财务管理基础 答案 沈艺峰 沈洪涛im09The Cost of Capital.docx
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财务管理基础答案沈艺峰沈洪涛im09TheCostofCapital
Chapter9
TheCostofCapital
LEARNINGOBJECTIVES
Afterreadingthischapter,studentsshouldbeableto:
∙Explainwhatismeantbyafirm’sweightedaveragecostofcapital.
∙Defineandcalculatethecomponentcostsofdebtandpreferredstock.
∙Explainwhyretainedearningsarenotfreeandusethreeapproachestoestimatethecomponentcostofretainedearnings.
∙Brieflyexplainwhythecostofnewcommonequityishigherthanthecostofretainedearnings,calculatethecostofnewcommonequity,andcalculatetheretainedearningsbreakpoint--whichisthepointwherenewcommonequitywouldhavetobeissued.
∙Brieflyexplainthetwoalternativeapproachesthatcanbeusedtoaccountforflotationcosts.
∙Calculatethefirm’scomposite,orweightedaverage,costofcapital.
∙Identifysomeofthefactorsthataffecttheoverall,compositecostofcapital.
∙Brieflyexplainhowfirmsshouldevaluateprojectswithdifferentrisks,andtheproblemsencounteredwhendivisionswithinthesamefirmallusethefirm’scompositeWACCwhenconsideringcapitalbudgetingprojects.
∙Listandbrieflyexplainthethreeseparateanddistincttypesofriskthatcanbeidentified,andexplaintheproceduremanyfirmsusewhendevelopingsubjectiverisk-adjustedcostsofcapital.
∙Listsomeproblemareasinestimatingthecostofcapital.
LECTURESUGGESTIONS
Chapter9usestherateofreturnconceptscoveredinpreviouschapters,alongwiththeconceptoftheweightedaveragecostofcapital(WACC),todevelopacorporatecostofcapitalforuseincapitalbudgeting.
WebeginbydescribingthelogicoftheWACC,andwhyitshouldbeusedincapitalbudgeting.Wenextexplainhowtoestimatethecostofeachcomponentofcapital,andhowtoputthecomponentstogethertodeterminetheWACC.WegoontodiscussfactorsthataffecttheWACC,howtoadjustthecostofcapitalforrisk,andestimatingprojectrisk.Weconcludethechapterwithadiscussiononsomeproblemareasinthecostofcapital.
Thedetailsofwhatwecover,andthewaywecoverit,canbeseenbyscanningBlueprints,Chapter9.Forothersuggestionsaboutthelecture,pleaseseethe“LectureSuggestions”inChapter2,wherewedescribehowweconductourclasses.
DAYSONCHAPTER:
3OF58DAYS(50-minuteperiods)
ANSWERSTOEND-OF-CHAPTERQUESTIONS
9-1ProbableEffecton
kd(1-T)ksWACC
a.Thecorporatetaxrateislowered.+0+
b.TheFederalReservetightenscredit.+++
c.Thefirmusesmoredebt;thatis,it
increasesitsdebt/assetsratio.++0
d.Thedividendpayoutratiois
increased.000
e.Thefirmdoublestheamountofcapital
itraisesduringtheyear.0or+0or+0or+
f.Thefirmexpandsintoarisky
newarea.+++
g.Thefirmmergeswithanotherfirm
whoseearningsarecounter-cyclical
bothtothoseofthefirstfirmand
tothestockmarket.---
h.Thestockmarketfallsdrastically,
andthefirm’sstockfallsalongwith
therest.0++
i.Investorsbecomemoreriskaverse.+++
j.Thefirmisanelectricutilitywitha
largeinvestmentinnuclearplants.
Severalstatesproposeabanon
nuclearpowergeneration.+++
9-2Beta(market)riskreferstotheproject’seffectonthecorporatebetacoefficient.Within-firm(corporate)riskreferstotheproject’seffectonthestabilityofthefirm’searnings.Stand-aloneriskreferstotheinherentriskinessoftheproject’sexpectedreturnswhenviewedalone.Theoretically,beta(market)riskisthemostrelevantmeasurebecauseofitseffectonstockprices.
9-3Thecostofcapitalforaverage-riskprojectswouldbethefirm’scostofcapital,10percent.Asomewhathighercostwouldbeusedformoreriskyprojects,andalowercostwouldbeusedforlessriskyones.Forexample,wemightuse12percentformoreriskyprojectsand9percentforlessriskyprojects.Thesechoicesarearbitrary.
9-4Eachfirmhasanoptimalcapitalstructure,definedasthatmixofdebt,preferred,andcommonequitythatcausesitsstockpricetobemaximized.Avalue-maximizingfirmwilldetermineitsoptimalcapitalstructure,useitasatarget,andthenraisenewcapitalinamannerdesignedtokeeptheactualcapitalstructureontargetovertime.Thetargetproportionsofdebt,preferredstock,andcommonequity,alongwiththecostsofthosecomponents,areusedtocalculatethefirm’sweightedaveragecostofcapital,WACC.
Theweightscouldbebasedeitherontheaccountingvaluesshownonthefirm’sbalancesheet(bookvalues)oronthemarketvaluesofthedifferentsecurities.Theoretically,theweightsshouldbebasedonmarketvalues,butifafirm’sbookvalueweightsarereasonablyclosetoitsmarketvalueweights,bookvalueweightscanbeusedasaproxyformarketvalueweights.Consequently,targetmarketvalueweightsshouldbeusedintheWACCequation.
9-5Anincreaseintherisk-freeratewillincreasethecostofdebt.
RememberfromChapter4,k=kRF+DRP+LP+MRP.Thus,ifkRFincreasessodoesk(thecostofdebt).Similarly,iftherisk-freerateincreasessodoesthecostofequity.FromtheCAPMequation,ks=kRF+(kM–kRF)b.Consequently,ifkRFincreaseskswillincreasetoo.
9-6Ingeneral,failingtoadjustfordifferencesinriskwouldleadthefirmtoaccepttoomanyriskyprojectsandrejecttoomanysafeones.Overtime,thefirmwouldbecomemorerisky,itsWACCwouldincrease,anditsshareholdervaluewouldsuffer.
SOLUTIONSTOEND-OF-CHAPTERPROBLEMS
9-140%Debt;60%Equity;kd=9%;T=40%;WACC=9.96%;ks=?
WACC=(wd)(kd)(1-T)+(wc)(ks)
0.0996=(0.4)(0.09)(1-0.4)+(0.6)ks
0.0996=0.0216+0.6ks
0.078=0.6ks
ks=13%.
9-2Pp=$47.50;Dp=$3.80;kp=?
kp=
kp=
=8%.
9-3P0=$30;D1=$3.00;g=5%;F=10%;ks=?
;ke=?
ks=
+g=
+0.05=15%.
ke=
+g=
+0.05
=
+0.05=16.11%.
9-4ProjectsA,B,C,D,andEwouldbeacceptedsinceeachproject’sreturnisgreaterthanthefirm’sWACC.
9-5kd(1-T)=0.12(0.65)=7.80%.
9-6kp=
=
=11.94%.
9-7a.ks=
+g
ks=
ks=14.83%.
b.F=($36.00-$32.40)/$36.00=$3.60/$36.00=10%.
c.ke=D1/[P0(1-F)]+g=$3.18/$32.40+6%=9.81%+6%=15.81%.
9-8CapitalSourcesAmountCapitalStructureWeight
Long-termdebt$1,15240.0%
Equity1,72860.0
$2,880100.0%
WACC=wdkd(1-T)+wcks=0.4(0.13)(0.6)+0.6(0.16)
=0.0312+0.0960=12.72%.
9-9ks=D1/P0+g=$2(1.07)/$24.75+7%
=8.65%+7%=15.65%.
WACC=wd(kd)(1-T)+wc(ks);wc=1-wd.
13.95%=wd(11%)(1-0.35)+(1-wd)(15.65%)
0.1395=0.0715wd+0.1565-0.1565wd
-0.017=-0.085wd
wd=0.20=20%.
9-10a.kd=10%,kd(1-T)=10%(0.6)=6%.
D/A=45%;D0=$2;g=4%;P0=$20;T=40%.
ProjectA:
Rateofreturn=13%.
ProjectB:
Rateofreturn=10%.
ks=$2(1.04)/$20+4%=14.40%.
b.WACC=0.45(6%)+0.55(14.40%)=10.62%.
c.Sincethefirm’sWACCis10.62%andeachoftheprojectsisequallyriskyandasriskyasthefirm’sotherassets,MECshouldacceptProjectA.Itsrateofreturnisgreaterthanthefirm’sWACC.ProjectBshouldnotbeaccepted,sinceitsrateofreturnislessthanMEC’sWACC.
9-11Debt=40%,Equity=60%.
P0=$22.50,D0=$2.00,D1=$2.00(1.07)=$2.14,g=7%.
ks=
+g=
+7%=16.51%.
WACC=(0.4)(0.12)(1-0.4)+(0.6)(0.1651)
=0.0288+0.0991=12.79%.
9-12Ifthefirm'sdividendyieldis5%anditsstockpriceis$46.75,thenextexpectedannualdividendcanbecomputed.
Dividendyield=D1/P0
5%=D1/$46.75
D1=$2.3375.
Next,thefirm'scostofnewcommonstockcanbedeterminedfromtheDCFapproachforthecostofequity.
ke=D1/[P0(1-F)]+g
ke=$2.3375/[$46.75(1-0.05)]+0.12
ke=17.26%.
9-13a.ExaminingtheDCFapproachtothecostofretainedearnings,theexpectedgrowthratecanbedeterminedfromthecostofcommonequity,price,andexpecteddividend.However,first,thisproblemrequiresthattheformulaforWACCbeusedtodeterminethecostofcommonequity.
WACC=wd(kd)(1-T)+wc(ks)
13.0%=0.4(10%)(1-0.4)+0.6(ks)
10.6%=0.6ks
ks=0.17667or17.67%.
Fromthecostofcommonequity,theexpectedgrowthratecannowbedetermined.
ks=D1/P0+g
0.17667=$3/$35+g
g=0.090952or9.10%.
b.Fromtheformulaforthelong-rungrowthrate:
g=(1-Div.payoutratio)ROE=(1-Div.payoutratio)(NI/Equity)
0.090952=(1-Div.payoutratio)($1,100million/$6,000million)
0.090952=(1–Div.payoutratio)0.1833333
0.496104=(1–Div.payoutratio)
Div.payoutratio=0.503896or50.39%.
9-14Iftheinvestmentrequires$5.9million,thatmeansthatitrequires$3.54million(60%)ofequitycapitaland$2.36million(40%)ofdebtcapital.Inthisscenario,thefirmwouldexhaustits$2millionofretainedearningsandbeforcedtoraisenewstockatacostof15%.Needing$2.36millionindebtcapital,thefirmcouldgetbyraisingdebtatonly10%.Therefore,itsweightedaveragecostofcapitalis:
WACC=0.4(10%)(1-0.4)+0.6(15%)=11.4%.
9-15a.Ifallprojectdecisionsareindependent,thefirmshouldacceptallprojectswhosereturnsexceedtheirrisk-adjustedcostsofcapital.Theappropriatecostsofcapitalaresummarizedbelow:
RequiredRateofCostof
ProjectInvestmentReturnCapital
A$4million14.0%12%
B$5million11.512
C$3million9.58
D$2million9.010
E$6million12.512
F$5million12.510
G$6million7.08
H$3million11.58
Therefore,ZiegeshouldacceptprojectsA,C,E,F,andH.
b.Withonly$13milliontoinvestinitscapitalbudget,ZiegemustchoosethebestcombinationofProjectsA,C,E,F,andH.Collectively,theprojectswou