Download - ACCA F9 Essential Text D09-J10
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ACCAPaperF9FinancialmanagementEssentialtext
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British library cataloguinginpublication data
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
Publishedby:KaplanPublishingUKUnit2TheBusinessCentreMollyMillarsLaneWokinghamBerkshireRG412QZ
ISBN9781847107541
KaplanFinancialLimited,2009
ThetextinthismaterialandanyothersmadeavailablebyanyKaplanGroupcompanydoesnotamounttoadviceonaparticularmatterandshouldnotbetakenassuch.Norelianceshouldbeplacedonthecontentasthebasisforanyinvestmentorotherdecisionorinconnectionwithanyadvicegiventothirdparties.Pleaseconsultyourappropriateprofessionaladviserasnecessary.KaplanPublishingLimitedandallotherKaplangroupcompaniesexpresslydisclaimallliabilitytoanypersoninrespectofanylossesorotherclaims,whetherdirect,indirect,incidental,consequentialorotherwisearisinginrelationtotheuseofsuchmaterials.
PrintedintheUKbyCPIWilliamClowes,BecclesNR347TL.
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 Capitalbudgetingandbasicinvestmentappraisaltechniques
19
Chapter 3 Investmentappraisaldiscountedcashflowtechniques
35
Chapter 4 Investmentappraisalfurtheraspectsofdiscountedcashflows
57
Chapter 5 Assetinvestmentdecisionsandcapitalrationing 87
Chapter 6 Investmentappraisalunderuncertainty 107
Chapter 7 Workingcapitalmanagement 127
Chapter 8 Workingcapitalmanagementinventorycontrol 155
Chapter 9 Workingcapitalmanagementaccountsreceivableandpayable
171
Chapter 10 Workingcapitalmanagementcashandfundingstrategies
187
Chapter 11 Foreignexchangerisk 215
Chapter 12 Interestraterisk 247
Chapter 13 Theeconomicenvironment 261
Chapter 14 Sourcesoffinance 275
Chapter 15 Thecostofcapital 299
Chapter 16 Capitalstructure 337
Chapter 17 Financialratios 367
Chapter 18 Dividendpolicy 391
Chapter 19 Businessvaluationsandmarketefficiency 397
Chapter 20 Questions&Answers 427
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chapterIntroduction
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How to Use the Materials TheseKaplanPublishinglearningmaterialshavebeen
carefullydesignedtomakeyourlearningexperienceaseasyaspossibleandtogiveyouthebestchancesofsuccessinyourexaminations.
Theproductrangecontainsanumberoffeaturestohelpyouinthestudyprocess.Theyinclude:
Thesectionsonthestudyguide,thesyllabusobjectives,theexaminationandstudyskillsshouldallbereadbeforeyoucommenceyourstudies.Theyaredesignedtofamiliariseyouwiththenatureandcontentoftheexaminationandgiveyoutipsonhowtobesttoapproachyourlearning.
Thecomplete text or essential textcomprisesthemainlearningmaterialsandgivesguidanceastotheimportanceoftopicsandwhereotherrelatedresourcescanbefound.Eachchapterincludes:
(1) Detailedstudyguideandsyllabusobjectives(2) Descriptionoftheexamination(3) Studyskillsandrevisionguidance(4) Completetextoressentialtext(5) Questionpractice
Thelearning objectivescontainedineachchapter,whichhavebeencarefullymappedtotheexaminingbody'sownsyllabuslearningobjectivesoroutcomes.Youshouldusethesetocheckyouhaveaclearunderstandingofallthetopicsonwhichyoumightbeassessedintheexamination.
Thechapter diagramprovidesavisualreferenceforthecontentinthechapter,givinganoverviewofthetopicsandhowtheylinktogether.
Thecontentforeachtopicareacommenceswithabriefexplanationordefinitiontoputthetopicintocontextbeforecoveringthetopicindetail.Youshouldfollowyourstudyingofthecontentwithareviewoftheillustration/s.Theseareworkedexampleswhichwillhelpyoutounderstandbetterhowtoapplythecontentforthetopic.
Introduction
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Test your understandingsectionsprovideanopportunitytoassessyourunderstandingofthekeytopicsbyapplyingwhatyouhavelearnedtoshortquestions.Answerscanbefoundatthebackofeachchapter.
Summary diagramscompleteeachchaptertoshowtheimportantlinksbetweentopicsandtheoverallcontentofthepaper.Thesediagramsshouldbeusedtocheckthatyouhavecoveredandunderstoodthecoretopicsbeforemovingon.
Question practiceisprovidedatthebackofeachtext.
Icon Explanations
Definition thesesectionsexplainimportantareasofKnowledgewhichmustbeunderstoodandreproducedinanexamenvironment.
Key Point identifiestopicswhicharekeytosuccessandareoftenexamined.
New identifiestopicsthatarebrandnewinpapersthatbuildon,andthereforealsocontain,learningcoveredinearlierpapers.
Expandable Text withintheonlineversionoftheworkbookisamoredetailedexplanationofkeyterms,thesesectionswillhelptoprovideadeeperunderstandingofcoreareas.Referencetothistextisvitalwhenselfstudying.
Test Your Understanding followingkeypointsanddefinitionsareexerciseswhichgivetheopportunitytoassesstheunderstandingofthesecoreareas.Withintheworkbooktheanswerstothesesectionsareleftblank,explanationstothequestionscanbefoundwithintheonlineversionwhichcanbehiddenorshownonscreentoenablerepetitionofactivities.
Illustration tohelpdevelopanunderstandingoftopicsandthetestyourunderstandingexercisestheillustrativeexamplescanbeused.
Exclamation Mark thissymbolsignifiesatopicwhichcanbemoredifficulttounderstand,whenreviewingtheseareascareshouldbetaken.
FormoredetailsaboutthesyllabusandtheformatofyourexampleaseseeyourCompleteTextorgoonline.
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Online subscribers Paper introductionPaper backgroundObjectives of the syllabusCore areas of the syllabusSyllabus objectivesThe examinationExamination formatPaperbased examination tips Study skills and revision guidancePreparing to studyEffective studyingThree ways of taking notes:RevisionFurther reading
YoucanfindfurtherreadingandtechnicalarticlesunderthestudentsectionofACCAswebsite.
Introduction
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ThefinancialmanagementfunctionChapter learning objectives
Uponcompletionofthischapteryouwillbeableto:
explainthenatureandpurposeoffinancialmanagement distinguishbetweenfinancialmanagementandfinancialand
managementaccounting discusstherelationshipbetweenfinancialobjectives,corporate
objectivesandcorporatestrategy identifyanddescribeavarietyoffinancialobjectives,including:
shareholderwealthmaximisation profitmaximisation earningspersharegrowth
identifyofstakeholders,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.
Financialmanagementshouldbedistinguishedfromotherimportantfinancialroles:
managementaccountingconcernedwithprovidinginformationforthemoredaytodayfunctionsofcontrolanddecisionmaking
financialaccountingconcernedwithprovidinginformationaboutthehistoricalresultsofpastplansanddecisions.
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Expandable text The investment decision
Expandable text The financing decision
Expandable text The dividend decision
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2The relationship between corporate strategy and corporate and financial objectives
Objectives/targetsdefinewhattheorganisationistryingtoachieve.Strategyconsidershowtogoaboutit.
Thefollowinglistcontainssomecommercialobjectives/targets,somefinancialobjectives/targetsandsomestrategies,allatdifferentlevelsofthebusiness.Identifywhichiswhich.
ImplementaJustInTime(JIT)inventorysystem. Increaseearningspershare(EPS)by5%onprioryear. Acquirearivalinashareforsharepurchase. Buyfournewcuttingmachinesfor$250,000each. Achievereturnsof15%onnewmanufacturinginvestment. Improvetheratioofcurrentassetstocurrentliabilitiesfrom1.7to
1.85. Reduceunsoldinventoryitemsby12%. Updatemanufacturingcapacitytoincorporatenewtechnology. ImprovebrandawarenesswithintheUK. Commercial
objectives /targetsFinancialobjectives /targets
Strategies
Corporatelevel
Businesslevel
Operationallevel
The financial management function
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Expandable text Financial roles
Expandable text Objectives and strategy
Test your understanding 1 Objectives and strategies
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3Financial objectivesShareholder wealth maximisation
Shareholderwealthmaximisationisafundamentalprincipleoffinancialmanagement.Youshouldseektounderstandthedifferentaspectsofthesyllabus(e.g.finance,dividendpolicy,investmentappraisal)withinthisunifyingtheme.
Manyotherobjectivesarealsosuggestedforcompaniesincluding:
profitmaximisation growth marketshare socialresponsibilities
4Stakeholder objectives and conflicts
Astakeholdergroupisonewithavestedinterestinthecompany.
Typicalstakeholdersforanorganisationwouldinclude:
Manyarguethatmanagersshouldbalancetheneedsandobjectivesofallstakeholders.
thecommunityatlarge companyemployees companymanagers/directors equityinvestors(ordinaryshareholders) customers suppliers financeproviders thegovernment.
Conflictbetweenandwithingroupsofstakeholdersandtheneedformanagementtobalancethevariousinterestsisakeyissue.
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Expandable text Maximising and satisficing
Expandable text Financial objectives
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Suggestthepotentialconflictsinobjectiveswhichcouldarisebetweenthefollowinggroupsofstakeholdersinacompany.
Stakeholders Potential conflictEmployees Shareholders Customers Communityat
large
Shareholders Financeproviders
Customers Shareholders/managers
Government Shareholders Shareholders Managers
5The role of management and goal congruenceAgency theory
Agencytheoryisoftenusedtodescribetherelationshipsbetweenthevariousinterestedpartiesinafirmandcanhelptoexplainthevariousdutiesandconflictsthatoccur:
Agencyrelationshipsoccurwhenoneparty,the principal,employsanotherparty,the agent,toperformataskontheirbehalf.Inparticular,directors(agents)actonbehalfofshareholders(principals).
Findingwaystoreducetheproblemsoftheagencyrelationshipandensurethatmanagerstakedecisionswhichareconsistentwiththeobjectivesofshareholdersisakeyissue
Managerial reward schemes
Onewaytohelpensurethatmanagerstakedecisionswhichareconsistentwiththeobjectivesofshareholdersistointroducecarefullydesignedremunerationpackages.Theschemesshould:
beclearlydefined,impossibletomanipulateandeasytomonitor
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Test your understanding 2 Stakeholder conflicts
Expandable text The stakeholder view
Expandable text Agency theory
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Commontypesofrewardschemesinclude:
linkrewardstochangesinshareholderwealth matchmanagerstimehorizonstoshareholderstimehorizons encouragemanagerstoadoptthesameattitudestoriskas
shareholders.
remunerationlinkedto: minimumprofitlevels economicvalueadded(EVA) turnovergrowth
executiveshareoptionschemes(ESOP).
GretschInc,alistedcompany,hasdevelopedahighlysuccessfulnewproductandisthusgrowingrapidly.However,withthisgrowththefirmisexperiencingcashflowproblems.Managersarecurrentlyawardedbonusesifthereisgrowthinreportedearningspershare(EPS).
Comment on the current remuneration scheme.
Corporate governance codes
Thedirector/shareholderconflicthasalsobeenaddressedbytherequirementsofanumberofcorporategovernancecodes.Thefollowingkeyareasrelatetothisconflict.
Nonexecutivedirectors(NEDs) importantpresenceontheboard mustgiveobligationtospendsufficienttimewiththecompany shouldbeindependent.
Executivedirectors separationofchairmanandchiefexecutiveofficer(CEO) submitforreelection cleardisclosureofemoluments outnumberedbytheNEDs.
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Test your understanding 3 Managerial reward schemes
Expandable text Managerial reward schemes
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Remunerationcommittees. Nominationcommittees. Annualgeneralmeeting(AGM).
Stock exchange listing requirements and other regulations
Althoughadherencetotheprinciplesofthecorporategovernancecodesisvoluntary,theyareoftenreferredtointhelistingrequirementsofstockexchanges.
6Measuring achievement of corporate objectives
Itisnecessaryformanagers,shareholdersandotherstakeholderstohavewaysofmeasuringtheprogressofthecompanytowardsitsobjectives.Thisiscommonlydoneviaratioanalysis.
Ratioanalysiscomparesandquantifiesrelationshipsbetweenfinancialvariables.
Ratioanalysiscanbegroupedintofourmaincategories:
ThespecificratioscoveredintheF9syllabuswillbelookedatindetailinchapter17althoughsomeofthemmayalreadybefamiliartoyoufrompreviouspapers.
Profitabilityandreturn Debtandgearing Liquidity Investor
7Objective setting in not for profit organisations
Theprimaryobjectiveofnotforprofitorganisations(NFPsorNPOs)isnottomakemoneybuttobenefitprescribedgroupsofpeople.
Aswithanyorganisation,NFPswilluseamixtureoffinancialandnonfinancialobjectives.
However,withNFPsthenonfinancialobjectivesareoftenmoreimportantandmorecomplexbecauseofthefollowing.
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Expandable text Other regulations
Expandable text Corporate governance codes
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Mostkeyobjectivesareverydifficulttoquantify,especiallyinfinancialterms,e.g.qualityofcaregiventopatientsinahospital.
MultipleandconflictingobjectivesaremorecommoninNFPs,e.g.qualityofpatientcareversusnumberofpatientstreated.
Value for money (VFM) and the 3 Es
VFMcanbedefinedasachievingthedesiredlevelandqualityofserviceatthemosteconomicalcost.
The three Es
Assessingwhethertheorganisationprovidesvalueformoneyinvolveslookingatallfunctioningaspectsoftheorganisation.Performancemeasureshavebeendevelopedtopermitevaluationofeachpartseparately.
VFM
Economy:Minimisingthecostsofinputsrequiredtoachieveadefinedlevelofoutput.
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Expandable text VFM
Expandable text Planning influences
Expandable text Financial objectives
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Efficiency:Ratioofoutputstoinputsachievingahighlevelofoutputinrelationtotheresourcesputin(inputdriven)orprovidingaparticularlevelofserviceatreasonableinputcost(outputdriven)
Effectiveness:Whetheroutputsareachievedthatmatchthepredeterminedobjectives.
Useofthe3EsasaperformancemeasureandawaytoassessVFMisakeyissueforexaminationquestionsthatrelatetoNFPsandpublicsectororganisations.
Asubsidisedcollegecanteenserviceistobeevaluatedbythelocalcounciltoassessamongstotherthings,whetheritisfinanciallysoundandoffersvalueformoney.
Suggest appropriate measures of achievement that could be set for the service.
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Expandable text 3Es
Test your understanding 4 Not for profit organisations
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Chapter summary
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The financial management function
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chapter 1
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Test your understanding answers
Commercialobjectives /targets
Financialobjectives /targets
Strategies
Corporatelevel
ImprovebrandawarenesswithintheUK.
IncreaseEPSby5%onprioryear.
Acquirerivalchaininashareforsharepurchase.
Businesslevel
Updatemanufacturingcapacitytoincorporatenewtechnology.
Achievereturnsof15%onnewmanufacturinginvestment.
Buyfournewcuttingmachinesfor$250,000each.
Operationallevel
Reduceunsoldinventoryitemsby12%.
Improvetheratioofcurrentassetstocurrentliabilitiesfrom1.7to1.85.
ImplementaJITinventorysystem.
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Test your understanding 1 Objectives and strategies
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Stakeholders Potential conflictEmployees Shareholders Employeesmayresistthe
introductionofautomatedprocesseswhichwouldimproveefficiencybutcostjobs.Shareholdersmayresistwagerisesdemandedbyemployeesasuneconomical.
Customers Communityatlarge
Customersmaydemandlowerpricesandgreaterchoice,butinordertoprovidethemacompanymayneedtosqueezevulnerablesuppliersorimportproductsatgreatenvironmentalcost.
Shareholders Financeproviders
Shareholdersmayencouragemanagementtopursueriskystrategiesinordertomaximisepotentialreturns,whereasfinanceproviderspreferstablelowerriskpoliciesthatensureliquidityforthepaymentofdebtinterest.
Customers Shareholders/managers
Customersmayrequirehigherservicelevels(suchas24ratherthan48hourdelivery)whichareresistedbyshareholdersastooexpensiveorbymanagementduetoincreasedworkload.
Government Shareholders Governmentwillofteninsistuponlevelsofwelfare(suchastheminimumwageandhealthandsafetypractices)whichwouldotherwisebeavoidedasanunnecessaryexpense.
Shareholders Managers Shareholdersareconcernedwiththemaximisationoftheirwealth.Managersmayinsteadpursuestrategiesfocusedongrowthasthesemaybringthegreatestpersonalrewards.
Note:Youmayhavecomeupwithdifferentsuggestions.Thepointistorecognisethatthereisahugerangeofpotentialconflictsofinterestandseniormanagementwillneedtoworktoachieveabalance.
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Test your understanding 2 Stakeholder conflicts
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Advantages
Disadvantages
GoalcongruencemanagerswillworktoachievegrowthinEPS,whichwillmakeshareholdersfeelthattheirwealthisincreasing.
Thefigureisdifficult(butnotimpossible!)tomanipulatefromoneperiodtoanotherasitwillbeaudited.
Thereislittleincentiveformanagerstocontrolworkingcapitalandcashflowapressingproblem.Growthmaybeattheexpenseofliquidityandultimatelycompromisethefirmsfuturesurvival.
Managersmaygainbonusessimplybecauseoftheproductsconcernedratherthantheirownefforts.AtargetgrowthinEPSwouldbebetter.
LongtermshareholdervalueandEPSarenotwellcorrelated. Thereisonlyonemeasurethatfocusesonfinaleffectsratherthan
operationalcauses.
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Test your understanding 3 Managerial reward schemes
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Financialmeasures:
Economytargets:
Efficiencytargets:
Effectivenesstargets:
proportionofoverallfundsspentonadministrationcosts abilitytostaywithinbudget/breakeven revenuetargetsmet.
costsofpurchasingprovisionsofsuitablenutritionalquality costsofnegotiatingforandpurchasingequipment negotiationofbulkdiscounts payratesforstaffofappropriatelevelsofqualification.
numbersofportionsproduced costpermealsold levelsofwastageofunpreparedandofcookedfood staffutilisation equipmentlife.
numbersusingthecanteen customersatisfactionratings nutritionalvalueofmealsserved.
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Test your understanding 4 Not for profit organisations
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The financial management function
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CapitalbudgetingandbasicinvestmentappraisaltechniquesChapter learning objectives
Uponcompletionofthischapteryouwillbeableto:
defineanddistinguishbetweencapitalandrevenueexpenditure distinguishbetweenexpenditureonnoncurrentassetsand
workingcapital describethecapitalbudgetingprocess explaintheroleofinvestmentappraisalinthecapitalbudgeting
process explaintherelationshipbetweenthecapitalbudgetingprocess
andthedevelopmentofcorporatestrategy definearelevantcashflow(anddistinguishitfromanaccounting
profit) identifyandcalculaterelevantcashflowsinascenario calculatethepaybackperiodanduseittoappraisean
investment discusstheusefulnessofpaybackasaninvestmentappraisal
method calculatereturnoncapitalemployed(ROCE)(accountingrateof
return)anduseittoappraiseaninvestment discusstheusefulnessofROCEasaninvestmentappraisal
method.
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1Capital investment
Whenabusinessspendsmoneyonnewnoncurrentassetsitisknownascapitalinvestmentorcapitalexpenditure.Spendingmaybefor:
Spendingisnormallyirregularandforlargeamounts.Itisexpectedtogeneratelongtermbenefits.
maintenance profitability expansion indirectpurposes.
Othertypesofexpenditureincurredbyabusinessincludes:
Revenueexpenditureregularspendingonthedaytodayrunningofthebusinesswherethebenefitisexpectedtolastforonlyonespecificaccountingperiod.
Workingcapitalinvestmentinvestmentinshorttermnetassets(inventory,receivablesandcashlessshorttermpayables).
Youmustbeabletodistinguishbetweencapitalandrevenueexpenditureandexpenditureonworkingcapital.
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Anenterprisespendsmoneyonthefollowing:
Identify the type of expenditure that each of the above represents.
annualrentalpaymentforthewarehouse anewforklifttrucktoreplaceonedamagedinanaccident increasedinventorytofulfilanewlywoncontract anautomaticmouldingmachinetostreamlineaproductionprocess.
2Capital budgeting and investment appraisal
Acapitalbudget:
isaprogrammeofcapitalexpenditurecoveringseveralyears includesauthorisedfutureprojectsandprojectscurrentlyunder
consideration.
Onestageinthecapitalbudgetingprocessisinvestment appraisal.Thisappraisalhasthefollowingfeatures:
assessmentofthelevelofexpectedreturnsearnedforthelevelofexpendituremade
estimatesoffuturecostsandbenefitsovertheprojectslife.
Twobasicappraisaltechniquesarecoveredinthischapter:
Moresophisticatedmethodsofinvestmentappraisalaredealtwithinthenextchapter.
ROCE Payback.
Examinationquestionsmayaskyoutocompareandcontrasttheuseofthesetwobasictechniques.
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Test your understanding 1 Expenditure classification
Expandable text Capital budgeting process
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3ROCE
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 2 ROCE
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Aprojectrequiresaninititalinvestmentof$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.
4Advantages and disadvantages of ROCE
Advantagesinclude:
Disadvantagesinclude:
simplicity linkswithotheraccountingmeasures.
noaccountistakenofprojectlife noaccountistakenoftimingofcashflows itvariesdependingonaccountingpolicies itmayignoreworkingcapital itdoesnotmeasureabsolutegain thereisnodefinitiveinvestmentsignal.
IntheexaminationitisimportantthatyoucandiscussthefeaturesofROCEasaninvestmentappraisaltechnique,inadditiontobeingabletocalculateit.
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Expandable text Initial capital cost
Expandable text Advantages and disadvantages of ROCE
Test your understanding 3 ROCE
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5Accounting profits and cash flows
Incapitalinvestmentappraisalitismoreappropriatetoevaluatefuturecashflowsthanaccountingprofits,because:
profitscannotbespent profitsaresubjective cashisrequiredtopaydividends.
6Cash flows and relevant costs
Forallmethodsofinvestmentappraisal,withtheexceptionofROCE,onlyrelevantcashflowsshouldbeconsidered.Theseare:
Ignore:
future incremental cashbased.
sunkcosts committedcosts noncashitems allocatedcosts.
Acompanyisevaluatingaproposedexpenditureonanitemofequipmentthatwouldcost$160,000.
Atechnicalfeasibilitystudyhasbeencarriedoutbyconsultants,atacostof$15,000,intobenefitsfrominvestingintheequipment.
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Expandable text Relevant costs
Test your understanding 4 Relevant costs
Expandable text Profits versus cash flows
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Ithasbeenestimatedthattheequipmentwouldhavealifeoffouryears,andannualprofitswouldbe$8,000,afterdeductingannualdepreciationof$40,000andanannualchargeof$25,000forashareoftheexistingfixedcostofthecompany.
What are the relevant cash flows for this?
Amanufacturingcompanyisconsideringtheproductionofanewtypeofwidget.Eachwidgetwilltaketwohourstomake.
Fixedoverheadsareapportionedonthebasisof$1perlabourhour.
Ifthenewwidgetsareproduced,thecompanywillhavetoemployanadditionalsupervisoratasalaryof$15,000pa.Thecompanywillproduce10,000widgetspa.
What are the relevant cash flows?
7Payback method of appraisal
Thepaybackperiodisthetimeaprojectwilltaketopaybackthemoneyspentonit.Itisbasedonexpectedcashflowsandprovidesameasureofliquidity.
Decision rule:
Constant annual cash flows
onlyselectprojectswhichpaybackwithinthespecifiedtimeperiod choosebetweenoptionsonthebasisofthefastestpayback
initialinvestmentPaybackperiod=
annualcashflow
Anexpenditureof$2millionisexpectedtogeneratenetcashinflowsof$500,000eachyearforthenextsevenyears.
What is the payback period for the project?
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Test your understanding 6 Payback with constant annual cash
Test your understanding 5 Relevant costs
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Apaybackperiodmaynotbeforanexactnumberofyears.Tocalculatethepaybackinyearsandmonthsyoushouldmultiplythedecimalfractionofayearby12tothenumberofmonths.
Aprojectwillinvolvespending$1.8millionnow.Annualcashflowsfromtheprojectwouldbe$350,000.
What is the expected payback period?
Uneven annual cash flows
Inpractice,cashflowsfromaprojectareunlikelytobeconstant.Wherecashflowsareuneven,paybackiscalculatedbyworkingoutthecumulativecashflowoverthelifeoftheproject.
Aprojectisexpectedtohavethefollowingcashflows:
What is the expected payback period?
Year Cash flow$000
0 (1,900)1 3002 5003 6004 8005 500
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Test your understanding 8 Payback with uneven cash flows
Test your understanding 7 Payback in years and months
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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
8Advantages and disadvantages of payback
Advantagesinclude:
Disadvantagesinclude:
itissimple itisusefulincertainsituations:
rapidlychangingtechnology improvinginvestmentconditions
itfavoursquickreturn: helpscompanygrowth minimisesrisk maximisesliquidity
itusescashflows,notaccountingprofit.
itignoresreturnsafterthepaybackperiod itignorestimings itissubjectivenodefinitiveinvestmentsignal itignoresprojectprofitability.
Intheexaminationitisimportantthatyoucandiscussthefeaturesofpaybackasaninvestmentappraisaltechniqueaswellasbeingabletodothecalculation.
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Expandable text Advantages and disadvantages of payback
Test your understanding 9 Payback with uneven cash flows
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Chapter summary
Capital budgeting and basic investment appraisal techniques
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Test your understanding answers
Annualrentalpaymentsforthewarehousearerevenueexpenditure.Thebenefitisonlyforthataccountingperiod.
Thenewforklifttruckisacapitalpurchase.Itismaintenancespendingasitreplacesonealreadyownedbutdamaged.
Theincreasedinventoryspendingisaninvestmentinworkingcapital.
Theautomaticmouldingmachineisalsoacapitalexpense.Howeversinceitwasboughttostreamlineaproductionprocess,thepurposeisprofitability.
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Test your understanding 1 Expenditure classification
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Annualcashflowsaretakentobeprofitbeforedepreciation.
Using average capital investment:
Averageannualdepreciation
= ($110,000$10,000)5
= $20,000 Averageannualprofit
= $24,400$20,000
= $4,400 Using initial cost:
ROCE Averageannualprofit = 100%
Initialcapitalcost
$4,400 = 100% =4%
$110,000
Averageannualprofits(asbefore)
=$4,400
Averagebookvalueofassets
=(Initialcapitalcost+Finalscrapvalue)2=($110,000+$10,000)2=$60,000
ROCE =$4,400$60,000100%=7.33%
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Test your understanding 2 ROCE
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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
The$15,000alreadyspentonthefeasibilitystudyisnotrelevant,becauseithasalreadybeenspent.(Itisasunkcost.)Depreciationandapportionedfixedoverheadsarenotrelevant.Depreciationisnotacashflowandapportionedfixedoverheadsrepresentcoststhatwillbeincurredanyway.
$Estimatedprofit 8,000Addbackdepreciation 40,000Addbackapportionedfixedcosts 25,000
Annualcashflows 73,000
Theprojectscashflowstobeevaluatedare:Years $Now(Year0)Purchaseequipment (160,000)14Cashflowfromprofits 73,000eachyear
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Test your understanding 4 Relevant costs
Test your understanding 3 ROCE
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Onlythe$15,000salaryisrelevant.Thefixedoverheadsarenotincrementaltothedecisionandshouldbeignored.
$2,000,000Paybackperiod= =4years
$500,000
$1,800,000Payback= =5.1429years
$350,000
0.1429ofayear12months=1.7months(rounded=2months)
Theanswercanthereforebestatedaseither:
assumingcashflowsoccurevenlythroughouttheyear.
5.1years 5years2months
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Test your understanding 7 Payback in years and months
Test your understanding 5 Relevant costs
Test your understanding 6 Payback with constant annual cash
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Year Cash flow Cumulative cash flow$000 $000
0 (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.
$500/800=0.625
Thereforepaybackisafter3.625years.
Paybackinyearsandmonthsiscalculatedbymultiplyingthedecimalfractionofayearby12months.Inthisexample,0.625years=7.5months(0.62512months),whichisroundedto8months.Sotherefore,paybackoccursafter3years8months.
Notethatifcashflowsweredeemedtoariseattheendoftheyearthenthepaybackperiodwouldbe4years.
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Test your understanding 8 Payback with uneven cash flows
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Thepaybackperiodwouldbecalculatedasfollows.
PaybackisbetweentheendofYear3andtheendofYear4,inotherwordsduringYear4.
Ifweassumeaconstantrateofcashflowthroughtheyear,wecouldestimatethatpaybackwillbethreeyears,plus($400/500)ofYear4,whichis3.8years.
0.8years=10months(0.812)
Wecouldthereforeestimatethatpaybackwouldbeafter3years10months.
Year Cash flow Cumulative cash flow$000 $000
0 (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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Test your understanding 9 Payback with uneven cash flows
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InvestmentappraisaldiscountedcashflowtechniquesChapter learning objectives
Uponcompletionofthischapteryouwillbeableto:
explaintheconceptofthetimevalueofmoney calculatethefuturevalueofasumbycompounding calculatethepresentvalue(PV)ofasinglesumusingformula calculatethePVofasinglesumusingdiscounttables calculatethePVofanannuityusingformula calculatethePVofanannuityusingannuitytables calculatethePVofaperpetuityusingformula calculatethePVofadvancedannuitiesandperpetuities calculatethePVofdelayedannuitiesandperpetuities explainthebasicprinciplebehindtheconceptofacostofcapital calculatethenetpresentvalue(NPV)ofaninvestmentanduseit
toappraisetheproposal discusstheusefulnessofNPVasaninvestmentappraisal
methodanditssuperiorityovernondiscountedcashflows(DCF)methods
calculatetheinternalrateofreturn(IRR)ofaninvestmentanduseittoappraisetheproposal
discusstheusefulnessofIRRasaninvestmentappraisalmethodanditssuperiorityovernonDCFmethods
discusstherelativemeritsofNPVandIRR.
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chapter
3
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1The time value of money
Moneyreceivedtodayisworthmorethanthesamesumreceivedinthefuture,i.e.ithasatime value.
Thisoccursforthreereasons:
potentialforearninginterest/costoffinance impactofinflation effectofrisk.
ThisisakeyconceptthroughouttheF9syllabus.
Discountedcashflow(DCF)techniquestakeaccountofthistimevalueofmoneywhenappraisinginvestments.
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Expandable text 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%.
Youhave$5,000toinvestnowforsixyearsataninterestrateof5%pa.
What will be the value of the investment after six years?
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Test your understanding 1 Compounding
Illustration 1 Compounding
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3Discounting
Inapotentialinvestmentproject,cashflowswillariseatmanydifferentpointsintime.Tomakeausefulcomparisonofthedifferentflows,theymustallbeconvertedtoacommonpointintime,usuallythepresentday,i.e.thecashflowsarediscounted.
Discounting a single sum
Thepresentvalue(PV)isthecashequivalentnowofmoneyreceivable/payableatsomefuturedate.
ThePVofafuturesumcanbecalculatedusingtheformula:
Thisisjustarearrangementoftheformulaweusedforcompounding.
(1+r)niscalledthediscountfactor(DF).TofindtheDF,forexampleifr=10%andn=5,youcan:
F P= = F(1+r)n
(1+r)n
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WhatisthePVof$115,000receivableinnineyears'timeifr=6%?
ShowyouranswerusingboththeformulaandtheDFtables.
Whatamountshouldbeinvestednowtoreceive$10,000infouryears'timeifr=8%pa.
Discounting annuities
Anannuityisaconstantannualcashflowforanumberofyears.
Apaymentof$1,000istobemadeeveryyearfor6years,thefirstpaymentoccurringinoneyearstime.Theinterestrateis10%.WhatisthePVoftheannuity?
Solution
ThePVofanannuitycouldbefoundbyaddingthePVsofeachpaymentseparately.
However,youcanseefromthetablethatthesumofalltheDFis4.354.
ThereforethePVcanbefoundmorequickly:
$1,0004.354=$4,354.
Time Payment DF @ 10%(from tables) PV$ $
T1 1,000 0.909 909T2 1,000 0.826 826T3 1,000 0.751 751T4 1,000 0.683 683T5 1,000 0.621 621T6 1,000 0.564
564
4.354
4,354
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Illustration 2 Discounting annuities
Test your understanding 2 Discounting a single sum
Test your understanding 3 Discounting a single sum
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Theannuity factor(AF)isthenamegiventothesumoftheindividualDF.
ThePVofanannuitycanthereforebequicklyfoundusingtheformula:
PV=AnnualcashflowAF
Likewithcalculatingadiscountfactor,theAFcanbefoundusinganannuityformulaorannuitytables.
Theformulais:
Forexample,forasixyearannuityat10%:
Note:theremightbeasmalldifferenceduetoroundings.
1(1+r)nAF=
r
Apaymentof$3,600istobemadeeveryyearforsevenyears,thefirstpaymentoccurringinoneyearstime.Theinterestrateis8%.WhatisthePVoftheannuity.
Discounting perpetuities
A perpetuityisanannualcashflowthatoccursforever.
Itisoftendescribedbyexaminersasacashflowcontinuingfortheforeseeablefuture.
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Test your understanding 4 Discounting annuities
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ThePVofaperpetuityisfoundusingtheformula:
or
cashflowPV=
r
1PV= cashflow
r1 isknownastheperpetuityfactor.r
WhatisthePVofapaymentof$5,736tobemadeannuallyfortheforeseeablefuture,startinginoneyearstime,iftheinterestrateis12%?
Theuseofannuityfactorsandperpetuityfactorsbothassumethatthefirstcashflowwillbeoccuringinoneyear'stime.Ifthisisnotthecase,youwillneedtoadjustyourcalculation.
Advanced annuities and perpetuities
Someregularcashflowsmaystartnow(atT0)ratherthaninoneyearstime(T1).
CalculatethePVbyignoringthepaymentatT0whenconsideringthenumberofcashflowsandthenaddingonetotheannuityorperpetuityfactor.
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Test your understanding 5
Expandable text Advanced perpetuities: An illustration
Expandable text Advanced annuities: An illustration
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FindthePVofthefollowingcashflows:
(1) Afifteenyearannuityof$300startingatonce.Interestratesare6%.(2) Aperpetuityof$33,000commencingimmediately.Interestratesare
22%.
Delayed annuities and perpetuities
SomeregularcashflowsmaystartlaterthanT1.
Thesearedealtwithby:
(1) applyingtheappropriatefactortothecashflowasnormal(2) discountingyouranswerbacktoT0.
ThefinancialdirectorofACohaspreparedthefollowingscheduletoenablehertoappraiseanewproject.Interestratesare10%.ShewantstocalculatethePVofthecashflowsusingtwodifferentassumptionsregardingtheprojectduration.
Theassumptionsareasfollows:
(a) Thattherealannualcashflowwillbe$250,000fromYear4fortheforeseeablefuture.
(b) Thattherealannualcashflowwillbe$250,000fromYear4toYear18.
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Test your understanding 6 Advanced annuities and perpetuities
Test your understanding 7 Delayed annuities and perpetuities
Expandable text Delayed annuities and perpetuities
Expandable text Delayed annuities: An illustration
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Required:
Find the sum of the PVs (known as the NPV) from the project under both assumptions.
Assumption (a)
Assumption (b)
Year T0 T1 T2 T3 T4onwards T4T18
$000 $000 $000 $000 $000 $000
Netcashflow
(2,000) (440) 363 399 250 250
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
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ifthecompanyhastwoormoremutuallyexclusiveprojectsunderconsiderationitshouldchoosetheonewiththehighestNPV
theNPVgivestheimpactoftheprojectonshareholderwealth.
Assumptions used in discounting
Unlesstheexaminertellsyouotherwise,thefollowingassumptionsaremadeaboutcashflowswhencalculatingthenetpresentvalue:
Alsonote,youshouldneverincludeinterestpaymentswithinanNPVcalculationasthesearetakenaccountofbythecostofcapital.
allcashflowsoccuratthestartorendofayear initialinvestmentsoccurT0 othercashflowsstartoneyearafterthat(T1).
Thecashflowsforaprojecthavebeenestimatedasfollows:
Thecostofcapitalis6%.
Convert these cash flows to a PV.
Add up the total of the PVs for each of the years.
Year $0 (25,000)1 6,0002 10,0003 8,0004 7,000
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44 KAPLAN PUBLISHING
Test your understanding 8 Net present value
Expandable text What does the NPV actually mean?
Expandable text Assumptions used in discounting
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Anorganisationisconsideringacapitalinvestmentinnewequipment.Theestimatedcashflowsareasfollows.
Thecompanyscostofcapitalis9%.
Calculate the NPV of the project to assess whether it should be undertaken.
Year Cash flow$
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.
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Expandable text Advantages and disadvantages of NPV
Test your understanding 9 Net present value
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7The 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:
NL
IRR=L+ (HL)
NLNH
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Expandable text IRR
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ThediagrambelowshowstheIRRasestimatedbytheformula.
ApotentialprojectspredictedcashflowsgiveaNPVof$50,000atadiscountrateof10%and$10,000atarateof15%.
Calculate the IRR.
FortheexaminationthechoiceofratestoestimatetheIRRislessimportantthanyourabilitytoperformthecalculationtoestimateit.
Abusinessundertakeshighriskinvestmentsandrequiresaminimumexpectedrateofreturnof17%paonitsinvestments.Aproposedcapitalinvestmenthasthefollowingexpectedcashflows:
Year 01234
$(50,000)18,00025,00020,00010,000
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Expandable text Calculating the IRR
Test your understanding 10 IRR
Test your understanding 11 IRR
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(1) CalculatetheNPVoftheprojectifthecostofcapitalis15%.(2) CalculatetheNPVoftheprojectifthecostofcapitalis20%.(3) UsetheNPVsyouhavecalculatedtoestimatetheIRRofthe
project.(4) Recommend,onfinancialgroundsalone,whetherthisprojectshould
goahead.
FindtheIRRofaninvestmentof$50,000iftheinflowsare:
(a) $5,000inperpetuity(b) $8,060foreightyears.
8Advantages and disadvantages of IRR
Advantages
TheIRRhasanumberofbenefits,e.g.it:
Disadvantages
considersthetimevalueofmoney isapercentageandthereforeeasilyunderstood usescashflowsnotprofits considersthewholelifeoftheproject meansafirmselectingprojectswheretheIRRexceedsthecostof
capitalshouldincreaseshareholders'wealth.
Itisnotameasureofabsoluteprofitability. Interpolationonlyprovidesanestimateandanaccurateestimate
requirestheuseofaspreadsheetprogramme. Itisfairlycomplicatedtocalculate.
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Test your understanding 12 IRR with even cashflows
Expandable text Calculating the IRR with even cash flows
Expandable text Calculating the IRR with perpetuities
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NonconventionalcashflowsmaygiverisetomultipleIRRswhichmeanstheinterpolationmethodcan'tbeused.
9NPV versus IRR
BothNPVandIRRareinvestmentappraisaltechniqueswhichdiscountcashflowsandaresuperiortothebasictechniquesdiscussedintheprevioussession.HoweveronlyNPVcanbeusedtodistinguishbetweentwomutuallyexclusiveprojects,asthediagrambelowdemonstrates:
TheprofileofprojectAissuchthatithasalowerIRRandapplyingtheIRRrulewouldpreferprojectB.Howeverinabsoluteterms,AhasthehigherNPVatthecompanyscostofcapitalandshouldthereforebepreferred.
NPVisthereforethebettertechniqueforchoosingbetweenprojects.
TheadvantageofNPVisthatittellsustheabsoluteincreaseinshareholderwealthasaresultofacceptingtheproject,atthecurrentcostofcapital.TheIRRsimplytellsushowfarthecostofcapitalcouldincreasebeforetheprojectwouldnotbeworthaccepting.
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Expandable text Advantages and disadvantages of IRR
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Chapter summary
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Test your understanding answers
F=$5,000(1+0.05)6
=$5,0001.3401
=$6,700
F 115,000 P= = =$68,068(usingformula)
(1+r)n (1+0.06)9
P=$115,0000.592=$68,080(usingtables)
Thedifferencebetweenthetwoanswersiscausedbyrounding.
TheamounttobeinvestedisthePVofthefuturesum.
P=$10,000/(1.08)4=$7,350
P=$10,0000.735=$7,350(usingtables).
Usingtheformula:
$3,6005.206=$18,741.60
NotethattheAFcouldhavebeentakenstraightfromthetables.
1(1+r)n 1(1.08)7 = =5.206
r 0.08
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Test your understanding 1 Compounding
Test your understanding 3 Discounting a single sum
Test your understanding 4 Discounting annuities
Test your understanding 2 Discounting a single sum
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5,7361 PV= =$47,800 0.12
(1) Thisisastandard14yearannuitywithoneadditionalpaymentatT0.
Step 1:Lookupthe14yearAF
AF=9.295
Step 2:Add19.295+1=10.295
Step 3:CalculatethePV30010.295=$3,088.50
Step 1:Calculatetheperpetuityfactor1/0.22=4.545
Step 2:Add14.545+1=5.545
Step 3:CalculatethePV33,0005.545=$182,982
(2) ThisissimplyastandardperpetuitywithoneadditionalpaymentatT0.
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Test your understanding 5
Test your understanding 6 Advanced annuities and perpetuities
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Assumption (a)
Assumption (b)
Year T0 T1 T2 T3 T4onwards T4 T18
$000 $000 $000 $000 $000 $000
Net cash flow
(2,000) (440) 363 399 250 250
Perpetuity factor(herediscountsthecashflowtoT3)
10.1=10
AF(herediscountsthecashflowtoT3)
15yr10%AF=7.606
DFs @ 10%
1.000
0.909
0.826
0.751
0.751
0.751
PV
(2,000)
(400)
300
300
1,878
1,428
NPV (a)
78
NPV (b) (372)
Year Cash flow DF PV$ 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
Aswewillsoonsee,$1,822isknownastheNPVoftheproject.
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Test your understanding 8 Net present value
Test your understanding 7 Delayed annuities and perpetuities
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Year Cash flow DF at 9% PV
$ $
0 (240,000) 1.000 (240,000)
1 80,000 0.917 73,360
2 120,000 0.842 101,040
3 70,000 0.772 54,040
4 40,000 0.708 28,320
5 20,000 0.650 13,000
NPV +29,760
ThePVofcashinflowsexceedsthePVofcashoutflowsby$29,760,whichmeansthattheprojectwillearnaDCFreturninexcessof9%,i.e.itwillearnasurplusof$29,760afterpayingthecostoffinancing.Itshouldthereforebeundertaken.
50,000 IRR= 10%+ (15%10%) =14.17%
50,000(10,000)
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Test your understanding 9 Net present value
Test your understanding 10 IRR
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Year Cash flow DF @ 15% PV @ 15% DF @ 20% PV @ 20%$ $ $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:
3,440 IRR = 15%+ (2015)%
(440(1,256) = 15% +3.7% = 18.7%
(4) TheprojectisexpectedtoearnaDCFreturninexcessofthetargetrateof17%,soonfinancialgrounds(ignoringrisk)itisaworthwhileinvestment.
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Test your understanding 11 IRR
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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)thatproducesanNPVof
nil. ThereforethePVofinflows(a)mustequalthePVofoutflows,
$50,000. IfthePVofinflows(a)istobe$50,000andthesizeofeach
inflowis$8,060,theDFrequiredmustbe50,0008,060=6.20.
Thediscountrate(c)forwhichthisisthe8yearfactorcanbefoundbylookingalongthe8yearrowofthecumulativeDFSshownintheannuitytable.
Thefigureof$6.210appearsunderthe6%columnsuggestinganIRRof6%istheclosest.
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Test your understanding 12 IRR with even cashflows
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InvestmentappraisalfurtheraspectsofdiscountedcashflowsChapter learning objectives
Uponcompletionofthischapteryouwillbeableto:
explaintheimpactofinflationoninterestratesanddefineanddistinguishbetweenrealandnominal(money)interestrates
explainthedifferencebetweentherealtermsandnominaltermsapproachestoinvestmentappraisal
usethenominal(money)termsapproachtoappraiseaninvestment
usetherealtermsapproachtoappraiseaninvestment explaintheimpactoftaxonDCFappraisals calculatethetaxcashflowsassociatedwithcapitalallowances
andincorporatethemintonetpresentvalues(NPV)calculations calculatethetaxcashflowsassociatedwithtaxableprofitsand
incorporatethemintoNPVcalculations explaintheimpactofworkingcapitalonanNPVcalculationand
incorporateworkingcapitalflowsintoNPVcalculations.
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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
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$1,000isinvestedinanaccountthatpays10%interestpa.Inflationiscurrently7%pa.
Find the real return on the investment.
If the real rate of interest is 8% and the rate of inflation is 5%, what should the money rate of interest be?
2The impact of inflation on cash flows
Wherecashflowshavenotbeenincreasedforexpectedinflationtheyareknownascurrent cash flows,orreal cash flows.
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.
Iftheexaminerspecifiesthatthecashflowsareincurrenttermsyouwillgenerallyneedtoputtheseinmoneytermsbeforeyoucandiscountthem(althoughseeothermethodsofdealingwithinflationbelow).
Makesureyoureadthequestioncarefully.SometimesyouwillbegiventhecashflowsinYear1termswithsubsequentinflation.
Forexampleifthequestiontellsyouthatsalesforthenext3yearsare100incurrenttermsbutareexpectedtoinflateby10%,thenwhatheactuallymeansisthatthesaleswillbe:Year1: 110Year2: 121 iethesearethecashflowsinmoneytermsYear3: 133.10
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Test your understanding 1 Money and real returns
Test your understanding 2 Money and real returns
Expandable text Illustration
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Forexampleifthequestionsays"Saleswillbe100inthefirstyear,butarethengoingtoinflateby10%forthenexttwoyears",thenthesaleswillbe:Year1: 100Year2: 110 comparethesetothepreviousexamplemakesureYear3: 121 youunderstandwhytheyaredifferent!
TheimpactofinflationcanbedealtwithintwodifferentwaysbothmethodsgivethesameNPV.
StormCoisevaluatingProjectX,whichrequiresaninitialinvestmentof$50,000.Expectednetcashflowsare$20,000paforfouryearsattodaysprices.Howevertheseareexpectedtoriseby5.5%pabecauseofinflation.Thefirmscostofcapitalis15%.
Find the NPV by:
(a) discountingmoneycashflows(b) discountingrealcashflows.
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Test your understanding 3 Money and real methods
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Aprojecthasthefollowingcashflowsbeforeallowingforinflation,i.e.theyarestatedattheirT0values.
Thecompanysmoneydiscountrateis15.5%.Thegeneralrateofinflationisexpectedtoremainconstantat5%.
Evaluate the project in terms of:
Timing Cash flow$
0123
(750)330242532
(a) realcashflowsandrealdiscountrates(b) moneycashflowsandmoneydiscountrates.
3Specific and general inflation rates
TheTYUsgivenabovehadallcashflowsinflatingatthegeneralrateofinflation.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.
Acompanyisconsideringacostsavingproject.Thisinvolvespurchasingamachinecosting$7,000,whichwillresultinannualsavings(inrealterms)onwagecostsof$1,000andonmaterialcostsof$400.
Thefollowingforecastsaremadeoftheratesofinflationeachyearforthenextfiveyears:
Wagecosts 10%Materialcosts 5%Generalprices 6%
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Test your understanding 5 General and specific inflation rates
Expandable text Specific and general inflation rates
-
Thecostofcapitalofthecompany,inrealterms,is8.5%.
Evaluate the project, assuming that the machine has a life of five years and no scrap value.
4Dealing with tax in NPV calculations
Sincemostcompaniespaytax,theimpactofcorporationtaxmustbeconsideredinanyinvestmentappraisal.
The impact of taxation on cash flows
CorporationtaxchargedonacompanysprofitsisarelevantcashflowforNPVpurposes.Itisassumed,unlessotherwisestatedinthequestion,that:
operatingcashinflowswillbetaxedatthecorporationtaxrate operatingcashoutflowswillbetaxdeductibleandattracttaxreliefatthe
corporationtaxrate taxispaidoneyearaftertherelatedoperatingcashflowisearned
(unlesstoldotherwise) investmentspendingattractscapitalallowances(orwritingdown
allowances(WDAs))whichgettaxrelief thecompanyisearningnettaxableprofitsoverall(thisavoidsany
issuesofcarryinglossesforwardstoreducefuturetaxation).
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Expandable text The impact of taxation on cash flows
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Capital allowances/WDAs
Fortaxpurposes,abusinessmaynotdeductthecostofanassetfromitsprofitsasdepreciation(inthewayitdoesforfinancialaccountingpurposes).
InsteadthecostmustbedeductedfromtaxableprofitsintheformofcapitalallowancesorWDAs.Thebasicrulesareasfollows:
WDAsarecalculatedonareducingbalancebasis(usuallyatarateof25%)
thetotalWDAsgivenoverthelifeofanassetequatetoitsfallinvalueovertheperiod(i.e.thecostlessanyscrapproceeds)
WDAsareclaimedasearlyaspossible WDAsaregivenforeveryyearofownershipexcepttheyearofdisposal intheyearofsaleorscrapabalancingallowance(BA)orbalancing
chargearises(BC).$
Originalcostofasset XCumulativecapitalallowancesclaimed (X) ___Writtendownvalueoftheasset XDisposalvalueoftheasset (X) ___Balancingallowanceorbalancingcharge X ___
Anassetwaspurchasedfor$100,000.Atthetimeofitsdisposal,thecumulativecapitalallowancesclaimedoverthelifeoftheassetwere$68,000.
Calculate the balancing allowance or balancing charge if the asset is disposed of for:
(a) $20,000(b) $40,000
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Expandable text Capital allowances
Test your understanding 6 Balancing allowance or charge
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Fortaxpurposescaremustbetakentoidentifytheexacttimeofassetpurchase.
Asset bought at the start of an accounting period:
Asset bought at the end of an accounting period:
AssetsareassumedtobeboughtatT0. Thiscouldbetheveryendofanaccountingperiod(e.g.31/21/X1)or
thestartofanother(e.g.1/1/X2). Thereisnodistinctionbetweenthesedatesfordiscounting,butthereis
fortax.
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Anassetisboughtonthefirstdayoftheyearfor$10,000andwillbeusedonaprojectforfouryearsafterwhichitwillbedisposedofonthefinaldayofyear4.Taxispayableat30%,oneyearinarrears,andcapitalallowancesareavailableat25%reducingbalance.
Required:
(a) CalculatetheWDAandhencethetaxsavingsforeachyeariftheproceedsondisposaloftheassetare$2,500.
(b) Howwouldyouranswerchangeiftheassetwasboughtonthelastdayofthepreviousaccountingperiod?
Acompanybuysanassetonthelastdayoftheaccountingperiodfor$26,000.Itwillbeusedonaprojectforthreeyearsafterwhichitwillbedisposedofonthefinaldayofyear3.Taxispayableat30%oneyearinarrears,andcapitalallowancesareavailableat25%reducingbalance.
(a) CalculatetheWDAandhencethetaxsavingsforeachyeariftheproceedsondisposaloftheassetare$12,500.
(b) Ifnettradingincomefromtheprojectis$16,000paandthecostofcapitalis8%calculatetheNPVoftheproject.
(c) Howwouldyouranswerchangeiftheassetwasboughtonthefirstdayoftheaccountingperiod?
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Test your understanding 8 NPV including tax
Expandable text Timing of asset purchase and sale
Test your understanding 7 NPV including tax
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5Incorporating working capital
Investmentinanewprojectoftenrequiresanadditionalinvestmentinworkingcapital,i.e.thedifferencebetweenshorttermassetsandliabilities.
Thetreatmentofworkingcapitalisasfollows:
Tocalculatetheworkingcapitalcashflowsyoushould:
Step 1:Calculatetheabsoluteamountsofworkingcapitalneededineachperiod
Step 2:Workouttheincrementalcashflowsrequiredeachyear
initialinvestmentisacostatthestartoftheproject iftheinvestmentisincreasedduringtheproject,theincreaseisa
relevantcashoutflow attheendoftheprojectalltheworkingcapitalisreleasedandtreated
asacashinflow.
Acompanyexpectssalesforanewprojecttobe$225,000inthefirstyeargrowingat5%pa.Theprojectisexpectedtolastfor4years.Workingcapitalequalto10%ofannualsalesisrequiredandneedstobeinplaceatthestartofeachyear.
Calculate the working capital flows for incorporation into the NPV calculation.
Acompanyanticipatessalesforthelatestventuretobe$300,000inthefirstyear.Salesarethenexpectedtoincreaseatarateof8%paoverthethreeyearlifeoftheproject.Workingcapitalequalto10%ofannualsalesisrequiredandneedstobeinplaceatthestartofeachyear.
Calculate the working capital flows.
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Test your understanding 9 Working capital
Test your understanding 10 Working capital
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6Laying out long NPV questions
Forthemajorityofinvestmentappraisalquestions,thefollowingproformaisrecommended:
7Dealing with questions with both tax and inflation.
Combiningtaxandinflationinthesamequestiondoesnotmakeitanymoredifficultthankeepingthemseparate.
Questionswithbothtaxandinflationarebesttackledusingthemoneymethod.
Inflatecostsandrevenues,wherenecessary,beforedeterminingtheirtaximplications.
Ensurethatthecostanddisposalvalueshavebeeninflated(ifnecessary)beforecalculatingWDAs.
Alwayscalculateworkingcapitalontheseinflatedfigures,unlessgiven. Useaposttaxmoneydiscountrate.
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AckbonoCoisconsideringapotentialprojectwiththefollowingforecasts:
Theinitialinvestmentwillbemadeonthefirstdayofthenewaccountingperiod.
Thesellingpriceperunitisexpectedtobe$100andthevariablecost$30perunit.Bothofthesefiguresaregivenintodaysterms.
Taxispaidat30%,oneyearaftertheaccountingperiodconcerned.
WDA'sareavailableat25%reducingbalance.
Thecompanyhasarealrequiredrateofreturnof6.8%.
Generalinflationispredictedtobe3%pabutthesellingpriceisexpectedtoinflateat4%andvariablecostsby5%pa
Determine the NPV of the project.
N.B. work in $ millions.
Now T1 T2 T3Initialinvestment($million) (1,000)Disposalproceeds($million) 200Demand(millionsofunits) 5 10 6
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Test your understanding 11 NPV with tax and inflation
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Chapter summary
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Test your understanding answers
Realreturn=$1,0001.1/1.07=$1.028.Areturnof2.8%.
(1+i)=(1+r)(1+h)=1.081.05=1.134
Moneyrate(i)=13.4%.
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Test your understanding 2 Money and real returns
Test your understanding 1 Money and real returns
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Discounting the money cash flows at the money rate the money method
Discountingmoneycashflowatthemoneyrate:Thecashflowsattodayspricesareinflatedby5.5%foreveryyeartotakeaccountofinflationandconvertthemintomoneyflows.Theyarethendiscountedusingthemoneycostofcapital.
Themoneycashflowsaretherefore:
Note:Thequestionsimplyreferstothefirmscostofcapital.Youcanassumethisisthemoneyrateifyouaregivenarealratetheexaminerwillalwaysspecify.
Time Working Money cash flow $
0 (50,000) =(50,000)1 20,0001.055 =21,1002 20,000(1.055)2 =22,2613 20,000(1.055)3 =23,4854 20,000(1.055)4 =24,776
Time Money cash flow Discount rate PV$ 15% $
0 (50,000) 1 (50,000)1 21,100 0.870 18,3572 22,261 0.756 16,8293 23,485 0.658 15,4534 24,776 0.572 14,172
_______NPV= 14,811
_______
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Test your understanding 3 Money and real methods
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Discounting the real cash flows at the real rate the real method.
Calculatetherealratebyremovingthegeneralinflationfromthemoneycostofcapital:
Therealratecannowbeappliedtotherealflowswithoutanyfurtheradjustments.
Note:Differencesduetorounding.
(1+i)(1+r)=
(1+h)
(1+1.15)(1+r)=
(1.055)
(1+r)= 1.09Therefore r= 0.09 i.e.9.%
Year Real cash flow Discount rate PV$ 9% $
0 (50,000) 1 (50,000)14 20,000 3.240 64,800
_______NPV= 14,800
_______
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(a) Realcashflowsandrealdiscountrates
Discountrateasperthequestionof15.5%includesinvestors/lendersinflationexpectationof5%.Hencerealdiscountrate,r,isgivenby:
1+i1+r=
1+h
1+0.1551+r= =1.10
1+0.05
Therefore ris 0.10 or10%
Timing Cash flow PV factor PV$ @10% $0 (750) 1.000 (750)1 330 0.909 3002 242 0.826 2003 532 0.751 400
____NVP 150
____
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Thediscountrateasperthequestionof15.5%isthemoneydiscountrate.
Toconvertrealcashflowsintomoneyflowstheywillneedtobeincreasedby5%eachyearfromyear0,toallowforinflation.
*1/1.155=0.866
1/1.1552=0.750
1/1.1553=0.649
Note:thateitherapproachyieldsidenticalconclusions(allowingforrounding).
(b) Moneycashflowsandmoneydiscountrates
Timing Real/ Inflation Money DF PVcash flow factor cash flow @ 15.5%
(a) (b) (a)(b)$ $ $
0 (750) 1 (750) 1.000 (750)1 330 1+0.05 346.5 0.866* 3002 242 (1+0.05)2 266.8 0.750 2003 532 (1+0.05)3 615.9 0.649 400
____NPV 150
____
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Since the question contains both specific and general inflation rates, the money method should be used
Step 1
Themoneymethodneedstobecalculatedusingtheinformationprovidedontherealrateofreturnandthegeneralrateofinflation
(1+i)=(1+r)(1+h)
(1+i)=(1.085)(1.06)
i=15%
Step 2
Inflatethecashflowsusingthespecificinflationratesanddiscountusingthemoneyratecalculatedabove.
ThereforeNPV=$(1,081)whichsuggeststheprojectisnotworthwhile.
T0 T1 T2 T3 T4 T5
$ $ $ $ $ $
Investment (7,000)
Wagessavings(inflating@10%)
1,100 1,210 1,331 1,464 1,610
Materialssavings(inflating@5%)
420 441 463 486 510
______ ______ ______ ______ ______ ______
Netcashflow (7,000) 1,520 1,651 1,794 1,950 2,120
PVfactor@15%
1.000 0.870 0.756 0.658 0.572 0.497
______ ______ ______ ______ ______ ______
PVofcashflow
(7,000) 1,322 1,248 1,180 1,115 1,054
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Test your understanding 5 General and specific inflation rates
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(a) $Originalcostofasset 100,000Cumulativecapitalallowancesclaimed (68,000)
_______Writtendownvalueoftheasset 32,000Disposalvalueoftheasset (20,000)
_______BA(adeductionagainstprofits) 12,000
_______(b) $
Originalcostofasset 100,000Cumulativecapitalallowancesclaimed (68,000)
_______Writtendownvalueoftheasset 32,000Disposalvalueoftheasset (40,000)
_______BC(taxablewithprofits) (8,000)
_______
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Test your understanding 6 Balancing allowance or charge
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(a)
Note:
Time $ Tax saving @ 30%
Timing of tax relief
T0 Initialinvestment 10,000
T1 WDA@25% (2,500) 750 T2
_______
Writtendownvalue
7,500
T2 WDA@25% (1,875) 563 T3
_______
Writtendownvalue
5,625
T3 WDA@25% (1,406) 422 T4
Writtendownvalue
4,219
T4 Saleproceeds (2,500)
_______
T4 BA 1,719 516 T5
totalWDAs=2,500+1,875+1,406+1,719=7,500=fallinvalueoftheasset
totaltaxrelief=750+563+422+516=22517,50030%(WDAsxtaxrate)
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Test your understanding 7 NPV including tax
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Note:
(b) TheassetisstillboughtattimeT0butfallsintothepreviousaccountingperiodfortaxpurposes.TheoverallvalueofWDAsclaimedandthereforethetotaltaxsavingremainsunchanged,butthetimingandamountoftheindividualamountswillalter.Becauseofthetimevalueofmoney,thiswillimpactthefinalNPV.
Time Tax saving @ 30%
Timing of relief
$ $
T0 Initialinvestment 10,000
T0 WDA@25% (2,500) 750 T1
_______
Writtendownvalue
7,500
T1 WDA@25% (1,875) 563 T2
_______
Writtendownvalue
5,625
T2 WDA@25% (1,406) 422 T3
_______
Writtendownvalue
4,219
T3 WDA@25% (1,055) 317 T4
_______
3,164
T4 Saleproceeds (2,500)
_______
T4 BA 664 199 T5
totalWDAs=2,500+1,875+1,406+1,055+664=7,500=fallinvalueoftheasset
totaltaxrelief=750+563+422+317+199=22517,500x30%(WDAsxtaxrate)
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(a) Time Tax saving Timing of
@ 30% tax relief
$ $
T0 Initialinvestment 26,000
T0 WDA@25% (6,500) 1,950 T1
__________
Writtendownvalue 19,500
T1 WDA@25% (4,875) 1,463 T2
__________
Writtendownvalue 14,625
T2 WDA@25% (3,656) 1,097 T3
__________
Writtendownvalue 10,969
Saleproceeds (12,500)
__________
T3 BC (1,531) (460) T4
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Test your understanding 8 NPV including tax
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(b)
Time T0 T1 T2 T3 T4
$ $ $ $ $
Nettradinginflows 16,000 16,000 16,000
Taxpayable(30%) (4,800) (4,800) (4,800)
Initialinvestment (26,000)
Scrapproceeds 12,500
TaxreliefonWDAs 1,950 1,463 1,097 (460)
Netcashflows (26,000) 17,950 12,663 24,797 (5,260)
DF@8% 1.000 0.926 0.857 0.794 0.735
PV (26,000) 16,622 10,852 19,689 (3,866)
NPV $17,297
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(c)
TheNPVislowerasaresultofthepurchasebeingdelayed.
Time Tax saving @30%
Timing of tax reief
$ $T0 Initial
investment26,000
T1 WDA@25% (6,500) 1,950 T2 ______
Writtendownvalue
19,500
T2 WDA@25% (4,875) 1,463 T3 ______
Writtendownvalue
14,625
Saleproceeds (12,500) ______ T3 Balancing
allowance2,125 638 T4
Time T0 T1 T2 T3 T4
Nettradinginflows
$ $ $ $ $
Nettradinginflows
16,000 16,000 16,000
Taxpayable(30%)
(4,800) (4,800) (4,800)
Initialinvestment
(26,000)
Scrapproceeds
12,500
TaxreliefonWDAs
1,950 1,463 638
Netcashflows (26,000) 16,000 13,150 25,163 (4,162)DF@8% 1.000 0.926 0.857 0.794 0.735PV (26,000) 14,816 11,270 19,979 (3,059)NPV $17,006
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Solution
Step 1:Calculatetheabsoluteamountsofworkingcapitalneededovertheproject:
Step 2:Workouttheincrementalinvestmentrequiredeachyear(rememberthatthefullinvestmentisreleasedattheendoftheproject):
T0 T1 T2 T3 T4
$ $ $ $ $
Sales 225,000 236,250 248,063 260,466
Workingcapitalrequired(10%sales)
22,500 23,625 24,806 26,047
T0 T1 T2 T3 T4
$ $ $ $ $
Working 22,5000
23,62522,500
24,80623,625
26,04724,806
26,0470
Workingcapitalinvestment
(22,500) (1,125) (1,181) (1,241) 26,047
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Test your understanding 9 Working capital
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Step 1:Calculatetheabsoluteamountsofworkingcapitalneededovertheproject:
T0 T1 T2 T3
$ $ $ $
Sales 300,000 324,000 349,920
Workingcapitalrequired
30,000 32,400 34,992
Step 2:Workouttheincrementalinvestmentrequiredeachyear,rememberingtoreleasealltheworkingcapitalattheendoftheproject
T0 T1 T2 T3
$ $ $ $
Working 32,40030,000
34,99232,400
Capitalinvestment (30,000) (2,400) (2,592) 34,992
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Test your understanding 10 Working capital
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$ millions T0 T1 T2 T3 T4Sales(W1) 520 1082 675Variablecosts(W1) (158) (331) (208)
_____ _____ _____Nettradinginflows 362 751 467Taxpayable(30%) (109) (225) (140)Initialinvestment (1,000)Scrapproceeds 200TaxreliefonWDAs(W2) 75 56 109
_____ _____ _____ _____ _____Netcashflows (1,000) 362 717 498 (31)DF@10%(W3) 1 0.909 0.826 0.751 0.683
_____ _____ _____ _____ _____PV (1,000) 329 592 374 (21)
NPV 274_____
W1: revenue and costs
Revenueandcostsneedtobeexpressedinmoneyterms.
e.g.revenueatT2=$10m100(1.04)2=$1,081.6m.
W2: WDAs
Time $m Tax saving Timing of
tax relief$m
T0 Initialinvestment 1000T1 WDA@25% (250) 75 T2
_____Writtendownvalue 750
T2 WDA@25% (188) 56 T3_____
Writtendownvalue 562Saleproceeds (200)
_____T3 BA 362 109 T4
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Test your understanding 11 NPV with tax and inflation
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W3: Discount rate
(1+i)=(1+r)(1+h)=1.0681.03=1.10,givingamoneyrate(i)=10%.
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AssetinvestmentdecisionsandcapitalrationingChapter learning objectives
Uponcompletionofthischapteryouwillbeableto:
evaluatethechoicebetweenleasinganassetandborrowingtobuyusingthebeforeandaftertaxcostsofdebt
defineandcalculateanequivalentannualcost(EAC) evaluateassetreplacementdecisionsusingEACs explaincapitalrationinginthecontextofcapitalbudgeting defineanddistinguishbetweendivisibleandindivisibleprojects calculateprofitabilityindexesfordivisibleinvestmentprojectsand
usethemtoevaluateinvestmentdecisions calculatethenetpresentvalue(NPV)ofcombinationsofnon
divisibleinvestmentprojectsandusetheresultstoevaluateinvestmentdecisions.
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5
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1Lease versus buy
Oncethedecisionhasbeenmadetoacquireanassetforaninvestmentproject,adecisionstillneedstobemadeastohowtofinanceit.Thechoicesthatwewillconsiderare:
TheNPVsofthefinancingcashflowsforbothoptionsarefoundandcomparedandthelowestcostoptionselected.
lease buy.
Thefinancedecisionisconsideredseparatelyfromtheinvestmentdecision.Theoperatingcostsandrevenuesfromtheinvestmentwillbecommonineachcase.
OnlytherelevantcashflowsarisingasaresultofthetypeoffinanceareincludedintheNPVcalculation.
Leasing
Theassetisneverownedbytheusercompanyfromtheperspectiveofthetaxman.
Implications
Therelevantcashflowswouldthusbe:
ThefinancecompanyreceivestheWDAsastheowneroftheasset. TheuserreceivesnoWDAsbutisabletooffsetthefullrentalpayment
againsttax.
theleasepayments
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taxreliefontheleasepayments.
Buying
Theassumptionisthatbuyingrequirestheuseofabankloan(forthesakeofcomparability).Theuseristheowneroftheasset.
Implication
Therelevantcashflowswouldbe:
TheuserwillreceiveWDAsontheassetandtaxrelieffortheinterestpayableontheloan.
thepurchasecost anyresidualvalue anyassociatedtaximplicationsduetoWDAs.
DonotincludetheinterestpaymentsorthetaxreliefarisingonthemintheNPVcalculation,asthisisdealtwithviathecostofcapital(seebelow).
Cost of capital
Astheinterestpaymentsattracttaxreliefwemustusetheposttaxcostofborrowingasourdiscountrate.Asallfinancingcashflowsareconsideredtoberiskfree,thisrateisusedforbothleasingandbuying.
Posttaxcostofborrowing=Costofborrowing(1Taxrate).
(Note:insomequestionsyoumayfindthatacompanyisnotpayingtaxandsothepretaxratewouldbeappropriate.)
WalsheyCohasalreadydecidedtoacceptaprojectandisnowconsideringhowtofinanceit.
Theassetcouldbeleasedoverfouryearsatarentalof$36,000pa,payableatthestartofeachyear.
Taxispayableat30%,oneyearinarrears.Theposttaxcostofborrowingis10%.
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Expandable text Lease versus buy
Test your understanding 1 Leasing calculations
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Required:
Calculatethenetpresentvalueoftheleasingoption.
Afirmhasdecidedtoacquireanewmachinetoneutralisethetoxicwasteproducedbyitsrefiningplant.Themachinewouldcost$6.4millionandwouldhaveaneconomiclifeoffiveyears.
Capitalallowances(CAs)of25%paonareducingbalancebasisareavailablefortheinvestment.
Taxationof30%ispayableonoperatingcashflows,oneyearinarrears.
Thefirmintendstofinancethenewplantbymeansofafiveyearfixedinterestloanatapretaxcostof11.4%pa,principalrepayableinfiveyearstime.
Asanalternative,aleasingcompanyhasproposedafinanceleaseoverfiveyearsat$1.42millionpapayableinadvance.
Scrapvalueofthemachineundereachfinancingalternativewillbezero.
Evaluate the two options for acquiring the machine and advise the company on the best alternative.
2Replacement decisions
Oncethedecisionhasbeenmadetoacquireanassetforalongtermproject,itisquitelikelythattheassetwillneedtobereplacedperiodicallythroughoutthelifeoftheproject.
Wheretherearecompetingreplacementsforaparticularassetwemustcomparethepossiblereplacementstrategiesavailable.
Aproblemariseswhere
equivalentassetsavailablearelikelytolastfordifferentlengthsoftimeor
anasset,oncebought,mustbereplacedatregularintervals.
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Expandable text Other considerations
Test your understanding 2 Lease versus buy
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Thedecisionweareconcernedwithhereishowoftenshouldtheassetbereplaced?
Equivalent annual costs (EACs)
Inordertodealwiththedifferenttimescales,theNPVofeachoptionisconvertedintoanannuityoranEAC.
TheEACistheequalannualcashflow(annuity)towhichaseriesofunevencashflowsisequivalentinPVterms.
Theformulausedis:
PVofcosts EAC= Annuityfactor(AF)
Theoptimum replacement period (cycle)willbetheperiodthathasthelowestEAC,althoughinpracticeotherfactorsmayinfluencethefinaldecision.
Themethodcanbesummarisedas:
(1) calculatetheNPVofeachstrategyorreplacementcycle(2) calculatetheEACforeachstrategy(3) choosethestrategywiththelowestEAC.
Key assumptions
Cashinflowsfromtradingareignoredsincetheywillbesimilarregardlessofthereplacementdecision.Inpracticeusinganolderassetmayresultinlowerquality,whichinturncouldaffectsales.
Theoperatingefficiencyofmachineswillbesimilarwithdifferingmachinesorwithmachinesofdifferingages.
Theassetswillbereplacedinperpetuityoratleastintotheforeseeablefuture.
Inmostquestionstaxandinflationareignored. AswithallNPVcalculationsnonfinancialaspectssuchaspollutionand
safetyareignored.Anoldermachinemayhaveahigherchanceofemployeeaccidentsandmayproducemorepollution.
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Expandable text Replacement decisions
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Amachinecosts$20,000.
Thefollowinginformationisalsoavailable:
Runningcosts(payableattheendoftheyear):
Tradeinallowance
Calculate the optimal replacement cycle if the cost of capital is 10%.
Year1 $5,000Year2 $5,500
Disposalafter1year: $16,000Disposalafter2years:
Adecisionhastobemadeonreplacementpolicyforvans.Avancosts$12,000andthefollowingadditionalinformationapplies:
Calculate the optimal replacement policy at a cost of capital of 15%.
Notethattheassetisonlymaintainedattheendoftheyearifitistobekeptforafurtheryear,i.e.therearenomaintenancecostsintheyearofreplacement.
Ignoretaxationandinflation.
Asset sold at end of year
Tradein allowance
Asset kept for
Maintenance cost at end of year
$ $1 9,000 1year 02 7,500 2years 1,500in1styear3 7,000 3years 2,700in2ndyear
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Test your understanding 4 Equivalent annual costs
Test your understanding 3 Equivalent annual costs
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Limitations of replacement analysis
Themodelassumesthatwhenanassetisreplaced,thereplacementisinallpracticalrespectsidenticaltothelastoneandthatthisprocesswillcontinuefortheforeseeablefuture.Howeverinpracticethiswillnotholdtrueowingto:
changingtechnology inflation changesinproductionplans.
3Capital rationingAn introduction
ShareholderwealthismaximisedifacompanyundertakesallpossiblepositiveNPVprojects.Capitalrationingiswherethereareinsufficientfundstodoso.Thisimpliesthatwhereinvestmentcapitalisrationed,shareholderwealthisnotbeingmaximised.
Ensureyouareabletodiscussthedifferencebetweenhard(external)andsoft(internal)capitalrationing.
Hard capital rationing:Anabsolutelimitontheamountoffinanceavailableisimposedbythelendinginstitutions.
Soft capital rationing:Acompanymayimposeitsownrationingoncapital.Thisiscontrarytotherationalviewofshareholderwealthmaximisation.
Single and multiperiod capital rationing
Singleperiodcapitalrationing:Shortageoffundsforthisperiodonly.
Multiperiodcapitalrationing:Shortageoffundsinmorethanoneperiod(outsidesyllabus)
Themethodfordealingwithsingleperiodcapitalrationingissimilartothelimitingfactoranalysisusedelsewhereindecisionmaking.
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Expandable text Reasons for hard or soft capital rationing
Expandable text Limitations of replacement analysis
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The profitability index (PI) and divisible projects
Ifaprojectisdivisible,anyfractionoftheprojectmaybeundertakenandthereturnsfromtheprojectareexpectedtobegeneratedinexactproportiontotheamountofinvestmentundertaken.Projectscannothoweverbeundertakenmorethanonce.
TheaimwhenmanagingcapitalrationingistomaximisetheNPVearnedper$1investedinprojects.
Wheretheprojects:
itisachievedby:
Theformulais:
aredivisible(i.e.canbedoneinpart) earncorrespondingreturnstoscale
(1) calculatingaPIforeachproject(seebelow)(2) rankingtheprojectsaccordingtotheirPI(3) allocatingfundsaccordingtotheprojectsrankingsuntiltheyareused
up.
NPVPI=
Investment
Acompanyhas$100,000availableforinvestmentandhasidentifiedthefollowing5investmentsinwhichtoinvest.Allinvestmentsmustbestartednow(Yr0).
Project Initial investment (Yr 0) $000 NPV $000C 40 20D 100 35E 50 24F 60 18G 50 (10)
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Test your understanding 5 Capital rationing with divisible
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Required:
Determinewhichprojectsshouldbechosentomaximisethereturntothebusiness.
Indivisible projects trial and error
Ifaprojectisindivisibleitmustbedoneinitsentiretyornotatall.
Whereprojectscannotbedoneinpart,theoptimalcombinationcanonlybefoundbytrialanderror.
ACohasthesameproblemasbeforebutthistimetheprojectsareindivisible.
Theinformationisreproducedbelow:
Acompanyhas$100,000availableforinvestmentandhasidentifiedthefollowing5investmentsinwhichtoinvest.Allinvestmentsmustbestartednow(Yr0).
Required:
Determinetheoptimalprojectselection.
Project Initial investment (Yr 0) $000 NPV $000C 40 20D 100 35E 50 24F 60 18G 50 (10)
Thekeyintheexaminationistoascertainwhetherornottheprojectsaredivisible.
DivisibleprojectscanberankedusingthePI.Combinationsofindivisibleprojectsmustbeconsideredonatrialanderrorbasis.
Mutuallyexclusive projects
Sometimesthetakingonofprojectswillprecludethetakingonofanother,e.g.theymaybothrequireuseofthesameasset.
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Test your understanding 6 Capital rationing with indivisible
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Inthesecircumstances,eachcombinationofinvestmentsistriedtoidentifywhichearnsthehigherlevelofreturns.
UsingthesamecompanyinformationforACo(divisibleprojects)theadditionalfactortobeconsideredisthatprojectsCandEaremutuallyexclusive.
Theinformationisreproducedbelow.
Acompanyhas$100,000availableforinvestmentandhasidentifiedthefollowing5investmentsinwhichtoinvest.Allinvestmentsmustbestartednow(Yr0).
Required:
Determinetheoptimalprojectselection.
Project Initial investment (Yr 0) $000 NPV $000 PI NPV/$C 40 20 0.5D 100 35 0.35E 50 24 0.48F 60 18 0.3G 50 (10) notworthwhile
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Test your understanding 7 Capital rationing with mutually
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Chapter summary
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Test your understanding answers
Cost of leasing:
*Or3.1700.909=2.882
Year Cash flows $ DF @10% PV $
03 Rentals (36,000) 1.000+2.487 (125,532)
25 Taxrelief 10,800 3.7910.909=2.882* 31,126
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NPV (94,406)
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Test your understanding 1 Leasing calculations
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(W1)CalculationofthetaxreliefonWDAsifassetbought:
Note:Theassetisboughtattimet=0asusualwiththefirstC