ACCA F9 Essential Text D09-J10

ACCAPaperF9FinancialmanagementEssentialtext

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Publishedby:KaplanPublishingUKUnit2TheBusinessCentreMollyMillarsLaneWokinghamBerkshireRG412QZ

ISBN9781847107541

KaplanFinancialLimited,2009

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Acknowledgements

WearegratefultotheAssociationofCharteredCertifiedAccountantsandtheCharteredInstituteofManagementAccountantsforpermissiontoreproducepastexaminationquestions.TheanswershavebeenpreparedbyKaplanPublishing.

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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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v

chapterIntroduction

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.

KAPLAN PUBLISHING vii

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.

1

chapter

1

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.

chapter 1

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Expandable text The investment decision

Expandable text The financing decision

Expandable text The dividend decision

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


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Expandable text Financial roles

Expandable text Objectives and strategy

Test your understanding 1 Objectives and strategies

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.

chapter 1

KAPLAN PUBLISHING 5

Expandable text Maximising and satisficing

Expandable text Financial objectives

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

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.

chapter 1

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Test your understanding 3 Managerial reward schemes

Expandable text Managerial reward schemes

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

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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KAPLAN PUBLISHING 9

Expandable text VFM

Expandable text Planning influences

Expandable text Financial objectives

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

Chapter summary

chapter 1

KAPLAN PUBLISHING 11

chapter 1


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.



Test your understanding 1 Objectives and strategies

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.

chapter 1


Test your understanding 2 Stakeholder conflicts

Advantages

Disadvantages

GoalcongruencemanagerswillworktoachievegrowthinEPS,whichwillmakeshareholdersfeelthattheirwealthisincreasing.

Thefigureisdifficult(butnotimpossible!)tomanipulatefromoneperiodtoanotherasitwillbeaudited.

Thereislittleincentiveformanagerstocontrolworkingcapitalandcashflowapressingproblem.Growthmaybeattheexpenseofliquidityandultimatelycompromisethefirmsfuturesurvival.

Managersmaygainbonusessimplybecauseoftheproductsconcernedratherthantheirownefforts.AtargetgrowthinEPSwouldbebetter.

LongtermshareholdervalueandEPSarenotwellcorrelated. Thereisonlyonemeasurethatfocusesonfinaleffectsratherthan

operationalcauses.



Test your understanding 3 Managerial reward schemes

Financialmeasures:

Economytargets:

Efficiencytargets:

Effectivenesstargets:

proportionofoverallfundsspentonadministrationcosts abilitytostaywithinbudget/breakeven revenuetargetsmet.

costsofpurchasingprovisionsofsuitablenutritionalquality costsofnegotiatingforandpurchasingequipment negotiationofbulkdiscounts payratesforstaffofappropriatelevelsofqualification.

numbersofportionsproduced costpermealsold levelsofwastageofunpreparedandofcookedfood staffutilisation equipmentlife.

numbersusingthecanteen customersatisfactionratings nutritionalvalueofmealsserved.

chapter 1


Test your understanding 4 Not for profit organisations

CapitalbudgetingandbasicinvestmentappraisaltechniquesChapter learning objectives


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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chapter

2

1Capital investment

Whenabusinessspendsmoneyonnewnoncurrentassetsitisknownascapitalinvestmentorcapitalexpenditure.Spendingmaybefor:

Spendingisnormallyirregularandforlargeamounts.Itisexpectedtogeneratelongtermbenefits.

maintenance profitability expansion indirectpurposes.

Othertypesofexpenditureincurredbyabusinessincludes:

Revenueexpenditureregularspendingonthedaytodayrunningofthebusinesswherethebenefitisexpectedtolastforonlyonespecificaccountingperiod.

Workingcapitalinvestmentinvestmentinshorttermnetassets(inventory,receivablesandcashlessshorttermpayables).

Youmustbeabletodistinguishbetweencapitalandrevenueexpenditureandexpenditureonworkingcapital.

Capital budgeting and basic investment appraisal techniques


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.

chapter 2


Test your understanding 1 Expenditure classification

Expandable text Capital budgeting process

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



Test your understanding 2 ROCE

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.

chapter 2


Expandable text Initial capital cost

Expandable text Advantages and disadvantages of ROCE


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.



Expandable text Relevant costs

Test your understanding 4 Relevant costs

Expandable text Profits versus cash flows

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?

chapter 2


Test your understanding 6 Payback with constant annual cash


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



Test your understanding 8 Payback with uneven cash flows

Test your understanding 7 Payback in years and months

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.

chapter 2


Expandable text Advantages and disadvantages of payback


Chapter summary




Annualrentalpaymentsforthewarehousearerevenueexpenditure.Thebenefitisonlyforthataccountingperiod.

Thenewforklifttruckisacapitalpurchase.Itismaintenancespendingasitreplacesonealreadyownedbutdamaged.

Theincreasedinventoryspendingisaninvestmentinworkingcapital.

Theautomaticmouldingmachineisalsoacapitalexpense.Howeversinceitwasboughttostreamlineaproductionprocess,thepurposeisprofitability.

chapter 2


Test your understanding 1 Expenditure classification

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%




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

chapter 2




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



Test your understanding 7 Payback in years and months


Test your understanding 6 Payback with constant annual cash

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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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




InvestmentappraisaldiscountedcashflowtechniquesChapter learning objectives


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.

35

chapter

3

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


Expandable text The time value of money

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

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



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


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.



Test your understanding 4 Discounting annuities

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

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.



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

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



Test your understanding 8 Net present value

Expandable text What does the NPV actually mean?

Expandable text Assumptions used in discounting

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


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



Expandable text IRR

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


(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.



Test your understanding 12 IRR with even cashflows

Expandable text Calculating the IRR with even cash flows

Expandable text Calculating the IRR with perpetuities

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

Chapter summary




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 4 Discounting annuities


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.



Test your understanding 5

Test your understanding 6 Advanced annuities and perpetuities

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 7 Delayed annuities and perpetuities

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)





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.

chapter 3



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.



Test your understanding 12 IRR with even cashflows

InvestmentappraisalfurtheraspectsofdiscountedcashflowsChapter learning objectives


explaintheimpactofinflationoninterestratesanddefineanddistinguishbetweenrealandnominal(money)interestrates

explainthedifferencebetweentherealtermsandnominaltermsapproachestoinvestmentappraisal

usethenominal(money)termsapproachtoappraiseaninvestment

usetherealtermsapproachtoappraiseaninvestment explaintheimpactoftaxonDCFappraisals calculatethetaxcashflowsassociatedwithcapitalallowances

andincorporatethemintonetpresentvalues(NPV)calculations calculatethetaxcashflowsassociatedwithtaxableprofitsand

incorporatethemintoNPVcalculations explaintheimpactofworkingcapitalonanNPVcalculationand

incorporateworkingcapitalflowsintoNPVcalculations.

57

chapter

4

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


$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


Expandable text Illustration

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.



Test your understanding 3 Money and real methods

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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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%



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

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



Expandable text Capital allowances

Test your understanding 6 Balancing allowance or charge

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.

chapter 4


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?



Test your understanding 8 NPV including tax

Expandable text Timing of asset purchase and sale


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.

chapter 4


Test your understanding 9 Working capital


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.



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

Chapter summary




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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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

_______




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

____




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

____

chapter 4


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



Test your understanding 5 General and specific inflation rates

(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

(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)




Note:

(b) TheassetisstillboughtattimeT0butfallsintothepreviousaccountingperiodfortaxpurposes.TheoverallvalueofWDAsclaimedandthereforethetotaltaxsavingremainsunchanged,butthetimingandamountoftheindividualamountswillalter.Becauseofthetimevalueofmoney,thiswillimpactthefinalNPV.

Time Tax saving @ 30%

Timing of relief

$ $


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 WDA@25% (6,500) 1,950 T1

__________

Writtendownvalue 19,500

T1 WDA@25% (4,875) 1,463 T2

__________


T2 WDA@25% (3,656) 1,097 T3

__________


Saleproceeds (12,500)

__________

T3 BC (1,531) (460) T4




(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



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

chapter 4



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




$ 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

chapter 4


Test your understanding 11 NPV with tax and inflation

W3: Discount rate

(1+i)=(1+r)(1+h)=1.0681.03=1.10,givingamoneyrate(i)=10%.



AssetinvestmentdecisionsandcapitalrationingChapter learning objectives


evaluatethechoicebetweenleasinganassetandborrowingtobuyusingthebeforeandaftertaxcostsofdebt

defineandcalculateanequivalentannualcost(EAC) evaluateassetreplacementdecisionsusingEACs explaincapitalrationinginthecontextofcapitalbudgeting defineanddistinguishbetweendivisibleandindivisibleprojects calculateprofitabilityindexesfordivisibleinvestmentprojectsand

usethemtoevaluateinvestmentdecisions calculatethenetpresentvalue(NPV)ofcombinationsofnon

divisibleinvestmentprojectsandusetheresultstoevaluateinvestmentdecisions.

87

chapter

5

1Lease versus buy

Oncethedecisionhasbeenmadetoacquireanassetforaninvestmentproject,adecisionstillneedstobemadeastohowtofinanceit.Thechoicesthatwewillconsiderare:

TheNPVsofthefinancingcashflowsforbothoptionsarefoundandcomparedandthelowestcostoptionselected.

lease buy.

Thefinancedecisionisconsideredseparatelyfromtheinvestmentdecision.Theoperatingcostsandrevenuesfromtheinvestmentwillbecommonineachcase.

OnlytherelevantcashflowsarisingasaresultofthetypeoffinanceareincludedintheNPVcalculation.

Leasing

Theassetisneverownedbytheusercompanyfromtheperspectiveofthetaxman.

Implications

Therelevantcashflowswouldthusbe:

ThefinancecompanyreceivestheWDAsastheowneroftheasset. TheuserreceivesnoWDAsbutisabletooffsetthefullrentalpayment

againsttax.

theleasepayments

Asset investment decisions and capital rationing


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%.

chapter 5


Expandable text Lease versus buy

Test your understanding 1 Leasing calculations

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.



Expandable text Other considerations

Test your understanding 2 Lease versus buy

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.

chapter 5


Expandable text Replacement decisions

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



Test your understanding 4 Equivalent annual costs

Test your understanding 3 Equivalent annual costs

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.

chapter 5


Expandable text Reasons for hard or soft capital rationing

Expandable text Limitations of replacement analysis

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)



Test your understanding 5 Capital rationing with divisible

Required:

Determinewhichprojectsshouldbechosentomaximisethereturntothebusiness.

Indivisible projects trial and error

Ifaprojectisindivisibleitmustbedoneinitsentiretyornotatall.

Whereprojectscannotbedoneinpart,theoptimalcombinationcanonlybefoundbytrialanderror.

ACohasthesameproblemasbeforebutthistimetheprojectsareindivisible.

Theinformationisreproducedbelow:


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.

chapter 5


Test your understanding 6 Capital rationing with indivisible

Inthesecircumstances,eachcombinationofinvestmentsistriedtoidentifywhichearnsthehigherlevelofreturns.

UsingthesamecompanyinformationforACo(divisibleprojects)theadditionalfactortobeconsideredisthatprojectsCandEaremutuallyexclusive.

Theinformationisreproducedbelow.


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



Test your understanding 7 Capital rationing with mutually

Chapter summary

chapter 5



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

_______

NPV (94,406)

_______



Test your understanding 1 Leasing calculations

(W1)CalculationofthetaxreliefonWDAsifassetbought:

Note:Theassetisboughtattimet=0asusualwiththefirstC

Documents

ACCA F9 Essential Text D09-J10