CorporatefinanceEighthEditionChapter7Investmentappraisal:applicationsandriskRelevantprojectcashflowsRelevantcashflowsareincrementalcashflowsarisingfromaninvestmentdecision,suchasinitialinvestment,cashfromsalesanddirectcostofsalesSunkcostsApportionedfixedcostsOpportunitycostsIncrementalworkingcapitalTaxationTaxreliefoncapitalexpenditureisgiventhroughcapitalallowances18%reducingbalancecapitalallowancesgivenonplantandmachineryinUK100%first-yearallowancesarecurrentlyofferedoncertainassettypesBalancingallowanceandbalancingchargeTaxation(continued)Example:Machinecosts￡200,00025%reducingbalancecapitalallowancesExpectedlifeofmachineis4yearsScrapvalueafter4yearsis￡20,000Corporationtaxis20%,

1yearinarrearsCalculatecapitalallowancesandassociatedtaxbenefitsCapitalallowances: TaxbenefitYear1:200,000×0.25=￡50,000￡10,000Year2:150,000×0.25=￡37,500 ￡7,500Year3:112,500×0.25=￡28,125 ￡

5,625Year4:84,375×0.25=￡21,094Balancingallowance*:￡43,281 ￡12,875*(84,375?21,094?20,000) ￡36,000Taxation(continued)Taxation(continued)TaxliabilityarisesontaxableprofitsTaxreliefisavailableonallowablecostssuchasmaterials,wagesandmaintenanceInterestpaymentsarenotrelevantcashflowsastheyareincludedinthediscountrateAfter-taxcashflowsmustbediscountedwitharelevantafter-taxcostofcapitalTimingoftaxliabilitiesandbenefitsInflationInflationcanhaveaseriouseffectoncapitalinvestmentdecisionsTherealvalueoffuturecashflowscanbeseriouslyreducedTheuncertaintyassociatedwiththevalueoffuturecashflowsisincreasedTherealcostofcapitalisfoundfromthenominal(ormoney)costofcapitalbymakinganadjustmentforinflation:

(1+realcostofcapital)×(1+rateofinflation) =(1+nominalcostofcapital)Formula: (1+r)×(1+i

)=(1+n)Inflation(continued)WemeetbothgeneralandspecificinflationInflationandworkingcapitalWecanuseeitheranominalorareal-termsapproachtoinvestmentappraisalNominalterms:nominalcashflowsarediscountedwithanominalcostofcapitalRealterms:realcashflowsdiscountedwitharealcostofcapitalInflation(continued)CashflowsinflatedwithspecificorgeneralinflationarenominalcashflowsNominalcashflowsdeflatedbygeneralrateofinflationarerealcashflowsNPVfoundbydiscountingrealcashflowswithrealcostofcapitalissameasNPVfoundbydiscountingnominalcashflowswithnominalcostofcapitalInflation(continued)RiskanduncertaintyRiskreferstoasetofuniquecircumstanceswhichcanbeassignedprobabilitiesUncertaintyimpliesprobabilitiescannotbeassignedtodifferentsetsofcircumstancesInpractice,theterms‘risk’and‘uncertainty’areoftenusedinterchangeablyRiskincreaseswithvariabilityofreturnsUncertaintyincreaseswithprojectlifeSensitivityanalysisAmethodofevaluatingprojectriskItexaminestheresponsivenessofprojectNPVtochangesinprojectvariablesOnlyonevariableischangedatatimeOnemethodinvolveschangingvariablesby

asetamountthenrecalculatingNPVAnothermethodinvolvesfindingthechangeinavariablewhichgivesazeroNPVSensitivityanalysis(continued)Sensitivityofprojectvariable =ProjectNPV/PVofprojectvariable(%)Example:PVofsalesrevenue=￡1.5mPVofvariablecosts=￡0.6mNPV=￡0.2mSalesrevenuesensitivity=0.2/1.5=13%Variablecostsensitivity=0.2/0.6=33%Salesvolumesensitivity=0.2/0.9=22%SensitivityanalysisindicatesthekeyorcriticalvariablesforaninvestmentprojectKeyprojectvariablesmaymeritfurtherinvestigationtocheckassumptionsKeyvariablesfocusattentionofmanagersonfactorswhichmightpreventsuccessSensitivityanalysis(continued)Problemswithsensitivityanalysis:OnlyonevariableatatimecanbechangedNoindicationisgivenoftheprobabilityofchangesinkeyprojectvariablesNotreallyamethodofanalysingprojectrisk,sinceprobabilitiesareignoredSensitivityanalysis(continued)PaybackPaybackrecognisesuncertaintybylookingatthenearfuture,andbyemphasisingliquidityandshort-termreturnsShorteningpaybackperiodisanintuitivewayofrecognisinghigherriskSmallfirmsmaybeconcernedwithliquidityNotrecommendedaswayofdealingwithriskduetoseriousshortcomingsasinvestmentappraisalmethodConservativeforecastsKnownalsoascertaintyequivalentsUncertainfuturecashflowsarereducedtoasmaller,moreconservativevalueReductionsmaybesubjectiveorappliedinconsistentlyUseofconservativeforecastsmayleadtorejectionofattractiveinvestmentprojectsRisk-adjustedrateclassesAppliesconceptofriskpremium,whichhastimepreferenceandriskpreferenceelementsHurdlerateincreasesforriskierprojectsHardtochooseriskpremiumforgivenprojectOnesolutionistoputprojectsinriskclassesandallocateriskpremiumsStilldifficulttoassessprojectriskandtoassignsomeprojectstodifferentclassesProblemswithrisk-adjustedrates:ProjectsarelikelytobeallocatedtoriskclassesonthebasisoftotalriskAllocationtoriskclassesislikelytotakeaccountofcompanyriskonlyRiskpremiumsarelikelytobederivedonanadhocbasisRisk-adjustedrateclasses(continued)ProbabilityanalysisandENPVProbabilitydistributionsofexpectedcashflowscanbeusedtoobtainexpectedNPVsProjectriskcanbeevaluatedbycalculating:theexpectednetpresentvalue(ENPV)theprobabilityofanegativeNPVtheprobabilityoftheworstcasethestandarddeviationofprojectNPVScenarioanalysisillustratesthisapproachProblemswithprobabilityanalysis:ScenarioanalysisassumesthatagivenstateisfixedoverthelifeoftheprojectProbabilityestimatesofeachstatearebasedonsubjectivejudgementENPVitselfisnotexpectedtooccurasitisthemeanNPVofsinglepointNPVestimatesProbabilityanalysisandENPV(continued)SimulationmodelsProbabilitydistributionsassignedtoeachprojectvariableSimulationmodelsdetermineeffectofsimultaneouschangesinseveralvariablesForexample,variablevaluescanbeselectedbyprobability-basedrandomnumbersComputermakeslargenumberofrunswithrandomnumbersreselectedateachrunRepeatedrunsbuildupprobabilitydistributionofNPVoutcomesSpreadsheetsoftwareandcheapcomputingpowerhaveincreaseduseofthismethodMoredetailedinformationonexpectedNPVmakesprojectevaluationmoredifficult,sincebothNPVanditsstandarddeviationneedtobeconsideredSimulationmodels(continued)DistinctivefeaturesofFDIProjectcashflowsmayneedevaluatinginaforeigncurrencyForeigntaxsystemversushometaxsystemProjectcashflowsversusparentcashflowsRestrictionofprojectcashflowremittancesExchangerateforecastsarerequiredParentshareholderperspectiveisparamount

MethodsofevaluatingFDIMostmultinationalsuseDCFmethodsinFDIevaluation,withIRRpreferredtoNPVUseofDCFappraisalmethodsdoesnotappeartohaveincreasedinrecentyearsManycompaniesdonotuseafter-taxparentcompanycashflowswhenevaluatingFDISomefirmsusecostofdebtasdiscountrateLocallevelFDIevaluationComparesFDIwithsimilarinvestmentprojectsinaforeigncountryIgnoresextentofremittancesIgnoresvalueofprojecttoparentcompanyshareholdersLocalprojectcashflowsmustbeidentifiedEffectonexistingexportsales?ParentlevelFDIevaluationActualreceiptsandpaymentsinparentcompanycurrencymustbeusedInitialinvestmentReturnsoninvestmentReceiptsfromintercompanytradeAccumulatedcontributionsTaxationconsiderationsParentlevelFDIevaluation(continued)Recommendedapproach:Forecastmoney-terms,after-taxcashflowsinlocalcurrencywhichcanberemittedForecastfutureexchangeratesConvertremittablecashflowsintohomecurrencyadjustingforanyfurtherUKtaxApplyafter-tax,risk-adjusteddiscountrateAcceptifNPVisfavourableTaxationandFDIDoubletaxationanditsreliefParentcompanypayshigheroflocaltaxordomestictaxonremittancesreceivedCapitalallowancesUKtaxliabilitycanbeassessedfromtaxableprofitsofforeignsubsidiaryUKliabilityreducedbytaxalreadypaidinordertofindUKtaxpayableFDIexampleWKsubsidiarysoldasgoingconcern,henceworkingcapitalnotrecoveredInitialinvestment:$5mCapitalallowance=$5m×0.2=$1,000,000Annualinterest=$500,000×0.1=$50,000Capitalallowancescanbedeductedtogivetaxableprofit,andthenaddedbackasanon-cashitemtogiveafter-taxcashflowsUKtaxchargecalculatedasfollows:Y1taxableprofit($)=2,190,000Y1taxableprofit(￡)=2,190,000/2.63=￡832,700UKtaxliability=832,700×0.24=￡199,848Localtaxpaid=832,700×0.20=￡166,540UKtaxpayable=199,848–166,540=￡33,308FDIexample(continued)Year 123 4 5 $000$000$000$000$000Cashprofits 32403499377940814408Capitalallowances

(1000)

(1000)

(1000)

(1000)(1000)Interest

(50)

(50)

(50)

(50)

(50)Profitbeforetax 21902449272930313358Tax

(438)

(490)

(546)

(606)

(672)Profitaftertax 17521959218324252686AddbackCAs 10001000100010001000After-taxcashflow

27522959318334253686FDIexample(continued)Year 123 4 5 $000$000$000$000$000After-taxCF 27522959318334253686Investment(5000)WC

(500)

(40)(43)

(47)

(50)

(54)Loan 500 (500)Sale 12,000Remittable

(5000)271229163136337515,132X-rate(B/￡)

2.502.632.762.903.043.19Netcash(￡)(2000)103110571081

11104744FDIexample(continued)FDIexample(continued)Year 0 1 2 3 4 5 ￡000￡000￡000￡000￡000￡000Netcash(￡)(2000)103110571081

11104744UKtax (33)(36)(38)

(40)

(42)UKaftertax(2000)

99810211043

10704702Lostsales

(82)(85)

(88)

(91)

(93)ParentCF

(2000)

916

9369559794609Discount 1.0000.8700.7560.6580.5720.497PV

(2000)7977086285602291NPV=￡2,984,000andsoinvestmentisworthwhile.EmpiricalfindingsDCFmethodsnowappeartobemorepopularthanpaybackInlargefirms,paybackisusedinconjunctionwithotherinvestmentappraisalmethodsInsmallfirms,usingpaybackalonecontinuestodeclineIRRismorepopularthanNPVinsmallfirmsNPVismostpopularmethodinlargefirmsExperienceandqualitativejudgementareimportantinreal-worldinvestmentdecisionsROCEistheleastpopularappraisalmethod,butisusedinconjunctionwithothermethodsSophisticatedmethodsofconsideringprojectrisktendnottobeusedWhereriskisconsidered,sensitivityanalysistendstobeusedEmpiricalfindings(continued)MostcompaniescorrectlyaccountforinflationwherethiswasconsideredMostcompaniesdonotusethecapitalassetpricingmodelAnincreasingnumberofcompaniesuseprobabilityanalysisOverall,cleardifferencesbetweenappraisalmethodsusedbysmallandlargefirmsEmpiricalfindings(continued)CorporatefinanceEighthEditionChapter8PortfoliotheoryandthecapitalassetpricingmodelRiskCompaniesfaceriskfromvariabilityinprojectcashflows.Investorsfaceriskfromvariabilityincapitalgainsanddividends.Rationalaimistominimiseriskforgivenlevelofreturn.Tocontrolriskitmustbeunderstoodandmeasured.ThemeasurementofriskRiskismeasuredbythestandarddeviationofthereturnsonashare,basedoneitherhistoricalreturnsorexpectedfuturereturns.Probability(left)/Historicdata(right)

Mean(top)/Standarddeviation(bottom)DistributionofreturnsonSandTTheconceptofdiversificationTotalriskcanbedividedintosystematicandunsystematicrisk.Systematicriskisduetosystematicfactorssuchaschangesininterestrates,businesscyclesandgovernmentpolicy.Unsystematicriskisspecifictoagivenshare.Unsystematicriskdecreasesasthenumberofinvestmentsinaportfolioincreases:thisiscalledportfoliodiversificationofrisk.DiversificationofriskTotalriskfallsasnumberofinvestmentsrisesThetwo-shareportfolioTheamountofriskdiversificationdependsoncorrelationbetweenreturnsandhenceonthevalueofthecorrelationcoefficient(CC).+1:nodiversificationofunsystematicrisk.–1:fulldiversificationofunsystematicrisk.0:nocorrelationbetweenreturnsandpartialdiversificationofunsystematicrisk.Thetwo-shareportfolio(continued)sp=

(Wx).(x)

+

(Wy).(y)

+

2

.Wx

.Wy.x.y.

x,y

222ssssr2ShareSMeanreturn:5.96%Standarddeviation:8.16%ShareTMeanreturn:9.10%Standarddeviation:13.39%Calculatedcorrelationcoefficient=–0.389.Thetwo-shareportfolio(continued)Portfoliowith80%Sand20%T:Return=(0.8×5.96)+(0.2×9.1)=6.59%Risk=((0.82×8.162)+(0.22×13.392)+ (2×0.8×0.2×8.16×13.39×–0.389))?=6.02%ThisgivespointAonnextslide.SeetextbookforpointsB,CandD.Thetwo-shareportfolio(continued)Thetwo-shareportfolio(continued)InvestorscanchooseportfoliosanywherealongthearcSABCDTinFigure8.3.TheriskoftheseportfoliosislessthanthatrepresentedbythestraightlineST.CombiningSandThasreducedtotalriskbydiversifyingunsystematicrisk.Asnumberofsharesintheportfolioincreases,the‘bat-wing’shapeinthenextdiagramarises.Thetwo-shareportfolio(continued)Four-shareportfolioRisk(standarddeviation)Return(%)0ABCDInvestorattitudestoriskInvestorattitudestorisk(continued)Investorsandtheirrisksaturationpoints

PortfoliotheoryRationalinvestorsinvestonlyontheefficientfrontier,therebymaximisingtheirutility.Ifrisk-freeassetsareavailable,investorswillcombinethemwiththemarketportfolio.Rationalinvestorsthenthereforeselecttheiroptimalportfolioonthecapitalmarketlineatapointoftangencywiththeirutilitycurves.Risk(standarddeviation)0Return(%)EFGHAIEnvelopecurve(riskyinvestments)Theenvelopecurve

Risk(standarddeviation)0Return(%)EFGHAIEfficientfrontierBTheefficientfrontier

ZRisk(standarddeviation)0

mRfReturn(%)MEFGHRmAIMarketportfolioCapitalmarketlineBThemarketportfolio

ZRisk(standarddeviation)0RfReturn(%)MEFGHNU0BAIOptimumpointifonlyriskyassetsareavailableNoriskfreeassetsavailable

ZRisk(standarddeviation)0RfReturn(%)MEFGHNU0U1U2PRp

pBAIRiskfreeassetsavailable

Portfoliotheoryisusedbymanyinstitutionalinvestors(e.g.insurancecompanies,pensionfunds)whohavelargediversifiedportfolios.Problemswithusingportfoliotheory:Borrowingattherisk-freerateIdentifyingthemarketportfolioConstructingthemarketportfolioChangingcompositionofmarketportfolioPortfoliotheory(continued)CAPM:anintroductionTheCAPMisamethodofsharevaluationdevelopedbyWilliamSharpein1964.Itisbasedonalinearrelationshipbetweenriskandreturn.Itisadevelopmentofportfoliotheory.Itconsidersthatsystematicriskistheonlyrelevantriskwhenvaluingshares.CAPMassumptionsInvestorsarerationalutilitymaximisers.Informationisfreelyavailable.Allinvestorshavesimilarexpectations.Investorscanborrowandlendattherisk-freerate.Investorsholddiversifiedportfolios,therebyeliminatingallunsystematicrisk.Capitalmarketsareperfect:NotaxesortransactioncostsFreeentryandexitManybuyersandsellersInformationiscostlessandfreelyavailableSingleperiodtransactionhorizon:returnsarecalculatedoverastandardperiod.usuallytakenas1year.CAPMassumptions(continued)Rj=Rf+βj(Rm–Rf)ThesecuritymarketlineCAPMcomponentsReturnofthemarket(Rm)Risk-freerateofreturn(Rf)Equityriskpremium(Rm–Rf)Betavalueofordinaryshares(βj)MeaningandcalculationofbetaBetaisseenasan‘indexofresponsiveness’ofchangesinasecurity’sreturnsrelativetochangesinreturnsonthemarket.Example:BP’sequitybeta=0.75Marketreturnincreasesby10%ReturnonBP’ssharesincreasesby7.5%Meaningandcalculationofbeta(continued)Betacanbefoundfrom:βj

=(σjxσmxρj,m)/σm2

where:σj=standarddeviationofreturnsonassetjσm=standarddeviationofmarketreturnsΡj,m=correlationcoefficientbetweenjandmσm2=varianceofreturnsonthemarketBetacanbefoundbyregressionanalysisofsecurityreturnsagainstmarketreturns.Betacanbefoundfromalineofbestfitofaplotofsecurityreturnsagainstmarketreturns.CompanybetavaluesarefoundintheBetaBookspublishedbytheLondonBusinessSchoolRiskMeasurementServiceandfromotherfinancialresourcessuchasDatastream.Meaningandcalculationofbeta(continued)Meaningandcalculationofbeta(continued)Security Beta WeightWeightedbetaBarclays 1.43 20% 0.286BP 1.49 35% 0.522Kingfisher 0.84 15% 0.126SevernTrent 0.53 20% 0.106Tesco 0.94 10% 0.094PortfolioBeta 1.134

Meaningandcalculationofbeta(continued)Returnofthemarket(Rm)ApproximatedbyusingstockexchangeindexsuchasFTSE100,forexample:Rm=[(FTSE1

–FTSE0)/FTSE0]+DividendYield.Calculatedonamovingaveragebasisfrommonthlyorannualdata.Equityriskpremiumcanbedeterminedoneithera‘geometric’oran‘a(chǎn)rithmetic’basis.Arithmeticriskpremiumoverestimatessogeometricriskpremiumisrecommended.Equityriskpremium(Rm–Rf)DimsonandBrealey(1978)found9%fortheperiod1918–77–nowseenastoohigh.Allanetal.(1986)found9.1%fortheperiod1919–84.Dimsonetal.(2002)gave4.5%fortheperiod1900–2001and7.2%for1951–2001.CreditSuisse(2018)foundERPintheUKfrom1968–2017tobe4.8%usingUKTreasurybills.Currentequityriskpremiumof3%to5%?Risk-freerate(Rf)Noassetsare

totallyrisk-free,butbondsissuedbygovernmentsofstablecountriesareseenasalmostrisk-free.Rfapproximatedbytheyieldtomaturityoftreasurybills(short-termgovernmentdebt).Shortmaturityasthesehavelowestrisk.ExampleofusingtheCAPMEquitybetaofBurberryGroupplc=1.14Risk-freerate(yieldonTreasurybills):1.0%Marketriskpremium(Rm–Rf):4.5%Rj=1%+(1.14×4.5%)=6.1%Thisrepresentsshareholders’requiredrateofreturnandhencethecostofequityofBurberryGroupplc.ImplicationsoftheCAPMInvestorswillrequirecompensationonlyforsystematicrisk,sinceunsystematicriskcanbeeradicatedbyportfoliodiversification.Securitieswithhighlevelsofsystematicriskshould,onaverage,yieldhighratesofreturn.Thereshouldbealinearrelationshipbetweensystematicriskandreturn.Correctlypricedsecuritiesshouldplotonthesecuritymarketline(SML).ImplicationsoftheCAPM(continued)EmpiricalevidenceEvidenceinyearsfollowingdevelopmentoftheCAPMwassupportive: SharpeandCooper(1972)foundportfolio betas(10ormoreshares)werestablewhile individualbetaswerenot. Jacob(1971)andBlack,JensenandScholes (1972)foundalinearrelationshipbetween systematicriskandreturn,butthefittedSML wasshallowerthanthetheoreticalSML.Empiricalevidence(continued)Evidenceinrecentyearsisnotsupportive:Black(1993)foundstrongrelationshipforNYSEover1931–65,poorrelationshipover1966–91.FamaandFrench(1992)said‘resultsdonotsupportthataveragestockreturnsarepositivelyrelatedtomarketbetas’forUSsharesfrom1963–90.Itseemsfactorsotherthansystematicriskhelp

todetermineasecurity’srequiredreturn.Empiricalevidence(continued)SoistheCAPMuseful?Atheoryshouldbejudgedonitsperformanceratherthanonitsassumptions.Portfoliobetasarerelativelystable.Strongevidenceonvalidityofsecuritymarketlinehasnowgivenwaytodoubts.IsthereabetteralternativetotheCAPM?PerhapsmultivariatemodelssuchasAPM(ArbitragePricingModel)?CorporatefinanceEighthEditionChapter9ThecostofcapitalandcapitalstructureWhatisthecostofcapital?Allprovidersoffinancerequirereturns.Therequiredreturnwillreflecttheriskoftheinvestmentandthereturnsofalternatives.Companiesneedinformationaboutthecostofdifferentsourcesoffinanceinordertofindtheoverallcostoffinanceandtomakeinvestmentandfinancingdecisions.Perhapsan‘optimum’capitalstructureexistswhichafirmcanseektoachieve.OrdinarysharesThecostofequitycanbefoundfromtherearrangeddividendgrowthmodel:Ke=costofequityP0=thecurrentexdividendsharepriceD1=thedividendreceivedeachyearg=theexpectedgrowthrateofdividendsgP0D1Ke+=Ordinaryshares(continued)CalculatingKeusingdividendgrowthmodel:Currentexdividendshareprice=417pCurrentdividendpershare=23pExpecteddividendgrowthrate=5%Nextyear’sdividend(D1)=23×1.05=24.2pKe=(24.2/417)+0.05=0.058+0.05=0.108Ke=10.8%Ordinaryshares(continued)ThecostofequitycanalsobefoundfromtheCAPM:

Rj=Rf+βj

(Rm–Rf)where:Rm=returnofthemarketRf=risk-freerateofreturn(Rm–Rf)=equityriskpremiumβj

=betavalueofordinaryshareRetainedearningsRetainedearningshaveanopportunitycostwhichisequaltothecostofequity.Thecostofretainedearningscanthusbefoundinthesamewayasthecostofequity.Itisamistaketoseeretainedearningsasafreesourceoffinance.PreferencesharesThecostofpreferencesharescanbefoundbydividingthepreferencedividendbytheexdividendmarketprice:Kps=costofpreferencesharesP0=currentexdividendpreferencesharepriceDp=preferencedividendP0DpKps=Preferenceshares(continued)Calculatingthecostofpreferenceshares:8%preferenceshares,nominalvalue:100pCurrentexdividendmarketprice:89pKp=(0.08×100)/89=0.09Kp=9.0%IrredeemablebondsLikepreferenceshares,bondsinvolveaconstantannualpaymentinperpetuityKd=costofdebtI=annualinterestpaymentP0=currentex-interestmarketpricenotethatinterestistax-deductibleP0IKd=Irredeemablebonds(continued)Calculatingthecostofirredeemablebonds:9%irredeemablebondsEx-interestmarketprice:￡108Corporationtax:30%Kid(beforetax)=9/108=8.3%Kid(aftertax)=8.3×(1

0.3)=5.8%RedeemablebondsRedeemablebondsinvolvesseveralfixedinterestpaymentsplusredemptionvalueI=interestpaymentRV=redemptionvalueorprincipalKd=costofdebtcapitaln=numberofyearstomaturityCT=corporationtaxrate)1()1()1()1()1(0RVCTICTICTIKdCTIP+

+

++++=L)21(Kd+)31(Kd+)n1(Kd+Redeemablebonds(continued)Thecostofdebtofredeemablebondsistheinternalrateofreturnofthevaluationmodelonthepreviousslide.Usingthismodeltofindtheafter-taxcostofdebtismoreaccuratethanmultiplyingthebefore-taxcostofdebtby(1

CT),sincetheredemptionvalueisnottax-deductible.Thecostofdebtcanbefoundusinglinearinterpolationorafinancialcalculator.Redeemablebonds(continued)Hawawini–Vorabondapproximationmodelcanalsobeusedtocalculatecostofdebt:

I+(P

NPD)

Kd=

n

P+0.6×(NPD

P)I =interestpayments(￡)P =parvalue(￡100)NPD =ex-interestmarketvalue(￡)n =numberofyearstomaturityRedeemablebonds(continued)UsingtheHawawini–Voramodel:5%redeemablebond(I=5,P=100)Ex-interestmarketpriceof￡96(NPD=96)Redemptionin6-years’time(n=6)5+(100

96)

Krd= 6 =5.8% 100+0.6×(96

100)After-taxcostofdebt=5.8×0.7=4.1%BankborrowingsBankborrowingsarenottradedandhavenomarketvaluethatinterestcanberelatedto.Costofbankborrowingscanbefoundbyusingaverageinterestpaidinagivenperiod.Alternatively,thecostoftradeddebtmaybeusedasthebestapproximation.Here,after-taxinterestrate=7x0.7=4.9%.CalculatingtheWACCMarketvaluesorbookvalues?BookvaluesarehistoricalMarketvaluesreflectcurrentrequirementsBeforeoraftertax?Before-taxWACCforbefore-taxcashflowsAfter-taxWACCforafter-taxcashflowsWhichtaxratetouse?CalculatingtheWACC(continued)Tofindtheaveragecostofcapital,weweightindividualcostsofcapitalbytheirproportionsinthefirm’scapitalstructureE=valueofequityD=valueofdebtE/(E+D)istheproportionofequityD/(E+D)istheproportionofdebt)()×1()(×EDDCTKdEDEKeWACC+

++=CalculatingtheWACC(continued)Costofequity: Ke=10.8%Costofpreferenceshares: Kp=9.0%Costofirredeemabledebt: Kid

=5.8%Costofredeemabledebt: Krd

=4.1%Costofbankloans: Kbl

=4.9%Note,relativecostsofthedifferentsourcesreflecttheirrelativerisks,i.e.reflecttherisk-returnhierarchyoffinancialsecurities.CalculatingtheWACC(continued)Weightingbymarketvalues(seetextbook):Equity: (10.8%×53,376)Preferenceshares: +(9.0%×8,010)Irredeemabledebt: +(5.8%×9,180)Redeemabledebt: +(4.1%×4,464)Bankdebt: +(4.9%×3,260) =736,071/78,290=9.4%=WACCAverageandmarginalcostThemarginalcostofcapitalisthecostoftheincrementalcapitalraised.Initially,ascheaperdebtisadded,averagecostofcapitalwillfall.Afteraminimum