corporatefinance公司理財(cái)CAPM課件

FIN751–T.Barkley–CAPMandWACCCAPMandWACCLectureNote5LN5.1FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCRisk,Return,

andCostofEquityFinancetheorymakesthreeassumptionsaboutinvestorbehavior:Investorspreferadollartodaytoadollartomorrow(theassumptionoftimepreference)Investorspreferlessrisktomore(theassumptionofriskpreference)Investorsprefermorewealthtoless(theassumptionofwealthpreference)LN5.2FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplicationsoftheBehavioralAssumptionsforRisk/ReturnAsimpleprediction:HigherriskwillbeaccompaniedbythedemandforhigherexpectedreturnsThus,toattractrisk-averseinvestorstoinvestinariskyasset(orproject,orfirm),…LN5.3FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplicationsoftheBehavioralAssumptionsforRisk/ReturnIfrfisarisk-freerateofreturnavailabletoinvestorsinthefinancialmarketplace,thenthereturnthatwouldbeexpectedonariskyasset‘i’,ri,is:

ri=rf+RiskPremiumLN5.4FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplicationsoftheBehavioralAssumptionsforRisk/ReturnCAPMsaysthatthisRiskPremiumisequaltothe“beta”(β)oftheasset,timesanumbercalled“MRP”:

RiskPremiumforAsseti=βi*MRPβireflectsMRPreflectsLN5.5FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplicationsoftheBehavioralAssumptionsforRisk/ReturnSummary:Therequiredrateofreturnequalstherisk-freerateplustheasset-specificriskpremium:

ri=rf+βi

×MRPThisistheCapitalAssetPricingModel(CAPM)LN5.6FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCGettingtoCAPMThreestepsarenecessary:DiversificationandRiskSystematicvs.UnsystematicRiskBetaandCAPMLN5.7FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC1.DiversificationandRiskSensible(or“rational”)investorswilldiversifytheirholdingsIntheprocess,theywillgetridofapartoftheirinvestmentriskthatisknownas“diversifiablerisk”(or“unsystematicrisk”)Despitethis,howevermuchtheydiversify,itwillnotbepossibletoeliminateallriskLN5.8FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC1.DiversificationandRisk(cont)Therearealwayssomecommon‘factors’(suchasinterestratemovements,politicalturbulence,oilpricehikes,etc.),whosefluctuationswillcreateunderlyingriskforall(ormost)assetsAsthenumberof(randomlychosen)assetsinaportfolioincreases,theriskreductionwillappearasfollowsLN5.9FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC1.DiversificationandRisk(cont)UnsystematicriskSystematicriskLN5.10FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC1.DiversificationandRisk(cont)UniqueriskMarketriskLN5.11FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC2.SystematicRiskPortfolioriskthatcannotbediversifiedawaybecauseoftheeffectofcommonfactorsintheeconomyonriskyassetsiscalled“systematic”risk,or“undiversifiable”riskLN5.12FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC2.SystematicRisk(cont)Whatinsightscanbegained?

LN5.13FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC2.SystematicRisk(cont)Thus,inmeasuringtheriskofanyasset,whatneedstobeexaminedishowmuchriskasingleassetcontributestosuchamarketportfolioLN5.14FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC3.BetaandCAPMThesystematicriskofariskyasset–thatis,theriskthatitcontributestothemarketportfolio,andtherefore,theriskforwhichariskpremiummustbepaid–ismeasuredbyitsbeta(β)Thebeta(β)measuresthesensitivityofexpectedreturnsonariskyassettomovementsinthemarketportfolioLN5.15FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC3.BetaandCAPM(cont)Moreprecisely,theβmeasuresthe%changeintheexpectedreturnonariskyassetforevery%changeintheexpectedreturnsofawell-diversifiedmarketportfolioExample:Astockhasβ=1.2Ifthe“market”movesupby1%,theexpectedreturnsonthestockmoveupby1.2%Similarly,ifthe“market”fallsby1%,thestock’sreturnswouldbeexpectedtofallby1.2%LN5.16FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC3.BetaandCAPM(cont)Whatistheβforthemarketportfolio?

Whatistheβforarisk-freeasset?

LN5.17FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCGraphicalDepictionofCAPMIftheexpectedreturnonanassetiswrittenasE(r),thenCAPMimpliesthatalinearrelationshipmustholdbetweenriskandexpectedreturnsInanefficientmarketequilibrium,all“fairlypriced”assetswilllieonthislineThisistheSecurityMarketLine(SML)LN5.18FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCTheSecurityMarketLine(SML)BetaMarketReturn=rm

RiskFreeReturn=rf1.0SecurityMarketLine(SML)E(r)LN5.19FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCAlgebraicDepictionofCAPMLN5.20FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCAPMTheCAPMgivesasimpleformulatocalculateafirm’scostofequityIfthe“beta”ofastockisknown,andifthecurrentreturnonarelativelyrisklessassetcanbeobservedthen,undercertainsimpleassumptionsforthemarketriskpremium,afirm’scostofequitycaneasilybeestimatedLN5.21FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCAPM–ExampleSupposeAT&Thasβ=0.52,thecurrentrisk-freerate(rf)=3.25%,andthemarketriskpremiumintheUS,MRP

=5.00%.Then, E(rAT&T)= =LN5.22FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplementingCAPMToimplementCAPM,threethingsarenecessary:

LN5.23FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplementingCAPM(cont)Risk-freerate:inpractice,itisproxiedbythecurrentrateofreturnofasafeassetsuchasUST-BillsorT-BondsForcapitalbudgetingandcorporatevaluationpurposes,alwaysuseT-BondsBeta:CanbecalculatedorlookedupeasilyMarketriskpremium:Thisiscalculatedasthedifferenceinthelong-run

historicalreturnofawell-diversifiedportfolioofstocksandthatofT-BondsorT-BillsItcapturestheideaofanaverageinvestor’sperceptionsofriskinthemarket,andthepremium(demandedforbearingthatrisk)LN5.24FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplementingCAPM(cont)IfT-Bondsareused,theMRPis5.0%IfT-Billsareused,theMRPis6.0%Forcapitalbudgeting/corporatevaluationpurposes,alwaysuse5.0%LN5.25FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCBeta:SomeAdditionalInsightsWhatisa“good”betaforacompanytohave?LN5.26FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCBeta:SomeAdditionalInsights(cont)Cananassethaveanegativebeta?LN5.27FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCBeta:SomeAdditionalInsights(cont)Canbetasfordifferentassetsbecombined?LN5.28FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCBeta:SomeAdditionalInsights(cont)Therearetwoimportanttypesofbetas:AssetbetasEquitybetasSupposeafirmhasassets(A)onthelefthandsideofthebalancesheetandhasequity(E)plusdebt(D)ontherighthandsideThen,A=E+DAssumenotaxesLN5.29FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCAssetBetaIfthisistrueandbetasarevalue-additive,then:

βA=βE×[E/(E+D)]+βD×[D/(E+D)] where:

βE= Equitybeta,

βA

= Assetbeta

βD= Debtbeta(usuallyassumedtobezero,ifthefirmhashigh-qualitydebt)LN5.30FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCAssetBeta(cont)IfβD=0andTc=0,then

βA=βE×[E/(E+D)]

OR

βE=βA×[1+(D/E)]

BusinessRiskFinancialRiskLN5.31FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCAssetBeta(cont)Withthetax-shieldbenefitofdebt,theformulabecomes:

βE=βA×[1+(1-Tc)(D/E)] whereTcisthe(marginal)corporatetaxrateLN5.32FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCUnleveringandReleveringGivenanunleveredor“all-equity”betaandaD/Eratio,anequitybetacanbecalculatedbyleveringtheassetbetaForourpurposes(andmostreal-worldapplications),thesimplerformulaissufficient(thatis,assumingβD=0andnotaxes)LN5.33FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCUnleveringandRelevering(cont)ThecostofequityissensitivetotheD/EratioWhenthelevelofdebtincreases,thecostofequitygoesupalso,reflectingthefactsthat:Debthaspriorityoverassetsonthefirm’sriskycashflows(assetrisk)Equityholdersonlygetwhatisleftafterdebtholdersarepaidofffirst(financialrisk)Theadjustmenttoreflecttheeffectsofleverageonthecostofequitycanbeunderstoodwithbetas,butitisnecessarytounleverandreleverbetasLN5.34FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCUnleveringandRelevering

–ExampleConsideracompanywith

βE =1.2

βD =0.0 D/E =1.0 (Ignoretaxes,forsimplicity)ThecompanywantstochangeitsD/Eratiofrom1.0to1.5.WhatisthenewβE?LN5.35FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCUnleveringandRelevering

–Example(cont)

βA =βE×[E/(E+D)] = =

βEnew =βA×[1+(D/E)] = =βEincreasedfrom1.2to___becauseoftheincreaseinfinancialriskLN5.36FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCWhatDeterminesBeta?Fourfactors(amongmany)playcrucialroles:

Thehighereachofthese,thehigherthebetaLN5.37FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCTheMarketRiskPremiuminSomeIndustrializedCountriesTheideaofthemarketriskpremiumisa“behavioralconstruct”inthatitattemptstocapturewhatatypicalinvestorhasrequiredasthepremiumovertherisk-freerateforholdingawell-diversifiedportfolioofstocksInordertoestimatethisnumber,thehistoricalaveragehastobelookedatoveralongtimehorizonLN5.38FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCostofCapitalLN5.39FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCostofCapitalThecostofafirm’scapitalistherateofreturnrequiredorexpectedbytheinvestorswhoinvestinthefirmTheexpectedrateofreturnfortheinvestor,inturn,dependsonthereturnstheycanobtainelsewherefromrisk-equivalentinvestmentsLN5.40FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCostofCapital(cont)Ifinvestorscannotreceiveatleasttherisk-equivalentrateofreturn,theywillsimplywithdrawtheirfundsfromthefirm,forcingittoincreaseitsreturnsDuetotheirdifferenttypesofexposuretorisk,equityholdersanddebtholdersarecompensatedwithdifferentreturnsontheirinvestmentsLN5.41FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCWeightedAverageCostofCapital(WACC)Eachasset(e.g.,aproject,adivision,oreventhefirm)isfinancedbyamixtureofdebt(D)andequity(E),whichinturndeterminethefirm’sD/EratioTherateofreturnthattheassetasawholehastogenerateforitsdebtholdersandequityholdersisitsweightedaveragecostofcapital(WACC)WACC=[E/(D+E)]×rE+[D/(D+E)]×rD×(1-Tc)LN5.42FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCWeightedAverageCostofCapital(cont)TocalculateWACC,thevaluesoffivevariablesareneeded:ValueofDebt (D)ValueofEquity (E)Marginaltaxrate (Tc)Costofdebtfinancing (rD)Costofequityfinancing (rE)LN5.43FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCDebtRatio[D/(D+E)]and

EquityRatio[E/(D+E)]Thevalueofdebt(D)ideallyshouldbeatitsmarketvalueThevalueofequity(E)shouldalwaysbeatmarketvalueThedebt-to-capitalratioisobtainedas: D/(D+E)Theequity-to-capitalratioisobtainedas: E/(D+E)Remember:

[D/(D+E)]+[E/(D+E)]=1LN5.44FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCDebtRatio[D/(D+E)]and

EquityRatio[E/(D+E)](cont)Theonlydebtthatisrelevantisthefirm’slong-termdebtInpractice,marketvaluesfordebtaredifficulttoobtain–thus,somecompromiseisneeded,andthebookvalueisusedonlyinthecaseofdebt(andassumingthatitishighqualitydebt)LN5.45FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCMarginalTaxRate(Tc)Thisisthemarginaltaxrate(i.e.,thetaxrateassociatedwithtakingonanewactivity),nottheaveragetaxrateInmanyinstances,however,thesetworatesarethesameLN5.46FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCostofDebtFinancing(rD)The(pre-tax)costofdebtissimplytheyield-to-maturityonthecompany’sdebtThecorrectcostofdebtisobtainedbyassessingthecurrentyields-to-maturityonlongtermbondsofequivalentcreditriskorratingItisnotthepastyield-to-maturityorthepastaverageinterestpaid,etc.BondratingsarepublishedbyagenciessuchasMoody’sorStandardandPoorsLN5.47FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCostofEquityFinancing(rE)InordertogetrE,itisnecessarytounderstandtherelationbetweenriskandreturnThis,inturn,requiresunderstanding:DiversificationandRiskReductionUnsystematicandSystematicRiskEfficientPortfoliosBetas,andthe(famous)CapitalAssetPricingModel(CAPM)LN5.48FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCAPMandWACCLectureNote5LN5.49FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCRisk,Return,

andCostofEquityFinancetheorymakesthreeassumptionsaboutinvestorbehavior:Investorspreferadollartodaytoadollartomorrow(theassumptionoftimepreference)Investorspreferlessrisktomore(theassumptionofriskpreference)Investorsprefermorewealthtoless(theassumptionofwealthpreference)LN5.50FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplicationsoftheBehavioralAssumptionsforRisk/ReturnAsimpleprediction:HigherriskwillbeaccompaniedbythedemandforhigherexpectedreturnsThus,toattractrisk-averseinvestorstoinvestinariskyasset(orproject,orfirm),…LN5.51FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplicationsoftheBehavioralAssumptionsforRisk/ReturnIfrfisarisk-freerateofreturnavailabletoinvestorsinthefinancialmarketplace,thenthereturnthatwouldbeexpectedonariskyasset‘i’,ri,is:

ri=rf+RiskPremiumLN5.52FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplicationsoftheBehavioralAssumptionsforRisk/ReturnCAPMsaysthatthisRiskPremiumisequaltothe“beta”(β)oftheasset,timesanumbercalled“MRP”:

RiskPremiumforAsseti=βi*MRPβireflectsMRPreflectsLN5.53FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplicationsoftheBehavioralAssumptionsforRisk/ReturnSummary:Therequiredrateofreturnequalstherisk-freerateplustheasset-specificriskpremium:

ri=rf+βi

×MRPThisistheCapitalAssetPricingModel(CAPM)LN5.54FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCGettingtoCAPMThreestepsarenecessary:DiversificationandRiskSystematicvs.UnsystematicRiskBetaandCAPMLN5.55FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC1.DiversificationandRiskSensible(or“rational”)investorswilldiversifytheirholdingsIntheprocess,theywillgetridofapartoftheirinvestmentriskthatisknownas“diversifiablerisk”(or“unsystematicrisk”)Despitethis,howevermuchtheydiversify,itwillnotbepossibletoeliminateallriskLN5.56FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC1.DiversificationandRisk(cont)Therearealwayssomecommon‘factors’(suchasinterestratemovements,politicalturbulence,oilpricehikes,etc.),whosefluctuationswillcreateunderlyingriskforall(ormost)assetsAsthenumberof(randomlychosen)assetsinaportfolioincreases,theriskreductionwillappearasfollowsLN5.57FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC1.DiversificationandRisk(cont)UnsystematicriskSystematicriskLN5.58FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC1.DiversificationandRisk(cont)UniqueriskMarketriskLN5.59FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC2.SystematicRiskPortfolioriskthatcannotbediversifiedawaybecauseoftheeffectofcommonfactorsintheeconomyonriskyassetsiscalled“systematic”risk,or“undiversifiable”riskLN5.60FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC2.SystematicRisk(cont)Whatinsightscanbegained?

LN5.61FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC2.SystematicRisk(cont)Thus,inmeasuringtheriskofanyasset,whatneedstobeexaminedishowmuchriskasingleassetcontributestosuchamarketportfolioLN5.62FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC3.BetaandCAPMThesystematicriskofariskyasset–thatis,theriskthatitcontributestothemarketportfolio,andtherefore,theriskforwhichariskpremiummustbepaid–ismeasuredbyitsbeta(β)Thebeta(β)measuresthesensitivityofexpectedreturnsonariskyassettomovementsinthemarketportfolioLN5.63FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC3.BetaandCAPM(cont)Moreprecisely,theβmeasuresthe%changeintheexpectedreturnonariskyassetforevery%changeintheexpectedreturnsofawell-diversifiedmarketportfolioExample:Astockhasβ=1.2Ifthe“market”movesupby1%,theexpectedreturnsonthestockmoveupby1.2%Similarly,ifthe“market”fallsby1%,thestock’sreturnswouldbeexpectedtofallby1.2%LN5.64FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACC3.BetaandCAPM(cont)Whatistheβforthemarketportfolio?

Whatistheβforarisk-freeasset?

LN5.65FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCGraphicalDepictionofCAPMIftheexpectedreturnonanassetiswrittenasE(r),thenCAPMimpliesthatalinearrelationshipmustholdbetweenriskandexpectedreturnsInanefficientmarketequilibrium,all“fairlypriced”assetswilllieonthislineThisistheSecurityMarketLine(SML)LN5.66FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCTheSecurityMarketLine(SML)BetaMarketReturn=rm

RiskFreeReturn=rf1.0SecurityMarketLine(SML)E(r)LN5.67FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCAlgebraicDepictionofCAPMLN5.68FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCAPMTheCAPMgivesasimpleformulatocalculateafirm’scostofequityIfthe“beta”ofastockisknown,andifthecurrentreturnonarelativelyrisklessassetcanbeobservedthen,undercertainsimpleassumptionsforthemarketriskpremium,afirm’scostofequitycaneasilybeestimatedLN5.69FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCAPM–ExampleSupposeAT&Thasβ=0.52,thecurrentrisk-freerate(rf)=3.25%,andthemarketriskpremiumintheUS,MRP

=5.00%.Then, E(rAT&T)= =LN5.70FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplementingCAPMToimplementCAPM,threethingsarenecessary:

LN5.71FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplementingCAPM(cont)Risk-freerate:inpractice,itisproxiedbythecurrentrateofreturnofasafeassetsuchasUST-BillsorT-BondsForcapitalbudgetingandcorporatevaluationpurposes,alwaysuseT-BondsBeta:CanbecalculatedorlookedupeasilyMarketriskpremium:Thisiscalculatedasthedifferenceinthelong-run

historicalreturnofawell-diversifiedportfolioofstocksandthatofT-BondsorT-BillsItcapturestheideaofanaverageinvestor’sperceptionsofriskinthemarket,andthepremium(demandedforbearingthatrisk)LN5.72FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCImplementingCAPM(cont)IfT-Bondsareused,theMRPis5.0%IfT-Billsareused,theMRPis6.0%Forcapitalbudgeting/corporatevaluationpurposes,alwaysuse5.0%LN5.73FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCBeta:SomeAdditionalInsightsWhatisa“good”betaforacompanytohave?LN5.74FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCBeta:SomeAdditionalInsights(cont)Cananassethaveanegativebeta?LN5.75FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCBeta:SomeAdditionalInsights(cont)Canbetasfordifferentassetsbecombined?LN5.76FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCBeta:SomeAdditionalInsights(cont)Therearetwoimportanttypesofbetas:AssetbetasEquitybetasSupposeafirmhasassets(A)onthelefthandsideofthebalancesheetandhasequity(E)plusdebt(D)ontherighthandsideThen,A=E+DAssumenotaxesLN5.77FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCAssetBetaIfthisistrueandbetasarevalue-additive,then:

βA=βE×[E/(E+D)]+βD×[D/(E+D)] where:

βE= Equitybeta,

βA

= Assetbeta

βD= Debtbeta(usuallyassumedtobezero,ifthefirmhashigh-qualitydebt)LN5.78FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCAssetBeta(cont)IfβD=0andTc=0,then

βA=βE×[E/(E+D)]

OR

βE=βA×[1+(D/E)]

BusinessRiskFinancialRiskLN5.79FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCAssetBeta(cont)Withthetax-shieldbenefitofdebt,theformulabecomes:

βE=βA×[1+(1-Tc)(D/E)] whereTcisthe(marginal)corporatetaxrateLN5.80FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCUnleveringandReleveringGivenanunleveredor“all-equity”betaandaD/Eratio,anequitybetacanbecalculatedbyleveringtheassetbetaForourpurposes(andmostreal-worldapplications),thesimplerformulaissufficient(thatis,assumingβD=0andnotaxes)LN5.81FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCUnleveringandRelevering(cont)ThecostofequityissensitivetotheD/EratioWhenthelevelofdebtincreases,thecostofequitygoesupalso,reflectingthefactsthat:Debthaspriorityoverassetsonthefirm’sriskycashflows(assetrisk)Equityholdersonlygetwhatisleftafterdebtholdersarepaidofffirst(financialrisk)Theadjustmenttoreflecttheeffectsofleverageonthecostofequitycanbeunderstoodwithbetas,butitisnecessarytounleverandreleverbetasLN5.82FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCUnleveringandRelevering

–ExampleConsideracompanywith

βE =1.2

βD =0.0 D/E =1.0 (Ignoretaxes,forsimplicity)ThecompanywantstochangeitsD/Eratiofrom1.0to1.5.WhatisthenewβE?LN5.83FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCUnleveringandRelevering

–Example(cont)

βA =βE×[E/(E+D)] = =

βEnew =βA×[1+(D/E)] = =βEincreasedfrom1.2to___becauseoftheincreaseinfinancialriskLN5.84FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCWhatDeterminesBeta?Fourfactors(amongmany)playcrucialroles:

Thehighereachofthese,thehigherthebetaLN5.85FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCTheMarketRiskPremiuminSomeIndustrializedCountriesTheideaofthemarketriskpremiumisa“behavioralconstruct”inthatitattemptstocapturewhatatypicalinvestorhasrequiredasthepremiumovertherisk-freerateforholdingawell-diversifiedportfolioofstocksInordertoestimatethisnumber,thehistoricalaveragehastobelookedatoveralongtimehorizonLN5.86FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCostofCapitalLN5.87FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCostofCapitalThecostofafirm’scapitalistherateofreturnrequiredorexpectedbytheinvestorswhoinvestinthefirmTheexpectedrateofreturnfortheinvestor,inturn,dependsonthereturnstheycanobtainelsewherefromrisk-equivalentinvestmentsLN5.88FIN751–T.Barkley–CAPManFIN751–T.Barkley–CAPMandWACCCostofCapital(cont)Ifinvestorscannotreceiveatleasttherisk-equivalentrateofreturn,theywillsimplywithdrawtheirfundsfromthefirm,forcingittoincreaseitsreturnsDuetotheirdifferenttype