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im09The Cost of Capital.docx

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

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