mìÄädFK=^ìÑ=~ääÖÉãÉáåÉ=däáÉÇÉêìåÖëÖêìåÇë®íòÉ=E¬=OSR=ed_F=ìåÇ= =
2. Organisation und Ergebnis der Finanzbuchhaltung
15
bêïÉáíÉêìåÖÉå= ÇÉê= jáåÇÉëíÖäáÉÇÉêìåÖ= EòK_K= ¬¬= OSU= ffI= fsI= sX= OSVX= OTO= fX= OTQ= ed_F= ïáêÇ=ÜáÉê=åáÅÜí=å®ÜÉê=ÉáåÖÉÖ~åÖÉåK= _Éá= âäÉáåÉå= h~éáí~äÖÉëÉääëÅÜ~ÑíÉå= E¬= OST= f= ed_F= êÉáÅÜí= Éë= ~ìëI= ÉáåÉ= e~åÇÉäëÄáä~åò= ~ìÑòìëíÉääÉå=ìåÇ=òì=îÉê∏ÑÑÉåíäáÅÜÉåI=ÇáÉ=åìê=ÇáÉ=áå=¬=OSS=ff=ìåÇ=fff=ed_=ãáí=_ìÅÜJ ëí~ÄÉå=ìåÇ=ê∏ãáëÅÜÉå=w~ÜäÉå=ÄÉòÉáÅÜåÉíÉå=mçëíÉå=ÉåíÜ®äí=E¬=OSS=f=pK=P=ed_FK=aáÉ= ~ääÖÉãÉáåÉå= däáÉÇÉêìåÖëÖêìåÇë®íòÉ= ÇÉë= ¬= OSR= ed_= ìåÇ= bêïÉáíÉêìåÖÉå= ÇÉê= jáåJ ÇÉëÖäáÉÇÉêìåÖ= â∏ååÉå= ~ÄÉê= ÉáåÉ= ïÉáíÉêÉ= råíÉêÖäáÉÇÉêìåÖ= ÉêÑçêÇÉêäáÅÜ= ã~ÅÜÉåK= ^ìÅÜ=Öêç≈É=ìåÇ=ãáííÉäÖêç≈É=h~éáí~äÖÉëÉääëÅÜ~ÑíÉå=â∏ååÉå=ÖÉãK=¬=OSR=sff=ed_=ÇáÉJ ëÉ= îÉêâΩêòíÉ= a~êëíÉääìåÖ= ï®ÜäÉåI= ëçÑÉêå= áã= ^åÜ~åÖ= ~ääÉ= ΩÄêáÖÉå= mçëáíáçåÉå= ÇÉë== ¬=OSS=ff=ìåÇ=fff=ed_=ÖÉëçåÇÉêí=~åÖÉÖÉÄÉå=ëáåÇK= aáÉ=ãáííÉäÖêç≈Éå=h~éáí~äÖÉëÉääëÅÜ~ÑíÉå=E¬=OST=ff=ed_F=Ü~ÄÉå=áÜêÉ=e~åÇÉäëÄáä~åò=áå= ÖäÉáÅÜÉê= tÉáëÉ= ïáÉ= ÇáÉ= Öêç≈Éå= h~éáí~äÖÉëÉääëÅÜ~ÑíÉå= òì= ÉêëíÉääÉåK= t~ë= ÇáÉ= sÉê∏ÑJ ÑÉåíäáÅÜìåÖ= ~åÄÉä~åÖíI= ëç= ÖÉåΩÖí= ÉáåÉ=îÉêâΩêòíÉ= _áä~åò= ïáÉ= ÄÉá=ÇÉå= âäÉáåÉå= h~éáJ í~äÖÉëÉääëÅÜ~ÑíÉå= E¬= OSS= f= ed_FK= wìë®íòäáÅÜ= ãΩëëÉå= ~ÄÉê= åçÅÜ= ÄÉëíáããíÉ= mçëíÉå= ÖÉãK=¬=POT=ed_=áå=ÇÉê=_áä~åò=çÇÉê=áã=^åÜ~åÖ=ÖÉëçåÇÉêí=~åÖÉÖÉÄÉå=ïÉêÇÉåK= aÉê= sçääëí®åÇáÖâÉáí= Ü~äÄÉê= ëÉá= åçÅÜ= Éêï®ÜåíI= Ç~ëë= ÑΩê= ÉáåÉ= oÉáÜÉ= îçå= _ê~åÅÜÉå= EòK_K= hê~åâÉåÜ®ìëÉêI= sÉêâÉÜêëìåíÉêåÉÜãÉåI= hêÉÇáíáåëíáíìíÉ= ìåÇ= sÉêëáÅÜÉêìåÖëìåJ íÉêåÉÜãÉåF=å~ÅÜ=¬=PPM=ed_=~ÄïÉáÅÜÉåÇÉ=_áä~åòÖäáÉÇÉêìåÖÉå=îçêÖÉëÉÜÉå=ëáåÇK= cΩê= báåòÉäìåíÉêåÉÜãÉå= ìåÇ= mÉêëçåÉåÜ~åÇÉäëÖÉëÉääëÅÜ~ÑíÉåI= ÇáÉ= åáÅÜí= ìåíÉê= Ç~ë=mìÄäd=Ñ~ääÉåI=ÖáÄí=Éë=âÉáåÉ=ÇÉí~áääáÉêíÉ=däáÉÇÉêìåÖëîçêëÅÜêáÑí=òìê=e~åÇÉäëÄáä~åòK= få=¬=OQT=f=ed_=ïÉêÇÉå=äÉÇáÖäáÅÜ=ÇáÉ=ÉäÉãÉåí~êÉå=hçãéçåÉåíÉå=E^åä~ÖÉJI=rãä~ìÑJ îÉêã∏ÖÉåI=báÖÉåâ~éáí~äI=pÅÜìäÇÉåI=oÉÅÜåìåÖë~ÄÖêÉåòìåÖëéçëíÉåF=çÜåÉ=cÉëíäÉÖìåÖ= ÉáåÉê= oÉáÜÉåÑçäÖÉ= ÖÉå~ååíK= aáÉëÉ= jáåÇÉëíÖäáÉÇÉêìåÖ= áëí= ~ääÉêÇáåÖë= ãáí= ÇÉê= cçêÇÉJ êìåÖ=îÉêÄìåÇÉåI=ÉáåÉ=ÜáåêÉáÅÜÉåÇÉ=^ìÑÖäáÉÇÉêìåÖ=ìåíÉê=_É~ÅÜíìåÖ=ÇÉê=dç_=îçêòìJ åÉÜãÉåK= pç= ãΩëëÉå= ÄÉáëéáÉäëïÉáëÉ= råíÉêéçëíÉå= Éñ~âí= ÄÉÖêáÑÑäáÅÜ= îçåÉáå~åÇÉê= ~ÄJ ÖÉÖêÉåòíI=p~äÇáÉêìåÖÉå=EsÉêêÉÅÜåìåÖLwìë~ããÉåÑ~ëëìåÖ=îÉêëÅÜáÉÇÉåÉê=mçëíÉåF=îÉêJ ãáÉÇÉå= ìåÇ= ÉáåÉ= Éáåã~ä= ÖÉï®ÜäíÉ= däáÉÇÉêìåÖ= áå= wìâìåÑí= ÄÉáÄÉÜ~äíÉå= ïÉêÇÉåK= ^ì≈ÉêÇÉã= ïáêÇ= ÇáÉëÉ= jáåÇÉëíÖäáÉÇÉêìåÖ= åçÅÜ= ÇìêÅÜ= ÉáåÉ= oÉáÜÉ= îçå= pçåÇÉêîçêJ ëÅÜêáÑíÉå=E¬¬=OQT=fffI=OQVI=ORN=ed_F=ÉêÖ®åòíK= k~ÅÜ=Ö®åÖáÖÉê=jÉáåìåÖ=ëçääíÉå=ÇáÉ=däáÉÇÉêìåÖëîçêëÅÜêáÑíÉå=ÑΩê=âäÉáåÉ=h~éáí~äÖÉëÉääJ ëÅÜ~ÑíÉå= E¬= OSS= f= ed_F= ^åÜ~äíëéìåâíÉ= ÑΩê= ÇáÉ= e~åÇÉäëÄáä~åò= îçå= báåòÉäìåíÉêåÉÜJ ãÉå=ìåÇ=mÉêëçåÉåÜ~åÇÉäëÖÉëÉääëÅÜ~ÑíÉå=ëÉáåK= cΩê=ÇáÉ=däáÉÇÉêìåÖ=ÇÉê=píÉìÉêÄáä~åò=ÖáÄí=Éë=âÉáåÉêäÉá=sçêëÅÜêáÑíÉåK=^ìÅÜ=ÜáÉê=â∏ååJ íÉå=ÇáÉ=däáÉÇÉêìåÖëîçêëÅÜêáÑíÉå=ÑΩê=âäÉáåÉ=h~éáí~äÖÉëÉääëÅÜ~ÑíÉå=E¬=OSS=f=ed_F=ÉáåÉ= lêáÉåíáÉêìåÖëÜáäÑÉ=ëÉáåK= =
2.2.4
Gewinn- und Verlustrechnung
k~ÅÜ=¬=OQO=ff=ed_=Ü~í= àÉÇÉê=h~ìÑã~åå=åÉÄÉå=ÇÉê=_áä~åò=ÉáåÉ=dÉÖÉåΩÄÉêëíÉääìåÖ= ÇÉê=^ìÑïÉåÇìåÖÉå=ìåÇ=bêíê®ÖÉ=~ìÑòìëíÉääÉåI=ïÉäÅÜÉ=~ìÅÜ=~äë=dÉïáååJ=ìåÇ=sÉêäìëíJ êÉÅÜåìåÖ=EdìsF=ÄÉòÉáÅÜåÉí=ïáêÇK=aáÉëÉ=ëçää=ÇáÉ=bêíê~Öëä~ÖÉ=ÇÉë=råíÉêåÉÜãÉåë=~ÄJ ÄáäÇÉåI=áåÇÉã= ëáÉ= ÇÉå= bêÑçäÖ= EbáÖÉåâ~éáí~ä®åÇÉêìåÖF=å~ÅÜ= ^êíI= e∏ÜÉ= ìåÇ= nìÉääÉå= Ç~êëíÉääíK=k~ÅÜ=¬=OTR=ed_=Ç~êÑ=ÇáÉ=dìs=ÉåíïÉÇÉê=å~ÅÜ=ÇÉã=dÉë~ãíâçëíÉåîÉêÑ~ÜêÉå= EmêçÇìâíáçåëÉêÑçäÖëêÉÅÜåìåÖF= çÇÉê= å~ÅÜ= ÇÉã= rãë~íòâçëíÉåîÉêÑ~ÜêÉå= E^Äë~íòÉêJ ÑçäÖëêÉÅÜåìåÖF= ÖÉëí~äíÉí= ïÉêÇÉåK= aáÉëÉ= ÄÉáÇÉå= sÉêÑ~ÜêÉå= ïÉêÇÉå= ~ääÉêÇáåÖë= Éêëí= å~ÅÜ=_ÉÜ~åÇäìåÖ=ÇÉê=~ääÖÉãÉáåÉå=_ìÅÜìåÖëíÉÅÜåáâ=ìåíÉê=^=PKPKS=Éêâä®êíK= =
16
A. Technik und Ergebnis der Buchführung
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2. Organisation und Ergebnis der Finanzbuchhaltung
=
17
_Éá=ìåÑÉêíáÖÉå=ìåÇ=ÑÉêíáÖÉå=bêòÉìÖåáëëÉå=ÉêÖÉÄÉå=ëáÅÜ=áã=fåÇìëíêáÉÄÉíêáÉÄ=îçå= _áä~åòëíáÅÜí~Ö= òì= _áä~åòëíáÅÜí~Ö= sÉê®åÇÉêìåÖÉå= ÇÉë= i~ÖÉêÄÉëí~åÇÉëK= rã= Éáå= ~ìëë~ÖÉâê®ÑíáÖÉë= g~ÜêÉëÉêÖÉÄåáë= ÉêãáííÉäå= òì= â∏ååÉåI= ëáåÇ= i~ÖÉêÄÉëí~åÇëÉêJ Ü∏ÜìåÖÉå= ~äë= bêíê~Ö= ìåÇ= i~ÖÉêÄÉëí~åÇëîÉêãáåÇÉêìåÖÉå= ~äë= ^ìÑï~åÇ= òì= ÄìÅÜÉå=EîÖäK=`=QKTKOFK= råíÉê= ~âíáîáÉêíÉå= báÖÉåäÉáëíìåÖÉå= EîÖäK= `= VF= îÉêëíÉÜí= ã~å= ëÉäÄëí= ÉêëíÉääíÉ= dÉÖÉåëí®åÇÉ=ÇÉë=^åä~ÖÉîÉêã∏ÖÉåë=Ej~ëÅÜáåÉåI=^åä~ÖÉåI=dÉÄ®ìÇÉI=ÉíÅKFI=ÇáÉ= Ç~ë= råíÉêåÉÜãÉå= ΩÄäáÅÜÉêïÉáëÉ= ÑΩê= hìåÇÉå= ÉêëíÉääíI= áã= ÄÉíê~ÅÜíÉíÉå= c~ää= àÉJ ÇçÅÜ=ëÉäÄëí=~äë=mêçÇìâíáçåëãáííÉä=åìíòÉå=ã∏ÅÜíÉK= råíÉê= ÇÉå= ëçåëíáÖÉå= ÄÉíêáÉÄäáÅÜÉå= bêíê®ÖÉå= = EòK_K= sÉê®ì≈ÉêìåÖ= îçå= ÖÉJ Äê~ìÅÜíÉå= dÉÖÉåëí®åÇÉå= ÇÉë= ^åä~ÖÉîÉêã∏ÖÉåëF= ëáåÇ= bêíê®ÖÉ= òìë~ããÉåÖÉJ Ñ~ëëíI= ÇáÉ= ïÉÇÉê= ~ìë= ÇÉã= ^Äë~íò= ÇÉê= ÄÉíêáÉÄäáÅÜÉå= iÉáëíìåÖÉå= åçÅÜ= ~ìë= ÇÉã= cáå~åò~åä~ÖÉîÉêã∏ÖÉå=ÜÉêêΩÜêÉå=åçÅÜ=~ì≈ÉêçêÇÉåíäáÅÜÉ=bêíê®ÖÉ=ëáåÇK= wìã= j~íÉêá~ä~ìÑï~åÇ= EîÖäK= `= NKPF= ÖÉÜ∏êÉå= ^ìÑïÉåÇìåÖÉå= ÑΩê= oçÜJI= eáäÑëJ= ìåÇ=_ÉíêáÉÄëëíçÑÑÉI=ÑΩê=ÄÉòçÖÉåÉ=t~êÉå=ìåÇ=ÑΩê=ÄÉòçÖÉåÉ=aáÉåëíäÉáëíìåÖÉåK= fã= mÉêëçå~ä~ìÑï~åÇ= EîÖäK= `= PKOF= ÑáåÇÉå= ëáÅÜ= i∏ÜåÉ= ìåÇ= dÉÜ®äíÉêI= ëçòá~äÉ= ^ÄÖ~ÄÉå= ìåÇ= ^ìÑïÉåÇìåÖÉå= ÑΩê= ^äíÉêëîÉêëçêÖìåÖLråíÉêëíΩíòìåÖ= EòK_K= w~ÜJ äìåÖÉå=~å=råíÉêëíΩíòìåÖëâ~ëëÉåI=_áäÇìåÖ=îçå=mÉåëáçåëêΩÅâëíÉääìåÖÉåFK== aáÉ=^ÄëÅÜêÉáÄìåÖÉå==EîÖäK=a=OF=ëáåÇ=ìåíÉêÖäáÉÇÉêí=áå== ^ÄëÅÜêÉáÄìåÖÉå= ~ìÑ= áãã~íÉêáÉääÉ= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ= ÇÉë= ^åä~ÖÉJ îÉêã∏ÖÉåë= ìåÇ= p~ÅÜ~åä~ÖÉå= ëçïáÉ= ~âíáîáÉêíÉ= ^ìÑïÉåÇìåÖÉå= ÑΩê= ÇáÉ= fåÖ~åÖëÉíòìåÖ=ìåÇ=bêïÉáíÉêìåÖ=ÇÉë=dÉëÅÜ®ÑíëÄÉíêáÉÄë= ^ÄëÅÜêÉáÄìåÖÉå= ~ìÑ= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ= ÇÉë= rãä~ìÑîÉêã∏ÖÉåëI= ëçïÉáí=ÇáÉëÉ=ÇáÉ=áå=ÇÉê=h~éáí~äÖÉëÉääëÅÜ~Ñí=ΩÄäáÅÜÉå=^ÄëÅÜêÉáÄìåÖÉå=EàÉ= å~ÅÜ=_ê~åÅÜÉ=ìåÇ=råíÉêåÉÜãÉåëÖê∏≈É=ìåíÉêëÅÜáÉÇäáÅÜF=ΩÄÉêëÅÜêÉáíÉå= ^ì≈Éêéä~åã®≈áÖÉ=^ÄëÅÜêÉáÄìåÖÉå=ÖÉãK=¬=ORP=ff=pK=P=ed_=~ìÑ=Ç~ë=^åä~ÖÉîÉêJ ã∏ÖÉå=ëáåÇ=å~ÅÜ=¬=OTT=fff=ed_=ÖÉëçåÇÉêí=~ìëòìïÉáëÉå=çÇÉê=å®ÜÉê=áã=^åä~åÖ= òì=ÄÉëÅÜêÉáÄÉåK=båíëéêÉÅÜÉåÇÉë=Öáäí=ÑΩê=~ì≈Éêéä~åã®≈áÖÉ=^ÄëÅÜêÉáÄìåÖÉå=áã= rãä~ìÑîÉêã∏ÖÉå=ÖÉãK=¬=ORP=fff=pK=P=ed_K= råíÉê=ÇÉå=ëçåëíáÖÉå=ÄÉíêáÉÄäáÅÜÉå=^ìÑïÉåÇìåÖÉå==EòK_K=sÉêäìëíÉ=~ìë=ÇÉã= ^ÄÖ~åÖ= îçå= dÉÖÉåëí®åÇÉå= ÇÉë= ^åä~ÖÉîÉêã∏ÖÉåëI= _áäÇìåÖ= îçå= oΩÅâëíÉääìåJ ÖÉåF= ëáåÇ= ^ìÑïÉåÇìåÖÉå= òìë~ããÉåÖÉÑ~ëëíI= ÇáÉ= ïÉÇÉê= ~ìë= ÇÉã= ^Äë~íò= ÇÉê= ÄÉíêáÉÄäáÅÜÉå= iÉáëíìåÖÉå= åçÅÜ= ~ìë= ÇÉã= cáå~åò~åä~ÖÉîÉêã∏ÖÉå= ÜÉêêΩÜêÉåI== çÇÉê=~ì≈ÉêçêÇÉåíäáÅÜÉ=^ìÑïÉåÇìåÖÉå=ëáåÇK== cáå~åòÉêíê®ÖÉ=ìãÑ~ëëÉå== bêíê®ÖÉ= ~ìë= _ÉíÉáäáÖìåÖÉå= EîäÖK= `= NMFW= a~òì= ò®ÜäÉå= aáîáÇÉåÇÉå= çÇÉê= dÉïáåå~åíÉáäÉ=~ìë=_ÉíÉáäáÖìåÖÉå=E¬=OTN=f=ed_F=~å=h~éáí~äJ=çÇÉê=mÉêëçJ åÉåÜ~åÇÉäëÖÉëÉääëÅÜ~ÑíÉåK= _Éá= ÉêÜ~äíÉåÉå= dÉïáåå~ìëëÅÜΩííìåÖÉå= îçå= h~éáí~äÖÉëÉääëÅÜ~ÑíÉå= áëí= ÇÉê= _ÉíÉáäáÖìåÖëÉêíê~Ö= ÉáåëÅÜäáÉ≈äáÅÜ= ÇÉê= ~åêÉJ ÅÜÉåÄ~êÉå=h~éáí~äÉêíê~ÖJ=ìåÇ=h∏êéÉêëÅÜ~ÑíëíÉìÉê=òì=ÉêÑ~ëëÉåK= bêíê®ÖÉ= ~ìë= ~åÇÉêÉå= tÉêíé~éáÉêÉå= ìåÇ= ^ìëäÉáÜìåÖÉå= ÇÉë= cáå~åò~åä~J ÖÉîÉêã∏ÖÉåë= EîÖäK= `= NMI= NNFW= eáÉêòì= ÖÉÜ∏êÉå= aáîáÇÉåÇÉå= îçå= råíÉêJ åÉÜãÉå=òì=ÇÉåÉå=âÉáå=_ÉíÉáäáÖìåÖëîÉêÜ®äíåáë=ÄÉëíÉÜíI=wáåëÉå=~ìë=ÑÉëíJ îÉêòáåëäáÅÜÉå= tÉêíé~éáÉêÉå= ìK®K= ëçïáÉ= wáåëÉå= ~ìë= ä~åÖÑêáëíáÖÉå= a~êäÉJ ÜÉåëîÉêÖ~ÄÉåK=
18
A. Technik und Ergebnis der Buchführung
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wáåëÉå=ìåÇ=®ÜåäáÅÜÉ=^ìÑïÉåÇìåÖÉå=EîÖäK=`=NOFW=eáÉêìåíÉê=Ñ~ääÉå=wáåëJ ~ìëÖ~ÄÉå=~ìÑ=_~åâëÅÜìäÇÉåI=~ìë=âìêòÑêáëíáÖÉå=a~êäÉÜÉåëîÉêÄáåÇäáÅÜâÉáJ íÉå= ìK®K= ëçïáÉ= aáë~Öáç~ìÑïÉåÇìåÖÉåI= mêçîáëáçåë~ìÑïÉåÇìåÖÉåI= _~åâJ ëéÉëÉå=~ìë=cáåå~åòÖÉëÅÜ®ÑíÉå=ìK®K=
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2. Organisation und Ergebnis der Finanzbuchhaltung
2.2.5
19
Anhang
a~= _áä~åò= ìåÇ= dìs= åìê= èì~åíáí~íáîÉ= fåÑçêã~íáçåÉå= ÉåíÜ~äíÉå= ìåÇ= Ç~ãáí= ÑΩê= ëáÅÜ== ~ääÉáå=çÑí=ïÉåáÖ=~ìëë~ÖÉâê®ÑíáÖ=ëáåÇI=ëçääíÉ=ÇÉê=g~ÜêÉë~ÄëÅÜäìëë=òìë®íòäáÅÜÉ=fåÑçêã~J íáçåÉå= òìê= bêä®ìíÉêìåÖ= ìåÇ= a~êëíÉääìåÖ= ÇÉê= bêíê~ÖëJI= cáå~åòJ= ìåÇ= sÉêã∏ÖÉåëä~ÖÉ= ÉåíÜ~äíÉåK=aáÉëÉ=^åÑçêÇÉêìåÖ=ÉêÑΩääí=ÇÉê=ëçÖK=^åÜ~åÖK=aáÉ=_áä~åò=ìåÇ=ÇáÉ=dìs=îçå= h~éáí~äÖÉëÉääëÅÜ~ÑíÉå= ìåÇ= Ü~ÑíìåÖëÄÉëÅÜê®åâíÉå= mÉêëçåÉåÖÉëÉääëÅÜ~ÑíÉå= ëáåÇ= å~ÅÜ== ¬=OSQ=f=ed_=ìã=ÉáåÉå=^åÜ~åÖ=òì=ÉêïÉáíÉêåK=aáÉëÉê=ÉêÑΩääí=ÑçäÖÉåÇÉ=cìåâíáçåÉåW= bêä®ìíÉêìåÖ=ÇÉê=_áä~åò=ìåÇ=dìsW= bë= ïÉêÇÉå= ÄÉáëéáÉäëïÉáëÉ= ÇáÉ= ~åÖÉï~åÇíÉå= _áä~åòáÉêìåÖëJ= ìåÇ= _ÉïÉêíìåÖëJ ãÉíÜçÇÉå=Éêâä®êí=ëçïáÉ=^ÄïÉáÅÜìåÖÉå=òìã=sçêà~Üê=ÄÉÖêΩåÇÉíK= hçêêÉâíìêÑìåâíáçåW= hçêêÉâíìêÉå=ÇÉê=sÉêã∏ÖÉåëJI=cáå~åòJ=ìåÇ=bêíê~Öëä~ÖÉI=ÇáÉ=~ìÑÖêìåÇ=ÄÉëçåÇÉJ êÉê=rãëí®åÇÉ=ÉêÑçêÇÉêäáÅÜ=ëáåÇI=ïÉêÇÉå=~ìÑÖÉÑΩÜêíK= båíä~ëíìåÖ=îçå=_áä~åò=ìåÇ=dìsW= _ÉëíáããíÉ=fåÑçêã~íáçåÉå=ïÉêÇÉå=~ìë=_áä~åò=çÇÉê=dìs=áå=ÇÉå=^åÜ~åÖ=îÉêä~J ÖÉêí=EòK_K=i~ìÑòÉáíÉå=îçå=cçêÇÉêìåÖÉå=ìåÇ=sÉêÄáåÇäáÅÜâÉáíÉåFK= bêÖ®åòìåÖ=îçå=_áä~åò=ìåÇ=dìsW= wìë®íòäáÅÜÉ= fåÑçêã~íáçåÉåI= ÇáÉ= åáÅÜí= áå= _áä~åò= çÇÉê= dìs= ÉåíÜ~äíÉå= ëáåÇ= EòK_K= ^åò~Üä=ÇÉê=_ÉëÅÜ®ÑíáÖíÉåFI=ïÉêÇÉå=áã=^åÜ~åÖ=~ìÑÖÉåçããÉåK= hçåâêÉí= ÄÉáåÜ~äíÉí= ÇÉê= ^åÜ~åÖ= ìåíÉê= ~åÇÉêÉã= ÑçäÖÉåÇÉ= fåÑçêã~íáçåÉå= E¬¬= OUQ= ÑK= ed_=ìåÇ=¬=NSM=^âídFW= bêä®ìíÉêìåÖÉå=òìê=_áä~åò= ^åÖÉï~åÇíÉ=_áä~åòáÉêìåÖëJ=ìåÇ=_ÉïÉêíìåÖëãÉíÜçÇÉå= ûåÇÉêìåÖ=ÇÉê=ÄáëÜÉêáÖÉå=_áä~åòáÉêìåÖëJ=ìåÇ=_ÉïÉêíìåÖëãÉíÜçÇÉå= sçêà~ÜêÉëò~ÜäÉå= oÉëíä~ìÑòÉáí=ÑΩê=~ääÉ=cçêÇÉêìåÖÉå=[=N=g~Üê= oÉëíä~ìÑòÉáí=ÑΩê=~ääÉ=sÉêÄáåÇäáÅÜâÉáíÉå=Y=N=g~Üê=ìåÇ=[=R=g~ÜêÉ= sÉêÄáåÇäáÅÜâÉáíÉå=ÖÉÖÉåΩÄÉê=dÉëÉääëÅÜ~ÑíÉêå= e~ÑíìåÖëîÉêÜ®äíåáëëÉ=EtÉÅÜëÉäI=_ΩêÖëÅÜ~ÑíÉåF= ^ìÑÖäáÉÇÉêìåÖ=òìë~ããÉåÖÉÑ~ëëíÉê=mçëáíáçåÉå= bêä®ìíÉêìåÖÉå=òìê=dÉïáååJ=ìåÇ=sÉêäìëíêÉÅÜåìåÖW= sçêà~ÜêÉëò~ÜäÉå= ^ìÑÖäáÉÇÉêìåÖ=òìë~ããÉåÖÉÑ~ëëíÉê=mçëáíáçåÉå= ^ìÑÖäáÉÇÉêìåÖ= rãë~íòÉêä∏ëÉ= å~ÅÜ= q®íáÖâÉáíëÄÉêÉáÅÜ= ëçïáÉ= å~ÅÜ= ÖÉçÖê~J éÜáëÅÜ=ÄÉëíáããíÉå=j®êâíÉå= òìë®íòäáÅÜÉ=fåÑçêã~íáçåÉåW= ëçåëíáÖÉ=Ñáå~åòáÉääÉ=sÉêéÑäáÅÜíìåÖÉå= ÇìêÅÜëÅÜåáííäáÅÜÉ=^êÄÉáíåÉÜãÉêò~Üä= jáíÖäáÉÇÉê=ÇÉê=dÉëÅÜ®ÑíëÑΩÜêìåÖ=Eãáí=^åÖ~ÄÉå=ÄÉê=ÇÉêÉå=_ÉòΩÖÉF= _ÉíÉáäáÖìåÖÉå=~å=îÉêÄìåÇÉåÉå=råíÉêåÉÜãÉå= dÉïáååîÉêïÉåÇìåÖëîçêëÅÜä~Ö= =
20
A. Technik und Ergebnis der Buchführung
2.2.6
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Lagebericht
dÉã®≈=¬=OSQ=f=ed_=ëáåÇ=Öêç≈É=ìåÇ=ãáííÉäÖêç≈É=h~éáí~äÖÉëÉääëÅÜ~ÑíÉå=E¬=OST=ed_F= òìê= bêëíÉääìåÖ= ÉáåÉë= i~ÖÉÄÉêáÅÜíë= îÉêéÑäáÅÜíÉíK= häÉáåÉ= h~éáí~äÖÉëÉääëÅÜ~ÑíÉå= E¬= OST= ed_F=ëáåÇ=Ç~îçå=ÄÉÑêÉáíK=^ìÑëíÉääìåÖëéÑäáÅÜíáÖ=ëáåÇ=~ìÅÜ=êÉÅÜåìåÖëäÉÖìåÖëéÑäáÅÜíáJ ÖÉ= råíÉêåÉÜãÉå= å~ÅÜ= ÇÉã= mìÄäd= E¬= R= mìÄädF= ìåÇ= ÄÉëíáããíÉ= dãÄe= C= `çK= hdë== E¬=OSQ=f=pK=P=ed_FK= aÉê= i~ÖÉÄÉêáÅÜí= áëí= òìë~ããÉå= ãáí= ÇÉã= g~ÜêÉë~ÄëÅÜäìëë= ÖÉãK= ¬= OSQ= f= ed_= áååÉêJ Ü~äÄ=ÇÉê=ÉêëíÉå=ÇêÉá=jçå~íÉ=å~ÅÜ=ÇÉã=_áä~åòëíáÅÜí~Ö=~ìÑòìëíÉääÉåK=bê=ÉêÑΩääí=ÖÉÖÉåJ ΩÄÉê= ÇÉå= ^ÇêÉëë~íÉå= ÇÉë= g~ÜêÉë~ÄëÅÜäìëëÉë= ÉáåÉ= oÉÅÜÉåëÅÜ~ÑíëJ= ìåÇ= fåÑçêã~íáçåëJ ÑìåâíáçåI= Ç~= Éê= ëçïçÜä= báåÄäáÅâ= áå= ÇáÉ= ÖÉÖÉåï®êíáÖÉ= ~äë= ~ìÅÜ= áå= ÇáÉ= òìâΩåÑíáÖÉ= ïáêíëÅÜ~ÑíäáÅÜÉ=i~ÖÉ=EáåëÄÉëçåÇÉêÉ=oáëáâÉåF=ÇÉë=råíÉêåÉÜãÉåë=ÖÉï®ÜêíK=k~ÅÜ=¬=OUV= ed_=ëçää=ÇÉê=i~ÖÉÄÉêáÅÜí=Éáå=ÇÉå=í~íë®ÅÜäáÅÜÉå=sÉêÜ®äíåáëëÉå=ÉåíëéêÉÅÜÉåÇÉë=_áäÇ= îÉêãáííÉäåK=wìã=jáåÇÉëíáåÜ~äí=ò®ÜäÉå=ÄÉáëéáÉäëïÉáëÉ=ÑçäÖÉåÇÉ=_Éëí~åÇíÉáäÉW= táêíëÅÜ~ÑíëÄÉêáÅÜí=EdÉëÅÜ®ÑíëîÉêä~ìÑ=ìåÇ=i~ÖÉFW= o~ÜãÉåÄÉÇáåÖìåÖÉå=EÖÉë~ãíïáêíëÅÜ~ÑíäáÅÜÉ=ìåÇ=_ê~åÅÜÉåëáíì~íáçåF= råíÉêåÉÜãÉåëëáíì~íáçå= E_ÉëÅÜ~ÑÑìåÖI= mêçÇìâíáçåI= ^Äë~íòI= ^ìÑíê~Öëä~ÖÉI= lêÖ~åáë~íáçåI=sÉêï~äíìåÖI=êÉÅÜíäáÅÜÉ=råíÉêåÉÜãÉåëëíêìâíìêI=ÁF= Ñáå~åòáÉääÉ=iÉáëíìåÖëáåÇáâ~íçêÉå=EbêÖÉÄåáëÉåíïáÅâäìåÖI=bêÖÉÄåáëâçãéçJ åÉåíÉåI=iáèìáÇáí®íI=h~éáí~ä~ìëëí~ííìåÖI=ÁF= åáÅÜíÑáå~åòáÉääÉ= iÉáëíìåÖëáåÇáâ~íçêÉå= ErãïÉäíÄÉä~åÖÉI=båíïáÅâäìåÖ=ÇÉë= hìåÇÉåëí~ããÉëI=eìã~åâ~éáí~äI=ÖÉëÉääëÅÜ~ÑíäáÅÜÉ=oÉéìí~íáçåI=ÁF= mêçÖåçëÉJ= ìåÇ= oáëáâçÄÉêáÅÜí= Eîçê~ìëëáÅÜíäáÅÜÉ= båíïáÅâäìåÖ= ãáí= ïÉëÉåíäáÅÜÉå= `Ü~åÅÉå=ìåÇ=oáëáâÉå=ãáí=^åÖ~ÄÉ=ÇÉê=òìÖêìåÇÉ=äáÉÖÉåÇÉå=^åå~ÜãÉåFW= `Ü~åÅÉåJ=ìåÇ=oáëâçâ~íÉÖçêáÉå=Ek~íìêÉêÉáÖåáëëÉI=êÉÅÜíäáÅÜÉI=ïáêíëÅÜ~ÑíäáJ ÅÜÉ= ìåÇ= éçäáíáëÅÜÉ= o~ÜãÉåÄÉÇáåÖìåÖÉåI= qÉÅÜåçäçÖáÉI= _ÉëÅÜ~ÑÑìåÖëJI= ^Äë~íòJ=ìåÇ=h~éáí~äã~êâíI=^ìÑÄ~ìJ=ìåÇ=^Ää~ìÑçêÖ~åáë~íáçåI=ÁF= oáëáâçã~å~ÖÉãÉåí=EfÇÉåíáÑáâ~íáçåI=_ÉïÉêíìåÖI=píÉìÉêìåÖII=ÁF= k~ÅÜíê~ÖëÄÉêáÅÜí= EÄÉëçåÇÉêÉ= sçêÖ®åÖÉ= å~ÅÜ= pÅÜäìëë= ÇÉë= dÉëÅÜ®Ñíëà~ÜêÉë= ïáÉ= òK_K=^ÄëÅÜäìëë=ïáÅÜíáÖÉê=sÉêíê®ÖÉF= cçêëÅÜìåÖëJ= ìåÇ= båíïáÅâäìåÖëÄÉêáÅÜí= EwáÉäÉI= pÅÜïÉêéìåâíÉI= fåîÉëíáíáçåÉåI= jáí~êÄÉáíÉêI=bêÖÉÄåáëëÉI=ÁF= wïÉáÖåáÉÇÉêä~ëëìåÖëÄÉêáÅÜí= ElêíÉ= ìåÇ= q®íáÖâÉáíëÑÉäÇÉê= ÇÉê= káÉÇÉêä~ëëìåÖÉåI= sÉê®åÇÉêìåÖÉå=ÖÉÖÉåΩÄÉê=ÇÉã=sçêà~ÜêF= bêÖ®åòìåÖëÄÉêáÅÜí=EÄÉá=^âíáÉåÖÉëÉääëÅÜ~ÑíÉå=ÖÉãK=¬=PNO=fff=^âídW=_ÉòáÉÜìåÖÉå= òì=îÉêÄìåÇÉåÉå=råíÉêåÉÜãÉåI=^ÄÜ®åÖáÖâÉáíëîÉêÜ®äíåáëëÉF= aÉë= tÉáíÉêÉå= ëáåÇ= áã= ëçÖK= wìë~íòÄÉêáÅÜí= ïÉáíÉêÉ= ÑêÉáïáääáÖÉ= ^åÖ~ÄÉå= ã∏ÖäáÅÜK= a~òì= ò®ÜäÉå= òK_K= jÉÜêà~ÜêÉëΩÄÉêëáÅÜíÉå= òì= _áä~åòÇ~íÉåI= bêÖÉÄåáëÇ~íÉåI= hÉååò~ÜJ äÉåI=aáîáÇÉåÇÉ=çÇÉê=^âíáÉåâìêëK= =
3.
Technik der Buchführung
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22
A. Technik und Ergebnis der Buchführung
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24
A. Technik und Ergebnis der Buchführung
3.2 Buchungen auf Bestandskonten 3.2.1
Auflösung der Bilanz in Konten
bë= ï®êÉ= ®ì≈Éêëí= ìãëí®åÇäáÅÜ= ìåÇ= òÉáíê~ìÄÉåÇ= å~ÅÜ= àÉÇÉã= dÉëÅÜ®ÑíëîçêÑ~ää= ÉáåÉ= åÉìÉ=_áä~åò=òì=ÉêëíÉääÉåI=ÇáÉ=ÇÉå=~âíìÉääÉå=pí~åÇ=ÇÉë=sÉêã∏ÖÉåë=ìåÇ=ÇÉê=pÅÜìäÇÉå= ~ìÑïÉáëíK= a~ÜÉê= ïáêÇ= ÇáÉ= _áä~åò= òì= _ÉÖáåå= ÉáåÉë= àÉÇÉå= dÉëÅÜ®Ñíëà~ÜêÉë= Ebê∏ÑÑJ åìåÖëÄáä~åòF=áå=ÉáåòÉäåÉ=oÉÅÜåìåÖëëíÉääÉå=EëçÖK=hçåíÉåF=~ìÑÖÉíÉáäíI=~ìÑ=ÇÉåÉå=ÇáÉ= ÉáåòÉäåÉå=_ìÅÜìåÖÉå=îçêÖÉåçããÉå=ïÉêÇÉåK=cΩê=àÉÇÉå=_áä~åòéçëíÉå=ÉñáëíáÉêí=~äëç= Éáå=ÉáÖÉåÉë=hçåíçK=wìã=g~ÜêÉëÉåÇÉ=ïÉêÇÉå=ÇáÉëÉ=Ç~åå=ïáÉÇÉê=òì=ÉáåÉê=pÅÜäìëëÄáJ ä~åò=òìë~ããÉåÖÉÑ~ëëíK= cΩê=ÇáÉëÉ=hçåíÉå=ÖáÄí=Éë=îÉêëÅÜáÉÇÉåÉ=a~êëíÉääìåÖëJ=ÄòïK=cΩÜêìåÖëÑçêãÉåK= =
3.2.1.1
Konto in Staffelform
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3. Technik der Buchführung
25
aÉê=sçêíÉáä=ÇáÉëÉê=hçåíÉåÑçêã=äáÉÖí=Ç~êáåI=Ç~ëë=ëí®åÇáÖ=ÇÉê=~âíìÉääÉ=pí~åÇ=ÇÉë=hçåJ íçë=ÉêëáÅÜíäáÅÜ=áëíK=aÉê=k~ÅÜíÉáä=ÜáåÖÉÖÉå=ÄÉëíÉÜí=Ç~êáåI=Ç~ëë=báåJ=ìåÇ=^ìëò~ÜäìåÖÉå= åáÅÜí= ÖÉíêÉååí= Ç~êÖÉëíÉääí= ïÉêÇÉåK= aÉã= â~åå= ÑçäÖÉåÇÉ= hçåíÉåÑçêã= ^ÄÜáäÑÉ= ëÅÜ~ÑJ ÑÉåK= =
3.2.1.2
Konto in Reihenform
_Éáã= hçåíç= áå= oÉáÜÉåÑçêã= ÉêÑçäÖí= ÉáåÉ= qêÉååìåÖ= ÇÉê= wìJ= ìåÇ= ^ÄÖ®åÖÉ= ÇìêÅÜ= sÉêïÉåÇìåÖ= îÉêëÅÜáÉÇÉåÉê= pé~äíÉå= áã= hçåíçK= báåÉ= âçåíáåìáÉêäáÅÜÉ= bêãáííäìåÖ= ÇÉë= wïáëÅÜÉåëí~åÇÉë=ÉêÑçäÖí=åáÅÜíK= ⌦= a~ë=_~åââçåíç=~ìë=OKNKN=ïΩêÇÉ=Ç~åå=ïáÉ=ÑçäÖí=~ìëëÉÜÉåW= ==
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3.2.1.3
T-Konto
^ìÅÜ=ÄÉá=ÇÉê=äÉíòíÉå=a~êëíÉääìåÖë~êíI=ÇÉã=qJ=hçåíçI=ÉêÑçäÖí=ÉáåÉ=qêÉååìåÖ=îçå=wìJ= ìåÇ= ^ÄÖ®åÖÉåK= k~ÅÜ= ÄìÅÜÜ~äíÉêáëÅÜÉê= hçåîÉåíáçå= ïÉêÇÉå= ^åÑ~åÖëÄÉëí~åÇ= ìåÇ= wìÖ®åÖÉ=~ìÑ=ÇÉê=äáåâÉå=pÉáíÉI=^ÄÖ®åÖÉ=~ìÑ=ÇÉê=êÉÅÜíÉå=pÉáíÉ=ÇÉë=hçåíçë=ÉêÑ~ëëíK=aáÉ= äáåâÉ=pÉáíÉ=ÇÉë=hçåíçë=ïáêÇ=~äë=pçääëÉáíÉI=ÇáÉ=êÉÅÜíÉ=~äë=e~ÄÉåëÉáíÉ=ÄÉòÉáÅÜåÉíK= ⌦= cΩê=ÇáÉ=_ÉáëéáÉäò~ÜäÉå=~ìë=PKOKNKN=ÉêÖáÄí=ëáÅÜ=Ç~ãáíW== = pçää= MNKMNK= ^åÑ~åÖëÄÉëí~åÇ=
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26
A. Technik und Ergebnis der Buchführung
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3.2.2
Wesen von Bestandskonten
táÉ= ÄÉêÉáíë= Éêï®ÜåíI= ïáêÇ= ÇáÉ= _áä~åò= òìã= _ÉÖáåå= ÇÉë= dÉëÅÜ®Ñíëà~ÜêÉë= áå= ÉáåòÉäåÉ= _Éëí~åÇëâçåíÉå= ~ìÑÖÉëé~äíÉåK= aáÉ= hçåíÉåI= ÇáÉ= ~ìë= ÇÉå= mçëíÉå= ÇÉê= ^âíáîëÉáíÉ= ÉåíJ ëíÉÜÉåI=ÄÉòÉáÅÜåÉí=ã~å=~äë=~âíáîÉ=_Éëí~åÇëâçåíÉå=çÇÉê=^âíáîâçåíÉåI=ÇáÉ=hçåíÉå= ÇÉê= m~ëëáîëÉáíÉ= ~äë= é~ëëáîÉ= _Éëí~åÇëâçåíÉå= çÇÉê= m~ëëáîâçåíÉåK= j~å= ÄÉòÉáÅÜåÉí= ÇáÉëÉ=hçåíÉå=~äë=_Éëí~åÇëâçåíÉåI=Ç~=ëáÉ=_Éëí®åÇÉ=~ìë=ÇÉê=_áä~åò=ΩÄÉêåÉÜãÉåK= _Éá=ÇÉå=^âíáîâçåíÉå=ïáêÇ=ÇÉê=tÉêí=ÇÉë=^åÑ~åÖëÄÉëí~åÇÉë=áåë=pçää=ΩÄÉêåçããÉåI= Ç~=Éê=áå=ÇÉê=_áä~åò=ÉÄÉåÑ~ääë=äáåâë=ëíÉÜíK=wìÖ®åÖÉ=ïÉêÇÉå=áã=pçää=ìåÇ=^ÄÖ®åÖÉ=áã= e~ÄÉå= ÉêÑ~ëëíK= få= ÇÉê= oÉÖÉä= áëí= ÄÉá= ~âíáîÉå= _Éëí~åÇëâçåíÉå= ÇáÉ= pìããÉ= ~ìë= ^åJ Ñ~åÖëÄÉëí~åÇ= ìåÇ= wìÖ®åÖÉå= Öê∏≈Éê= ~äë= ÇáÉ= pìããÉ= ÇÉê= ^ÄÖ®åÖÉK= a~ÜÉê= í~ìÅÜí= pÅÜäìëëÄÉëí~åÇ= ÄòïK= ÇÉê= p~äÇç= òìã= ^ìëÖäÉáÅÜ= ÇÉë= hçåíçë= áå= ÇÉê= oÉÖÉä=áã= e~ÄÉå= ~ìÑK=báå=ëçäÅÜÉê=p~äÇçI=ÇÉê=ÇáÉ=pçääëÉáíÉ=~ìëÖäÉáÅÜíI=ÜÉá≈í=pçääë~äÇçK= aÉê= ^åÑ~åÖëÄÉëí~åÇ= ÇÉê=m~ëëáîâçåíÉå= ÜáåÖÉÖÉå= ÉêëÅÜÉáåí= áã= e~ÄÉå= ÇÉë= hçåíçëI= Ç~=Éê=~ìë=ÇÉê=êÉÅÜíÉå=pÉáíÉ=ÇÉê=_áä~åò=ëí~ããíK=aáÉëÉ=hçåíÉå~êí=åáããí=áã=e~ÄÉå=òì= ìåÇ=áã=pçää=~ÄK=aÉê=p~äÇç=ÇÉê=é~ëëáîÉå=_Éëí~åÇëâçåíÉå=áëí=~ìÑ=ÇÉê=pçääëÉáíÉ=òì=ÑáåJ ÇÉåK=bë=Ü~åÇÉäí=ëáÅÜ=ÜáÉê=ìã=ÉáåÉå=ëçÖK=e~ÄÉåë~äÇçI=Ç~=ÇáÉëÉê=ÇáÉ=ÄÉá=m~ëëáîâçåJ íÉå=áå=ÇÉê=oÉÖÉä=Öê∏≈ÉêÉ=e~ÄÉåëÉáíÉ=~ìëÖäÉáÅÜíK=
28
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3.2.3
Konteneröffnung
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3.2.4
Verbuchung von Geschäftsvorfällen
aìêÅÜ= àÉÇÉå= dÉëÅÜ®ÑíëîçêÑ~ää= E^âíáîí~ìëÅÜI= m~ëëáîí~ìëÅÜI= _áä~åòîÉêä®åÖÉêìåÖI= _áJ ä~åòîÉêâΩêòìåÖF= ïÉêÇÉå= ãáåÇÉëíÉåë= òïÉá= mçëíÉå= ÇÉê= _áä~åò= ~åÖÉëéêçÅÜÉå= ÄòïK= îÉê®åÇÉêíK=a~=ÑΩê=àÉÇÉå=_áä~åòéçëíÉå=Éáå=ÉáÖÉåÉë=_Éëí~åÇëâçåíç=ÖÉÑΩÜêí=ïáêÇI=ïÉêJ ÇÉå=~äëç=ÇìêÅÜ=àÉÇÉå=dÉëÅÜ®ÑíëîçêÑ~ää=~ìÅÜ=EãáåÇÉëíÉåëF=òïÉá=hçåíÉå=~åÖÉëéêçJ ÅÜÉåK=aáÉëÉ=q~íë~ÅÜÉ=áëí=áå=ÇÉê=ëçÖK=açééáâI=ÇÉã=póëíÉã=ÇÉê=açééÉäíÉå=_ìÅÜJ ÑΩÜêìåÖ= Eå~ÅÜ= dìëí~î= cêÉáí~ÖFI= îÉê~åâÉêíK= páÉ= ÄÉë~ÖíI= Ç~ëë= àÉÇÉê= dÉëÅÜ®ÑíëîçêÑ~ää= ~ìÑ=ãáåÇÉëíÉåë=òïÉá=hçåíÉå=îÉêÄìÅÜí=ïÉêÇÉå=ãìëëK= _Éá= ÇÉê= _É~êÄÉáíìåÖ= îçå= dÉëÅÜ®ÑíëîçêÑ®ääÉå= áå= ÇÉê= _ìÅÜÑΩÜêìåÖ= áëí= ~ääÖÉãÉáå= ÑçäJ ÖÉåÇÉ=sçêÖÉÜÉåëïÉáëÉ=òì=ÉãéÑÉÜäÉåW= NK dêΩåÇäáÅÜÉ= páÅÜíìåÖ= ÇÉê= îçêÜ~åÇÉåÉå= _ÉäÉÖÉ= ìåÇ= mêΩÑìåÖ= ~ìÑ= ë~ÅÜäáÅÜÉ= ìåÇ= êÉÅÜåÉêáëÅÜÉ= oáÅÜíáÖâÉáí= ÇÉê= fåÜ~äíÉW= a~ÄÉá= ëáåÇ= cêÉãÇÄÉäÉÖÉ= Eîçå= ÑêÉãÇÉå= cáêãÉå= çÇÉê= _ÉÜ∏êÇÉå= ÉáåÖÉÖ~åÖÉåÉ= pÅÜêáÑíëíΩÅâÉW= òK_K= báåÖ~åÖëêÉÅÜåìåÖÉåI= hçåíç~ìëòΩÖÉ=ÇÉê=_~åâI=nìáííìåÖÉå=ÑΩê=_~êò~ÜäìåÖÉåI=ìëïKF=ìåÇ=báÖÉåÄÉäÉÖÉ= EòK_K= hçéáÉå= îçå= ^ìëÖ~åÖëêÉÅÜåìåÖÉåI= j~íÉêá~äÉåíå~ÜãÉëÅÜÉáåÉI= içÜåäáëíÉåI= ìëïKF=òì=ìåíÉêëÅÜÉáÇÉåK= =
30
A. Technik und Ergebnis der Buchführung
OK dÉÇ~åâäáÅÜÉ=_É~åíïçêíìåÖ=ÑçäÖÉåÇÉê=cê~ÖÉå=òìã=dÉëÅÜ®ÑíëîçêÑ~ääW= ~F tÉäÅÜÉ=hçåíÉå=ëáåÇ=ÄÉíêçÑÑÉå\= ÄF rã=ïÉäÅÜÉ=^êí=îçå=hçåíç=Ü~åÇÉäí=Éë=ëáÅÜ\= ÅF táÉ=îÉê®åÇÉêå=ëáÅÜ=ÇáÉ=hçåíÉå\= ÇF ^ìÑ=ïÉäÅÜÉã=hçåíç=ïáêÇ=áã=pçää=ìåÇ=~ìÑ=ïÉäÅÜÉã=áã=e~ÄÉå=ÖÉÄìÅÜí\= PK bêëíÉääìåÖ=ÇÉê=ëçÖK=_ìÅÜìåÖë~åïÉáëìåÖW= aáÉ= ~ìÅÜ= ~äë= _ìÅÜìåÖëë~íò= ÄÉòÉáÅÜåÉíÉ= _ìÅÜìåÖë~åïÉáëìåÖ= ëéêáÅÜí= áå= áÜêÉê= ÉáåÑ~ÅÜÉå=cçêã= ÖÉå~ì=òïÉá=hçåíÉå=~åK=báåÉë=ïáêÇ=~ìÑ=ÇÉê=pçääJI=Ç~ë=~åÇÉêÉ= ~ìÑ= ÇÉê= e~ÄÉåëÉáíÉ= îÉê®åÇÉêíK= aáÉ= pçääÄìÅÜìåÖ= ïáêÇ= ÖêìåÇë®íòäáÅÜ= òìÉêëí= ÖÉJ å~ååíK= =
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3. Technik der Buchführung
31
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32
A. Technik und Ergebnis der Buchführung
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3. Technik der Buchführung
33
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3.2.5
Kontenabschluss
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34
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3. Technik der Buchführung
35
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3.2.6
Buchung von Konteneröffnung und -abschluss
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36
A. Technik und Ergebnis der Buchführung
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38
A. Technik und Ergebnis der Buchführung
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39
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A. Technik und Ergebnis der Buchführung
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46
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3. Technik der Buchführung
47
aÉê=dÉëÉíòÖÉÄÉê=Ü~í=~ìë=dêΩåÇÉå=ÇÉê=qê~åëé~êÉåòI=ÇÉë=dä®ìÄáÖÉêëÅÜìíòÉë=ìåÇ=ÇÉê= råíÉêåÉÜãÉåëÄÉëíÉìÉêìåÖI=ÇÉê=dÉïáååJ=ìåÇ=sÉêäìëíêÉÅÜåìåÖ=ÇÉå=sçêòìÖ=ÖÉÖÉÄÉå= ìåÇ=ÇáÉëÉ=òìê=mÑäáÅÜí=E¬=OQO=fff=ed_F=ÑΩê=łråíÉêåÉÜãÉê =ÖÉã~ÅÜíK= =
3.3.2
Verbuchung von Aufwendungen und Erträgen
3.3.2.1
Variante A
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3.3.2.2
Variante B
rã=ÇáÉ=ëÅÜïÉêïáÉÖÉåÇÉå=k~ÅÜíÉáäÉ=ÇÉê=s~êá~åíÉ=^=òì=ÄÉëÉáíáÖÉåI=ïáêÇ=áå=s~êá~åíÉ= _=ÑΩê=àÉÇÉ=^ìÑï~åÇëJ=ìåÇ=bêíê~Öë~êí=Éáå=ëÉé~ê~íÉë=hçåíç=ÉáåÖÉêáÅÜíÉíI=~ìÑ=ÇÉã=ÇáÉ= dÉÖÉåÄìÅÜìåÖ= ~å= píÉääÉ= ÇÉë= báÖÉåâ~éáí~äâçåíçë= ÉêÑçäÖÉå= â~ååK= aáÉëÉ= hçåíÉå= ÄÉJ òÉáÅÜåÉí=ã~å=~äë=ëçÖK=bêÑçäÖëâçåíÉåK== =
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48
A. Technik und Ergebnis der Buchführung
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Kontenabschluss
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3. Technik der Buchführung
49
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3.3.4
Zusammensetzung des Gesamterfolgs
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3. Technik der Buchführung
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52
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Einfacher Geschäftsgang (mit Erfolgskonten)
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56
A. Technik und Ergebnis der Buchführung =
3.3.6
Umsatz- und Gesamtkostenverfahren
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3. Technik der Buchführung
57
⌦= _ÉáëéáÉäW= fã= g~åì~ê= ÇÉë= g~ÜêÉë= OMMT= ïìêÇÉå= áå= ÉáåÉã= råíÉêåÉÜãÉå= îçã= mêçÇìâí= u= PMM= píΩÅâ= ÖÉÑÉêíáÖíK= sÉêâ~ìÑí= ïìêÇÉå= ~ääÉêÇáåÖë= åìê= OMM= píΩÅâ= òì= NMIMM= bìêç= àÉ= píΩÅâK= aáÉ=ãáí=ÇÉê=eÉêëíÉääìåÖ=ÇÉê=PMM=píΩÅâ=îÉêÄìåÇÉåÉå=^ìÑïÉåÇìåÖÉå=ÄÉäáÉÑÉå=ëáÅÜ=áå= ÇÉê=mÉêáçÇÉ=~ìÑ=NKUMMIMM=bìêçK=^å=åÉìíê~äÉå=^ìÑïÉåÇìåÖÉå=ÑáÉäÉå=OMMIMM=bìêç=~åK= kÉìíê~äÉ=bêíê®ÖÉ=äáÉÖÉå=åáÅÜí=îçêK= k~ÅÜ=ÇÉã=rãë~íòâçëíÉåîÉêÑ~ÜêÉå=ëáåÇ=ÇÉã=rãë~íò=îçå=OMM ⋅ NMIMM=Z=OKMMMIMM=bìêç= ÇáÉ=eÉêëíÉääìåÖë~ìÑïÉåÇìåÖÉå=ÇÉê=~ÄÖÉëÉíòíÉ=jÉåÖÉ=îçå=OMM ⋅ SIMM=Z=NKOMMIMM=bìêç= ìåÇ= ÇáÉ= åÉìíê~äÉå= ^ìÑïÉåÇìåÖÉå= îçå= OMMIMM= bìêç= ÖÉÖÉåΩÄÉêòìëíÉääÉå= EeáåïÉáëW= aÉê= eÉêëíÉääìåÖë~ìÑï~åÇ= àÉ= píΩÅâ= ÉêÖáÄí= ëáÅÜ= ~äë= NKUMMIMM : PMM= Z= SIMM= bìêçFK= a~ë= mÉêáçÇÉåÉêÖÉÄåáë=ÉêÖáÄí=ëáÅÜ=Ç~ãáí=ÑçäÖÉåÇÉêã~≈ÉåK= = p= ========dìs=å~ÅÜ=rhs= e= ^ìÑï~åÇ=~ÄÖÉëK=jÉåÖÉ=
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58
A. Technik und Ergebnis der Buchführung
3.3.7
Gesamtzusammenhang Bestands- und Erfolgskonten
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60
A. Technik und Ergebnis der Buchführung
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62
A. Technik und Ergebnis der Buchführung
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B. RECHTLICHER HINTERGRUND
= In diesem Kapitel werden Ihnen die rechtlichen Grundlagen der Buchführung vermittelt. Es wird verdeutlicht,
aus welchen Rechtsquellen die Buchführungsvorschriften entspringen,
welche Personen- bzw. Unternehmensgruppen zur Buchführung verpflichtet sind,
wie die Buchführung und ihr Ergebnis (Jahresabschluss) beschaffen sein muss (Grundsätze ordnungsmäßiger Buchführung und Bilanzierung),
in welchen Teilschritten die Bilanz bis zur Veröffentlichung entwickelt wird und
welche Strafen bei Verstoß gegen Rechnungslegungsvorschriften zu erwarten sind.
Der Schwerpunkt liegt dabei bei der Betrachtung deutscher handels- und steuerrechtlicher Vorschriften. Internationale Rechnungslegung wird weder in diesem noch in den Folgekapiteln behandelt. =
=
1.
Rechtsquellen
=
1.1 Allgemeines ^ääÖÉãÉáå= áëí= òìå®ÅÜëí= òì= ë~ÖÉåI= Ç~ëë= ëáÅÜ= ÇáÉ= oÉÅÜíëÖêìåÇä~ÖÉå= ÑΩê= ÇáÉ= oÉÅÜJ åìåÖëäÉÖìåÖ= áã= âçÇáÑáòáÉêíÉå= oÉÅÜí= EdÉëÉíòÉFI= oÉÅÜíëéêÉÅÜìåÖ= EbáåòÉäÑ~ääìêíÉáäÉF= ìåÇ= áå= ÇÉå= dêìåÇë®íòÉå= çêÇåìåÖëã®≈áÖÉê= _ìÅÜÑΩÜêìåÖ= ìåÇ= _áä~åòáÉêìåÖ= Edç_I= dç_áäF= äáÉÖÉåK= ^ìÑÖêìåÇ= áÜêÉê= ÉåçêãÉå= _ÉÇÉìíìåÖ= ïáêÇ= ÇÉå= dç_= ìåÇ= ÇÉå= dç_áä= ìåíÉê=_=P=Éáå=ÉáÖÉåÉê=^ÄëÅÜåáíí=ÖÉïáÇãÉíK== aáÉ=oÉÅÜíëéêÉÅÜìåÖ=~äë=oÉÅÜíëÖêìåÇä~ÖÉ=ëçää=åìê=ÇÉê=sçääëí®åÇáÖâÉáí=Ü~äÄÉê=~ìÑÖÉJ ÑΩÜêí= ìåÇ= åáÅÜí= áã= aÉí~áä= ÄÉÜ~åÇÉäí= ïÉêÇÉåK= wì= oÉÅÜíëéêÉÅÜìåÖ= áã= _áä~åòêÉÅÜí= âçããí= Éë= Ç~ååI= ïÉåå= ÖÉëÉíòäáÅÜÉ= sçêëÅÜêáÑíÉå= ìåâä~ê= ëáåÇK= páÉ= Ü~ÄÉå= ÉêÜÉÄäáÅÜÉ= âä®êÉåÇÉ=táêâìåÖ=ÄÉá=ÇÉê=^ìëäÉÖìåÖ=ò~ÜäêÉáÅÜÉê=ìåâä~êÉê=dÉëÉíòÉëîçêëÅÜêáÑíÉåK=cΩê= Ç~ë= e~åÇÉäëêÉÅÜí= ëáåÇ= ÇáÉ= wáîáäÖÉêáÅÜíÉ= E_ìåÇÉëÖÉêáÅÜíëÜçÑ= ~äë= çÄÉêëíÉ= píÉääÉF= òìJ ëí®åÇáÖI= ïÉäÅÜÉ= àÉÇçÅÜ= ~ìÑÖêìåÇ= ÇÉë= ÖÉêáåÖÉå= fåíÉêÉëëÉë= ÇÉê= _áä~åò~ÇêÉëë~íÉå= ~å= ÇÉê= ÖÉêáÅÜíäáÅÜÉå= hä®êìåÖ= ÄÉá= e~åÇÉäëÄáä~åò~åë®íòÉå= â~ìã= í®íáÖ= ïÉêÇÉåK= aáÉ= ÑΩê= Ç~ë=píÉìÉêêÉÅÜí=òìëí®åÇáÖÉå=cáå~åòÖÉêáÅÜíÉ=ìåÇ=ÇÉê=_ìåÇÉëÑáå~åòÜçÑ=E_ceF=Ü~ÄÉå= ÜáåÖÉÖÉå=ÉáåÉ=ìåÖÉÜÉìÉêÉ=w~Üä=îçå=ÖÉêáÅÜíäáÅÜÉå=oÉÅÜíëÄÉÜÉäÑÉå=ÇìêÅÜòì~êÄÉáíÉåK= aáÉ=Ç~ê~ìë=êÉëìäíáÉêÉåÇÉ=oÉÅÜíëéêÉÅÜìåÖ=Ü~í=òï~ê=âÉáåÉå=dÉëÉíòÉëÅÜ~ê~âíÉêI=ÇçÅÜ= â~åå= ëáÅÜ= ÇÉê= píÉìÉêéÑäáÅÜíáÖÉ= áå= ÖäÉáÅÜÖÉä~ÖÉêíÉå= c®ääÉå= ~ìÑ= Ç~ë= ÖΩåëíáÖÉêÉ= rêíÉáä= ÄÉêìÑÉåK=sçå=ÇÉå=cáå~åò®ãíÉêå=ïÉêÇÉå=ÇáÉëÉ=rêíÉáäÉ=áå=ÇÉê=oÉÖÉä=ïáÉ=dÉëÉíòÉ=ÄÉJ Ü~åÇÉäí= ìåÇ= ~åÖÉï~åÇíI= ëçÑÉêå= Ç~ë= cáå~åò~ãí= åáÅÜí= áå= oÉîáëáçå= ÄÉáã= _ìåÇÉëÑáJ å~åòÜçÑ=ÖÉÜí=ìåÇ=âÉáå=káÅÜí~åïÉåÇìåÖëÉêä~ëë=ÉêÑçäÖíK= jáí= ÇÉã= âçÇáÑáòáÉêíÉå= oÉÅÜí= Ee~åÇÉäëJ= ìåÇ= píÉìÉêêÉÅÜíF= ~äë= dêìåÇä~ÖÉ= ÇÉê= oÉÅÜJ åìåÖëäÉÖìåÖ=ïáêÇ=ëáÅÜ=åìå=áã=cçäÖÉåÇÉå=å®ÜÉê=ÄÉÑ~ëëíK=báå=ÖêçÄÉê=§ÄÉêÄäáÅâ=Ç~òì= áëí=òìå®ÅÜëí=áå=å~ÅÜÑçäÖÉåÇÉê=^ÄÄáäÇìåÖ=Ç~êÖÉëíÉääíK= = =
e~åÇÉäëêÉÅÜí=
píÉìÉêêÉÅÜí=
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péÉòáÉääW= êÉÅÜíëÑçêãëéÉòáJ ÑáëÅÜW=^âídI= dãÄedI=dÉåd=
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66
B. Rechtlicher Hintergrund =
1.2 Gesetzliche Bestimmungen im Handelsrecht aáÉ= oÉÅÜåìåÖëäÉÖìåÖëîçêëÅÜêáÑíÉå= ÑΩê= ÇáÉ= e~åÇÉäëÄáä~åò= ÄÉÑáåÇÉå= ëáÅÜ= áã= ed_I= áåëÄÉëçåÇÉêÉ= áã= ÇêáííÉå= _ìÅÜ= łe~åÇÉäëÄΩÅÜÉê K= aáÉëÉë= ÖäáÉÇÉêí= ëáÅÜ= áå= ÇáÉ= ^ÄJ ëÅÜåáííÉ=łsçêëÅÜêáÑíÉå=ÑΩê=~ääÉ=h~ìÑäÉìíÉ =ENFI=łbêÖ®åòÉåÇÉ=sçêëÅÜêáÑíÉå=ÑΩê=h~éáí~äJ ÖÉëÉääëÅÜ~ÑíÉå = EOFI= łbêÖ®åòÉåÇÉ= sçêëÅÜêáÑíÉå= ÑΩê= dÉåçëëÉåëÅÜ~ÑíÉå = EPF= ìåÇ= łbêJ Ö®åòÉåÇÉ=sçêëÅÜêáÑíÉå=ÑΩê=ÄÉëíáããíÉ=dÉëÅÜ®ÑíëòïÉáÖÉ =EQFK== wì= ÇÉå= fåÜ~äíÉå= ÇÉê= ^ÄëÅÜåáííÉ= ENF= ìåÇ= EOF= ÄÉíê~ÅÜíÉ= ã~å= òìå®ÅÜëí= ÑçäÖÉåÇÉ= ^ÄJ ÄáäÇìåÖK= = = = =
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sçêëÅÜêáÑíÉå=ÑΩê=~ääÉ=h~ìÑäÉìíÉ=
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1. Rechtsquellen
1.2.1
67
Allgemeingültige Vorschriften
wìå®ÅÜëí= ëáåÇ= ÇáÉ= áå= ÇÉå= ¬¬= OPUJOSP= ed_= îÉê~åâíÉêíÉå= ~ääÖÉãÉáåÉå= oÉÅÜåìåÖëäÉJ ÖìåÖëîçêëÅÜêáÑíÉå= ÑΩê= ~ääÉ= h~ìÑäÉìíÉ= òì= ÄÉ~ÅÜíÉåK= aáÉëÉ= ïÉêÇÉå= àÉÇçÅÜ= ÑΩê= ÄÉJ ëíáããíÉ=oÉÅÜíëÑçêãÉå=ÉêÖ®åòí=çÇÉê=ÉêëÉíòíK= =
1.2.2
Rechtsformspezifische Vorschriften
aáÉëÉ=sçêëÅÜêáÑíÉå=ÖÉäíÉå=ÑΩê=h~éáí~äÖÉëÉääëÅÜ~ÑíÉå=òìë®íòäáÅÜ=çÇÉê=ÉêëÉíòÉåÇ=òì=ÇÉå= ~ääÖÉãÉáåÖΩäíáÖÉå= sçêëÅÜêáÑíÉå= áã= ÉêëíÉå= ^ÄëÅÜåáííK= a~ÜÉê= Äê~ìÅÜÉå= báåòÉäìåíÉêJ åÉÜãÉå= ìåÇ= mÉêëçåÉåÖÉëÉääëÅÜ~ÑíÉå= ÄÉáëéáÉäëïÉáëÉ= ÑçäÖÉåÇÉ= ^åÑçêÇÉêìåÖÉå= åáÅÜí= ÉêÑΩääÉåW=
bêëíÉääìåÖ=îçå=^åÜ~åÖ=ìåÇ=i~ÖÉÄÉêáÅÜí=E¬¬=OUQJOUV=ed_FW= cΩê=báåòÉäìåíÉêåÉÜãÉå=ìåÇ=mÉêëçåÉåÖÉëÉääëÅÜ~ÑíÉå=áëí=ÇáÉ=^ìÑëíÉääìåÖ=îçå=_áJ ä~åò=ìåÇ=dìs=~ìëêÉáÅÜÉåÇK=
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lÑÑÉåäÉÖìåÖ=E¬¬=PORJPOV=ed_FW= báåÉ= báåêÉáÅÜìåÖ= ÇÉë= g~ÜêÉë~ÄëÅÜäìëëÉë= ÄÉáã= e~åÇÉäëêÉÖáëíÉê= çÇÉê= ÇÉëëÉå= sÉê∏ÑÑÉåíäáÅÜìåÖ=áëí=åáÅÜí=åçíïÉåÇáÖI=ëçÑÉêå=Ç~ë=mìÄäd=åáÅÜí=ÖêÉáÑíK=
däáÉÇÉêìåÖëîçêëÅÜêáÑíÉå=ÄÉá=_áä~åò=ìåÇ=dìs=E¬¬=OSRJOTU=ed_FW= bë= áëí= ÉáåÉ= däáÉÇÉêìåÖ= áå= ÉáåÑ~ÅÜÉê= cçêã= ã∏ÖäáÅÜK= t~ÜäïÉáëÉ= Ç~êÑ= ëáÅÜ= ~ÄÉê= ÇÉååçÅÜ=ÑΩê=ÇáÉ=~ìëÑΩÜêäáÅÜÉ=cçêã=ÉåíëÅÜáÉÇÉå=ïÉêÇÉåK=
sÉêëÅÜ®êÑíÉ=dÉåÉê~äåçêã=ÇÉë=¬=OSQ=ff=ed_I=ëçÖK=łíêìÉ=~åÇ=Ñ~áê=îáÉï =Eg~ÜêÉëJ ~ÄëÅÜäìëë= ëçää= Éáå= ÇÉå= í~íë®ÅÜäáÅÜÉå= sÉêÜ®äíåáëëÉå= ÉåíëéêÉÅÜÉåÇÉë= _áäÇ= ÇÉê= sÉêã∏ÖÉåëJI=cáå~åòJ=ìåÇ=bêíê~Öëä~ÖÉ=îÉêãáííÉäåFW= bë= Öáäí= ÑΩê= mÉêëçåÉåÖÉëÉääëÅÜ~ÑíÉå= ìåÇ= báåòÉäìåíÉêåÉÜãÉå= åìê= ÇáÉ= ÉáåÑ~ÅÜÉ= dÉåÉê~äåçêã= ÇÉê= ¬¬= OQOI= OQP= ed_= E_áä~åò= ìåÇ= dìs= ìåíÉê= ^åïÉåÇìåÖ= ÇÉê= dç_}ë=ÉêëíÉääÉåFK=pçãáí=ÉåíÑ~ääÉå=^åÜ~åÖë~åÖ~ÄÉå=å~ÅÜ=¬=OUQ=ÑÑ=ed_K=
=
få=ÇáÉëÉã=wìë~ããÉåÜ~åÖ=áëí=ÇÉê=oÉÅÜíëÑçêã=ÇÉê=dãÄe=C=`çK=hd=ÄÉëçåÇÉêÉ=_ÉJ ÇÉìíìåÖ= ÄÉáòìãÉëëÉåK= bë= Ü~åÇÉäí= ëáÅÜ= ÜáÉêÄÉá= òï~ê= ìã= âÉáåÉ= h~éáí~äÖÉëÉääëÅÜ~ÑíI= ÇçÅÜ=ãΩëëÉå=ÇáÉ=sçêëÅÜêáÑíÉå=ÇÉê=¬¬=OSQJOUV=ìåÇ=PNSJPOU=ed_=íêçíòÇÉã=~åÖÉïÉåJ ÇÉí= ïÉêÇÉåI= ïÉåå=ÇáÉ= sçê~ìëëÉíòìåÖÉå= ÇÉë= ¬=OSQ~= ed_= EâÉáåÉ= å~íΩêäáÅÜÉ= mÉêëçå= ~äë=éÉêë∏åäáÅÜ=Ü~ÑíÉåÇÉê=dÉëÉääëÅÜ~ÑíÉêF=ÉêÑΩääí=ëáåÇK= däÉáÅÜÉë= Öáäí= ~ääÖÉãÉáå= ÑΩê= ~ääÉ= çÑÑÉåÉå= e~åÇÉäëÖÉëÉääëÅÜ~ÑíÉå= ìåÇ= hçãã~åÇáíÖÉJ ëÉääëÅÜ~ÑíÉåI=ÄÉá=ÇÉåÉå=åáÅÜí=ïÉåáÖëíÉåë=Éáå=éÉêë∏åäáÅÜ=Ü~ÑíÉåÇÉê=dÉëÉääëÅÜ~ÑíÉê=ÉáJ åÉ=å~íΩêäáÅÜÉ=mÉêëçå=çÇÉê=ÉáåÉ=led=çÇÉê=hd=ãáí=ÉáåÉê=å~íΩêäáÅÜÉå=mÉêëçå=~äë=éÉêJ ë∏åäáÅÜ=Ü~ÑíÉåÇÉã=dÉëÉääëÅÜ~ÑíÉê=áëíK= jáí= ÇáÉëÉê= oÉÖÉäìåÖ= ïáêÇ= ÇÉê= wïÉÅâ= îÉêÑçäÖíI= ÉáåÉ= â~éáí~äáëíáëÅÜ= çêáÉåíáÉêíÉ= mÉêëçJ åÉåÖÉëÉääëÅÜ~Ñí=ÉáåÉê=h~éáí~äÖÉëÉääëÅÜ~Ñí=ÖäÉáÅÜòìëíÉääÉåK= =
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68
B. Rechtlicher Hintergrund
1.2.3
Größenabhängige Vorschriften
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1. Rechtsquellen
69
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1.2.4
Branchenabhängige Vorschriften
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hê~åâÉåÜ®ìëÉê=Ehê~åâÉåÜ~ìëJ_ìÅÜÑΩÜêìåÖëJslF=
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70
B. Rechtlicher Hintergrund
1.3 Gesetzliche Bestimmungen im Steuerrecht píÉìÉêêÉÅÜíäáÅÜÉ=oÉÅÜåìåÖëäÉÖìåÖëîçêëÅÜêáÑíÉå=ëáåÇ=ìK~K=áå=bpíd=ìåÇ=^l=îÉê~åâÉêíK= wÉåíê~äÉ= _ÉÇÉìíìåÖ= Ü~í= Ç~ë= j~≈ÖÉÄäáÅÜâÉáíëéêáåòáéI= ΩÄÉê= ïÉäÅÜÉë= ~ìÅÜ= Ü~åÇÉäëJ êÉÅÜíäáÅÜÉ=sçêëÅÜêáÑíÉå=áã=ëíÉìÉêêÉÅÜíäáÅÜÉå=g~ÜêÉë~ÄëÅÜäìëë=^åïÉåÇìåÖ=ÑáåÇÉåK=
1.3.1
Maßgeblichkeit der Handelsbilanz für die Steuerbilanz
e~åÇÉäëêÉÅÜíäáÅÜÉ=sçêëÅÜêáÑíÉå=ëáåÇ=ÖêìåÇë®íòäáÅÜ=~ìÅÜ=ÑΩê=ÇáÉ=bêëíÉääìåÖ=ÇÉê=píÉìJ ÉêÄáä~åò=ìåÇ=ÇÉê=ëíÉìÉêäáÅÜÉå=dÉïáååJ=ìåÇ=sÉêäìëíêÉÅÜåìåÖ=êÉäÉî~åíI=Éë=ëÉá=ÇÉååI= áã= píÉìÉêêÉÅÜí= ëáåÇ= ~ÄïÉáÅÜÉåÇÉ= sçêëÅÜêáÑíÉå= ÉåíÜ~äíÉå= E¬= R= f= pK= N= bpídFK= aáÉëÉê= p~ÅÜîÉêÜ~äí=ïáêÇ=~äë=dêìåÇë~íò=ÇÉê= j~≈ÖÉÄäáÅÜâÉáí=ÇÉê=e~åÇÉäëÄáä~åò=ÑΩê=ÇáÉ= píÉìÉêÄáä~åò= ÄÉòÉáÅÜåÉíK= j~å= â~åå= ~äëç= ë~ÖÉåI= Ç~ëë= ÖêìåÇë®íòäáÅÜ= ~ääÉ= Ü~åÇÉäëJ êÉÅÜíäáÅÜÉå= sçêëÅÜêáÑíÉå= E^åë~íòI= ^ìëïÉáëI= _ÉïÉêíìåÖW= îäÖK= _= PKOF= ïáÉ= ÄÉáëéáÉäëJ ïÉáëÉ= ^âíáîáÉêìåÖëJ= ìåÇ= m~ëëáîáÉêìåÖëîÉêÄçíÉ= çÇÉê= ^âíáîáÉêìåÖëJ= ìåÇ= m~ëëáîáÉJ êìåÖëéÑäáÅÜíÉå=~ìÅÜ=ÑΩê=ÇáÉ=píÉìÉêÄáä~åò=êÉäÉî~åí=ëáåÇK=^âíáîáÉêìåÖ=áëí=Ç~ÄÉá=ÇÉê=^åJ ë~íò= ÉáåÉë= sÉêã∏ÖÉåëÖÉÖÉåëí~åÇë= Ee~åÇÉäëêÉÅÜíF= ÄòïK= ÉáåÉë= táêíëÅÜ~ÑíëÖìíë== EpíÉìÉêêÉÅÜíF=~ìÑ=ÇÉê=^âíáîëÉáíÉ=ÇÉê=_áä~åòK=m~ëëáîáÉêìåÖ=áëí=ÇÉê=^åë~íò=ÉáåÉê=pÅÜìäÇ= ~ìÑ=ÇÉê=m~ëëáîëÉáíÉ=ÇÉê=_áä~åòK=_ÉëíÉÜí=~äëç=ÄÉáëéáÉäëïÉáëÉ=ÇáÉ=mÑäáÅÜí=ÉáåÉå=mâï=áå= ÇáÉ= e~åÇÉäëÄáä~åò= ~ìÑòìåÉÜãÉåI= ëç= áëí= ÇáÉëÉê= ~ìÅÜ= áå= ÇáÉ= píÉìÉêÄáä~åò= ~ìÑòìåÉÜJ ãÉåI=ëçÑÉêå=ÇáÉë=åáÅÜí=ÇìêÅÜ=ÉáåÉ=ëíÉìÉêäáÅÜÉ=pçåÇÉêîçêëÅÜêáÑí=îÉêÄçíÉå=ïáêÇK= = =
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1. Rechtsquellen
1.3.2
71
Umgekehrte Maßgeblichkeit
jìëë=ëáÅÜ=ÇáÉ=e~åÇÉäëÄáä~åò=ÑΩê=ÇÉå=c~ääI=Ç~ëë=ÇÉê=_áä~åòáÉêÉåÇÉ=ëíÉìÉêäáÅÜÉ=sçêíÉáJ äÉ=åìíòÉå=ïáääI=~å=ÇÉê=píÉìÉêÄáä~åò=~ìëêáÅÜíÉåI=ëç=ëéêáÅÜí=ã~å=îçå=ÇÉê=rãâÉÜêìåÖ= ÇÉê=j~≈ÖÉÄäáÅÜâÉáíK==dÉã®≈=¬=R=f=pK=O=bpíd=ëáåÇ=łëíÉìÉêêÉÅÜíäáÅÜÉ=t~ÜäêÉÅÜíÉ=áå= §ÄÉêÉáåëíáããìåÖ= ãáí= ÇÉê= Ü~åÇÉäëêÉÅÜíäáÅÜÉå= _áä~åò= ~ìëòìΩÄÉå K= aáÉë= ÄÉÇÉìíÉíI= Ç~ëë= ëíÉìÉêêÉÅÜíäáÅÜÉ= sÉêÖΩåëíáÖìåÖÉå= åìê= áå= ^åëéêìÅÜ= ÖÉåçããÉå= ïÉêÇÉå= â∏åJ åÉåI=ïÉåå=ÇáÉëÉ=áå=ÖäÉáÅÜÉê=tÉáëÉ=~ìÅÜ=áå=ÇÉê=e~åÇÉäëÄáä~åò=Äáä~åòáÉêí=ïÉêÇÉåK= ⌦= _ÉáëéáÉäW= a~ë= píÉìÉêêÉÅÜí= ëáÉÜí= áå= ¬= T= Ö= bpíd= ÉáåÉ= pçåÇÉê~ÄëÅÜêÉáÄìåÖ= EÄÉá= sçêäáÉÖÉå= ÄÉJ ëíáããíÉê=sçêê~ìëëÉíòìåÖÉåF=îçêI=ÇáÉ=Ç~ë=e~åÇÉäëêÉÅÜí=åáÅÜí=âÉååíK=táää=ÇÉê=_áä~åJ òáÉêÇÉåÇÉ=ÇáÉëÉ= pçåÇÉê~ÄëÅÜêÉáÄìåÖ= îçêåÉÜãÉåI= áëí= Éê= ïÉÖÉå= ¬=R= f= pK= O= bpíd= ÖÉJ òïìåÖÉåI= ~ìÅÜ= áå= ÇÉê= e~åÇÉäëÄáä~åò= ÇáÉëÉ= ^ÄëÅÜêÉáÄìåÖ= òì= í®íáÖÉåK= a~= Ç~ë= e~åJ ÇÉäëêÉÅÜí=ÉáåÉ=ÇÉê~êíáÖÉ=^ÄëÅÜêÉáÄìåÖ=~ÄÉê=åáÅÜí=âÉååíI=Éêã∏ÖäáÅÜí=¬=ORQ=ed_=ΩÄÉê= Éáå= t~ÜäêÉÅÜí= ÄÉá= åìê= ëíÉìÉêäáÅÜ= òìä®ëëáÖÉå= ^ÄëÅÜêÉáÄìåÖÉå= ÇáÉ= ^åïÉåÇìåÖ= ÇÉê= ^ÄëÅÜêÉáÄìåÖ=áå=ÇÉê=e~åÇÉäëÄáä~åòK= bë=Öáäí=~äëçW=¬=R=f=pK=O=bpíd=→=¬=ORQ=ed_=→=¬=R=f=pK=N=bpíd= =
1.3.3
Durchbrechung der Maßgeblichkeit
sÉêÄáÉíÉí=ÉáåÉ=ëíÉìÉêêÉÅÜíäáÅÜÉ=sçêëÅÜêáÑí=ÇáÉ=§ÄÉêå~ÜãÉ=îçå=mçëáíáçåÉå=ìåÇ=tÉêíJ ~åë®íòÉå= ~ìë= ÇÉê= e~åÇÉäëÄáä~åò= áå= ÇáÉ= píÉìÉêÄáä~åòI= ëç= ëéêáÅÜí= ã~å= îçå= ÇÉê= ëçÖK= aìêÅÜÄêÉÅÜìåÖ=ÇÉê=j~≈ÖÉÄäáÅÜâÉáíK= aáÉëÉ=aìêÅÜÄêÉÅÜìåÖ=äáÉÖí=ÄÉáëéáÉäëïÉáëÉ=îçê= ÄÉá= ÇÉê= m~ëëáîáÉêìåÖëéÑäáÅÜí= ÑΩê= łaêçÜîÉêäìëíêΩÅâëíÉääìåÖÉå = EîÖäK= a= SKOKNF= áå= ÇÉê= e~åÇÉäëÄáä~åòI= ÇÉã= Éáå= m~ëëáîáÉêìåÖëîÉêÄçí= áå= ÇÉê= píÉìÉêÄáä~åò= ÖÉÖÉåΩJ ÄÉêëíÉÜíK= ÄÉá= îÉêëÅÜáÉÇÉåÉå= _áä~åòáÉêìåÖëï~ÜäêÉÅÜíÉåI= ïÉåå= ~ìë= ÄÉëíáããíÉå= Ü~åÇÉäëJ êÉÅÜíäáÅÜÉå=^âíáîáÉêìåÖëï~ÜäêÉÅÜíÉå=ëíÉìÉêêÉÅÜíäáÅÜÉ=^âíáîáÉêìåÖëÖÉÄçíÉ=ïÉêJ ÇÉå=EòK_K=ÄÉáã=aáë~ÖáçW=îÖäK=a=QKOKNF=çÇÉê=~ìë=ÉáåÉã=Ü~åÇÉäëêÉÅÜíäáÅÜÉå=m~ëJ ëáîáÉêìåÖëï~ÜäêÉÅÜí= EòK_K= ^ìÑï~åÇëêΩÅâëíÉääìåÖÉåW= îÖäK= a= SKOKNF= Éáå= ëíÉìÉêJ êÉÅÜíäáÅÜÉë=m~ëëáîáÉêìåÖëîÉêÄçí=ïáêÇK= ÄÉá=ÇÉå=tÉêí~åë~íòï~ÜäêÉÅÜíÉåI=ïÉáä=òK_K=ÄÉá=bêãáííäìåÖ=ÇÉê=eÉêëíÉääâçëíÉå=áå= ÇÉê= píÉìÉêÄáä~åò= ÄÉëíáããíÉ= hçëíÉå~êíÉå= ÉáåÄÉòçÖÉå= ïÉêÇÉå= ãΩëëÉåI= ÑΩê= ÇáÉ= å~ÅÜ=e~åÇÉäëêÉÅÜí=Éáå=tÉêí~åë~íòJt~ÜäêÉÅÜí=ÉáåÖÉê®ìãí=ïáêÇ=EîÖäK=`=VKNFK= dêìåÇë®íòäáÅÜ= ÖáäíI= Ç~ëë= tÉêí~åë®íòÉ= ÇÉê= e~åÇÉäëÄáä~åò= åìê= Ç~åå= áå= ÇáÉ= píÉìÉêÄáJ ä~åò=ΩÄÉêåçããÉå=ïÉêÇÉå=â∏ååÉåI=ïÉåå=ëáÉ=ÇÉå=ëíÉìÉêêÉÅÜíäáÅÜÉå=_ÉïÉêíìåÖëêÉJ ÖÉäå= ÉåíëéêÉÅÜÉåK= páåÇ= ~äëç= ÇáÉ= Ü~åÇÉäëêÉÅÜíäáÅÜÉå= tÉêí~åë®íòÉ= ~ìÑ= dêìåÇ= ÇÉê= ëíêÉåÖÉêÉå= ëíÉìÉêäáÅÜÉå= sçêëÅÜêáÑíÉå= åáÅÜí= òìä®ëëáÖI= ëç= ÖÉÜÉå= ÑΩê= ÇáÉ= píÉìÉêÄáä~åò= ÇáÉ= ëíÉìÉêäáÅÜÉå= sçêëÅÜêáÑíÉå= îçêK= aáÉë= ÑΩÜêí= òì= îçåÉáå~åÇÉê= ~ÄïÉáÅÜÉåÇÉå= e~åJ ÇÉäëJ=ìåÇ=píÉìÉêÄáä~åòÉåK= = = =
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2.1 Buchführungspflicht nach Handelsrecht gÉÇÉê= h~ìÑã~åå= áëí= áå= ÇÉê= _ìåÇÉëêÉéìÄäáâ= aÉìíëÅÜä~åÇ= å~ÅÜ= ¬= OPU= f= ed_= îÉêJ éÑäáÅÜíÉíI=_ΩÅÜÉê=å~ÅÜ=ÇÉå=dêìåÇë®íòÉå=çêÇåìåÖëã®≈áÖÉê=_ìÅÜÜ~äíìåÖ=ìåÇ=_áä~åJ òáÉêìåÖ= òì= ÑΩÜêÉåI= ìã= ÇáÉ= sÉêã∏ÖÉåëJ= ìåÇ= bêíê~Öëä~ÖÉ= ëÉáåÉê= råíÉêåÉÜãìåÖ= ÖÉJ ÖÉåΩÄÉê= òK_K= píÉìÉêÄÉÜ∏êÇÉåI= ~åÇÉêÉå= ëí~~íäK= fåëíáíìíáçåÉå= çÇÉê= dä®ìÄáÖÉêå= çÑÑÉåJ äÉÖÉå=òì=â∏ååÉåK=tÉê=áëí=åìå=~ÄÉê=å~ÅÜ=ÇÉã=dÉëÉíò=h~ìÑã~åå=ìåÇ=ïÉê=åáÅÜí\=aáÉ= ^åíïçêí=~ìÑ=ÇáÉëÉ=cê~ÖÉ=ÄòïK=ÇáÉ=h~ìÑã~ååëÉáÖÉåëÅÜ~Ñí=áëí=áã=e~åÇÉäëÖÉëÉíòÄìÅÜ= ¬¬=NJT=ÇÉÑáåáÉêíK= k~ÅÜ= ¬= N= f= ed_= áëí= ÇÉêàÉåáÖÉ= h~ìÑã~åå= Eh~ìÑã~åå= âê~Ñí= _Éí®íáÖìåÖFI= ÇÉê= Éáå= e~åÇÉäëÖÉïÉêÄÉ= ÄÉíêÉáÄíK= báå= dÉïÉêÄÉÄÉíêáÉÄ= áëí= Ç~ÄÉá= ÇìêÅÜ= ÑçäÖÉåÇÉ= jÉêâã~äÉ= ÅÜ~ê~âíÉêáëáÉêíW=
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74
B. Rechtlicher Hintergrund
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2. Buchführungspflichten
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Grundsätze ordnungsmäßiger Buchführung
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78
B. Rechtlicher Hintergrund =
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3. Grundsätze ordnungsmäßiger Buchführung
79
aÉë=tÉáíÉêÉå=ÉñáëíáÉêí=ÉáåÉ=ëçÖK=^Ää~ìÑÜÉããìåÖK=få=ÇÉê=oÉÖÉä=áëí=Éë=Éêä~ìÄíI= ÇáÉ=dÉëÅÜ®ÑíëìåíÉêä~ÖÉå=å~ÅÜ=^Ää~ìÑ=ÇÉê=^ìÑÄÉï~ÜêìåÖëÑêáëí= òì=îÉêåáÅÜíÉåK= h~åå=ÇáÉ=cáå~åòîÉêï~äíìåÖ=~ÄÉê=òK_K=åçÅÜ=ÇìêÅÜ=ÉáåÉå=píÉìÉêÄÉëÅÜÉáÇ=ÉáåÉ= píÉìÉê=ÉêÜÉÄÉå=E¬¬=NSVJNTN=^lFI=ëç=ÇΩêÑÉå=ÇáÉ=ÄÉíêçÑÑÉåÉå=råíÉêä~ÖÉå=åáÅÜí= îÉêåáÅÜíÉí=ïÉêÇÉåK=
3.2 Bilanzierungsgrundsätze fååÉêÜ~äÄ= ÇÉê= _áä~åòáÉêìåÖëÖêìåÇë®íòÉ= ëáåÇ= åÉÄÉå= ~ääÖÉãÉáåÉå= o~ÜãÉåÖêìåÇë®íJ òÉå=îçê=~ääÉã=^åë~íòJI=^ìëïÉáëJ=ìåÇ=_ÉïÉêíìåÖëîçêëÅÜêáÑíÉå=òì=ìåíÉêëÅÜÉáÇÉåK=^åJ ë~íòîçêëÅÜêáÑíÉå=êÉÖÉäåI=çÄ=Éáå=p~ÅÜîÉêÜ~äí=E^åä~ÖÉÖÉÖÉåëí~åÇI=oΩÅâëíÉääìåÖI=sÉêJ ÄáåÇäáÅÜâÉáíI= oÉÅÜåìåÖë~ÄÖêÉåòìåÖëéçëíÉåI= ÉíÅKF= áå= ÇÉê= _áä~åò= ~ìëÖÉïáÉëÉå= ïÉêJ ÇÉå=ãìëë=E^åë~íòÖÉÄçíÉFI=Ç~êÑ=E^åë~íòï~ÜäêÉÅÜíÉF=çÇÉê=åáÅÜí=Ç~êÑ=E^åë~íòîÉêÄçíÉFK= ^ìëïÉáëîçêëÅÜêáÑíÉå= êÉÖÉäåI= ~å= ïÉäÅÜÉê= píÉääÉ= ÇÉê= däáÉÇÉêìåÖ= ÇÉë= g~ÜêÉë~ÄJ ëÅÜäìëëÉë=ÇáÉ=Äáä~åòáÉêíÉå=mçëáíáçåÉå=òì=ÉêÑ~ëëÉå=ëáåÇK=jáí=ïÉäÅÜÉã=tÉêí=ÇáÉ=áå=ÇÉê= _áä~åò= ìåÇ= dìs= ~åÖÉëÉíòíÉå= mçëáíáçåÉå= ~åòìëÉíòÉå= ëáåÇI= ïáêÇ= ÇìêÅÜ= ÇáÉ= _ÉïÉêJ íìåÖëîçêëÅÜêáÑíÉå= ÇÉÑáåáÉêíK= ^åë~íòJ= ìåÇ= ^ìëïÉáëîçêëÅÜêáÑíÉå= ïÉêÇÉå= îçê= ~ääÉã= áã= h~éáíÉä= `I= _ÉïÉêíìåÖëîçêëÅÜêáÑíÉå= áã= h~éáíÉä= a= ÄÉÜ~åÇÉäíK= ^ääÖÉãÉáåÉ= dêìåÇJ ë®íòÉ=ìåÇ=_ÉïÉêíìåÖëîçêëÅÜêáÑíÉå=ïÉêÇÉå=áã=cçäÖÉåÇÉå=å®ÜÉê=Éê∏êíÉêíK=
3.2.1
Allgemeine Grundsätze
NK=dêìåÇë~íò=ÇÉê=sçääëí®åÇáÖâÉáí= k~ÅÜ=¬=OQS=f=ed_=ëáåÇ=ë®ãíäáÅÜÉ=^âíáî~=ìåÇ=m~ëëáî~I=^ìÑïÉåÇìåÖÉå=ìåÇ=bêíê®ÖÉ= òì= ÉêÑ~ëëÉåK= = aÉê= ^ìëïÉáë= Ü~í= áå= bìêç= òì=ÉêÑçäÖÉå= E¬=OQQ= ed_FK= pÉäÄëí= ÄÉá=ÉáåÉã= tÉêí=îçå=kìää=áëí=ÇÉê=jáåÇÉëí~ìëïÉáë=ÉáåÉê=jÉêâéçëáíáçå=EòK_K=bêáååÉêìåÖëïÉêí=îçå= NIMM= bìêçF= îçêòìåÉÜãÉåK= ¬= OQS= ff= ed_= îÉêÄáÉíÉí= ÇÉë= tÉáíÉêÉå= ÇáÉ= sÉêêÉÅÜåìåÖ= îçå=^âíáî~=ãáí=m~ëëáî~=ëçïáÉ=^ìÑïÉåÇìåÖÉå=ãáí=bêíê®ÖÉå=E_êìííçéêáåòáéFK== fåÑçêã~íáçåÉåI= ÇáÉ= òïáëÅÜÉå= _áä~åòëíáÅÜí~Ö= ìåÇ= _áä~åò~ìÑëíÉääìåÖëòÉáíéìåâí= ÄÉJ â~ååí=ïÉêÇÉåI=ëáåÇ=ÉÄÉåÑ~ääë=òì=ÄÉêΩÅâëáÅÜíáÖÉåK=bë=áëí=áå=ÇáÉëÉã=wìë~ããÉåÜ~åÖ= òïáëÅÜÉå=ïÉêíÉêÜÉääÉåÇÉå=ìåÇ=ïÉêíÄÉÖêΩåÇÉåÇÉå=q~íë~ÅÜÉå=òì=ìåíÉêëÅÜÉáÇÉåK= =
=
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tÉêíÉêÜÉääÉåÇÉ=q~íë~ÅÜÉå=E¬=ORO=f=kêK=Q=ed_F=ÄÉòáÉÜÉå=ëáÅÜ=~ìÑ=p~ÅÜîÉêÜ~äíÉ= ÇÉë=~ÄÖÉä~ìÑÉåÉå=dÉëÅÜ®Ñíëà~ÜêÉëK=få=ÇÉê=k~ÅÜÑçäÖÉéÉêáçÇÉ=ÉêïçêÄÉåÉ=ÄÉëëÉJ êÉ=hÉååíåáëëÉ=ëáåÇ=ÄÉá=ÇÉê=_áä~åòÉêëíÉääìåÖ=ÑΩê=Ç~ë=sçêà~Üê=òì=ÄÉêΩÅâëáÅÜíáÖÉåK=
80
B. Rechtlicher Hintergrund
⌦= _ÉáëéáÉäÉW= = J= j®åÖÉäêΩÖÉå=îçå=hìåÇÉå=~å=áã=~ÄÖÉä~ìÑÉåÉå=dÉëÅÜ®Ñíëà~Üê=~ìëÖÉJ äáÉÑÉêíÉå=bêòÉìÖåáëëÉå= = J= báå= pÅÜìäÇåÉê= ãÉäÇÉí= Äáë= òìê= _áä~åò~ìëíÉääìåÖ= hçåâìêë= ~åI= ïçÄÉá= ÇáÉ=w~ÜäìåÖëìåÑ®ÜáÖâÉáí=~ÄÉê=ÄÉêÉáíë=îçê=_áä~åòëíáÅÜí~Ö=ÄÉëí~åÇK=aáÉ= cçêÇÉêìåÖ=áëí=~äë=ìåÉáåÄêáåÖäáÅÜ=~ÄòìëÅÜêÉáÄÉå=EîäÖK=a=PKQKOFK= tÉêíÄÉÖêΩåÇÉåÇÉ=q~íë~ÅÜÉå=ÄÉòáÉÜÉå=ëáÅÜ=~ìÑ=bêÉáÖåáëëÉI=ÇáÉ=ëáÅÜ=å~ÅÜ=ÇÉã= _áä~åòëíáÅÜí~Ö= ÉêÉáÖåÉí= Ü~ÄÉåK= aáÉ= ÄÉíêÉÑÑÉåÇÉå= bêÉáÖåáëëÉ= ëáåÇ= ÇÉã= åÉìÉå= dÉëÅÜ®Ñíëà~Üê=òìòìçêÇåÉåK= ⌦= _ÉáëéáÉäÉW= = J= j®åÖÉäêΩÖÉå=îçå=hìåÇÉå=~å=áã=åÉìÉå=dÉëÅÜ®Ñíëà~Üê=~ìëÖÉäáÉÑÉêíÉå= bêòÉìÖåáëëÉå= = J= fåëçäîÉåò= ÉáåÉë= pÅÜìäÇåÉêë= áã= cçäÖÉà~ÜêI= ïçÄÉá= òìã= _áä~åòëíáÅÜí~Ö= åçÅÜ= âÉáåÉ= w~ÜäìåÖëëÅÜïáÉêáÖâÉáíÉå= îçêä~ÖÉåK= aáÉëÉ= q~íë~ÅÜÉ= Ç~êÑ= áå= ÇÉê= _áä~åò= ÇÉë= ~ÄÖÉä~ìÑÉåÉå= dÉëÅÜ®Ñíëà~ÜêÉë= åáÅÜí= ÄÉêΩÅâëáÅÜíáÖ= ïÉêÇÉåI=Ç~=ëáÉ=òìã=_áä~åòëíáÅÜí~Ö=åáÅÜí=îçêä~ÖK= =
Ziel des Grundsatzes:
Erfassung aller Vermögensgegenstände, Rückstellungen, Verbindlichkeiten, Rechnungsabgrenzungsposten, Erträge und Aufwendungen.
= OK=dêìåÇë~íò=ÇÉê=_áä~åòâä~êÜÉáí=ìåÇ=§ÄÉêëáÅÜíäáÅÜâÉáí= aáÉëÉê=Ñçêã~äÉ=dêìåÇë~íò=áëí=áå=¬=OQP=ff=ed_=âçÇáÑáòáÉêíK=pçïçÜä=ÇáÉ=däáÉÇÉêìåÖ=~äë= ~ìÅÜ=ÇáÉ=mçëíÉåÄÉòÉáÅÜåìåÖ=ëçää=ìåíÉê=_É~ÅÜíìåÖ=ÇÉê=ÖÉëÉíòäáÅÜÉå=sçêëÅÜêáÑíÉå=ëç= ÖÉëí~äíÉí=ëÉáåI=Ç~ëë=ÇÉê=_áä~åòäÉëÉê=Éáå=ΩÄÉêëáÅÜíäáÅÜÉë=w~ÜäÉåïÉêâ=îçêÑáåÇÉíK=_ÉòΩÖJ äáÅÜ=ÇÉê=_áä~åòÖäáÉÇÉêìåÖ=ÖáÄí=Éë=òK_K=ÑΩê=h~éáí~äÖÉëÉääëÅÜ~ÑíÉå=áå=¬=OSS=ed_=ÖÉå~ìÉ= sçêëÅÜêáÑíÉå=EbáåÉ=bêÖ®åòìåÖ=ÇáÉëÉê=jáåÇÉëíÖäáÉÇÉêìåÖ=áã=fåíÉêÉëëÉ=ÇÉê=_áä~åòâä~êJ ÜÉáí=áëí=ã∏ÖäáÅÜKFK=fã=báåòÉäåÉå=ìãÑ~ëëí=ÇÉê=dêìåÇë~íò=ÇÉê=hä~êÜÉáí=ÇêÉá=^ëéÉâíÉK= ^åÖÉãÉëëÉåÉ=däáÉÇÉêìåÖëíáÉÑÉ=îçå=_áä~åò=ìåÇ=dìsW=báåÉ=òì=íáÉÑÉ=råíÉêÖäáÉÇÉJ êìåÖ=ÇÉê=mçëíÉå=â~åå=~ääÉêÇáåÖë=ïáÉÇÉêìã=òì=råΩÄÉêëáÅÜíäáÅÜâÉáí=ÑΩÜêÉåK= báåÇÉìíáÖÉ=mçëíÉåÄÉòÉáÅÜåìåÖ=áå=_áä~åò=ìåÇ=dìsW=aÉã=g~ÜêÉë~ÄëÅÜäìëëJiÉëÉê= ãΩëëÉå= ÇáÉ= áåÜ~äíäáÅÜÉå= råíÉêëÅÜáÉÇÉ= ÇÉê= ÉáåòÉäåÉå= mçëíÉå= ÇÉìíäáÅÜ= ïÉêÇÉåK= bë= ëáåÇ= ~äëç= ÄÉáëéáÉäëïÉáëÉ=_ÉíÉáäáÖìåÖÉå= EbáÖÉåíΩãÉêêÉÅÜíÉF= ìåÇ= ^ìëäÉáÜìåJ ÖÉå=Edä®ìÄáÖÉêêÉÅÜíÉF=ÇÉìíäáÅÜ=áå=ÇÉê=_ÉòÉáÅÜåìåÖ=òì=íêÉååÉåK= sÉêêÉÅÜåìåÖëîÉêÄçíW=¬=OQS=ff=ed_=îÉêÄáÉíÉí=ÇáÉ=sÉêêÉÅÜåìåÖ=îçå=^âíáî~=ìåÇ= m~ëëáî~= ìåÇ= îçå= ^ìÑïÉåÇìåÖÉå= ìåÇ= bêíê®ÖÉå= ãáíÉáå~åÇÉêK= aáÉë= ëçää= ÉáåÉå= ã∏ÖäáÅÜëí= ÜçÜÉå= fåÑçêã~íáçåëÖÉÜ~äí= ÇÉë= g~ÜêÉë~ÄëÅÜäìëëÉë= áã= fåíÉêÉëëÉ= ÇÉë= iÉëÉêë= Ö~ê~åíáÉêÉåK= pç= áëí= ÄÉáëéáÉäëïÉáëÉ= Éáå= ë~äÇáÉêíÉê= ^ìëïÉáë= ÇÉë= kÉííçJ dÉäÇîÉêã∏ÖÉåë=EZ=h~ëëÉ=H=_~åâÖìíÜ~ÄÉå=H=âìêòÑêáëíáÖÉ=cçêÇÉêìåÖÉå=Ó=âìêòJ ÑêáëíáÖÉ=sÉêÄáåÇäáÅÜâÉáíÉåF=åáÅÜí=òìä®ëëáÖK= aÉê=_áä~åòâä~êÜÉáí=ÇáÉåí=~ì≈ÉêÇÉã=ÇáÉ=ÇÉí~áääáÉêíÉ=^åÖ~ÄÉ=îçå=fåÑçêã~íáçåÉå=ΩÄÉê= ÇáÉ=~åÖÉï~åÇíÉå=_ÉïÉêíìåÖëãÉíÜçÇÉå=EòK_K=jÉíÜçÇÉå=ÇÉê=sçêê~íëÄÉïÉêíìåÖF=ìåÇ= ÇÉêÉå=ûåÇÉêìåÖK= =
3. Grundsätze ordnungsmäßiger Buchführung
81
^ÄëÅÜäáÉ≈ÉåÇ= ëÉá= åçÅÜ= Éêï®ÜåíI= Ç~ëë= ~ìÅÜ= ÉáåÉ= bêÑçäÖëëé~äíìåÖ= îçêòìåÉÜãÉå= áëíK= aáÉë= ÄÉÇÉìíÉíI= Ç~ëë= ÑçäÖÉåÇÉ= ^ìÑïÉåÇìåÖÉå= ìåÇ= bêíê®ÖÉ= ÖÉëçåÇÉêí= ~ìëÖÉïáÉëÉå= ïÉêÇÉå=ãΩëëÉå== _ÉíêáÉÄäáÅÜÉ=^ìÑïÉåÇìåÖÉå=ìåÇ=bêíê®ÖÉW== c~ääÉå=áã=o~ÜãÉå=ÇÉê=bêÑΩääìåÖ=ÇÉë=_ÉíêáÉÄëòïÉÅâë=~å=EòK_K=i∏ÜåÉI=j~íÉêá~äI= sÉêï~äíìåÖëâçëíÉåF= _ÉíêáÉÄëÑêÉãÇÉ=^ìÑïÉåÇìåÖÉå=ìåÇ=bêíê®ÖÉW== píÉÜÉå=ãáí=ÇÉã=_ÉíêáÉÄëòïÉÅâ=áå=âÉáåÉêäÉá=wìë~ããÉåÜ~åÖ=EòK_K=péÉåÇÉåF= mÉêáçÇÉåÑêÉãÇÉ=^ìÑïÉåÇìåÖÉå=ìåÇ=bêíê®ÖÉW= tìêÇÉå=åáÅÜí=áå=ÇÉã=g~Üê=ÖÉÄìÅÜíI=áå=ÇÉã=ÇÉê=bêÑçäÖ=ÉêòáÉäí=ïìêÇÉ=EòK_K=píÉìJ Éêå~ÅÜò~ÜäìåÖÉå=~ìë=ÑêΩÜÉêÉå=g~ÜêÉåF= ^ì≈ÉêçêÇÉåíäáÅÜÉ=^ìÑïÉåÇìåÖÉå=ìåÇ=bêíê®ÖÉW= páåÇ=~ì≈ÉêçêÇÉåíäáÅÜ=ÜçÅÜ=ìåÇ=Ñ~ääÉå=®ì≈Éêëí=ëÉäíÉå=~å=EòK_K=bêíê®ÖÉ=~ìë=sÉêJ ëáÅÜÉêìåÖëäÉáëíìåÖÉåI=sÉêäìëí=~ìë=_~åÇëÅÜ~ÇÉåF= =
Ziel des Grundsatzes:
Verständliche Informationsübermittlung
= PK=dêìåÇë~íò=ÇÉê=_áä~åòï~ÜêÜÉáí= aáÉ=dêìåÇë®íòÉ=ÇÉê=oáÅÜíáÖâÉáí=ìåÇ=táääâΩêÑêÉáÜÉáí=ïÉêÇÉå=çÑí=ìåíÉê=ÇÉã=_ÉÖêáÑÑ=_áJ ä~åòï~ÜêÜÉáí=òìë~ããÉåÖÉÑ~ëëíK== råíÉê=oáÅÜíáÖâÉáí=Eë~ÅÜÄÉòçÖÉåÇÉ=t~ÜêÜÉáíF=ïáêÇ=ÇáÉ=çÄàÉâíáîÉ=§ÄÉêÉáåëíáããìåÖ= òïáëÅÜÉå=ÇÉå=^ìëë~ÖÉå=îçå=_ìÅÜÑΩÜêìåÖ=ëçïáÉ=g~ÜêÉë~ÄëÅÜäìëë=ìåÇ=ÇÉå=òìÖêìåJ ÇÉ=äáÉÖÉåÇÉå=p~ÅÜîÉêÜ~äíÉå=îÉêëí~åÇÉåK=aÉê=dêìåÇë~íò=ÇÉê=oáÅÜíáÖâÉáí=ìãÑ~ëëí= ëçJ ïçÜä=ÇáÉ=Ñçêã~äÉ=~äë=~ìÅÜ=ÇáÉ=ã~íÉêáÉääJáåÜ~äíäáÅÜÉ=pÉáíÉ=ÇÉë=g~ÜêÉë~ÄëÅÜäìëëÉëK=fåJ Ü~äíäáÅÜ= êáÅÜíáÖ= ãΩëëÉå= ÇáÉ= áã= g~ÜêÉë~ÄëÅÜäìëë= ~åÖÉÖÉÄÉåÉå= tÉêíÉ= ëÉáå= EâçêêÉâíÉ= _ÉêÉÅÜåìåÖ=ìåíÉê=_ÉêΩÅâëáÅÜíáÖìåÖ=ÇÉê=dç_=ìåÇ=Ü~åÇÉäëêÉÅÜíäáÅÜÉê=oÉÅÜåìåÖëäÉJ ÖìåÖëîçêëÅÜêáÑíÉåFK=cçêã~ä=ÖÉÜí=Éë=Ç~êìãI=ÇáÉ=g~ÜêÉë~ÄëÅÜäìëëéçëáíáçåÉå=áÜêÉã=fåJ Ü~äí=ìåÇ=ÇÉå=ÖÉëÉíòäáÅÜÉå=sçêëÅÜêáÑíÉå=ÉåëéêÉÅÜÉåÇ=òì=ÄÉòÉáÅÜåÉåK=bë=ÇΩêÑÉå=~äëç= ÄÉáëéáÉäëïÉáëÉ=dÉÄ®ìÇÉ=åáÅÜí=~äë=ã~ëÅÜáåÉääÉ=^åä~ÖÉå=ÄÉòÉáÅÜåÉí=ïÉêÇÉåK= _Éá= pÅÜ®íòìåÖÉå= ìåÇ= bêãÉëëÉåëÉåíëÅÜÉáÇìåÖÉå= áëí= ÇÉê= dêìåÇë~íò= ÇÉê= táääâΩêJ ÑêÉáÜÉáí==EéÉêëçåÉåÄÉòçÖÉåÉ=t~ÜêÜÉáíF=òì=ÄÉ~ÅÜíÉåK=báå=tÉêí~åë~íò=áã=g~ÜêÉë~ÄJ ëÅÜäìëë= Ç~êÑ= ÇÉãå~ÅÜ= åáÅÜí= ïáääâΩêäáÅÜ= ëÉáåI= Éê= ãìëë= ~ìë= çêÇåìåÖëÖÉã®≈Éå= _ÉäÉJ ÖÉåI=_ΩÅÜÉêå=ìåÇ=êÉáÑäáÅÜÉå=§ÄÉêäÉÖìåÖÉå=ÄÉêìÜÉåK=aÉê= _áä~åòáÉêÉåÇÉ=ãìëë=ëìÄJ àÉâíáî= îçå= ÇÉê= oáÅÜíáÖâÉáí= ÇÉê= pÅÜ®íòìåÖ= ÄòïK= ÇÉê= òìÖêìåÇÉ= äáÉÖÉåÇÉå= ^åå~ÜãÉå= ΩÄÉêòÉìÖí=ëÉáå=ìåÇ=Ç~êÑ=åáÅÜí=ÄÉïìëëí=îçå=ëÉáåÉê=§ÄÉêòÉìÖìåÖ=~ÄïÉáÅÜÉåI=ìã=ÄáJ ä~åòéçäáíáëÅÜÉ=çÇÉê=ëíÉìÉêäáÅÜÉ=wáÉäÉ=òì=ÉêêÉáÅÜÉåK= =
Ziel des Grundsatzes:
Verbot wissentlich falscher Bilanzansätze
=
82
B. Rechtlicher Hintergrund
QK=dêìåÇë~íò=ÇÉê=táêíëÅÜ~ÑíäáÅÜâÉáí=ìåÇ=tÉëÉåíäáÅÜâÉáí= _Éá=àÉÇÉê=ÉáåòÉäåÉå=j~≈å~ÜãÉ=ÇÉê=_ìÅÜÑΩÜêìåÖ=ìåÇ=ÄÉá=ÇÉê=^ìÑëíÉääìåÖ=ÇÉë=g~ÜJ êÉë~ÄëÅÜäìëëÉë=ãìëë=ÇáÉ=sÉêÜ®äíåáëã®≈áÖâÉáí=ÇÉê=jáííÉä=ÖÉï®ÜêäÉáëíÉí=ëÉáåK=^ìÑ=ÉáåÉ= ÖÉêáåÖÑΩÖáÖÉ=sÉêÄÉëëÉêìåÖ=ÇÉê=dÉå~ìáÖâÉáí=ìåÇ=Ç~ãáí=ÇÉë=fåÑçêã~íáçåëÖÉÜ~äíÉë=ÑΩê= ÇáÉ=^ÇêÉëë~íÉå=â~åå=îÉêòáÅÜíÉí=ïÉêÇÉåI=ïÉåå=ÇÉê=Ç~ãáí=îÉêÄìåÇÉåÉ=^ìÑï~åÇ=ìåJ îÉêÜ®äíåáëã®≈áÖ=ÜçÅÜ=áëíK=bë=ï®êÉ=òK_K=∏âçåçãáëÅÜ=åáÅÜí=îÉêíêÉíÄ~êI=áå=ÉáåÉã=_~ìJ ã~êâí= àÉÇÉ= ÉáåòÉäåÉ= pÅÜê~ìÄÉ= ÉáåòÉäå= òì= ÄÉïÉêíÉåK= aáÉëÉê= dêìåÇë~íò= ëíÉääí= Ç~ÜÉê= ÇáÉ= oÉÅÜíÑÉêíáÖìåÖ= ÑΩê= ~ääÉ= Ö®åÖáÖÉå= _ÉïÉêíìåÖëîÉêÉáåÑ~ÅÜìåÖëîÉêÑ~ÜêÉå= EîÖäK= a= PKOKNF=Ç~êK= _Éá= ÇÉê= _ÉìêíÉáäìåÖ= ÇÉê= lêÇåìåÖëã®≈áÖâÉáí= ÇÉê= _ìÅÜÑΩÜêìåÖ= áëí= Éë= îçå= _ÉÇÉìJ íìåÖI= çÄ= ÇáÉ= j®åÖÉä= áã= eáåÄäáÅâ= ~ìÑ= ÇáÉ= dÉåÉê~äåçêãÉå= ïÉëÉåíäáÅÜ= ëáåÇ= çÇÉê= åáÅÜíK= aáÉ= ^ÄÖêÉåòìåÖ= òïáëÅÜÉå= ïÉëÉåíäáÅÜÉå= ìåÇ= ìåïÉëÉåíäáÅÜÉå= báåÑäΩëëÉåI= fåJ Ñçêã~íáçåÉå=çÇÉê=_ÉÉáåíê®ÅÜíáÖìåÖÉå=áëí=åáÅÜí=ÖÉëÉíòíäáÅÜ=ÖÉêÉÖÉäí=ìåÇ=ÄäÉáÄí=Ç~ÜÉê= ÇÉê=_ÉìêíÉáäìåÖ=ÇÉë=_áä~åòáÉêÉåÇÉå=ÄòïK=ÇÉë=^ÄëÅÜäìëëéêΩÑÉêë=ΩÄÉêä~ëëÉåK= =
3.2.2
Bewertungsgrundsätze nach § 252 HGB
NK=dêìåÇë~íò=ÇÉê=_áä~åòáÇÉåíáí®í= aáÉëÉê=dêìåÇë~íò=ÄÉë~ÖíI=Ç~ëë=ÇáÉ=bê∏ÑÑåìåÖëÄáä~åò=ÉáåÉë=g~ÜêÉë=ãáí=ÇÉê=pÅÜäìëëÄáJ ä~åò=ÇÉë=sçêà~ÜêÉë=ΩÄÉêÉáåëíáããÉå=ãìëë=E¬=ORO=f=kêK=N=ed_FK== aáÉ= cçäÖÉ= ÇÉê= _áä~åòáÇÉåíáí®í= áëí= ÇáÉ= ëçÖK= wïÉáëÅÜåÉáÇáÖâÉáí= ÇÉê= _áä~åòK= aáÉëÉ= ÄÉJ ë~ÖíI=Ç~ëë=~ääÉ=Äáä~åòÄÉòçÖÉåÉå=_ìÅÜìåÖÉå=ÖÉÖÉåä®ìÑáÖÉ=^ìëïáêâìåÖÉå=~ìÑ=ÇáÉ=_áJ ä~åò=ìåÇ=ÇÉå=dÉïáåå=ÇÉë=cçäÖÉà~ÜêÉë=EçÇÉê=ãÉÜêÉêÉê=cçäÖÉà~ÜêÉF=Ü~ÄÉåK= ⌦= _ÉáëéáÉäW== báåÉ=ÖÉïáååãáåÇÉêåÇÉ=pçåÇÉê~ÄëÅÜêÉáÄìåÖ=~ìÑ=ÉáåÉ=^åä~ÖÉ=áã=g~Üê=MS=ÑΩÜêí=Ç~òìI= Ç~ëë= ÇÉê= ^åÑ~åÖëïÉêí= áå= MT= ÉåíëéêÉÅÜÉåÇ= åáÉÇêáÖÉêI= ÇáÉ= ^ÄëÅÜêÉáÄìåÖëÄ~ëáë= ÇÉê= cçäÖÉà~ÜêÉ=ãáíÜáå=ÉåíëéêÉÅÜÉåÇ=åáÉÇêáÖÉê=ìåÇ=ÇÉê=dÉïáåå=ÉåíëéêÉÅÜÉåÇ=Ü∏ÜÉê=áëíK== =
Ziel des Grundsatzes:
Schutz gegen Bilanzmanipulation =
OK=dêìåÇë~íò=ÇÉê=_áä~åòâçåíáåìáí®í=ÄòïK=JëíÉíáÖâÉáí= aáÉ= ÑçêãÉääÉ= _áä~åòëíÉíáÖâÉáí= ëÅÜêÉáÄí= ÇáÉ= _ÉáÄÉÜ~äíìåÖ= ÇÉê= cçêã= ìåÇ= däáÉÇÉêìåÖ= îçå=~ìÑÉáå~åÇÉêÑçäÖÉåÇÉå=_áä~åòÉå=ìåÇ=dìsJoÉÅÜåìåÖÉå=îçê=E¬=OSR=f=ed_FK=råJ íÉê= ÄÉëçåÇÉêÉå= rãëí®åÇÉå= ëáåÇ= ^ÄïÉáÅÜìåÖÉå= ÄÉá= ~ìÑÉáå~åÇÉêÑçäÖÉåÇÉå= däáÉÇÉJ êìåÖÉå=ã∏ÖäáÅÜI=ÇáÉ=~ÄÉê=áã=^åÜ~åÖ=~åòìÖÉÄÉå=ìåÇ=òì=ÄÉÖêΩåÇÉå=ëáåÇK= ^ìÅÜ=ïÉåå=ÇáÉëÉê=dêìåÇë~íò=åìê=ÑΩê=h~éáí~äÖÉëÉääëÅÜ~ÑíÉå=âçÇáÑáòáÉêí=ïìêÇÉI=Ç~=åìê= ÑΩê= ÇáÉëÉ=ÉáåÉ= ÄÉëíáããíÉ= jáåÇÉëíÖäáÉÇÉêìåÖ= îçêÖÉëÅÜêáÉÄÉå=áëíI= áëí= Éê= ÇÉååçÅÜ= ÑΩê= ~ääÉ=oÉÅÜíëÑçêãÉå=ÖΩäíáÖK== j~íÉêáÉääÉ=_áä~åòëíÉíáÖâÉáí=ÜáåÖÉÖÉå=îÉêéÑäáÅÜíÉí=ÇÉå=_áä~åòáÉêÉåÇÉå=òìê=âçåíáåìáÉêJ äáÅÜÉå= ^åïÉåÇìåÖ= ÇÉê= ÖäÉáÅÜÉå= _ÉïÉêíìåÖëãÉíÜçÇÉå= Eéä~åã®≈áÖ= ìåÇ= ëóëíÉã~J íáëÅÜ= îçêÖÉåçããÉåÉ= _ÉïÉêíìåÖëã~≈å~ÜãÉåF= áå= ~ìÑÉáå~åÇÉêÑçäÖÉåÇÉå= _áä~åòÉå= EdäÉáÅÜã®≈áÖâÉáí=ÇÉê=_ÉïÉêíìåÖëãÉíÜçÇÉå=å~ÅÜ=¬=ORO=f=kêK=S=ed_FK=pç=ëáåÇ=ÄÉáJ =
3. Grundsätze ordnungsmäßiger Buchführung
83
ëéáÉäëïÉáëÉ= ÉáåÉ= dêìééÉåÄÉïÉêíìåÖ= ãáí= aìêÅÜëÅÜåáííëïÉêíÉå= E¬= ORS= ed_I= îÖäK= a= PKOKNF=çÇÉê=ÇáÉ=báåÄÉòáÉÜìåÖ=ÇÉê=sÉêï~äíìåÖëâçëíÉå=áå=ÇáÉ=eÉêëíÉääâçëíÉå=E¬=ORR=ff= ed_I= îÖäK= `= VKNF= ÄÉáòìÄÉÜ~äíÉåK= aáÉ= _áä~åòëíÉíáÖâÉáí= ìãÑ~ëëí= ~ääÉêÇáåÖë= âÉáåÉ= ^åJ ë~íòëíÉíáÖâÉáíI=~äëç=åáÅÜí=ÇáÉ=mÑäáÅÜí=ÇÉê=ëíÉíáÖÉå=^ìëΩÄìåÖ=îçå=^åë~íòï~ÜäêÉÅÜíÉåK= =
Ziel des Grundsatzes:
Gewährleistung der Vergleichbarkeit des Unternehmenserfolgs und -vermögens im Zeitablauf =
PK=dêìåÇë~íò=ÇÉê=cçêíÑΩÜêìåÖ=ÇÉê=råíÉêåÉÜãÉåëí®íáÖâÉáí= aáÉëÉê=~ìÅÜ=~äë=dçáåÖJ`çåÅÉêåJmêáåòáé=E¬=ORO=f=kêK=O=ed_F=ÄÉòÉáÅÜåÉíÉ=dêìåÇë~íò= ÄÉë~ÖíI= Ç~ëë= åçêã~äÉêïÉáëÉ= ÇáÉ= cçêíÑΩÜêìåÖ= ÇÉê= dÉëÅÜ®Ñíëí®íáÖâÉáí= áå= ÉáåÉã= ΩÄÉêJ ëÉÜÄ~êÉå= âΩåÑíáÖÉå= wÉáíê~ìã= îçå= ãáåÇÉëíÉåë= ÉáåÉã= g~Üê=å~ÅÜ= ÇÉã= _áä~åòëíáÅÜí~Ö= ~åòìåÉÜãÉå= áëí= ìåÇ= Ç~ÜÉê= ÄÉá= ÇÉê= _ÉïÉêíìåÖ= ÇÉê= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ= ÉáåÉ= ã∏ÖäáÅÜÉ= sÉê®ì≈ÉêìåÖ= ÇÉë= dÉë~ãíìåíÉêåÉÜãÉåë= çÇÉê= ÇÉëëÉå= iáèìáÇ~íáçå= áå= báåJ òÉäíÉáäÉå=EłwÉêëÅÜä~ÖìåÖ F=âÉáåÉ=_É~ÅÜíìåÖ=ÑáåÇÉíK=^ÄëÅÜä®ÖÉI=ÇáÉ=ÄÉá=wÉêëÅÜä~ÖìåÖ= åçíïÉåÇáÖ= ï®êÉåI= ìã= âìêòÑêáëíáÖ= ÉáåÉå= h®ìÑÉê= òì= ÑáåÇÉåI= ÇΩêÑÉå= Ç~ÜÉê= ÄÉáëéáÉäëJ ïÉáëÉ=åáÅÜí=îÉêêÉÅÜåÉí=ïÉêÇÉåK= = ^ÄïÉáÅÜìåÖ=îçã=dêìåÇë~íò= s= = cçêíÑΩÜêìåÖëJ=ìåÇ=iáèìáÇ~íáçåëïÉêí= = =
Ziel des Grundsatzes:
Vermeidung abschlagsbedingter negativer Auswirkungen auf die Werte von Vermögensgegenständen =
QK=dêìåÇë~íò=ÇÉê=píáÅÜí~ÖëÄÉïÉêíìåÖ= aáÉ= _áä~åò= áëí= ~äë= wÉáíéìåâíêÉÅÜåìåÖ= ëíáÅÜí~ÖëÄÉòçÖÉåK= _áä~åòëíáÅÜí~Ö= áëí= ãÉáëí= ÇÉê= PNKNOK= bë= ÖáÄí= ~ÄÉê= ~ìÅÜ=îçã= h~äÉåÇÉêà~Üê= ~ÄïÉáÅÜÉåÇÉ= dÉëÅÜ®Ñíëà~ÜêÉ= ãáí= ~åÇÉJ êÉå= _áä~åòëíáÅÜí~ÖÉå= EòK_K= PMKMSKI= PMKMVKFK= a~ë= sÉêã∏ÖÉå= ìåÇ= ~ìÅÜ= ÇáÉ= cáå~åòä~ÖÉ= ëáåÇ=~ìÑ=ÇáÉëÉå=píáÅÜí~Ö=ÄÉòçÖÉå=Ç~êòìëíÉääÉå=E¬=ORO=f=kêK=P=ed_FK= bë=ÇΩêÑÉå=áå=ÇÉê=_áä~åò=åìê=~ääÉ=~ã=píáÅÜí~Ö=îçêÜ~åÇÉåÉå=sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ= ìåÇ=pÅÜìäÇÉå=ãáí=áÜêÉã=píáÅÜí~ÖëïÉêí=~åÖÉëÉíòí=ïÉêÇÉåK=^ääÉ=Äáë=òìã=píáÅÜí~Ö=îÉêJ ìêë~ÅÜíÉå= bêÑçäÖëïáêâìåÖÉå= ëáåÇ= òì= ÄÉêΩÅâëáÅÜíáÖÉåK= ^ääÉ= ëé®íÉê= ~åÖÉÑ~ääÉåÉå= bêJ ÉáÖåáëëÉ=ÇΩêÑÉå=åáÅÜí=ãÉÜê=ÄÉêΩÅâëáÅÜíáÖí=ïÉêÇÉåK== dÉê~ÇÉ= ÇÉëïÉÖÉå= ãΩëëíÉå= ~ìÅÜ= fåÑçêã~íáçåÉå= ΩÄÉê= ÇáÉ= sÉêÜ®äíåáëëÉ= ~ã= _áä~åòJ ëíáÅÜí~ÖI=ÇáÉ=ÇÉå=_áä~åòáÉêÉåÇÉå=Éêëí=òïáëÅÜÉå=_áä~åòëíáÅÜí~Ö=ìåÇ=J~ìÑëíÉääìåÖ=ÉêêÉáJ ÅÜÉåI=ÄÉêΩÅâëáÅÜíáÖí=ïÉêÇÉå=EïÉêí~ìÑÜÉääÉåÇÉ=q~íë~ÅÜÉåI=îÖäK=_=PKOKNFK= aÉê=¬=ORP=fff=pK=P=ed_=ÄÉëÅÜêÉáÄí=ÇáÉ=ÉáåòáÖÉ=^ìëå~ÜãÉ=îçã=píáÅÜí~Öëéêáåòáé=ìåÇ= òï~ê= ÇáÉ= ^ÄëÅÜêÉáÄìåÖ= ÇÉë= rãä~ìÑîÉêã∏ÖÉåë= ~ìÑ= ÇÉå= áå= å®ÅÜëíÉê= wìâìåÑí= òì= ÉêJ ï~êíÉåÇÉå=åáÉÇêáÖÉêÉå=tÉêíK=aáÉëÉ=^ÄëÅÜêÉáÄìåÖ=áëí=áã=píÉìÉêêÉÅÜí=åáÅÜí=òìä®ëëáÖK= =
84
B. Rechtlicher Hintergrund
Ziel des Grundsatzes:
Ansatz und Bewertung sollen sich auf den Bilanzstichtag beziehen. Aus Vorsichtsgründen sind ausnahmsweise werterhellende Tatsachen zu berücksichtigen. =
RK=dêìåÇë~íò=ÇÉê=báåòÉäÄÉïÉêíìåÖ= k~ÅÜ=¬=ORO=f=kêK=P=ed_=ìåÇ=¬=S=f=kêK=N=bpíd=ëáåÇ=~ääÉ=sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ=ÄòïK= táêíëÅÜ~ÑíëÖΩíÉê= òìã= _áä~åòëíáÅÜí~Ö= ÉáåòÉäå= òì= ÄÉïÉêíÉåK= aáÉë= ÄÉÇÉìíÉí= åìå= ~ÄÉê= åáÅÜíI=Ç~ëë=òK_K=àÉÇÉë=_~ìíÉáä=ÉáåÉë=mâïë=ÉáåòÉäå=òì=ÄÉïÉêíÉå=áëíI=Ç~=ÇáÉëÉ=báåòÉäJ íÉáäÉ=åìê=òìë~ããÉå=ÑìåâíáçåëÑ®ÜáÖ=ëáåÇ=ìåÇ=áÜêÉå=tÉêí=åìê=áã=dÉë~ãíòìë~ããÉåJ Ü~åÖ=ÉêÜ~äíÉåK=aáÉ=âäÉáåëíÉ=òì=ÄÉïÉêíÉåÇÉ=báåÜÉáí=ÄÉëíÉÜí=Ç~ÜÉê=~ìë=ãÉÜêÉêÉå=báåJ òÉäíÉáäÉåI=ÇáÉ=áå=ÉáåÉã=ëÉÜê=ÉåÖÉå=cìåâíáçåëJ=ìåÇ=kìíòÉåòìë~ããÉåÜ~åÖ=ëíÉÜÉåK= ^ìë= táêíëÅÜ~ÑíäáÅÜâÉáíëÖêΩåÇÉå= ëáåÇ= ~ÄÉê= áå= ÇÉê= mê~ñáë= ÑçäÖÉåÇÉ= ^ìëå~ÜãÉå= îçå= ÇáÉëÉã=dêìåÇë~íò=ΩÄäáÅÜ=ìåÇ=òìä®ëëáÖW= dêìééÉåÄÉïÉêíìåÖW=ÖäÉáÅÜ~êíáÖÉ=dΩíÉê=ïÉêÇÉå=òì=ÉáåÉê=dêìééÉ=òìë~ããÉåÖÉJ Ñ~ëëí=ìåÇ=~äë=dêìééÉ=ÄÉïÉêíÉí=E¬=OQM=fs=ed_I=îÖäK=a=PKOKNF= cÉëíïÉêí= ÑΩê= ÉáåÉ= dêìééÉ= îçå= dÉÖÉåëí®åÇÉåW= òK_K= pÅÜê~ìÄÉåI= eçíÉäéçêòÉää~å= E¬=OQM=fff=ed_I=îÖäK=a=PKOKNF= sÉêÄê~ìÅÜëÑçäÖÉîÉêÑ~ÜêÉå=ÄÉá=sçêê~íëÄÉïÉêíìåÖ=E¬=ORS=pK=N=ed_I=îÖäK=a=PKOKNF= m~ìëÅÜ~äïÉêíÄÉêáÅÜíáÖìåÖÉå=ÄÉá=Éáåï~åÇÑêÉáÉå=cçêÇÉêìåÖÉå=EîÖäK=a=PKPKRF= m~ìëÅÜ~äÉ=d~ê~åíáÉêΩÅâëíÉääìåÖÉå=EîÖäK=a=SF= =
Ziel des Grundsatzes:
Verhinderung der Verrechnung von positiven und negativen Wertänderungen bei verschiedenen Vermögensgegenständen (Gewährleistung der Nachvollziehbarkeit der Bewertung für Dritte und Schutz vor Bilanzmanipulation) sowie Erreichung größerer Genauigkeit bei der Bewertung =
SK=dêìåÇë~íò=ÇÉê=mÉêáçÇÉå~ÄÖêÉåòìåÖ= bêíê®ÖÉ=ìåÇ=^ìÑïÉåÇìåÖÉå=ÇΩêÑÉå=åìê=áå=ÇÉã=dÉëÅÜ®Ñíëà~Üê=~åÖÉëÉíòí=ïÉêÇÉåI=áå= Ç~ë= ëáÉ= ïáêíëÅÜ~ÑíäáÅÜ= ÄÉíê~ÅÜíÉí= Ñ~ääÉåK= ^ìÑ= ÇÉå= wÉáíéìåâí= ÇÉê= w~ÜäìåÖ= âçããí= Éë= Ç~ÄÉá= åáÅÜí= ~å= E¬= ORO= f= kêK= R= ed_FK= fååÉêÜ~äÄ= ÇáÉëÉë= dêìåÇë~íòÉë= ìåíÉêëÅÜÉáÇÉí= ã~å=~ääÖÉãÉáå=òïáëÅÜÉå=ÉáåÉê=^ÄÖêÉåòìåÖ=ÇÉê=p~ÅÜÉ=å~ÅÜ=ìåÇ=ÉáåÉê=^ÄÖêÉåòìåÖ= ÇÉê=wÉáí=å~ÅÜK= ^ÄÖêÉåòìåÖ=ÇÉê=p~ÅÜÉ=å~ÅÜW=oÉ~äáëáÉêíÉå=bêíê®ÖÉå=ëáåÇ=ÇáÉ=òì=áÜêÉê=bêòáÉäìåÖ= ÉêÑçêÇÉêäáÅÜÉå= ^ìÑïÉåÇìåÖÉå= òìòìçêÇåÉåK= ^ìëÖ~ÄÉå= ïÉêÇÉå= áå= ÇÉê= mÉêáçÇÉ= òìã=^ìÑï~åÇI=áå=ÇÉê=ÇáÉ=ë~ÅÜäáÅÜ=Ç~òìÖÉÜ∏êáÖÉå=bêíê®ÖÉ=êÉ~äáëáÉêí=ïÉêÇÉåK= ⌦= _ÉáëéáÉäW=fã=g~Üê=OMMR=ÜÉêÖÉëíÉääíÉ=bêòÉìÖåáëëÉ=â∏ååÉå=~ìÑÖêìåÇ=îçå=^Äë~íòJ ëÅÜïáÉêáÖâÉáíÉå= Éêëí= áã= g~Üê= OMMS= îÉêâ~ìÑí= ïÉêÇÉåK= _áë= òìã= ^åÑ~ääÉå= ÇÉê= bêJ íê®ÖÉ= áã= g~Üê= OMMS= ÇΩêÑÉå= âÉáåÉ= ÇÉå= bêòÉìÖåáëëÉå= òìêÉÅÜÉåÄ~êÉå= ^ìëÖ~ÄÉå= EòK_K=i∏ÜåÉI=j~íÉêá~äI=ÉíÅKF=~ìÑï~åÇëïáêâë~ã=ïÉêÇÉåK=bêëí=áã=g~Üê=OMMS=ÉêÖÉJ ÄÉå= ÇáÉ= ïáêíëÅÜ~ÑíäáÅÜ= òìë~ããÉåÖÉÜ∏êÉåÇÉå= bêíê®ÖÉ= ìåÇ= ^ìÑïÉåÇìåÖÉå= ÉáJ åÉå=ëáååîçääÉå=g~ÜêÉëÉêÑçäÖK= =
3. Grundsätze ordnungsmäßiger Buchführung
85
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báåÉ= ÖÉå~ìÉ= ÄìÅÜìåÖëíÉÅÜåáëÅÜÉ= _ÉÜ~åÇäìåÖ= ÇáÉëÉê= ^ÄÖêÉåòìåÖÉå= ÇìêÅÜ= íê~åëáëíçêáëÅÜÉ= E§ÄÉêíê~ÖìåÖ= îçå= dÉïáåå~ìëïáêâìåÖÉå= áå= ëé®íÉêÉ= mÉêáçÇÉåX= _ëéK= NF= ìåÇ= ~åíáòáé~íáîÉ= EsçêïÉÖå~ÜãÉ= îçå= dÉïáåå~ìëïáêâìåÖÉå= ~ìë= ÇÉê= w~ÜäìåÖëéÉêáçÇÉX=_ëéK=OF=oÉÅÜåìåÖë~ÄÖêÉåòìåÖëéçëíÉå=ÑçäÖí=ìåíÉê=a=QK=
=
Ziel des Grundsatzes:
Gewinn/Verlust wird demjenigen Geschäftsjahr zugeordnet, in dem er verursacht wurde (periodengerechte Erfolgsermittlung) =
TK=dêìåÇë~íò=ÇÉê=sçêëáÅÜí= aáÉëÉë= mêáåòáé= ÇÉê= îçêëáÅÜíáÖÉå= _ÉïÉêíìåÖ= E¬= ORO= f= kêK= Q= ed_F= ÄÉë~ÖíI= Ç~ëë= ÇÉê= g~ÜêÉë~ÄëÅÜäìëë=~ääÉ=oáëáâÉåI=ÇáÉ=îçê~ìëëáÅÜíäáÅÜ=ÄÉëíÉÜÉåI=ÄÉêΩÅâëáÅÜíáÖÉå=ìåÇ=ÇáÉ= sÉêã∏ÖÉåëJ= ìåÇ= bêíê~Öëä~ÖÉ= îçêëáÅÜíáÖ= ÉáåëÅÜ®íòÉå= ãìëëK= aÉê= h~ìÑã~åå= ëçää= ëáÅÜ= ~äëç= ã∏ÖäáÅÜëí= ~êã= ÄòïK= åáÅÜí= êÉáÅÜÉê= ~äë= Éê= áëí= Ç~êëíÉääÉåK= a~ÄÉá= ÇΩêÑÉå= ~ÄÉê= ÇáÉ= dêìåÇë®íòÉ=ÇÉê=oáÅÜíáÖâÉáí=ìåÇ=táääâΩêÑêÉáÜÉáí=åáÅÜí=îÉêäÉíòí=ïÉêÇÉåK=aáÉë=ÄÉÇÉìíÉíI= Ç~ëë=ëáÅÜ=ÇÉê=h~ìÑã~åå=åáÅÜí=ÇìêÅÜ=ìåÖÉêÉÅÜíÑÉêíáÖíÉ=^åë®íòÉ=ëç=~êã=êÉÅÜåÉíI=Ç~ëë= Éê=~ìÑÖêìåÇ=ÉáåÉë=Ç~ÇìêÅÜ=åáÉÇêáÖÉêÉå=dÉïáååÉë=ïÉåáÖÉê=aáîáÇÉåÇÉ=~å=ÇáÉ=^âíáçJ å®êÉ=~ìëëÅÜΩííÉå=ìåÇ=~ìÅÜ=ïÉåáÖÉê=píÉìÉêå=ÄÉò~ÜäÉå=ãìëëK= aÉê=dêìåÇë~íò=ÇÉê=sçêëáÅÜí=ÄÉêìÜí=~ìÑ=òïÉá=råíÉêéêáåòáéáÉåW= =
^K=oÉ~äáë~íáçåëéêáåòáé== a~ë=oÉ~äáë~íáçåëéêáåòáé=ÄÉ~åíïçêíÉí=ÇáÉ=cê~ÖÉI=áå=ïÉäÅÜÉã=g~Üê=bêíê®ÖÉ=EéÉêáçÇáëáÉêJ íÉ= báåå~ÜãÉåF= ~åÑ~ääÉåI= ÇÉåÉå= Ç~åå= ÇáÉ= ^ìÑïÉåÇìåÖÉå= EéÉêáçÇáëáÉêíÉ= ^ìëÖ~ÄÉåF= å~ÅÜ= ÇÉã= mêáåòáé= ÇÉê= ë~ÅÜäáÅÜÉå= ^ÄÖêÉåòìåÖ= òìÖÉçêÇåÉí= ïÉêÇÉåK= pçãáí= ïáêÇ= ÇìêÅÜ= Ç~ë= oÉ~äáë~íáçåëéêáåòáé= ~ìÅÜ= ÖÉêÉÖÉäíI= áå= ïÉäÅÜÉã= g~Üê= ÇÉê= dÉïáåå= ~ìë= ÉáJ åÉã=dÉëÅÜ®Ñí=òì=îÉêÄìÅÜÉå=áëíK= bë=ÖáäíW== a~ë= oÉ~äáë~íáçåëéêáåòáé= ÄÉë~ÖíI= Ç~ëë= dÉïáååÉ= Éêëí= Ç~åå= ~ìëÖÉïáÉëÉå= ïÉêÇÉå=ÇΩêÑÉåI=ïÉåå=ëáÉ=ÇìêÅÜ=rãë®íòÉ=îÉêïáêâäáÅÜí=ïçêÇÉå=ëáåÇK=bë=ÑçäÖí= Ç~ê~ìë= å~íΩêäáÅÜ= ìãÖÉâÉÜêíI= Ç~ëë= dÉïáååÉI= ÇáÉ= ~ã= _áä~åòëíáÅÜí~Ö= åçÅÜ= åáÅÜí=êÉ~äáëáÉêí=ïçêÇÉå=ëáåÇI=áã=g~ÜêÉë~ÄëÅÜäìëë=åáÅÜí=~ìëÖÉïáÉëÉå=ïÉêÇÉå= ÇΩêÑÉåK=
86
B. Rechtlicher Hintergrund
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3. Grundsätze ordnungsmäßiger Buchführung
87
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B. Rechtlicher Hintergrund
e∏ÅÜëíïÉêíéêáåòáéW= få= ÇÉê= sÉêÖ~åÖÉåÜÉáí= ïìêÇÉ= Éáå= cêÉãÇï®ÜêìåÖëâêÉÇáí= áå= e∏ÜÉ= îçå= N= jáçK= rpJaçää~ê=EtÉÅÜëÉäâìêë=Ç~ã~äëW=NIMM=€=Z=NIMM=AF=~ìÑÖÉåçããÉåK=wìã=_áä~åòJ ëíáÅÜí~Ö=äáÉÖí=ÇÉê=tÉÅÜëÉäâìêë=ÄÉá=NIOR=€=Z=NIMM=AK=a~ë=a~êäÉÜÉå=áëí=åìå=~ìÑJ ÖêìåÇ=ÇÉë=e∏ÅÜëíïÉêíéêáåòáéë=åáÅÜí=ä®åÖÉê=ãáí=N=jáçK= bìêç=ëçåÇÉêå=ãáí=NIOR= jáçK=bìêç=áå=ÇÉê=_áä~åò=~åòìëÉíòÉåK=
oΩÅâëíÉääìåÖ=ÑΩê=ÇêçÜÉåÇÉ=sÉêäìëíÉ=~ìë=ëÅÜïÉÄÉåÇÉå=dÉëÅÜ®ÑíÉåW= ^Äë~íòã~êâíW=báåÉ=pÅÜêÉáåÉêÉá=ÉêÜ®äí=~ã=_áä~åòëíáÅÜí~Ö=åçÅÜ=ÉáåÉå=^ìÑíê~Ö=áã= tÉêí= îçå= NMKMMM= bìêçI= ÇÉê= çÜåÉ= Öêç≈É= §ÄÉêäÉÖìåÖÉå= îçêÉáäáÖ= ~åÖÉåçããÉå= ïáêÇ=ìåÇ=ÇÉê=áã=j®êò=ÇÉë=cçäÖÉà~ÜêÉë=~ìëòìÑΩÜêÉå=áëíK=k~ÅÜ=ÖÉå~ìÉê=h~äâìä~J íáçå=ëíÉääí=ã~å=åìå=~ÄÉê=ÑÉëíI=Ç~ëë=ëáÅÜ=ÇáÉ=hçëíÉå=ÑΩê=ÇÉå=^ìÑíê~Ö=~ìÑ=NRKMMM= bìêç=ÄÉä~ìÑÉåK=bë=áëí=Ç~ÜÉê=å~ÅÜ=ÇÉã=fãé~êáí®íëéêáåòáé=ÉáåÉ=oΩÅâëíÉääìåÖ=ÑΩê= ÇêçÜÉåÇÉ=sÉêäìëíÉ=~ìë=ëÅÜïÉÄÉåÇÉå=dÉëÅÜ®ÑíÉå=EÄÉáÇÉ=m~êíÉáÉå=Ü~ÄÉå=åçÅÜ= åáÅÜí=ÖÉäÉáëíÉíF=áå=e∏ÜÉ=îçå=RKMMMIMM=bìêç=òì=ÄáäÇÉåK= _ÉëÅÜ~ÑÑìåÖëã~êâíW= báå= m`Je®åÇäÉê= ÄÉëíÉääí= NM= hçãéäÉííêÉÅÜåÉê= òì= ÉáåÉã= cÉëíéêÉáë=îçå=NKNMMIMM=bìêç=~ìë=hçêÉ~K=tÉÇÉê=iáÉÑÉêìåÖ=åçÅÜ=_Éò~ÜäìåÖ=ëáåÇ= ÄáëÜÉê=ÉêÑçäÖíK=a~=ÇÉê=sÉêâ~ìÑëéêÉáë=~ìÑ=ÇÉã=ÇÉìíëÅÜÉå=j~êâí=Äáë=òìã=_áä~åòJ ëíáÅÜí~Ö= ~ìÑ= NKMMMIMM= bìêç= ~ÄÖÉêìíëÅÜí= áëíI= ÇêçÜí= àÉ= dÉê®í= Éáå= sÉêäìëí= îçå= NMMIMM=bìêçI=ëç=Ç~ëë=ÉáåÉ=oΩÅâëíÉääìåÖ=îçå=NKMMMIMM=bìêç=òì=ÄáäÇÉå=áëíK=
=
Ziel des Grundsatzes:
Bevorzugung einer pessimistischen Bewertung bei Unsicherheit und damit Schutz der Gläubiger vor Bilanzmanipulation
=
= = =
4.
Schritte der Rechnungslegung
= =
aáÉ= _áä~åòÉêëíÉääìåÖ= ÉêÑçäÖí= åáÅÜí= ~ãI= ëçåÇÉêå= òìã= àÉïÉáäáÖÉå= píáÅÜí~ÖK= páÉ= ÉêÑçäÖí= ~äëç=Éêëí=å~ÅÜ=^Ää~ìÑ=ÇÉë=ÄÉíêÉÑÑÉåÇÉå=dÉëÅÜ®Ñíëà~ÜêÉëK=bë=â∏ååÉå=Ç~ÄÉá=îÉêëÅÜáÉJ ÇÉåÉ=pí~ÇáÉå=ìåíÉêëÅÜáÉÇÉå=ïÉêÇÉåK== =
=
sçêÖ~åÖ=
j~≈å~ÜãÉ=
bêÖÉÄåáë=
^ÄëÅÜäìëë=ÇÉê=cáå~åòJ ÄìÅÜÜ~äíìåÖ=
^ÄëÅÜäìëë=ÇÉê=hçåíÉå=
îçêä®ìÑáÖÉ= _áä~åò=
båíïáÅâäìåÖ=ÇÉê=_áä~åò=
sçêå~ÜãÉ=ÇÉê=^ÄëÅÜäìëëJ ÄìÅÜìåÖÉå=
~ìÑÖÉëíÉääíÉ= _áä~åò=
cêÉáïáääáÖÉ=çÇÉê=ÖÉëÉíòäáÅÜ= îçêÖÉëÅÜêáÉÄÉåÉ=_áä~åòJ éêΩÑìåÖ=
sçêä~ÖÉ=ÇÉê=~ìÑÖÉëíÉääíÉå= _áä~åò=òìê=mêΩÑìåÖ=ÇìêÅÜ= ^ìÑëáÅÜíëê~íLtáêíëÅÜ~ÑëéêΩÑÉê
ÖÉéêΩÑíÉ= _áä~åò=
cÉëíëíÉääìåÖ=ÇÉê=_áä~åò= ÇìêÅÜ=Ç~ë=ÖÉëÉääëÅÜ~ÑíëJ îÉêíê~ÖäáÅÜLÖÉëÉíòäáÅÜ= îçêÖÉëÅÜêáÉÄÉåÉ=lêÖ~å=
_ÉëÅÜäìëëÑ~ëëìåÖ=ΩÄÉê=ÇáÉ= ÖÉéêΩÑíÉ=_áä~åò=
ÑÉëíÖÉëíÉääíÉ= _áä~åò=
lÑÑÉåäÉÖìåÖ=ÇÉê=_áä~åò=
sÉê∏ÑÑÉåíäáÅÜìåÖ=ÇÉê= _áä~åò=EÉîíäK=mìÄäáòáí®íëÉêJ äÉáÅÜíÉêìåÖÉåF=
çÑÑÉåÖÉäÉÖíÉ= _áä~åò=
= = = = = = = = = = = = = = = = = = =
^ÄÄáäÇìåÖ=PQW=^ääÖÉãÉáåÉ=pÅÜêáííÉ=ÇÉê=oÉÅÜåìåÖëäÉÖìåÖ= =
jáí= ÇÉå= äÉíòíÉå= îáÉê= mÜ~ëÉå= ~ìë= ÇÉê= îçêÜÉêÖÉÜÉåÇÉå=^ÄÄáäÇìåÖ= ïáêÇ= ëáÅÜ= åìå=áã= cçäÖÉåÇÉå=áã=aÉí~áä=ÄÉÑ~ëëíK=aáÉ=mÜ~ëÉå=Éáåë=ìåÇ=òïÉá=ïÉêÇÉå=áã=h~éáíÉä=a=~ìëJ ÑΩÜêäáÅÜ=ÄÉíê~ÅÜíÉíK=
4.1 Aufstellung mÉêëçåÉåÜ~åÇÉäÖÉëÉääëÅÜ~ÑíÉå= EledI= hdF= ìåÇ= báåòÉäìåíÉêåÉÜãÉå= EÉKhKF= ãΩëëÉå= å~ÅÜ= ¬= OQP= fff= ed_= ÇÉå= g~ÜêÉë~ÄëÅÜäìëë= áååÉêÜ~äÄ= ÇÉê= ÉáåÉã= çêÇåìåÖëÖÉã®≈Éå= =
90
B. Rechtlicher Hintergrund
dÉëÅÜ®ÑíëÖ~åÖ=ÉåíëéêÉÅÜÉåÇÉå=wÉáí=EáKÇKoK=SJV=jçå~íÉF=~ìÑëíÉääÉåK=k~ÅÜ=_ceJrêíÉáä= E_pí_äK=NVUQ=^ÄëK=O=pK=OOTF=Ç~êÑ=ÇáÉëÉê=wÉáíê~ìã=åáÅÜí=ä®åÖÉê=~äë=N=g~Üê=ÄÉíê~ÖÉåK= mìÄäáòáí®íëéÑäáÅÜíáÖÉ= báåòÉäâ~ìÑäÉìíÉ= ìåÇ= mÉêëçåÉåÜ~åÇÉäëÖÉëÉääëÅÜ~ÑíÉå= Ü~ÄÉå= ÇÉå= g~ÜêÉë~ÄëÅÜäìëë=áå=ÇÉå=ÉêëíÉå=P=jçå~íÉå=å~ÅÜ=^Ää~ìÑ=ÇÉë=dÉëÅÜ®Ñíëà~ÜêÉë=E¬=R=fI=ff= mìÄädF=çÜåÉ=^åÜ~åÖ=ìåÇ=i~ÖÉÄÉêáÅÜí=òì=ÉêëíÉääÉåK= dêç≈É= ìåÇ= ãáííÉäÖêç≈É= h~éáí~äÖÉëÉääëÅÜ~ÑíÉå= Ü~ÄÉå= ÇÉå= g~ÜêÉë~ÄëÅÜäìëë= ÉÄÉåÑ~ääë= áå=ÇÉå=ÉêëíÉå=P=jçå~íÉå=~ìÑòìëíÉääÉå=E¬=OSQ=f=pK=O=ed_FK=häÉáåÉ=h~éáí~äÖÉëÉääëÅÜ~ÑJ íÉå=Ü~ÄÉå=S=jçå~íÉ=wÉáí=E¬=OSQ=f=pK=P=ed_FK=aáÉ=^ìÑëíÉääìåÖ=ÇÉë=g~ÜêÉë~ÄëÅÜäìëëÉë= ÉêÑçäÖí=ÇìêÅÜ=ÇáÉ=dÉëÅÜ®ÑíëÑΩÜêìåÖ=ÄòïK=ÇÉå=sçêëí~åÇ=E¬=OSQ=f=pK=N=ed_FK= =
4.2 Prüfung kìê=ãáííÉäÖêç≈É=ìåÇ=Öêç≈É=h~éáí~äÖÉëÉääëÅÜ~ÑíÉå=ëáåÇ=å~ÅÜ=¬=PNS=f=ed_=éêΩÑìåÖëJ éÑäáÅÜíáÖK= báåòÉäìåíÉêåÉÜãÉå= ìåÇ= mÉêëçåÉåÜ~åÇÉäëÖÉëÉääëÅÜ~ÑíÉå= ëáåÇ= åìê= Ç~åå= éêΩÑìåÖëéÑäáÅÜíáÖI=ïÉåå=ëáÉ=ÇÉã=mìÄäáòáí®íëÖÉëÉíò=ìåíÉêäáÉÖÉå=E¬=S=mìÄädFK= =
4.3 Feststellung råíÉê= ÇÉê= cÉëíëíÉääìåÖ= ÇÉë= g~ÜêÉë~ÄëÅÜäìëëÉë= îÉêëíÉÜí= ã~å= ÇáÉ= q~íë~ÅÜÉI= Ç~ëë= ÇÉê= g~ÜêÉë~ÄëÅÜäìëë= ÑΩê= êÉÅÜíëîÉêÄáåÇäáÅÜ= Éêâä®êí= ïáêÇK= _Éá= ÉáåÉê= ^âíáÉåÖÉëÉääëÅÜ~Ñí= ÖÉJ ëÅÜáÉÜí= ÇáÉë= êÉÖÉäã®≈áÖ= ÇìêÅÜ= ÇÉå= sçêëí~åÇ= ìåÇ= ÇÉå= ^ìÑëáÅÜíëê~í= E¬¬= NTNI= NTO= ^âídFK=fã=^ìëå~ÜãÉÑ~ää=â~åå=ÇáÉ=cÉëíëíÉääìåÖ=~ääÉáå=ÇìêÅÜ=ÇáÉ=e~ìéíîÉêë~ããäìåÖ= ÉêÑçäÖÉå=E¬=NTP=^âídFK=_Éá=ÇÉê=dãÄe=ÉêÑçäÖí=ÇáÉ=cÉëíëíÉääìåÖ=ÇìêÅÜ=ÇáÉ=dÉëÉääëÅÜ~ÑJ íÉêK=aáÉ=cÉëíëíÉääìåÖëÑêáëí=ÄÉíê®Öí= ÑΩê=ãáííÉäÖêç≈É=ìåÇ=Öêç≈É=h~éáí~äÖÉëÉääëÅÜ~ÑíÉå=U= jçå~íÉ= E¬= QO= ~= ff= dãÄedI= ¬= NTR= f= ^âídFK= häÉáåÉ= h~éáí~äÖÉëÉääëÅÜ~ÑíÉå= Ü~ÄÉå= NN= jçå~íÉ=wÉáíK= =
4.4 Offenlegung
îÖäK=ïïïKÉÄìåÇÉë~åòÉáÖÉêKÇÉ=
a~ë= ëÉáí= MNKMNKOMMT= ÖÉäíÉåÇÉ= dÉëÉíò= ΩÄÉê= ÉäÉâíêçåáëÅÜÉ= e~åÇÉäëJI= råíÉêåÉÜãÉåëJ= ìåÇ= dÉåçëëÉåëÅÜ~ÑíëêÉÖáëíÉê= EberdF= ÄêáåÖí= ÑΩê= ÇáÉ= ^ÄëÅÜäìëëéìÄäáòáí®í= ìåÇ= ÇáÉ== çÑÑÉåäÉÖìåÖëéÑäáÅÜíáÖÉå=råíÉêåÉÜãÉå=ÉáåÉ=oÉáÜÉ=îçå=ïáÅÜíáÖÉå=ûåÇÉêìåÖÉåK= lÑÑÉåäÉÖìåÖëéÑäáÅÜíáÖI=~äëç=îÉêéÑäáÅÜíÉíI=áÜêÉå=g~ÜêÉë~ÄëÅÜäìëë=åáÅÜí=åìê=òì=ÉêëíÉääÉåI= ëçåÇÉêå= ~ìÅÜ= ÇÉê= £ÑÑÉåíäáÅÜâÉáí= òìÖ®åÖäáÅÜ= òì= ã~ÅÜÉåI= ëáåÇ= áåëÄÉëçåÇÉêÉ= å~ÅÜ= ïáÉ=îçê=ÑçäÖÉåÇÉ=råíÉêåÉÜãÉåëíóéÉåW=
~ääÉ=h~éáí~äÖÉëÉääëÅÜ~ÑíÉå=E^dI=hd~^I=dãÄeF=
mÉêëçåÉåÖÉëÉääëÅÜ~ÑíÉå= çÜåÉ= ÉáåÉ= å~íΩêäáÅÜÉ=mÉêëçå=~äë= éÉêë∏åäáÅÜ= Ü~ÑíÉåÇÉå= dÉëÉääëÅÜ~ÑíÉê=EòK_K=dãÄe=C=`çK=hdF=
å~ÅÜ= ÇÉã= mìÄäáòáí®íëÖÉëÉíò= òìê= lÑÑÉåäÉÖìåÖ= îÉêéÑäáÅÜíÉíÉ= råíÉêåÉÜãÉå= E~äëç= råíÉêåÉÜãÉåI=ÇáÉ=áå=ÇêÉá=~ìÑÉáå~åÇÉêÑçäÖÉåÇÉå=dÉëÅÜ®Ñíëà~ÜêÉå=òïÉá=ÇÉê=ÇêÉá= jÉêâã~äÉ=ÇÉë=¬=N=f=mìÄäd=ÉêÑΩääÉåF=
jáí= ^Ää~ìÑ= ÇÉë= g~ÜêÉë= OMMS= ÉåíÑ®ääí= ÇáÉ= ÄáëÜÉê= îçêÖÉëÅÜêáÉÄÉåÉ= báåêÉáÅÜìåÖ= ÇÉê= oÉÅÜåìåÖëìåíÉêä~ÖÉå= ÄÉáã= e~åÇÉäëêÉÖáëíÉêK= pí~ííÇÉëëÉå= ëáåÇ= ÇáÉ= råíÉêä~ÖÉå= ÄÉáã= =
4. Schritte der Rechnungslegung
91
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94
B. Rechtlicher Hintergrund
5.2 Steuerrechtliche Sanktionen cΩê=ÇáÉ=báåÜ~äíìåÖ=ÇÉê=ëíÉìÉêêÉÅÜíäáÅÜÉå=_ìÅÜÑΩÜêìåÖëîçêëÅÜêáÑíÉå=ëáåÇ=ÖêìåÇë®íòJ äáÅÜ= ÇáÉ= píÉìÉêéÑäáÅÜíáÖÉåI= ~äëç= ÇáÉ= báåòÉäìåíÉêåÉÜãÉê= ìåÇ= ÇáÉ= dÉëÉääëÅÜ~ÑíÉê= îçå= mÉêëçåÉåÖÉëÉääëÅÜ~ÑíÉå=E¬=PP=f=^lF=ëçïáÉ=ÇáÉ=ÖÉëÉíòäáÅÜÉå=sÉêíêÉíÉê=ÇÉê=h~éáí~äÖÉJ ëÉääëÅÜ~ÑíÉåI=dÉåçëëÉåëÅÜ~ÑíÉå=ìåÇ=~åÇÉêÉê=àìêáëíáëÅÜÉê=mÉêëçåÉå=E¬=PQ=^lF=Ü~ÑíÄ~êK= wìë®íòäáÅÜ=Ü~ÑíÉå=~ääÉ=_Éîçääã®ÅÜíáÖíÉå=EòK_K=píÉìÉêÄÉê~íÉêF=éÉêë∏åäáÅÜ=åÉÄÉå=ÇÉã= píÉìÉêéÑäáÅÜíáÖÉå=E¬=UM=áKsKã=¬=NVN=ffI=SV=^lFI=ïÉåå=áåÑçäÖÉ=îçêë®íòäáÅÜÉê=çÇÉê=ÖêçÄ= Ñ~Üêä®ëëáÖÉê= sÉêäÉíòìåÖ= ÇÉê= áÜåÉå= ~ìÑÉêäÉÖíÉå= mÑäáÅÜíÉå= píÉìÉê~åëéêΩÅÜÉ= îÉêâΩêòí== çÇÉê=bêëí~ííìåÖÉå=çÇÉê=sÉêÖΩíìåÖÉå=òì=råêÉÅÜí=ÖÉï®Üêí=ïçêÇÉå=ëáåÇK= aáÉ=_ìÅÜÑΩÜêìåÖ=ìåÇ=ÇáÉ=^ìÑòÉáÅÜåìåÖÉå=ÇÉë=píÉìÉêéÑäáÅÜíáÖÉå=â∏ååÉå=åìê=Ç~åå= dêìåÇä~ÖÉ=ÑΩê=ÇáÉ=_ÉëíÉìÉêìåÖ=ëÉáåI=ïÉåå=ëáÉ=âçêêÉâí=å~ÅÜ=ëíÉìÉêäáÅÜÉå=sçêëÅÜêáÑJ íÉå=E¬¬=NQMJNQU=^lF=ÉêëíÉääí=ïìêÇÉåK=dÉê~ÇÉ=Ç~ÜÉê=ëíÉääí=ÇáÉ=sçêå~ÜãÉ=Ñ~äëÅÜÉê=báåJ íê~ÖìåÖÉå= áå= ÇÉå= _ΩÅÜÉêå= ÉáåÉ= rêâìåÇÉåÑ®äëÅÜìåÖ= å~ÅÜ= ¬¬= OSTI= OSU= píd_= Ç~êK= h∏ååÉå= ÇáÉ= _ΩÅÜÉê= ~ìÑÖêìåÇ= îçå= j®åÖÉäå= åáÅÜí= ~äë= dêìåÇä~ÖÉ= ÇÉê= _ÉëíÉìÉêìåÖ= îÉêïÉåÇÉí=ïÉêÇÉåI=ïáêÇ=ÇáÉ=píÉìÉêÄÉãÉëëìåÖëÖêìåÇä~ÖÉ=îçå=ÇÉå=cáå~åòÄÉÜ∏êÇÉå= ÖÉëÅÜ®íòíK== qóéáëÅÜÉ=p~åâíáçåÉåI=ÇáÉ=Ç~ë=píÉìÉêêÉÅÜí=ÑΩê=ÇÉå=píÉìÉêéÑäáÅÜíáÖÉå=îçêëáÉÜíI=ëáåÇ=áå= å~ÅÜÑçäÖÉåÇÉê=^ÄÄáäÇìåÖ=Ç~êÖÉëíÉääíW= = = =
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C. LAUFENDE BUCHUNGEN IN INDUSTRIEBETRIEBEN = In diesem Kapitel wird näher auf eine Reihe ausgewählter Buchungsvorgänge eingegangen, die im Laufe eines Geschäftsjahres in einem Industriebetrieb regelmäßig anfallen können. Das Spektrum reicht dabei
von typischen bei der Produktion von Erzeugnissen notwendigen Buchungen (Einkauf von Roh-, Hilfs- und Betriebsstoffen, Anlagen, etc.; Verbuchung von Personalaufwand; Kreditaufnahme)
über den Kauf und Verkauf diverser Anlagegegenstände (z.B. Maschinen, Fahrzeuge, Wertpapiere)
bis zum Verkauf von hergestellten Erzeugnissen.
Anders als in der gängigen Buchführungsliteratur lernen Sie dabei nicht nur, ob und wie (bzw. unter welchen Bilanzpositionen) gewisse Vorfälle zu verbuchen sind, sondern erhalten auch einen detaillierten Einblick, wie die zu verbuchenden Euro-Werte zu bestimmen (Bewertungsvorschriften) sind. = = = =
1.
Beschaffung von Werkstoffen und Handelswaren I
=
1.1 Produktionsfaktoren und Leistungserstellung fã=dÉÖÉåë~íò=òì=e~åÇÉäëÄÉíêáÉÄÉåI=ÇáÉ=áÜêÉ=ÉáåÖÉâ~ìÑíÉå=t~êÉå=ìåîÉê®åÇÉêí=EòòÖäK= ÉáåÉë= dÉïáåå~ìÑëÅÜä~ÖÉëF= ïÉáíÉêîÉê®ì≈ÉêåI= ÉåíëíÉÜÉå= áå= ÉáåÉã= fåÇìëíêáÉÄÉíêáÉÄ= ÇìêÅÜ= ÇáÉ= sÉêÄáåÇìåÖ= ÇÉê= ÄÉíêáÉÄëïáêíëÅÜ~ÑíäáÅÜÉå= mêçÇìâíáçåëÑ~âíçêÉå= ^êJ ÄÉáíI= _ÉíêáÉÄëãáííÉä= ìåÇ= tÉêâëíçÑÑÉ= dΩíÉêI= ÇáÉ= Ç~åå= ~ìÑ= ÇÉã= ^Äë~íòã~êâí= òìê= bêòáÉäìåÖ=îçå=rãë~íòÉêä∏ëÉå=~åÖÉÄçíÉå=ïÉêÇÉåK= =
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98
C. Laufende Buchungen in Industriebetrieben
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106
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Rabatte
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107
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109
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1.5.4
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Grundlagen
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3.2.1.1
Steuern
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Sozialversicherungsbeiträge
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134
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3.2.2
Buchungen
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Lohn- und Gehaltszahlung
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3. Verbuchung weiterer Produktionsfaktoren
135
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136
C. Laufende Buchungen in Industriebetrieben
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3. Verbuchung weiterer Produktionsfaktoren
137
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138
C. Laufende Buchungen in Industriebetrieben
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Vermögenswirksame Leistungen
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3. Verbuchung weiterer Produktionsfaktoren
139
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Sofortrabatte
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150
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160
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5.1.2
Bestimmungen des Umsatzsteuergesetzes
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5. Umsatzsteuer
163
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164
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174
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Geringwertige Wirtschaftsgüter
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Sachanlagegüter
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188
C. Laufende Buchungen in Industriebetrieben
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190
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191
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192
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193
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8.
Verkauf von beweglichen und unbeweglichen Anlagegütern
=
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8.1 Auswirkung auf den Unternehmenserfolg _Éáã=báåâ~ìÑ=îçå=^åä~ÖÉÖΩíÉêå=ïÉêÇÉå=ÇáÉ=ÖÉë~ãíÉå=^åëÅÜ~ÑÑìåÖëâçëíÉå=~ìÑ=ÇÉå= ÉåíëéêÉÅÜÉåÇÉå= ^âíáîâçåíÉå= ÉêÑ~ëëíK= aÉê= tÉêí= ÇáÉëÉê= ^åä~ÖÉÖΩíÉê= ïáêÇ= àÉÇçÅÜ= ÇìêÅÜ=ÇÉå=báåë~íò=áã=_ÉíêáÉÄ=îÉêãáåÇÉêíK=aáÉëÉ=tÉêíãáåÇÉêìåÖ=ïáêÇ=à®ÜêäáÅÜ=Eòìã= _áä~åòëíáÅÜí~ÖF=~äë=ëçÖK=^ÄëÅÜêÉáÄìåÖ=EîÖäK=a=OKNF=ÇáêÉâí=áã=e~ÄÉå=ÇÉê=p~ÅÜ~åä~ÖÉJ âçåíÉå=ÖÉÄìÅÜíK=aÉê=áã=_Éëí~åÇëâçåíç=îÉêÄäÉáÄÉåÇÉ=tÉêí=ïáêÇ=~äë=ëçÖK=_ìÅÜïÉêí= ÄÉòÉáÅÜåÉíK=aáÉëÉê=áëí=ÄÉáã=sÉêâ~ìÑ=ÉáåÉë=^åä~ÖÉÖìíÉë=~ìëòìÄìÅÜÉåK=bêÑçäÖí=ÇÉê= sÉêâ~ìÑ=åìå=~ÄÉê=ÄÉáëéáÉäëïÉáëÉ=áå=ÇÉê=jáííÉ=ÇÉë=dÉëÅÜ®Ñíëà~ÜêÉëI=ëç=áëí=Äáë=òì=ÇáÉJ ëÉã= wÉáíéìåâí= ÄÉêÉáíë= ÉáåÉ= tÉêíãáåÇÉêìåÖ= ÉêÑçäÖíI= ÇáÉ= ~ÄÉê= Éêëí= òìã= g~ÜêÉëÉåÇÉ= ÄÉêΩÅâëáÅÜíáÖí=ïÉêÇÉå=ïΩêÇÉK=a~ÜÉê=áëí=îçê=ÇÉê=_ìÅÜìåÖ=ÇÉë=sÉêâ~ìÑë=ÉáåÉ=~åíÉáäáJ ÖÉ= ^ÄëÅÜêÉáÄìåÖ= ÇìêÅÜòìÑΩÜêÉåI= ìã= ÇÉå= ~âíìÉääÉå= _ìÅÜïÉêí= òìã= wÉáíéìåâí= ÇÉë= sÉêâ~ìÑë=òì=ÉêãáííÉäåK= aáÉë= ïáêÇ= ~ÄÉê= Éêëí= áã= ^ÄëÅÜåáíí= a= OKNKQKO= ÇÉí~áääáÉêí= ÄÉÜ~åÇÉäíK= fã= cçäÖÉåÇÉå= áëí= Ç~ÜÉê=ëíÉíë=ÇÉê=_ìÅÜïÉêí=òìã=wÉáíéìåâí=ÇÉë=sÉêâ~ìÑë=Eå~ÅÜ=ÉêÑçäÖíÉê=~åíÉáäáÖÉê=^ÄJ ëÅÜêÉáÄìåÖF=~åÖÉÖÉÄÉåK= aÉê=sÉêâ~ìÑ=ÉáåÉë=^åä~ÖÉÖìíÉë=â~åå=åìå=ÇÉå=bêÑçäÖ=EdÉïáååLsÉêäìëíF=ÉáåÉë=råíÉêJ åÉÜãÉåë=~ìÑ=ÇêÉá=îÉêëÅÜáÉÇÉåÉ=^êíÉå=ÄÉÉáåÑäìëëÉåW= =
196
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8.2 Buchungen 8.2.1
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8.2.2
Variante B (ohne Interimskonto)
táêÇ= ~ìÑ= ÇáÉ= sÉêïÉåÇìåÖ= ÇÉë= fåíÉêáãëâçåíçë= RQNM= îÉêòáÅÜíÉíI= ëç= ä~ìíÉå= ÇáÉ== _ìÅÜìåÖëë®íòÉ=~ìë=`=UKOKN=ïáÉ=ÑçäÖíW= =
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200
C. Laufende Buchungen in Industriebetrieben
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8.2.3
Inzahlungnahme gebrauchter Anlagegüter
tÉêÇÉå= ÄÉáã= h~ìÑ= åÉìÉê= p~ÅÜ~åä~ÖÉÖΩíÉê= ÖÉÄê~ìÅÜíÉ= ^åä~ÖÉÖÉÖÉåëí®åÇÉ= áå= w~ÜJ äìåÖ=ÖÉÖÉÄÉåI=ëç=âçããí=Éë=áå=ÇÉê=_ìÅÜÜ~äíìåÖ=òì=ÉáåÉê=sÉêÄáåÇìåÖ=ÇÉë=báåJ=ìåÇ= sÉêâ~ìÑëÄÉêÉáÅÜÉëK= aáÉ= sÉêÄáåÇäáÅÜâÉáí= ~ìë= ÇÉã= _ÉòìÖ= ÇÉë= åÉìÉå= dìíÉë= ïáêÇ= ãáí= ÇÉê=cçêÇÉêìåÖ=~ìë=ÇÉã=sÉêâ~ìÑ=ÇÉë=ÖÉÄê~ìÅÜíÉå=dìíÉë=îÉêêÉÅÜåÉíK= ^ìÅÜ= ÜáÉê= â~åå= ïáÉÇÉê= ãáí= çÇÉê= çÜåÉ= sÉêïÉåÇìåÖ= ÉáåÉë= fåíÉêáãëâçåíçë= ÖÉÄìÅÜí= ïÉêÇÉåK= =
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8. Verkauf von beweglichen und unbeweglichen Anlagegütern
201
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202
C. Laufende Buchungen in Industriebetrieben
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9.
Aktivierte Eigenleistungen
= táêÇ= Éáå= ^åä~ÖÉÖìí= áã= råíÉêåÉÜãÉå= ÇìêÅÜ= ÉáÖÉåÉ= ^êÄÉáíÉê= ÖÉÄ~ìí= ìåÇ= ~åëÅÜäáÉJ ≈ÉåÇ=áã=_ÉíêÉáÄ=ÉáåÖÉëÉíòí=çÇÉê=ÇáÉ=jçåí~ÖÉ=ÉáåÉë=ÖÉâ~ìÑíÉå=^åä~ÖÉÖÉÖÉåëí~åÇÉë= ÇìêÅÜ=ÉáÖÉåÉ=^êÄÉáíëâê®ÑíÉ=ÇìêÅÜÖÉÑΩÜêíI=ëç=ëéêáÅÜí=ã~å=îçå=ÉáåÉê=ëçÖK=báÖÉåäÉáëJ íìåÖK= _Éîçê= ÉáåÉ= ëçäÅÜÉ= iÉáëíìåÖ= áå= ÇÉê= _ìÅÜÜ~äíìåÖ= ÉêÑ~ëëí= ïÉêÇÉå= â~ååI= ãìëë= ÇÉê=tÉêí=ÇÉë=mêçÇìâíÉë=çÇÉê=ÇÉê=jçåí~ÖÉäÉáëíìåÖ=ÉêãáííÉäí=ïÉêÇÉåK=
9.1 Wertermittlung rã=å®ÜÉê=~ìÑ=ÇáÉ=tÉêíÉêãáííäìåÖ=ÉáåÖÉÜÉå=òì=â∏ååÉåI=áëí=òìå®ÅÜëí=Éáå=âäÉáåÉê=bñJ âìêë=áå=ÇáÉ=hçëíÉåJ=ìåÇ=iÉáëíìåÖëêÉÅÜåìåÖ=ÉêÑçêÇÉêäáÅÜK= aáÉ=pÉäÄëíâçëíÉå=ÉáåÉë=mêçÇìâíÉë=ëÉíòÉå=ëáÅÜ=ÜáÉê=~ìë=ëçÖK=báåòÉäJ=ìåÇ=dÉãÉáåJ âçëíÉå= òìë~ããÉåK= báåòÉäâçëíÉå= ëáåÇ= hçëíÉåI= ÇáÉ= ÉáåÉã= mêçÇìâí= EhçëíÉåíê®ÖÉêF= ÇáêÉâí= òìÖÉçêÇåÉí= ïÉêÇÉå=â∏ååÉåK= pçåÇÉêÉáåòÉäâçëíÉå= ëáåÇ= ÉÄÉåÑ~ääë= ÇáêÉâí= òìJ çêÇÉåÄ~êI=Ñ~ääÉå=àÉÇçÅÜ=åáÅÜí=êÉÖÉäã®≈áÖ=~åI=ëçåÇÉêå=ãÉáëí=åìê=~ìÑ=ÉáåÉå=ÄÉëíáããJ íÉå= ^ìÑíê~Ö= ÄÉòçÖÉåK= dÉãÉáåâçëíÉå= ÜáåÖÉÖÉå= ïÉêÇÉå= ÉáåÉã= mêçÇìâí= ãáí= eáäÑÉ= îçå=sÉêíÉáäìåÖëëÅÜäΩëëÉäå=òìÖÉçêÇåÉíI=Ç~=ëáÉ=åáÅÜí=ÇáêÉâí=òìêÉÅÜÉåÄ~ê=ëáåÇK= =
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204
C. Laufende Buchungen in Industriebetrieben =
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9. Aktivierte Eigenleistungen
205
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10. Kauf und Verkauf von Aktien
211
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222
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Gebühren und Zinsen (unter Kaufleuten)
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Privatkonto
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13. Privatkonto
243
aìêÅÜ= ÇáÉ= mêáî~íÉåíå~ÜãÉ= îÉêêáåÖÉêí= ëáÅÜ= ëçïçÜä= ÇÉê=h~ëëÉåÄÉëí~åÇ= ~äë= ~ìÅÜ= Ç~ë= báÖÉåâ~éáí~ä=E_ìÅÜìåÖ=áã= pçää=ÇÉë=mêáî~íâçåíçëF=ÇÉë=råíÉêåÉÜãÉåëK=rãë~íòëíÉìÉê= Ñ®ääí=åáÅÜí=~åK= = ⌦= dÉäÇÉåíå~ÜãÉ=OW= aÉê= råíÉêåÉÜãÉê= ΩÄÉêïÉáëí= ÇáÉ= oÉÅÜåìåÖ= ÑΩê= ÇáÉ= oÉé~ê~íìê= ëÉáåÉë= éêáî~íÉå= mâïë= ΩÄÉê=Ç~ë=cáêãÉåÄ~åââçåíçK=aáÉ=oÉÅÜåìåÖ=ä~ìíÉí=~ìÑ=OPOIMM=bìêç=EÄêìííçFK= = _Éå∏íáÖÉ=hçåíÉåW= =
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244
C. Laufende Buchungen in Industriebetrieben
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13. Privatkonto
245
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246
C. Laufende Buchungen in Industriebetrieben
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13. Privatkonto
247
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14.
Steuern
=
14.1 Verbuchung nach Steuerkategorien _Éá= ÇÉê= ÄìÅÜÜ~äíÉêáëÅÜÉå= bêÑ~ëëìåÖ= îçå= píÉìÉêå= ëáåÇ= ~ääÖÉãÉáå= ÑçäÖÉåÇÉ= píÉìÉêJ â~íÉÖçêáÉå=òì=ìåíÉêëÅÜÉáÇÉåW= = = = = = = =
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14.1.1 Aktivierungspflichtige Steuern ^âíáîáÉêìåÖëéÑäáÅÜíáÖÉ= píÉìÉêåI= ïáÉ= Éíï~= ÇáÉ= dêìåÇÉêïÉêÄëíÉìÉê= EîÖäK= `= TKN= J= TKPFI= ïÉêÇÉå=ÇáêÉâí=~ìÑ=ÇÉã=ÉåíëéêÉÅÜÉåÇÉå=~âíáîÉå=_Éëí~åÇëâçåíç=îÉêÄìÅÜíK=páÉ=ëíÉääÉå= ^åëÅÜ~ÑÑìåÖëåÉÄÉåâçëíÉå= Ç~êI= ÇáÉ= ~âíáîáÉêí= ïÉêÇÉå= ãΩëëÉåK= a~ÇìêÅÜ= ëáåÇ= ÇáÉëÉ= píÉìÉêå=òìå®ÅÜëí=ÉêÑçäÖëåÉìíê~ä=ìåÇ=ïÉêÇÉå=Éêëí=ÄÉá=^ÄëÅÜêÉáÄìåÖ=ÇÉë=^åä~ÖÉÖìíÉë= EîÖäK=a=OKNF=òìã=^ìÑï~åÇK= =
⌦= _ÉáëéáÉäW= h~ìÑ= ÉáåÉë= ìåÄÉÄ~ìíÉå= dêìåÇëíΩÅâë= òì= NMMKMMMIMM= bìêç= ÇìêÅÜ= _~åâΩÄÉêïÉáëìåÖK= aáÉ=dêìåÇÉêïÉêÄëíÉìÉê=äáÉÖí=ÄÉá=ΩÄäáÅÜÉå=PIR=B=îçã=h~ìÑéêÉáëK= =
= h~ìÑéêÉáë= H==dêìåÇÉêïÉêÄëíÉìÉê=PIR=B=
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C. Laufende Buchungen in Industriebetrieben
hçåíÉåÇ~êëíÉääìåÖW= =
p= OUMM=
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táÉ= ÄÉêÉáíë= ~ìë= ÇÉã= h~éáíÉä= òìã= h~ìÑ= îçå= ìåÄÉïÉÖäáÅÜÉå= p~ÅÜ~åä~ÖÉÖΩíÉêå= ÄÉJ â~ååí=áëíI=áëí=ÇáÉ=dêìåÇÉêïÉêÄëíÉìÉê=ÄÉáã=c~ää=ÇÉë=h~ìÑë=ÉáåÉë=dêìåÇëíΩÅâë=ãáí=dÉJ Ä®ìÇÉ=~åíÉáäëã®≈áÖ=~ìÑòìëé~äíÉåK== =
14.1.2 Betriebliche Aufwandsteuern wì= ÇÉå= ÄÉíêáÉÄäáÅÜÉå= píÉìÉêåI= ÇáÉ= ÄÉá= ^åÑ~ää= ëçÑçêí= ~äë= ^ìÑï~åÇ= ÖÉÄìÅÜí= ïÉêÇÉåI= ò®ÜäÉå=ÑçäÖÉåÇÉ=mçëíÉå=ÇÉê=hçåíÉåÖêìééÉå=TMI=TT=ìåÇ=TUW= =
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dÉïÉêÄÉâ~éáí~äëíÉìÉê= sÉêã∏ÖÉåëíÉìÉê= dêìåÇëíÉìÉê=E≠=dêìåÇÉêïÉêÄëíÉìÉêF= hê~ÑíÑ~ÜêòÉìÖëíÉìÉê= tÉÅÜëÉäëíÉìÉê= dÉëÉääëÅÜ~ÑíëíÉìÉê= ^ìëÑìÜêò∏ääÉ= sÉêÄê~ìÅÜëëíÉìÉêå= pçåëíáÖÉ=ÄÉíêáÉÄäáÅÜÉ=píÉìÉêå= dÉïÉêÄÉÉêíê~ÖëíÉìÉê= h∏êéÉêëÅÜ~ÑíëíÉìÉê== h~éáí~äÉêíê~ÖëíÉìÉê= ^ìëäK=nìÉääÉåëíÉìÉê== i~íÉåíÉ=píÉìÉêå== pçåëíáÖÉ=píÉìÉêå=îçã=báåâçããÉå=ìåÇ=bêíê~Ö== pçåëíáÖÉ=píÉìÉêå=
q~ÄÉääÉ=OQW=_ÉíêáÉÄäáÅÜÉ=^ìÑï~åÇëíÉìÉêå=EhçåíÉåF= aáÉ=_ìÅÜìåÖ=ÉáåÉë=~åÑ~ääÉåÇÉå=^ìÑï~åÇë=ÇáÉëÉê=^êí=ÉêÑçäÖí=áã=pçää=ÉáåÉë=ÇÉê=çÄÉå= ÖÉå~ååíÉå=hçåíÉåK=páÉ=ëáåÇ=ïáÉ=àÉÇÉ=píÉìÉê=îçå=ÉáåÉê=_Éä~ëíìåÖ=ÇìêÅÜ=rpí=ÄÉÑêÉáíK= =
14.1.3 Private Steuern píÉìÉêåI= ÇáÉ=ÇáÉ=mÉêëçå= ÇÉë= råíÉêåÉÜãÉêë= ÄÉíêÉÑÑÉå= E_ÉáëéáÉäÉW= báåâçããÉåëíÉìÉêI= háêÅÜÉåëíÉìÉêI= dêìåÇëíÉìÉê= ÑΩê= mêáî~íÖêìåÇëíΩÅâÉI= píÉìÉê= ÑΩê= éêáî~íÉ= hÑòF= ìåÇ= ÇìêÅÜ=dÉäÇÉê=ÇÉë=råíÉêåÉÜãÉåë=ÄÉÖäáÅÜÉå=ïÉêÇÉåI=ëáåÇ=~ìÑ=ÇÉã=mêáî~íâçåíç=ÇÉë= àÉïÉáäáÖÉå=dÉëÉääëÅÜ~ÑíÉêë=òì=ÉêÑ~ëëÉåK= =
14. Steuern
251
⌦= _ÉáëéáÉäW= _~åâΩÄÉêïÉáëìåÖ=ÇÉê=hÑòJpíÉìÉê=áå=e∏ÜÉ=îçå=URMIMM=bìêç=ÑΩê=ÇÉå=mêáî~íJmâï=ÇÉë= råíÉêåÉÜãÉêëK== = _Éå∏íáÖÉ=hçåíÉåW= =
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= 14.1.4 Steuern als durchlaufende Posten bë=ÖáÄí=ÖÉïáëëÉ=píÉìÉêåI=ÇáÉ=ÇÉå=bêÑçäÖ=ÉáåÉë=råíÉêåÉÜãÉåë=åáÅÜí=ÄÉÉáåÑäìëëÉåK=wì= ÇáÉëÉå=ò®ÜäÉåI=ïáÉ=ÄÉêÉáíë=ÄÉÜ~åÇÉäíI=Éíï~=ÇáÉ=rãë~íòëíÉìÉê=ìåÇ=ÇáÉ=içÜåJ=ìåÇ= háêÅÜÉåëíÉìÉê=ÇÉê=jáí~êÄÉáíÉêK=aáÉëÉ=píÉìÉêå=ëíÉääÉå=ÑΩê=Ç~ë=råíÉêåÉÜãÉå=âÉáåÉå= ^ìÑï~åÇ=Ç~êK=páÉ=ïÉêÇÉå=äÉÇáÖäáÅÜ=îçã=råíÉêåÉÜãÉå=ÉáåÄÉÜ~äíÉå=ìåÇ=êÉÖÉäã®≈áÖ= ~å=Ç~ë=cáå~åò~ãí=~ÄÖÉÑΩÜêíK= =
⌦= _ÉáëéáÉäW= mçëíÄ~åâΩÄÉêïÉáëìåÖ= ÇÉê= ÉáåÄÉÜ~äíÉåÉå= içÜåëíÉìÉê= ÑΩê= ÇÉå= ~ÄÖÉä~ìÑÉåÉå= jçå~íK= aáÉ=píÉìÉêÜ∏ÜÉ=äáÉÖí=ÄÉá=QKRNOIMM=bìêçK= = _Éå∏íáÖÉ=hçåíÉåW= =
QUPM=Ó=pçåëíáÖÉ=sÉêÄáåÇäáÅÜâÉáíÉå=ÖÉÖÉåΩÄÉê=ÇÉå=cáå~åòÄÉÜ∏êÇÉå= OURM=Ó=mçëíÖáêçÖìíÜ~ÄÉå== = _ìÅÜìåÖëë~íòW= =
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C. Laufende Buchungen in Industriebetrieben =
14.2 Steuerrückerstattungen und -nachzahlungen gÉ=å~ÅÜÇÉã=çÄ=Éë=ëáÅÜ=ìã=ÇáÉ=oΩÅâÉêëí~ííìåÖ=ÉáåÉê=éêáî~íÉå=çÇÉê=ÉáåÉê=ÄÉíêáÉÄJ äáÅÜÉå= píÉìÉê= Ü~åÇÉäíI= áëí= ÄÉá= ÇÉê= sÉêÄìÅÜìåÖ= ÉáåÉ= ÇÉê= áå= å~ÅÜÑçäÖÉåÇÉê= q~ÄÉääÉ= ~ìÑÖÉÑΩÜêíÉå= hçåíÉåÖêìééÉå= òì= îÉêïÉåÇÉåK= fã= c~ääÉ= ÇÉê= ÄÉíêáÉÄäáÅÜÉå= píÉìÉê= áëí= òìÇÉã=òì=ÄÉëíáããÉåI=çÄ=ÇáÉ=píÉìÉêêΩÅâÉêëí~ííìåÖ=Ç~ë=~âíìÉääÉ=çÇÉê=Éáå=~ÄÖÉä~ìÑÉJ åÉë= táêíëÅÜ~Ñíëà~Üê= ÄÉíêáÑÑíK= pç= ëáåÇ= áã= ÉêëíÖÉå~ååíÉå= c~ää= ëçåëíáÖÉ= ÄÉíêáÉÄäáÅÜÉ= bêJ íê®ÖÉ= ìåÇ= áã= òïÉáíÉå= c~ää= éÉêáçÇÉåÑêÉãÇÉ= bêíê®ÖÉ= òì= îÉêÄìÅÜÉåK= aáÉ= oΩÅâÉêëí~íJ íìåÖ=ÉáåÉê=éêáî~íÉå=píÉìÉê=áëí=ÜáåÖÉÖÉå=~äë=mêáî~íÉáåä~ÖÉ=òì=ÉêÑ~ëëÉåK= =
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14. Steuern
253
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D. JAHRESABSCHLUSS = Inhalt dieses Kapitels sind die im Rahmen des Jahresabschlusses durchzuführende Bewertung der Vermögensgegenstände (bzw. Wirtschaftsgüter) und Schulden und die damit verbundenen Buchungen. Es wird also konrekt die Frage beantwortet, mit welchem Wert diese Gegenstände in die Bilanz eingehen. Die Schwerpunkte liegen dabei in der Bewertung
des Sachanlagevermögens,
des Umlaufvermögens (Vorräte, Wertpapiere, Forderungen),
des Eigenkapitals,
der Rückstellungen und Rechnungsabgrenzungsposten und
der Verbindlichkeiten.
Es wird sich auf die Behandlung ausgewählter handels- und steuerrechtlicher Bewertungsvorschriften beschränkt. Internationale Rechnungslegungsvorschriften (US-GAAP: Generally Accepted Accounting Principles, IFRS: International Financial Reporting Standards) werden nicht thematisiert. = = = = =
1.
Buchungskreislauf
=
táÉ= ÇáÉ= å~ÅÜÑçäÖÉåÇÉ= a~êëíÉääìåÖ= òÉáÖíI= áëí= ÇáÉ= _ìÅÜÑΩÜêìåÖ= Éáå= ëáÅÜ= ~ääÉ= g~ÜêÉ= ïáÉÇÉêÜçäÉåÇÉê=hêÉáëä~ìÑI=ÇÉê=ëáÅÜ=~ìë=îáÉê=e~ìéíÄÉëí~åÇíÉáäÉå=òìë~ããÉåëÉíòíK== = =
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2. Bewertung des Anlagevermögens
261
báåÉ=^Äå~ÜãÉ=ÇÉê=kìíòìåÖëãÉåÖÉ=â~åå=ÄÉÇáåÖí=ëÉáå=ÇìêÅÜ=
ÖÉÄê~ìÅÜëÄÉÇáåÖíÉå=Eåçêã~äÉåFI=íÉÅÜåáëÅÜÉå=sÉêëÅÜäÉá≈=E^ÄåìíòìåÖFI=
êìÜÉåÇÉå=sÉêëÅÜäÉá≈=EòK_K=ÇìêÅÜ=sÉêïáííÉêìåÖI=sÉêêçëíÉåF=çÇÉê=
pìÄëí~åòîÉêêáåÖÉêìåÖ=EòK_K=ÄÉá=háÉ≈ÖêìÄÉåFK=
báå= ^Ää~ìÑ= ÇÉê= kìíòìåÖëòÉáí= áëí= îçê= ~ääÉã= ÄÉá= áãã~íÉêáÉääÉå= sÉêã∏ÖÉåëÖÉÖÉåëJ í®åÇÉå=òì=ÄÉ~ÅÜíÉåK=pç=áëí=ÄÉáëéáÉäëïÉáëÉ=Éáå=ÉåíÖÉäíäáÅÜ=ÉêïçêÄÉåÉë=m~íÉåí=Äáë=òì= ÇÉëëÉå=^ìëä~ìÑÉå=~ÄòìëÅÜêÉáÄÉåK= sÉêäáÉêí= Éáå= ~ÄåìíòÄ~êÉêI= ã~íÉêáÉääÉê= ^åä~ÖÉÖÉÖÉåëí~åÇ= ÇìêÅÜ= éÉêã~åíÉåíÉ= mÑäÉÖÉ= îçå=mÉêáçÇÉ=òì=mÉêáçÇÉ=åáÅÜí=~å=tÉêíI=ëç=áëí=Éê=ÇÉååçÅÜ=~ÄòìëÅÜêÉáÄÉåI=Ç~=ÇáÉ=^åJ ëÅÜ~ÑÑìåÖâçëíÉå= íêçíòÇÉã= ΩÄÉê= ÇáÉ= kìíòìåÖëÇ~ìÉê= òì= îÉêíÉáäÉå= ëáåÇK= báåÉ= mÉêáçJ ÇÉå~ÄÖêÉåòìåÖ=â~åå=~äëç=~äë=ïÉáíÉêÉ=^ÄëÅÜêÉáÄìåÖëìêë~ÅÜÉ=ÄÉíê~ÅÜíÉí=ïÉêÇÉåK= =
e~åÇÉäëêÉÅÜíäáÅÜ=áëí=ÇáÉ=éä~åã®≈áÖÉ=^ÄëÅÜêÉáÄìåÖ=áå=¬=ORP=ff=pK=N=ìåÇ=O=ed_=ÖÉJ êÉÖÉäíK= aáÉëÉê= ÄÉëíáããíI= Ç~ëë= ÄÉá= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉå= ÇÉë= ^åä~ÖÉîÉêã∏ÖÉåëI= ÇÉêÉå= kìíòÉå= òÉáíäáÅÜ= ÄÉÖêÉåòí= áëí= E~ÄåìíòÄ~êÉ= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉF= ÇáÉ= ^åJ ëÅÜ~ÑÑìåÖëJ= çÇÉê= eÉêëíÉääìåÖëâçëíÉå= ìã= éä~åã®≈áÖÉ= ^ÄëÅÜêÉáÄìåÖÉå= òì= îÉêãáåJ ÇÉêå=ëáåÇK=píÉìÉêêÉÅÜíäáÅÜ=ëáåÇ=^ÄëÉíòìåÖ=ÑΩê=^ÄåìíòìåÖ=áå=¬=T=f=ìåÇ=ff=bpíd=ìåÇ= ^ÄëÉíòìåÖ=ÑΩê=pìÄëí~åòîÉêêáåÖÉêìåÖ=áå=¬=T=sf=bpíd=ÖÉêÉÖÉäíK= =
gÉÇÉê= éä~åã®≈áÖÉå= ^ÄëÅÜêÉáÄìåÖ= äáÉÖí= å~ÅÜ= ¬= ORP= ff= ed_= Éáå= ëçÖK= ^ÄëÅÜêÉáJ ÄìåÖëéä~å= òì= dêìåÇÉI= áå= ÇÉã= ÇáÉ= sÉêíÉáäìåÖ= ÇÉê= ^åëÅÜ~ÑÑìåÖëJ= çÇÉê= eÉêëíÉäJ äìåÖëâçëíÉå=~ìÑ=ÇáÉ=g~ÜêÉ=ÇÉê=îçê~ìëëáÅÜíäáÅÜÉå=kìíòìåÖëÇ~ìÉê=ÑÉëíÖÉäÉÖí=ïáêÇK= aáÉëÉê=^ÄëÅÜêÉáÄìåÖëéä~å=ÄÉáåÜ~äíÉí=^ÄëÅÜêÉáÄìåÖëÄ~ëáëI=ÖÉëÅÜ®íòíÉ=kìíòìåÖëÇ~ìJ ÉêI= _ÉÖáåå= ÇÉê= éä~åã®≈áÖÉå= ^ÄëÅÜêÉáÄìåÖI= ^ÄëÅÜêÉáÄìåÖëãÉíÜçÇÉ= ìåÇ= ÇÉå= ÖÉJ ëÅÜ®íòíÉå= iáèìáÇ~íáçåëÉêä∏ëLoÉëíÄìÅÜïÉêí= ~ã= båÇÉ= ÇÉê= kìíòìåÖëÇ~ìÉêK= aÉê= ^ÄJ ëÅÜêÉáÄìåÖëéä~å= áëí= _Éëí~åÇíÉáä= ÇÉë= ëçÖK= ^åä~ÖÉëéáÉÖÉäëI= ÇÉê= ÑΩê= àÉÇÉë= ^åä~ÖÉÖìí= åÉÄÉå= ÇÉå= ïáÅÜíáÖëíÉå= íÉÅÜåáëÅÜÉå= a~íÉå= ìåÇ= fåîÉåí~êåìããÉêå= òìê= ÉáåÇÉìíáÖÉå== fÇÉåíáÑáòáÉêìåÖ= ÇÉë= dÉÖÉåëí~åÇÉë= îçê= ~ääÉã= ÇáÉ= ÑΩê= ÇáÉ= ^ÄëÅÜêÉáÄìåÖ= êÉäÉî~åíÉå= a~íÉå=ÉåíÜ®äíK== =
2.1.1
Abschreibungsbasis
aáÉ= ^åëÅÜ~ÑÑìåÖëâçëíÉå= E¬= ORR= f= ed_I= e= SKO= bpíeF= ÄáäÇÉå= ëçïçÜä= áã= e~åÇÉäëJ= ~äë= ~ìÅÜ= áã= píÉìÉêêÉÅÜí= ÇáÉ= _ÉêÉÅÜåìåÖëÖêìåÇä~ÖÉ= ÑΩê= ÇáÉ= éä~åã®≈áÖÉ= ^ÄëÅÜêÉáJ ÄìåÖ=E¬=ORP=^ÄëK=N=p~íò=N=ed_F=ÄòïK=^ÄëÉíòìåÖ=E¬=S=^ÄëK=N=kêK=N=p~íò=N=ìåÇ=kêK=O= p~íò= N= bpídFK= aáÉë= Öáäí= ~ääÉêÇáåÖë= åáÅÜí= ÑΩê= ^åä~ÖÉÖÉÖÉåëí®åÇÉI= ÇáÉ= îçã= råíÉêåÉÜJ ãÉå= áå= báÖÉåäÉáëíìåÖ= ÜÉêÖÉëíÉääí= ïÉêÇÉåK= få= ÇáÉëÉã= c~ää= ëáåÇ= ÇáÉ= eÉêëíÉääìåÖëJ âçëíÉå= EîäÖK= `= V= ÑΩê= råíÉêëÅÜáÉÇÉ= òïáëÅÜÉå= Ü~åÇÉäëêÉÅÜíäáÅÜ= ìåÇ= ëíÉìÉêêÉÅÜíäáÅÜ= ÉêãáííÉäíÉå=eÉêëíÉääâçëíÉåF=~äë=^ÄëÅÜêÉáÄìåÖëJ=ÄòïK=^ÄëÉíòìåÖëÄ~ëáë=ÜÉêòìåÉÜãÉåK= =
2.1.2
Nutzungsdauer
aáÉ=ï~ÜêëÅÜÉáåäáÅÜÉ=éä~åã®≈áÖÉ=kìíòìåÖëÇ~ìÉê=ÉáåÉë=^åä~ÖÉÖìíÉë=ÄÉëÅÜêÉáÄí=ÇÉå= wÉáíê~ìãI= áå= ÇÉã= Éáå= ~ÄåìíòÄ~êÉê= ^åä~ÖÉÖÉÖÉåëí~åÇ= îçê~ìëëáÅÜíäáÅÜ= áã= råíÉêåÉÜJ ãÉå=ÉáåÖÉëÉíòí=ïÉêÇÉå=â~ååK==
262
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e~åÇÉäëêÉÅÜíäáÅÜ=ïáêÇ=ÇáÉ=kìíòìåÖëÇ~ìÉê=ÄÉïÉÖäáÅÜÉê=sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ=ìåJ íÉê=_É~ÅÜíìåÖ=ÇÉë=sçêëáÅÜíëéêáåòáéë=ìåÇ=ÇÉë=mêáåòáéë=ÇÉê=táääâΩêÑêÉáÜÉáí=ÖÉëÅÜ®íòíK= píÉìÉêêÉÅÜíäáÅÜ= ÉåíÜ~äíÉå= ^Ñ^Jq~ÄÉääÉå= ~ääÖÉãÉáåÉ= ìåÇ= Äê~åÅÜÉåëéÉòáÑáëÅÜÉ= ÄÉJ íêáÉÄëÖÉï∏ÜåäáÅÜÉ= kìíòìåÖëÇ~ìÉêå= ÑΩê= ÉáåÉ= sáÉäò~Üä= ÄÉïÉÖäáÅÜÉê= táêíëÅÜ~ÑíÖΩíÉêI= îçå=ÇÉåÉå=ãáí=áåÇáîáÇìÉääÉê=_ÉÖêΩåÇìåÖ=~ÄÖÉïáÅÜÉå=ïÉêÇÉå=â~ååK=_Éá=dÉÄ®ìÇÉå= ëáåÇ=ÇáÉ=kìíòìåÖëÇ~ìÉêå=áåÇáêÉâí=áå=¬=T=fs=ìåÇ=s=bpíd=ÑÉëíÖÉäÉÖíK== =
2.1.3
Abschreibungsmethode (inkl. Verbuchung)
a~= ÇÉê= tÉêíãáåÇÉêìåÖëîÉêä~ìÑ= ìåíÉêëÅÜáÉÇäáÅÜ= ëÉáå= â~ååI= ëíÉÜÉå= ÉáåÉ= oÉáÜÉ= îçå= ^ÄëÅÜêÉáÄìåÖëîÉêÑ~ÜêÉå= òìê= sÉêÑΩÖìåÖI= ìã= ÇáÉ= í~íë®ÅÜäáÅÜÉ= ä~ìÑÉåÇÉ= tÉêíãáåÇÉJ êìåÖ=ã∏ÖäáÅÜëí=Éñ~âí=~ÄÄáäÇÉå=òì=â∏ååÉåK=^ÄÜ®åÖáÖ=îçå=ÇÉê=^êí=ÇÉê=sÉêíÉáäìåÖ=ÇÉê= ^åëÅÜ~ÑÑìåÖëJ=ìåÇ=eÉêëíÉääìåÖëâçëíÉå=E^ehF=~ìÑ=ÇáÉ=kìíòìåÖëÇ~ìÉê=ÉñáëíáÉêÉå=ìK~K= ÑçäÖÉåÇÉ=jÉíÜçÇÉåW= =
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2. Bewertung des Anlagevermögens
2.1.3.1
263
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2. Bewertung des Anlagevermögens
269
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2.1.3.3
Progressive Abschreibung
báåÉ=ïÉáíÉêÉ=^ÄëÅÜêÉáÄìåÖëãÉíÜçÇÉ=áëí=ÇáÉ=ëçÖK=éêçÖêÉëëáîÉ=^ÄëÅÜêÉáÄìåÖK=páÉ=îÉêJ íÉáäí= ÇáÉ= ^åëÅÜ~ÑÑìåÖëJ= çÇÉê= eÉêëíÉääìåÖëâçëíÉå= ÉáåÉë= ^åä~ÖÉÖìíÉë= áå= à®ÜêäáÅÜ= E~J êáíÜãÉíáëÅÜ= çÇÉê= ÖÉçãÉíêáëÅÜF= ëíÉáÖÉåÇÉå= ^ÄëÅÜêÉáÄìåÖëÄÉíê®ÖÉå= ~ìÑ= ÇáÉ= kìíòìåÖëÇ~ìÉêK= ^ìÑ= ÇáÉëÉ=^êí= ìåÇ= tÉáëÉ= â~åå= áå= ÇÉå=ÉêëíÉå= kìíòìåÖëà~ÜêÉå= ÉáåÉ= åáÉÇêáÖÉ= ìåÇ= áå= ÇÉå= äÉíòíÉå= kìíòìåÖëà~ÜêÉå= ÉáåÉ= ÜçÜÉ= ^ÄëÅÜêÉáÄìåÖ= ~åÖÉëÉíòí= ïÉêÇÉåK= ^ìÑÖêìåÇ= ÇÉê= åáÉÇêáÖÉå= ^ÄëÅÜêÉáÄìåÖÉå= òì= _ÉÖáåå= ÇÉê= kìíòìåÖëÇ~ìÉê= ìåÇ=ÇÉê=Ç~ãáí=îÉêÄìåÇÉåÉå=dÉÑ~Üê=ÇÉê=§ÄÉêÄÉïÉêíìåÖ=ÇÉë=sÉêã∏ÖÉåëÖÉÖÉåëí~åJ ÇÉë=áëí=ÇáÉëÉ=jÉíÜçÇÉ=åáÅÜí=ãáí=ÇÉã=sçêëáÅÜíëéêáåòáé=îÉêÉáåÄ~êK=páÉ=áëí=Ç~ÜÉê=Ü~åJ ÇÉäëêÉÅÜíäáÅÜ= åìê= òìä®ëëáÖI= ïÉåå= ëáÉ= ÇÉå= dç_= ÉåíëéêáÅÜíK= páÉ= ÄáÉíÉí= ëáÅÜ= Éíï~= ÄÉá= ä®åÖÉêÉå= ^åä~ìÑòÉáíÉå= Äáë= òìê= kìíòìåÖ= EòK_K= ÄÉá= hê~ÑíïÉêâÉåI= lÄëíéä~åí~ÖÉåF= ~åK= píÉìÉêêÉÅÜíäáÅÜ=áëí=ÇáÉëÉ=jÉíÜçÇÉ=ÖêìåÇë®íòäáÅÜ=îÉêÄçíÉåK== =
2.1.3.4
Leistungsabschreibung
aáÉëÉê=^ÄëÅÜêÉáÄìåÖëãÉíÜçÇÉ=ïáêÇ=çÑí=òìÖÉëÅÜêáÉÄÉåI=Ç~ëë=ëáÉ=ÇáÉ=ÉáåòáÖÉ=áëíI=ÇáÉ= ÇÉå= í~íë®ÅÜäáÅÜÉå= tÉêíîÉêäìëí= ÉáåÉê= ^åä~ÖÉ= áååÉêÜ~äÄ= ÉáåÉê= oÉÅÜåìåÖëéÉêáçÇÉ= ~ã= ÉÜÉëíÉå= ÄÉëÅÜêÉáÄíK= bë= ÉêÑçäÖí= âÉáåÉ= Ääç≈É= ^ìÑíÉáäìåÖ= ÇÉê= ^åëÅÜ~ÑÑìåÖëJ= çÇÉê= eÉêëíÉääìåÖëâçëíÉå= ~ìÑ= ÇáÉ= kìíòìåÖëÇ~ìÉê= EwÉáí~ÄëÅÜêÉáÄìåÖFK= pí~ííÇÉëëÉå= ÖÉÜí= ã~å=Ç~îçå=~ìëI=Ç~ëë=ÇáÉ=^ÄåìíòìåÖ=òÉáíìå~ÄÜ®åÖáÖ=ÉêÑçäÖíI=ìåÇ=ÉêãáííÉäí=ÇÉå=^ÄJ ëÅÜêÉáÄìåÖëÄÉíê~Ö=~åÜ~åÇ=ÇÉê=í~íë®ÅÜäáÅÜÉå=^åä~ÖÉåäÉáëíìåÖ=ÄòïK=JÄÉ~åëéêìÅÜìåÖ= EòK_K=j~ëÅÜáåÉåëíìåÇÉåI=háäçãÉíÉêò~ÜäI=píΩÅâò~ÜäFK=aáÉ=iÉáëíìåÖë~ÄëÅÜêÉáÄìåÖ=ÄáÉJ íÉí=ëáÅÜ=~äëç=ÄÉá=ëí~êâ=ëÅÜï~åâÉåÇÉê=få~åëéêìÅÜå~ÜãÉ=ÇÉë=dÉÖÉåëí~åÇë=~åK=k~ÅÜJ íÉáä= ÇÉê= jÉíÜçÇÉ= áëí= Éë= ~ÄÉêI= Ç~ëë= áå= oìÜÉòÉáíÉå=âÉáåÉ=^ÄëÅÜêÉáÄìåÖ= ÇìêÅÜÖÉÑΩÜêí= ïáêÇ=ìåÇ=ëç=ÇÉê=oìÜÉîÉêëÅÜäÉá≈=åáÅÜí=ÄÉêΩÅâëáÅÜíáÖí=ïáêÇK== káÅÜí=åìê=Ü~åÇÉäëJ=ëçåÇÉêå=~ìÅÜ=ëíÉìÉêêÉÅÜíäáÅÜ=E¬=T=f=pK=S=bpídF=áëí=ÇáÉëÉ=^ÄëÅÜêÉáJ ÄìåÖëãÉíÜçÇÉ= ÄÉá= ÄÉïÉÖäáÅÜÉå= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉå= ÄòïK= táêíëÅÜ~ÑíëÖΩíÉêå= ÇÉë=^åä~ÖÉîÉêã∏ÖÉåë=òìä®ëëáÖK=bë=áëí=~ÄÉê=åçíïÉåÇáÖI=ÉáåÉå=k~ÅÜïÉáë=ΩÄÉê=ÇáÉ=~åJ Ñ~ääÉåÇÉ=iÉáëíìåÖ=òì=ÑΩÜêÉåK=pç=áëí=ÄÉá=ÉáåÉã=mâï=ÄÉáëéáÉäëïÉáëÉ=Éáå=c~ÜêíÉåÄìÅÜ= îçêòìïÉáëÉåK= wìê=_ÉêÉÅÜåìåÖ=ÇÉê=^ÄëÅÜêÉáÄìåÖëJL^ÄëÉíòìåÖëÄÉíê®ÖÉ=ïáêÇ=ÑçäÖÉåÇÉ=cçêãÉä=ÉáåJ ÖÉëÉíòíW= =
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270
D. Jahresabschluss
⌦= _ÉáëéáÉäW== báåÉ= j~ëÅÜáåÉ= ïìêÇÉ= áå= ÇÉê= e~åÇÉäëÄáä~åò= òì= eÉêëíÉääìåÖëâçëíÉå= áå= e∏ÜÉ= îçå= NPKQRMIMM= bìêç= áå= báÖÉåäÉáëíìåÖ= ÉêëíÉääí= ìåÇ= ~åëÅÜäáÉ≈ÉåÇ= áã= ÉáÖÉåÉå= _ÉíêáÉÄ= ÉáåJ ÖÉëÉíòíK= aáÉ= ÖÉëÅÜ®íòíÉ= cÉêíáÖìåÖëâ~é~òáí®í= ÇÉê= ^åä~ÖÉ= îçê= ^ìëëÅÜÉáÇÉå= ~ìë= ÇÉã= _ÉíêáÉÄ=ä~Ö=ÄÉá=NSKMMM=píìåÇÉåI=îçå=ÇÉåÉå=~ìÑÖêìåÇ=ëÅÜäÉÅÜíÉê=^ìÑíê~Öëä~ÖÉ=áã=ÉêëJ íÉå= kìíòìåÖëà~Üê= ~ääÉêÇáåÖë= åìê= NKRMM= píìåÇÉå= áå= ^åëéêìÅÜ= ÖÉåçããÉå= ïÉêÇÉå= âçååíÉåK= ^ÄëÅÜêÉáÄìåÖëèìçíÉ=Z=
NKRMM ⋅ NMM Z=VIPTR=B= NSKMMM
= ^ÄëÅÜêÉáÄìåÖëJtÉêí=ENK=kìíòìåÖëà~ÜêF=Z=VIPTR=B=îçå=NPKQRMIMM=Z=NKOSMIVQ=bìêç= = 2.1.3.5
Absetzung für Substanzverringerung
_Éá= _ÉêÖÄ~ììåíÉêåÉÜãÉåI= píÉáåÄêΩÅÜÉå= ìåÇ= ~åÇÉêÉå= _ÉíêáÉÄÉåI= ÇáÉ= ÉáåÉå= sÉêÄê~ìÅÜ=ÇÉê=pìÄëí~åò=ãáí=ëáÅÜ=ÄêáåÖÉåI=ëáåÇ=áã=píÉìÉêêÉÅÜí=^ÄëÉíòìåÖÉå=ÑΩê=pìÄJ ëí~åòîÉêêáåÖÉêìåÖÉå=~å=píÉääÉ=ÇÉê=^ÄëÉíòìåÖ=ÑΩê=^ÄåìíòìåÖ=å~ÅÜ=¬=T=f=bpíd=òìä®ëJ ëáÖK=eáÉê=ïáêÇ=ÇÉê=^ÄëÉíòìåÖ=Ç~ë=j~≈=ÇÉë=ÉáåÖÉíêÉíÉåÉå=pìÄëí~åòîÉêòÉÜêë=òìÖêìåJ ÇÉÖÉäÉÖíK= =
2.1.4
Besonderheiten
2.1.4.1
Abschreibung bei Zugang während des Geschäftsjahresjahres
_ÉÖáåå= ÇÉê= ëíÉìÉêêÉÅÜíäáÅÜÉå= ^ÄëÉíòìåÖ= ÑΩê= ^ÄåìíòìåÖ= Eo= TKQ= f= bpíoF= áëí= ÇÉê= wÉáíJ éìåâí= ÇÉê= ^åëÅÜ~ÑÑìåÖ= çÇÉê= eÉêëíÉääìåÖ= EåáÅÜí= ÇÉê= fåÖÉÄê~ìÅÜå~ÜãÉFK= _Éáã= wìJ Ö~åÖ= ÉáåÉë= ^åä~ÖÉÖìíÉë= ï®ÜêÉåÇ= ÇÉë= dÉëÅÜ®Ñíëà~ÜêÉë= ãìëë= ÇáÉ= ^Ñ^= Ç~ÜÉê=òÉáí~åJ íÉáäáÖ= Ełéêç= ê~í~= íÉãéçêáë F= ÉêÑçäÖÉåI= ÇKÜK= ÇáÉ= ^Ñ^= ïáêÇ= ÑΩê= ëç= îáÉäÉ= jçå~íÉ= ~åÖÉJ ëÉíòíI=ïáÉ=Ç~ë=^åä~ÖÉÖìí=ÇÉã=_ÉíêáÉÄ=òìê=sÉêÑΩÖìåÖ=ëí~åÇK=aÉê=^åëÅÜ~ÑÑìåÖëãçå~í= Öáäí=Ç~ÄÉá=~äë=îçääÉê=jçå~íK== =
⌦= _ÉáëéáÉäW= táêÇ=Éáå=^åä~ÖÉÖìí=áã=jçå~í=j®êò=ÖÉâ~ìÑíI=ëç=Ç~êÑ=åìê=NMLNO=ÇÉê=g~ÜêÉëJ^Ñ^=~åÖÉJ ëÉíòí=ïÉêÇÉåK= =
cΩê= ÇÉå= c~ää= ÇÉê= ^åëÅÜ~ÑÑìåÖJ= çÇÉê= eÉêëíÉääìåÖ= Ö~äí= Äáë= òìã= MNKMNKOMMQ= ÇáÉ= ëçÖK= sÉêÉáåÑ~ÅÜìåÖëêÉÖÉäK= i~Ö= Ç~ë= a~íìã= ÇÉê= ^åëÅÜ~ÑÑìåÖ= áå= ÇÉê= ÉêëíÉå= g~ÜêÉëÜ®äÑíÉ= Eg~åì~ê= J= gìåáFI= ÇìêÑíÉ= ÇáÉ=îçääÉ= g~ÜêÉëJ^Ñ^= ÖÉäíÉåÇ= ÖÉã~ÅÜí= ïÉêÇÉåK= _Éá= _ÉòìÖ= áã= òïÉáíÉå=e~äÄà~Üê=Egìäá=J=aÉòÉãÄÉêF=ï~ê=òì=ÄÉêΩÅâëáÅÜíáÖÉåI=Ç~ëë=åìê=ÇáÉ=Ü~äÄÉ=g~ÜJ êÉëJ^Ñ^=áå=^åëéêìÅÜ=ÖÉåçããÉå=ïÉêÇÉå=âçååíÉK= e~åÇÉäëêÉÅÜíäáÅÜ=ÖáÄí=Éë=ÜáåëáÅÜíäáÅÜ=ÇÉë=^ÄëÅÜêÉáÄìåÖëÄÉÖáååë=âÉáåÉ=âçÇáÑáòáÉêíÉå= sçêëÅÜêáÑíÉåK=aáÉ=dç_=ã~ÅÜÉå=~ÄÉê=ÇáÉ=òÉáí~åíÉáäáÖÉ=^ÄëÅÜêÉáÄìåÖ=òìê=dêìåÇêÉÖÉäK==
2. Bewertung des Anlagevermögens
2.1.4.2
271
Abschreibung bei Abgang während des Geschäftsjahres
táÉ= ÄÉêÉáíë= ÄÉÜ~åÇÉäí= ïìêÇÉI= ïáêÇ= Ç~ë= båÇÉ= ÇÉê= éä~åã®≈áÖÉå= ^ÄëÅÜêÉáÄìåÖ= ÇìêÅÜ= Ç~ë= ^ìëëÅÜÉáÇÉå= ÇÉë= ^åä~ÖÉÖÉÖÉåëí~åÇÉë= ~ìë= ÇÉã= _ÉíêáÉÄ= ÄÉá= ^Ää~ìÑ= ÇÉê= kìíòìåÖëÇ~ìÉê=ÄÉëíáããíK=a~ë=båÇÉ=ÇÉê=éä~åã®≈áÖÉå=^ÄëÅÜêÉáÄìåÖ=ïáêÇ=~ÄÉê=~ìÅÜ= ÇìêÅÜ=ÇÉå=sÉêâ~ìÑ=îçå=p~ÅÜ~åä~ÖÉå=EîÖäK=`=UF=ìåÇ=ÄÉá=ÇÉêÉå=mêáî~íÉåíå~ÜãÉ=EîÖäK= `= NPKOKNF= ÇìêÅÜ= ÇÉå= råíÉêåÉÜãÉê= ÉáåÖÉäÉáíÉíK= få= ÇáÉëÉå= ÄÉáÇÉå= c®ääÉå= ëáåÇ= ~ÄJ ëÅÜêÉáÄìåÖëíÉÅÜåáëÅÜÉ= _ÉëçåÇÉêÜÉáíÉå= òì= ÄÉ~ÅÜíÉåK= e~åÇÉäëJ= ìåÇ= ëíÉìÉêêÉÅÜíäáÅÜ= Edç_I= o= TKQ= sfff= bpíoF= áëí= å®ãäáÅÜ= áã= c~ääÉ= ÇÉë= ^ìëëÅÜÉáÇÉåë=îçê= ^Ää~ìÑ= ÇÉê= kìíJ òìåÖëÇ~ìÉê= ÇáÉ= äÉíòíÉ= ^ÄëÅÜêÉáÄìåÖ= ÄòïK= ^ÄëÉíòìåÖ= áããÉê= òÉáí~åíÉáäáÖ= îçêòìåÉÜJ ãÉåK=aáÉë=ïáêÇ=åìå=~åÜ~åÇ=ÉáåÉë=ÉáåÑ~ÅÜÉå=_ÉáëéáÉäë=Éêä®ìíÉêíK= =
⌦= _ÉáëéáÉäW= =
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2.1.4.5
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2.2.1
277
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Außerplanmäßige Abschreibung in der Handelsbilanz
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Handelsrechtlicher Tageswert
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2. Bewertung des Anlagevermögens
279
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2.2.3
Außerplanmäßige Abschreibung in der Steuerbilanz
2.2.3.1
Teilwertabschreibung
dÉã®≈=¬=S=f=kêK=NK=pK=O=bpíd=â~åå=Éáå=ëçÖK=åáÉÇêáÖÉêÉê=qÉáäïÉêí=~åÖÉëÉíòí=ïÉêÇÉåI= ïÉåå= ÉáåÉ= Ç~ìÉêÜ~ÑíÉ= tÉêíãáåÇÉêìåÖ= îçêäáÉÖíK= aáÉëÉë= t~ÜäêÉÅÜí= ïáêÇ= ~ÄÉê= ~ìÑJ ÖêìåÇ= ÇÉê= j~≈ÖÉÄäáÅÜâÉáí= ÇÉê= e~åÇÉäëJ= ÑΩê= ÇáÉ= píÉìÉêÄáä~åò= ÄÉá= Ç~ìÉêÜ~ÑíÉê= tÉêíJ ãáåÇÉêìåÖ=òìê=mÑäáÅÜíI=Ç~=áå=ÇÉê=e~åÇÉäëÄáä~åò=ÖÉãK=¬=ORP=ff=pK=P=ed_=ÉáåÉ=^ÄëÉíJ òìåÖëéÑäáÅÜí=ÄÉëíÉÜíK= aáÉ=ëíÉìÉêäáÅÜÉ=qÉáäïÉêí~ÄëÅÜêÉáÄìåÖ=Öáäí=åìê=ÑΩê=Ç~ìÉêÜ~ÑíÉ=tÉêíãáåÇÉêìåÖÉåK=_Éá= îçêΩÄÉêÖÉÜÉåÇÉê=tÉêíãáåÇÉêìåÖ=áëí=ÇáÉ=ëíÉìÉêäáÅÜÉ=qÉáäïÉêí~ÄëÅÜêÉáÄìåÖ=åáÅÜí=òìJ ä®ëëáÖK= aáÉë= Öáäí= ìå~ÄÜ®åÖáÖ= îçå= dÉëÉääëÅÜ~ÑíëÑçêã= çÇÉê= h~íÉÖçêáÉ= ÇÉë= ^åä~ÖÉîÉêJ ã∏ÖÉåë=EîÖäK=^ÄÄáäÇìåÖ=URFK= báåÉ= qÉáäïÉêí~ÄëÅÜêÉáÄìåÖ= ÉêÑçäÖí= áå= e∏ÜÉ= ÇÉê= aáÑÑÉêÉåò= òïáëÅÜÉå= _ìÅÜïÉêí= ìåÇ= åáÉÇêáÖÉêÉã=qÉáäïÉêíK= 2.2.3.2
Steuerrechtlicher Teilwert
aÉê= qÉáäïÉêí= áëí= áã= dÉÖÉåë~íò= òì= ÇÉå= ÜáëíçêáëÅÜÉå= ^åëÅÜ~ÑÑìåÖëJ= ìåÇ= eÉêëíÉäJ äìåÖëâçëíÉå=çÇÉê=òìã=_ìÅÜïÉêí=Éáå=~âíìÉääÉê=wÉáíïÉêíK=k~ÅÜ=¬=S=f=kêK=N=pK=P=bpíd= áëí=ÇÉê=qÉáäïÉêí=Éáå=_Éíê~ÖI=ÇÉå==
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280
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Wertaufholung
_Éá=tÉÖÑ~ää=ÇÉë=dêìåÇÉë=ÑΩê=ÇáÉ=qÉáäïÉêí~ÄëÅÜêÉáÄìåÖ=ÄÉëíÉÜí=ÖÉãK=¬=S=f=kêK=N=pK=Q= ìåÇ= kêK= O= pK= P= bpíd= ëíÉìÉêêÉÅÜíäáÅÜ= Éáå= ëíêÉåÖÉë= tÉêí~ìÑÜçäìåÖëÖÉÄçí= ëçïçÜä= ÑΩê= báåòÉäìåíÉêåÉÜãÉå= ìåÇ= mÉêëçåÉåÖÉëÉääëÅÜ~ÑíÉå= ~äë= ~ìÅÜ= ÑΩê= h~éáí~äÖÉëÉääëÅÜ~ÑíÉåK= tÉêíçÄÉêÖêÉåòÉ=ëáåÇ=~ìÅÜ=ÜáÉê=ÇáÉ=ÑçêíÖÉÑΩÜêíÉå=^åëÅÜ~ÑÑìåÖëJ=çÇÉê=eÉêëíÉäJ äìåÖëâçëíÉåK=
2.2.4
Verbuchung d. außerplanmäßigen Abschreibung b. Sachanlagen
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2.2.5
Verbuchung d. außerplanm. Abschreibung b. Wertpapieren
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Bewertung des Umlaufvermögens
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3.1 Allgemeine Bewertungsgrundsätze 3.1.1
Anschaffungskostenprinzip
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3.1.2
Strenges Niederstwertprinzip
få=ÇÉê=e~åÇÉäëÄáä~åò=Öáäí=áã=rãä~ìÑîÉêã∏ÖÉå=ëçïçÜä=ÄÉá=Ç~ìÉêÜ~ÑíÉê=~äë=~ìÅÜ=îçêJ ΩÄÉêÖÉÜÉåÇÉê=tÉêíãáåÇÉêìåÖ=å~ÅÜ=¬=ORP=fff=ed_=ÉáåÉ=^ÄïÉêíìåÖëéÑäáÅÜí=~ìÑ=ÇÉå= åáÉÇêáÖÉêÉå=q~ÖÉëïÉêí=EëíêÉåÖÉë=káÉÇÉêëíïÉêíéêáåòáéFK== få=ÇÉê=píÉìÉêÄáä~åò=ÄÉëíÉÜí=ÄÉá=Ç~ìÉêÜ~ÑíÉê=tÉêíãáåÇÉêìåÖ=ÉáåÉ=^ÄïÉêíìåÖëéÑäáÅÜí= å~ÅÜ=¬=S=f=kêK=O=pK=O=bpíd=áKsKãK=¬=R=f=pK=N=bpídK=_Éá=åìê=îçêΩÄÉêÖÉÜÉåÇÉê=tÉêíãáåJ ÇÉêìåÖ=áëí=ÉáåÉ=^ÄïÉêíìåÖ=~ìÑ=ÇÉå=åáÉÇêáÖÉêÉå=qÉáäïÉêí=îÉêÄçíÉåK= = =
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^ÄÄáäÇìåÖ=UTW=^ì≈Éêéä~åã®≈áÖÉ=^ÄëÅÜêÉáÄìåÖÉå=Erãä~ìÑîÉêã∏ÖÉåF= =
288
D. Jahresabschluss
^å= ÇáÉëÉê= píÉääÉ= ëÉá= Éêï®ÜåíI= Ç~ëë= áã= rãä~ìÑîÉêã∏ÖÉå= åìê= ~ì≈Éêéä~åã®≈áÖÉ= ìåÇ= âÉáåÉ= éä~åã®≈áÖÉå= ^ÄëÅÜêÉáÄìåÖÉå= ÉñáëíáÉêÉåK= eáåëáÅÜíäáÅÜ= ÇÉê= tÉêí~ìÑÜçJ äìåÖ= ÄÉá= tÉÖÑ~ää= ÇÉë= dêìåÇÉë= ÑΩê= ÇáÉ= ~ì≈Éêéä~åã®≈áÖÉ= ^ÄëÅÜêÉáÄìåÖ= ÖÉäíÉå= áã= rãä~ìÑîÉêã∏ÖÉå=ÇáÉ=ÖäÉáÅÜÉå=sçêëÅÜêáÑíÉå=ïáÉ=áã=^åä~ÖÉîÉêã∏ÖÉå=EîÖäK=a=OKOKOKPI= OKOKPKPFK=
=
3.2 Bewertung von Vorräten 3.2.1
Allgemeines
táÉ= ÄÉêÉáíë= ÄÉÜ~åÇÉäí= ïìêÇÉI= áëí= òìê= bêãáííäìåÖ= ÇÉê= _Éëí~åÇëîÉê®åÇÉêìåÖÉå= ~å= oçÜJI=eáäÑëJ=ìåÇ=_ÉíêáÉÄëëíçÑÑÉå=EîÖäK=_=NKVKNF=ëçïáÉ=ÑÉêíáÖÉå=ìåÇ=ìåÑÉêíáÖÉå=bêòÉìÖJ åáëëÉå= EîÖäK= _= QKTKOF= Éáå= sÉêÖäÉáÅÜ= òïáëÅÜÉå= ^åÑ~åÖëJ= ìåÇ= pÅÜäìëëÄÉëí~åÇ= ÇÉë= àÉJ ïÉáäáÖÉå=_Éëí~åÇëâçåíçë=îçêòìåÉÜãÉåK= =
p=
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3. Bewertung des Umlaufvermögens
3.2.2
289
Ausgewählte Bewertungsvereinfachungsverfahren für Stoffe
3.2.2.1
Durchschnittsverfahren
sçêê~íëîÉêã∏ÖÉå= ëçïáÉ= ~åÇÉêÉ= ÖäÉáÅÜÉ= sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ= ÇÉë= ^åä~ÖÉJ= ìåÇ= rãä~ìÑîÉêã∏ÖÉåë=EáåëÄÉëçåÇÉêÉ=tÉêíé~éáÉêÉFI=ïÉäÅÜÉë=òì=ëÅÜï~åâÉåÇÉå=mêÉáëÉå= ÉáåÖÉâ~ìÑí=ïìêÇÉ=ìåÇ=Ç~ë=ï®ÜêÉåÇ=ÇÉë=dÉëÅÜ®Ñíëà~ÜêÉë=ÉáåÉê=Ü®ìÑáÖÉå=cäìâíì~íáçå= ìåíÉêäáÉÖíI= ëçääíÉ= å~ÅÜ= ÇÉã= ëçÖK= aìêÅÜëÅÜåáííëïÉêíîÉêÑ~ÜêÉå= ÄÉïÉêíÉí= ïÉêÇÉåK= aáÉë=áëí=îçêíÉáäÜ~ÑíI=Ç~=~ã=båÇÉ=ÇÉë=dÉëÅÜ®Ñíëà~ÜêÉëà~ÜêÉë=åáÅÜí=ãÉÜê=çÜåÉ=pÅÜïáÉJ êáÖâÉáíÉå= ÑÉëíëíÉääÄ~ê= áëíI= ïÉäÅÜÉ= t~êÉå= îÉêâ~ìÑí= ìåÇ= ïÉäÅÜÉ= t~êÉå= åçÅÜ= îçêÜ~åJ ÇÉå= ëáåÇK= aÉê= tÉêí= ÇÉë= pÅÜäìëëÄÉëí~åÇÉë= ÉåíëíÉÜí= ÜáÉêÄÉá= ~ìë= ÇÉã= mêçÇìâí= ÇÉê= ÇìêÅÜ= ÇáÉ= fåîÉåíìê= ÑÉëíÖÉëíÉääÉå= píΩÅâò~ÜäÉå= ìåÇ= ÇÉå= ëçÖK= ÇìêÅÜëÅÜåáííäáÅÜÉå= ^åëÅÜ~ÑÑìåÖëâçëíÉåK= =
p_ Z píΩÅâò~Üä ⋅ ÇìêÅÜëÅÜåáííäáÅÜÉ ^åëÅÜ~ÑÑìåÖâçëíÉå = =
aáÉ= ÇìêÅÜëÅÜåáííäáÅÜÉå= ^åëÅÜ~ÑÑìåÖëâçëíÉå= ÉêÖÉÄÉå= ëáÅÜ= àÉ= å~ÅÜ= ^ìëéê®ÖìåÖ= ÇÉë= aìêÅÜëÅÜåáííëïÉêíîÉêÑ~ÜêÉåëW= =
NK=dÉïçÖÉåÉë=aìêÅÜëÅÜåáííëîÉêÑ~ÜêÉåW= _Éá=ÇáÉëÉê=~ìÅÜ=~äë=łmÉêáçÇÉåJaìêÅÜëÅÜåáííëéêÉáëãÉíÜçÇÉ =ÄÉòÉáÅÜåÉíÉ=^ìëéê®ÖìåÖ= ïáêÇ= ÇÉê= aìêÅÜëÅÜåáíí= ~ìë= ^åÑ~åÖëÄÉëí~åÇ= ìåÇ= ~ääÉå= wìâ®ìÑÉå= ÉêãáííÉäíK= aáÉë= áëí= Ü~åÇÉäëJ= E¬= OQM= fs= áKsKãK= ¬= ORS= ed_= ìåÇ= ^ap= ¬= ORS= kêK= ORF= ìåÇ= ëíÉìÉêêÉÅÜíäáÅÜ== Eo=SKU=fff=pK=P=bpíoF=òìä®ëëáÖK= =
⌦= _ÉáëéáÉäW= báåÉ=h~éáí~äÖÉëÉääëÅÜ~Ñí=îÉêòÉáÅÜåÉíÉ=ÑΩê=ÉáåÉå=oçÜëíçÑÑ=ÑçäÖÉåÇÉ=_Éëí~åÇëîÉê®åÇÉêJ ìåÖÉåK= aáÉëÉ= q~ÄÉääÉ= ëçää= ~äë= dêìåÇä~ÖÉ= ÑΩê= ~ääÉ= åçÅÜ= ÑçäÖÉåÇÉå= sÉêÑ~ÜêÉåëÄÉáJ ëéáÉäÉ=ÇáÉåÉåK= =
=
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jÉåÖÉ=áå=âÖ=
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=
p_=
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=
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OKMMMI MM + PKRMMI MM + NOKRMMI MM + QKVOMI MM OOKVOMI MM = = QI QN bìêç L âÖ = RMM + NKMMM + OKRMM + NKOMM RKOMM aÉê=tÉêí=ÇÉë=pÅÜäìëëÄÉëí~åÇÉë=áëí=ÇÉãå~ÅÜ=QIQN ⋅ OKMMM=Z=UKUOMIMM=bìêçK= =
=
q=
290
D. Jahresabschluss
OK=däÉáíÉåÇÉë=aìêÅÜëÅÜåáííëîÉêÑ~ÜêÉåW= _Éá=ÇáÉëÉã=ÉÄÉåÑ~ääë=Ü~åÇÉäëJ=ìåÇ=ëíÉìÉêêÉÅÜíäáÅÜ=òìä®ëëáÖÉå=sÉêÑ~ÜêÉå=ïÉêÇÉå=ÇáÉ= ÇìêÅÜëÅÜåáííäáÅÜÉå= ^åëÅÜ~ÑÑìåÖâçëíÉå= å~ÅÜ= àÉÇÉã= wìÖ~åÖ= ÉêêÉÅÜåÉí= ìåÇ= ëáåÇ= ëç= dêìåÇä~ÖÉ=ÑΩê=ÇáÉ=_ÉïÉêíìåÖ=ÇÉê=Äáë=òìã=å®ÅÜëíÉå=wìÖ~åÖ=~ìÑíêÉíÉåÇÉå=^ÄÖ®åÖÉK= =
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3.2.2.2
Behandlung der Verfahrensergebnisse beim Jahresabschluss
iáÉÑÉêå= åìå= ÇáÉ= îçêÜÉêÖÉÜÉåÇ= ÄÉëÅÜêáÉÄÉåÉå= sÉêÑ~ÜêÉå= ÇÉå= tÉêí= E^åëÅÜ~ÑÑìåÖëJ âçëíÉåF=ÇÉë=sçêê~íëëÅÜäìëëÄÉëí~åÇÉëI=ëç=áëí=ÇáÉëÉê=òìã=_áä~åòëíáÅÜí~Ö=ãáí=ÇÉã=qÉáäJ ïÉêí= ÄòïK= q~ÖÉëïÉêí= òì= îÉêÖäÉáÅÜÉåI= ìã= ÇÉå= äÉíòíÉåÇäáÅÜÉå= tÉêí~åë~íò= áå= ÇÉê== _áä~åò=òì=ÑáåÇÉåK= =
=⌦ ⌦=_ÉáëéáÉäW= ^åÖÉåçããÉå=Ç~ë=aìêÅÜëÅÜåáííëïÉêíîÉêÑ~ÜêÉå=äáÉÑÉêí=ÑΩê=ÉáåÉå=oçÜëíçÑÑ=EpÅÜäìëëÄÉJ ëí~åÇW= NMM= âÖF= ÇìêÅÜëÅÜåáííäáÅÜÉ= ^åëÅÜ~ÑÑìåÖëâçëíÉå= îçå= VIOM= bìêçLâÖK= wìã= _áJ ä~åòëíáÅÜí~Ö=äáÉÖÉå=åìå=ÇÉê=báåÑ~ÅÜÜÉáí=Ü~äÄÉê=ÇÉê=qÉáäJ=ìåÇ=q~ÖÉëïÉêí=ÄÉáW= =
3. Bewertung des Umlaufvermögens
291
~F= Ç~ìÉêÜ~Ñí=VINM=bìêçLâÖ=
ÅF= îçêΩÄÉêÖÉÜÉåÇ=VINM=bìêçLâÖ=
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ÇF= îçêΩÄÉêÖÉÜÉåÇ=VIPM=bìêçLâÖ=
a~ë= aìêÅÜëÅÜåáííëïÉêíîÉêÑ~ÜêÉå= áëí= Ü~åÇÉäëJ= ìåÇ= ëíÉìÉêêÉÅÜíäáÅÜ= òìä®ëëáÖI= ëç= Ç~ëë= ëáÅÜ=ìåíÉê=_É~ÅÜíìåÖ=ÇÉë=ëíêÉåÖÉå=káÉÇÉêëíïÉêíéêáåòáéë=Ea=PKNKOF=ìåÇ=ÇÉë=^åëÅÜ~ÑJ ÑìåÖëâçëíÉåéêáåòáéë=Ea=PKNKNF=ÑçäÖÉåÇÉ=_áä~åò~åë®íòÉ=ÉêÖÉÄÉå=ïΩêÇÉåK= =
=
e~åÇÉäëÄáä~åò=
~F= q~ÖÉëïÉêí=Y=^h= ^åë~íòéÑäáÅÜí=ÇÉë=åáÉÇêáÖÉJ êÉå=q~ÖÉëïÉêíÉë=
ÄF= q~ÖÉëïÉêí=[=^h= j~ñK=^åë~íò=ÇÉê=^h=
ÅF= q~ÖÉëïÉêí=Y=^h= ^åë~íòéÑäáÅÜí=ÇÉë=åáÉÇêáÖÉJ êÉå=q~ÖÉëïÉêíÉë=
ÇF= q~ÖÉëïÉêí=[=^h= j~ñK=^åë~íò=ÇÉê=^h=
píÉìÉêÄáä~åò= VINM ⋅ NMM = VNMI MM
VIOM ⋅ NMM = VOMI MM
VINM ⋅ NMM = VNMI MM
VIOM ⋅ NMM = VOMI MM
=
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qÉáäïÉêí=Y=^h= ^åë~íòéÑäáÅÜí=ÇÉë= åáÉÇêáÖÉêÉå=qÉáäïÉêíÉë=
VINM ⋅ NMM
qÉáäïÉêí=[=^h= j~ñK=^åë~íò=ÇÉê=^h=
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qÉáäïÉêí=Y=^h=
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= VNMI MM
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=
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3.2.3
Besonderheiten bei fertigen und unfertigen Erzeugnissen
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3. Bewertung des Umlaufvermögens
293
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3.3 Bewertung von Forderungen 3.3.1
Allgemeines
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294
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3.3.2
Abschreibung uneinbringlicher Forderungen
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3. Bewertung des Umlaufvermögens
295
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3. Bewertung des Umlaufvermögens
297
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3.3.3
Zahlungseingänge aus abgeschriebenen Forderungen
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3.3.4
Bewertung zweifelhafter Forderungen (EWB)
wïÉáÑÉäÜ~ÑíÉ= cçêÇÉêìåÖÉå= Ehçåíç= OQTMF= ïÉêÇÉå= ~ã= _áä~åòëíáÅÜí~Ö= ãáí= ÇÉã= ï~ÜêëÅÜÉáåäáÅÜÉå= tÉêí= EbáåÖ~åÖF= ~åÖÉëÉíòíK= páÉ= ïÉêÇÉå= ~äëç= ìã= ÇÉå= îÉêãìíÉíÉå= kÉííç~ìëÑ~ää= ÄÉêáÅÜíáÖíK= sçê~ìëëÉíòìåÖ= ÑΩê= ÉáåÉ= ïÉáíÖÉÜÉåÇ= òìîÉêä®ëëáÖÉ= pÅÜ®íòìåÖ= ÇÉë= îçê~ìëëáÅÜíäáÅÜÉå= łsÉêäìëíÉë = ëáåÇ= å~íΩêäáÅÜ= ~ìëêÉáÅÜÉåÇÉ= fåÑçêã~íáçåÉå= ΩÄÉê= ÇáÉ=Ñáå~åòáÉääÉå=sÉêÜ®äíåáëëÉ=ÇÉë=hìåÇÉåK=a~=ÇÉê=^ìëÑ~ää=åçÅÜ=åáÅÜí=ãáí=páÅÜÉêÜÉáí= ÑÉëíëíÉÜíI=Éêä~ìÄí=Ç~ë=cáå~åò~ãí=âÉáåÉ=hΩêòìåÖ=ÇÉê=rãë~íòëíÉìÉê=E¬=NT=f=rpídFK== =
3. Bewertung des Umlaufvermögens
299
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3. Bewertung des Umlaufvermögens
303
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3.3.5
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3. Bewertung des Umlaufvermögens
311
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Aktive und passive Rechnungsabgrenzung
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4. Rechnungsabgrenzungsposten
315
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4. Rechnungsabgrenzungsposten
317
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4.2.2
Sonstige Forderungen und Verbindlichkeiten
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5.1 Einzelunternehmen und Personengesellschaften cΩê= báåòÉäìåíÉêåÉÜãÉå= ìåÇ= mÉêëçåÉåÜ~åÇÉäëÖÉëÉääëÅÜ~ÑíÉå= EledI= hdF= ëÅÜêÉáÄí= ÇÉê=¬=OQT=f=ed_=äÉÇáÖäáÅÜ=îçêI=Ç~ëë=Ç~ë=báÖÉåâ~éáí~ä=ÖÉëçåÇÉêí=~ìëòìïÉáëÉå=áëíI=ìåÇ= ÉáåÉ=ÜáåêÉáÅÜÉåÇÉ=^ìÑÖäáÉÇÉêìåÖ=îçêÖÉåçããÉå=ïÉêÇÉå=ëçääK=péÉòáÉääÉ=oÉÖÉäìåÖÉå= ÄÉëíÉÜÉå=åáÅÜíK= t~ë=ÇáÉ=sÉêíÉáäìåÖ=ÇÉë=g~ÜêÉëÉêÖÉÄåáëëÉë=~åÄÉä~åÖíI=ëç=ÉñáëíáÉêÉå=òï~ê=ÖÉëÉíòäáÅÜÉ= oÉÖÉäìåÖÉåI=ÇçÅÜ=ëíÉääÉå=ÇáÉëÉ=âÉáå=òïáåÖÉåÇÉë=oÉÅÜí=Ç~êK=aáÉë=ÄÉÇÉìíÉíI=Ç~ëë=áã= dÉëÉääëÅÜ~ÑíëîÉêíê~Ö=ÄÉäáÉÄáÖ=Ç~îçå=~ÄÖÉïáÅÜÉå=ïÉêÇÉå=â~ååK==
5.1.1
Einzelunternehmen
qóéáëÅÜ=ÑΩê=báåòÉäìåíÉêåÉÜãÉå=áëíI=Ç~ëë=ÇÉê=råíÉêåÉÜãÉê=ÑΩê=~ääÉ=sÉêÄáåÇäáÅÜâÉáíÉå= ëÉáåÉê= råíÉêåÉÜãìåÖ= ~ääÉáå= ìåÇ= ìåÄÉëÅÜê®åâí= Eãáí= dÉëÉääëÅÜ~ÑíëJ= ìåÇ= mêáî~íîÉêJ ã∏ÖÉåF= Ü~ÑíÉíK= dÉê~ÇÉ= Ç~ÜÉê= ëíÉÜí= áÜã= ~ìÅÜ= ÇÉê= ÉêïáêíëÅÜ~ÑíÉíÉ= dÉïáåå= áå= îçääÉê= e∏ÜÉ=òìK= ^ìÑÖêìåÇ=ÇÉê=ÉåÖÉå=sÉêÑäÉÅÜíìåÖ=îçå=mêáî~íëJ=ìåÇ=råíÉêåÉÜãÉåëëéÜ®êÉ=âçããí=Éë= áå= ÇÉê= oÉÖÉä= òì= qê~åë~âíáçåÉå= òïáëÅÜÉå= ÇÉã= mêáî~íJ= ìåÇ= _ÉíêáÉÄëîÉêã∏ÖÉåK= ^ìÑ= ÇÉã=báÖÉåâ~éáí~äâçåíç=ÇÉë=råíÉêåÉÜãÉêë=ïÉêÇÉå=Ç~ÜÉê=åáÅÜí=åìê=ÇáÉ=bêÑçäÖÉ=ëçåJ ÇÉêå=~ìÅÜ=éêáî~íÉ=båíå~ÜãÉå=ìåÇ=báåä~ÖÉå=îÉêÄìÅÜíK=^ìë=dêΩåÇÉå=ÇÉê=§ÄÉêëáÅÜíJ äáÅÜâÉáí= ïÉêÇÉå= ÇáÉëÉ= båíå~ÜãÉå= ìåÇ= báåä~ÖÉåI= ïáÉ= ÄÉêÉáíë= ÄÉÜ~åÇÉäíI= ~ìÑ= ÇÉã= ëçÖK=mêáî~íâçåíç=EîÖäK=^ÄëÅÜåáíí=`=NPF=ÖÉÄìÅÜíI=ïÉäÅÜÉë=~ã=båÇÉ=ÇÉë=dÉëÅÜ®Ñíëà~ÜJ êÉë=ΩÄÉê=Ç~ë=hçåíç=łbáÖÉåâ~éáí~ä =~ÄÖÉëÅÜäçëëÉå=ïáêÇK= aáÉ=bêÑçäÖëîÉêÄìÅÜìåÖ=ìåÇ=Ç~ãáí=ÇáÉ=bêãáííäìåÖ=ÇÉë=báÖÉåâ~éáí~äëÅÜäìëëÄÉëí~åÇÉë= ÄÉá=báåòÉäìåíÉêåÉÜãÉå=ëçää=åìå=ÇáêÉâí=~åÜ~åÇ=ÉáåÉë=ÉáåÑ~ÅÜÉå=_ÉáëéáÉäë=Ç~êÖÉëíÉääí= ïÉêÇÉåK= =
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324
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5.1.2
Offene Handelsgesellschaft (OHG)
aáÉ= çÑÑÉåÉ= e~åÇÉäëÖÉëÉääëÅÜ~Ñí= E¬¬= NMRJNSM= ed_F= áëí= Éáå= wìë~ããÉåëÅÜäìëë= îçå= ãáåÇÉëíÉåë= òïÉá= mÉêëçåÉå=òìã= wïÉÅâ= ÇÉë= _ÉíêáÉÄë=ÉáåÉë= e~åÇÉäëÖÉïÉêÄÉë=ìåíÉê= ÖÉãÉáåë~ãÉê= råíÉêåÉÜãìåÖK= aáÉ= e~ÑíìåÖ= ÇÉê= dÉëÉääëÅÜ~ÑíÉê= áëí= ïáÉ= ÄÉá= ÇÉê= báåJ =
5. Rechsformabhängige Eigenkapitalbilanzierung und Erfolgsbuchung
325
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5.1.3
Kommanditgesellschaft (KG)
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326
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5.2.2
Rücklagen
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5. Rechsformabhängige Eigenkapitalbilanzierung und Erfolgsbuchung
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5.2.2.1
Kapitalrücklage
báåÉ= ^d= áëí= ÖêìåÇë®íòäáÅÜ= îÉêéÑäáÅÜíÉíI= áÜê= dêìåÇâ~éáí~ä= áå= ^âíáÉå= òì= îÉêÄêáÉÑÉåK= dáÄí= ÉáåÉ= ^d= ÇáÉëÉ= ^âíáÉå= òì= ÉáåÉã= Ü∏ÜÉêÉå= mêÉáë= ~äë= áÜêÉå= kÉååÄÉíê~Ö= ~ìëI= ëç= ÄÉòÉáÅÜåÉí=ã~å=ÇáÉ=aáÑÑÉêÉåò=òïáëÅÜÉå=kÉååïÉêí=ìåÇ=^ìëÖ~ÄÉJLbãáëëáçåëâìêë=~äë= ^ÖáçK= aÉê= kÉååïÉêí= ÇÉê= ^âíáÉå= ïáêÇ= áã= ÖÉòÉáÅÜåÉíÉå= h~éáí~ä= ÉêÑ~ëëíI= Ç~ë= ^Öáç= áå= ÇÉê=h~éáí~äêΩÅâä~ÖÉ=E¬=OTO=ff=kêK=N=ed_FK== _Éå∏íáÖí=ÉáåÉ=^d=ïÉáíÉêÉë=h~éáí~ä=ìåÇ=â~åå=ëáÉ=ëáÅÜ=åáÅÜí=ΩÄÉê=cêÉãÇâ~éáí~ä=Ñáå~åJ òáÉêÉåI= ÄÉëíÉÜí= ÇáÉ= j∏ÖäáÅÜâÉáí= ÇÉê= h~éáí~äÉêÜ∏ÜìåÖK= a~ÄÉá= ïÉêÇÉå= åÉìÉ= ^âíáÉå= EàìåÖÉ= ^âíáÉåF= ~ìëÖÉÖÉÄÉåK= ^ìÅÜ= ÜáÉê= â~åå= Éë= ïáÉÇÉê= òì= ÉáåÉê= báåëíÉääìåÖ= áå= ÇáÉ= h~éáí~äêΩÅâä~ÖÉ= âçããÉåK= káÅÜí= òì= îÉêÖÉëëÉå= áëíI= Ç~ëë= ~ìÅÜ= wìò~ÜäìåÖÉå= ÇÉê= dÉJ ëÉääëÅÜ~ÑíÉê=E¬=OTO=ff=kêK=P=ìK=Q=ed_F=ÇáÉ=h~éáí~äêΩÅâä~ÖÉ=ÉêÜ∏ÜÉå=â∏ååÉå=EïÉáíÉêÉ= bêÜ∏ÜìåÖëÖêΩåÇÉ=îÖäK=¬=OTO=ff=ed_FK== dêìåÇë®íòäáÅÜ=ÖáäíI=Ç~ëë=ÜáÉê=jáííÉä=îçå=~ì≈Éå=ÇìêÅÜ=ÇáÉ=dÉëÉääëÅÜ~ÑíÉê=ÇÉê=dÉëÉääJ ëÅÜ~Ñí=òìÖÉÑΩÜêí=ïÉêÇÉåK= = ^êíÉå=îçå=h~éíá~äÉêÜ∏ÜìåÖÉå= s =
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5.2.2.2
Gewinnrücklagen
aáÉëÉ=cçêã=ÇÉê=oΩÅâä~ÖÉ= ïáêÇ=~ìë=ÇÉã=îÉêëíÉìÉêíÉã=dÉïáååI=~äëç=~ìë=áåíÉêå=ÉêJ ïáêíëÅÜ~ÑíÉíÉå=jáííÉäå=ÖÉÄáäÇÉí=E¬=OTO=fff=ed_FK= NK=dÉëÉíòäáÅÜÉ=oΩÅâä~ÖÉ= aáÉëÉ=mçëáíáçå=ÖáÄí=Éë=äÉÇáÖäáÅÜ=ÄÉá=^âíáÉåÖÉëÉääëÅÜ~ÑíÉå=E¬=NRM=^âídF=ÄòïK=~ìÅÜ=ÄÉá= hd~^K=R=B=ÇÉë=g~ÜêÉëΩÄÉêëÅÜìëëÉë=Eå~ÅÜ=píÉìÉêåI=~ÄòΩÖäáÅÜ=sÉêäìëíîçêíê~ÖF=ïÉêÇÉå= ëç= ä~åÖÉ= áå= ÇáÉ= ÖÉëÉíòäáÅÜÉ= oΩÅâä~ÖÉ= ÉáåÖÉëíÉääíI= Äáë= ÇáÉëÉ= òìë~ããÉå= ãáí= ÇÉå= h~éáí~äêΩÅâä~ÖÉå= EçÜåÉ= wìò~ÜäìåÖÉå= å~ÅÜ= ¬= OTO= ff= kêK= Q= ed_F= NM= B= ÇÉë= dêìåÇâ~éáí~äë=ÉêêÉáÅÜí=Ü~íK= OK=oΩÅâä~ÖÉ=ÑΩê=ÉáÖÉåÉ=^åíÉáäÉ= bêïáêÄí=ÉáåÉ=h~éáí~äÖÉëÉääëÅÜ~Ñí=ÉáÖÉåÉ=^åíÉáäÉ=E^âíáÉåI=dÉëÅÜ®Ñíë~åíÉáäÉFI=ëç=ÄÉÇÉìJ íÉí=ÇáÉë=ÉáåÉ=oΩÅâò~ÜäìåÖ=ÇÉë=ÇÉå=^åíÉáäÉå=ÉåíëéêÉÅÜÉåÇÉå=ÖÉòÉáÅÜåÉíÉå=h~éáí~äë= EìåÇ=ÉáåÉê=ÉîíäK=~åíÉáäáÖÉå=h~éáí~äêΩÅâä~ÖÉFK=aÉê=rãÑ~åÖ=~ìëÖÉÖÉÄÉåÉê=^åíÉáäÉ=®åJ ÇÉêí= ëáÅÜ= Ç~ÇìêÅÜ= åáÅÜíI= ëç= Ç~ëë= Ç~ë= Äáä~åòáÉääÉ= báÖÉåâ~éáí~ä= ìåîÉê®åÇÉêí= ÄäÉáÄíK= aÉååçÅÜ=ëáåÇ=~ÄÉê=~ìë=ÇÉã=e~ÑíìåÖëâ~éáí~ä=jáííÉä=~ÄÖÉÑäçëëÉåI=Ç~=ÇáÉ=åìå=áã=^åJ ä~ÖÉîÉêã∏ÖÉå=~ìÑí~ìÅÜÉåÇÉå=ÉáÖÉåÉå=^åíÉáäÉ=áã=fåëçäîÉåòÑ~ää=ïÉêíäçë=ëÉáå=â∏ååÉåK= a~=ëáÅÜ=~ÄÉê=ÇáÉ=dä®ìÄáÖÉê=~ìÑ=Ç~ë=sçêÜ~åÇÉåëÉáå=ÇÉë=ÑÉëíÖÉëÅÜêáÉÄÉåÉå=ÖÉòÉáÅÜJ åÉíÉå=h~éáí~äë=îÉêä~ëëÉå=â∏ååÉå=ãΩëëÉåI=Öáäí=åìåW== ^âíáÉåÖÉëÉääëÅÜ~ÑíÉå= ÇΩêÑÉå= ÖÉãK= ¬= RS= ^âíd= âÉáåÉ= ÉáÖÉåÉå= ^âíáÉå= òÉáÅÜåÉåI= ÇKÜK= ÄÉá=bãáëëáçå=ÉêïÉêÄÉåK=_ÉÖêΩåÇÉí=ïáêÇ=ÇáÉëÉ=_ÉëíáããìåÖ=ãáí=çÄáÖÉê=^êÖìãÉåí~J íáçå= ìåÇ= ~ì≈ÉêÇÉã= Ç~ãáíI=Ç~ëë= ÇáÉ= wÉáÅÜåìåÖ= òì=ÉáåÉê=êÉ~äÉå= h~éáí~ä~ìÑÄêáåÖìåÖ= ÑΩê= ÇáÉ= dÉëÉääëÅÜ~Ñí= ÑΩÜêÉå= ãìëëK= báåÉ= rãÖÉÜìåÖ= ï®êÉ= ~ÄÉê= ã∏ÖäáÅÜI= ïÉåå= òìJ å®ÅÜëí=Éáå=aêáííÉê=ÇáÉ=^âíáÉå=ÉêïáêÄí=ìåÇ=áÜã=ÇáÉ=dÉëÉääëÅÜ~Ñí=ÇáÉëÉ=ïáÉÇÉê=~Äâ~ìÑíK= a~ãáí=ÉêêÉáÅÜí=ÇáÉ=dÉëÉääëÅÜ~Ñí=ÇÉå=pí~íìëI=~äë=Ü®ííÉ=ëáÉ=ÇáÉ=^âíáÉå=ÄÉá=bãáëëáçå=ÉêJ ïçêÄÉåK= a~ÜÉê= áëí= ÇÉã= sÉêÄçí= ÇÉê= wÉáÅÜåìåÖ= ÉáÖÉåÉê= ^âíáÉå= ~ìÅÜ= Éáå= sÉêÄçí= ~å= ÇáÉ= pÉáíÉ= ÖÉëíÉääí= ïçêÇÉåI= ÉáÖÉåÉ= ^âíáÉå= òì= ÉêïÉêÄÉåK= báå= ëçäÅÜÉë= sÉêÄçí= ÇÉë= bêJ ïÉêÄë=ÉáÖÉåÉê=^åíÉáäÉ=ÖáÄí=Éë=~ìÅÜ=ÑΩê=ÇáÉ=dãÄe=E¬=PM=f=dãÄedFK= aÉê=¬=TN=f=^âíd=êÉÖÉäí=~ääÉêÇáåÖë=~ÅÜí=c®ääÉ=ÇÉë=~ìëå~ÜãëïÉáëÉ=ã∏ÖäáÅÜÉå=bêïÉêÄë= ÉáÖÉåÉê=^âíáÉåK=aáÉëÉê=áëí=áå=ÇáÉëÉå=c®ääÉå=åìê=òìä®ëëáÖI=ïÉåå=ÇáÉ=dÉëÉääëÅÜ~Ñí=ÉáåÉ= oΩÅâä~ÖÉ= ÑΩê= ÉáÖÉåÉ= ^åíÉáäÉ= E¬= OTO= fs= ed_F= ÇìêÅÜ= sÉêïÉåÇìåÖ= ÇÉë= g~ÜêÉëΩÄÉêJ ëÅÜìëëÉë= çÇÉê= ÉáåÉë= dÉïáååîçêíê~ÖÉë= ÄáäÇÉå= â~ååI= ~äëç= çÜåÉ= Ç~ë= dêìåÇâ~éáí~ä== çÇÉê=ÉáåÉ=å~ÅÜ=ÇÉã=dÉëÉíò=çÇÉê=p~íòìåÖ=òì=ÄáäÇÉåÇÉ=oΩÅâä~ÖÉ=òì=ãáåÇÉêåK=aáÉëÉ= oΩÅâä~ÖÉ= Ü~í= áããÉê= ÇáÉëÉäÄÉ= e∏ÜÉ= ~ìÑòìïÉáëÉå= ïáÉ= ÇáÉ= ~ìÑ= ÇÉê= ^âíáîëÉáíÉ= ~åÖÉJ ëÉíòíÉå=ÉáÖÉåÉå=^åíÉáäÉK=a~=ÇáÉ=oΩÅâä~ÖÉ=åáÅÜí=~ìÑÖÉä∏ëí=ïÉêÇÉå=Ç~êÑI=ëçä~åÖÉ=ÇáÉ= ÉáÖÉåÉå=^åíÉáäÉ=îçå=ÇÉê=dÉëÉääëÅÜ~Ñí=ÖÉÜ~äíÉå=ïÉêÇÉåI=Ü~í=ëáÉ=ÉáåÉ=ëçÖK=^ìëëÅÜΩíJ íìåÖëëéÉêêÑìåâíáçåK=få=e∏ÜÉ=ÇÉê=oΩÅâä~ÖÉ=Ç~êÑ=~äëç=âÉáåÉ=^ìëëÅÜΩííìåÖ=~å=ÇáÉ=dÉJ ëÉääëÅÜ~ÑíÉê= ÉêÑçäÖÉåK= aáÉ= oΩÅâä~ÖÉ= áëí= Ç~åå= ~ìÑòìä∏ëÉåI= ïÉåå= ÇáÉ= ÉáÖÉåÉå= ^åíÉáäÉ= ïáÉÇÉê= ~ìëÖÉÖÉÄÉåI= îÉê®ì≈ÉêíI= ÉáåÖÉòçÖÉå= çÇÉê= å~ÅÜ= ÇÉã= ëíêÉåÖÉå= káÉÇÉêëíJ ïÉêíéêáåòáé=~ì≈Éêéä~åã®≈áÖ=~ÄÖÉëÅÜêáÉÄÉå=ïÉêÇÉåK= ^ìÑ= ÑΩê= dãÄeë= ÖáÄí= Éë= ^ìëå~ÜãÉå= îçã= ÖÉåÉêÉääÉå= bêïÉêÄëîÉêÄçíK= aáÉëÉ= ëáåÇ= áå== ¬=PP=dãÄed=åìê=áå=cçêã=~ääÖÉãÉáåÉê=sçê~ìëëÉíòìåÖÉå=ÖÉå~ååí=ìåÇ=åáÅÜí=ïáÉ=áã= ^âíd=âçåâêÉí=~ìÑÖÉÑΩÜêíK= wìë~ããÉåÑ~ëëÉåÇ=â~åå=~äëç=ÖÉë~Öí=ïÉêÇÉåI=Ç~ëë=ÇÉê=hçêêÉâíìêéçëíÉå=łoΩÅâä~ÖÉå= ÑΩê=ÉáÖÉåÉ=^åíÉáäÉ =îÉêÜáåÇÉêå=ëçääI=Ç~ëë=ÇìêÅÜ=ÇáÉ=^âíáîáÉêìåÖ=îçå=ÉáÖÉåÉå=^åíÉáJ äÉå= ÇÉê= ÉåíëéêÉÅÜÉåÇÉ= dÉÖÉåïÉêí= ~å= ÇáÉ= ^åíÉáäëÉáÖåÉê= ~ìëÖÉëÅÜΩííÉí= ìåÇ= ëç= Ç~ë= e~ÑíìåÖëâ~éáí~ä=ÑΩê=ÇáÉ=dä®ìÄáÖÉê=îÉêãáåÇÉêí=ïáêÇK= =
5. Rechsformabhängige Eigenkapitalbilanzierung und Erfolgsbuchung
333
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5.2.3
Ergebnisverwendung und Eigenkapitalausweis
5.2.3.1
Grundlagen
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5.2.3.2
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Rückstellungen
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6.2.1
Ansatzkriterien in Handels- und Steuerbilanz
aáÉ= å~ÅÜÑçäÖÉåÇÉ= ^ÄÄáäÇìåÖ= òÉáÖí= ÇáÉ= ïáÅÜíáÖëíÉå= ^åë~íòéÑäáÅÜíÉåI= JîÉêÄçíÉ= ìåÇ== Jï~ÜäêÉÅÜíÉ=ÑΩê=oΩÅâëíÉääìåÖÉå=áå=ÇÉê=e~åÇÉäëJ=ìåÇ=píÉìÉêÄáä~åòK= =
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6. Rückstellungen
343
eáåëáÅÜíäáÅÜ=ÇÉê=j~≈ÖÉÄäáÅÜâÉáí=ÄÉá=oΩÅâëíÉääìåÖÉå=áëí=ÑÉëíòìëíÉääÉåI=Ç~ëë=ÖêìåÇë®íòJ äáÅÜ=m~ëëáîáÉêìåÖëÖÉÄçíÉ=áå=ÇÉê=e~åÇÉäëÄáä~åò=ãáí=m~ëëáîáÉêìåÖëÖÉÄçíÉå=áå=píÉìÉêÄáJ ä~åò= ìåÇ= m~ëëáîáÉêìåÖëï~ÜäêÉÅÜíÉ= áå= ÇÉê= e~åÇÉäëÄáä~åò= ãáí= m~ëëáîáÉêìåÖëîÉêÄçíÉå= áå=ÇÉê=píÉìÉêÄáä~åò=ÉáåÜÉêÖÉÜÉåK=iÉÇáÖäáÅÜ=ÄÉá=oΩÅâëíÉääìåÖÉå=ÑΩê=ÇêçÜÉåÇÉ=sÉêäìëJ íÉ=~ìë=ëÅÜïÉÄÉåÇÉå=dÉëÅÜ®ÑíÉå=ïáêÇ=~ìë=ÉáåÉã=Ü~åÇÉäëêÉÅÜíäáÅÜÉå=m~ëëáîáÉêìåÖëJ ÖÉÄçí=Éáå=ëíÉìÉêêÉÅÜíäáÅÜÉë=m~ëëáîáÉêìåÖëîÉêÄçíK=
6.2.2
Ausgewählte Vorschriften der Rückstellungsbewertung
6.2.2.1
Bewertung nach vernünftiger kaufmännischer Beurteilung
k~ÅÜ= ¬= ORP= f= pK= O= ed_= áëí= ÇÉê= ï~ÜêëÅÜÉáåäáÅÜëíÉ= tÉêí= ÇÉê= sÉêéÑäáÅÜíìåÖ= ã~≈ÖÉÄJ äáÅÜK= aáÉë= ÄÉÇÉìíÉí= âçåâêÉíI= Ç~ëë= píÉìÉêêΩÅâëíÉääìåÖÉå= ÉáåÇÉìíáÖ= òì= ÄÉêÉÅÜåÉå= ëáåÇI= mÉåëáçåëêΩÅâëíÉääìåÖÉå= ëí~íáëíáëÅÜÉ= a~íÉå= òìÖêìåÇÉ= äáÉÖÉå= ãΩëëÉå= ìåÇ= ~åJ ëçåëíÉå=pÅÜ®íòìåÖÉå=îçêòìåÉÜãÉå=ëáåÇK=_Éá=ÇÉê=tÉêíÉêãáííäìåÖ=ëáåÇ=òìÇÉã=âΩåÑJ íáÖÉ= sçêíÉáäÉ= áå= wìë~ããÉåÜ~åÖ= ãáí= ÉáåÉê= sÉêéÑäáÅÜíìåÖ= ÖÉÖÉåòìêÉÅÜÉå= EòK_K= ^åJ ëéêΩÅÜÉ=~å=ÉáåÉ=sÉêëáÅÜÉêìåÖFK= 6.2.2.2
Grundsatz der Vorsicht
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344
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345
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Verbindlichkeiten
=
7.1 Allgemeines sÉêÄáåÇäáÅÜâÉáíÉå= ëáåÇ= sÉêéÑäáÅÜíìåÖÉåI= ÇáÉ= ~ã= _áä~åòëíáÅÜí~Ö= áÜêÉê= e∏ÜÉ= ìåÇ= c®ääáÖâÉáí= å~ÅÜ= ÑÉëíëíÉÜÉåK= dÉÖäáÉÇÉêí= å~ÅÜ= dä®ìÄáÖÉêÖêìééÉå= ÖÉÜ∏êÉå= Ç~òì= ÇáÉ= ÑçäÖÉåÇÉå=mçëáíáçåÉåW= ^åäÉáÜÉå= EëÉÜê= ä~åÖÑêáëíáÖÉ= cêÉãÇÑáå~åòáÉêìåÖ= ãáí= ÉáåÉã= ëÉÜê= Öêç≈Éå= sçäìãÉåI= òK_K= ^ìëÖ~ÄÉ= îçå= fåÇìëíêáÉçÄäáÖ~íáçåÉåI= t~åÇÉäëÅÜìäÇîÉêëÅÜêÉáÄJ ìåÖÉåI=léíáçåëëÅÜìäÇîÉêëÅÜêÉáÄìåÖÉåF= sÉêÄáåÇäáÅÜâÉáíÉå= ÖÉÖÉåΩÄÉê= hêÉÇáíáåëíáíìíÉå= E_~åââêÉÇáíÉI= áå= e∏ÜÉ= ÇÉê= hêÉÇáíëìããÉI=åáÅÜí=ÇÉë=í~íë®ÅÜäáÅÜ=~ìëÄÉò~ÜäíÉå=_Éíê~ÖëF= ÉêÜ~äíÉåÉ= ^åò~ÜäìåÖÉå= ~ìÑ= _ÉëíÉääìåÖÉå= E^åò~ÜäìåÖÉå= îçå= hìåÇÉåI= áåëÄÉëçåÇÉêÉ=òìê=sçêÑáå~åòáÉêìåÖ=îçå=ä~åÖÑêáëíáÖÉå=cÉêíáÖìåÖë~ìÑíê®ÖÉåF= sÉêÄáåÇäáÅÜâÉáíÉå= ~ìë= iáÉÑÉêìåÖÉå= ìåÇ= iÉáëíìåÖÉå= EiáÉÑÉê~åíÉåâêÉÇáíI= ÇKÜK= Ç~ë= råíÉêåÉÜãÉå= Ü~í= iáÉÑÉêìåÖÉå= çÇÉê= iÉáëíìåÖÉå= ÉêÜ~äíÉåI= çÜåÉ= Ç~ÑΩê= ÉáåÉå=dÉÖÉåäÉáëíìåÖ=ÉêÄê~ÅÜí=òì=Ü~ÄÉåF= sÉêÄáåÇäáÅÜâÉáíÉå= ~ìë= ÇÉê= ^åå~ÜãÉ= ÖÉòçÖÉåÉê= tÉÅÜëÉä= ìåÇ= ÇÉê= ^ìëëíÉääìåÖ= ÉáÖÉåÉê= tÉÅÜëÉä= EtÉÅÜëÉä= ëáåÇ= Ç~ÄÉá= tÉêíé~éáÉêÉI= ÇáÉ= ëÉäÄJ ëí®åÇáÖÉ=w~ÜäìåÖëîÉêéÑäáÅÜíìåÖÉå=ÉåíÜ~äíÉåKF= sÉêÄáåÇäáÅÜÉáíÉå= ÖÉÖÉåΩÄÉê= îÉêÄìåÇÉåÉå= råíÉêåÉÜãÉå= Ew~ÜäìåÖëîÉêJ éÑäáÅÜíìåÖÉå=ÖÉÖÉåΩÄÉê=råíÉêåÉÜãÉå=òK_K=áååÉêÜ~äÄ=ÉáåÉê=hçåòÉêåëF= sÉêÄáåÇäáÅÜâÉáíÉå= ÖÉÖÉåΩÄÉê= råíÉêåÉÜãÉåI= ãáí= ÇÉåÉå= Éáå= _ÉíÉáäáÖJ ìåÖëîÉêÜ®äíåáë= ÄÉëíÉÜí= Ew~ÜäìåÖëîÉêéÑäáÅÜíìåÖÉå= ÖÉÖÉåΩÄÉê= råíÉêåÉÜãÉåI= ÇáÉ= ÇìêÅÜ= ÉáåÉ= Ç~ìÉêÜ~ÑíÉ= _ÉíÉáäáÖìåÖ= ãáí= ÇÉã= ÉáÖÉåÉå= råíÉêåÉÜãÉå= îÉêÄìåÇÉå=ëáåÇF= ëçåëíáÖÉ=sÉêÄáåÇäáÅÜâÉáíÉå=Ep~ããÉäéçëíÉå=êÉëíäáÅÜÉê=sÉêÄáåÇäáÅÜâÉáíÉåI=òK_K= píÉìÉêëÅÜìäÇÉåI= pçòá~ä~ÄÖ~ÄÉåI= pÅÜìäÇÉå= ÖÉÖÉåΩÄÉê= káÅÜíÄ~åâÉå= çÇÉê= ~åÇÉêÉå=råíÉêåÉÜãÉåI=sÉêÄáåÇäáÅÜâÉáíÉå=~ìë=içÜåI=ÁF= =
7.2 Ansatz und Bewertung 7.2.1
Allgemeines
k~ÅÜ=¬=OQS=f=pK=N=ed_=ãΩëëÉå=ÖêìåÇë®íòäáÅÜ=~ääÉ=pÅÜìäÇÉå=áã=g~ÜÉêë~ÄëÅÜäìëë=ÉåíJ Ü~äíÉå= ëÉáåK= wìÇÉã= áëí= ÇáÉ= e∏ÜÉ= îçå= sÉêÄáåÇäáÅÜâÉáíÉå= ãáí= ÉáåÉê= oÉëíä~ìÑòÉáí= îçå= Äáë=òì=ÉáåÉã=g~Üê=å~ÅÜ=ÖÉëçåÇÉêí=~ìëòìïÉáëÉå=E¬=OSU=s=ed_FK=aÉê= dÉë~ãíÄÉíê~Ö= ëçïáÉ= ïÉáíÉêÉ= aÉí~áäë= òì= sÉêÄáåÇäáÅÜâÉáíÉå= ãáí= ÉáåÉê= oÉëíä~ìÑòÉáí= îçå= ãÉÜê= ~äë= R= g~ÜêÉå= ìåÇ= ÖÉëáÅÜÉêíÉ= sÉêÄáåÇäáÅÜâÉáíÉå= EòK_K= ÇìêÅÜ= dêìåÇéÑ~åÇêÉÅÜíÉI= mÑ~åÇJ êÉÅÜíÉ= ~å= ÄÉïÉÖäáÅÜÉå= p~ÅÜÉåI= páÅÜÉêìåÖëΩÄÉêÉáÖåìåÖI= páÅÜÉêìåÖë~ÄíêÉíìåÖF= ëáåÇ= =
348
D. Jahresabschluss
áã= ^åÜ~åÖ= ~åòìÖÉÄÉå= E¬= OUR= kêK= N= ~I= Ä= ed_FK= ^ì≈ÉêÇÉã= ëáåÇ= sÉêÄáåÇäáÅÜâÉáíÉå= ÖÉÖÉåΩÄÉê=dÉëÉääëÅÜ~ÑíÉêå=ÖÉëçåÇÉêí=~ìëòìïÉáëÉå=E¬=QO=fff=dãÄedFK=
7.2.2
Rückzahlungsbetrag
k~ÅÜ= ¬= ORP= f= pK= O= ed_= ëáåÇ= sÉêÄáåÇäáÅÜâÉáíÉå= Ü~åÇÉäëêÉÅÜíäáÅÜ= ãáí= ÇÉã= oΩÅâò~ÜäìåÖëÄÉíê~Ö= EbêÑΩääìåÖëÄÉíê~ÖF= ~åòìëÉíòÉåK= fëí= ÇÉê= oΩÅâò~ÜäìåÖëÄÉíê~Ö= Ü∏ÜÉê= ~äë= ÇÉê= ^ìëò~ÜäìåÖëÄÉíê~ÖI= ëç= Ç~êÑ= ÇÉê= råíÉêëÅÜáÉÇëÄÉíê~Ö= Eaáë~ÖáçF= ~äë= oÉÅÜåìåÖë~ÄÖêÉåòìåÖëéçëíÉå= ~ìÑ= ÇÉê= ^âíáîëÉáíÉ= ~ìëÖÉïáÉëÉå= ïÉêÇÉå= E¬= ORM= fff= ed_I=îÖäK=a=QKOKNFK=píÉìÉêêÉÅÜíäáÅÜ=ëáåÇ=sÉêÄáåÇäáÅÜâÉáíÉå=ãáí=áÜêÉå=^åëÅÜ~ÑÑìåÖëJ âçëíÉå=~åòìëÉíòÉå=E¬=S=f=kêK=P=áKsKãK=kêK=O=bpídFK=^äë=^åëÅÜ~ÑÑìåÖëâçëíÉå=ïáÉÇÉêìã= Öáäí= ÇÉê= oΩÅâò~ÜäìåÖëÄÉíê~Ö= ÇÉê= sÉêÄáåÇäáÅÜâÉáí= Ee= SKNM= bpíeW= píáÅÜïçêí= ^åJ ëÅÜ~ÑÑìåÖëâçëíÉåFK=
7.2.3
Handelsrechtliches Höchstwertprinzip
sÉêÄáåÇäáÅÜâÉáíÉåI= ÇáÉ= áå= ÑêÉãÇÉê= t®ÜêìåÖ= òìêΩÅâòìò~ÜäÉå= ëáåÇ= Es~äìí~îÉêÄáåÇJ äáÅÜâÉáíÉåFI=ëáåÇ=ãáí=ÇÉã=dÉäÇâìêë=EsÉêâ~ìÑ=îçå=cêÉãÇï®ÜêìåÖÉå=ÇìêÅÜ=ÇáÉ=_~åâF= ìãòìêÉÅÜåÉå= ìåÇ= òì= Äáä~åòáÉêÉåK= aÉê= dÉäÇâìêë= áëí= Ç~ÜÉê= êÉäÉî~åíI= Ç~= ÇÉê= pÅÜìäÇåÉê= ~ã= c®ääáÖâÉáíëí~Ö= ÇÉå= bêÑΩääìåÖëÄÉíê~Ö= ÄÉá= ëÉáåÉê= _~åâ= ÖÉÖÉå= bìêç= â~ìÑÉå=ãìëëK= wì=àÉÇÉã=_áä~åòëíáÅÜí~Ö=ëáåÇ=báåÄìÅÜìåÖëâìêë=ìåÇ=_áä~åòëíáÅÜí~Öëâìêë=Eq~ÖÉëïÉêíF= òì= îÉêÖäÉáÅÜÉåK= iáÉÖí= ÇÉê= _áä~åòëíáÅÜí~Öëâìêë= ΩÄÉê= ÇÉã= báåÄìÅÜìåÖëâìêëI= ãìëë= ~ìÑÖêìåÇ= ÇÉë= fãé~êáí®íëéêáåòáéë= ÇáÉ= sÉêÄáåÇäáÅÜâÉáí= Ü∏ÜÉê= ÄÉïÉêíÉí= ïÉêÇÉå= Ee∏ÅÜëíïÉêíéêáåòáéFK= a~ÄÉá= áëí= Éë= åáÅÜí= îçå= _Éä~åÖI= çÄ= Éë= ëáÅÜ= ìã= ÉáåÉ= Ç~ìÉêÜ~ÑíÉ=çÇÉê=åìê=ìã=ÉáåÉ=îçêΩÄÉêÖÉÜÉåÇÉ=bêÜ∏ÜìåÖ=Ü~åÇÉäíK= aÉê=ÄÉá=ÇÉê=_ÉÖêΩåÇìåÖ=ÇÉê=sÉêÄáåÇäáÅÜâÉáí=ÉêãáííÉäíÉ=oΩÅâò~ÜäìåÖëÄÉíê~Ö=ëíÉääí= ÖêìåÇë®íòäáÅÜ= ÇáÉ= _ÉïÉêíìåÖëìåíÉêÖêÉåòÉ= Ç~êI= Ç~= ÄÉá= ^ÄïÉêíìåÖ= ìåíÉê= ÇáÉëÉå= tÉêí= ìåêÉ~äáëáÉêíÉ= dÉïáååÉ= ~ìëÖÉïáÉëÉå= ïÉêÇÉå= ïΩêÇÉåI= ï~ë= å~ÅÜ= ÇÉã= oÉ~äáë~íáçåëéêáåòáé= åáÅÜí= òìä®ëëáÖ= áëíK= báå= t®ÜêìåÖëÖÉïáåå= ÉåíëíÉÜí= Éêëí= ÄÉá= ÇÉê= òìâΩåÑíáÖÉå=í~íë®ÅÜäáÅÜÉå=qáäÖìåÖ=ÇÉê=sÉêÄáåÇäáÅÜâÉáíK=iáÉÖí=ÇÉê=_áä~åòëíáÅÜí~Öëâìêë= ~äëç=ìåíÉê=ÇÉã=báåÄìÅÜìåÖëâìêëI=Ç~êÑ=ÇÉê=tÉêí~åë~íò=åáÅÜí=îÉêãáåÇÉêí=ïÉêÇÉåK=
7.2.4
Bewertung in Handels- und Steuerbilanz im Vergleich
k~ÅÜ=¬=S=f=kêK=O=bpíd=ÉêÑçäÖí=áã=píÉìÉêêÉÅÜí=ÇáÉ=_ÉïÉêíìåÖ=îçå=sÉêÄáåÇäáÅÜâÉáíÉå= ãáí=ÇÉå=^åëÅÜ~ÑÑìåÖëâçëíÉå=EoΩÅâò~ÜäìåÖëÄÉíê~ÖF=çÇÉê=ÇÉã=qÉáäïÉêíK= _Éá=Ç~ìÉêÜ~ÑíÉê=tÉêíÉêÜ∏ÜìåÖ=áëí=ÇÉê=^åë~íò=ÇÉë=Ü∏ÜÉêÉå=qÉáäïÉêíë=mÑäáÅÜíK=_Éá=åìê= îçêΩÄÉêÖÉÜÉåÇÉê= bêÜ∏ÜìåÖ= Ç~êÑ= Ç~ÖÉÖÉå= ëíÉìÉêäáÅÜ= âÉáå= Ü∏ÜÉêÉê= tÉêí= ~åÖÉëÉíòí= ïÉêÇÉåK= e~í= ëáÅÜ= ÇÉê= qÉáäïÉêí= å~ÅÜ= ÉáåÉê= îçê~åÖÉÖ~åÖÉåÉå= bêÜ∏ÜìåÖ= ïáÉÇÉê= îÉêãáåÇÉêí= ÄòïK=áëí=ÇáÉ=bêÜ∏ÜìåÖ=åáÅÜí=ãÉÜê=Ç~ìÉêÜ~ÑíI=áëí=ëíÉìÉêäáÅÜ=òïáåÖÉåÇ=ÉáåÉ=tÉêíêÉÇìJ òáÉêìåÖ=Äáë=òìã=ÖÉëìåâÉåÉå=qÉáäïÉêí=ÄòïK=ã~ñáã~ä=Äáë=òìê=_ÉïÉêíìåÖëìåíÉêÖêÉåJ òÉ=EoΩÅâò~ÜäìåÖëÄÉíê~ÖF=îçêòìåÉÜãÉåK= e~åÇÉäëêÉÅÜíäáÅÜ=ÄÉëíÉÜí=ëçïçÜä=ÄÉá=îçêΩÄÉêÖÉÜÉåÇÉê=~äë=~ìÅÜ=ÄÉá=Ç~ìÉêÜ~ÑíÉê=bêJ Ü∏ÜìåÖ= Éáå= ^ìÑïÉêíìåÖëÖÉÄçíK= aáÉ= oÉÖÉäìåÖÉå= òìê= tÉêí~ìÑÜçäìåÖ= ÖÉäíÉå= ~å~äçÖ= òì=ÇÉå=ëíÉìÉêäáÅÜÉåK= =
7. Verbindlichkeiten
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350
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E. AUFGABEN =
Aufgabengebiet Inventur, Bilanz, Distanzrechnung Buchung auf Bestandskonten Buchung auf Erfolgskonten Beschaffung von Produktionsmitteln Verbuchung weiterer Produktionsfaktoren
Aufgabennummern 1-6 7 - 11 12 13 - 18 19
Lohn- und Gehaltsabrechnung
20 - 22
Verkauf von Fertigerzeugnissen und Handelswaren
23 - 29
Umsatzsteuer
30
Kauf und Verkauf von Anlagegütern
31 - 36
Aktivierte Eigenleistungen
37 - 39
Kauf und Verkauf von Wertpapieren
40 - 44
Fremdfinanzierung
45 - 51
Privatkonto
52
Steuern
53
Sachanlagenbewertung (nur Steuerrecht vor 31.12.05)
54 - 57
Forderungsbewertung
58 - 62
Wertpapierbewertung (nur Steuerrecht)
63 - 64
Vorratsbewertung (nur Steuerrecht)
65 - 66
Verbindlichkeitsbewertung (nur Steuerrecht) Rechungsabgrenzung und Rückstellungen Umsatz- und Gesamtkostenverfahren
67 68 - 71 72=
1.
Aufgabenstellungen
= ^ìÑÖ~ÄÉ=N= _Éá= dÉëÅÜ®ÑíëÉê∏ÑÑåìåÖ= EMRKNOKOMMSF= ÉêÖáÄí= ÇáÉ= fåîÉåíìê= ÉáåÉë= j∏ÄÉäÑ~Äêáâ~åíÉå= EjìëíÉêã~åå=dãÄeI=jΩåÅÜÉåF=ÑçäÖÉåÇÉ=_Éëí®åÇÉW= =
sÉêã∏ÖÉåW= j~ëÅÜáåÉå= iáÉÑÉêï~ÖÉå= mÉêëçåÉåâê~Ñíï~ÖÉå= _ÉÄ~ìíÉë=dêìåÇëíΩÅâ= dÉëÅÜ®Ñíë~ìëëí~ííìåÖ= _ÉíêáÉÄëÖÉÄ®ìÇÉ= sçêê®íÉ= h~ëëÉåÄÉëí~åÇ= _~åâÖìíÜ~ÄÉå=uvJ_~åâ= _~åâÖìíÜ~ÄÉå=^_J_~åâ=
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PMKQRMIMM=bìêç= NMKONMIMM=bìêç= QSMKMMMIMM=bìêç=
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^ìÑÖ~ÄÉ=O= aáÉ=_áä~åò=ÉáåÉë=råíÉêåÉÜãÉåë=ïÉáëí=ÑçäÖÉåÇÉ=tÉêíÉ=~ìëW= =
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354
E. Aufgaben
^ìÑÖ~ÄÉ=P= få= òïÉá= ~ìÑÉáå~åÇÉê= ÑçäÖÉåÇÉå= g~ÜêÉå= ÉêãáííÉäí= ÇáÉ= pÅÜêÉáåÉêÉá= p®ÖÉò~Üå= ÄÉá= ÇÉê= fåîÉåíìê=ÑçäÖÉåÇÉ=ÄÉêÉáíë=ÖêìééáÉêíÉ=_Éëí®åÇÉW= =
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ORKPQMIMM= NRMKMMMIMM= TPNKMMMIMM= ORKSMMIMM= TOKQMMIMM= RQKPMMIMM= OORKMMMIMM= UKRNMIMM= PRKPMMIMM= TSKPOQIMM= NRQKPMMIMM=
=
~F==bêëíÉääÉå=páÉ=ÑΩê=ÄÉáÇÉ=g~ÜêÉ=ÇáÉ=_áä~åòÉå=ÇÉê=pÅÜêÉáåÉêÉáK= ÄF==bêãáííÉäå=páÉ=ÇáÉ=éêçòÉåíì~äÉ=sÉê®åÇÉêìåÖ=ÇÉë=cêÉãÇâ~éáí~äëK= ÅF== fëí= Ç~ë= råíÉêåÉÜãÉå=áã= g~Üê= OMMP= áå= ÇÉê= i~ÖÉ= ãáí=ÇÉå= îçêÜ~åÇÉåÉå= ÑäΩëëáÖÉå= jáííÉäå=~ääÉ=îçêÜ~åÇÉåÉå=âìêòÑêáëíáÖÉå=pÅÜìäÇÉå=òì=ÄÉò~ÜäÉå\= =
^ìÑÖ~ÄÉ=Q= aáÉ= îÉêÉáåÑ~ÅÜíÉ= _áä~åò= ÉáåÉë= råíÉêåÉÜãÉåë= ïÉáëí= cêÉãÇâ~éáí~ä= áå= e∏ÜÉ= îçå= SRMKMMMIMM= bìêç= ~ìÑK= aÉã= ÖÉÖÉåΩÄÉê= ëíÉÜÉå= ~ìÑ= ÇÉê= ^âíáîëÉáíÉ= ^åä~ÖÉîÉêã∏ÖÉå= îçå=PRMKMMMIMM=bìêç=ìåÇ=rãä~ìÑîÉêã∏ÖÉå=îçå=OMMKMMMIMM=bìêç=~ìÑK= bêãáííÉäå= páÉ= ãáííÉäë= çêÇåìåÖëÖÉã®≈Éê= oÉÅÜåìåÖ= EqJhçåíÉåJcçêãF= ÇáÉ= e∏ÜÉ= ÇÉë= báÖÉåâ~éáí~äë=ìåÇ=ÄÉëÅÜêÉáÄÉå=páÉ=ÇÉå=îçêäáÉÖÉåÇÉå=pçåÇÉêÑ~ääK= =
^ìÑÖ~ÄÉ=R= aáÉ= báÖÉåâ~éáí~äÄÉëí®åÇÉ= ÉáåÉë= råíÉêåÉÜãÉåë= ΩÄÉê= îÉêëÅÜáÉÇÉåÉ= mÉêáçÇÉå= ÉåíïáJ ÅâÉäíÉå=ëáÅÜ=ïáÉ=ÑçäÖíW= =
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1. Aufgabenstellungen
355
PMKMMMIMM= bìêçFK= a~ë= ^åä~ÖÉîÉêã∏ÖÉå= ÄäáÉÄ= áå= ÇÉê= ÖÉë~ãíÉå= oÉÅÜåìåÖëéÉêáçÇÉ= ìå~åÖÉí~ëíÉí=ìåÇ=ä~Ö=áå=ÇÉê=pÅÜäìëëÄáä~åò=ÄÉá=QMMKMMMIMM=bìêçK= bêãáííÉäå= páÉ= ÇÉå= tÉêí= ÇÉë= rãä~ìÑîÉêã∏ÖÉåë= áå= ÇÉê= bê∏ÑÑåìåÖëÄáä~åò= ÇÉë= dÉJ ëÅÜ®Ñíëà~ÜêÉë=OMMSK= =
^ìÑÖ~ÄÉ=T= dÉÄÉå= páÉ= ÑΩê= àÉÇÉå= ÇÉê= ÑçäÖÉåÇÉå= dÉëÅÜ®ÑíëîçêÑ®ääÉ= ~åI= ïÉäÅÜÉ= _áä~åòéçëáíáçåÉå= ÄÉêΩÜêí=ïÉêÇÉåI=ïáÉ=ëáÅÜ=ÇáÉëÉ=îÉê®åÇÉêåI=ïÉäÅÜÉ=^êí=îçå=_áä~åò®åÇÉêìåÖ=îçêäáÉÖí= ìåÇ=ïÉäÅÜÉ=^ìëïáêâìåÖÉå=ëáÅÜ=Ç~ÇìêÅÜ=~ìÑ=ÇáÉ=_áä~åòëìããÉ=ÉêÖÉÄÉåK= ~F= rãï~åÇäìåÖ=ÉáåÉê=âìêòÑêáëíáÖÉå=_~åâîÉêÄáåÇäáÅÜâÉáíK=áå=ÉáåÉ=ä~åÖÑêáëíáÖÉ=_~åâJ îÉêÄáåÇäáÅÜâÉáíW=NMMKMMMIMM== ÄF= _~êÉáåò~ÜäìåÖ=~ìÑ=Ç~ë=_~åââçåíçW=NKMMMIMM== ÅF= _~åâΩÄÉêïÉáëìåÖ=~å=ÉáåÉå=iáÉÑÉê~åíÉåW=PKRMMIMM== ÇF= mçëíÖáêçΩÄÉêïÉáëìåÖ=ÇÉê=ãçå~íäáÅÜÉå=qáäÖìåÖ=ÉáåÉê=eóéçíÜÉâW=OKMMMIMM=== ÉF= báå=hìåÇÉ=ÄÉÖäÉáÅÜí=ëÉáåÉ=oÉÅÜåìåÖ=éÉê=_~åâΩÄÉêïÉáëìåÖW=PKMMMIMM== ÑF= h~ìÑ=ÉáåÉê=åÉìÉå=cÉêíáÖìåÖëã~ëÅÜáåÉ=~ìÑ=wáÉäW=NNKRMMIMM== ÖF= sÉêâ~ìÑ=ÉáåÉë=ÖÉÄê~ìÅÜíÉå=mâïë=ÖÉÖÉå=_~åâëÅÜÉÅâW=PKSMMIMM== =
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^ìÑÖ~ÄÉ=V= dÉÄÉå=páÉ=ÇáÉ=_ìÅÜìåÖëë®íòÉ=ÑΩê=ÑçäÖÉåÇÉ=dÉëÅÜ®ÑíëîçêÑ®ääÉ=~å=ìåÇ=ëíÉääÉå=páÉ=ÇáÉ= p~ÅÜîÉêÜ~äíÉ=àÉïÉáäë=~ìÑ=qJhçåíÉå=Ç~ê=EàÉ=dÉëÅÜ®ÑíëîçêÑ~ää=åìê=Éáå=_ìÅÜìåÖëë~íò>FK=
356
E. Aufgaben
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1. Aufgabenstellungen
357
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358
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1. Aufgabenstellungen
359
^ìÑÖ~ÄÉ=NV= _áäÇÉå=páÉ=ÇáÉ=_ìÅÜìåÖëë®íòÉ=òì=ÑçäÖÉåÇÉå=dÉëÅÜ®ÑíëîçêÑ®ääÉåK= ~F= aáÉ=iÉ~ëáåÖÖÉÄΩÜê=ÑΩê=ÉáåÉå=mâï=ïáêÇ=Ä~ê=ÄÉò~ÜäíW=RKRMMIMM=bìêç=åÉííç= ÄF= §ÄÉêïÉáëìåÖ= ÇÉê= ãçå~íäáÅÜÉå= jáÉíÉ= ÑΩê= ÇáîÉêëÉ= i~ÖÉêê®ìãÉW= PKOMMIMM= bìêç== åÉííç= ÅF= báåÖ~åÖ=ÉáåÉê=oÉÅÜåìåÖ=îçã=péÉÇáíÉìêI=ÇÉê=ÑΩê=ÇáÉ=_ÉäáÉÑÉêìåÖ=ÇÉê=hìåÇÉå=òìJ ëí®åÇáÖ=áëíW=NKOMMIMM=bìêç=åÉííç= ÇF= w~ÜäìåÖ= ÇÉê= m~ÅÜí= ÑΩê= ÉáåÉå= i~ÖÉêéä~íò= ÇìêÅÜ= mçëíΩÄÉêïÉáëìåÖW= RMMIMM= bìêç== åÉííç= ÉF= _Éí~åâìåÖ=ÉáåÉë=cáêãÉåJmâïëK=aáÉ=nìáííìåÖ=ä~ìíÉí=~ìÑ=PRIRM=bìêçK= ÑF= h~ìÑ=îçå=oÉÅÜåìåÖëÑçêãìä~êÉå=ÖÉÖÉå=_~åâΩÄÉêïÉáëìåÖW=NNVIMM=bìêç=Äêìííç= =
^ìÑÖ~ÄÉ=OM= aáÉ= pÉâêÉí®êáå= ÉáåÉë= råíÉêåÉÜãÉåë= îÉêÇáÉåí= ãçå~íäáÅÜ= NKORMIMM= bìêç= ÄêìííçK= ^å= ^ÄòΩÖÉå= Ñ~ääÉå= içÜåëíÉìÉêW= NPTIRM= bìêçI= háêÅÜÉåëíÉìÉêW= NOIMM= bìêçI= pçäáÇ~êáí®íëòìJ ëÅÜä~ÖW= SIOR= bìêç= ëçïáÉ= ^k^= òì= oÉåíÉåJI= ^êÄÉáíëäçëÉåJI= hê~åâÉåJ= ìåÇ= mÑäÉÖÉîÉêJ ëáÅÜÉêìåÖW=NONIUU=bìêçI=QMISP=bìêçI=UMISP=bìêçI=NMISP=bìêç=~åK= ~F= dÉÄÉå=páÉ=~ääÉ=_ìÅÜìåÖÉå=~åI=ÇáÉ=~ã=båÇÉ=ÇÉë=jçå~íë=îçå=ÇÉê=içÜåÄìÅÜÜ~äJ íìåÖ=òì=í®íáÖÉå=ëáåÇK= ÄF= _ìÅÜÉå=páÉ=ÇáÉ=_~åâΩÄÉêïÉáëìåÖ=ÇÉê=ÉáåÄÉÜ~äíÉåÉå=píÉìÉêå=ìåÇ=ÇÉê=pçòá~äîÉêJ ëáÅÜÉêìåÖëÄÉáíê®ÖÉ=òì=_ÉÖáåå=ÇÉë=cçäÖÉãçå~íëK= =
^ìÑÖ~ÄÉ=ON= báå= cäáÉ≈Ä~åÇ~êÄÉáíÉê= ÄáííÉí= ~ã= NMK= ÇÉë= jçå~íë= ìã= ÉáåÉå= sçêëÅÜìëë= îçå= NKMMMIMM= bìêçI=ìã=ìåîçêÜÉêÖÉëÉÜÉåÉ=oÉé~ê~íìêÉå=~å=ëÉáåÉã=tçÜåÜ~ìë=òì=ÄÉò~ÜäÉåK= ~F= _ìÅÜÉå=páÉ=ÇáÉ=_~åâΩÄÉêïÉáëìåÖ=ÇÉë=sçêëÅÜìëëÉëK= ÄF= ^ã=båÇÉ=ÇÉë=jçå~íë=ïáêÇ=ÇáÉëÉê=sçêëÅÜìëë=ãáí=ÇÉê=~âíìÉääÉå=içÜåò~ÜäìåÖ=îÉêJ êÉÅÜåÉíI= ëç= Ç~ëë= ÇÉê= jáí~êÄÉáíÉê= åìê= åçÅÜ= ÉáåÉå= kÉííçäçÜå= îçå= NKQTMIMM= bìêç= ÉêÜ®äíK=^å=^ÄòΩÖÉå=ÑáÉäÉå=píÉìÉêå=áå=e∏ÜÉ=îçå=PVMIMM=bìêç=ìåÇ=pçòá~äîÉêëáÅÜÉJ êìåÖëÄÉáíê®ÖÉ=E^k^F=îçå=UPMIMM=bìêç=~åK=bêãáííÉäå=páÉ=åìå=ÇáÉ=e∏ÜÉ=ÇÉë=_êìíJ íçäçÜåë=ìåÇ=ÄìÅÜÉå=páÉ=ÇáÉ=§ÄÉêïÉáëìåÖK= =
^ìÑÖ~ÄÉ=OO= aÉê= råíÉêåÉÜãÉê= j~ñ= kÉìêÉáÅÜ= áëí= îÉêéÑäáÅÜíÉí= ~ääÉ= ëÉáåÉ= ^êÄÉáíåÉÜãÉê= òì= îÉêëáJ ÅÜÉêåK=^ã=g~ÜêÉë~åÑ~åÖ=ÖÉÜí=Ç~ÜÉê=ÇáÉ=_Éáíê~ÖëêÉÅÜåìåÖ=ÇÉê=_ÉêìÑëÖÉåçëëÉåëÅÜ~Ñí= áå=e∏ÜÉ=îçå=PKQRMIMM==ÉáåK=aáÉ=oÉÅÜåìåÖ=ïáêÇ=ìåîÉêòΩÖäáÅÜ=éÉê=mçëíÄ~åâΩÄÉêïÉáJ ëìåÖ=ÄÉÖäáÅÜÉåK= ~F= _ìÅÜÉå=páÉ=ÇÉå=sçêÖ~åÖK== ÄF= _ÉëÅÜêÉáÄÉå= páÉ= ÇáÉ= ^ìëïáêâìåÖÉå= ÇáÉëÉê= _ìÅÜìåÖ= ~ìÑ= Ç~ë= báÖÉåâ~éáí~ä= ÇÉë= råíÉêåÉÜãÉåëK= =
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360
E. Aufgaben
^ìÑÖ~ÄÉ=OP= báå= dÉëÅÜ®Ñíëã~åå= ÉêêÉÅÜåÉí= ÑΩê= ÉáåÉë= ëÉáåÉê= mêçÇìâíÉ= pÉäÄëíâçëíÉå= áå= e∏ÜÉ= îçå= NKOUMIMM=bìêçK=dêìåÇë®íòäáÅÜ=ÖÉï®Üêí=Éê=ëÉáåÉå=pí~ããâìåÇÉå=ÄÉá=ÉáåÉã=ism=îçå= NKUMMIMM=bìêç=ÉáåÉå=qêÉìÉê~Ä~íí=îçå=NM=BK= ~F= jáí=ïÉäÅÜÉã=dÉïáåå=Ebìêç=ìåÇ=mêçòÉåíF=êÉÅÜåÉí=ÇÉê=dÉëÅÜ®Ñíëã~åå\= ÄF= ^ìÑÖêìåÇ= ëí~êâÉê= hçåâìêêÉåò= áëí= Éê= ÖÉòïìåÖÉå= ÇÉå= ism= ìã= U= B= òì= ëÉåâÉåK= tÉäÅÜÉ=^ìëïáêâìåÖÉå=Ü~í=ÇáÉë=~ìÑ=ÇÉå=dÉïáåå\= =
^ìÑÖ~ÄÉ=OQ= få=ÇÉê=h~äâìä~íáçå=ÉáåÉë=báåòÉäéêçÇìâíìåíÉêåÉÜãÉåë=ÑáåÇÉå=ëáÅÜ=ÑçäÖÉåÇÉ=tÉêíÉW= o~Ä~íí=áå=BW=SI=o~Ä~íí=áå=bìêçW=QNMIMM= bêãáííÉäå=páÉ=ÇÉå=ismK= =
^ìÑÖ~ÄÉ=OR= _áäÇÉå=páÉ=ÇáÉ=_ìÅÜìåÖëë®íòÉ=òì=ÑçäÖÉåÇÉå=dÉëÅÜ®ÑíëîçêÑ®ääÉåK= ~F= wáÉäîÉêâ~ìÑ= îçå= cÉêíáÖÉêòÉìÖåáëëÉåW= wáÉäîÉêâ~ìÑëéêÉáë= PKQRMIMM= bìêçI= NM= B= o~J Ä~ííK= qê~åëéçêíâçëíÉå= áå= e∏ÜÉ= îçå=PMMIMM= bìêç= ïÉêÇÉå= ÇÉã= hìåÇÉå=áå= oÉÅÜJ åìåÖ=ÖÉëíÉääíK= ÄF= _~êâ~ìÑ=îçå=sÉêé~ÅâìåÖëã~íÉêá~äW=OKMMMIMM=bìêç=Äêìííç= ÅF= báå=hìåÇÉ=ëÉåÇÉí=EiÉáÜJFsÉêé~ÅâìåÖ=òìêΩÅâW=dìíëÅÜêáÑí=PQMIMM=bìêç=åÉííç= ÇF= ^ìÑÖêìåÇ=ÉáåÉê=j®åÖÉäêΩÖÉ=ÉêÜ~äíÉå=ïáê=NLP=ÉáåÉê=iáÉÑÉêìåÖ=òìêΩÅâK=aÉê=oÉÅÜJ åìåÖëÄÉíê~Ö=ÄÉäáÉÑ=ëáÅÜ=~ìÑ=PKONMIMMbìêç=ÄêìííçK= =
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1. Aufgabenstellungen
361
íáçå= pÉäÄëíâçëíÉå= îçå= RTSITM= bìêç= ìåÇ= QM= B= dÉïáååK= i~åÖà®ÜêáÖÉå= hìåÇÉå= ïáêÇ= Éáå=qêÉìÉê~Ä~íí=îçå=R=B=ÉáåÖÉê®ìãíK== ~F= ^å= ÉáåÉå= ä~åÖà®ÜêáÖÉå= ÖìíÉå= hìåÇÉå= ïáêÇ= ~ã= OMKMRKOMMT= ÑçäÖÉåÇÉ= oÉÅÜåìåÖ= îÉêë~åÇíK=_ìÅÜÉå=páÉ=ÇáÉëÉK= jΩÜäïÉÖ=T= VOTNQ=mäÉóëíÉáå= mäÉóëíÉáåI=ÇÉå=OMKMRKOMMT=
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^ìÑÖ~ÄÉ=PM= bêãáííÉäå= ìåÇ= ÄìÅÜÉå= E_~åâΩÄÉêïÉáëìåÖF= páÉ= ~åÜ~åÇ= ÑçäÖÉåÇÉê= dÉëÅÜ®ÑíëîçêÑ®ääÉ= ÇáÉ=rãë~íòëíÉìÉêîÉêÄáåÇäáÅÜâÉáí=ÄòïK=JÑçêÇÉêìåÖ=ÖÉÖÉåΩÄÉê=ÇÉã=cáå~åò~ãíK=píÉääÉå= páÉ=Ç~òì=ÇáÉ=sçêÖ®åÖÉ=~ìÑ=ÇÉå=hçåíÉå=OSMM=ìåÇ=QUMM=áå=qJhçåíÉåJcçêã=Ç~êK=
362
E. Aufgaben
~F= ÄF= ÅF= ÇF= ÉF= ÑF= ÖF= ÜF= áF=
sÉêâ~ìÑ=îçå=cÉêíáÖÉêòÉìÖåáëëÉå=~ìÑ=wáÉäX=t~êÉåïÉêíW=RRKMMMIMM=bìêç= h~ìÑ=îçå=eÉáò∏ä=ÖÉÖÉå=_~åâëÅÜÉÅâX=QKTSMIMM=bìêçX=Äêìííç= sÉêâ~ìÑ=ÉáåÉê=ÖÉÄê~ìÅÜíÉå=_çÜêã~ëÅÜáåÉX=NUMIMM=bìêçX=åÉííç= h~ìÑ=îçå=_Ωêçã∏ÄÉäåX=_~êò~ÜäìåÖ=áå=e∏ÜÉ=îçå=NPKUMQIMM=bìêç== _Éò~ÜäìåÖ=ÇÉê=hÑòJpíÉìÉê=ÇìêÅÜ=_~åâΩÄÉêïÉáëìåÖX=NKOMMIMM=bìêç== sÉêâ~ìÑ=îçå=cÉêíáÖÉêòÉìÖåáëëÉå=å~ÅÜ=dêç≈Äêáí~ååáÉåX=iáëíÉåéêÉáë=NOKPMMIMM=bìêç== h~ìÑ=îçå=c~ÅÜòÉáíëÅÜêáÑíÉåX=RQIMM=bìêçX=åÉííç= oΩÅâëÉåÇìåÖ=ÑÉÜäÉêÜ~ÑíÉê=cêÉãÇÄ~ìíÉáäÉX=NOMIMM=bìêçX=åÉííç= báå=hìåÇÉ=ëÉåÇÉí=iÉáÜîÉêé~ÅâìåÖ=òìêΩÅâX=NNVIMM=bìêçX=Äêìííç= =
^ìÑÖ~ÄÉ=PN= fã=wìÖÉ=ÉáåÉê=ÖÉéä~åíÉå=_ÉíêáÉÄëîÉêÖê∏≈ÉêìåÖ=â~ìÑí=Éáå=dÉëÅÜ®Ñíëã~åå=Éáå=ìåÄÉJ Ä~ìíÉë=dêìåÇëíΩÅâK=wì=ÇáÉëÉã=dÉëÅÜ®Ñí=ëáåÇ=ÑçäÖÉåÇÉ=a~íÉå=ÄÉâ~ååíW= =
dêìåÇëíΩÅâëéêÉáë= dêìåÇÉêïÉêÄëíÉìÉê= dêìåÇëíÉìÉê= dêìåÇÄìÅÜÉáåíê~Ö= j~âäÉêÖÉÄΩÜê= kçí~êâçëíÉå= _É~êÄÉáíìåÖëâçëíÉå=EeóéçíÜÉâF=
ORMKMMMIMM= PIR=B= RTMIMM= SMMIMM= NMKPMMIMM= OKRMMIMM= VRMIMM=
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^ìÑÖ~ÄÉ=PO= ^ã= MVKMQK= â~ìÑí= Éáå= råíÉêåÉÜãÉê= òìê= bêïÉáíÉêìåÖ= ëÉáåÉë= cìÜêé~êâë= = ÉáåÉå= åÉìÉå= häÉáåíê~åëéçêíÉê= òìã= iáëíÉåéêÉáë= îçå= NTKUMMIMM= bìêçK= ^ìÑÖêìåÇ= ÇÉê= ÖìíÉå= dÉJ ëÅÜ®ÑíëÄÉòáÉÜìåÖÉå=òìã=^ìíçÜ~ìë=ïÉêÇÉå=Éáå=o~Ä~íí= îçå=R=B=ìåÇ=Éáå=pâçåíç~ÄJ òìÖ=îçå=OIR=B=ÄÉá=w~ÜäìåÖ=áååÉêÜ~äÄ=îçå=NQ=q~ÖÉå=ÖÉï®ÜêíK=cΩê=ÇáÉ=§ÄÉêÑΩÜêìåÖ= ÇÉë=c~ÜêòÉìÖë=ïÉêÇÉå=ORMIMM=bìêç=ìåÇ=ÑΩê=ÇáÉ=ÉêëíÉ=q~åâÑΩääìåÖ=PRITM=bìêç=Äêìííç= áå= oÉÅÜåìåÖ= ÖÉëíÉääíK= aáÉ= hçëíÉå= ÑΩê= ÇáÉ= wìä~ëëìåÖI= ïÉäÅÜÉ= îçã= råíÉêåÉÜãÉê= ëÉäÄëí=îçêÖÉåçããÉå=ïìêÇÉI=ÄÉä~ìÑÉå=ëáÅÜ=~ìÑ=Öä~ííÉ=NMMIMM=bìêçK== ~F= _ìÅÜÉå=páÉ=ÇáÉ=báåÖ~åÖëêÉÅÜåìåÖ>= ÄF= _ìÅÜÉå=páÉ=ÇáÉ=§ÄÉêïÉáëìåÖ=ÇÉê=oÉÅÜåìåÖ=~ã=NVKMQK=ìåÇ=ÇáÉ=_~êò~ÜäìåÖ=ÇÉê= wìä~ëëìåÖëÖÉÄΩÜê=ÇìêÅÜ=ÇÉå=råíÉêåÉÜãÉêK= ÅF= jáí=ïÉäÅÜÉã=tÉêí=áëí=ÇáÉëÉë=c~ÜêòÉìÖ=åìå=áå=ÇÉå=_ΩÅÜÉêå=~âíáîáÉêí\= =
^ìÑÖ~ÄÉ=PP= cΩê=ÉáåÉ=åÉì=ÖÉÄáäÇÉíÉ=^ÄíÉáäìåÖ=áååÉêÜ~äÄ=ÉáåÉë=råíÉêåÉÜãÉåë=ïÉêÇÉå=P=pÅÜêÉáÄJ íáëÅÜëíΩÜäÉ=òì=áåëÖÉë~ãí=NKOMMIMM=bìêç=ÉáåÖÉâ~ìÑíK=a~êΩÄÉê=Üáå~ìë=ïìêÇÉ=îçã=ÖäÉáJ ÅÜÉå= báåêáÅÜíìåÖëÜ~ìë= åçÅÜ= ÉáåÉ= ÉäÉÖ~åíÉ= píÉÜä~ãéÉ= ÑΩê= RMIMM= bìêç= ÄÉòçÖÉå= EN= iáÉÑÉêìåÖI=N=oÉÅÜåìåÖFK=^å=_ÉòìÖëâçëíÉå=ÑáÉäÉå=áåëÖÉë~ãí=OMIMM=bìêç=~åK= ~F= _ìÅÜÉå=páÉ=ÇáÉ=báåÖ~åÖëêÉÅÜåìåÖ=áå=ÇÉê=píÉìÉêÄáä~åòK= ÄF= tÉäÅÜÉ=^ìëïáêâìåÖÉå=Ü~í=ÇÉê=h~ìÑ=ÇáÉëÉê=^êíáâÉä=~ìÑ=ÇáÉ=dìsJoÉÅÜåìåÖ\=
1. Aufgabenstellungen
363
^ìÑÖ~ÄÉ=PQ= få=ÇÉê=_ìÅÜÜ~äíìåÖ=ëáåÇ=ÑçäÖÉåÇÉ=dÉëÅÜ®ÑíëîçêÑ®ääÉ=òì=ÉêÑ~ëëÉåW= ~F= báå=_~ììåíÉêåÉÜãÉå=ïìêÇÉ=Ç~ãáí=ÄÉ~ìÑíê~ÖíI=ÇáÉ=a~ÅÜÖÉëÅÜçëëÉ=ÉáåÉë=sÉêï~äJ íìåÖëÖÉÄ®ìÇÉë=òì=ïÉáíÉêÉå=_Ωêçê®ìãÉå=~ìëòìÄ~ìÉåK=aáÉ=ÉåÇÖΩäíáÖÉ=oÉÅÜåìåÖ= ÄÉä®ìÑí=ëáÅÜ=~ìÑ=NVMKMMMIMM=bìêç=åÉííçK= ÄF= cΩê=ÇáÉ=oçìíáåÉéêΩÑìåÖ=ìåÇ=âäÉáåÉêÉ=oÉé~ê~íìêÉå=~å=ÇÉê=eÉáòìåÖë~åä~ÖÉ=ÉáåÉë= i~ÖÉêÖÉÄ®ìÇÉë= ïÉêÇÉå= ~å= ÇÉå= Ç~ãáí= ÄÉ~ìÑíê~ÖíÉå= e~åÇïÉêâÉê= OVTIRM= bìêç= Äêìííç=ΩÄÉêïáÉëÉåK= dÉÄÉå= páÉ= ÇáÉ= å∏íáÖÉå= _ìÅÜìåÖëë®íòÉ= ~å= ìåÇ= ÄÉÖêΩåÇÉå= páÉ= ÇáÉ= t~Üä= ÇÉê= ÉåíJ ëÅÜÉáÇÉåÇÉå=hçåíÉåK= = ^ìÑÖ~ÄÉ=PR= aìêÅÜ=ÉáåÉå=råÑ~ää=ïáêÇ=Éáå=iáÉÑÉêï~ÖÉå=íçí~ä=òÉêëí∏êí=ìåÇ=ãìëë=ãáí=ÉáåÉã=sÉêäìëí= îçå=ÖÉå~ì=NMKRMMIMM=bìêç=òì=RVRIMM=bìêç=Äêìííç=~å=ÉáåÉå=pÅÜêçííÜ®åÇäÉê=îÉêâ~ìÑí= ïÉêÇÉåK=_ìÅÜÉå=páÉ=ÇÉå=sçêÑ~ää=çÜåÉ=fåíÉêáãëJhçåíçK== = ^ìÑÖ~ÄÉ=PS= tÉÖÉå=òìåÉÜãÉåÇÉê=oÉé~ê~íìê~åÑ®ääáÖâÉáí=ÉáåÉê=sÉêé~ÅâìåÖë~åä~ÖÉ=ïáêÇ=Éáå=åÉìJ Éë= jçÇÉää= ÑΩê= SMKMVRIMM= bìêç= Äêìííç= ~ìÑ= wáÉä= ÄÉòçÖÉåK= cΩê= qê~åëéçêíI= sÉêé~ÅâìåÖ= ìåÇ=jçåí~ÖÉ=ïÉêÇÉå=RPRIRM=bìêç=Ä~ê=ÄÉò~ÜäíK=aÉê=eÉêëíÉääÉê=Éêâä®êí=ëáÅÜ=ÄÉêÉáíI=ÇáÉ= ~äíÉ=^åä~ÖÉ=E_ìÅÜïÉêí=ÄÉá=sÉêâ~ìÑW=UKONMIMM=bìêçF=ÑΩê=UKPQMIMM=bìêç=åÉííç=áå=w~ÜJ äìåÖ=òì=åÉÜãÉåK=aÉê=oÉÅÜåìåÖë~ìëÖäÉáÅÜ=ÉêÑçäÖí=ÇìêÅÜ=_~åâΩÄÉêïÉáëìåÖK= ~F= _ìÅÜÉå=páÉ=ÇÉå=sçêÖ~åÖK= ÄF= a~=Ç~ë=_~åââçåíç=ÇìêÅÜ=ÇÉå=h~ìÑ=òì=ëí~êâ=ΩÄÉêòçÖÉå=ïáêÇ=ëçää=Éáå=_Éíê~Ö=áå= e∏ÜÉ= îçå= OMKMMMIMM= bìêç= ÄÉá= ÇÉê= e~ìëÄ~åâ= áå= Éáå= âìêòÑêáëíáÖÉë= a~êäÉÜÉå= ìãJ ÖÉï~åÇÉäí=ïÉêÇÉåK=táÉ=ä~ìíÉí=ÇÉê=òì=îÉêïÉåÇÉåÇÉ=_ìÅÜìåÖëë~íò\= = ^ìÑÖ~ÄÉ=PT= wìê=^ìëÇÉÜåìåÖ=ÇÉê=mêçÇìâíáçåëâ~é~òáí®í=ïáêÇ=îçå=ÉáåÉê=pÅÜêÉáåÉêÉá=ÉáåÉ=ïÉáíÉêÉ= `k`Jcê®ëÉ= ÉáåÖÉâ~ìÑíK= aÉê= iáëíÉåÉáåâ~ìÑëéêÉáë= äáÉÖí= ÄÉá= ORKMMMIMM= bìêç= ìåÇ= ïáêÇ= ìåîÉêòΩÖäáÅÜ= ÄÉá= iáÉÑÉêìåÖ= éÉê= _~åâΩÄÉêïÉáëìåÖ= ÄÉÖäáÅÜÉåK= qê~åëéçêíâçëíÉå= áå= e∏ÜÉ=îçå=STUIPM=bìêç=Äêìííç=ïÉêÇÉå=Ä~ê=ÄÉò~ÜäíK=rã=ÇáÉ=j~ëÅÜáåÉ=áå=_ÉíêáÉÄ=òì= åÉÜãÉåI=ï~ê=Éë=ÉêÑçêÇÉêäáÅÜ=ÇìêÅÜ=ÉáÖÉåÉ=jáí~êÄÉáíÉê=ÉáåÉå=_ÉíçåëçÅâÉä=ìåÇ=ÉáåÉå= ÖÉÉáÖåÉíÉå= píêçã~åëÅÜäìëë= ÄÉêÉáíëíÉääÉå= òì= ä~ëëÉåK= aáÉ= Ç~ãáí= áã= wìë~ããÉåÜ~åÖ= ëíÉÜÉåÇÉå= ^ìÑïÉåÇìåÖÉå= ÄÉä~ìÑÉå= ëáÅÜ= ~ìÑ= ÖÉå~ì= VUMIMM= bìêçK= cΩê= ÇáÉ= jçåí~ÖÉ= ÇìêÅÜ=ÇáÉ=eÉêëíÉääÉêÑáêã~=ÑáÉäÉå=PMMIMM=bìêç=~åK= ~F= dÉÄÉå=páÉ=~ääÉ=åçíïÉåÇáÖÉå=_ìÅÜìåÖÉå=~åK= ÄF= bêãáííÉäå=páÉ=ÇáÉ=e∏ÜÉ=ÇÉê=^åëÅÜ~ÑÑìåÖëâçëíÉåK= ÅF= råãáííÉäÄ~ê=å~ÅÜ=ÇÉê=_Éò~ÜäìåÖ=ïáêÇ=ÑΩê=ÇáÉ=cÉêíáÖìåÖë~åä~ÖÉ=Éáå=t~êíìåÖëîÉêJ íê~Ö= ~ÄÖÉëÅÜäçëëÉåK= aÉê= g~ÜêÉëÄÉáíê~Ö= îçå= PMMMIMM= bìêç= ÑΩê= ÇÉå= wÉáíê~ìã= MNKMPKNVVS= Äáë= OUKMOKNVVT= ïáêÇ= éÉê= _~åâΩÄÉêïÉáëìåÖ= ÄÉò~ÜäíK= _ìÅÜÉå= páÉ= ÇáÉ= w~ÜäìåÖK= aáÉ= òìë®íòäáÅÜÉ= oÉÅÜåìåÖë~ÄÖêÉåòìåÖëÄìÅÜìåÖ= ãìëë= åáÅÜí= ~åÖÉÖÉJ ÄÉå=ïÉêÇÉåK= =
364
E. Aufgaben
^ìÑÖ~ÄÉ=PU= báåÉ= sÉêé~ÅâìåÖë~åä~ÖÉ= EkìíòìåÖëÇ~ìÉêW= R= g~ÜêÉF= ïáêÇ= áå= báÖÉåäÉáëíìåÖ= ÉêëíÉääí= ìåÇ=áå=_ÉíêáÉÄ=ÖÉåçããÉåK=_Éá=ÇÉê=eÉêëíÉääìåÖ=ÑáÉä=ÑçäÖÉåÇÉê=^ìÑï~åÇ=~åW= =
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^ìÑÖ~ÄÉ=PV= wìê= bêïÉáíÉêìåÖ= ÇÉê= mêçÇìâíáçåëâ~é~òáí®í= ïìêÇÉ= áã= j~á= OMMO= ÉáåÉ= cÉêíáÖìåÖëã~J ëÅÜáåÉ=ÖÉâ~ìÑíI=ÑΩê=ÇáÉ=ÑçäÖÉåÇÉ=hçëíÉå=EåÉííçF=~åÑáÉäÉåW= =
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1. Aufgabenstellungen
365
^ìÑÖ~ÄÉ=QN= báå=råíÉêåÉÜãÉå=ÄÉ~ìÑíê~Öí=ëÉáåÉ=e~ìëÄ~åâ=NRM=^âíáÉå=ÉáåÉë=`ÜÉãáÉâçåòÉêåë=òìê= âìêòÑêáëíáÖÉå= dÉäÇ~åä~ÖÉ= â~ìÑÉåK= aáÉ= _~åâä~ëíëÅÜêáÑí= ÑΩê= ÇáÉëÉ= qê~åë~âíáçå= ÄÉä®ìÑí= ëáÅÜ=ÄÉá=_ÉêÉÅÜåìåÖ=îçå=N=B=péÉëÉå=~ìÑ=RKQTMIMM=bìêçK= ~F= _ìÅÜÉå=páÉ=ÇÉå=h~ìÑK= ÄF= wì=ïÉäÅÜÉã=píΩÅââìêë=ïìêÇÉå=ÇáÉ=^âíáÉå=ÄÉòçÖÉå\= = ^ìÑÖ~ÄÉ=QO= sçê=ÉáåáÖÉê=wÉáí=ïìêÇÉå=îçå=ÇÉê=cáêã~=pÅÜ∏å=~ìë=ëéÉâìä~íáîÉå=dêΩåÇÉå=VM=pçä~êáÅJ ^âíáÉå=òì=ÉáåÉã=píΩÅââìêë=îçå=NMIRM=bìêç=ÖÉâ~ìÑíK=a~=åìå=~ÄÉê=âìêòÑêáëíáÖ=äáèìáÇÉ= jáííÉä=ÄÉå∏íáÖí=ïìêÇÉåI=ÉåíëÅÜáÉÇ=ëáÅÜ=ÇáÉ=dÉëÅÜ®ÑíëÑΩÜêìåÖ=Ç~òì=ÇáÉëÉ=tÉêíé~éáÉJ êÉ=~Äòìëíç≈ÉåK=aìêÅÜ=ÇÉå=sÉêâ~ìÑ=âçååíÉ=Éáå=bêíê~Ö=ÄòïK=hìêëÖÉïáåå=îçå=RNMIMM== bìêç=ÉêòáÉäí=ïÉêÇÉåK= ~F= wì=ïÉäÅÜÉã=hìêë=ïìêÇÉ=îÉêâ~ìÑí\= ÄF= dÉÄÉå=páÉ=ÇáÉ=_ìÅÜìåÖëë®íòÉ=ÑΩê=ÇÉå=h~ìÑ=ìåÇ=ÇÉå=sÉêâ~ìÑ=ÇáÉëÉê=^âíáÉå=~åK= = ^ìÑÖ~ÄÉ=QP= ^ã=ONKMPK=EtÉêíëíÉääìåÖF=ïÉêÇÉå=UBáÖÉ=fåÇìëíêáÉçÄäáÖ~íáçåÉå=òìã=hìêë=îçå=NMO=B= îÉêâ~ìÑíK=aÉê=kÉååïÉêí=äáÉÖí=ÄÉá=TKMMMIMM=bìêçK=wáåëíÉêãáå=áëí=ÇÉê=MNKNOK= ~F= bêãáííÉäå=páÉ=ÇÉå=wáåë~åëéêìÅÜ=ÇÉë=h®ìÑÉêë=ìåÇ=ÇÉë=sÉêâ®ìÑÉêëK= ÄF= bêêÉÅÜåÉå=páÉ=ÇáÉ=e∏ÜÉ=ÇÉë=~ìëã~ÅÜÉåÇÉå=_Éíê~ÖÉëK= = ^ìÑÖ~ÄÉ=QQ= cçäÖÉåÇÉ=a~íÉå=ÉáåÉë=ÑÉëíîÉêòáåëäáÅÜÉå=tÉêíé~éáÉêë=ëÉáåÉå=ÄÉâ~ååíW= =
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^ìÑÖ~ÄÉ=QR= báå=hêÉÇáí=ïáêÇ=å~ÅÜ=ÉáåÉê=i~ìÑòÉáí=îçå=ÖÉå~ì=V=jçå~íÉå=ÉáåëÅÜäáÉ≈äáÅÜ=S=B=wáåëÉå= EéK~KF=ãáí=QTKMORIMM=bìêç=òìêΩÅâÄÉò~ÜäíK= ~F= _ìÅÜÉå=páÉ=ÇáÉ=^ìëò~ÜäìåÖ=ÇÉë=hêÉÇáíë=òì=VV=BK= ÄF= táÉ=ä~ìíÉí=ÇÉê=_ìÅÜìåÖëë~íò=ÄÉá=oΩÅâò~ÜäìåÖ=ÇÉë=hêÉÇáíë\= ÅF= _ÉêÉÅÜåÉå=páÉ=ÇáÉ=ÉÑÑÉâíáîÉ=sÉêòáåëìåÖ=ÇáÉëÉê=cêÉãÇÑáå~åòáÉêìåÖK= =
366
E. Aufgaben
^ìÑÖ~ÄÉ=QS= báå= iáÉÑÉê~åí= ÄÉä~ëíÉí= ÉáåÉå= báåòÉäÜ®åÇäÉê= ÑΩê= ÉáåÉ= oÉÅÜåìåÖ= ΩÄÉê= SKRMMIMM= bìêç= ~ìÑÖêìåÇ=ïáÉÇÉêÜçäíÉã=w~ÜäìåÖëîÉêòìÖ=ãáí=NNIR=B=sÉêòìÖëòáåëÉå=ÑΩê=SM=q~ÖÉ=EêÉäK= wáåëë~íòFK=^ì≈ÉêÇÉã=ïÉêÇÉå=j~ÜåëéÉëÉå=áå=e∏ÜÉ=îçå=N=B=ÇÉë=oÉÅÜåìåÖëÄÉíê~ÖÉë= ÉêÜçÄÉåK= cΩÜêÉå=páÉ=ÇáÉ=å∏íáÖÉå=_ìÅÜìåÖÉå=ìåÇ=_ÉêÉÅÜåìåÖÉå=ÇìêÅÜ=ìåÇ=òï~ê= ~F= ~ìë=páÅÜí=ÇÉë=iáÉÑÉê~åíÉå=ìåÇ= ÄF= ~ìë=páÅÜí=ÇÉë=báåòÉäÜ®åÇäÉêëK= =
^ìÑÖ~ÄÉ=QT= ^ã= MNKMQK= ÉêÜ®äí= Éáå= j∏ÄÉäÜ~ìë= ÉáåÉ= e~åÇÉäëï~êÉåäáÉÑÉêìåÖ= EÑêÉá= e~ìëFK= aáÉ= ÄÉáJ äáÉÖÉåÇÉ=oÉÅÜåìåÖ=ÉåíÜ®äí=ÑçäÖÉåÇÉ=hçåÇáíáçåÉåW= =
_Éá= w~ÜäìåÖ= áååÉêJ PR=q~ÖÉ=w~ÜäìåÖëòáÉä= _Éá= w~ÜäìåÖëîÉêòìÖ= _ÉêÉÅÜåìåÖ= îçå== Ü~äÄ= îçå= NQ= q~ÖÉå= çÜåÉ=^ÄòìÖ= NO= B= éK= ~K= sÉêòìÖëòáåëÉå= ìåÇ= MIR= B= OIR=B=pâçåíç= j~ÜåëéÉëÉå= =
~F= rã= ÇÉå= pâçåíç= áå= ^åëéêìÅÜ= òì= åÉÜãÉå= ï®êÉ= Éáå= _~åââêÉÇáí= áå= e∏ÜÉ= îçå= SNKQORIMM=bìêç=åçíïÉåÇáÖK=_ìÅÜÉå=páÉ=ÇáÉ=báåÖ~åÖëêÉÅÜåìåÖK= ÄF= tÉäÅÜÉê=ÉÑÑÉâíáîÉ=wáåëë~íò=ÉåíëéêáÅÜí=ÇÉã=pâçåíçÉêíê~Ö\= ÅF= _ìÅÜÉå=páÉ=ÇáÉ=_~åâΩÄÉêïÉáëìåÖ=~ã=MTK=gìåáK= ÇF= bêãáííÉäå=páÉ=ÇáÉ=e∏ÜÉ=ÇÉê=òìë®íòäáÅÜÉå=hçëíÉå=EåÉÄÉå=ÇÉã=tÉêí=ÇÉê=e~åÇÉäëJ ï~êÉåFI=ÇáÉ=ÇÉã=j∏ÄÉäÜ~ìë=ÇìêÅÜ=ÇáÉ=îÉêé~ëëíÉ=pâçåíç~ìëåìíòìåÖ=ÉåíëíÉÜÉåK= =
^ìÑÖ~ÄÉ=QU= báå=råíÉêåÉÜãÉê=Éêï®Öí=òìê=cáå~åòáÉêìåÖ=ÉáåÉë=åÉìÉå=mâïë=ÉåíïÉÇÉê=ÉáåÉå=hçåJ íçâçêêÉåíJhêÉÇáí=çÇÉê=Éáå=a~êäÉÜÉå=áå=e∏ÜÉ=îçå=SKRMMIMM=bìêç=ÑΩê=OR=q~ÖÉ=áå=^åJ ëéêìÅÜ=òì=åÉÜãÉåK=aáÉëÉ=pÅÜìäÇ=ÄÉ~ÄëáÅÜíáÖí=Éê=ãáí=ÉáåÉã=ÇÉãå®ÅÜëí=òìíÉáäìåÖëJ êÉáÑÉå= _~ìëé~êîÉêíê~Ö= ~ìëòìÖäÉáÅÜÉåK= bë= áëí= îçå= ÉáåÉã= ~âíìÉääÉå= hçåíçëí~åÇ= îçå= MIMM=bìêç=~ìëòìÖÉÜÉåK=aÉë=tÉáíÉêÉå=ÉêÖÉÄÉå=ëáÅÜ=ÑçäÖÉåÇÉ=_ÉÇáåÖìåÖÉåW= =
aáëéçJhêÉÇáí=
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^ìÑÖ~ÄÉ=QV= wìê= ^åëÅÜ~ÑÑìåÖ= ÉáåÉë= åÉìÉå= cáêãÉåJmâïë= ëçää= Éáå= ^åëÅÜ~ÑÑìåÖëÇ~êäÉÜÉå= Eo~íÉåJ âêÉÇáíF= áå= e∏ÜÉ= îçå= PSKQTMIMM= bìêç= ~ìÑÖÉåçããÉå= ïÉêÇÉåK= aáÉ= i~ìÑòÉáí= äáÉÖí= ÄÉá= ÉáåÉê=sÉêòáåëìåÖ=îçå=MIRS=B=éK=jKI=ÉáåÉê=Éáåã~äáÖÉå=_É~êÄÉáíìåÖëÖÉÄΩÜê=îçå=MIR=B= ìåÇ=ÉáåÉê=oÉëíëÅÜìäÇîÉêëáÅÜÉêìåÖ=îçå=NMIMM=bìêç=éêç=jçå~í=ÄÉá=PS=jçå~íÉåK=aáÉ= ^ìëò~ÜäìåÖ=ÉêÑçäÖí=òì=VV=BK= ~F= bêãáííÉäå=páÉ=ÇáÉ=ãçå~íäáÅÜ=òì=ò~ÜäÉåÇÉ=o~íÉK= ÄF= _ìÅÜÉå=páÉ=ÇáÉ=^ìëò~ÜäìåÖ=ÇÉë=hêÉÇáíë=~ìÑ=Ç~ë=cáêãÉåÄ~åââçåíçK=
1. Aufgabenstellungen
367
ÅF== _ìÅÜÉå=páÉ=ÇáÉ=§ÄÉêïÉáëìåÖ=ÇÉê=ÉêëíÉå=o~íÉK= ÇF==_ÉêÉÅÜåÉå=páÉ=ÇáÉ=dÉë~ãíò~ÜäìåÖ=EPS=jçå~íÉF=~å=ÇÉå=hêÉÇáíÖÉÄÉêK= = ^ìÑÖ~ÄÉ=RM= ^ã=PNKNOK=E_áä~åòëíáÅÜí~ÖF=äáÉÖÉå=áå=ÉáåÉã=råíÉêåÉÜãÉå=ÑçäÖÉåÇÉ=a~íÉå=îçêW= =
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bêãáííÉäå=páÉ=ÇáÉ=e∏ÜÉ=ÇÉê=éêáî~íÉå=båíå~ÜãÉå=ìåÇ=ÄìÅÜÉå=páÉ=ÇÉå=^ÄëÅÜäìëë=ÇÉë= hçåíçë=PMMNK= = ^ìÑÖ~ÄÉ=RN= _ìÅÜÉå=páÉ=ÑçäÖÉåÇÉ=sçêÖ®åÖÉW= ~F= _~åâΩÄÉêïÉáëìåÖ=ÇÉê=dêìåÇÉêïÉêÄëíÉìÉê=EPIR=BF=ÑΩê=ÇÉå=h~ìÑ=ÉáåÉë=ÄÉÄ~ìíÉå= dêìåÇëíΩÅâë= EtÉêí= ÇÉë= sÉêï~äíìåÖëÖÉÄ®ìÇÉë= W= ONMKMMMIMM= bìêçX= dêìåÇëíΩÅâëJ ïÉêíW=RMMKMMMIMM=bìêçFK= ÄF= ^å=dêìåÇëíÉìÉê=Ñ~ääÉå=ÑΩê=Ç~ë=ÄÉá=~F=ÖÉâ~ìÑíÉ=dêìåÇëíΩÅâ=PKQRMIMM=bìêç=~åK=aÉê= Ñ®ääáÖÉ=_Éíê~Ö=ïáêÇ=ÇìêÅÜ=mçëíÄ~åâΩÄÉêïÉáëìåÖ=ÄÉÖäáÅÜÉåK= ÅF= aÉê=Ñ®ääáÖÉ=g~ÜêÉëÄÉáíê~Ö=ÑΩê=ÇáÉ=hê~ÑíÑ~ÜêòÉìÖëíÉìÉê=ÇÉê=ÄÉíêáÉÄäáÅÜÉå=c~ÜêòÉìÖÉ= ïáêÇ=îçã=råíÉêåÉÜãÉåëÄ~åââçåíç=éÉê=i~ëíëÅÜêáÑí=ÉáåÖÉòçÖÉåI=OKOPMIMM=bìêçK= ÇF= aÉê=råíÉêåÉÜãÉê=ÄÉÖäÉáÅÜí=ëÉáåÉ=báåâçããÉåëíÉìÉêëÅÜìäÇ=áå=e∏ÜÉ=îçå=RSTIMM= bìêç=ÇìêÅÜ=_~êò~ÜäìåÖ=E~ìë=ÇÉê=råíÉêåÉÜãÉåëâ~ëëÉF=ÄÉáã=cáå~åò~ãíK= ÉF= a~ë= råíÉêåÉÜãÉå= ΩÄÉêïÉáëí= ÇáÉ= ÉáåÄÉÜ~äíÉåÉ= içÜåJ= ìåÇ= háêÅÜÉåëíÉìÉê= ÇÉê= jáí~êÄÉáíÉê=~å=Ç~ë=cáå~åò~ãíI=PKQRSIMM=bìêçK= ÑF= §ÄÉêïÉáëìåÖ=ÇÉê=rpíJw~Üää~ëí=áå=e∏ÜÉ=îçå=NKOSTIMM=bìêç=Es~êá~åíÉ=^F= ÖF= ^ìÑ=ÇÉã=_~åââçåíç=ÖÉÜí=ÉáåÉ=dÉïÉêÄÉëíÉìÉêêΩÅâÉêëí~ííìåÖ=îçå=OKPQMIMM=bìêç= ÉáåK= ÜF= ^ìÑÖêìåÇ=ÉáåÉë=_ìÅÜìåÖëÑÉÜäÉêë=ïìêÇÉ=áã=îÉêÖ~åÖÉåÉå=g~Üê=îçã=råíÉêåÉÜãÉê= ÑΩê= ëÉáå= tçÜåÜ~ìë= òì= îáÉä= dêìåÇëíÉìÉê= ~å= Ç~ë= cáå~åò~ãí= ΩÄÉêïáÉëÉåK= aáÉ= oΩÅâÉêëí~ííìåÖ=~ìÑ=Ç~ë=cáêãÉåÄ~åââçåíç=ÄÉä®ìÑí=ëáÅÜ=~ìÑ=STIMM=bìêçK= = ^ìÑÖ~ÄÉ=RO= báåÉ= j~ëÅÜáåÉ= ãáí= ÉáåÉê= ÄÉíêáÉÄëÖÉï∏ÜåäáÅÜÉå= kìíòìåÖëÇ~ìÉê= îçå= R= g~ÜêÉå= ëíÉÜí= òì=_ÉÖáåå=ÇÉë=OK=kìíòìåÖëà~ÜêÉë=å~ÅÜ=ÇìêÅÜÖÉÑΩÜêíÉê=äáåÉ~êÉê=^Ñ^=åçÅÜ=ãáí=ÉáåÉå= oÉëíÄìÅÜïÉêí=îçå=NRKQRMIMM=bìêç=òì=ÄìÅÜÉK== ~F= jáí= ïÉäÅÜÉå= ^åëÅÜ~ÑÑìåÖëâçëíÉå= ïìêÇÉ= ÇáÉëÉë= ^åä~ÖÉÖìí= Éáåëíã~äáÖ= ~âíáîáÉêí= EbêïÉêÄ=áå=ÇÉê=NK=e®äÑíÉ=ÇÉë=g~ÜêÉëF\= ÄF= ^ã= båÇÉ= ÇÉê= kìíòìåÖëÇ~ìÉê= ïáêÇ= ÑÉëíÖÉëíÉääíI= Ç~ëë= Ç~ë= dìí= îçê~ìëëáÅÜíäáÅÜ= åçÅÜ= O= g~ÜêÉ= ä®åÖÉê= òì= åìíòÉå= ëÉáå= ïáêÇK= bêêÉÅÜåÉå= páÉ= ÇáÉ= e∏ÜÉ= ÇÉë= ^Ñ^J _Éíê~ÖÉë=áã=RK=kìíòìåÖëà~ÜêK= =
368
E. Aufgaben
^ìÑÖ~ÄÉ=RP= báå= m~åòÉêëÅÜê~åâ= ëíÉÜí= áã= äÉíòíÉå= kìíòìåÖëà~Üê= å~ÅÜ= ÄáëÜÉêáÖÉê= ÇÉÖêÉëëáîÉê= ^Ñ^= îçå= à®ÜêäáÅÜ= NM= B= åçÅÜ= ãáí= PKQSTINO= bìêç= áå= ÇÉå= _ΩÅÜÉêåK= a~ë= råíÉêåÉÜãÉå= Ü~í= ëáÅÜ=ÖÉÖÉå=ÉáåÉå=tÉÅÜëÉä=~ìÑ=ÇáÉ=äáåÉ~êÉ=^Ñ^=ÉåíëÅÜáÉÇÉåK= ~F= _ìÅÜÉå= páÉ= ÇáÉ= ^ÄëÅÜêÉáÄìåÖ= áã= äÉíòíÉå= kìíòìåÖëà~ÜêI= ïÉåå= Ç~ë= ^åä~ÖÉÖìí= åáÅÜí=ãÉÜê=ïÉáíÉê=ÖÉåìíòí=ïÉêÇÉå=â~ååK= ÄF= sçå=ïÉäÅÜÉê=kìíòìåÖëÇ~ìÉê=áëí=ã~å=áã=råíÉêåÉÜãÉå=~ìëÖÉÖ~åÖÉå\== =
^ìÑÖ~ÄÉ=RQ= báå=^åä~ÖÉÖÉÖÉåëí~åÇ=ãáí=ÉáåÉê=ÄÉíêáÉÄëÖÉï∏ÜåäáÅÜÉå=kìíòìåÖëÇ~ìÉê=îçå=Q=g~ÜêÉå= ëíÉÜí= å~ÅÜ= òïÉáã~äáÖÉêI= éä~åã®≈áÖÉêI= äáåÉ~êÉê= ^Ñ^= åçÅÜ= ãáí= TKPQMIMM= bìêç= áå= ÇÉê= píÉìÉêÄáä~åòK= ~F= bêãáííÉäå=páÉ=ÇáÉ=^åëÅÜ~ÑÑìåÖëâçëíÉå=ÇÉë=^åä~ÖÉÖìíÉë=ìåÇ=ÇáÉ=e∏ÜÉ=ÇÉë=à®ÜêäáJ ÅÜÉå=^Ñ^J_Éíê~ÖÉëK= ÄF= _ÉÖêΩåÇÉå=páÉ=êÉÅÜåÉêáëÅÜI=ï~êìã=ÇáÉ=äáåÉ~êÉ=ÇÉê=ÇÉÖêÉëëáîÉå=^Ñ^=îçêÖÉòçÖÉå= ïìêÇÉK= =
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^ìÑÖ~ÄÉ=RS= báåÉ= j~ëÅÜáåÉ= ïìêÇÉ= ~ã= MNKNMKOMMN= òì= ^åëÅÜ~ÑÑìåÖëâçëíÉå= îçå= PUMIMM= bìêç= ÄÉJ ëÅÜ~ÑÑíK=i~ìí=^Ñ^Jq~ÄÉääÉ=ïáêÇ=ÉáåÉ=ÄÉíêáÉÄëÖÉï∏ÜåäáÅÜÉ=kìíòìåÖëÇ~ìÉê=îçå=U=g~ÜJ êÉå= ~åÖÉëÉíòíK= a~= Ç~ë= råíÉêåÉÜãÉå= ëíÉíë= ëíÉìÉêäáÅÜ= ÖΩåëíáÖ= ~ÄëÅÜêÉáÄÉå= ã∏ÅÜíÉI= ïáêÇ=ÇáÉ=j~ëÅÜáåÉ=òìã=PNKNOKOMMN=~äë=dtd=áå=ÇÉê=píÉìÉêÄáä~åò=îçää=~ÄÖÉëÉíòíK= ~F= dÉÄÉå=páÉ=ÇÉå=åçíïÉåÇáÖÉå=_ìÅÜìåÖëë~íò=~åK= ÄF= aáÉ= j~ëÅÜáåÉ= ïáêÇ= åìå= ~ÄÉê= îçã= cáå~åò~ãí= åáÅÜí= ~äë= ÖÉêáåÖïÉêíáÖÉë= táêíJ ëÅÜ~ÑíëÖìí= ~åÉêâ~ååíK= tÉäÅÜÉ= _ìÅÜìåÖÉå= ëáåÇ= åìå= ÉêÑçêÇÉêäáÅÜ\= bë= áëí= Ç~îçå= ~ìëòìÖÉÜÉåI=Ç~ëë=ïÉáíÉêÜáå=Ü∏ÅÜëíã∏ÖäáÅÜ=~ÄÖÉëÅÜêáÉÄÉå=ïÉêÇÉå=ëçääK= ÅF= tÉäÅÜÉ= ^ìëïáêâìåÖÉå= Ü~í= ÇáÉëÉ= ^Ñ^JhçêêÉâíìê= ~ìÑ= ÇÉå= råíÉêåÉÜãÉåëÉêÑçäÖ= EbìêçJ_Éíê~ÖF\= =
=
1. Aufgabenstellungen
369
^ìÑÖ~ÄÉ=RT= fã=g~Üê=OMMN=â~ìÑíÉ=Ç~ë=råíÉêåÉÜãÉå=uv=Éáå=ìåÄÉÄ~ìíÉë=dêìåÇëíΩÅâK=^ìÑ=ÇáÉëÉã= ïìêÇÉ= ÉáåÉ= i~ÖÉêÜ~ääÉ= EÖÉëÅÜ®íòÉ= kìíòìåÖëÇ~ìÉê= OR= g~ÜêÉF= ÖÉÄ~ìíI= ÇáÉ= ~ã= MNKMRKOMMO=łáå=_ÉíêáÉÄ =ÖÉåçããÉå=ïìêÇÉK=a~òì=äáÉÖÉå=ÑçäÖÉåÇÉ=a~íÉå=îçêW= =
dêìåÇëíΩÅâ= = = = = =
h~ìÑéêÉáë= dêìåÇëíÉìÉê= dêìåÇÉêïÉêÄëíÉìÉê= dêìåÇÄìÅÜÖÉÄΩÜê= sÉêãÉëëìåÖëâçëíÉå= kçí~êá~íëÖÉÄΩÜêÉå=
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i~ÖÉêÜ~ääÉ= =
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dêìåÇëíΩÅâ= dÉÄ®ìÇÉ==
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370
E. Aufgaben
~F= bêãáííÉäå= páÉ= ÇáÉ= łw~ÜäìåÖëèìçíÉ = ìåÇ= ÖÉÄÉå= páÉ= ÉáåÉå= ã∏ÖäáÅÜÉå= dÉëÅÜ®ÑíëJ îçêÑ~ää=~åK= ÄF= táÉ= ÜçÅÜ= áëí= ÇÉê= rãë~íòëíÉìÉêÄÉíê~ÖI= ÇÉê= ~ìë= ÇáÉëÉã= dÉëÅÜ®Ñí= ~å= Ç~ë= cáå~åòJ ~ãí=~ÄòìÑΩÜêÉå=áëí\= ÅF= tÉäÅÜÉ= _ìÅÜìåÖ= ï~ê= ÉêÑçêÇÉêäáÅÜI= ~äë= ÄÉâ~ååí= ïìêÇÉI= Ç~ëë= ÇáÉ= cçêÇÉêìåÖ= ã∏ÖäáÅÜÉêïÉáëÉ=òì=ÉáåÉã=ÖÉïáëëÉå=qÉáä=~ìëÑ~ääÉå=â∏ååíÉ\= = ^ìÑÖ~ÄÉ=RV= fã=dÉëÅÜ®Ñíëà~Üê=OMMO=â~ã=Éë=~ã=_áä~åòëíáÅÜí~Ö=òì=ÑçäÖÉåÇÉê=_ìÅÜìåÖW= =
PSTM=
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aáÉ=ÄÉêÉáíë=îçêÜ~åÇÉåÉ=bt_=ÄÉäáÉÑ=ëáÅÜ=~ìÑ=QKOMMIMM=bìêçK=aÉë=tÉáíÉêÉå=áëí=Ç~îçå= ~ìëòìÖÉÜÉåI=Ç~ëë=Éë=áã=g~Üê=OMMO=åìê=ÉáåÉ=cçêÇÉêìåÖ=Ö~ÄI=ÇáÉ=~äë=òïÉáÑÉäÜ~Ñí=ÉáåJ ÖÉëíìÑí=ïìêÇÉK=j~å=êÉÅÜåÉíÉ=ãáí=ÉáåÉã=ï~ÜêëÅÜÉáåäáÅÜÉå=báåÖ~åÖ=îçå=QM=BK= bêãáííÉäå=páÉ=ÇáÉ=e∏ÜÉ=ÇáÉëÉê=òïÉáÑÉäÜ~ÑíÉå=cçêÇÉêìåÖK= = ^ìÑÖ~ÄÉ=SM= a~ë= hçåíç= PSTM= ïÉáëí= ~ìë= ÇÉã= sçêà~Üê= ÉáåÉå= _Éëí~åÇ= îçå= NKPQMIMM= bìêç= ~ìëK= fã= ä~ìÑÉåÇÉå=dÉëÅÜ®Ñíëà~Üê=áëí=âÉáåÉ=ÉáåòáÖÉ=cçêÇÉêìåÖ=òïÉáÑÉäÜ~Ñí=ÖÉïçêÇÉåK== ~F= _ìÅÜÉå=páÉ=ÇáÉ=^åé~ëëìåÖ=ÇÉë=hçåíçë=PSTM=~ã=båÇÉ=ÇÉë=dÉëÅÜ®Ñíëà~ÜêÉëK= ÄF= t~ë=ÖÉëÅÜáÉÜí=ÇìêÅÜ=ÇáÉëÉ=_ìÅÜìåÖ=ãáí=ÇÉã=hçåíç=PSTM\= = ^ìÑÖ~ÄÉ=SN= fã= îÉêÖ~åÖÉåÉå= dÉëÅÜ®Ñíëà~Üê= ä~Ö= ÇÉê= _Éëí~åÇ= ~å= ëáÅÜÉêÉå= cçêÇÉêìåÖÉå= ÄÉá= PMKPQRIMM=bìêçK=bë=ïìêÇÉ=ãáí=ÉáåÉã=aÉäâêÉÇÉêÉë~íò=îçå=O=B=ÖÉêÉÅÜåÉíK=wìã=PNKNOK= ÇÉë=~âíìÉääÉå=dÉëÅÜ®Ñíëà~ÜêÉë=áëí=åìå=ÉáåÉ=eÉê~ìÑëÉíòìåÖ=ÇÉê=m~ìëÅÜ~äïÉêíÄÉêáÅÜíáJ ÖìåÖ=îçå=VUMIMM=bìêç=ÉêÑçêÇÉêäáÅÜK== ~F= _ìÅÜÉå=páÉ=ÇáÉ=eÉê~ìÑëÉíòìåÖK= ÄF= bêãáííÉäå=páÉ=ÇÉå=_Éëí~åÇ=~å=ëáÅÜÉêÉå=cçêÇÉêìåÖÉå=áã=~âíìÉääÉå=dÉëÅÜ®Ñíëà~ÜêI= ïÉåå=Ç~îçå=~ìëòìÖÉÜÉå=áëíI=Ç~ëë=âÉáåÉêäÉá=òïÉáÑÉäÜ~ÑíÉ=cçêÇÉêìåÖÉå=îçêäáÉÖÉåK= = ^ìÑÖ~ÄÉ=SO= aÉê=ÖÉë~ãíÉ=cçêÇÉêìåÖëÄÉëí~åÇ=ÉáåÉê=råíÉêåÉÜãìåÖ=ÄÉä®ìÑí=ëáÅÜ=~ã=NKNOK=ÇÉë=dÉJ ëÅÜ®Ñíëà~ÜêÉë=~ìÑ=OVMKOOTIMU=bìêçK=bë=äáÉÖÉå=Äáë=òì=ÇáÉëÉã=a~íìã=âÉáåÉêäÉá=òïÉáÑÉäJ Ü~ÑíÉ= cçêÇÉêìåÖÉå= îçêK= _áä~åòëíáÅÜí~Ö= áëí= ÇÉê= PNKNOK= aÉê= mêçòÉåíë~íò= ÇÉê= m~ìëÅÜ~äJ ïÉêíÄÉêáÅÜíáÖìåÖ=äáÉÖí=ÄÉá=ÉáåÉã=bêÑ~ÜêìåÖëïÉêí=îçå=P=BK= ^ã=SKNOK=ïáêÇ=ÉáåÉ=ÄáëÜÉê=Éáåï~åÇÑêÉáÉ=cçêÇÉêìåÖ=EPKNTTIPM=bìêçF=ìåÉêï~êíÉí=ìåJ ÉáåÄêáåÖäáÅÜK=aÉê=^ìëÑ~ää=äáÉÖí=ÄÉá=NMM=BK= ^ã= VKNOK= ÄáííÉí= Éáå= hìåÇÉ= ìã= ÉáåÉå= Éáåãçå~íáÖÉå= w~ÜäìåÖë~ìÑëÅÜìÄK= pÉáåÉ= sÉêJ ÄáåÇäáÅÜâÉáí=ÄÉä®ìÑí=ëáÅÜ=~ìÑ=OTKPROIUM=bìêçK=aÉê=dÉëÅÜ®ÑíëäÉáíìåÖ=áëí=ÄÉâ~ååíI=Ç~ëë= ëáÅÜ=ÇáÉëÉê=hìåÇÉ=áå=ÉáåÉê=ÉñíêÉã=âêáíáëÅÜÉå=ïáêíëÅÜ~ÑíäáÅÜÉå=páíì~íáçå=ÄÉÑáåÇÉí=ìåÇ= êÉÅÜåÉí=ÇÉëÜ~äÄ=ÄÉêÉáíë=ãáí=ÉáåÉã=ï~ÜêëÅÜÉáåäáÅÜÉå=^ìëÑ~ää=îçå=RM=BK=
1. Aufgabenstellungen
371
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^ìÑÖ~ÄÉ=SQ= fã= tÉêíé~éáÉêÇÉéçí= ÉáåÉê= dãÄe= ÄÉÑáåÇÉí= ëáÅÜ= Éáå= ^âíáÉåé~âÉí= Eä~åÖÑêáëíáÖÉ= dÉäÇJ ~åä~ÖÉFI=ΩÄÉê=ïÉäÅÜÉë=ÑçäÖÉåÇÉ=a~íÉå=îçêäáÉÖÉåW= =
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372
E. Aufgaben
ÅF= kÉÜãÉå=páÉ=~åI=ÇáÉ=^âíáÉå=Ñ~ääÉå=ÇìêÅÜ=ÇÉå=hçåâìêë=ÇÉê=^âíáÉåÖÉëÉääëÅÜ~Ñí=~ìÑ= ÉáåÉå=qÉáäïÉêí=îçå=MIMM=bìêçK=tÉäÅÜÉ=_ìÅÜìåÖ=áëí=Ç~åå=òìã=PNKNOKOMMN=áå=ÇÉê= píÉìÉêÄáä~åò=ÉêÑçêÇÉêäáÅÜ\= =
^ìÑÖ~ÄÉ=SR= ^ã= PNKNOKOMMO= äáÉÖí= ÇÉê= pÅÜäìëëÄÉëí~åÇ= ÉáåÉë= eáäÑëëíçÑÑë= áå= ÇÉê= píÉìÉêÄáä~åò= ÄÉá= PKMMM= píΩÅâ= ¶= MIOP= bìêçLpíΩÅâK= fã= i~ìÑÉ= ÇÉë= dÉëÅÜ®Ñíëà~ÜêÉë= ïìêÇÉå= ÑçäÖÉåÇÉ== h®ìÑÉ=EÖäÉáÅÜÉê=iáÉÑÉê~åíF=ÖÉí®íáÖíW= =
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aÉê=qÉáäïÉêí=äáÉÖí=~ã=PNKNOKOMMP=ÄÉá=MIOR=bìêçLpíΩÅâK=aÉê=sÉêÄê~ìÅÜ=~å=eáäÑëëíçÑÑÉå= ä~Ö=áã=g~Üê=OMMP=ÄÉá=UKMMM=píΩÅâK== ~F= jáí= ïÉäÅÜÉã= tÉêí= ÖÉÜÉå= ÇáÉëÉ= eáäÑëëíçÑÑÉ= å~ÅÜ= ÇÉã= aìêÅÜëÅÜåáííëïÉêíJ îÉêÑ~ÜêÉå=áå=ÇáÉ=pÅÜäìëëÄáä~åò=å~ÅÜ=píÉìÉêêÉÅÜí=Éáå\= ÄF= táÉ=ÜçÅÜ=ï~ê=ÇÉê=ïÉêíã®≈áÖÉ=oçÜëíçÑÑîÉêÄê~ìÅÜ=áã=g~Üê=OMMP\= ÅF= píÉääÉå= páÉ= çÄáÖÉ= sçêÖ®åÖÉ= ~ìÑ= ÇÉå= hçåíÉå= SMOMI= SMONI= SMOO= ìåÇ= OMOM= ΩÄÉêJ ëáÅÜíäáÅÜ= Ç~ê= EqJhçåíÉåF= ìåÇ= ÖÉÄÉå= páÉ= ÇáÉ= ÇáÉ= Ç~òìÖÉÜ∏êáÖÉå= sçê~ÄëÅÜäìëëJ ÄìÅÜìåÖÉå=ìåÇ=^ÄëÅÜäìëëÄìÅÜìåÖÉå=~åK= =
^ìÑÖ~ÄÉ=SS= _Éáã= ìåÑÉêíáÖÉå= bêòÉìÖåáë= uv= ïìêÇÉ= ~ã= PNKNOKOMMN= Éáå= _Éëí~åÇ= îçå= NPKQRMIMM== bìêç=~ìëÖÉïáÉëÉåK=báå=píΩÅâ=îÉêìêë~ÅÜíÉ=ÄáëÜÉê=j~íÉêá~äâçëíÉå=áå=e∏ÜÉ=îçå=NQIRM= bìêçI=cÉêíáÖìåÖëâçëíÉå=îçå=NMIOM=bìêç=ìåÇ=pçåÇÉêÉáåòÉäâçëíÉå=ÇÉê=cÉêíáÖìåÖ=îçå= PIQM=bìêçK=aáÉ=dÉãÉáåâçëíÉåë®íòÉ=ä~ìíÉå=ïáÉ=ÑçäÖíW=jdh=PM=BI=cdh=NP=BI=stdh= R=BK=fã=i~ìÑÉ=ÇÉë=g~ÜêÉë=OMMO=â~ã=Éë=òì=wìÖ®åÖÉå=îçå=PMM=píΩÅâ=ìåÇ=ÖÉã®≈=âìJ ãìäáÉêíÉå=j~íÉêá~äÉåíå~ÜãÉëÅÜÉáåÉå=òì=^ÄÖ®åÖÉå=îçå=QMM=píΩÅâK=_Éá=ÇÉå=ÑÉêíáÖÉå= bêòÉìÖåáëëÉå= â~ã= Éë= ÄÉá= ÉáåÉã= ^åÑ~åÖëÄÉëí~åÇ= îçå= QKRMMIMM= bìêç= òì= ÉáåÉê= _ÉJ ëí~åÇëãáåÇÉêìåÖ=îçå=PKQMMIMM=bìêçK= ~F= bêãáííÉäå=ìåÇ=ÄìÅÜÉå=páÉ=ÇáÉ=_Éëí~åÇëîÉê®åÇÉêìåÖ=~å=ìåÑÉêíáÖÉå=bêòÉìÖåáëëÉå= ~ã=PNKNOKOMMOI=ïÉåå=ÇÉê=p_=áå=ÇÉê=píÉìÉêÄáä~åò=ã∏ÖäáÅÜëí=ÖÉêáåÖ=~ìëÖÉïáÉëÉå= ïÉêÇÉå=ëçääK= ÄF= píÉääÉå= páÉ= ÇÉå= ÖÉë~ãíÉå= p~ÅÜîÉêÜ~äí= ~ìÑ= qJhçåíÉå= Ç~ê= EhçåíÉå= ONMMI= OOMMI= ROMM=ìåÇ=UMOMFK= =
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1. Aufgabenstellungen
373
~F= _ìÅÜÉå=páÉ=ÇÉå=oÉÅÜåìåÖëÉáåÖ~åÖK= ÄF= ^ã=PNKNOKOMMN=ä~Ö=ÇÉê=hìêë=ÇÉë=rpJaçää~ê=ÄÉá== NK=NIPM=bìêç= OK=NIMR=bìêç= =
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374
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~F= _ìÅÜÉå=páÉ=ÇáÉ=_áäÇìåÖ=ÇÉê=oΩÅâëíÉääìåÖ=ìåÇ=ÇÉå=^ÄëÅÜäìëë=ÇÉë=oΩÅâëíÉääìåÖëJ âçåíçë=~ã=PNKNOKOMMPK= ÄF= fã=cêΩÜà~Üê=OMMQ=ëáåÇ=~ìÑÖêìåÇ=ëÅÜäÉÅÜíÉê=ïáêíëÅÜ~ÑíäáÅÜÉê=i~ÖÉ=ÇÉê=^d=ÇáîÉêëÉ= o~íáçå~äáëáÉêìåÖëã~≈å~ÜãÉå=ÉêÑçêÇÉêäáÅÜI=ïÉäÅÜÉ=~ìÅÜ=ÉáåÉå=^ÄÄ~ì=ÇÉê=_ÉäÉÖJ ëÅÜ~Ñí=ÉáåëÅÜäáÉ≈ÉåK=^ìÑÖêìåÇ=ÉáåÉê=Öêç≈òΩÖáÖÉå=^ÄÑáåÇìåÖëò~ÜäìåÖ=ëíáããí=ÉáJ åÉ=Öê∏≈ÉêÉ=w~Üä=ÇÉê=jáí~êÄÉáíÉê=ÇÉê=_ÉÉåÇáÖìåÖ=ÇÉë=^êÄÉáíëîÉêÜ®äíåáëëÉë=òìK=báJ åÉ=eÉê~ÄëÉíòìåÖ=ÇÉê=oΩÅâëíÉääìåÖ=ìã=NMMKMMMIMM=bìêç=ëÅÜÉáåí=åìå=~åÖÉÄê~ÅÜíK= ÅF= ^ã=PNK=gìäá=OMMP=ÖÉÜí=Éáå=ä~åÖà®ÜêáÖÉê=jáí~êÄÉáíÉê=áå=ÇÉå=ïçÜäîÉêÇáÉåíÉå=oìÜÉJ ëí~åÇK= bë= ÉêÑçäÖí= ÇáÉ= ÉêëíÉ= w~ÜäìåÖ= ~ìë= ÇÉê= ÄÉíêáÉÄäáÅÜÉå= ^äíÉêëîÉêëçêÖìåÖ= áå= e∏ÜÉ=îçå=RMMIMM=bìêçK= =
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= RK=dÉëÅÜ®Ñíë~ìëëí~ííìåÖ=äíK=sÉêòK=O= = ffK=rãä~ìÑîÉêã∏ÖÉå= = NK=sçêê®íÉ=äíK=sÉêòK=P= = OK=_~åâÖìíÜ~ÄÉå= = = uvJ_~åâ= = = ^_J_~åâ=
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bìêç=
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376
E. Aufgaben
ÄF= k~ÅÜ= ¬= ORT= ed_= ëáåÇ= fåîÉåí~êÉ= NM= g~ÜêÉ= ~ìÑòìÄÉï~ÜêÉåK= aáÉ= cêáëí= ÄÉÖáååí= ~Ä= ÇÉã=PNKNOK=ÇÉë=h~äÉåÇÉêà~ÜêÉëK=aáÉë=ÄÉÇÉìíÉí=áã=çÄáÖÉå=c~ääI=Ç~ëë=Ç~ë=fåîÉåí~ê= Äáë=òìã=PNKNOKOMNS=åáÅÜí=îÉêåáÅÜíÉí=ïÉêÇÉå=Ç~êÑK= = ÅF= a~ë= fåîÉåí~ê= ïΩêÇÉ= ~ìÑÖêìåÇ= òì= îáÉäÉê= aÉí~áäë= ~å= §ÄÉêëáÅÜíäáÅÜâÉáí= îÉêäáÉêÉåK= a~ÜÉê=ÄÉÇáÉåí=ã~å=ëáÅÜ=ëçÖK=sÉêòÉáÅÜåáëëÉ=ìã=ìãÑ~åÖêÉáÅÜÉ=^ìÑäáëíìåÖÉå=~ìë= ÇÉã=fåîÉåí~ê=~ìëòìÖäáÉÇÉêåK= =
^ìÑÖ~ÄÉ=O= a~=ÇáÉ=e∏ÜÉ=ÇÉê=^âíáî~=ìåÇ=ÇÉê=m~ëëáî~=áããÉê=ΩÄÉêÉáåëíáããÉå=ãΩëëÉåI=ÉåíëéêáÅÜí= ÇÉê=tÉêí=ÇÉë=dÉë~ãíâ~éáí~äë=ÖÉå~ì=ÇÉã=ÇÉë=dÉë~ãíîÉêã∏ÖÉåëK=aáÉëÉë=ÄÉä®ìÑí=ëáÅÜ= ~äëç= ~ìÑ= QURKMMMIMM= bìêçK= a~ë= báÖÉåâ~éáí~ä= ÉêêÉÅÜåÉí= ëáÅÜ= ~äë= aáÑÑÉêÉåò= ÇÉë= dÉJ ë~ãíâ~éáí~äë= ìåÇ= ÇÉë= cêÉãÇâ~éáí~äëK= aáÉ= _áä~åò= ïÉáëí= ~äëç= ÉáåÉå= báÖÉåâ~éáí~äïÉêí= NF îçå=QURKMMMIMM=Ó=TOKRMMIMM=Z=QNOKRMMIMM=bìêç=~ìë= K=aáÉ=_ÉêÉÅÜåìåÖ=ÇÉë=rãä~ìÑJ îÉêã∏ÖÉåë= ÉêÑçäÖí= ~ìÑ= ®ÜåäáÅÜÉ= tÉáëÉK= bë= ÄÉíê®Öí= dÉë~ãíîÉêã∏ÖÉå= Ó= ^åä~ÖÉîÉêJ OF ã∏ÖÉå=Z=QURKMMMIMM=Ó=PQMKMMMIMM=Z=NQRKMMMIMM=bìêç= K= =
^=
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rãä~ìÑîÉêã∏ÖÉå= =
dÉë~ãíîÉêã∏ÖÉå=
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2. Lösungen
377
^=
===_áä~åò=OMMP=
NK=^s= _ÉÄ~ìíÉ=dêìåÇëíΩÅâÉ= _ÉíêáÉÄëÖÉÄ®ìÇÉ= cìÜêé~êâ= dÉëÅÜ®Ñíë~ìëëí~ííìåÖ= OK=rs= sçêê®íÉ= cçêÇÉêìåÖÉå= _~åâ= h~ëëÉ=
= NRMKMMMIMM= TPNKMMMIMM= TOKQMMIMM= RQKPMMIMM= = NRQKPMMIMM= ORKSMMIMM= ORKPQMIMM= UKRNMIMM
m=
NK=bh= OK=ch= i~åÖÑêK=_~åâîÉêÄK= hìêòÑêK=_~åâîÉêÄK= sÉêÄáåÇäK=~ìë=ii= = = = = =
UUQKUOSIMM= = OORKMMMIMM= PRKPMMIMM= TSKPOQIMM= = = = = =
=
NKOONKQRMIMM = NKOONKQRMIMM= = aáÉ=mçëíÉå=ÇÉê=^âíáîëÉáíÉ=ëáåÇ=å~ÅÜ=áÜêÉê=iáèìáÇáí®í=ÄòïK=áÜêÉê=łdÉäÇå®ÜÉ =òì=ÖäáÉJ ÇÉêåK= gÉ= ÉáåÑ~ÅÜÉê= Éë= áëí= ÉáåÉå= sÉêã∏ÖÉåëÖÉÖÉåëí~åÇ= òì= dÉäÇ= òì= ã~ÅÜÉåI= ÇÉëíç= ïÉáíÉê= ìåíÉå= áëí= Éê= áå= ÇÉê= _áä~åò= òì= ÑáåÇÉåK= içÖáëÅÜÉêïÉáëÉ= í~ìÅÜí= Ç~ÜÉê= ÇÉê= h~ëJ ëÉåÄÉëí~åÇ= ~å= äÉíòíÉê= píÉääÉ= ÇÉê= ^âíáîéçëíÉå~ìÑäáëíìåÖ= ~ìÑK= EaáÉ= ~âíáîÉ= oÉÅÜåìåÖëJ ~ÄÖêÉåòìåÖ=ëÉá=ÜáÉê=~ì≈Éê=^ÅÜí=ÖÉä~ëëÉåI=Ç~=~ìÑ=ëáÉ=Éêëí=áå=ëé®íÉêÉå=h~éáíÉäå=å®ÜÉê= ÉáåÖÉÖ~åÖÉå=ïáêÇKF=
^ìÑ=ÇÉê=m~ëëáîëÉáíÉ=ÜáåÖÉÖÉå=ïáêÇ=å~ÅÜ=ÇÉê=cêáëíáÖâÉáí=ëçêíáÉêíK=hìêòÑêáëíáÖÉë=áëí=ïÉáJ íÉê=ìåíÉå=ìåÇ=i~åÖÑêáëíáÖÉë=ïÉáíÉê=çÄÉå=~åÖÉëáÉÇÉäíK= aìêÅÜ= ÇáÉ= ^ìÑëìããáÉêìåÖ= ~ääÉê= ^âíáîïÉêíÉ= ÉêÜ®äí= ã~å= ÇÉå= tÉêí= ÇÉë= sÉêã∏ÖÉåëK= aáÉëÉê= ÉåíëéêáÅÜí= ÇÉã= dÉë~ãíâ~éáí~ä= EpìããÉ= ~ääÉê= m~ëëáîéçëíÉå= Z= báÖÉåâ~éáí~ä= H= cêÉãÇâ~éáí~äFI= ëç= Ç~ëë= Ç~ë= báÖÉåâ~éáí~ä= ~äë= aáÑÑÉêÉåò= ~ìë= dÉë~ãíâ~éáí~ä= ìåÇ= cêÉãÇâ~éáí~ä=ÉêãáííÉäí=ïÉêÇÉå=â~ååK= =
ÄF=
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câ=OMMO= = = =
= câ=OMMP= = = OQMKMMMIMM= = OORKMMMIMM= NQKPMMIMM= = PRKPMMIMM= QSKPNOIMM= = TSKPOQIMM=
=
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= = = aáÑÑÉêÉåò=Z=PSKMNOIMM=
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sÉê®åÇÉêìåÖ=áå=B= =
PSKMNOI MM ⋅ NMM = NNIVU=B= PMMKSNOI MM
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âìêòÑêáëíáÖÉ=pÅÜìäÇÉå=
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a~ë= råíÉêåÉÜãÉå= áëí= ~äëç= åáÅÜí= áå= ÇÉê= i~ÖÉ= ëÉáåÉ= âìêòÑêáëíáÖÉå= pÅÜìäÇÉå= ãáí= ÇÉå= ÑäΩëëáÖÉå=jáííÉäå=òì=ÇÉÅâÉåK= =
378
E. Aufgaben
^ìÑÖ~ÄÉ=Q= =
^=
=========_áä~åò=
^s= rs= káÅÜí= ÇìêÅÜ= báÖÉåâ~éáJ í~ä=ÖÉÇÉÅâíÉê=cÉÜäÄÉíê~Ö=
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m=
PRMKMMMIMM= câ= OMMKMMMIMM= =
SRMKMMMIMM= =
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= få= ÇáÉëÉã= c~ää= ΩÄÉêëíÉáÖí= ÇÉê= tÉêí= ÇÉë= cêÉãÇâ~éáí~äë= ÇÉå= ÇÉë= dÉë~ãíîÉêã∏ÖÉåë= E^sHrsFK=a~ÇìêÅÜ=łêìíëÅÜí =Ç~ë=báÖÉåâ~éáí~ä=~ìÑ=ÇáÉ=^âíáîëÉáíÉ=EåÉÖK=báÖÉåâ~éáí~äFK= bë= äáÉÖí= ÉáåÉ= ëçÖK= råíÉêÄáä~åò= îçêK= fã= mêáåòáé= ï®êÉ= ~äëç= ëçÖ~ê= Ç~ë= báÖÉåâ~éáí~ä= ÑêÉãÇ=Ñáå~åòáÉêíK= aáÉ=ëçÖK=łÖçäÇÉåÉ=oÉÖÉä =ÄÉë~Öí=~ÄÉêW=wìãáåÇÉëí=ä~åÖÑêáëíáÖÉ=^åä~ÖÉå=E^sF=ëçääíÉå= ãáí=báÖÉåâ~éáí~ä=çÇÉê=òìê=kçí=~ìÅÜ=ãáí=ä~åÖÑêáëíáÖÉå=cêÉãÇâ~éáí~ä=Ñáå~åòáÉêí=ëÉáåK= = ^ìÑÖ~ÄÉ=R= =
bêÑçäÖ=mÉêáçÇÉ=N=Z= OOMKMMMIMM=Ó=NUMKMMMIMM== Z=
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táÉ= ~åÜ~åÇ= ÇÉë= îçêäáÉÖÉåÇÉå= w~ÜäÉåã~íÉêá~äë= ëÉÜê= Öìí= òì= ÉêâÉååÉå= áëíI= ÖÉÜí= ÄÉá= ÇÉê=êÉáåÉå=_Éíê~ÅÜíìåÖ=ÇÉë=dÉë~ãíÉêÑçäÖÉë=EmÉêáçÇÉ=N=Äáë=PF=ÇáÉ=fåÑçêã~íáçå=ΩÄÉê= ÇÉå=sÉêäìëí=áå=ÇÉê=mÉêáçÇÉ=O=âçãéäÉíí=îÉêäçêÉåK=dä®ìÄáÖÉê=ìåÇ=~åÇÉêÉ=fåíÉêÉëëÉåëJ ÖêìééÉå=ïΩêÇÉå=ÇáÉ=båíïáÅâäìåÖ=ÇÉë=råíÉêåÉÜãÉåë=~äë=ÇìêÅÜÖÉÜÉåÇ=éçëáíáî=ÉáåJ ëÅÜ®íòÉåK= rã= ÇáÉëÉ= łq®ìëÅÜìåÖ = òì= îÉêÜáåÇÉêåI= ëÅÜêÉáÄí= ÇÉê= dÉëÉíòÖÉÄÉê= ÉáåÉ= à®ÜêäáÅÜÉ= bêJ ãáííäìåÖ=ÇÉë=bêÑçäÖÉë=îçêK== = ^ìÑÖ~ÄÉ=S= =
=
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= aáëí~åòêÉÅÜåìåÖ= =
2. Lösungen
379
câJ^_=Z=
PMKMMMI MM ⋅ NMM =Z=PMMKMMMIMM== NM
=
aáÉ= pìããÉ= ~ìë= bâ= ìåÇ= câ= ÉêÖáÄí= Ç~ë= áå= ÇÉê= bê∏ÑÑåìåÖëÄáä~åò= ~ìëÖÉïáÉëÉåÉ= dÉJ ë~ãíâ~éáí~ä= ÄòïK= Ç~ë= dÉë~ãíîÉêã∏ÖÉå= ERQMKMMMIMM= bìêçFK= aáÉ= aáÑÑÉêÉåò= ~ìë= dÉJ ë~ãíîÉêã∏ÖÉå=ìåÇ=^åä~ÖÉîÉêã∏ÖÉå=EQMMKMMMIMM=bìêçF=äáÉÑÉêí=Ç~åå=ëÅÜäáÉ≈äáÅÜ=ÇÉå= ÖÉëìÅÜíÉå=tÉêí=Éë=rãä~ìÑîÉêã∏ÖÉåëK= =
^=
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báÖÉåâ~éáí~ä= i~åÖÑêK=_~åâîÉêÄK= sÉêÄáåÇäK=~K=ii= = =
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380
E. Aufgaben
p=
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=====RMMIMM==
bê∏ÑÑåìåÖëÄáä~åòâçåíç=
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báÖÉåâ~éáí~ä=
bê∏ÑÑåìåÖëÄáä~åòâçåíç=
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bê∏ÑÑåìåÖëÄáä~åòâçåíç=
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OPKRMMIMM== ==TKMMMIMM==
2. Lösungen
381
ÅF= _ìÅÜìåÖëë®íòÉW= NK=dÉëÅÜ®Ñíë~ìëëí~ííìåÖ=
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sÉêÄáåÇäáÅÜâK=~ìë=ii=
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OK=sÉêÄáåÇäáÅÜâK=~ìë=ii=
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382
E. Aufgaben
^ìÑÖ~ÄÉ=NM=
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~F= p=
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e=
^_=
ORKMMMIMM= Á=
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aìêÅÜ= ÇáÉ= dÉëÅÜ®ÑíëîçêÑ®ääÉ= áã= i~ìÑÉ= ÇÉë= g~ÜêÉë=áëí=åìå=ÇÉê=c~ää=ÉáåÖÉíêÉíÉåI=Ç~ëë=ëáÅÜ= ÇÉê= p_= ÇÉë= hçåíçë= cçêÇÉêìåÖÉå= ~ìÑ= kìää= bìêç= ÄÉä®ìÑíK= bë= ÖáÄí= Ç~ÜÉê= âÉáåÉå= ^ÄJ ëÅÜäìëëÄìÅÜìåÖëë~íòK= wìÇÉã= áëí= òì= ÄÉãÉêJ âÉåI= Ç~ëë= ÇáÉëÉë= hçåíç= åìå= ~ìÅÜ= åáÅÜí= ãÉÜê=áå=ÇÉê=pÅÜäìëëÄáä~åò=~ìÑí~ìÅÜíK=
OUKMMMIMM=
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a~= ÇáÉ= ^ÄÄìÅÜìåÖÉå= îçã= _~åââçåíç= ÇáÉ= e∏ÜÉ= ÇÉê= báåä~ÖÉå= ΩÄÉêëíÉáÖÉåI âçããí= Éë= òì=ÉáåÉã=åÉÖ~íáîÉå=_Éëí~åÇK=a~ÇìêÅÜ=â~åå= Ç~ë= _~åââçåíç= åáÅÜí= ïÉáíÉê= ~äë= ~âíáîÉê= _áä~åòéçëíÉå= ÖÉÑΩÜêí= ïÉêÇÉåK= aÉê= = pÅÜäìëëÄÉëí~åÇ= ÇÉë= hçåíçë= ïáêÇ= Ç~ÜÉê= ~ìÑ= Ç~ë= m~ëëáîâçåíç= łhìêòÑêáëíáÖÉ= _~åâîÉêÄáåÇJ äáÅÜâÉáíÉå =ÖÉÄìÅÜíK=
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_ìÅÜìåÖëë~íòW= _~åâ= TKOQMIMM=
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bê∏ÑÑåìåÖ=ÇÉë=hçåíçë=łh~ëëÉ W=^åÑ~åÖëÄÉëí~åÇ=RKPMMIMM=
ÄF= NK=
h~ëëÉ=
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h~ëëÉ==
PKMMMIMM= QKRMMIMM=
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PKMMMIMM= QKRMMIMM==
OK= sÉêâ~ìÑ=ÉáåÉê=ÖÉÄê~ìÅÜíÉå=cÉêíáÖìåÖëã~ëÅÜáåÉW=sÉêâ~ìÑëÉêä∏ë=QKRMMIMM=
2. Lösungen
383
ÇF= NK= dÉëÅÜ®Ñíë~ìëí~ííìåÖ=NKRMMIMM= =
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h~ëëÉ=
NKRMMIMM=
OK= _~êâ~ìÑ=ÉáåÉë=åÉìÉå=^âíÉåëÅÜê~åâëW=báåâ~ìÑëéêÉáë=NKRMMIMM=K=
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ÄF== p=
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aáÉ=_ìÅÜìåÖ=ÇÉë=dÉïáååë=ÑΩÜêí=òì=ÉáåÉê=píÉáÖÉêìåÖ=ÇÉë=báÖÉåâ~éáí~äëK== Em~ëëáîâçåíçW=wìå~ÜãÉ=áã=e~ÄÉåF= =
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B=
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bìêç= NTKRVMIMM=
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NPKRMMIMM=
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=
PIR=
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bìêç= SKPQMIMM=
PQMIMM=
SKMMMIMM=
ONMIMM=
SKONMIMM=
384
E. Aufgaben
òì=~F== aÉê=wbm=ÉåíëéêáÅÜí=ÄÉá=ÇÉê=_ÉêÉÅÜåìåÖ=ÇÉë=ibm=NMM=B=Ó=NP=B=Z=UT=BK=jáíJ íÉäë= aêÉáë~íòêÉÖÉäìåÖ= ìåÇ=aáÑÑÉêÉåòÄáäÇìåÖ= â∏ååÉå= ~ääÉ= ïÉáíÉêÉå= ÑÉÜäÉåÇÉå= tÉêíÉ=ÉêãáííÉäí=ïÉêÇÉåK= òì=ÄF==_wh= ìåÇ= o~Ä~íí= ëáåÇ= ΩÄÉê= aáÑÑÉêÉåòÉåI= mêçòÉåíïÉêíÉ=ΩÄÉê= ÇÉå= aêÉáë~íò= òì= ÄÉëíáããÉåK= òì=ÅF== aáÉ=_wh=áå=e∏ÜÉ=îçå=ONMIMM=bìêç=ÉåíëéêÉÅÜÉå=PIR=BK=jáí=eáäÑÉ=ÇÉë=aêÉáë~íJ òÉë=ëáåÇ=Ç~åå=bm=ìåÇ=wbm=ÉáåÑ~ÅÜ=òì=ÉêêÉÅÜåÉåK== =
^ìÑÖ~ÄÉ=NQ= aáÉ=spí=áëí=~ìÑ=ÇÉå=kÉííçï~êÉåïÉêí=EwbmF=ìåÇ=~ìÅÜ=~ìÑ=ÇáÉ=_wh=òì=ÄÉêÉÅÜåÉåK= =
~F= SMMM= =
SMMN=
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OQKTRMIMM=
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^ìÑÖ~ÄÉ=NR= ~F= _êìííçëâçåíçW=RMIPM: NMM ⋅ NNV=Z=RVIUS= rpíJhçêêÉâíìêW=RVIUS=Ó=RMIPM=Z=VIRS= §ÄÉêïÉáëìåÖëÄÉíê~ÖW=PKQRMIMM=Ó=RVIUS=Z=PKPVMINQ= pâçåíç=áå=BW=RVIUS ⋅ NMM : PKQRMIMM=Z=NITQ=B= ÄF= kÉííçëâçåíçW=PQIRM : NNV ⋅ NMM=Z=OUIVV= rpíJhçêêÉâíìêW=PQIRM=Ó=OUIVV=Z=RIRN= oÉÅÜåìåÖëÄÉíê~ÖW=PQIRM ⋅ NMM : P=Z=NKNRMIMM= §ÄÉêïÉáëìåÖëÄÉíê~ÖW=NKNRMIMM=Ó=PQIRM=Z=NKNNRIRM= ÅF= kÉííçëâçåíçW=NOIOM : NV ⋅ NMM=Z=SQION= _êìííçëâçåíçW=NOIOM=H=SQION=Z=TSIQN= oÉÅÜåìåÖëÄÉíê~ÖW=QKPPQIMR=H=TSIQN=Z=QKQNMIQS= pâçåíç=áå=BW=TSIQN ⋅ NMM : QKQNMIQS=Z=NITP=B= = ^ìÑÖ~ÄÉ=NS= ~F= SMOM=
RKNTNIOR=
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SMON=
NOSIMR=
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NKMMSIQV==
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SKPMPITV=
2. Lösungen
385
=
tÉêí=~ìÑ=hçåíç=SMOM=Z=ERMM=ä ⋅ NMIRM=bìêçLäF=Ó=NIRM=B==
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tÉêí=~ìÑ=hçåíç=SMON=Z=kÉííçïÉêí=ÇÉê=_wh=Z=NRMIMM: NNV ⋅ NMM==
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386
E. Aufgaben
ÅF= QQMM=
QROIPV=
~å=
SMOM=
ONSIMM=
ER=B=îK=QKPOMIMMF= EQ=B=îK=EQKPOM=Ó=ONSFF=
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RKQTVIVR= = QROIPV= =
Z==oÉëíëÅÜìäÇ= Ó==pâçåíçI=åÉ= Ó==píÉìÉêâçêêÉâíìê=
RKMOTIRS== = UQIRM== Z=EO=B=îK=RKMOTIRSF: NNV ⋅ NMM= NSIMR== Z=NV=B=îK=UQIRM=
Z==§ÄÉêïÉáëìåÖ= =
QKVOTIMN== =
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QQMM=
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RKMOTIRS=
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QKVOTIMN=
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SMOO=
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NSIMR=
ÉF= = = ^_= H== wìÖ~åÖ=MPKMQK= H== wìÖ~åÖ=NNKMTK= H== wìÖ~åÖ=MQKNOK= H== _wh= Ó== k~ÅÜä~ëë= Ó== p_=
NOKMMMIMM== PKUMMIMM== RKVRMIMM== QKNMQIMM= UORIMM= PVPISS= PKTPNIPQ=
Z== sÉêÄê~ìÅÜ=
Z=SMM=qçååÉå ⋅ OMIMM=bìêçLqçååÉ= = = Z=QKPOMIMM=Ó=ONSIMM== Z=POMIMM=H=OURIMM=H=OOMIMM== Z=NQRIMM=H=NSQINS=H=UQIRM== =
OOKRRQIMM= =
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UMNM=
PKTPNIPQ=
~å=
OMOM=
PKTPNIPQ=
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SMOM= =
ÑF= p=
UKOSUISS=
===OMOM=
UMMM= NOKMMMIMM =
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→=_Éëí~åÇëãáåÇÉêìåÖ=Z=UKOSUISS==
^_=Z=NOKMMMIMM===[==p_=Z=PKTPNIPQ=
NOKMMMIMM
UMNM= SMOM=
= = = = =
= =
~å=
OMOM=
UKOSUISS=
e= = p=
=============SMOM=
e=
PKTPNIPQ= = QQMM= UKOSUISS= = QQMM=
PKUMMIMM RKVRMIMM
QQMM= SMOO=
ONSIMM= PVPISS=
NOKMMMIMM= = QQMM= = = SMOM= = = OMOM=
QKPOMIMM UORIMM UKOSUISS
UMOM= = =
OOKRRQIMM= = =
=
OPKNSPISS=
= = =
OPKNSPISS
2. Lösungen
387
p=
==SMON=
e= = p=
=============SMOO=
e=
Á= QQMM= QQMM=
POMIMM= SMOM= OURIMM= = OOMIMM= =
UORIMM= = SMOM= = = = = = =
PVPISS= Á= = QQMM= = QQMM=
NQRIMM= NSQINS= UQIRM=
=
UORIMM= =
UORIMM= = =
PVPISS= =
PVPISS=
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RKRMMIMM=
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NKMQRIMM==
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SKRQRIMM=
PKOMMIMM=
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PKOMMIMM=
NKOMMIMM= OOUIMM=
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NKQOUIMM=
RMMIMM=
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RMMIMM=
OVIUP= RIST==
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OUUM=
PRIRM=
NMMIMM= NVIMM==
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ÄF= STMM= =
ÅF= SNQM= = OSMM= =
ÇF= STMM= =
ÉF= SMPM= = OSMM= =
ÑF= SUMM= = OSMM= =
wì= ÉFW= _Éá= _Éí~åâìåÖëîçêÖ®åÖÉå= áëí= áå= ÇÉê= oÉÖÉä= E~ÄÖÉëÉÜÉå= îçå= w~ÜäìåÖÉå= éÉê= pÅÜÉÅâ=çÇÉê=hêÉÇáíâ~êíÉF=îçå=_~êò~ÜäìåÖÉå=~ìëòìÖÉÜÉåK=aÉê=nìáííìåÖëÄÉíê~Ö=áëí=~äJ ëç= áããÉê= ~äë= Äêìííç= òì= ÄÉíê~ÅÜíÉåK= ^äíÉêå~íáî= â~åå= ÇáÉ= sÉêÄìÅÜìåÖ= ÇÉë= ^ìÑï~åÇë= ~ìÅÜ=~ìÑ=ÇÉã=hçåíç=SMRM=Ó=^ìÑïÉåÇìåÖÉå=ÑΩê=båÉêÖáÉ=îÉêÄìÅÜí=ïÉêÇÉåK= =
^ìÑÖ~ÄÉ=OM= ~F= = = = = =
dÉÜ~äíëò~ÜäìåÖ= = SPMM= NKORMIMM= = = = =
~å= = =
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NKORMIMM== NPTIRM== NOIMM== SIOR== NONIUU== QMISP== UMISP== NMISP== UQMIQU==
=
=
388
E. Aufgaben
=
^d^=J=pçòá~äîÉêëáÅÜÉêìåÖW= =
=
SQNM=
ORPITT=
~å=
QUQM=
ORPITT=
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NRRITR=
~å=
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NRRITR=
RMTIRQ=
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RMTIRQ=
^ìÑÖ~ÄÉ=ON= ~F= OSRM= NKMMMIMM=
~å=
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E^k^=H=^d^F=
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Ó==^k^=J=pçòá~äîÉêëáÅÜÉêìåÖÉå=
UPMIMM==
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NKMMMIMM==
Z==kÉííçäçÜå=
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SOMM= = = =
PKSVMIMM= = = =
~å= = = =
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NKQTMIMM= PVMIMM= UPMIMM= NKMMMIMM=
SQMM=
=
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ÄF= aáÉ= _Éáíê®ÖÉ= òìê= _ÉêìÑëÖÉåçëëÉåëÅÜ~Ñí= ïÉêÇÉå= ~ìÑ= ÇÉã= ^ìÑï~åÇëâçåíç= SQOM= Ewìå~ÜãÉ= áã= pçää>F= ÉêÑ~ëëíI= ïÉäÅÜÉë= ~ã= g~ÜêÉëÉåÇÉ= ΩÄÉê= Ç~ë= dìsJhçåíç= ~ÄJ ÖÉëÅÜäçëëÉå=ïáêÇK=aáÉë=ÄÉÇÉìíÉíI=Ç~ëë=àÉÇÉ=_ìÅÜìåÖ=ÇáÉëÉê=^êí=Ç~ë=_ÉíêáÉÄëÉêJ ÖÉÄåáë= ÄòïK= ÇÉå= dÉïáåå= ÇÉë= råíÉêåÉÜãÉåë= ãáåÇÉêí= E^ìÑï~åÇëâçåíÉå= ÉêJ ëÅÜÉáåÉå=ÄÉá=^ÄëÅÜäìëë=áã=pçää=ÇÉë=dìsJhçåíçëFK=a~=Éë=ëáÅÜ=ÄÉáã=hçåíç=dìs= ìã= Éáå= råíÉêâçåíç= ÇÉë= báÖÉåâ~éáí~äë= Ü~åÇÉäíI= ÄÉïáêâí= ÉáåÉ= ^ìÑï~åÇëÄìÅÜìåÖ= ÖäÉáÅÜòÉáíáÖ= ÉáåÉ= báÖÉåâ~éáí~äãáåÇÉêìåÖ= E^Äå~ÜãÉ= ÇÉë= báÖÉåâ~éáí~äë= áã= pçääI= Ç~=Éë=ëáÅÜ=ìã=Éáå=m~ëëáîâçåíç=Ü~åÇÉäí>FK= =
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wìê=sÉêÇÉìíäáÅÜìåÖ=ëçää=ÇáÉ=å~ÅÜÑçäÖÉåÇÉ=dê~Ñáâ=ÇáÉåÉåK=bë=ïáêÇ=Ç~îçå=~ìëÖÉJ Ö~åÖÉåI=Ç~ëë=áã=råíÉêåÉÜãÉå=âÉáåÉ=~åÇÉêÉå=^ìÑïÉåÇìåÖÉå=ìåÇ=bêíê®ÖÉ=~åÖÉJ Ñ~ääÉå= ëáåÇI= ìã= ëç= ÇáÉ= ^ìëïáêâìåÖ= ÇáÉëÉê= ÉáåÉå= _ìÅÜìåÖ= ~ìÑ= Ç~ë= báÖÉåâ~éáí~ä= ÄÉëëÉê=Ç~êòìëíÉääÉåK=
2. Lösungen
389
^=
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m=
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PKQRMIMM=
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= =
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aêÉáë~íò=→ ism=Z=QNM ⋅ NMM : S=Z=SKUPPIPP= ^ìÑÖ~ÄÉ=OR= ~F= OQMM= =
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sçã=wsm=áëí=ÇÉê=o~Ä~íí=ÄÉêÉáíë=~ÄÖÉòçÖÉåI=ëç=Ç~ëë=ÇÉê=tÉêí=~ìÑ=RMMM=Z=PKQRMIMM= H=PMMIMM=Z=PKTRMIMM=áëíK=
=
ÄF= SMQM= = =
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390
E. Aufgaben
ÅF= RMMM= =
PQMIMM=
QUMM=
SQISM==
= ~å=
OQMM=
QMQISM=
OQMM=
NKMTMIMM=
=
ÇF= RMMM=
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NTMIUQ==
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NKQRMIMM= =
OVMIMM= Z=NKQRMIMM : NMM ⋅ OM=
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NRNIPM= Z=NKTQMIMM : VO ⋅ U=
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a~=ÇÉê=hìåÇÉ=åìê=ÉáåÉ=jÉåÖÉ=îçå=NM=píΩÅâ=ÄÉòáÉÜíI=ïáêÇ=òìã=ism=îÉêâ~ìÑíK=
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OQMM= OOKRQUINO=
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2. Lösungen
391
^ìÑÖ~ÄÉ=OU= ~F= OQMM=
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EURMIMM=Ó=R=BF=
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ÄF==pâçåíç=áå=B=Z=NMM=Ó=ENKNQNINP ⋅ NMM : NKNSQIQOF=Z=O=B= =
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_sm=Z=UPPIMM : NMM ⋅ VR=Z=TVNIPR=
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dÉïáåå=áå=bìêç=Z=TVNIPR==Ó=RTSITM=Z=ONQISR=
=
==================
dÉïáåå=áå=B=Z=ONQISR ⋅ NMM : RTSITM=Z=PTIOO=B=
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aÉê=dÉïáåå=ïΩêÇÉ=~äëç=îçå=QM=B=~ìÑ=PTIOO=B=ÇÉê=pÉäÄëíâçëíÉå=ëáåâÉåK= =
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tÉêí=~ìÑ=QUMM=Z=ENSINR=H=PIQOF: NMM ⋅ NV=Z=PITO==
= = = = =
=
392
E. Aufgaben
^ìÑÖ~ÄÉ=OV= =
p=
hçåíç=ROMM=
e=
OOMM=
NNKRMMIMM== ONMM=
POKMMMIMM=
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2. Lösungen
393
^ìÑÖ~ÄÉ=PN= ~F= =
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PMIMM== Z=PRITM : NNV ⋅ NMM=
NTKNVMIMM==
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PKOSSINM==
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=
394
E. Aufgaben
ÄF= oÉÅÜåìåÖë~ìëÖäÉáÅÜW= =
QQMM=
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pâçåíç=EåÉííçFI=ÖÉë~ãí=Z=OIR=B=NTKNVMIMM=Z=QOVITR=
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píÉìÉêâçêêÉâíìê=Z=NV=B=îK=QOVITR=Z=UNISR== =
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NMMIMM=
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2. Lösungen
=
395
_Éáã=báåâ~ìÑ=ÇÉê=i~ãéÉ=ÜáåÖÉÖÉå=áëí=ÇáêÉâí=Éáå=^ìÑï~åÇëâçåíç=ÄÉíêçÑÑÉåI=ïÉäJ ÅÜÉë= ÄÉá= ^ÄëÅÜäìëë= ΩÄÉê= ÇáÉ= dìsJoÉÅÜåìåÖ= ÇÉå= dÉïáåå= ÇÉë= råíÉêåÉÜãÉåë= ãáåÇÉêíK=
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ÄF= SNSM= =
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^ääÉ=êÉÖÉäã®≈áÖ=~ìÑíêÉíÉåÇÉå=oÉé~ê~íìêÉå=EÉêÑçêÇÉêäáÅÜ=ÇìêÅÜ=ÖÉï∏ÜåäáÅÜÉ=^ÄJ åìíòìåÖF=ïÉêÇÉå=ëçÑçêí=~äë=^ìÑï~åÇ=ÖÉÄìÅÜíK=
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aÉê=_ìÅÜïÉêí=~ìÑ=ÇÉã=hçåíç=MUQM=ä®ëëí=ëáÅÜ=~ìë=ÇÉã=~ääÖÉãÉáåÉå=_ìÅÜÑΩÜêìåÖëJ éêáåòáé=łpìããÉ=ÇÉê=pçääÄìÅÜìåÖÉå=Z=pìããÉ=ÇÉê=e~ÄÉåÄìÅÜìåÖÉå =~ÄäÉáíÉåK=aáÉ= píÉìÉê=â~åå=~ìë=ÇÉã=ÖÉÖÉÄÉåÉå=_êìííçîÉêâ~ìÑëéêÉáë=ÉêêÉÅÜåÉí=ïÉêÇÉåK= =
^ìÑÖ~ÄÉ=PS= ~F= wáÉäâ~ìÑ=ÇÉë=åÉìÉå=jçÇÉääëW= =
MTSM=
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396
E. Aufgaben
^ìÑä∏ëìåÖ=ÇÉë=fåíÉêáãëâçåíçë= =
RQNM=
=
=
UKPQMIMM= =
~å=
MTSM=
UKONMIMM=
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RQSM=
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~å=
QOMM=
OMKMMMIMM=
OUMM=
PMKNMTIMM=
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ÄF= OUMM=
OMKMMMIMM=
= ^ìÑÖ~ÄÉ=PT= ~F= MTOM= =
ORKPMMIMM=
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QKUMTIMM=
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H==jçåí~ÖÉ=
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H==qê~åëéçêí=
RTMIMM==
H==báÖÉåäÉáëíìåÖ=
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Z==^åëÅÜ~ÑÑìåÖëâçëíÉå=
OSKURMIMM==
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ÅF= SNSM= =
PKMMMIMM=
OSMM=
RTMIMM=
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PKRTMIMM=
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= cj= H==ci= H==pbhcb=
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OMMIMM== PMMIMM== OMIMM==
Z==trd=åK=eo= H==jdh=NR=B= H==cdh=NM=B=
= = =
ROMIMM== PMIMM== PMIMM==
Z==trd=åK=bpío= H==stdh=P=B=
= =
RUMIMM== NTIQM==
Z==tld=åK=eo=ìK=bpío=
=
RVTIQM===
2. Lösungen
397
ÄF= MTSM=
RUMIMM=
~å=
RPMM=
RUMIMM=
=
=
a~ãáí=ÇÉê=ëíÉìÉêéÑäáÅÜíáÖÉ=dÉïáåå=ã∏ÖäáÅÜëí=åáÉÇêáÖ=~ìëÖÉïáÉëÉå=ïáêÇI=ëçääíÉ=áå= ÇÉê= píÉìÉêÄáä~åò= ã∏ÖäáÅÜëí= ïÉåáÖ= ~âíáîáÉêí= ïÉêÇÉå= Etrd= åK= bpíoFK= a~ÇìêÅÜ= ëíÉÜí=ÇÉå=ÄÉêÉáíë=áã=dìsJhçåíç=ÖÉÄìÅÜíÉå=^ìÑïÉåÇìåÖÉå=Éáå=ÖÉêáåÖÉêÉê=bêíê~Ö= ÖÉÖÉåΩÄÉêK=aÉê=dÉïáåå=Ñ®ääí=åáÉÇêáÖÉê=~ìëK=
=
^ìÑÖ~ÄÉ=PV= ~F= wáåë~ìÑï~åÇW= =
TRNM=
ORMIMM=
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NMKMMMIMM== UMMIMM== NRMIMM== OQRIMM==
Z==îçêä®ìÑáÖÉ=^â=
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ÄF=
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PMMIMM== QMMIMM== NQMIMM==
= = îçêä®ìÑáÖÉ=^â= = Ó==mêÉáëå~ÅÜä~ëë= = Ó==pâçåíç=
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Z==báÖÉåäÉáëíìåÖ=
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398
E. Aufgaben
hêÉÇáíòáåëÉå=E^ìÑï~åÇF=
Ó=ORMIMM==
báÖÉåäÉáëíìåÖ=Ebêíê~ÖF=
H=UQMIMM==
dÉïáååëíÉáÖÉêìåÖ=
H=RVMIMM==
=
^ìÑÖ~ÄÉ=QM= NK= hìêëïÉêí=Z=PM=píΩÅâ ⋅ QMIMM=Z=NKOMMIMM=bìêç= OK== hìêë=Z=NKQRMIMM : VM=píΩÅâ=Z=NSINN=bìêç= PK==== kÉååïÉêí= hìêëïÉêí=
hìêëîÉêäìëí=
=
NRKMMMIMM= = NPKQTMIMM= =
NKRPMIMM= hìêë=Z=NMM=Ó=ENKRPM ⋅ NMM : NRKMMMIMMF=Z=UVIUM=B=
a~= Éë= ëáÅÜ= ìã= ÉáåÉå= hìêëîÉêäìëí= Ü~åÇÉäíI= ãìëë= ÇÉê= ~âíìÉääÉ= hìêë= ìåíÉê= NMM= B= äáÉÖÉåK=bë=ïáêÇ=~äëç=ÉáåÑ~ÅÜ=ÇÉê=éêçòÉåíì~äÉ=^åíÉáä=ÇÉë=sÉêäìëíÉë=~ã=kÉååïÉêí= îçå=NMM=~ÄÖÉòçÖÉåK=_Éá=ÉáåÉã=ÉåíëéêÉÅÜÉåÇÉå=hìêëÖÉïáåå=ï®êÉ=ÇÉê=mêçòÉåíJ ïÉêí=òì=NMM=òì=~ÇÇáÉêÉåK=
QK===kÉååïÉêí=Z=QKTTMIRMIMM: NMNIRM ⋅ NMM=Z=QKTMMIMM=bìêç= RK===hìêëïÉêí=Z=OTKMMMIMM : NMM ⋅ NMP=Z=OTKUNMIMM=bìêç= =
dÉë~ãíïÉêí=ÇÉë=aÉéçíë=Z=hìêëïÉêí=N=H=hìêëïÉêí=O=H=Á=H=hìêëïÉêí=R=Z=QUKTMMIRM== =
^ìÑÖ~ÄÉ=QN= ~F= OTOM= ÄF= = = =
=
RKQTMIMM=
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= hìêëïÉêí= H== N=B=péÉëÉå=
RKQNRIUQ== ENMM=BF= RQINS== EN=BF=
Z== _~åâä~ëíëÅÜêáÑí= =
RKQTMIMM== ENMN=BF=
=
hìêëïÉêí=Z=RKQTMIMM : NMN ⋅ NMM=Z=RKQNRIUQ=bìêç=
=
píΩÅââìêë=Z=RKQNRIUQ : NRM=Z=PSINN=bìêç=
=
^ìÑÖ~ÄÉ=QO= ~F== = hìêëïÉêí= H==N=B=péÉëÉå=
VQRIMM== Z=VM ⋅ NMIRM== ORIMM== N=B=îçã=htGX=ãáåÇK=ORIMM==
Z==_~åâä~ëíëÅÜêáÑí=Ebáåâ~ìÑF= H==dÉïáåå=
VTMIMM== = RNMIMM== =
Z==_~åâÖìíëÅÜêáÑí=EsÉêâ~ìÑF=
NKQUMIMM= =
=
= =
G=N=B=îK=ht=Z=VIQR=bìêç →=péÉëÉå=ãáåÇK=ORIMM=bìêç
2. Lösungen
=
399
= hìêëïÉêí= =Ó==N=B=péÉëÉå=
NKRMRIMM== NMM=B= ORIMM== N=B=îçã=htGX=ãáåÇK=ORIMM==
Z==_~åâÖìíëÅÜêáÑí=EsÉêâ~ìÑF=
NKQUMIMM== VV=B=
=
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=
G=péÉëÉå=Z==NKQUMIMM: VV ⋅ N=Z=NQIVR → péÉëÉå=ãáåÇK=ORIMM=bìêç
=
sÉêâ~ìÑëâìêë=Z=NKRMRIMM: VM=píΩÅâ=Z=NSITO=bìêçLpíK=
=
ÄF==h~ìÑW= =
OTOM=
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sÉêâ~ìÑW=
=
OUMM=
=
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VTMIMM=
~å=
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NKQUMIMM=
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^ìÑÖ~ÄÉ=QP= ~F==wáåë~åëéêìÅÜ=ÇÉë=sÉêâ®ìÑÉêë=EMNKNOK=J=OMKMPKF=Z=
=
wáåë~åëéêìÅÜ=ÇÉë=h®ìÑÉêë=EONKMPK=J=PMKNNKF=Z=
ÄF=
TKMMMI MM ⋅ U ⋅ NNM =Z=NTNINN== NMM ⋅ PSM
TKMMMI MM ⋅ U ⋅ ORM =Z=PUUIUV== NMM ⋅ PSM
= = hìêëïÉêí= H==wáåë~åëéêìÅÜ=ÇÉë=sÉêâ®ìÑÉêë=
TKNQMIMM== Z=TKMMMIMM : NMM ⋅ NMO= NTNINN== =
Z==~ìëã~ÅÜÉåÇÉê=_Éíê~Ö=
TKPNNINN== =
=
^ìÑÖ~ÄÉ=QQ= ~F== = hìêëïÉêí= H==wáåë~åëéêìÅÜ=ÇÉë=sÉêâ®ìÑÉêë=
NRKRORIMM== Z=NRKMMMIMM : NMM ⋅ NMPIR= VQSIUU= =
Z==~ìëã~ÅÜÉåÇÉê=_Éíê~Ö= H==péÉëÉå= H==_ìÅÜìåÖëÖÉÄΩÜê=
NSKQTNIUU= = TTISP= Z=MIR=B=îK=htX=ãáåÇK=ORIMM== RIRM= =
Z==_~åâä~ëíëÅÜêáÑí=
NSKRRRIMN= =
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wáåë~åëéêìÅÜ=ÇÉë=sÉêâ®ìÑÉêë=EMNKMUK=J=MPKMSKF=Z=
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NTKNMOITR= NSKRRRIMN= RQTITQ=
NRKMMMI MM ⋅ TIR ⋅ PMP =Z=VQSIUU== NMM ⋅ PSM
400
E. Aufgaben
= hìêëïÉêí= H==wáåë~åëéêìÅÜ=ÇÉë=sÉêâ®ìÑÉêë=
NTKNMMIMM== Z=URIRM ⋅ MIR : NMM= VPITR== =
Z==~ìëã~ÅÜÉåÇÉê=_Éíê~Ö= Ó= péÉëÉå= Ó= _ìÅÜìåÖëÖÉÄΩÜê=
NTKNVPITR== = URIRM== = RIRM== =
Z==_~åâÖìíëÅÜêáÑí=
NTKNMOITR== =
=
=
hìêë=Z= NTKNMM ⋅ NMM =Z=NNQ=B= NRKMMM
= ^ìÑÖ~ÄÉ=QR= ~F=
= = hêÉÇáí= H==wáåë=EêÉäK=wáåëë~íò=Z=QIRBF=
QRKMMMIMM== OKMORIMM==
ENMMIMM=BF= EQIRM=BF=
Z==oΩÅâò~ÜäìåÖ=
QTKMORIMM==
ENMQIRM=BF=
=
=
êÉäK=wáåëë~íò=Z=ES ⋅ VF : NO=Z=QIR=B= =
=
OUMM=
QQKRRMIMM=
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TRVM=
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= ~å=
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=
=
tÉêí=~ìÑ=OUMM=Z=VV=B=îK=QRKMMMIMM=bìêç=
=
ÄF= QOMM= =
QRKMMMIMM=
TRNM=
OKMORIMM=
~å=
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QTKMORIMM=
=
ÅF= hêÉÇáíâçëíÉå=ÑΩê=V=jçå~íÉ=Z=QRMIMM=H=OKMORIMM=Z=OKQTRIMM=bìêç= =
=
ÉÑÑÉâíáîÉ=sÉêòáåëìåÖ=Z=
OKQTRI MM ⋅ NMM ⋅ NO =Z=TIQN=B= QQKRRMI MM ⋅ V
=
^ìÑÖ~ÄÉ=QS= ~F= OQMM= = =
UOQIUR=
~å=
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wáåëÉå=Z=NNIR=B=îK=SKRMMIMM=Z=TQTIRM=bìêç=
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j~ÜåëéÉëÉå=Z=N=B=îK=SKRMMIMM=Z=SRIMM=bìêç=
=
rpí=Z=NV=B=îK=SRIMM==Z=NOIPR=bìêç= =
=
kìê=ÇáÉ=j~ÜåëéÉëÉå=ëáåÇ=ìãë~íòëíÉìÉêéÑäáÅÜíáÖK=páÉ=ÖÉäíÉå=~äë=kÉÄÉåÑçêÇÉêìåÖK= =
=
2. Lösungen
401
ÄF= TRNM=
TQTIRM=
=
STRM=
SRIMM=
=
OSMM=
NOIPR=
= ~å=
QQMM=
UOQIUR=
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SPKMMMIMM=
=
^ìÑÖ~ÄÉ=QT= ~F= SMUM=
ROKVQNINU=
=
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NMKMRUIUO==
~å=
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aÉê= _~åââêÉÇáí= ÉåíëéêáÅÜí= ÇÉã= §ÄÉêïÉáëìåÖëÄÉíê~Ö= å~ÅÜ= ^ÄòìÖ= ÇÉë= pâçåíçëI= ÇKÜK=ÖÉå~ì=VTIR=BK=aáÉ=ÖÉë~ãíÉ=sÉêÄáåÇäáÅÜâÉáí=ÉêêÉÅÜåÉí=ëáÅÜ=Ç~ãáí=ïáÉ=ÑçäÖíW=
=
sÉêÄáåÇäáÅÜâÉáí=Z=SNKQORIMM : VTIR ⋅ NMM=Z=SPKMMMIMM=bìêç=
ÄF= pâçåíçÉêíê~Ö=Z=OIR=B=îK=SPKMMMIMM=Z=NKRTRIMM== =
q~ÖÉ=ÑΩê=wáåëÄÉêÉÅÜåìåÖ=Z=PR=q~ÖÉ=Ó=NQ=q~ÖÉ=Z=ON=q~ÖÉ=
=
éÉÑÑ=Z=
NKRTRI MM ⋅ NMM ⋅ PSM =Z=QPIVS=B= SNKQORI MM ⋅ ON
=
ÅF= QQMM=
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j~ÜåëéÉëÉå=Z=MIR=B=îK=SPKMMMIMM=Z=PNRIMM=
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wáåëí~ÖÉW=
→ NV=B=rpí=Ç~ê~ìÑ=Z=RVIUR=
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båÇÉ=ÇÉë=êÉÖìä®êÉå=w~ÜäìåÖëòáÉäë=
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SPKMMMI MM ⋅ NO ⋅ PN =Z=SRNIMM= NMM ⋅ PSM
=
ÇF=
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NKRTRIMM== SRNIMM== PNRIMM==
OKRQNIMM==
=
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káÅÜí=åìê=j~ÜåëéÉëÉå=ìåÇ=sÉêòìÖëòáåëÉåI=ëçåÇÉêå=~ìÅÜ=ÇÉê=pâçåíç=ëÉäÄëí=ëáåÇ= ~äë=òìë®íòäáÅÜÉ=hçëíÉå=òì=ÄÉíê~ÅÜíÉåI=Ç~=ÇÉê=oÉÅÜåìåÖëÄÉíê~Ö=áå=îçääÉê=e∏ÜÉ=òì= ÄÉÖäÉáÅÜÉå=áëíK=báå=åáÅÜí=ÖÉåìíòíÉê=pâçåíçÉêíê~Ö=ïáêÇ=òìã=wáåë~ìÑï~åÇ=ÑΩê=ÇÉå= iáÉÑÉê~åíÉåâêÉÇáí=ìåÇ=ëç=òì=hçëíÉåK=
402
E. Aufgaben
^ìÑÖ~ÄÉ=QU= ^ìëò~ÜäìåÖëÄÉíê~Ö=aáëéçJhêÉÇáí=Z=^ìëò~ÜäìåÖëÄÉíê~Ö=a~êäÉÜÉå=Z=SKRMMIMM= =
hêÉÇáíâçëíÉå=
aáëéçJhêÉÇáí=
wáåë= _É~êÄÉáíìåÖëÖÉÄΩÜê= Z=dÉë~ãí= =
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a~êäÉÜÉå=
SPINV== MIMM== SPINV==
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PSINN== POIRM== SUISN==
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wáåë=Ea~êäÉÜÉåF=Z=
SKRMMI MM ⋅ NQ ⋅ OR =Z=SPINV= NMM ⋅ PSM
SKRMMI MM ⋅ U ⋅ OR =Z=PSINN== NMM ⋅ PSM
=
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éÉÑÑ=EaáëéçJhêÉÇáíF=Z= éÉÑÑ=Ea~êäÉÜÉåF=Z=
SPINV ⋅ NMM ⋅ PSM =Z=NQ=B= SKRMM ⋅ OR
SUI SN ⋅ NMM ⋅ PSM =Z=NRIOM=B= SKRMM ⋅ OR
=
táÉ= ÄÉêÉáíë= ~ìë= ÇÉå= åáÉÇêáÖÉêÉå= hêÉÇáíâçëíÉå= ÉêëáÅÜíäáÅÜ= ï~êI= òÉáÖí= ëáÅÜ= åìå= ~ìÅÜ= áã=ÉÑÑÉâíáîÉå=wáåëë~íòI=Ç~ëë=ÇÉê=aáëéçJhêÉÇáí=ÇáÉ=ÄÉëëÉêÉ=^äíÉêå~íáîÉ=áëíK= = =
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=
NKMNPIMS== OMQIOP== RIMT= NMIMM=
EPSKQTMIMM : PSF= = EEMIR=B=îK=PSKQTMIMM=F : PSF= =
NKOPOIPS=
=
=
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PSKQTM ⋅ MIRS ⋅ PS =Z=TKPROIPR → wáåëLjçå~í=Z=TKPROIPR : PS=Z=OMQIOP== NMM
=
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2. Lösungen
403
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404
E. Aufgaben
= ^åëÅÜ~ÑÑìåÖëâçëíÉå= Ó= ^Ñ^=NK=g~Üê=
NVKPNOIRM== ENMM=BF= PKUSOIRM== EOM=BF=
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tÉêí=~ìÑ=OSMM=Z=NV=B=îK=QPQITR=
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2. Lösungen
ÄF=
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405
= = oÉÅÜåìåÖëÄÉíê~ÖI=Äêìííç= Ó= NV=B=rpí=
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406
E. Aufgaben
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2. Lösungen
407
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408
E. Aufgaben
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2. Lösungen
409
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= =
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Z== ï~ÜêëÅÜÉáåäáÅÜÉê=^ìëÑ~ääI=Äêìííç= Ó== rpí=
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ENNV=BF= ENV=BF=
ESM=BF= =
Z== ï~ÜêëÅÜÉáåäáÅÜÉê=^ìëÑ~ääI=åÉííç= Ó= îçêÜ~åÇÉåÉ=bt_=
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a~= Éë= áã= dÉëÅÜ®Ñíëà~Üê= âÉáåÉ= òïÉáÑÉäÜ~ÑíÉå= cçêÇÉêìåÖÉå= Ö~ÄI= áëí= ~ìÅÜ= âÉáåÉ= bt_=ÄòïK=ÉáåÉ=bt_=áå=e∏ÜÉ=îçå=MIMM=bìêç=åçíïÉåÇáÖK=a~ë=hçåíç=PSTM=ïáêÇ= ~äëç=ìã=ëÉáåÉå=^åÑ~åÖëÄÉëí~åÇ=~ìÑ=MIMM=bìêç=ÜÉê~ÄÖÉëÉíòíK=
ÄF= a~ë=hçåíç=ÉêäáëÅÜíI=Ç~=Éë=åìå=ÉáåÉå=_Éëí~åÇ=îçå=MIMM=bìêç=~ìÑïÉáëíK= =
^ìÑÖ~ÄÉ=SN= ~F= SVRP=
VUMIMM=
~å=
PSUM=
VUMIMM=
ÄF= sçêà~ÜêW= =
= ëáÅÜÉêÉ=cçêÇÉêìåÖÉåI=Äêìííç= Ó= rpí=
PMKPQRIMM== QKUQRIMM==
Z==ëáÅÜÉêÉ=cçêÇÉêìåÖÉåI=åÉííç= =
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Ç~îçå=O=B======================== =
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NNV=B= NV=B=
Z==ëáÅÜÉêÉ=cçêÇÉêìåÖÉåI=åÉííç=
TQKRMMIMM= Z=NKQVMIMM : O ⋅ NMM=
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NKQVMIMM= = RNMIMM= =
= =
VUMIMM= =
=
=
Z==eÉê~ìÑëÉíòìåÖ= =
410
E. Aufgaben
^ìÑÖ~ÄÉ=SO= ~F= SKNOKW= =
SVRN=
=
QUMM=
OKSTMIMM= RMTIPM==
= ~å=
OQMM=
PKNTTIPM=
OTKPROIUM=
~å=
OQMM=
OTKPROIUM=
NNKSURIUM=
~å=
RMMM=
VKUOMIMM=
=
=
QUMM=
NKUSRIUM=
OPMIMM=
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VKNOKW=
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OQTM=
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SNQM=
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QPITM==
~å=
EZ=VKTMMIMM==H=NOMIMM=F=
=
ÄF= = dÉë~ãíÉê=cçêÇÉêìåÖëÄÉëí~åÇ=~ã=NKNOK= Ó==^ìëÑ~ää=îçã=SKNOK= Ó==wïÉáÑÉäÜ~ÑíÉ=cçêÇÉêìåÖ=îçã=VKNOK= H==kÉìÉ=cçêÇÉêìåÖ=îçã=NRKNOK=
OVMKOOTIMU== PKNTTIPM= OTKPROIUM== NNKSURIUM=
= = = =
Z==ëáÅÜÉêÉ=cçêÇÉêìåÖÉåI=Äêìííç= Ó==rpí=
OTNKPUOITU== QPKPPMIMO==
ENNV=BF= ENV=BF=
Z==ëáÅÜÉêÉ=cçêÇÉêìåÖÉåI=åÉííç=
OOUKMROITS==
ENMM=BF=
=
=
SKUQNIRU== TKNUNIRU==
= =
Z==eÉê~ÄëÉíòìåÖ=
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PSUM=
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~å=
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=
ÅF= ëáÅÜÉêÉ=cçêÇÉêìåÖÉåI=åÉííç=Z=
TKNUNIRU ⋅ NMM =Z=OPVKPUSIMM= P
=
^ìÑÖ~ÄÉ=SP= ~F= = hìêëïÉêí=ENPM ⋅ ORIMMF= H==péÉëÉå=
PKORMIMM== POIRM==
Z==_~åâä~ëíëÅÜêáÑí=
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=
= =
=
= Ç~îçå=P=B=mt_= Ó==îçêÜ~åÇÉåÉ=mt_=
NRMM=
PKOUOIRM=
~å=
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PKOUOIRM=
=
2. Lösungen
411
ÄF= qÉáäïÉêí=òìã=PNKNOKOMMO=Z=TM=B=îK=PKOUOIRM==Z=OKOVTITR=bìêç== NK==iáÉÖí= áã= cáå~åò~åä~ÖÉîÉêã∏ÖÉå= îçå= h~éáí~äÖÉëÉääëÅÜ~ÑíÉå= ÉáåÉ= åìê= îçêΩJ ÄÉêÖÉÜÉåÇÉ= tÉêíãáåÇÉêìåÖ= îçêI= ëç= Ç~êÑ= áå= ÇÉê= píÉìÉêÄáä~åò= ÇÉê= åáÉÇêáÖÉêÉ= qÉáäïÉêí= åáÅÜí= ~åÖÉëÉíòí= ïÉêÇÉå= Eáå= e~åÇÉäëÄáä~åò= ÜáåÖÉÖÉå= ^ÄëÅÜêÉáJ ÄìåÖëï~ÜäêÉÅÜíFK= bë= ÑáåÇÉí= âÉáåÉ= qÉáäïÉêí~ÄëÅÜêÉáÄìåÖ= EâÉáåÉ= _ìÅÜìåÖF= ëí~ííK= aÉê= tÉêí~åë~íò= ÉåíëéêáÅÜí= ÇÉå= ^åëÅÜ~ÑÑìåÖëâçëíÉå= áå= e∏ÜÉ= îçå= PKOUOIRM=bìêçK= OK==_Éá= ÉáåÉê= Ç~ìÉêÜ~ÑíÉå= tÉêíãáåÇÉêìåÖ= áëí= ÇáÉ= ^ÄëÅÜêÉáÄìåÖ= ëíÉìÉêêÉÅÜíäáÅÜ= EïáÉ=~ìÅÜ=Ü~åÇÉäëêÉÅÜíäáÅÜF=mÑäáÅÜíK= =
=
= ^åëÅÜ~ÑÑìåÖëâçëíÉå=
PKOUOIRM==
Ó= qÉáäïÉêí=
OKOVTITR==
Z==qÉáäïÉêí~ÄëÅÜêÉáÄìåÖ= =
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=
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~å=
NRMM=
VUQITR=
=
ÅF= qÉáäïÉêí=òìã=PNKNOKOMMP=Z=NOM=B=îK=PKOUOIRM==Z=PKVPVIMM=bìêç= _Éá= tÉÖÑ~ää= ÇÉê= Ç~ìÉêÜ~ÑíÉå= tÉêíãáåÇÉêìåÖ= Öáäí= Éáå= tÉêí~ìÑÜçäìåÖëÖÉÄçí= Äáë= ã~ñK= òì= ÇÉå= ^åëÅÜ~ÑÑìåÖëâçëíÉåI= ÇáÉ= ÇáÉ= ~ÄëçäìíÉ= tÉêíçÄÉêÖêÉåòÉ= Ç~êëíÉääÉåK= aÉê=_áä~åò~åë~íò=òìã=PNKNOKOMMP=äáÉÖí=~äëç=ÄÉá=PKOUOIRM=bìêçK= =
=
wìëÅÜêÉáÄìåÖW=
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NRMM=
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OTOM=
PKOUOIRM=
=
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fã= rãä~ìÑîÉêã∏ÖÉå=ÜÉêêëÅÜí=å~ÅÜ=píÉìÉêêÉÅÜí=Éáå=^ÄïÉêíìåÖëîÉêÄçí=ÄÉá=îçêΩJ ÄÉêÖÉÜÉåÇÉêI=ÉáåÉ=^ÄïÉêíìåÖëéÑäáÅÜí=ÄÉá=Ç~ìÉêÜ~ÑíÉê=tÉêíãáåÇÉêìåÖK=
=
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TQOM=
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eáåëáÅÜíäáÅÜ= wìëÅÜêÉáÄìåÖ= ÖÉäíÉå= áã= rãä~ìÑîÉêã∏ÖÉåI= ÇáÉëÉäÄÉå= sçêëÅÜêáÑíÉå= ïáÉ=áã=^åä~ÖÉîÉêã∏ÖÉåK=
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PNKNOKOMMPW=
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^ìÑÖ~ÄÉ=SQ= ~F=
=
= = hìêëïÉêí= H==péÉëÉå=EN=BF=
NKRMMKMMMIMM== NRKMMMIMM==
Z= ^åëÅÜ~ÑÑìåÖëâçëíÉå=
NKRNRKMMMIMM==
VUQITR=
412
E. Aufgaben =
=
^åò~Üä=ÇÉê=^âíáÉå=Z=NKRMMKMMMIMM : SMIMMLpíΩÅâ=Z=ORKMMM=píΩÅâ= =
=
^åíÉáä=~ã=ÖÉòÉáÅÜåÉíÉå=h~éáí~ä=Z=
EORKMMMI MM ⋅ ORF ⋅ NMM =Z=OMIUP=B= PKMMMKMMMI MM
=
== k~ÅÜ=¬=OTN=f=ed_=äáÉÖí=ÉáåÉ=_ÉíÉáäáÖìåÖ=áã=wïÉáÑÉä=Ç~åå=îçêI=ïÉåå=ÇÉê=^åíÉáä= ÇÉë= ^âíáÉåé~âÉíë= ~ã= ÖÉòÉáÅÜåÉíÉå= h~éáí~ä= OM= B=ΩÄÉêëíÉáÖíI= ï~ë= áå= ÇáÉëÉê= ^ìÑJ Ö~ÄÉ=ÇÉê=c~ää=áëíK= ÄF= a~=hìêëëÅÜï~åâìåÖÉå=ÄÉá=^âíáÉå=åçêã~ä=ëáåÇI=áëí=Ç~îçå=~ìëòìÖÉÜÉåI=Ç~ëë=åìê= ÉáåÉ=îçêΩÄÉêÖÉÜÉåÇÉ=tÉêíãáåÇÉêìåÖ=îçêäáÉÖíK=aKÜK=ëçïçÜä=áå=ÇÉê=pÅÜäìëëÄáä~åò= OMMM= ~äë= ~ìÅÜ= OMMN= áëí= Ç~ë= ^âíáÉåé~âÉí= òì= ëÉáåÉå= ^åëÅÜ~ÑÑìåÖëâçëíÉå= îçå= NKRNRKMMMIMM=bìêç=~åòìëÉíòÉåK=báåÉ=^ÄëÅÜêÉáÄìåÖ=~ìÑ=ÇÉå=åáÉÇêáÖÉêÉå=qÉáäïÉêí= áëí=åáÅÜí=òìä®ëëáÖK= ÅF= _Éá=Ç~ìÉêÜ~ÑíÉê=tÉêíãáåÇÉêìåÖ=ÄÉëíÉÜí=^ÄëÅÜêÉáÄìåÖëéÑäáÅÜíW= =
=
TQMM= NKRNRKMMMIMM=
~å=
NPMM=
NKRNRKMMMIMM=
=
^ìÑÖ~ÄÉ=SR= ~F= = = ^_=
PKMMM=píΩÅâ= =
H==wìÖ®åÖÉ=
SKOMM=píΩÅâ= Z=ENKOMM=H=OKTMM=H=RMM=H=NKVMMF=Ó=NMM=
Ó= sÉêÄê~ìÅÜ=
UKMMM=píΩÅâ= =
Z==p_=
NKOMM=píΩÅâ= =
=
=
=
=
jÉåÖÉ=áå=píK=
ibm=
^_=
=
PKMMM=
ONKMPK= =
NKOMM=
ORKMTK= =
OKTMM=
MNKNMK= =
RMM=
PNKNOK= = = N
=
NKVMM= VKPMMG=
=
OMQIMM= QUSIMM= NMRIMM= QNUIMM= =
=
=
=
_ÉòìÖëâçëíÉå= mêÉáëå~ÅÜä®ëëÉ=
=
=
=
NMMIMM=
=
MIMM=
=
RMIMM=
=
NMMIMM=
=
= = = =
=
^â= EbìêçF=
SVMIMM= N
OVPIUM=
O
QQOIVQ=
P
NPQIMM=
Q
QSPIRS=
NMIOM= = QPIMS= = ONIMM= = RQIQQ= =
OKMOQIPM=
=R=B=îK=OMQIMM=
O=
T=B=îK=QUSIMM=H=O=B=îK=EQUSIMM=Ó=T=BF=Z=PQIMO=H=O=B=îK=QRNIVU==Z=PQIMO=H=VIMQ== NMM=píΩÅâ ⋅ MION=bìêçLpíΩÅâ=
P= Q=
R=B=îK=QNUIMM=H=_çåìë=Z=OMIVM=H=PPIRQ=
G=ÜáÉê=oΩÅâëÉåÇìåÖ=åçÅÜ=ÉåíÜ~äíÉå= =
=
2. Lösungen
413
_çåìëÄÉêÉÅÜåìåÖW= =
iáÉÑÉêìåÖW=ONKMPK=
NVPIUM== Z=OMQIMM=Ó=NMIOM==
iáÉÑÉêìåÖW=ORKMTK=
QQOIVQ== Z=QUSIMM=Ó=QPIMS==
iáÉÑÉêìåÖW=MNKNMK=
UQIMM== Z=NMRIMM=Ó=ONIMM==
iáÉÑÉêìåÖW=PNKNOK=
PVTINM== Z=QNUIMM=Ó=OMIVM==
Z=dÉë~ãíï~êÉåïÉêí=
=
NKNNTIUQ== → _çåìë=Z=P=B=îK=NKNNTIUQ=Z=PPIRQ=bìêç=
= →=Õ=^â=Z=OKMOQIPM=bìêç=W=EVKPMM=Ó=NMMF=píΩÅâ=Z=MIOO=bìêçLpíΩÅâ= = _ÉïÉêíìåÖW= tÉêí=ÇK=p_=å~ÅÜ=Õ=^â=Z=NKOMM=píΩÅâ ⋅ MIOO=bìêç=LpíΩÅâ=Z=OSQIMM= tÉêí=ÇK=p_=å~ÅÜ=qt=Z=NKOMM=píΩÅâ ⋅ MIOR=bìêçLpíΩÅâ=Z=PMMIMM=
=
qt=[=^â → _áä~åò~åë~íò=Z=OSQIMM=
=
k~ÅÜ=ÇÉã=^åëÅÜ~ÑÑìåÖëïÉêíéêáåòáé=ëáåÇ=ÇáÉ=^eh=ÇáÉ=~ÄëçäìíÉ=tÉêíçÄÉêÖêÉåòÉK= a~ÜÉê= Ç~êÑ= ÇÉê= Ü∏ÜÉêÉ= qÉáäïÉêí= ïÉÇÉê= å~ÅÜ= e~åÇÉäëJ= åçÅÜ= å~ÅÜ= píÉìÉêêÉÅÜí= ~åÖÉëÉíòí=ïÉêÇÉåK=
=
ÄF= sÉêÄê~ìÅÜ=Z=^_=H=wìÖ®åÖÉ=Ó=p_= =
sÉêÄê~ìÅÜ=Z=SVMIMM=H=NKPPQIPM=Ó=OSQIMM=Z=NKTSMIPM=
=
ÅF= =
p= UMMM=
===OMOM=
e= = p=
SVMIMM= UMNM=
OSQIMM= = QQMM=
GNVPIUM= QQMM=
ONIMM=
= SMOM=
QOSIMM= = QQMM=
GQRNIVU= SMOO=
QOIRU=
NMRIMM= UMOM=
NKTSMIPM=
=
SVMIMM= =
SVMIMM= = QQMM=
=
= =
= = QQMM=
G=å~ÅÜ=o~Ä~íí~ÄòìÖ=
= = SMOM=
ORMIMM
=
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=
= = OMOM=
QOSIMM
=
=
= =
= = = ==SMON=
= = = = = = e= = p=
QQMM= QQMM=
NMMIMM RMIMM
SMOM= =
QQMM=
NMMIMM
=
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ORMIMM
=
ORMIMM= = =
=
=
e=
=
= = p=
=
=============SMOM=
=
ORMIMM= = SMOM= = = =
GPVTINM= =
NKUOPIUU = = =============SMOO=
=
NKUOPIUU= = e=
QOIRU
QQMM= QQMM=
VIMQ= PPIRQ=
QOIRU
=
QOIRU=
= =
=
414
E. Aufgaben
sçê~ÄëÅÜäìëëÄìÅÜìåÖÉåW= SMOM=
ORMIMM=
~å=
SMON=
ORMIMM=
SMOO=
QOIRU=
~å=
SMOM=
QOIRU=
=
^ÄëÅÜäìëëÄìÅÜìåÖÉåW= UMNM=
OSQIMM=
~å=
OMOM=
OSQIMM=
UMOM=
NKTSMIPM=
~å=
SMOM=
NKTSMIPM=
=
^ìÑÖ~ÄÉ=SS= ~F=
= = j~íÉêá~äâçëíÉå=EZcj=H=jdhF= H==cÉêíáÖìåÖëâçëíÉå=EZ=ci=H=cdh=H=pbhcF=
NQIRM=bìêçLpí= NMIOM=bìêçLpí=
Z==tÉêíìåíÉêÖêÉåòÉ=å~ÅÜ=píÉìÉêêÉÅÜí= H==stdh=ER=BF=
OQITM=bìêçLpí= NIOQ=bìêçLpí=
Z==tÉêíçÄÉêÖêÉåòÉ=å~ÅÜ=píÉìÉêêÉÅÜí=
ORIVQ=bìêçLpí=
=
_Éëí~åÇëîÉê®åÇÉêìåÖ=Z=wìÖ®åÖÉ=Ó=^ÄÖ®åÖÉ=Z=PMM=píK=Ó=QMM=píK=Z=Ó=NMM=píK= =
a~ãáí=ÇÉê=p_=ã∏ÖäáÅÜëí=ÖÉêáåÖ=~ìëÖÉïáÉëÉå=ïáêÇI=ãìëë=ÉáåÉ=ÜçÜÉ=_Éëí~åÇëãáåÇÉJ êìåÖ=ÖÉÄìÅÜí=ïÉêÇÉåK=aáÉ=_Éëí~åÇëîÉê®åÇÉêìåÖ=ïáêÇ=~äëç=áå=ÇáÉëÉã=c~ää=òìê=tÉêíJ çÄÉêÖêÉåòÉ=~åÖÉëÉíòíK= _Éëí~åÇëãáåÇÉêìåÖ=Z=ORIVQ=bìêçLpí ⋅ NMM=pí=Z=OKRVPIRM= =
_ìÅÜìåÖW= =
ROMN=
OKRVPIRM=
~å=
ONMM=
OKRVPIRM=
=
=
ÄF= aáÉ=_Éëí~åÇîÉê®åÇÉêìåÖÉå=ïÉêÇÉå=áã=cçäÖÉåÇÉå=òìê=sÉêÉáåÑ~ÅÜìåÖ=ÇáêÉâí=áå=Ç~ë= e~ìéíâçåíç=ROMM=ÉáåÖÉÄìÅÜíK=aáÉ=hçåíÉå=ROMN=ìåÇ=ROMO=ïÉêÇÉå=~äëç=åáÅÜí=Éê∏ÑÑJ åÉí=ìåÇ=Ç~åå=ΩÄÉê=ROMM=~ÄÖÉëÅÜäçëëÉåK= =======
p=
===ONMM=
UMMM= NPKQRMIMM= UMNM=
=
= = p=
=
= ROMM=
NPKQRMIMM= = = = ==ROMM=
e= = p= NMKURSIRM= = UMMM=
OKRVPIRM= = ROMM=
NPKQRMIMM= = = = = = e= = p=
=============OOMM= QKRMMIMM= UMNM=
PKQMMIMM= =
TKVMMIMM= = = = =============UMOM=
ONMM= UMOM=
OKRVPIRM= OOMM= UMSIRM= =
PKQMMIMM= = = = = =
= ROMM= = =
=
PKQMMIMM= =
PKQMMIMM= = =
= =
e= TKVMMIMM= =
TKVMMIMM=
= e= UMSIRM= =
=
2. Lösungen
415
^ìÑÖ~ÄÉ=ST= ~F= SMMM= =
OPKMMMIMM=
~å=
QQMM=
EZ=OMKMMM ⋅ NINRF=
OPKMMMIMM=
=
ÄF= NK=qÉáäïÉêí=Z=OMKMMMIMM ⋅ NIPM=Z=OSKMMMIMM=bìêç= =
_áä~åò~åë~íò=Z=OPKMMMIMM==
=
_ÉÖêΩåÇìåÖW=a~=ÉáåÉ=hìêëëÅÜï~åâìåÖ=áå=ÇáÉëÉã=c~ää=~äë=åìê=îçêΩÄÉêÖÉÜÉåÇÉ= tÉêíÉêÜ∏ÜìåÖ=ÄÉíê~ÅÜíÉí=ïÉêÇÉå=â~ååI=Ç~êÑ=ÇÉê=Ü∏ÜÉêÉ=qÉáäïÉêí=áå=ÇÉê=píÉìÉêJ Äáä~åò=åáÅÜí=~åÖÉëÉíòí=ïÉêÇÉåK=
=
OK=qÉáäïÉêí=Z=OMKMMMIMM ⋅ NIMR=Z=ONKMMMIMM=bìêç=
=
_áä~åò~åë~íò=Z=OPKMMMIMM==
=
_ÉÖêΩåÇìåÖW= aÉê= ÄÉá= ÇÉê= _ÉÖêΩåÇìåÖ= ÇÉê= sÉêÄáåÇäáÅÜâÉáí= ÖÉÄìÅÜíÉ= oΩÅâò~ÜJ äìåÖëÄÉíê~Ö=ëíÉääí=ÇáÉ=~ÄëçäìíÉ=_ÉïÉêíìåÖëìåíÉêÖêÉåòÉ=Ç~êK=aÉê=åáÉÇêáÖÉêÉ=qÉáäJ ïÉêí=ÄäÉáÄí=~äëç=ìåÄÉêΩÅâëáÅÜíáÖíK=
=
ÅF= §ÄÉêïÉáëìåÖëÄÉíê~Ö=Z=OMKMMM ⋅ NIOM=Z=OQKMMMIMM=bìêç= =
=
QQMM=
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ANHANG = Hier im Anhang finden Sie einen für Lernzwecke verkürzten und modifizierten Auszug aus dem Industriekontenrahmen (Kontenplan). Auf eine detaillierte Darstellung der Kontenklasse 9 (Kosten- und Leistungsrechnung) wurde dabei verzichtet, da es sich hier um kein Thema der Buchführung handelt. Diesen Kontenplan finden Sie in digitaler Form auch im Online-Service. Im Online-Service finden Sie außerdem zwei Dokumente zur Auffrischung Ihrer Kenntnisse der Prozent- und Zinsrechnung.
Übungskontenplan gemäß IKR = hçåíÉåâä~ëëÉ=M ^âíáî~ fãã~íÉêáÉääÉ=sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ==ìåÇ=p~ÅÜ~åäÖÉå MM ^ìëëíÉÜÉåÇÉ=báåä~ÖÉå=ÄÉá=h~éáí~äÖÉëÉääëÅÜ~ÑíÉåW=~ìÑ=Ç~ë ÖÉòÉáÅÜåÉíÉ=h~éáí~äI=ÄÉá=hçãã~åÇáíÖÉëÉääëÅÜ~ÑíÉåW ~ìëëíÉÜÉåÇÉ=hçãã~åÇáíÉáåä~ÖÉåF MMNM=kçÅÜ=åáÅÜí=ÉáåÖÉÑçêÇÉêíÉ=báåä~ÖÉå= ========E¬=OTO=f=pK=O=ed_F MMOM=báåÖÉÑçêÇÉêíÉ=báåä~ÖÉå=E¬=OTO=f=pK=O=ed_F MN ^ìÑïÉåÇìåÖÉå=ÑΩê=ÇáÉ=fåÖ~åÖëÉíòìåÖ=ìåÇ=bêïÉáíÉêìåÖ ÇÉë=dÉëÅÜ®ÑíëÄÉíêáÉÄÉë=E¬=OSV=ed_F fãã~íÉêáÉääÉ=sÉêã∏ÖÉåëÖÉÖÉåëí®åÇÉ=E¬=OQU=ff=ed_F MO hçåòÉëëáçåÉåI=ÖÉïÉêÄäK=pÅÜìíòêÉÅÜíÉ=ìåÇ=®ÜåäáÅÜÉ= oÉÅÜíÉ=ìåÇ=tÉêíÉ=ëçïáÉ=iáòÉåòÉå=~å=ëçäÅÜÉå=oÉÅÜíÉå= ìåÇ=tÉêíÉå MONM=hçåòÉëëáçåÉå MOOM=dÉïÉêÄäáÅÜÉ=pÅÜìíòêÉÅÜíÉ MOPM=ûÜåäáÅÜÉ=oÉÅÜíÉ=ìåÇ=tÉêíÉ MOQM=iáòÉåòÉå=~å=oÉÅÜíÉå=ìåÇ=tÉêíÉå MP dÉëÅÜ®ÑíëJ=çÇÉê=cáêãÉåïÉêí MPNM=dÉëÅÜ®ÑíëJ=çÇÉê=cáêãÉåïÉêí MPOM=sÉêëÅÜãÉäòìåÖëãÉÜêïÉêí MQ dÉäÉáëíÉíÉ=^åò~ÜäìåÖÉå=~ìÑ=áãã~íÉêáÉääÉ=sÉêã∏ÖÉåëJ ÖÉÖÉåëí®åÇÉ p~ÅÜ~åä~ÖÉå MR dêìåÇëíΩÅâÉI=ÖêìåÇëíΩÅâëÖäÉáÅÜÉ=oÉÅÜíÉ=ìåÇ=_~ìíÉå= ÉáåëÅÜäK=ÇÉê=_~ìíÉå=~ìÑ=ÑêÉãÇÉå=dêìåÇëíΩÅâÉå MRMM=råÄÉÄ~ìíÉ=dêìåÇëíΩÅâÉ MRNM=_ÉÄ~ìíÉ=dêìåÇëíΩÅâÉ= MRPM=_ÉíêáÉÄëÖÉÄ®ìÇÉ MRQM=sÉêï~äíìåÖëÖÉÄ®ìÇÉ MRRM=^åÇÉêÉ=_~ìíÉå MRSM=dêìåÇëíΩÅâëÉáåêáÅÜíìåÖÉå MRTM=dÉÄ®ìÇÉÉáåêáÅÜíìåÖÉå MRVM=tçÜåÖÉÄ®ìÇÉ MS cêÉá
=
MT qÉÅÜåáëÅÜÉ=^åä~ÖÉå=ìåÇ=j~ëÅÜáåÉå MTMM=^åä~ÖÉå=ìåÇ=j~ëÅÜáåÉå=ÇÉê=båÉêÖáÉîÉêëçêÖìåÖ MTNM=^åä~ÖÉå=ÇÉê=j~íÉêá~ää~ÖÉêìåÖ=ìåÇ=JÄÉêÉáíëíÉääìåÖ MTOM=^åä~ÖÉå=ìåÇ=j~ëÅÜáåÉå=ÇÉê=ãÉÅÜ~åáëÅÜÉå=j~íÉêá~äJ =========ÄÉ~êÄÉáíìåÖI=JîÉê~êÄÉáíìåÖ=ìåÇ=Jìãï~åÇäìåÖ MTPM=^åä~ÖÉå=ÑΩê=t®êãÉJI=h®äíÉJ=ìåÇ=ÅÜÉãáëÅÜÉ=mêçòÉëëÉ= =========ëçïáÉ=®ÜåäáÅÜÉ=^åä~ÖÉå MTQM=^åä~ÖÉå=ÑΩê=^êÄÉáíëëáÅÜÉêÜÉáí=ìåÇ=rãïÉäíëÅÜìíò MTRM=qê~åëéçêí~åä~ÖÉå=ìåÇ=®ÜåäáÅÜÉ=_ÉíêáÉÄëîçêêáÅÜíìåÖÉå MTSM=sÉêé~ÅâìåÖë~åä~ÖÉå=ìåÇ=Jã~ëÅÜáåÉå MTTM=pçåëíáÖÉ=^åä~ÖÉå=ìåÇ=j~ëÅÜáåÉå MTUM=oÉëÉêîÉã~ëÅÜáåÉå=ìåÇ=J~åä~ÖÉåíÉáäÉ MTVM=dÉêáåÖïÉêíáÖÉ=^åä~ÖÉå=ìåÇ=j~ëÅÜáåÉå MU ^åÇÉêÉ=^åä~ÖÉåI=_ÉíêáÉÄëJ=ìåÇ=dÉëÅÜ®Ñíë~ìëëí~ííìåÖ MUMM=^åÇÉêÉ=^åä~ÖÉå MUNM=tÉêâëí®ííÉåÉáåêáÅÜíìåÖ MUOM=tÉêâòÉìÖÉI=tÉêâëÖÉê®íÉ=ìK=jçÇÉääÉI=mêΩÑJ=ìK= =========jÉëëãáííÉä MUPM=i~ÖÉê=ìåÇ=qê~åëéçêíÉáåêáÅÜíìåÖÉå MUQM=cìÜêé~êâ MURM=pçåëíáÖÉ=_ÉíêáÉÄë~ìëëí~ííìåÖ MUSM=_ΩêçãëÅÜáåÉåI=lêÖ~åáë~íáçåëãáííÉä=ìåÇ= ========hçããìåáâ~íáçåë~åä~ÖÉå MUTM=_Ωêçã∏ÄÉä=ìåÇ=ëçåëíK=dÉëÅÜ®Ñíë~ìëëí~ííìåÖ MUUM=oÉëÉêîÉíÉáäÉ=ÑΩê=_ÉíêáÉÄëJ=ìK=dÉëÅÜ®Ñíë~ìëëí~ííìåÖ MUVM=dÉêáåÖïÉêíáÖÉ=dÉÖÉåëí®åÇÉ=ÇÉê=_ÉíêáÉÄëJ=ìåÇ= ========dÉëÅÜ®Ñíë~ìëëí~ííìåÖ MV dÉäÉáëíÉíÉ=^åò~ÜäìåÖÉå=ìåÇ=^åä~ÖÉå=áã=_~ì MVMM=dÉäÉáëíÉíÉ=^åò~ÜäìåÖÉå=~ìÑ=p~ÅÜ~åä~ÖÉå MVRM=^åä~ÖÉå=áã=_~ì
422
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Schlagwortverzeichnis = ^Ää~ìÑÜÉããìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTV= ^ÄëÅÜäìëëÄìÅÜìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRU= = Ñçêã~äÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKORT= = ã~íÉêáÉääÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKORT= ^ÄëÅÜäìëëÖäáÉÇÉêìåÖëéêáåòáéKKKKKKKKKKKKKKKKKKKKKKKSM= ^ÄëÅÜêÉáÄìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTI=ORV= = ~ì≈Éêéä~åã®≈áÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOTV= = ÇÉÖêÉëëáîÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOSS= = ÖÉêáåÖïÉêíáÖÉë=táêíëÅÜ~ÑíëÖìí KKKKKKKKKKKKKKKOTP= = iÉáëíìåÖëJ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOSV= = äáåÉ~êÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOSP= = éêçÖêÉëëáîÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOSV= = òÉáí~åíÉáäáÖÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOTM= ^ÄëÅÜêÉáÄìåÖëÄ~ëáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOSN= ^ÄëÉíòìåÖ== = ÑΩê=^ÄåìíòìåÖI=pìÄëí~åòîÉêêáåÖÉêìåÖ KOTM= ^Äò~ÜäìåÖëÇ~êäÉÜÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOPN= ^âíáî~KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNO= ^âíáîí~ìëÅÜKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOO= ^åÑ~åÖëÄÉëí~åÇ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOS= ^åÖÉÄçíëâ~äâìä~íáçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNQP= ^åÖÉÄçíëîÉêÖäÉáÅÜ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVV= ^åÜ~åÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SI=NV= ^åä~ÖÉîÉêã∏ÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UI=NPI=ORV= ^ååìáí®íÉåÇ~êäÉÜÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOPO= ^åé~ëëìåÖë~ÄëÅÜêÉáÄìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKOVQ= ^åë~íòîçêëÅÜêáÑíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTV= ^åëÅÜ~ÑÑìåÖëJ=ìåÇ=eÉêëíÉääìåÖëâçëíÉå= ÑçêíÖÉÑΩÜêíÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUNI=OUP= = ÑçêíÖÉëÅÜêáÉÄÉåÇÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOUP= ^åëÅÜ~ÑÑìåÖëâçëíÉå KKKKKKKKKKKKKKKKKKKKKKKKKK NTPI=OMR= = å~ÅÜíê®ÖäáÅÜÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNTP= = JãáåÇÉêìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNTP= = JéêáåòáéKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTTI=OUT= ^åëÅÜ~ÑÑìåÖëåÉÄÉåâçëíÉåKKKKKKKKKKKKKKKK NTPI=NTU= ^åò~ÜäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNSI=NRQ= ^ìÑï~åÇ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQQ= = ~ì≈ÉêçêÇÉåíäáÅÜÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNU= = ÄÉêáÉÄëÄÉÇáåÖíÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRN= = ÄÉíêáÉÄäáÅÜÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNT= = cáå~åòJ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNU= = j~íÉêá~äJ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNT= = åÉìíê~äÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRN=
= mÉêëçå~äJ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NT= ^ìÑï~åÇëâçåíçKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QT= ^ìÑï~åÇëêΩÅâëíÉääìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKK PQN= ^ìëÖ~åÖëêÉÅÜåìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQR= ~ìëã~ÅÜÉåÇÉê=_Éíê~ÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONV= ^ìëëÅÜΩííìåÖëÄÉãÉëëìåÖëÑìåâíáçå KKKKKKKKKKKKK T= ~ìëëíÉÜÉåÇÉ=báåä~ÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POV= ^ìëïÉáëîçêëÅÜêáÑíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TV= = _~êÉáåâ~ìÑëéêÉáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VV= _~êîÉêâ~ìÑëéêÉáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQP= _É~êÄÉáíìåÖëÖÉÄΩÜêÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOS= _ÉäÉÖ~ìÑÄÉï~ÜêìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TU= _ÉêìÑëÖÉåçëëÉåëÅÜ~Ñí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQN= _Éëí~åÇë~ìÑå~ÜãÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NN= _Éëí~åÇëâçåíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OT= = ~âíáîÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OT= = é~ëëáîÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OT= _Éëí~åÇëãÉÜêìåÖ KKKKKKKKKKKKKKKKKKKKKKKK NTI=NOMI=NRU= _Éëí~åÇëãáåÇÉêìåÖ KKKKKKKKKKKKKKKKKKKKK NTI=NONI=NRV= ÄÉëí~åÇëçêáÉåíáÉêí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMM= ÄÉëí~åÇëçêáÉåíáÉêíÉ=_ìÅÜìåÖKKKKKKKKKKKKKKKKKKKK NOR= _Éëí~åÇëîÉê®åÇÉêìåÖ KKKKKKKKKKKKKKKKKKKKKKKK NNVI=NRT= _ÉíÉáäáÖìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONO= _ÉíêáÉÄëëíçÑÑ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VT= _ÉïÉêíìåÖëîçêëÅÜêáÑíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TV= _ÉòìÖëâçëíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMOI=NOR= _áä~åò KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKQI=SI=NN= = ~ìÑÖÉëíÉääíÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UV= = ÑÉëíÖÉëíÉääíÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UV= = ÖÉéêΩÑíÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UV= = çÑÑÉåÖÉäÉÖíÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UV= = îçêä®ìÑáÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UV= = JÄìÅÜ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK R= = JÖäÉáÅÜÖÉïáÅÜí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NO= = JÖäÉáÅÜìåÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NO= = JáÇÉåíáí®í KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUI=UO= = Jâä~êÜÉáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UM= = JëíÉíáÖâÉáíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UO= = JëíáÅÜí~Ö KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK T= = JîÉêâΩêòìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OP= = JîÉêä®åÖÉêìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OO= = Jï~ÜêÜÉáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UN=
432
_áä~åòáÉêìåÖëÖêìåÇë®íòÉ KKKKKKKKKKKKKKKKKKKKKKK TVI=UO= _çåìëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNMVI=NOTI=NQVI=NUM= _∏êëÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMV= _ìÅÜÑΩÜêìåÖ= = dêìåÇë®íòÉ=çêÇåìåÖëã®≈áÖÉêKKKKKKKKKKKKKKKK TT= _ìÅÜÑΩÜêìåÖëéÑäáÅÜí== = ÇÉêáî~íáîÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TR= = Ü~åÇÉäëêÉÅÜíäáÅÜÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TP= = çêáÖáå®êÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TR= = ëíÉìÉêêÉÅÜíäáÅÜÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TR= = sÉêëíç≈=ÖÉÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VPI=VQ= _ìÅÜÜ~äíÉêå~ëÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OS= _ìÅÜìåÖëäÉëÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PV= _ìÅÜìåÖëë~íò KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PM= _ìÅÜìåÖëîçêÖ®åÖÉ= = ÉêÑçäÖëåÉìíê~äÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QP= = ÉêÑçäÖëïáêâë~ãÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QP= = a~ãåìãKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOS= aÉäâêÉÇÉêÉë~íò KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PMQ= aáë~ÖáçKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOSI=OPRI=PNT= aáëí~åòêÉÅÜåìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QSI=OQT= aáîáÇÉåÇÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONT= açâìãÉåí~íáçåëÑìåâíáçå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKK S= açééáâKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OV= aìêÅÜëÅÜåáííëîÉêÑ~ÜêÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUV= = bÑÑÉâíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMV= bÑÑÉâíáîîÉêòáåëìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOS= báÖÉåÄÉäÉÖÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OV= báÖÉåâ~éáí~äKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK U= = JÄáä~åòáÉêìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POP= = JãÉÜêìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QSI=OQN= = JãáåÇÉêìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QSI=OQN= báÖÉåäÉáëíìåÖI=~âíáîáÉêíÉ KKKKKKKKKKKKKKKKKKKKKK NTI=OMP= báåÖ~åÖëêÉÅÜåìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMM= báåâ~ìÑëâ~äâìä~íáçå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VV= báåëí~åÇëéêÉáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VV= báåòÉä~ÄëÅÜêÉáÄìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OVQ= báåòÉäÄÉïÉêíìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UQ= báåòÉäâçëíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMP= báåòÉäìåíÉêåÉÜãÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POP= báåòÉäïÉêíÄÉêáÅÜíáÖìåÖ KKKKKKKKKKKKKKKKKKKKK OVQI=OVV= bêÑçäÖëâçåíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QT= bêÖÉÄåáë== = _ÉíêáÉÄëJ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NS= = ÇÉê=ÖÉï∏ÜåäáÅÜÉå=dÉëÅÜ®Ñíëí®íáÖâÉáí KKKK NS= = åÉìíê~äÉëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RN= = çêÇÉåíäáÅÜÉë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RN=
= oçÜJ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NS= = JîÉêïÉåÇìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PPP= bêáååÉêìåÖëïÉêíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSR= bêä∏ëÄÉêáÅÜíáÖìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQV= bê∏ÑÑåìåÖëÄáä~åò KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQI=OU= bê∏ÑÑåìåÖëÄáä~åòâçåíç KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PS= bêíê~ÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QQ= = ~ì≈ÉêçêÇÉåíäáÅÜÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NU= = ÄÉíêáÉÄäáÅÜÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NT= = ÄÉíêáÉÄëÄÉÇáåÖíÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RN= = cáå~åòJKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NT= = åÉìíê~äÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RN= bêíê~Öëâçåíç KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QT= bêíê~Öëä~ÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK T= = cÉÜäÄÉíê~Ö= = åáÅÜí=ÇìêÅÜ=báÖÉåâ~éáí~ä=ÖÉÇÉÅâíÉê KKKKKKK PR= cÉêíáÖìåÖëÖÉãÉáåâçëíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKK OMP= cÉêíáÖìåÖëä∏ÜåÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMP= cÉêíáÖìåÖëã~íÉêá~äKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMP= cáå~åÅÉJiÉ~ëáåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPP= cáå~åò~åä~ÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NP= cáå~åòÄìÅÜÜ~äíìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK Q= cáå~åòä~ÖÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK T= cçêÇÉêìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NP= = Éáåï~åÇÑêÉáÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OVQI=PMQ= = ìåÉáåÄêáåÖäáÅÜÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OVQ= = òïÉáÑÉäÜ~ÑíÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OVQI=OVU= = ëçåëíáÖÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PNV= = ìåÉáåÄêáåÖäáÅÜÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OVQ= cçêÇÉêìåÖëÄÉïÉêíìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OVP= cêÉáÄÉêìÑäÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TS= cêÉãÇÄ~ìíÉáä KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VT= cêÉãÇÄÉäÉÖÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OV= cêÉãÇÑáå~åòáÉêìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOR= cêÉãÇâ~éáí~äKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NP= cêÉãÇï®ÜêìåÖëîÉêÄáåÇäáÅÜâÉáíÉåKKKKKKKKKKKK PQV= cêáëíáÖâÉáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQ= = dÉÄ®ìÇÉÄ~ì KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NVP= dÉÖÉåâçåíçKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PM= dÉÜ~äíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNPPI=NPQ= dÉäÇÉáåä~ÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQS= dÉäÇÉåíå~ÜãÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQO= dÉãÉáåâçëíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMP= dÉãÉáåâçëíÉå=ÑΩê=e~åÇÉäëï~êÉåKKKKKKKKKKKKK NQQ= dÉãÉáåëÅÜ~ÑíëâçåíÉåê~ÜãÉå KKKKKKKKKKKKKKKKKKKKK SO= dÉåÉê~äåçêã KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TT= dÉë~ãíâçëíÉåîÉêÑ~ÜêÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RS=
433
dÉëÅÜ®Ñíëà~ÜêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKR= dÉëÅÜ®ÑíëîçêÑ~ää KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKR= dÉïÉêÄÉÄÉíêáÉÄ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTP= dÉïáåå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QSI=RM= dÉïáååJ=ìåÇ=sÉêäìëíâçåíçKKKKKKKKKKKKKKKKKKKKKKKKKKQU= dÉïáååJ=ìåÇ=sÉêäìëíêÉÅÜåK KKKKKKQI=SI=TI=NSI=QS= dÉïáååêΩÅâä~ÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKPPO= ÖÉòÉáÅÜåÉíÉë=h~éáí~ä KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKPOU= dä®ìÄáÖÉêëÅÜìíòKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKT= dçáåÖJ`çåÅÉêåJmêáåòáé KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUP= dêìåÇÄìÅÜ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QI=R= dêìåÇÉêïÉêÄëíÉìÉê KKKKKKKKKKKKKKKKKKKKKKKKKKK NUVI=NVN= dêìåÇâ~éáí~ä KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKPOU= dêìåÇëíΩÅâëâ~ìÑKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NUVI=NVN= = e~ÄÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOR= = Jë~äÇçKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOT= = JòáåëÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOOV= e~åÇÉäëÄΩÅÜÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKSS= e~åÇÉäëï~êÉåâ~äâìä~íáçå KKKKKKKKKKKKKKKKKKKKKKKKKKNQQ= e~ìéíÄìÅÜ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QI=R= eÉêëíÉääìåÖëâçëíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKK OMRI=OSN= eáäÑëëíçÑÑ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKVT= e∏ÅÜëíïÉêíéêáåòáé KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKPQU= = fãé~êáí®íëéêáåòáéKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUS= fåÇìëíêáÉâçåíÉåê~ÜãÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKRV= fåÑçêã~íáçåëÑìåâíáçåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKS= fåÜ~ÄÉê~âíáÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKONN= fåëçäîÉåò KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOVP= fåëí~åÇÜ~äíìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNUR= fåíÉêáãëâçåíçKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNVS= fåîÉåí~ê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKT= fåîÉåíìê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNM= fåîÉëíáíáçåëÇ~êäÉÜÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOPM= fåò~ÜäìåÖå~ÜãÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOMM= = g~ÜêÉë~ÄëÅÜäìëë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKS= g~ÜêÉëÑÉÜäÄÉíê~Ö KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNS= g~ÜêÉëΩÄÉêëÅÜìëë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNS= = h~éáí~ä KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNO= = JÖÉëÉääëÅÜ~Ñí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SUI=POT= = JêΩÅâä~ÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKPPN= h~ìÑ~ÄêÉÅÜìåÖ=ÄÉá=^âíáÉåKKKKKKKKKKKKKKKKKKKKKKKKKONO= h~ìÑã~ååKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTP= = cçêãJKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTQ= = âê~Ñí=_Éí®íáÖìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTP= = âê~Ñí=báåíê~ÖìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTQ=
= káÅÜíJ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TQ= háêÅÜÉåëíÉìÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPP= hçãã~åÇáíÖÉëÉääëÅÜ~Ñí KKKKKKKKKKKKKKKKKKKKKKKKKKKKK POR= hçãã~åÇáíáëí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POS= hçãéäÉãÉåí®ê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POR= hçåíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQ= = J~êíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RV= = JÖêìééÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RV= = Jâä~ëëÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RV= hçåíçÑΩÜêìåÖëÖÉÄΩÜêÉåKKKKKKKKKKKKKKKKKKKKKKKKKKK OOV= hçåíçâçêêÉåíâêÉÇáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOU= hçåíçëìããÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OS= hçëíÉå= == báå~êÄÉáíìåÖëJKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTQ= = cáå~åòáÉêìåÖëJ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTQ= = ä~ìÑÉåÇÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTQ= hêÉÇáí= = J~ìÑå~ÜãÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPR= = JÖÉÄΩÜêÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPSI=OPU= = JâçëíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOR= = JîÉêÖäÉáÅÜ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOR= = JòáåëÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPSI=OPU= = JòΩÅâò~ÜäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQM= hìêë= = JÖÉïáåå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONQ= = JîÉêäìëíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONQ= = JïÉêí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONM= = i~ÖÉÄÉêáÅÜí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SI=OM= i~ÖÉêäÉáëíìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NRU= iÉ~ëáåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPNI=OPPI=OQM= iáÉÑÉê~åíÉåâêÉÇáíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOU= iáÉÑÉêÄÉÇáåÖìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMR= äáèìáÇÉ=jáííÉä KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NP= iáèìáÇáÉêÄ~êâÉáíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQ= iáëíÉåÉáåâ~ìÑëéêÉáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VV= iáëíÉåîÉêâ~ìÑëéêÉáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQP= içÜå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPPI=NPQ= içÜåòìë~íòâçëíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQN= = j®åÖÉäêΩÖÉKKKKKKKKKKKKKKKKKKKKKKKKKNMTI=NOTI=NQVI=NUM= j~≈ÖÉÄäáÅÜâÉáíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TM= = aìêÅÜÄêÉÅÜìåÖ=ÇÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TN= = ìãÖÉâÉÜêíÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TN= j~íÉêá~äÖÉãÉáåâçëíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMP= jáÉíÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPO= jáííÉäÜÉêâìåÑíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NO= jáííÉäîÉêïÉåÇìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NO= =
434
k~ÅÜä~ëëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOTI=NQU= k~ãÉåë~âíáÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONN= kÉÄÉåÄΩÅÜÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK R= kÉååÄÉíê~Öë~âíáÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONN= kÉååïÉêíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONM= káÉÇÉêëíïÉêíéêáåòáé KKKKKKKKKKKKKKKKKKK OTTI=OUTI=OVQ= kìíòìåÖëÇ~ìÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OSN= kìíòìåÖëÉåíå~ÜãÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQP= çÑÑÉåÉ=e~åÇÉäëÖÉëÉääëÅÜ~Ñí KKKKKKKKKKKKKKKKKKKKKKK POQ= léÉê~íÉJiÉ~ëáåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPP= = m~ÅÜí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPO= m~ëëáî~ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NO= m~ëëáîí~ìëÅÜ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OO= m~ìëÅÜ~äëéÉëÉåë~íòKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONN= m~ìëÅÜ~äïÉêíÄÉêáÅÜíáÖìåÖ KKKKKKKKKKKKKKKKK OVQI=PMQ= mÉêáçÇÉå~ÄÖêÉåòìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UQ= mêÉáë~åÖ~ÄÉåîÉêçêÇåìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKK OOS= mêÉáëå~ÅÜä®ëëÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMRI=NUM= mêáî~íÉáåä~ÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQN= mêáî~íÉåíå~ÜãÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQN= mêçÇìâíáçåëÑ~âíçêÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VT= mêçòÉëëÖäáÉÇÉêìåÖëéêáåòáé KKKKKKKKKKKKKKKKKKKKKKKKKK SO= mìÄäáòáí®íëÖÉëÉíòKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SU= = o~Ä~íí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NMSI=NQUI=NUM= o~íÉåâêÉÇáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPM= oÉ~äáë~íáçåëéêáåòáéKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UR= oÉÅÜåìåÖë~ÄÖêÉåòìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PNP= = ~âíáîÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PNQ= = ~åíáòáé~íáîÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PNU= = é~ëëáîÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PNR= = íê~åëáëíçêáëÅÜÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PNQ= oÉÅÜåìåÖëäÉÖìåÖëîçêëÅÜêáÑíÉå= = ÖÉëÉíòäáÅÜÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SR= oÉÅÜåìåÖëïÉëÉå== = ÉñíÉêåÉëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK Q= = áåíÉêåÉëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK P= oÉÖÉäëíÉìÉêë~íòKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSO= oÉáÜÉåÑçêãKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OR= oÉáåîÉêã∏ÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTI=UI=V= oÉëíëÅÜìäÇîÉêëáÅÜÉêìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOS= oáÅÜíáÖâÉáíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TUI=UN= oçÜëíçÑÑ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VT= oΩÅâä~ÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PPM= oΩÅâëÉåÇìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NNMI=NOSI=NRM= oΩÅâëíÉääìåÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PQN= = p~ÅÜ~åä~ÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NP=
p~ÅÜÉáåä~ÖÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQS= p~ÅÜÉåíå~ÜãÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQQ= p~äÇç KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OS= pÅÜäìëëÄÉëí~åÇ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OS= pÅÜäìëëÄáä~åò KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PU= pÅÜäìëëÄáä~åòâçåíç KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PS= pÅÜìäÇÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTI=U= = âìêòÑêáëíáÖÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NP= = ä~åÖÑêáëíáÖÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NP= pÉäÄëíâçëíÉåéêÉáë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQP= pâçåíç KKKKKKKKKKKKKKKKKKKKKKKK NNMI=NOTI=NQVI=NUMI=NUO= pçäáÇ~êáí®íëòìëÅÜä~ÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPP= pçääKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OR= = Jë~äÇç KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OT= = JòáåëÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOV= pçåÇÉêÉáåòÉäâçëíÉå== = ÇÉê=cÉêíáÖìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMP= = ÇÉë=sÉêíêáÉÄë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OMP= pçòá~äîÉêëáÅÜÉêìåÖ= = ^êÄÉáíÖÉÄÉê~åíÉáä KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPR= = ^êÄÉáíåÉÜãÉê~åíÉáä KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPR= pçòá~äîÉêëáÅÜÉêìåÖëÄÉáíê®ÖÉ KKKKKKKKKKKKKKKKKKKKKK NPP= pí~ÑÑÉäÑçêã KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OQ= pí~ãã~âíáÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONN= pí~ããâ~éáí~ä KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK POU= píÉìÉêÄÉãÉëëìåÖëÖêìåÇä~ÖÉKKKKKKKKKKKKKKKKKKKKKKKKK T= píÉìÉêå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NU= = ~âíáîáÉêìåÖëéÑäáÅÜíáÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKK OQV= = ÄÉíêáÉÄäáÅÜÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORM= = ÇìêÅÜä~ìÑÉåÇÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORN= = éêáî~íÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORM= píÉìÉêå~ÅÜò~ÜäìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORP= píÉìÉêêΩÅâÉêëí~ííìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ORO= píáÅÜí~ÖëÄÉïÉêíìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UP= píçêåçÄìÅÜìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK PO= píΩÅâ~âíáÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONN= píΩÅââìêë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONM= póëíÉãÄΩÅÜÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK R= = qJhçåíçKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OR= q~ÖÉëïÉêí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTT= qÉáäïÉêíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTV= = §ÄÉêëáÅÜíäáÅÜâÉáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UM= §ÄÉêòáÉÜìåÖëòáåëÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOV= rãä~ìÑîÉêã∏ÖÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKUI=NPI=OUT= rãë~íòÉêä∏ëÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSI=NQR= rãë~íòâçëíÉåîÉêÑ~ÜêÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RS= rãë~íòëíÉìÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSNI=NSR=
435
= JÉêâä®êìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNSP= = JêΩÅâÉêëí~ííìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNSS= = Jîçê~åãÉäÇìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNSP= = Jîçê~ìëò~ÜäìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNST= råÑ~ääîÉêëáÅÜÉêìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNQN= = s~äìíáÉêìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKONV= sÉêÄáåÇäáÅÜâÉáíI=ëçåëíáÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKPNU= sÉêÄáåÇäáÅÜâÉáíëêΩÅâëíÉääìåÖÉå KKKKKKKKKKKKKKKKKPQN= îÉêÄê~ìÅÜëçêáÉåíáÉêí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNMM= sÉêÉáåÑ~ÅÜìåÖëêÉÖÉäKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOTM= sÉêäìëíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK QSI=RM= sÉêãáííäìåÖëÖÉÄΩÜêÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOOS= sÉêã∏ÖÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TI=NO= sÉêã∏ÖÉåëÖÉÖÉåëí~åÇKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTM= = áãã~íÉêáÉääÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNP= îÉêã∏ÖÉåëïáêâë~ãÉ=iÉáëíìåÖÉå KKKKKKKKKKKKKKKNPU= sÉêã∏ÖÉåëä~ÖÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKS= sÉêêÉÅÜåìåÖëîÉêÄçí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKUM= sÉêë~åÇâçëíÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNQS= sÉêëí®åÇäáÅÜâÉáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTU= sÉêíêáÉÄëÖÉãÉáåâçëíÉåKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOMP= sÉêï~äíìåÖëÖÉãÉáåâçëíÉåKKKKKKKKKKKKKKKKKKKKKKKKKOMP= sÉêòÉáÅÜåáëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNM= sçääëí®åÇáÖâÉáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TUI=TV= sçê~ÄëÅÜäìëëÄìÅÜìåÖÉå KKKKKKKKKKKKK RUI=NOOI=ORT= sçêê®íÉ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNP= sçêê~íëÄÉïÉêíìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKOUU= sçêëÅÜìëë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNPS= sçêëíÉìÉê KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSNI=NSR= sçêëíÉìÉêΩÄÉêëÅÜìëë~âíáîáÉêìåÖ KKKKKKKKKKKKKKKNSV=
= == == == == == ==
= =
sçêòìÖë~âíáÉKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONN= = t~êÉåÉáåë~íòKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NOO= tÉêâëíçÑÑîÉêÄê~ìÅÜ KKKKKKKKKKKKKKKKKKKKKKKKKKK NOOI=NOT= ïÉêíÄÉÖêΩåÇÉåÇ=q~íë~ÅÜÉå KKKKKKKKKKKKKKKKKKKKKKKK UM= ïÉêíÉêÜÉääÉåÇÉ=q~íë~ÅÜÉåKKKKKKKKKKKKKKKKKKKKKKKKKKK TV= tÉêíé~éáÉêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NPI=OMVI=PMU= = ÑÉëíîÉêòáåëäáÅÜÉëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONV= = JÄÉïÉêíìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OUQ= tÉêíëíÉääìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ONV= tÉëÉåíäáÅÜâÉáíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UO= táääâΩêÑêÉáÜÉáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UN= táêíëÅÜ~ÑíäáÅÜâÉáí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK UO= táêíëÅÜ~ÑíëÖìíKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TM= = ÖÉêáåÖÑΩÖáÖÉë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTR= = ÖÉêáåÖïÉêíáÖÉë KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NTRI=NTS= táêíëÅÜ~Ñíëà~ÜêKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK TR= = w~Üää~ëí KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKNSNI=NSOI=NSQI=NSR= = Jé~ëëáîáÉêìåÖKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NSU= w~ÜäìåÖëÉáåÖ®åÖÉ=~ìë== = ~ÄÖÉëÅÜêáÉÄÉåÉå=cçêÇÉêìåÖÉå KKKK OVTI=OVU= wáÉäÉáåâ~ìÑëéêÉáëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK VV= wáÉäîÉêâ~ìÑëéêÉáëKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK NQP= wáåëÇ~êäÉÜÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OPN= wáåëÉå KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK OOR= wìëÅÜêÉáÄìåÖ KKKKKKKKKKKKKKKKKKKKKKKKKKKKK OTUI=OUMI=PMV= wïÉÅâ~ìÑï~åÇ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RM= wïÉÅâÉêíê~Ö KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK RM= =
