估計風險參數(shù)和融資成本

1ESTIMATINGRISKPARAMETERSANDCOSTSOFFINANCING2CostofEquityThecostofequityistherateofreturninvestorsrequireonanequityinvestmentinafirm.ExpectedReturn=Risklessrate+Beta(RiskPremium)Thisexpectedreturntoequityinvestorsincludescompensationforthemarketriskintheinvestmentandisthecostofequity.3BetasIntheCAPM,thebetaofaninvestmentistheriskthattheinvestmentaddstoamarketportfolio.IntheAPMandMulti-factormodel,thebetasoftheinvestmentrelativetoeachfactorhavetobemeasured.4Therearethreeapproachesavailableforestimatingtheseparameters.：Thefirstistousehistoricaldataonmarketpricesforindividualinvestments.Thesecondistoestimatethebetasfromthefundamentalcharacteristicsoftheinvestment.Thethirdistouseaccountingdata.5HistoricalMarketBetasTheconventionalapproachforestimatingthebetaofaninvestmentisaregressionofthehistoricalreturnsontheinvestmentagainstthehistoricalreturnsonamarketindex.Intheory,thesestockreturnsontheassetsshouldberelatedtoreturnsonamarketportfolioInpractice,wetendtouseastockindex,suchastheS&P500,asaproxyforthemarketportfolio,andweestimatebetasforstocksagainsttheindex.6RegressionEstimatesofBetasThestandardprocedureforestimatingbetasistoregressstockreturns(Rj)againstmarketreturns(Rm)

Rj=a+bRmwherea=Interceptfromtheregressionb=Slopeoftheregression7Theinterceptoftheregressionprovidesasimplemeasureofperformanceoftheinvestmentduringtheperiodoftheregression,whenreturnsaremeasuredagainsttheexpectedreturnsfromthecapitalassetpricingmodel.Toseewhy,considerthefollowingrearrangementofthecapitalassetpricingmodel:8

Rj=Rf+β[Rm-Rf]=Rf(1-β)+βRmComparethisformulationofthereturnonaninvestmenttothereturnequationfromtheregression:

Rj=a+bRmThus,acomparisonoftheintercept(a)toRf(1-b)shouldprovideameasureofthestock'sperformance,atleastrelativetothecapitalassetpricingmodel.Insummary,then:Ifa>Rf(1-b)....Stockdidbetterthanexpectedduringregressionperiod.a=Rf(1-b)....Stockdidaswellasexpectedduringregressionperiod.a<Rf(1-b)....Stockdidworsethanexpectedduringregressionperiod.

9TheLimitationsofRegressionBetasThestandarddeviationistoohighAccuracyChangethemarketindex,returnperiodandpayintervalcannotalleviatetheproblemExcessivenoise10Beta:noiseestimation11Betaestimation:indexauthor12TheIndexGame…13FundamentalBetasthetypeofbusinessor

businessesthefirmisin.themoresensitivea

businessistomarketconditions,thehigheritsbeta.Thus,otherthingsremainingequal,cyclicalfirmscanbeexpectedtohavehigherbetasthannon-cyclicalfirms.DeterminantsofBetas14DegreeofOperatingLeverageAfirm

thathashighfixedcostsrelativetototalcostsissaidtohavehighoperatingleverage.thehighervarianceinoperatingincomewillleadtoahigherbetaforthe

firmwithhighoperatingleverage.DegreeofOperatingleverage=%ChangeinOperatingProfit/%ChangeinSales15DegreeofFinancialLeverageOtherthingsremainingequal,anincreaseinfinancialleveragewillincreasethe

betaoftheequityinafirm.thebetaofdebtis

zero,debthasataxbenefittothefirm,thenL=u(1+((1-t)D/E))

where,L=LeveredBetaforequityinthefirmu=Unleveredbetaofthefirmt=CorporatetaxrateD/E=Debt/EquityRatio16Bottom-upBeta:FirminMultipleBusinesses

Disneyin2023StartwiththeunleveredbetasforthebusinessesEstimatetheunleveredbetaforDisney’sbusinesses請估計迪斯尼企業(yè)旳杠桿性系數(shù)D/E=37.46%稅率=37.60%杠桿性系數(shù)=1.1258(1+(1-.376)(.3746))=1.3917Embraer’sBottom-upBetaBusiness UnleveredBeta D/ERatio LeveredbetaAerospace 0.95 18.95% 1.07 杠杠性Beta =非杠桿性Beta(1+(1-taxrate)(D/ERatio) =0.95(1+(1-.34)(.1895))=1.0718ComparableFirms?CananunleveredbetaestimatedusingU.S.andEuropeanaerospacecompaniesbeusedtoestimatethebetaforaBrazilianaerospacecompany?YesNoWhatconcernswouldyouhaveinmakingthisassumption?19BottomUpBetasthebetaforafirmisaweightedaverageofthebetasofallthedifferentbusinessesitisin.fivesteps:Weidentifythebusinessorbusinessesthefirmoperatesin.Wefindotherpubliclytradedfirmsinthesebusinessesandobtaintheirregressionbetasusethecompany'saverageD/Eontheiraveragebetacoefficientforleverage,estimationofbusinessaveragenonleveragedbetacoefficient.UnleveredBetaBusines=Betacomparable

firms

(1+((1-t)D/Eratiocomparablefirms))20Toestimateanunleveredbetaforthefirmthatweareanalyzing,we

takeaweightedaverageoftheunleveredbetasforthebusinessesitoperatesin,usingtheproportionoffirmvaluederivedfromeachbusinessastheweights.

UnleveredBeta

firm=∑(UnleveredBetaj*ValueWeightj)Finally,weestimatethecurrentmarketvaluesofdebtandequityofthefirmandusethisdebttoequityratiotoestimatealeveredbeta.21AccountingBetasestimatethemarketriskparametersfromaccounting

earningsratherthanfromtradedprices.threepotentialpitfalls1、accountingearningstendtobesmoothedoutrelativetotheunderlyingvalueofthecompany2、accountingearningscanbeinfluencedbynon-operatingfactors3、fewobservations22FromBetastoCostofEquitywecannowestimatetheexpectedreturnfrominvestinginequityatanyfirm.IntheCAPM,thisexpectedreturncanbewrittenas:ExpectedReturn=RisklessRate+Beta*ExpectedRiskPremiumwheretherisklessratewouldbetherateonalong-termgovernmentbond,thebetawouldbeeitherthehistorical,fundamentaloraccountingbetasdescribedaboveandtheriskpremiumwouldbeeitherthehistoricalpremiumoranimpliedpremium.23Inthearbitragepricingandmulti-factormodel,theexpectedreturnwouldbewrittenasfollows:

j=nExpectedReturn=RisklessRate＋∑βj×RiskPremiumj

j=1wheretherisklessrateisthelongtermgovernmentbondrate,bjisthebetarelativetofactorjestimatedusinghistoricaldataorfundamentalsandRiskPremiumjistheriskpremiumrelativetofactorj,estimatedusinghistoricaldata.24FromCostofEquitytoCostofCapitalWhileequityisundoubtedlyanimportantandindispensableingredientofthefinancingmixforeverybusiness,itisbutoneingredient.Mostbusinessesfinancesomeormuchoftheiroperationsusingdebtorsomesecuritythatisacombinationofequityanddebt.Thecostsofthesesourcesoffinancingaregenerallyverydifferentfromthecostofequityandthecostoffinancingforafirmshouldreflecttheircostsaswell,inproportiontotheiruseinthefinancingmix.Intuitively,thecostofcapitalistheweightedaverageofthecostsofthedifferentcomponentsoffinancing--includingdebt,equityandhybridsecurities--usedbyafirmtofunditsfinancialrequirements.25CalculatingtheCostofDebtThecostofdebtmeasuresthecurrentcosttothefirmofborrowingfundstofinanceprojects.Ingeneralterms,itisdeterminedbythefollowingvariables:Therisklessrate:Astherisklessincreases,thecostofdebtforfirmswillalsoincrease.Thedefaultrisk.Asthedefaultriskofafirmincreases,thecostofborrowingmoneywillalsoincrease.Thetaxadvantageassociatedwithdebt:Sinceinterestistaxdeductible,theafter-taxcostofdebtisafunctionofthetaxrate.Thetaxbenefitthataccruesfrompayinginterestmakestheafter-taxcostofdebtlowerthanthepre-taxcost.Furthermore,thisbenefitincreasesasthetaxrateincreases.

After-taxcostofdebt=Pre-taxcostofdebt(1-taxrate)26Whenthereisnoratingavailabletoestimatethe

costofdebt,therearetwo

alternatives:1.RecentBorrowingHistory:Manyfirmsthatarenotratedstillborrowmoneyfrom

banksandotherfinancialinstitutions.Bylookingatthemostrecentborrowings

madebyafirm,wecangetasenseofthetypesofdefaultspreadsbeingcharged

thefirmandusethesespreadstocomeupwithacostofdebt.2.Estimateasyntheticrating:Analternativeistoplaytheroleofaratingsagencyandassignaratingtoafirmbaseduponitsfinancialratios;thisratingiscalleda

syntheticrating.

Interestcoverageratio=operatingincome/interestexpenses27InterestCoverageRatio,

RatingandSpreadInterestCoverageRatio

Rating

Spread

(2023) Spread

(2023)>8.50 (>12.50)AAA 0.75% 0.35%6.50-8.50(9.5-12.5)AA 1.00%0.50% 5.50-6.50(7.5-9.5)A+ 1.50%0.70%4.25-5.50(6-7.5) A 1.80%0.85%3.00-4.25(4.5-6) A– 2.00%1.00%2.50-3.00(4-4.5) BBB 2.25%1.50%2.25-2.50(3.5-4) BB+ 2.75%2.00% 2.00-2.25(3-3.5) BB 3.50%2.50%1.75-2.00(2.5-3) B+ 4.75%3.25%1.50-1.75(2-2.5) B 6.50%4.00%1.25-1.50(1.5-2) B– 8.00%6.00%0.80-1.25(1.25-1.5)CCC 10.00% 8.00%0.65-0.80(0.8-1.25)CC 11.50% 10.00%0.20-0.65(0.5-0.8)C 12.70% 12.00%<0.20 (<0.5) D 15.00% 20.00%28CalculatingtheCostofHybridSecuritiesCostofPreferredStockPreferredstocksharessomeofthecharacteristicsofdebt-thepreferreddividendispre-specifiedatthetimeoftheissueandispaidoutbeforecommondividend–andsomeofthecharacteristicsofequity-thepaymentsofpreferreddividendarenottaxdeductible.Ifpreferredstockisviewedasperpetual,thecostofpreferredstockcanbewrittenasfollows:Kps＝PreferredDividendpershare／MarketPriceperpreferredshare29Intermsofrisk,preferredstockissaferthancommonequity,becausepreferreddividendsarepaidbeforedividendsoncommonequity.Itis,however,riskierthandebtsinceinterestpaymentsondebtaremadepriortopreferreddividendpayments.Consequently,onapre-taxbasis,itshouldcommandahighercostthandebtandalowercostthanequity.30CalculatingtheWeightsofDebtandEquityComponents

Nowthatwehavethecostsofdebt,equityandhybridsecurities,wehavetoestimatetheweightsthatshouldbeattachedtoeach.Beforewediscusshowbesttoestimateweights,wedefinewhatweincludeindebt.Wethenmaketheargumentthatweightsusedshouldbebaseduponmarketvalueandnotbookvalue.31Whatisdebt?

Theanswertothisquestionmayseemobvioussincethebalancesheetforafirmshowstheoutstandingliabilitiesofafirm.Thereare,however,limitationswithusingtheseliabilitiesasdebtinthecostofcapitalcomputation.Thefirstisthatsomeoftheliabilitiesonafirm’sbalancesheet,suchasaccountspayableandsuppliercredit,arenotint