風(fēng)險(xiǎn)回報(bào)與資本成本論述(英文版)課件

Return,Risk,andtheSecurityMarketLine

TypesofReturnsExpectedReturnsandVariances Portfolios Announcements,Surprises,andExpectedReturns Risk:SystematicandUnsystematic DiversificationandPortfolioRisk SystematicRiskandBeta TheSecurityMarketLine TheSMLandtheCostofCapital SummaryandConclusionsReturn,Risk,andtheSecurityTypesofReturnsTotalMonetaryreturn=DividendIncome+CapitalGainEganinvestmentof￡1000risesinvalueto￡1500providingacapitalgainof￡500.Overthesameperiodthedividendincomeis5%=￡50.Totalreturnisthen￡500+￡50=￡550.Totalmonetaryreturnisanabsolutemeasureofreturns.Ittellsyouhowmuchmoneyyouhavemadein￡’s.ItisoftenmoreusefultoknowthePercentageReturn.ThePercentageReturnisthetotalmonetaryreturndividedbytheamountofcapitalinvested.PercentageReturn=Dividends+CapitalGains amountinvestedOr Rit=Dit+(Pit–Pit-1)=Div.Yield+%capitalgain

Pit-1TypesofReturnsTotalMonetaryExpectedReturnsandVariances:BasicIdeasThequantificationofriskandreturnisacrucialaspectofmodernfinance.Itisnotpossibletomake“good”(i.e.,value-maximizing)financialdecisionsunlessoneunderstandstherelationshipbetweenriskandreturn.Rationalinvestorslikereturnsanddislikerisk.Considerthefollowingproxiesforreturnandrisk: Expectedreturn-weightedaverageofthedistributionofpossiblereturnsinthefuture. Varianceofreturns-ameasureofthedispersionofthedistributionofpossiblereturnsinthefuture. Howdowecalculatethesemeasures?.ExpectedReturnsandVariancesCalculatingtheExpectedReturn.

Example1

sE(R)=(pixRi)

i=1

pi Ri

Probability Returnin ipixRi

StateofEconomy ofstateistatei+1%changeinGNP .25 -5%i=1-1.25%+2%changeinGNP .50 15%i=27.5%+3%changeinGNP .25 35%i=38.75%Expectedreturn= (-1.25+7.50+8.75)= 15%CalculatingtheExpectedReturCalculatingtheVariance

(Example1ofCalculatingtheexpectedreturn) Var(R)

i (Ri–E(R))2 pix(Ri–E(R))2i=1 (-0.05-0.15)2=0.04 0.25*0.04=0.01i=2 (0.15-0.15)2=0 0.5*0=0i=3 (0.35-0.15)2=0.04 0.25*0.04=0.01Var(R)=.02Whatisthestandarddeviation?

CalculatingtheVariance

(ExamExpectedReturnsandVariances

Example2

Stateofthe Probability Returnon Returnon

economy ofstate assetA assetBBoom 0.40 30% -5%Bust 0.60 -10% 25% 1.00A. Expectedreturns E(RA)= 0.40x(.30)+0.60x(-.10)=.06=6% E(RB)= 0.40x(-.05)+0.60x(.25)=.13=13%ExpectedReturnsandVariancesExample:ExpectedReturnsandVariances(concluded)B. Variances Var(RA) = 0.40x(.30-.06)2+0.60x(-.10-.06)2

= .0384 Var(RB) = 0.40x(-.05-.13)2+0.60x(.25-.13)2

= .0216C. Standarddeviations SD(RA) = .0384=.196=19.6% SD(RB) = .0216=.147=14.7%Example:ExpectedReturnsandCalculatingExpectedReturnsandVarianceinpracticeThemostcommonmethodistouseatimeseriesofreturnscalculatedfrompastpricesanddividends.dayBPpricediv.Ret.=Ret.Monday4300Tuesday4350(435-430)/4300.0116Wednesday4370(437-435)/4350.0046Thursday4410(441-437)/4370.0092Friday4350(435-441)/441-0.0136Monday4350(435-435)/4350.0000Tuesday4200(420-435)/435-0.0345CalculatingExpectedReturnsaCalculatingExpectedReturnsandVarianceinpractice(2)E(Ri)isassumedtobeequaltothesampleaveragereturn=(0.0116+0.0046+0.0092-0.0136+0-0.0345)/6=-0.00378Tocalculatethevariancewecalculatethedeviationforeachday’sreturnfromtheexpectedreturn,squaretomakeitpositiveandthendividebyn-1.Inthiscasen=6.CalculatingExpectedReturnsaCalculatingExpectedReturnsandVarianceinpractice(3)Ret.Rit-E(Rit)(Rit-E(Rit))^20.01160.01540.000240.00460.00840.000070.00920.01290.00017-0.0136-0.00980.000100.00000.00380.00001-0.0345-0.03070.00094-0.003780.00031CalculatingExpectedReturnsaMeasuringriskIfweweretoplotthedailyreturnsonasecurityoveralongperiodthenitmightlooksomethinglikeanormaldistribution(picturenextslide)Whatwewanttodoistosummarisethispictureassimplyaspossible.Themeanistheexpectedreturn,thespreadorvariationisthestandarddeviationorvariance.WearguethatthisspreadrepresentsrisktoinvestorsandhencethattheSt.Dev.orvarianceisameasureoftheriskofashare.Infactreturndistributionsdon’tusuallylookexactlylikethis.Theytendtohaveatruncatedlefttailandalongerrighttail.Variancemaynotbethebestmeasureofrisk.MeasuringriskIfweweretoplDescribingadistributionDescribingadistributionPortfolioExpectedReturnsandVariancesWhatwehavedonesofarisdescribetheriskandreturnofindividualsecurities.Wealsowanttobeabletodescribetheriskandreturnofportfoliosofsecurities.Wehavetwoequivalentalternativesopentous.Component-Wecandeterminethereturnandriskoftheportfoliobycombiningthereturnsandrisksofthesecuritiesthatmakeuptheportfolio.Security-Wecantreattheportfolioasjustanothersecurityandcalculateitsreturnandriskaswehavebeendoing.Bothoftheseapproachesgivethesameanswerbutthefirstallowsustoseehowindividualsecuritiesaffectthereturnandriskofaportfolio.PortfolioExpectedReturnsandPortfolioExpectedReturnsandVariances

(usingreturnsfromExample2)Portfolioweights:put50%inAssetAand50%inAssetB: Stateofthe Probability Return Return Returnon

economy ofstate onA onB portfolio Boom 0.40 30% -5% 12.5% Bust 0.60 -10% 25% 7.5% 1.00PortfolioExpectedReturnsandExample:PortfolioExpectedReturnsandVariances(continued)

Calculateexpectedreturns:Securityapproach E(RP) = 0.40x(.125)+0.60x(.075)=.095=9.5%Componentapproach E(RP) = .50xE(RA)+.50xE(RB)=9.5%Calculatevarianceofportfolio:Securityapproach Var(RP) = 0.40x(.125-.095)2+0.60x(.075-.095)2=.0006PortfolioapproachThesumofthevariancesisnotthevarianceoftheportfolio Var(RP) .50xVar(RA)+.50xVar(RB)Example:PortfolioExpectedReFtthisweekOlympus–sagacontinues–resignationofPresident,openletterbymajorshareholder,questions(atlast!)byJapanesePressandGovernment.Eurozone–thedeal–moreofthesame,bigger(voluntary)haircuts,moreausteritybutthedebtorstrikesback(Greekreferendum).MFGlobalcollapse–broker-dealersufferingfromeurozoneratingsdowngrades($6.3bnexposure).Managementgreed–hugeincreaseinseniormanagementpayoverlastyear.FtthisweekOlympus–sagaconTheStorysofarOuraimistorelatereturntorisk.Basicprincipleisthatinvestorsrequirearewardfortakingonrisk.Thelargertherisk,thelargerthereward.Buthowarewetomeasureriskandreturn?Manydifferenttypesofrisk.Weconcentrateonriskasperceivedbythecapitalmarkets.Thepriceofashareatanytimereflectseverythingthatisknownaboutthecompany.Suggeststhatwecanusepricechangestoprovideinformationaboutthecompany.Byexaminingthedistributionofpercentagepricechanges(returns)wecandeterminethelikelyorexpectedreturn,andthedispersionofreturnsthatmightoccur.TheStorysofarOuraimistoThestorysofar(2)Anobviousmeasureofexpectedreturnisthearithmeticmean.Ameasureofdispersionisthevariance.Thisisusedasameasureoftheriskofashare.Thevarianceisareasonablemeasureifthedistributionofreturnsissymmetric.Mostcompaniesarenotheldinisolationbutareheldaspartofaportfolio.Weusetwoshareportfoliostodemonstratehowriskchanges.TheproportionofeachcompanyintheportfolioisknownastheportfolioWeight.Ourinterestisinhowonecompanyrelatestoanother.Weareconcernedaboutthejointdistributionofreturns.Thestorysofar(2)AnobviousJointDistributionofreturns probability Returnon SecurityX ReturnonSecurityYJointDistributionofreturnsCovarianceandCorrelationTheCovarianceisameasureofhowthetwosecuritiesarerelated.SimilartoVariancebutusescrossdeviations. Variance=E(RAt–E(RAt))(RAt–E(RAt))

Covariance=average(deviationofreturnonAfromitsmean)*(deviationofreturnonBfromitsmean) CAB=E(RAt–E(RAt))((RBt–E(RBt)) CorrelationisastandardisedCovariance. CorrelationbetweenAandBistheCovariancebetweenAandBdividedbythestandarddeviationofAtimesthestandarddeviationofB.

AB

=CovAB/A

B

CovarianceandCorrelationTheCovarianceandCorrelationTheriskofaportfolioiscomprisedoftheriskoftheindividualsecuritiesplusthecorrelationbetweenthem.Iftherearetwosecuritiesthentheriskoftheportfoliocanbecalculatedfromthevarianceofeachsecurityplusthecorrelationbetweenthem.Fortwosecuritieswehave:

p2

=X12Var1+X22Var2+2X1X2Cov12 Remember: Cov12=1

2

12 p2=X12

12+X22

22+2X1X2

1

2

12

Cov12=E[(R1t-E(R1t))(R2t-E(R2t))]=E[(R2t-E(R2t))(R1t- E(R1t))] =Cov21CovarianceandCorrelationTheTwosecurityPortfolioSelectionExample

Rpt =X1R1t+X2R2t E(Rpt) =E(X1R1t+X2R2t)=X1E(R1t)+X2E(R2t)

p2 = E(Rpt-E(Rpt))2 p2 = E[X1R1t+X2R2t-(X1E(R1t)+X2E(R2t))]2 p2 = E[X1(R1t-E(R1t))+X2(R2t-E(R2t))]2Fromalgebraweknowthat(a+b)2=a2+b2+2ab p2=X12E(R1t-E(R1t))2+X22E(R2t-E(R2t))2

+2X1X2E(R1t- E(R1t))(R2t-E(R2t)) =X12

12+X22

22+2X1X2Cov12TwosecurityPortfolioSelectHowCorrelationaffectsrisk(2securityexample)HowCorrelationaffectsrisk(HowCorrelationaffectsrisk(2securityexample)

HowCorrelationaffectsrisk(HowCorrelationaffectsrisk(2securityexample)HowCorrelationaffectsrisk(TheEffectofcorrelationonPortfolioVarianceStockAreturns0.050.040.030.020.010-0.01-0.02-0.03-0.04-0.050.050.040.030.020.010-0.01-0.02-0.03StockBreturns0.040.030.020.010-0.01-0.02-0.03Portfolioreturns:

50%Aand50%BTheEffectofcorrelationonPCovarianceandCorrelation:morethan2securitiesOnewayofthinkingofthecovarianceofsecuritieswithinaportfolioistovisualiseamatrixofsecurities.Eachsecuritymustpairwitheachother.Ifthenumbersarethesameitisavariance,otherwiseacovariance.egiftherearefivesecuritieswecanthinkof:security1234511=1variance1,2correlation1,3correlation1,41,522,1correlation2,2variance2,32,42,533,13,23,3Variance3,43,544,14,24,34,4variance4,555,15,25,35,45,5varianceCovarianceandCorrelation:moComponentsofPortfolioRisk

ComponentsofPortfolioRisk

VarianceCovarianceExpression

VarianceCovarianceExpressionCovarianceandCorrelation(cont.)Impactofcorrelation(covariance)SizeofportfolioNumberofvariancesNumberofdistinctcorrelations(covariances)22133355101010451001004950CovarianceandCorrelation(coStandardDeviationsofAnnualPortfolioReturns

(3)

(2) RatioofPortfolio

(1) AverageStandard StandardDeviationto

NumberofStocks DeviationofAnnual StandardDeviation

inPortfolio PortfolioReturns(%) ofaSingleStock 1 49.24 1.00 10 23.93 0.49 50 20.20 0.41 100 19.69 0.40 300 19.34 0.39 500 19.27 0.39 1,000 19.21 0.39FiguresfromTable1inMeirStatman,“HowManyStocksMakeaDiversifiedPortfolio?”JournalofFinancialandQuantitativeAnalysis22(September1987),pp.353–64,andderivedfromE.J.EltonandM.J.Gruber,“RiskReductionandPortfolioSize:AnAnalyticSolution,”JournalofBusiness50(October1977),pp.415–37.StandardDeviationsofAnnualPortfolioDiversificationAverageannual

standarddeviation(%)Numberofstocks

inportfolioDiversifiableriskNondiversifiable

risk49.223.919.21102030401000PortfolioDiversificationAveraDiversification:analyticalsolutionDiversification:analyticalsoDiversification:analyticalsolution(2)Diversification:analyticalsoDiversification:analyticalsolution(3)Ifweweretolookatthecasewherecovariancesarenotequaltozerowewouldfindthattheriskofalargeportfolioofstocksisapproximatelyequaltotheaveragecovariancebetweenallthestocks.

P2

CovAVDiversification:analyticalsoPeterBernsteinonRiskandDiversification“Bigrisksarescarywhenyoucannotdiversifythem,especiallywhentheyareexpensivetounload;eventhewealthiestfamilieshesitatebeforedecidingwhichhousetobuy.Bigrisksarenotscarytoinvestorswhocandiversifythem;bigrisksareinteresting.Nosinglelosswillmakeanyonegobroke...bymakingdiversificationeasyandinexpensive,financialmarketsenhancethelevelofrisk-takinginsociety.”P(pán)eterBernstein,inhisbook,CapitalIdeas

PeterBernsteinonRiskandDiHowcorrelationaffectsrisk:TheEfficientFrontierHowcorrelationaffectsrisk:FTthisweekOlympus–admitswrongdoing.Eurozone–manyinterestingarticleshighlightingthe‘power’ofGreece,Germanroleandinterest,dangerstoItalyandothers.Focusononearticle: RobertJenkins,Insight(nov.8)-Greekrestructuring–exitfromtheeurozoneGreekgovtdecidesonexit.Greekcitizensandcompanieswithdraweurodepositswhilsttheyarestilleuros.Foreignlendersstoplendingandrecallloansasquicklyaspossible.Govt.announcesanewdrachma.Capitalcontrolsareintroduced.Govtdebtisredenominatedindrachma.FTthisweekOlympus–admitswOlympussharepriceOlympussharepriceFTthisweek(cont)–GreekrestructuringValueofthedrachmaplunges,Greekinflationsoars.Disputesoverprivatesectordebt.Aretheyindrachmaoreuros?Ifdrachmathenforeignbankshaveaproblem–assetvalueshavefallen.IfineurosthenGreekborrowershaveaproblemContagioncommences.Portugesecitizensthinkitmighthappentothemandmoveouteurosfromthebanks.Similarmovesinseveralothercountries.Europeanbanksindifficultiesbecauseofexposuretoeurodebtofvariouscountrieswithlikelydifficulties.Counterpartyriskmeansmarketinbankloansdriesup.Banklendinghalts!BankscollapseunlessGovtrescuethem.FTthisweek(cont)–GreekreTheStorytodateTheriskofaportfoliodependsontheCovarianceorCorrelationbetweenassets.Varianceisimportantforanindividualassetbutbecomeslessandlessimportantasaportfolioincludesmoreandmorestocks.Theriskofaportfoliodependsontheaveragecovariancebetweenstocks.Therelationshipbetweenriskandreturncanberepresentedgraphicallybyaquadraticfrontier.ThebestcombinationsofriskandreturnareontheEfficientFrontier.Theshapeofthefrontierarisesfromthecovariancebetweenassets.TheStorytodateTheriskofaHowCorrelationaffectsrisk:ariskfreeassetHowCorrelationaffectsrisk:HowCorrelationaffectsrisk:ariskfreeasset(2)HowCorrelationaffectsrisk:Tobin’sSeparationTheoremTobin’sSeparationTheoremSimplifyingourRiskMeasureOurmessagesofarhasbeenthatwhenweaddsecuritiestogetherriskisaffectedbythecorrelation(covariance)betweenthem.Becausesecuritiesarelessthanperfectlycorrelated,riskisreduced.Whilstthisisusefulasaconceptitisoperationallyverydifficulttouse.Thenumberofcorrelationsthatweneedtoconsidertoconstructoptimalportfoliosusingthissortofapproachisverylarge.Weneedtofindsomeothermeasureofriskthatwillenableustosimplifytheproblem.Onesuchmeasureisthebetaofasecurityorportfolio.Thebetaofasecuritycanbethoughtofas: the(standardised)sumofthesecurity’scovariancewithallsecuritiesSinceallsecuritiesisjustanotherwayofsayingthemarket,thebetaofasecurityis: the(standardised)covarianceofthesecuritywiththemarketSimplifyingourRiskMeasureOuEstimatingBetaBetaisusuallyestimatedusinglinearregression.BetaisanoutputfromtheMarketModel.Thisassumesthatthereisalinearrelationshipbetweenthereturnonthemarketandthereturnonashare.Returnsonashareareregressedagainstreturnsonamarketindex.

Rit=ai+biRmtcit

aiisthealphaofshareI biisthebetaofshareIEstimatingBetaBetaisusuallyBetaCoefficientsforSelectedCompanies(Table10.7)

Beta

Company Coefficient(

i)Alcatel-Lucent 1.44L’Oreal 0.45SAP 0.56Siemens 1.51Daimler 1.25PhilipsElectron 0.92Renault 1.64Volkswagen 0.40Source:Hillier,Ross,Westerfield,Jaffe,Jordan.CorporateFinance.BetaCoefficientsforSelectedPortfolioBetaCalculations

PortfolioBetahasaverydesirablecharacteristic.Itisthe(weighted)averageoftheindividualbetas.

Amount Portfolio

Stock Invested Weights Beta(1) (2) (3) (4) (3)x(4)HaskellMfg. $6,000 50% 0.90 0.450Cleaver,Inc. 4,000 33% 1.10 0.367RutherfordCo. 2,000 17% 1.30 0.217Portfolio $12,000 100% 1.034PortfolioBetaCalculationsPoCash(risklessasset),PortfolioExpectedReturnsandBetasAssumeyouwishtoholdaportfolioconsistingofariskyassetAandcash(arisklessasset).Giventhefollowinginformation,calculateportfolioexpectedreturnsandportfoliobetas,lettingtheproportionoffundsinvestedinassetArangefrom0to125%. AssetAhasabeta(

)of1.2andanexpectedreturnof18%. ThereturnoncashattheCentralBank(risk-freerate)is7%. AssetAweights:0%,25%,50%,75%,100%,and125%.Cash(risklessasset),PortfolCash(risklessasset),PortfolioExpectedReturnsandBetas

Proportion Proportion Portfolio

Investedin Investedin Expected Portfolio AssetA(%)Risk-freeAsset(%) Return(%) Beta 0 100 7.00 0.00 25 75 9.75 0.30 50 50 12.50 0.60 75 25 15.25 0.90 100 0 18.00 1.20 125 -25 20.75 1.50Plotthisandmeasuretheslope-(.18-.07)/1.2=0.092.Thisistheriskpremiumperunitofsystematicrisk.Cash(risklessasset),PortfolCash(risklessasset),PortfolioExpectedReturnsandBetasExpectedreturn18%7% 0 1.2betaSlope=(.18-.07)/1.2=.092Cash(risklessasset),PortfolReturn,Risk,andEquilibriumKeyissues:Whatistherelationshipbetweenriskandreturn?Whatdoessecuritymarketequilibriumlooklike? Thefundamentalconclusionisthattheratiooftheriskpremiumtobetaisthesameforeveryasset.Inotherwords,thereward-to-riskratioisconstantandequalto

E(Ri)-Rfslope=Reward/riskratio=

iReturn,Risk,andEquilibriumKReturn,Risk,andEquilibrium(concluded)Example: AssetAhasanexpectedreturnof12%andabetaof1.40.AssetBhasanexpectedreturnof8%andabetaof0.80.Aretheseassetsvaluedcorrectlyrelativetoeachotheriftherisk-freerateis5%? a. ForA,(.12-.05)/1.40=________ b. ForB,(.08-.05)/0.80=________Whatwouldtherisk-freeratehavetobefortheseassetstobecorrectlyvalued? (.12-Rf)/1.40=(.08-Rf)/0.80 Rf=________Return,Risk,andEquilibriumTheCapitalAssetPricingModelTheCapitalAssetPricingModel(CAPM)-anequilibriummodeloftherelationshipbetweenriskandreturn.Whatdeterminesanasset’sexpectedreturn? Therisk-freerate-thepuretimevalueofmoney Themarketriskpremium-therewardforbearingsystematicrisk Thebetacoefficient-ameasureoftheamountofsystematicriskpresentinaparticularasset TheCAPM:E(Ri)=Rf

+[E(RM)-Rf]xiTheCapitalAssetPricingModeCapitalAssetPricingModel(2)Expectedreturnonassetiisalinearfunctionoftheriskfreerateandtheassetsmarginalrisk(beta)timestheexpectedriskpremiumonthemarket. E(Ri)=Rf+(E(Rm)-Rf)iiisthebetaofasecurity.Itisderivedfromthemarketmodelandrepresentsthemarginalriskofanasset.Theinvestorisassumedtoberational.Assuchtheinvestorwillknowthatbyholdingadiversifiedportfolioofassetss/hecangetridofalltheunsystematicrisk.Theinvestorcan’thowever,getridofthesystematicormarketrisk.Inconsequencetobearmarketrisktheinvestordemandscompensationrelatedtotheamountofmarketrisk.Allassetreturnsarerelatedtotheirrisk.InequilibriumallassetswillplotonthestraightlinegivenrepresentingtheCAPM.ThestraightlineisknownastheSecurityMarketLine.CapitalAssetPricingModel(2TheCapitalAssetPricingModel:assumptions(3)InvestorsselectefficientportfoliosInvestorshavethesamedecisionhorizonandoverthisperiodmeansandvariancesexist.

CapitalMarketsareperfect:

Assetsinfinitelydivisible,notransactioncosts,

informationiscostlessandavailabletoallNotaxesIndividualscanborrowasmuchoraslittleastheywishatthesameborrowingandlendingrateRfHomogeneousExpectationsandPortfolioOpportunitiesTheCapitalAssetPricingModeTheSecurityMarketLine(SML)Assetexpected

return(E(Ri))Asset

beta(

i)=E(RM)–RfE(RM)Rf

M

=1.0TheSecurityMarketLine(SML)TheCostofCapital:IssuesKeyissues:Whatdowemeanby“costofcapital”Howcanwecomeupwithanestimate?Preliminaries 1. Vocabulary—thefollowingallmeanthesamething: a. Requiredreturn b. Appropriatediscountrate c. Costofcapital(orcostofmoney) 2. Thecostofcapitalisanopportunitycost—itdepends onwherethemoneygoes,notwhereitcomesfrom. 3. Fornow,assumethefirm’scapitalstructure(mixof debtandequity)isfixed.TheCostofCapital:IssuesTheWeightedAverageCostofCapitalCapitalstructureweights 1. Let: E = themarketvalueoftheequity. D = themarketvalueofthedebt. Then: V = E+D,soE/V+D/V=100% 2. Sothefirm’scapitalstructureweightsareE/VandD/V. 3. Interestpaymentsondebtaretax-deductible,sotheaftertaxcostofdebtisthepretaxcostmultipliedby (1-corporatetaxrate). Aftertaxcostofdebt=RDx(___________) 4. Thustheweightedaveragecostofcapitalis WACC=(E/V)xRE+(D/V)xRDx(1-Tc)TheWeightedAverageCostofCExample:EastmanChemical’sWACCEastmanChemicalhas80millionsharesofcommonstockoutstanding.Thebookvalueis$19.10andthemarketpriceis$62.375pershare.T-billsyield5%,andthemarketriskpremiumisassumedtobe8.5%.Thestockbetais1.1.Thefirmhasthreedebtissuesoutstanding. Coupon BookValue MarketValue Yield-to-Maturity 6.375% $499m $521m 5.70% 7.250% $495m $543m 6.50% 7.625% $200m $226m 6.60%Example:EastmanChemical’sWAExample:EastmanChemical’sWACC(concluded)Costofequity(SMLapproach): RE=.05+1.1x(.085)=.05+.0935=.143514.4%Costofdebt:

Multiplytheproportionoftotaldebtrepresentedbyeachissuebyitsyieldtomaturity;theweightedaveragecostofdebt=6.2%Capitalstructureweights: Marketvalueofequity= 80millionx$62.375=$4990m

Marketvalueofdebt= $521m+$543m+$226m=$1290mV=$4990m+$1290m=$6280m D/V=$1.29/$6.28=.205421%E/V=$4.99/$6.28=.794679%WACC

=(.79x.144)+(.21x.062x.65)=.122212.2%Example:EastmanChemical’sWAExample:TheSMLApproachAccordingtotheCAPM: RE=Rf+Ex(RM-Rf)

1. Gettherisk-freeratefromfinancialpress—manyusethe1-yearTreasurybillrate,say6%.2. Getestimatesofmarketriskpremiumandsecuritybeta.

a. Riskpremiumhistorical--_________%

b. Beta—historical

(1) Investmentinformationservices-e.g.,Bloomberg

(2) Estimatefromhistoricaldata3. Supposethebetais1.40,then,usingtheapproach: RE = Rf+

Ex(RM-Rf) = 0.06+1.40x________ = ________%Example:TheSMLApproachAccorCostsofDebtCostofdebt 1. Thecostofdebt,RD,istheinterestrateonnewborrowing. 2. Thecostofdebtisobservable: a. Yieldoncurrentlyoutstandingdebt. b. Yieldsonnewly-issuedsimilarly-ratedbonds. 3. Thehistoricdebtcostisirrelevant--why? Example:Wesolda20-year,12%bond10yearsagoat par.Itiscurrentlypricedat86.Whatisourcostofdebt? Theyieldtomaturityis_______%,sothisiswhatwe useasthecostofdebt,not12%.CostsofDebtCostofdebtSummaryofCapitalCostCalculations TheWeightedAverageCostofCapital A. TheWACCistherequiredreturnonthefirmasawhole.Itis theappropriatediscountrateforcashflowssimilarinrisktothefirm. B. TheWACCiscalculatedas WACC=(E/V)xRE+(D/V)xRDx(1-Tc) whereTcisthecorporatetaxrate,Eisthemarketvalueofthefirm’sequity,Disthemarketvalueofthefirm’sdebt,and

V=E+D.SummaryofCapitalCostCalculTheSecurityMarketLineandtheWeightedAverageCostofCapitalExpected

return(%)BetaSMLWACC=15%=8%Incorrect

acceptanceIncorrect

rejectionBA161514Rf=7A

=.60firm

=1.0B

=1.2IfafirmusesitsWACCtomakeaccept/rejectdecisionsforalltypesofprojects,itwillhaveatendencytowardincorrectlyacceptingriskyprojectsandincorrectlyrejectinglessriskyprojects.TheSecurityMarketLineandtSummaryofRiskandReturnI. Totalrisk-thevariance(orthestandarddeviation)ofanasset’sreturn.II. Totalreturn-theexpectedreturn+theunexpectedreturn.III. Systematicanduns