acca - f9 - study text - 2014/2015

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ACCA

PaperF9

FinancialManagement

EssentialText



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British library cataloguinginpublication data

AcataloguerecordforthisbookisavailablefromtheBritishLibrary.

Publishedby:KaplanPublishingUKUnit2TheBusinessCentreMollyMillarsLaneWokinghamBerkshireRG412QZ

KaplanFinancialLimited,2014

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PrintedandboundinGreatBritain.

Acknowledgements

WearegratefultotheAssociationofCharteredCertifiedAccountantsandtheCharteredInstituteofManagementAccountantsforpermissiontoreproducepastexaminationquestions. TheanswershavebeenpreparedbyKaplanPublishing.

Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,withoutthepriorwrittenpermissionofKaplanPublishing.

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Contents

Page

Chapter 1 Thefinancialmanagementfunction 1

Chapter 2 Basicinvestmentappraisaltechniques 19

Chapter 3 Investmentappraisaldiscountedcashflowtechniques

37

Chapter 4 Investmentappraisalfurtheraspectsofdiscountedcashflows

69

Chapter 5 Assetinvestmentdecisionsandcapitalrationing 99

Chapter 6 Investmentappraisalunderuncertainty 123

Chapter 7 Workingcapitalmanagement 147

Chapter 8 Workingcapitalmanagementinventorycontrol 177

Chapter 9 Workingcapitalmanagementaccountsreceivableandpayable

199

Chapter 10 Workingcapitalmanagementcashandfundingstrategies

219

Chapter 11 Theeconomicenvironmentforbusiness 239

Chapter 12 Financialmarketsandthetreasuryfunction 251

Chapter 13 Foreignexchangerisk 269

Chapter 14 Interestraterisk 301

Chapter 15 Sourcesoffinance 319

Chapter 16 Dividendpolicy 345

Chapter 17 Thecostofcapital 355

Chapter 18 Capitalstructure 403

Chapter 19 Financialratios 437

Chapter 20 Businessvaluationsandmarketefficiency 465

Chapter 21 Questions&Answers 505

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v

chapterIntroduction



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How to Use the Materials TheseKaplanPublishinglearningmaterialshavebeencarefullydesignedtomakeyourlearningexperienceaseasyaspossibleandtogiveyouthebestchancesofsuccessinyourexaminations.

Theproductrangecontainsanumberoffeaturestohelpyouinthestudyprocess.Theyinclude:

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Thecomplete text or essential textcomprisesthemainlearningmaterialsandgivesguidanceastotheimportanceoftopicsandwhereotherrelatedresourcescanbefound.Eachchapterincludes:

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Thelearning objectivescontainedineachchapter,whichhavebeencarefullymappedtotheexaminingbody'sownsyllabuslearningobjectivesoroutcomes.Youshouldusethesetocheckyouhaveaclearunderstandingofallthetopicsonwhichyoumightbeassessedintheexamination.

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Introduction

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Tricky topicWhenreviewingtheseareascareshouldbetakenandallillustrationsandtestyourunderstandingexercisesshouldbecompletedtoensurethatthetopicisunderstood.

Online subscribers

Syllabus

Syllabus objectives

The examination

Examination format

Paperbased examination tips

Study skills and revision guidance

Preparing to study

Effective studying

Three ways of taking notes

Revision

Further reading

YoucanfindfurtherreadingandtechnicalarticlesunderthestudentsectionofACCA'swebsite.

Introduction

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KAPLAN PUBLISHING ix

FORMULAE AND TABLES

Economic order quantity

H

o

CDC2

=

Miller-Orr Model

Return point = Lower limit + ( 31 spread)

31

43

rate interestcashflowsofvariancecostntransactio

3=Spread

The Capital Asset Pricing Model

E(ri) = Rf + i(E(rm) Rf)

The asset beta formula

a =

d

de

de

de

e T))(1V+V

T)(1V+T))(1V+(V

V

The Growth Model

)gr()g1(DP

e

00

+=

Gordons growth approximation

g = bre

The weighted average cost of capital

)T(1k V+V

V+k V+V

V=WACC dde

de

de

e

The Fisher formula

(1+i) = (1+r)(1+h)

Purchasing power parity and interest rate parity

)h+(1)h+(1

xS=Sb

c01 )i+(1

)i+(1xS=F

b

c00



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Present value table

Present value of 1, i.e. (1 + r)n

Where r = discount rate

n = number of periods until payment

Discount rate (r)

Periods (n) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621

6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424

10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386

11 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 12 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 15 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239

Discount rate (r)

Periods (n) 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

1 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 2 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 3 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 4 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.516 0.499 0.482 5 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402

6 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335 7 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 8 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 9 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194

10 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162

11 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 12 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112 13 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093 14 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078 15 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065



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KAPLAN PUBLISHING xi

Annuity table

Present value of an annuity of 1, i.e. r

r)+(11 n

Where r = discount rate

n = number of periods until payment

Discount rate (r)

Periods (n) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791

6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355 7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 8 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759

10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145

11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 8.495 12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 13 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.103 14 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 7.367 15 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.061 7.606

Discount rate (r)

Periods (n) 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

1 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 2 1.713 1.690 1.668 1.647 1.626 1.605 1.585 1.566 1.547 1.528 3 2.444 2.402 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106 4 3.102 3.037 2.974 2.914 2.855 2.798 2.743 2.690 2.639 2.589 5 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 2.991

6 4.231 4.111 3.998 3.889 3.784 3.685 3.589 3.498 3.410 3.326 7 4.712 4.564 4.423 4.288 4.160 4.039 3.922 3.812 3.706 3.605 8 5.146 4.968 4.799 4.639 4.487 4.344 4.207 4.078 3.954 3.837 9 5.537 5.328 5.132 4.946 4.772 4.607 4.451 4.303 4.163 4.031

10 5.889 5.650 5.426 5.216 5.019 4.833 4.659 4.494 4.339 4.192

11 6.207 5.938 5.687 5.453 5.234 5.029 4.836 4.656 4.486 4.327 12 6.492 6.194 5.918 5.660 5.421 5.197 4.968 4.793 4.611 4.439 13 6.750 6.424 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533 14 6.982 6.628 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.611 15 7.191 6.811 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675



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ThefinancialmanagementfunctionChapter learning objectives

Uponcompletionofthischapteryouwillbeableto:

explainthenatureandpurposeoffinancialmanagement distinguishbetweenfinancialmanagementandfinancialand

managementaccounting discusstherelationshipbetweenfinancialobjectives,corporate

objectivesandcorporatestrategy identifyanddescribeavarietyoffinancialobjectives,including:

shareholderwealthmaximisation profitmaximisation earningspersharegrowth

identifystakeholders,theirobjectivesandpossibleconflicts discussthepossibleconflictbetweenstakeholderobjectives discusstheroleofmanagementinmeetingstakeholder

objectives,includingtheuseofagencytheory explainwaystoencouragetheachievementofstakeholder

objectives,including: managerialrewardschemes regulatoryrequirements

discusstheimpactofnotforprofitstatusonfinancialandotherobjectives

discussthenatureandimportanceofValueforMoneyasanobjectiveinnotforprofitorganisations

discusswaysofmeasuringtheachievementofobjectivesinnotforprofitorganisations.

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1The nature and purpose of financial management

Financialmanagementisconcernedwiththeefficientacquisitionanddeploymentofbothshortandlongtermfinancialresources,toensuretheobjectivesoftheenterpriseareachieved.

Decisionsmustbetakeninthreekeyareas:

investmentbothlongterminvestmentinnoncurrentassetsandshortterminvestmentinworkingcapital

financefromwhatsourcesshouldfundsberaised? dividendshowshouldcashfundsbeallocatedtoshareholdersand

howwillthevalueofthebusinessbeaffectedbythis?

The financial management function

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An understanding of these three key areas is fundamental for the examination.

Intakingthesedecisions,thefinancialmanagerwillneedtotakeaccountof:

TheF9syllabuscoversallthesekeyaspectsoffinancialmanagement.

theorganisation'scommercialandfinancialobjectives thebroadereconomicenvironmentinwhichthebusinessoperates thepotentialrisksassociatedwiththedecisionandmethodsof

managingthatrisk.

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The investment decision

The dividend decision

The financing decision



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Financialmanagementshouldbedistinguishedfromotherimportantfinancialroles:

managementaccountingconcernedwithprovidinginformationforthemoredaytodayfunctionsofcontrolanddecisionmaking

financialaccountingconcernedwithprovidinginformationaboutthehistoricalresultsofpastplansanddecisions.

2The relationship between corporate strategy and corporate and financial objectives

Objectives/targetsdefinewhattheorganisationistryingtoachieve.Strategyconsidershowtogoaboutit.

3Financial objectives Shareholder wealth maximisation

Shareholderwealthmaximisationisafundamentalprincipleoffinancialmanagement.Youshouldseektounderstandthedifferentaspectsofthesyllabus(e.g.finance,dividendpolicy,investmentappraisal)withinthisunifyingtheme.

Manyotherobjectivesarealsosuggestedforcompaniesincluding:

profitmaximisation growth marketshare socialresponsibilities


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Financial rolesObjectives and strategyMaximising and satisficingAdditional question Objective s and strategyFinancial objectives



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4Stakeholder objectives and conflicts

Astakeholdergroupisonewithavestedinterestinthecompany.

Typicalstakeholdersforanorganisationwouldinclude:

Internal

Connected

External

Manyarguethatmanagersshouldbalancetheneedsandobjectivesofallstakeholders.

companyemployees companymanagers/directors

equityinvestors(ordinaryshareholders) customers suppliers financeproviders(debtholders/bankers) competitors

thegovernment thecommunityatlarge pressuregroups regulators.

Conflictbetweenandwithingroupsofstakeholdersandtheneedformanagementtobalancethevariousinterestsisakeyissue.

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Additional question Stakeholder conflicts

The stakeholder view



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5The role of management and goal congruence Agency theory

Agencytheoryisoftenusedtodescribetherelationshipsbetweenthevariousinterestedpartiesinafirmandcanhelptoexplainthevariousdutiesandconflictsthatoccur:

Agencyrelationshipsoccurwhenoneparty,the principal,employsanotherparty,the agent,toperformataskontheirbehalf.Inparticular,directors(agents)actonbehalfofshareholders(principals).

How to reduce the problems caused by agency relationships

Findingwaystoreducetheproblemsoftheagencyrelationshipandensurethatmanagerstakedecisionswhichareconsistentwiththeobjectivesofshareholdersisakeyissue.

Managerial reward schemes

Onewaytohelpensurethatmanagerstakedecisionswhichareconsistentwiththeobjectivesofshareholdersistointroducecarefullydesignedremunerationpackages.Theschemesshould:

Commontypesofrewardschemesinclude:

beclearlydefined,impossibletomanipulateandeasytomonitor linkrewardstochangesinshareholderwealth matchmanagerstimehorizonstoshareholderstimehorizons encouragemanagerstoadoptthesameattitudestoriskas

shareholders.

remunerationlinkedto: minimumprofitlevels economicvalueadded(EVA) revenuegrowth

executiveshareoptionschemes(ESOP).


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Agency theory

Additional question Managerial reward schemes

Managerial reward schemes



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Corporate governance codes

Thedirector/shareholderconflicthasalsobeenaddressedbytherequirementsofanumberofcorporategovernancecodes.Thefollowingkeyareasrelatetothisconflict.

Nonexecutivedirectors(NEDs) importantpresenceontheboard mustgiveobligationtospendsufficienttimewiththecompany shouldbeindependent.

Executivedirectors separationofchairmanandchiefexecutiveofficer(CEO) submitforreelection cleardisclosureoffinancialrewards outnumberedbytheNEDs.

Remunerationcommittees. Nominationcommittees. Annualgeneralmeeting(AGM).

Stock exchange listing requirements and other regulations

Althoughadherencetotheprinciplesofthecorporategovernancecodesisvoluntary,theyareoftenreferredtointhelistingrequirementsofstockexchanges.

6Measuring achievement of corporate objectives

Itisnecessaryformanagers,shareholdersandotherstakeholderstohavewaysofmeasuringtheprogressofthecompanytowardsitsobjectives. Thisiscommonlydoneviaratioanalysis.

Ratioanalysiscomparesandquantifiesrelationshipsbetweenfinancialvariables.

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Corporate governance codes

Other regulations



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Ratioanalysiscanbegroupedintofourmaincategories:

ThespecificratioscoveredintheF9syllabuswillbelookedatindetailinchapter19althoughsomeofthemmayalreadybefamiliartoyoufrompreviouspapers.

Profitabilityandreturn Debtandgearing Liquidity Investor

7Objective setting in not for profit organisations

Theprimaryobjectiveofnotforprofitorganisations(NFPsorNPOs)isnottomakemoneybuttobenefitprescribedgroupsofpeople.

Aswithanyorganisation,NFPswilluseamixtureoffinancialandnonfinancialobjectives.

However,withNFPsthenonfinancialobjectivesareoftenmoreimportantandmorecomplexbecauseofthefollowing.

Mostkeyobjectivesareverydifficulttoquantify,especiallyinfinancialterms,e.g.qualityofcaregiventopatientsinahospital.

MultipleandconflictingobjectivesaremorecommoninNFPs,e.g.qualityofpatientcareversusnumberofpatientstreated.

Value for money (VFM) and the 3 Es

VFMcanbedefinedasachievingthedesiredlevelandqualityofserviceatthemosteconomicalcost.


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Objective setting in NFPs

VFM



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The three Es

Assessingwhethertheorganisationprovidesvalueformoneyinvolveslookingatallfunctioningaspectsoftheorganisation.Performancemeasureshavebeendevelopedtopermitevaluationofeachpartseparately.

VFM

Economy:Minimisingthecostsofinputsrequiredtoachieveadefinedlevelofoutput.

Efficiency:Ratioofoutputstoinputsachievingahighlevelofoutputinrelationtotheresourcesputin(inputdriven)orprovidingaparticularlevelofserviceatreasonableinputcost(outputdriven)

Effectiveness:Whetheroutputsareachievedthatmatchthepredeterminedobjectives.

Useofthe3EsasaperformancemeasureandawaytoassessVFMisakeyissueforexaminationquestionsthatrelatetoNFPsandpublicsectororganisations.

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KAPLAN PUBLISHING 9

3Es

Measuring the achievement of objectives in NFPs



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Asubsidisedcollegecanteenserviceistobeevaluatedbythelocalcounciltoassessamongstotherthings,whetheritisfinanciallysoundandoffersvalueformoney.

Suggest appropriate measures of achievement that could be set for the service.

Which of the following is NOT one of the three main types of decision facing the financing manager in a company?

A DividenddecisionB InvestmentdecisionC EconomicdecisionD Financingdecision

Theagencyproblemisadrivingforcebehindthegrowingimportanceattachedtosoundcorporategovernance.

In this context, the 'agents' are the:

A CustomersB ShareholdersC ManagersD Auditors


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Test your understanding 1 Not for profit organisations

Test your understanding 3




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Which of the following is an example of a financial objective that a company might choose to pursue?

A ProvisionofgoodwagesandsalariesB DealinghonestlyandfairlywithcustomersonalloccasionsC ProducingenvironmentallyfriendlyproductsD Restrictingthelevelofgearingtobelowaspecifiedtargetlevel

In the context of managing performance in 'not for profit' organisations, which of the following definitions is incorrect?

A Valueformoneymeansprovidingaserviceinawaywhichiseconomical,efficientandeffective

B Economymeansdoingthingscheaply: notspending$2whenthesamethingcanbeboughtfor$1

C Efficiencymeansdoingthingsquickly: minimisingtheamountoftimethatisspentonagivenactivity

D Effectivenessmeansdoingtherightthings: spendingfundssoastoachievetheorganisation'sobjectives

Which of the following is a problem associated with managerial reward schemes?

A Byrewardingperformance,aneffectiveschemecreatesanorganisationfocusedoncontinuousimprovement

B Schemesbasedonsharescanmotivateemployees/managerstoactinthelongterminterestsofthecompany

C Selfinterestedperformancemaybeencouragedattheexpenseofteamwork

D Effectiveschemesattractandkeeptheemployeesvaluabletoanorganisation

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Chapter summary





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chapter 1




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chapter 1


Answer to additional question Objectives and strategy

Answer to additional question Managerial reward schemes

Answer to additional question Stakeholder conflicts



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Test your understanding answers

Financialmeasures:

Economytargets:

Efficiencytargets:

Effectivenesstargets:

proportionofoverallfundsspentonadministrationcosts abilitytostaywithinbudget/breakeven revenuetargetsmet.

costsofpurchasingprovisionsofsuitablenutritionalquality costsofnegotiatingforandpurchasingequipment negotiationofbulkdiscounts payratesforstaffofappropriatelevelsofqualification.

numbersofportionsproduced costpermealsold levelsofwastageofunpreparedandofcookedfood staffutilisation equipmentlife.

numbersusingthecanteen customersatisfactionratings nutritionalvalueofmealsserved.

Answer C

Financialmanagementaimstoensurethatthemoneyisavailabletofinanceprofitableprojectsandtoselectthoseprojectswhichthecompanyshouldundertake. Onceprofitshavebeenmadethedecisionthenneedstobemadeabouthowmuchtodistributetotheownersandhowmuchtoreinvestforthefuture.



Test your understanding 1 Not for profit organisations




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Answer C

Theseparationofownershipandcontrolcreatesasituationwheremanagersactastheagentsoftheowners(shareholders).

Answer D

Thisisafinancialobjectivethatrelatestothelevelofriskthatthecompanyaccepts.

Answer C

Efficiencymeansdoingthingswell: gettingthebestuseoutofwhatmoneyisspenton.

Answer C

Thisidentifiesatypicalproblemassociatedwithmanymanagerialrewardschemes.

chapter 1








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BasicinvestmentappraisaltechniquesChapter learning objectives


definearelevantcashflow(anddistinguishitfromanaccountingprofit)

identifyandcalculaterelevantcashflowsinascenario calculatethepaybackperiodanduseittoappraisean

investment discusstheusefulnessofpaybackasaninvestmentappraisal

method calculatereturnoncapitalemployed(ROCE)(accountingrateof

return)anduseittoappraiseaninvestment discusstheusefulnessofROCEasaninvestmentappraisal

method.

19

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1Investment appraisal process

Onestageinthecapitalbudgetingprocessis investment appraisal.Thisappraisalhasthefollowingfeatures:

assessmentofthelevelofexpectedreturnsearnedforthelevelofexpendituremade

estimatesoffuturecostsandbenefitsovertheprojectslife.

Twobasicappraisaltechniquesarecoveredinthischapter:

Moresophisticatedmethodsofinvestmentappraisalaredealtwithinthenextchapter.

ROCE Payback.

Examinationquestionsmayaskyoutocompareandcontrasttheuseofthesetwobasictechniques.

Basic investment appraisal techniques




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2ROCE

Thisisalsoknownasaccountingrateofreturn(ARR).

oralternatively:

Theaverageinvestmentcanbecalculatedas:

AverageannualprofitsbeforeinterestandtaxROCE= 100%

Initialcapitalcosts

AverageannualprofitsbeforeinterestandtaxROCE= 100%

Averagecapitalinvestment

Initialinvestment +scrapvalueAveragecapitalinvestment=

2

Intheexamyoushouldusetheinitialcapitalcostunlessyouaretoldotherwise. However,theROCEcalculationbasedontheaveragecapitalinvestmentisthemethodmostcommonlyaskedforintheexam. Thiswillbemadeclearinthequestion.

Decision rule:

IftheexpectedROCEfortheinvestmentisgreaterthanthetargetorhurdlerate(asdecidedbymanagement)thentheprojectshouldbeaccepted.

Aprojectinvolvestheimmediatepurchaseofanitemofplantcosting$110,000.Itwouldgenerateannualcashflowsof$24,400forfiveyears,startinginYear1.Theplantpurchasedwouldhaveascrapvalueof$10,000infiveyears,whentheprojectterminates.Depreciationisonastraightlinebasis.

Determine the project's ROCE using:

(a) initialcapitalcosts(b) averagecapitalinvestment

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Test your understanding 1 ROCE



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Aprojectrequiresaninitialinvestmentof$800,000andthenearnsnetcashinflowsasfollows:

Inaddition,attheendofthesevenyearprojecttheassetsinitiallypurchasedwillbesoldfor$100,000.

Determine the projects ROCE using:

Year 1 2 3 4 5 6 7Cashinflows($000) 100 200 400 400 300 200 150

(a) initialcapitalcosts(b) averagecapitalinvestment.

3Advantages and disadvantages of ROCE

Advantagesinclude:

Disadvantagesinclude:

simplicity linkswithotheraccountingmeasures.

noaccountistakenofprojectlife noaccountistakenoftimingofcashflows itvariesdependingonaccountingpolicies itmayignoreworkingcapital itdoesnotmeasureabsolutegain thereisnodefinitiveinvestmentsignal.

IntheexaminationitisimportantthatyoucandiscussthefeaturesofROCEasaninvestmentappraisaltechnique,inadditiontobeingabletocalculateit.



Advantages and disadvantages of ROCE

Initial capital cost




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4Accounting profits and cash flows

Incapitalinvestmentappraisalitismoreappropriatetoevaluatefuturecashflowsthanaccountingprofits,because:

profitscannotbespent profitsaresubjective cashisrequiredtopaydividends.

5Cash flows and relevant costs

Forallmethodsofinvestmentappraisal,withtheexceptionofROCE,onlyrelevantcashflowsshouldbeconsidered.Theseare:

Ignore:

future incremental cashbased.

sunkcosts committedcosts noncashitems allocatedcosts.

Amanufacturingcompanyisconsideringtheproductionofanewtypeofwidget.Eachwidgetwilltaketwohourstomake.

Fixedoverheadsareapportionedonthebasisof$1perlabourhour.

Ifthenewwidgetsareproduced,thecompanywillhavetoemployanadditionalsupervisoratasalaryof$15,000pa.Thecompanywillproduce10,000widgetspa.

What are the relevant cash flows?

chapter 2


Relevant costs

Test your understanding 3 Relevant costs

Profits versus cash flows



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6Payback method of appraisal

Thepaybackperiodisthetimeaprojectwilltaketopaybackthemoneyspentonit.Itisbasedonexpectedcashflowsandprovidesameasureofliquidity.

Decision rule:

Constant annual cash flows

onlyselectprojectswhichpaybackwithinthespecifiedtimeperiod choosebetweenoptionsonthebasisofthefastestpayback

initialinvestmentPayback period=

annualcashflow

Anexpenditureof$2millionisexpectedtogeneratenetcashinflowsof$500,000eachyearforthenextsevenyears.

What is the payback period for the project?

Apaybackperiodmaynotbeforanexactnumberofyears. Tocalculatethepaybackinyearsandmonthsyoushouldmultiplythedecimalfractionofayearby12tothenumberofmonths.

Aprojectwillinvolvespending$1.8millionnow.Annualcashflowsfromtheprojectwouldbe$350,000.

What is the expected payback period?

Uneven annual cash flows

Inpractice,cashflowsfromaprojectareunlikelytobeconstant.Wherecashflowsareuneven,paybackiscalculatedbyworkingoutthecumulativecashflowoverthelifeoftheproject.



Test your understanding 4 Payback with constant annual cash

Test your understanding 5 Payback in years and months

Additional question Relevant costs



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Aprojectisexpectedtohavethefollowingcashflows:

What is the expected payback period?

Year Cash flow$000

0 (1,900)1 3002 5003 6004 8005 500

Calculate the payback period in years and months for the following project:

Year Cash flow$000

0 (3,100)1 1,0002 9003 8004 5005 500

7Advantages and disadvantages of payback

Advantagesinclude:

itissimple itisusefulincertainsituations:

rapidlychangingtechnology improvinginvestmentconditions

chapter 2


Test your understanding 6 Payback with uneven cash flows




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Disadvantagesinclude:

itfavoursquickreturn: helpscompanygrowth minimisesrisk maximisesliquidity

itusescashflows,notaccountingprofit.

itignoresreturnsafterthepaybackperiod itignoresthetimingsofthecashflows itissubjectivenodefinitiveinvestmentsignal itignoresprojectprofitability.

Intheexaminationitisimportantthatyoucandiscussthefeaturesofpaybackasaninvestmentappraisaltechniqueaswellasbeingabletodothecalculation.

Which of the following is an example of a relevant cash flow to be considered in an investment appraisal process for a new project?

A MarketresearchexpenditurealreadyincurredB AdditionaltaxthatwillbepaidonextraprofitsgeneratedC Centrallyallocatedoverheadsthatarenotaconsequenceof

undertakingtheprojectD Taxallowabledepreciation



Advantages and disadvantages of payback




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Garfieldplcisconsideringwhethertoenterintoanewproject. Themachinerywhichwouldbeusedtoproducethegoodsforthecontractwaspurchasedsevenyearsagoatacostof$80,000,withanestimatedlifeoftenyears. Depreciationisonastraightlinebasis. Themachineryhasbeenidleforsometime,andifnotusedonthiscontractwouldbescrappedandsoldimmediatelyforanestimated$5,000. Afteruseonthiscontractthemachinerywouldhavenovalue,andwouldhavetobedismantledanddisposedofatacostof$1,500.

Ignoring the time value of money (covered later in Chapter 3), what is the relevant cost of the machine to the new contract?

A $3,500B $5,000C $6,500D $24,500

Which of the following is an advantage of the payback method of investment appraisal?

A Ittakesaccountofthetimingofthecashflowswithinthepaybackperiod

B ItusesaccountingprofitsratherthancashflowsC Ittakesaccountofthecashflowsaftertheendofthepayback

periodandthereforethetotalprojectreturnD Itcanbeusedasascreeningdeviceasafirststageineliminating

obviouslyinappropriateprojectspriortomoredetailedevaluation

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Which of the following statements is not true?

A Thereturnoncapitalemployedmethodofinvestmentappraisaltakesaccountofthelengthoftheproject

B FocusonanearlypaybackperiodcanenhanceliquidityC InvestmentriskisincreasedifthepaybackperiodislongerD Shortertermforecastsarelikelytobemorereliable

Acornplcisconsideringpurchasinganewmachineatacostof$110,400thatwillbeoperatedforfouryears,afterwhichtimeitwillbesoldforanestimated$9,600. Acornusesastraightlinepolicyfordepreciation.

Forecastoperatingprofitstobegeneratedbythemachineareasfollows:

Select the payback period (PP) and the average return on capital employed (ROCE), calculated as average annual profits divided by the average investment.

Year $1 39,6002 19,6003 22,4004 32,400

A PP:2.02years ROCE:47.5%B PP:3.89years ROCE:25.8%C PP:3.89years ROCE:47.5%D PP:2.02years ROCE:25.8%







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Chapter summary

chapter 2




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Answer to additional question Relevant costs



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Annualcashflowsaretakentobeprofitbeforedepreciation.

Using average capital investment:

Averageannualprofits(asbefore)=$4,400

Averageannualdepreciation

= ($110,000$10,000)5

= $20,000Averageannualprofit

= $24,400$20,000

= $4,400Using initial cost:

AverageannualprofitROCE = 100%

Initialcapitalcost

$4,400= 100% =4%

$110,000

Initialcost+Finalscrapvalue

Averagebookvalueofassets

=

2

$110,000+$10,000= =$60,000

2

AverageannualprofitROCE = 100%

Averagebookvalueofassets

$4,400

= 100% =7.33%$60,000

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Thisusesprofitsratherthancashflows.

(a)

Averageannualinflows=$1,750,0007 =$250,000Averageannualdepreciation=($800,000$100,000)7 =$100,000(Anet$700,000isbeingwrittenoffasdepreciationover7years.)Averageannualprofit=$250,000$100,000 =$150,000Theaveragecapitalinvestedis(800,000+100,000)2 =$450,000

Averageannualprofit $150,000ROCE= 100= 100=18.75%

Initialcapitalcost $800,000 (b)

Averageannualprofit $150,000ROCE= 100= 100=33.33%

Averagecapitalinvestment $450,000

Onlythe$15,000salaryisrelevant.Thefixedoverheadsarenotincrementaltothedecisionandshouldbeignored.

$2,000,000Payback period= =4years

$500,000



Test your understanding 4 Payback with constant annual cash

Test your understanding 3 Relevant costs




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$1,800,000Payback= =5.1429years

$350,000

0.1429ofayear12months=1.7months(rounded=2months)

Theanswercanthereforebestatedaseither:

assumingcashflowsoccurevenlythroughouttheyear.

5.1years 5years2months

Year Cash flow Cumulative cash flow

$000 $0000 (1,900) (1,900)1 300 (1,600)2 500 (1,100)3 600 (500)4 800 3005 500 800

Inthetableaboveacolumnisaddedforcumulativecashflowsfortheprojecttodate.Figuresinbracketsarenegativecashflows.

Eachyearscumulativefigureissimplythecumulativefigureatthestartoftheyearplusthefigureforthecurrentyear.Thecumulativefigureeachyearisthereforetheexpectedpositionasattheendofthatyear.

PaybackisbetweentheendofYear3andtheendofYear4thatisduringYear4.Thisisthepointatwhichthecumulativecashflowchangesfrombeingnegativetopositive.Ifweassumeaconstantrateofcashflowthroughouttheyear,wecouldestimatethatpaybackwillbethreeyearsplus($500/800)ofYear4.Thisisbecausethecumulativecashflowisminus$500atthestartoftheyearandtheYear4cashflowwouldbe$800.

chapter 2


Test your understanding 5 Payback in years and months




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$500/800=0.625

Thereforepaybackisafter3.625years.

Paybackinyearsandmonthsiscalculatedbymultiplyingthedecimalfractionofayearby12months.Inthisexample,0.625years=7.5months(0.62512months),whichisroundedto8months.Sotherefore,paybackoccursafter3years8months.

Notethatifcashflowsweredeemedtoariseattheendoftheyearthenthepaybackperiodwouldbe4years.

Thepaybackperiodwouldbecalculatedasfollows.

PaybackisbetweentheendofYear3andtheendofYear4,inotherwordsduringYear4.

Ifweassumeaconstantrateofcashflowthroughtheyear,wecouldestimatethatpaybackwillbethreeyears,plus($400/500)ofYear4,whichis3.8years.

0.8years=10months(0.812)

Wecouldthereforeestimatethatpaybackwouldbeafter3years10months.

Year Cash flow Cumulative cash flow

$000 $0000 (3,100) (3,100)1 1,000 (2,100)2 900 (1,200)3 800 (400)4 500 1005 500 600






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Answer B

Anycostincurredinthepast(A),oranycommittedcostswhichwillbeincurredregardlessofwhetherornotaninvestmentisundertaken(C),arenotrelevantcashflows. Theyhaveoccurred,orwilloccur,whateverinvestmentdecisionistaken. Anycostswhichdonotrepresentanactualcashflow(D)shouldalsobeignored.

Answer C

$Lossofopportunitytogainrevenue 5,000Payfordismantle 1,500

6,500

Answer D

Thepaybackmethodignoresboththetimingofthecashflowswithinthepaybackperiod(A)andthecashflowsaftertheendofthepaybackperiod(C). Thepaybackmethodusescashflowsratherthanaccountingprofits(B).

Answer A

TheROCEmethodfailstotakeaccountofthelifeoftheproject.

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Answer A

PP:

Depreciationmustbeaddedbacktotheannualprofitfiguretoderivetheannualcashflows.

Annualdepreciation($110,400$9,600)/4years=$25,200

Adding$25,200toeachyear'sprofitfigureproducesthefollowingcashflows.

Paybackperiod=2years+(800/(47,600)1year)=2.02years

Ifyouselectedapaybackperiodof3.89yearsyoubasedyourcalculationsontheaccountingprofitsafterthedeductionofdepreciation.Thecalculationofthepaybackperiodshouldbebasedoncashflows.

ROCE:

Averageprofit=$(39,600+19,600+22,400+32,400)/4=$28,500Averageinvestment=$(110,400+9,600)/2=$60,000ROCE=$(28,500/60,000)100%=47.5%

IfyouselectedaROCEof25.8%youcalculatedtheROCEusingtheopeninginvestmentratherthantheaverageinvestment.

Cash flow

Cumulative cash flow

$ $Initialinvestment (110,400) (110,400)Year1 64,800 (45,600)Year2 44,800 (800)Year3 47,600 46,800






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InvestmentappraisaldiscountedcashflowtechniquesChapter learning objectives


explaintheconceptofthetimevalueofmoney calculatethefuturevalueofasumbycompounding calculatethepresentvalue(PV)ofasinglesumusingaformula calculatethePVofasinglesumusingdiscounttables calculatethePVofanannuityusingaformula calculatethePVofanannuityusingannuitytables calculatethePVofaperpetuityusingaformula calculatethePVofadvancedannuitiesandperpetuities calculatethePVofdelayedannuitiesandperpetuities explainthebasicprinciplebehindtheconceptofacostofcapital calculatethenetpresentvalue(NPV)ofaninvestmentanduseit

toappraisetheproposal discusstheusefulnessofNPVasaninvestmentappraisal

methodanditssuperiorityovernondiscountedcashflows(DCF)methods

calculatetheinternalrateofreturn(IRR)ofaninvestmentanduseittoappraisetheproposal

discusstheusefulnessofIRRasaninvestmentappraisalmethodanditssuperiorityovernonDCFmethods

discusstherelativemeritsofNPVandIRR.

37

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1The time value of money

Moneyreceivedtodayisworthmorethanthesamesumreceivedinthefuture,i.e.ithasatime value.

Thisoccursforthreereasons:

potentialforearninginterest/costoffinance impactofinflation effectofrisk.

ThisisakeyconceptthroughouttheF9syllabus.

Discountedcashflow(DCF)techniquestakeaccountofthistimevalueofmoneywhenappraisinginvestments.

Investment appraisal discounted cash flow techniques


The time value of money



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2Compounding

Asuminvestedtodaywillearninterest.Compoundingcalculatesthefutureorterminalvalueofagivensuminvestedtodayforanumberofyears.

Tocompoundasum,thefigureisincreasedbytheamountofinterestitwouldearnovertheperiod.

Aninvestmentof$100istobemadetoday.Whatisthevalueoftheinvestmentaftertwoyearsiftheinterestrateis10%?

Solution

The$100willbeworth$121intwoyearsataninterestrateof10%.

Thisisafairlystraightforwardcalculation. However,ifthequestionaskedforthevalueoftheinvestmentafter20years,itwouldtakealotlonger.

$Valueafteroneyear 1001.1= 110Valueaftertwoyears 1101.1= 121

So,tospeeduptheprocess,wecanuseaformulatocalculatethefuturevalueofasuminvestednow. Theformulais:

F=P(1+r)n

whereF=Futurevalueafternperiods

P=PresentorInitialvalue

r=Rateofinterestperperiod

n=Numberofperiods

Theterminalvalueisthevalue,innyears'time,ofasuminvestednow,ataninterestrateofr%.

chapter 3


Illustration 1 Compounding



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Youhave$5,000toinvestnowforsixyearsataninterestrateof5%pa.

What will be the value of the investment after six years?

3Discounting

Inapotentialinvestmentproject,cashflowswillariseatmanydifferentpointsintime.Tomakeausefulcomparisonofthedifferentflows,theymustallbeconvertedtoacommonpointintime,usuallythepresentday,i.e.thecashflowsarediscounted.

Discounting a single sum

Thepresentvalue(PV)isthecashequivalentnowofmoneyreceivable/payableatsomefuturedate.

ThePVofafuturesumcanbecalculatedusingtheformula:

Thisisjustarearrangementoftheformulaweusedforcompounding.

(1+r)niscalledthediscountfactor(DF).

FP= = F(1+r)n

(1+r)n

WhatisthePVof$115,000receivableinnineyears'timeifr=6%?



Test your understanding 2 Discounting a single sum

Test your understanding 1 Compounding



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4The cost of capital

Intheabovediscussionswereferredtotherateofinterest.Thereareanumberofalternativetermsusedtorefertotherateafirmshouldusetotakeaccountofthetimevalueofmoney:

costofcapital discountrate requiredreturn.

Whatevertermisused,therateofinterestusedfordiscountingreflectsthecostofthefinancethatwillbetiedupintheinvestment.

5The Net Present Value (NPV)

ToappraisetheoverallimpactofaprojectusingDCFtechniquesinvolvesdiscountingalltherelevantcashflowsassociatedwiththeprojectbacktotheirPV.

Ifwetreatoutflowsoftheprojectasnegativeandinflowsaspositive,theNPVoftheprojectisthesumofthePVsofallflowsthatariseasaresultofdoingtheproject.

TheNPVrepresentsthesurplusfunds(afterfundingtheinvestment)earnedontheproject,therefore:

iftheNPVispositivetheprojectisfinanciallyviable iftheNPViszerotheprojectbreakseven iftheNPVisnegativetheprojectisnotfinanciallyviable ifthecompanyhastwoormoremutuallyexclusiveprojectsunder

considerationitshouldchoosetheonewiththehighestNPV theNPVgivestheimpactoftheprojectonshareholderwealth.

chapter 3


What does the NPV actually mean?



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Assumptions used in discounting

Unlesstheexaminertellsyouotherwise,thefollowingassumptionsaremadeaboutcashflowswhencalculatingthenetpresentvalue:

Alsonote,youshouldneverincludeinterestpaymentswithinanNPVcalculationasthesearetakenaccountofbythecostofcapital.

allcashflowsoccuratthestartorendofayear initialinvestmentsoccurT0 othercashflowsstartoneyearafterthat(T1).

Thecashflowsforaprojecthavebeenestimatedasfollows:

Thecostofcapitalis6%.

Convert these cash flows to a PV.

Calculate the net present value (NPV) of the project to assess whether it should be undertaken.

Year $0 (25,000)1 6,0002 10,0003 8,0004 7,000



Assumptions used in discounting

Test your understanding 3 Net present value



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Anorganisationisconsideringacapitalinvestmentinnewequipment.Theestimatedcashflowsareasfollows.

Thecompanyscostofcapitalis9%.

Calculate the NPV of the project to assess whether it should be undertaken.

Year Cash flow$

0 (240,000)1 80,0002 120,0003 70,0004 40,0005 20,000

6Advantages and disadvantages of using NPV

Advantages

TheoreticallytheNPVmethodofinvestmentappraisalissuperiortoallothers.Thisisbecauseit:

Disadvantages

considersthetimevalueofmoney isanabsolutemeasureofreturn isbasedoncashflowsnotprofits considersthewholelifeoftheproject shouldleadtomaximisationofshareholderwealth.

Itisdifficulttoexplaintomanagers Itrequiresknowledgeofthecostofcapital Itisrelativelycomplex.

chapter 3



Advantages and disadvantages of NPV



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7Timesaving in the exam

AlthoughyouwillbeabletoperformalmostanyNPVcalculationusingtheaboveinformation,thereareanumberoftimesavingtechniquesthatcanhelpyouintheexam.

Present Value Tables

(1+r)niscalledthediscountfactor(DF). IntheexamyouwillbeprovidedwithaPresentValuetablethatgivesthediscountfactorsforvariousdifferentdiscountratesovervarioustimeperiod. So,tofindtheDF,forexampleifr=10%andn=5,youcan:

Whatamountshouldbeinvestednowtoreceive$10,000infouryears'timeifr=8%pa.

Showyourworkingsusingtheformulaapproachandthencomparethiswithusingthepresentvaluetable.

Discounting annuities

Anannuityisaconstantannualcashflowforanumberofyears.



Test your understanding 5 Discounting using tables



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Apaymentof$1,000istobemadeeveryyearfor3years,thefirstpaymentoccurringinoneyearstime.Theinterestrateis10%.WhatisthePVoftheannuity?

Solution

ThePVofanannuitycouldbefoundbyaddingthePVsofeachpaymentseparately.

However,youcanseefromthetablethatthesumofalltheDFis2.486.

ThereforethePVcanbefoundmorequickly:

$1,0002.486=$2,486.

Time Payment DF @ 10% (from tables)

PV

$ $T1 1,000 0.909 909T2 1,000 0.826 826T3 1,000 0.751 751

2.486 2,486

Theannuity factor(AF)isthenamegiventothesumoftheindividualDF.

ThePVofanannuitycanthereforebequicklyfoundusingtheformula:

PV=AnnualcashflowAF

Likewithcalculatingadiscountfactor,theAFcanbefoundusingaformula.

Theformulais:

1(1+r)nAF=

r

chapter 3


Illustration 2 Discounting annuities



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Apaymentof$3,600istobemadeeveryyearforsevenyears,thefirstpaymentoccurringinoneyearstime.Theinterestrateis8%.WhatisthePVoftheannuity.

Annuity Tables

JustasyouareprovidedwithaPresentValueTableintheexamshowingprecalculateddiscountfactors,youwillalsobeprovidedwithanAnnuityTable(sometimesreferredtoasaCumulativePresentValueTable),whichprovidesprecalculatedannuityfactorsforvariousdifferentdiscountratesovervariousperiods.

Soagain,youhaveachoice. Forexample,forathreeyearannuityat10%:

Note:theremightbeasmalldifferenceduetoroundings.

Thetablesshouldnotbeusedasasubstituteforknowinghowtousetheformula. Remember,thetablesonlycoverasmallrangeofdiscountratesandtimeperiodsandyoumayberequiredtocalculateadiscountfactororannuityfactorforvariablesoutsideofthisrange.

Apaymentof$11,400istobemadeeveryyearfor13years,thefirstpaymentoccurringinoneyearstime.Theinterestrateis5%.WhatisthePVoftheannuity.

Showyouworkingsusingboththeformulaapproachandtheannuitytable.



Test your understanding 6 Discounting annuities

Test your understanding 7 Discounting annuities using tables



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Discounting perpetuities

A perpetuityisanannualcashflowthatoccursforever.

Itisoftendescribedbyexaminersasacashflowcontinuingfortheforeseeablefuture.

ThePVofaperpetuityisfoundusingtheformula

cashflowPV=

r or 1

PV=cashflow r

1 isknownastheperpetuityfactor. r

ThePVofagrowing perpetuityisfoundusingtheformula

1PV=cashflowatT1

r g1

isknownastheperpetuityfactor,withgrowthrg

Calculate the present value of the following, assuming a discount rate of 10%.

(1) $3,000receivedinoneyear'stimeandforever(2) $3,000receivedinoneyear'stime,thengrowingby2%perannum

inperpetuity

chapter 3


Test your understanding 8 Discounting perpetuities



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Advanced and delayed annuities and perpetuities

Theuseofannuityfactorsandperpetuityfactorsbothassumethatthefirstcashflowwillbeoccurringinoneyear'stime.Annuityorperpetuityfactorswillthereforediscountthecashflowsbacktogivethevalueoneyearbeforethefirstcashflowarose.Forstandardannuitiesandperpetuitiesthisgivesthepresent(T0)valuesincethefirstcashflowstartedatT1.

Becareful:ifthisisnotthecase,youwillneedtoadjustyourcalculation.

Advanced annuities and perpetuities

Someregularcashflowsmaystartnow(atT0)ratherthaninoneyear'stime(T1).

CalculatethePVbyignoringthepaymentatT0whenconsideringthenumberofcashflowsandthenaddingonetotheannuityorperpetuityfactor.

Delayed annuities and perpetuities

SomeregularcashflowsmaystartlaterthanT1.

Thesearedealtwithby:

(1) applyingtheappropriatefactortothecashflowasnormal(2) discountingyouranswerbacktoT0.



Delayed annuities: An illus trationAdvanced annuities: An illustrationAdvanced perpetuities : An illus trationAdditional question Adv anced annuities and perpetuitiesAdditional question Delayed annuities and perpetuities



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8The Internal Rate of Return (IRR)

TheIRRisanotherprojectappraisalmethodusingDCFtechniques.

TheIRRrepresentsthediscountrateatwhichtheNPVofaninvestmentiszero.Assuchitrepresentsabreakevencostofcapital.

Decision rule:

projectsshouldbeacceptediftheirIRRisgreaterthanthecostofcapital.

Calculating the IRR using linear interpolation

Thestepsinlinearinterpolationare:

where:

L=Lowerrateofinterest

H=Higherrateofinterest

NL=NPVatlowerrateofinterest

NH=NPVathigherrateofinterest.

(1) CalculatetwoNPVsfortheprojectattwodifferentcostsofcapital(2) UsethefollowingformulatofindtheIRR:

chapter 3


IRR



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ThediagrambelowshowstheIRRasestimatedbytheformula.

ApotentialprojectspredictedcashflowsgiveaNPVof$50,000atadiscountrateof10%and$10,000atarateof15%.

Calculate the IRR.

FortheexaminationthechoiceofratestoestimatetheIRRislessimportantthanyourabilitytoperformthecalculationtoestimateit.



Calculating the IRR

Test your understanding 9 IRR



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Abusinessundertakeshighriskinvestmentsandrequiresaminimumexpectedrateofreturnof17%paonitsinvestments.Aproposedcapitalinvestmenthasthefollowingexpectedcashflows:

Year 01234

$(50,000)18,00025,00020,00010,000

(1) CalculatetheNPVoftheprojectifthecostofcapitalis15%.(2) CalculatetheNPVoftheprojectifthecostofcapitalis20%.(3) UsetheNPVsyouhavecalculatedtoestimatetheIRRofthe

project.(4) Recommend,onfinancialgroundsalone,whetherthisprojectshould

goahead.

FindtheIRRofaninvestmentof$50,000iftheinflowsare:

(a) $5,000inperpetuity(b) $8,060foreightyears.

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Test your understanding 11 IRR with even cash flows

Calculating the IRR with even cash flows

Calculating the IRR with perpetuities



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9Advantages and disadvantages of IRR

Advantages

TheIRRhasanumberofbenefits,e.g.it:

TheNPVmethodwouldsuggestthatProjectAmakesforabetterinvestment(itsimplycomparestheabsolutevalueoftheNPV). This,however,doesnotreflecttherelativesizeoftheinvestmenttobemadeinthisproject. A$20minvestmentislikelytohavehigherrisksandahigherreturnmightbeexpectedthanonly$0.2m. TheIRR,ontheotherhand,clearlyshowsthatProjectBprovidesamuchhigherreturnoninvestmentandaccountsforthefactthatProjectBinvolvesamuchsmallerscaleofinvestment.

Disadvantages

considersthetimevalueofmoney isapercentageandthereforeeasilyunderstood usescashflowsnotprofits considersthewholelifeoftheproject meansafirmselectingprojectswheretheIRRexceedsthecostof

capitalshouldincreaseshareholders'wealth isagoodwaytocompareprojectsofdifferentscales. Considerthe

followingtwoprojects: Project A Project B

Initialinvestment $20m $0.5mPresentvalueofreturns $20.2m $0.6mNPV $0.2m $0.1mIRR 2% 15%

Itisnotameasureofabsoluteprofitability. Interpolationonlyprovidesanestimateandanaccurateestimate

requirestheuseofaspreadsheetprogramme. Itisfairlycomplicatedtocalculate. NonconventionalcashflowsmaygiverisetomultipleIRRswhich

meanstheinterpolationmethodcan'tbeused.



Advantages and disadvantages of IRR



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10NPV versus IRR

BothNPVandIRRareinvestmentappraisaltechniqueswhichdiscountcashflowsandaresuperiortothebasictechniquesdiscussedintheprevioussession.HoweveronlyNPVcanbeusedtodistinguishbetweentwomutuallyexclusiveprojects,asthediagrambelowdemonstrates:

TheprofileofprojectAissuchthatithasalowerIRRandapplyingtheIRRrulewouldpreferprojectB.Howeverinabsoluteterms,AhasthehigherNPVatthecompanyscostofcapitalandshouldthereforebepreferred.

NPVisthereforethebettertechniqueforchoosingbetweenprojects.

TheadvantageofNPVisthatittellsustheabsoluteincreaseinshareholderwealthasaresultofacceptingtheproject,atthecurrentcostofcapital.TheIRRsimplytellsushowfarthecostofcapitalcouldincreasebeforetheprojectwouldnotbeworthaccepting.

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PepperCoiscontemplatingthreeavailableinvestmentopportunities,thecashflowsofwhicharegivenbelow.

Ineachcasetheinitialinvestmentrepresentsthepurchaseofplantandequipmentwhoserealisablevaluewillbe20%ofinitialcost,receivableinadditiontotheaboveflowattheendofthelifeoftheproject.

Required:

Foreachofthethreeprojects:

Project Initial investment Cash flow

Y1 Y2 Y3 Y4 Y5

$000 $000 $000 $000 $000 $000

E (125) 50 50 50 50

F (120) 15 15 15 15 200

G (170) 120 80

(a) Calculatetheaccountingrateofreturn(basedontheaverageinvestmentmethod)

(b) Calculatethepaybackperiod(c) Calculatethenetpresentvalueusingadiscountrateof10%(d) Calculatetheinternalrateofreturn

The higher risk of a project can be recognised by decreasing

A thecostoftheinitialinvestmentoftheprojectB theestimatesoffuturecashinflowsfromtheprojectC theinternalrateofreturnoftheprojectD therequiredrateofreturnoftheproject



Test your understanding 12 Appraisal techniques




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Which of the following statements about net present value (NPV) and internal rate of return (IRR) methods are correct?

(i) AninvestmentwithapositiveNPVisfinanciallyviable(ii) NPVisasuperiormethodofinvestmentappraisaltoIRR(iii) ThegraphofNPVagainstdiscountratehasanegativeslopefor

mostprojects(iv) NPVisthepresentvalueofexpectedfuturenetcashreceiptsless

thecostoftheinvestmentA (i)and(ii)onlyB (ii)and(iv)onlyC (i),(ii)and(iii)onlyD (i),(ii),(iii)and(iv)

Which of the following is not an advantage of the IRR?

A ItconsidersthewholelifeoftheprojectB ItusescashflowsnotprofitsC ItisameasureofabsolutereturnD Itconsidersthetimevalueofmoney

Arburyplchasmadeaninvestmentwithanetpresentvalue(NPV)of$42,000at10%andanNPVof($22,000)at20%.

What is the internal rate of return of the project?

A 31.0%B 16.6%C 15.0%D 13.4%

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Acompanyisconsideringatwoyearprojectwhichhastwoannualinternalratesofreturn,namely10%and25%. Thesumoftheundiscountedcashflowsispositive.

The project will necessarily have a positive net present value, when the annual cost of capital is

A Morethan25%B Morethan10%C Between10%and25%D Lessthan25%






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Chapter summary

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Answer to additional question advanced

Answer to additional question delayed



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F=$5,000(1+0.05)6

=$5,0001.3401

=$6,700

F 115,000P= = =$68,068

(1+r)n (1+0.06)9

Year Cash flow DF PV$ at 6% $

0 (25,000) 1.000 (25,000)1 6,000 0.943 5,6582 10,000 0.890 8,9003 8,000 0.840 6,7204 7,000 0.792 5,544

1,822

TheNPVoftheprojectispositiveat$1,822. Theprojectshouldthereforebeaccepted.

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Test your understanding 2 Discounting a single sum

Test your understanding 1 Compounding




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Year Cash flow DF at 9% PV$ $

0 (240,000) 1.000 (240,000)1 80,000 0.917 73,3602 120,000 0.842 101,0403 70,000 0.772 54,0404 40,000 0.708 28,3205 20,000 0.650 13,000

NPV +29,760

ThePVofcashinflowsexceedsthePVofcashoutflowsby$29,760,whichmeansthattheprojectwillearnaDCFreturninexcessof9%,i.e.itwillearnasurplusof$29,760afterpayingthecostoffinancing.Itshouldthereforebeundertaken.

TheamounttobeinvestedisthePVofthefuturesum.

P=$10,000/(1.08)4=$7,350

P=$10,0000.735=$7,350(usingtables).

Usingtheformula:

$3,6005.206=$18,741.60

1(1+r)n 1(1.08)7 = =5.206

r 0.08



Test your understanding 6 Discounting annuities

Test your understanding 5 Discounting using tables




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Usingtheformula:

$11,4009.394=$107,091.60

Fromtheannuityfactortables,theAF=9.394.

1(1+r)n 1(1.05)13 = =9.394

r 0.05

$3,000(1) PV= =$30,000

0.1

$3,000(2) PV= =$37,500

0.10.02

50,000IRR= 10%+ (15%10%) =14.17%

50,000(10,000)

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Test your understanding 8 Discounting perpetuities


Test your understanding 7 Discounting annuities using tables



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Year Cash flow

DF @ 15% PV @ 15% DF @ 20% PV @ 20%

$ $ $ 0 (50,000) 1.000 (50,000) 1.000 (50,000)1 18,000 0.870 15,660 0.833 14,9942 25,000 0.756 18,900 0.694 17,3503 20,000 0.658 13,160 0.579 11,5804 10,000 0.572 5,720 0.482 4,820

NPV +3,440 (1,256)

TheIRRisabove15%butbelow20%.

Usingtheinterpolationmethod:

(1) TheNPVis+3,440at15%.(2) TheNPVis1,256at20%.(3) TheestimatedIRRistherefore:

3,440IRR= 15%+ (2015)%

(3,440(1,256)= 15% +3.7%= 18.7%

(4) TheprojectisexpectedtoearnaDCFreturninexcessofthetargetrateof17%,soonfinancialgrounds(ignoringrisk)itisaworthwhileinvestment.






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Annualinflow $5,000(a) IRR= 100= 100=10%

Initialinvestment $50,000

(b) NPVcalculation

Cash flow DF(c) % PV$ $

Time0 Investment (50,000) 1 (50,000)18 Inflow 8,060 (b) (a)

NPV Nil

Theaimistofindthediscountrate(c)thatproducesanNPVofnil.

Thereforethepresentvalueofinflows(a)mustequalthepresentvalueofoutflows,$50,000.

Ifthepresentvalueofinflows(a)istobe$50,000andthesizeofeachinflowis$8,060,thediscountfactorrequiredmustbe50,0008,060=6.203.

Thediscountrate(c)forwhichthisisthe8yearfactorcanbefoundbylookingalongthe8yearrowofthecumulativediscountfactorsshownintheannuitytable.

Thefigureof$6.210appearsunderthe6%columnsuggestinganIRRof6%istheclosest.

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Test your understanding 11 IRR with even cash flows



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(a) Accounting rate of return

ForeachprojecttheARRhasbeencalculatedas:

anddepreciationhasbeencalculatedasinitialinvestmentscrapvalue.

Project E

Project F

Project G

Project E

Project F

$120k(4$15k)=$60k

$60k$200k=0.3

Paybackthereforehappensafter4.3yearsorapprox4years,4months

(Totalcashflowsdepreciation)projectlifeARR= 100%

(Initialinvestment+scrapvalue)2

($200k$100k)4ARR= 100% =33.3%

($125k+$25k)2

($260k$96k)5ARR= 100% =45.6%

($120k+$24k)2

($200k$136k)2ARR= 100% =31.4%

($170k+$34k)2 (b) Payback

$125kPayback= =2.5years

$50k



Test your understanding 12 Appraisal techniques



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Project G

$170k$120k=$50k

$50k$80k=0.63

Paybackthereforehappensafter1.63years,orapprox1yearsand7months

Project E

NPV=($125k)+$50k3.170+$25k0.683=$50.6k

Project F

NPV=($120k)+$15k3.170+$200k0.621+$24k0.621=$66.7k

Project G

NPV=($170k)+$120k0.909+$80k0.826+$34k0.826=$33.2k

NPV@20%

Project E

NPV=($125k)+$50k2.589+$25k0.482=$16.5k

Project F

NPV=($120k)+$15k2.589+$200k0.402+$24k0.402=$8.9k

Project G

NPV=($170k)+$120k0.833+$80k0.694+$34k0.694=$9.1k

IRRs=

(c) NPV @ 10%

(d) Internal rate of return

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Project E

Project F

Project G

$50.6kIRR= 10%+ (20%10%) =24.8%

$50.6k$16.5k

$66.7kIRR= 10%+ (20%10%) =21.5%

$66.7k$8.9k

$33.2kIRR= 10%+ (20%10%) =23.8%

$33.2k$9.1k

Answer B

Theinternalrateofreturn(C)andthecostoftheinitialinvestment(A)areindependentoftheriskoftheproject. Thehighertheriskoftheproject,thegreater(notless)istherequiredrateofreturn(D).

Answer D

Allfourstatementsarecorrect. TheNPVmethodisextensivelyusedinpracticetoascertainwhetheraprojectisaviableinvestmentornot.







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Answer C

IRRisbasedondiscountedcashflowprinciples. Itthereforeconsidersallofthecashflowsinaproject(A),doesnotincludenotionalaccountingcostssuchasdepreciation(B)anditconsidersthetimevalueofmoney(D).

Itisnotanabsolutemeasureofreturn,however,astheIRRisexpressedasapercentage. TwoprojectscanhavethesameIRRbutverydifferentcashflows. Cisthereforeanincorrectstatement.

Answer B

TheIRRcanbecalculatedusingthefollowingformula.

If:

a=10%b=20%A=$42,000B=($22,000)

Then:IRR=a%+(A/(AB))(ba)%=10+0.6610=16.6%

Ifyouselected31.0%youdidnotaccountcorrectlyforthefactthattheNPVwasnegativeatadiscountrateof20%. Youtreatedthe$22,000NPVasapositivefigureinthecalculation. Ifyouselected13.4%youswappedAandBroundintheformula,usingA=$22,000andB=$42,000. Ifyouselected15.0%youhavesimplycalculatedthemidpointofthetworatesinsteadofusingtheIRRformula.

Answer A

ThegraphwouldbeUshapedwithanegativeNPVbetween10%and25%andpositiveNPVsatlessthan10%ormorethan25%.

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InvestmentappraisalfurtheraspectsofdiscountedcashflowsChapter learning objectives


explaintheimpactofinflationoninterestratesanddefineanddistinguishbetweenrealandnominal(money)interestrates

explainthedifferencebetweentherealtermsandnominaltermsapproachestoinvestmentappraisal

usethenominal(money)termsapproachtoappraiseaninvestment

usetherealtermsapproachtoappraiseaninvestment explaintheimpactoftaxonDCFappraisals calculatethetaxcashflowsassociatedwithtaxallowable

depreciationandincorporatethemintonetpresentvalues(NPV)calculations

calculatethetaxcashflowsassociatedwithtaxableprofitsandincorporatethemintoNPVcalculations

explaintheimpactofworkingcapitalonanNPVcalculationandincorporateworkingcapitalflowsintoNPVcalculations.

69

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4



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1The impact of inflation on interest rates

Inflationisageneralincreaseinpricesleadingtoageneraldeclineintherealvalueofmoney.

Intimesofinflation,thefundproviderswillrequireareturnmadeupoftwoelements:

Theoverallrequiredreturniscalledthemoneyornominalrateofreturn.

realreturnfortheuseoftheirfunds(i.e.thereturntheywouldwantiftherewerenoinflationintheeconomy)

additionalreturntocompensateforinflation.

Therealandmoney(nominal)returnsarelinkedbytheformula:

(1+i)=(1+r)(1+h)

where

i=moneyrate

r=realrate

h=inflation

Investment appraisal further aspects of discounted cash flows




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$1,000isinvestedinanaccountthatpays10%interestpa.Inflationiscurrently7%pa.

Find the real return on the investment.

Iftherealrateofinterestis8%andtherateofinflationis5%,whatshouldthemoneyrateofinterestbe?

2The impact of inflation on cash flows

Wherecashflowshavenotbeenincreasedforexpectedinflationtheyaredescribedasbeingin current prices,ortoday's prices.

Wherecashflowshavebeenincreasedtotakeaccountofexpectedinflationtheyareknownasmoney cash flows,ornominal cash flows.Remember,iftheydotakeinflationintoaccount,theyrepresentexpectedflowsofmoney,hencethetermmoneycashflows.

You can assume that cash flows you are given in the exam are the money cash flows unless told otherwise.

Iftheexaminerspecifiesthatthecashflowsareincurrentpricetermsyouwillgenerallyneedtoputtheseinmoneytermsbeforeyoucandiscountthem(althoughseeothermethodsofdealingwithinflationbelow).

Makesureyoureadthequestioncarefully.SometimesyouwillbegiventhecashflowsinYear1termswithsubsequentinflation.

Forexampleifthequestiontellsyouthatsalesforthenext3yearsare$100incurrenttermsbutareexpectedtoinflateby10%,thenwhatheactuallymeansisthatthesaleswillbe:Year1: $110Year2: $121 i.e.thesearethecashflowsinmoneytermsYear3: $133.10

chapter 4


Illustration of relationship between inflation and interest rates

Test your understanding 2 Money and real returns

Test your understanding 1 Money and real returns



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Forexampleifthequestionsays"Saleswillbe$100inthefirstyear,butaretheygoingtoinflateby10%forthenexttwoyears",thenthesaleswillbe:Year1:$100Year2:$110 comparethesetothepreviousexamplemakesureYear3:$121 youunderstandwhytheyaredifferent!

TheimpactofinflationcanbedealtwithintwodifferentwaysbothmethodsgivethesameNPV.

StormCoisevaluatingProjectX,whichrequiresaninitialinvestmentof$50,000.Expectednetcashflowsare$20,000perannumforfouryearsattodaysprices.Howevertheseareexpectedtoriseby5.5%pabecauseofinflation.Thefirmsmoneycostofcapitalis15%.

Find the NPV by:

(a) discountingmoneycashflows(b) discountingrealcashflows.



Test your understanding 3 Money and real methods



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Aprojecthasthefollowingcashflowsbeforeallowingforinflation,i.e.theyarestatedattheirT0values.

Thecompanysmoneydiscountrateis15.5%.Thegeneralrateofinflationisexpectedtoremainconstantat5%.

Evaluate the project in terms of:

Timing Cash flow$

0123

(750)330242532

(a) realcashflowsandrealdiscountrates(b) moneycashflowsandmoneydiscountrates.

3Specific and general inflation rates

TheTYUs givenabovehadallcashflowsinflatingatthegeneralrateofinflation.Inpractice,inflationdoesnotaffectallcoststothesameextent.Insomeinvestmentappraisalquestionsyoumaybegiveninformationonmorethanoneinflationrate. Inthesesituationsyouwillhaveinformationonbothspecificinflationratesandgeneralinflationrates.

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Test your understanding 4 Money and real methods



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Insituationswhereyouaregivenanumberofspecificinflationrates,therealmethodoutlinedabovecannotbeused.

Thefollowinggivesausefulsummaryofhowtoapproachexaminationquestions.

Ifaquestioncontainsbothtaxandinflation,itisadvisabletousethemoneymethod.

Intheexamination,forashortlifeproject,withcashflowsinflatingatdifferentrates,itisbesttosettheNPVcalculationoutwiththecashflowsdownthesideandthetimeacrossthetop.



Specific and general inflation rates



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Acompanyisconsideringacostsavingproject.Thisinvolvespurchasingamachinecosting$7,000,whichwillresultinannualsavings(inrealterms)onwagecostsof$1,000andonmaterialcostsof$400.

Thefollowingforecastsaremadeoftheratesofinflationeachyearforthenextfiveyears:

Thecostofcapitalofthecompany,inrealterms,is8.5%.

Evaluate the project, assuming that the machine has a life of five years and no scrap value.

Wagecosts 10%Materialcosts 5%Generalprices 6%

4Dealing with tax in NPV calculations

Sincemostcompaniespaytax,theimpactofcorporationtaxmustbeconsideredinanyinvestmentappraisal.

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Test your understanding 5 General and specific inflation rates



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The impact of taxation on cash flows

CorporationtaxchargedonacompanysprofitsisarelevantcashflowforNPVpurposes.Itisassumed,unlessotherwisestatedinthequestion,that:

operatingcashinflowswillbetaxedatthecorporationtaxrate operatingcashoutflowswillbetaxdeductibleandattracttaxreliefatthe

corporationtaxrate investmentspendingattractstaxallowabledepreciation thecompanyisearningnettaxableprofitsoverall(thisavoidsany

issuesofcarryinglossesforwardstoreducefuturetaxation). taxispaidoneyearaftertherelatedoperatingcashflowisearned

(unlesstoldotherwise)

Taxallowable depreciation

Fortaxpurposes,abusinessmaynotdeductthecostofanassetfromitsprofitsasdepreciation(inthewayitdoesforfinancialaccountingpurposes).

Insteadthecostmustbedeductedfromtaxableprofitsintheformoftaxallowabledepreciation.Thebasicrulesareasfollows:

taxallowabledepreciationiscalculatedbasedonthewrittendownvalueoftheassets(thiswilleitherbeonareducingbalanceorstraightlinebasisreadthequestioncarefully)

thetotalamountoftaxallowabledepreciationgivenoverthelifeofanassetwillequatetoitsfallinvalueovertheperiod(i.e.thecostlessanyscrapproceeds)

taxallowabledepreciationisclaimedasearlyaspossible taxallowabledepreciationisgivenforeveryyearofownershipexcept

theyearofdisposal intheyearofsaleorscrapabalancingallowance(BA)orbalancing

chargearises(BC).



The impact of taxation on cash flows



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$Originalcostofasset XCumulativetaxallowabledepreciationclaimed (X)

Writtendownvalueoftheasset XDisposalvalueoftheasset (X)

Balancingallowanceorbalancingcharge X

Anassetisboughtfor$10,000andwillbeusedonaprojectforfouryearsafterwhichitwillbedisposedof.Taxispayableat30%,oneyearinarrears,andtaxallowabledepreciationisavailableat25%reducingbalance.

Required:

(a) Calculatethetaxallowabledepreciationandhencethetaxsavingsforeachyeariftheproceedsondisposaloftheassetare$2,500.

(b) Howwouldyouranswerchangeiftheassetwassoldfor$5,000?(c) Ifnettradingincomefromtheprojectis$8,000pa,basedonyour

answertopart(a)andacostofcapitalof10%,calculatetheNPVoftheproject.

Fortaxpurposescaremustbetakentoidentifytheexacttimeofassetpurchaserelativetotheaccountingperiodend. However,unlessyouaretoldotherwiseintheexamyoushouldassumethatanassetispurchasedonthefirstdayofanaccountingperiod(T0)andthatthefirstamountoftaxallowabledepreciationisgivenoneyearlateratT1.

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Test your understanding 6 Balancing allowance or charge

Timing of asset purchase and sale

Taxallowable depreciation

Additional question: Timing of asset purchase and sale



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5Incorporating working capital

Investmentinanewprojectoftenrequiresanadditionalinvestmentinworkingcapital,i.e.thediffer

acca - f9 - study text - 2014/2015

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