costofcapitalformulas-mcgraw-hill资本成本公式-麦格劳山

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1、CostofCapitalFormulasWehavegatheredtogetherhere(andinsomecasesrepeated)thederivationsofsomeoftheformulasusedinChapter19.Wecoverfivetopics:1.DerivingtheWACCformula.2.DoesWACCnecessarilydeclinewhenleverageincreases?3.Leveringandunlevering.4.TheMiles-Ezzellformula.5.TheMMformu

2、la.DerivingWACCWestartwithafirm^sexpectedoperatingcashflowsCi,C2,...，Withallequityfinancing,theseflowswouldbediscountedattheopportunitycostofcapitalr.ButweassumethefirmisfinancedwithdebtataconstantratioL.Thatis,itfollowsFinancingRule2,sothatD/V=Lineachfutureperiod.Consider

3、firmvalueinthenext-to-lastperiod:Vtj=D「i+Et亠Wecanwritethetotalcashpayofftodebtandequityinvestorsintwoways:CashpayoffinT=Ct+Tct「dDt-i=VT.i(l+rDD/V+rEE/V)TcroDistheinteresttaxshield.EquatethetwoexpressionsandsolveforV「iasafunctionofCt+TcD二VT.i(1+rDD/V+rEE/V)VT-1二l+(l-Tc)rDDA^

4、4-rEEA^-1+WACCThelogicrepeatsforT-2.NotethatthecashpayoffatT・1includesVT.j：CashpayoffinT-l=Ct-i+TcrDDT-2+VT-i=Vt-2(1+rDD/V+rEE/V)Ctj+Vy-i1+WACCC「i+Ct1+WACC(i+WACC)2Wecancontinueallthewaybacktot=0:Tv0=S—~~t=1(1+WACC)DoesWACCnecessarilydeclineasleverageincreases?TheWACCformul

5、aseemstosaythatthecostofcapitaldecreaseswithleveragebecauseofinteresttaxshields.Thatisnotnecessarilyso.Suppose,forexample,thattheextrapersonaltaxondebtinterestexactlyoffsetstheadvantageofthecorporateinteresttaxshield.InthatcaseWACC=(1-Tc)rDD/V+rEE/V=r,andMM5spropositionIIbe

6、comesre=r+(r-m(1-Tc))D/E.Also,thesecuritymarketlinewouldhavetopassthroughtheafter-taxrisk-freerate.IfyourtaskissimplytoestimateWACCatthefirm'sexistingdebtratio,youdorftneedtoknowanythingabouttaxespaidbyinvestors.ButifyoutrytocalculateWACCatadifferentdebtratio,youneedtoknowh

7、owroand止changewithleverage.Therelationshipsofmand止withD/Vcandependoninvestortaxes.Inpracticemostfinancialmanagersdonottrytoadjustforinvestortaxes;theyimplicitlyassumeTp=Tpe-WeadoptthisassumptionbelowandinChapter19.LeveringandUnleveringHereisamarket-valuebalancesheetincorpor

8、atingthevalueofinteresttaxshields.FirmvalueifDall-equityfinancedPV(Taxshields)EVVS