Explainwhatismeantbyafirmsweightedaveragecostofcapital. TheCostofCapital
LearningObjectives
Chapter10
Afterreadingthischapter,studentsshouldbeableto:
Defineandcalculatethecomponentcostsofdebtandpreferredstock.Explainwhythecostofdebtis
taxadjustedandthecostofpreferredisnot.
Explainwhyretainedearningsarenotfreeandusethreeapproachestoestimatethecomponentcost
ofretainedearnings.
Brieflyexplainthetwoalternativeapproachesthatcanbeusedtoaccountforflotationcosts. Briefly explain why the cost of new common equity is higher than the cost of retained earnings,
calculatethecostofnewcommonequity,andcalculatetheretainedearningsbreakpointwhichisthe pointwherenewcommonequitywouldhavetobeissued.
Calculatethefirmscomposite,orweightedaverage,costofcapital. IdentifysomeofthefactorsthataffecttheWACCdividingthemintofactorsthefirmcannotcontrol
andthosetheycan.
Brieflyexplainhowfirmsshouldevaluateprojectswithdifferentrisks,andtheproblemsencountered
when divisions within the same firm all use the firms composite WACC when considering capital budgetingprojects.
Listsomeproblemswithcostofcapitalestimates.
Chapter10:TheCostofCapital
LearningObjectives
243
LectureSuggestions
Chapter10usestherateofreturnconceptscoveredinpreviouschapters,alongwiththeconceptofthe weighted average cost of capital (WACC), to develop a corporate cost of capital for use in capital budgeting. WebeginbydescribingthelogicoftheWACC,andwhyitshouldbeusedincapitalbudgeting.Wenext explainhowtoestimatethecostofeachcomponentofcapital,andhowtoputthecomponentstogetherto determinetheWACC. WegoontodiscussfactorsthataffecttheWACCandhowtoadjustthecostof capital for risk. We conclude the chapter with a discussion on some problems with cost of capital estimates. Whatwecover,andthewaywecoverit,canbeseenbyscanningtheslidesandIntegratedCase solutionforChapter10,whichappearsattheendofthischaptersolution.Forothersuggestionsaboutthe lecture,pleaseseetheLectureSuggestionsinChapter2,wherewedescribehowweconductourclasses.
DAYSONCHAPTER:3OF58DAYS(50minuteperiods)
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LectureSuggestions
Chapter10:TheCostofCapital
AnswerstoEndOfChapterQuestions
101
ProbableEffecton rd (1T) s r WACC a. Thecorporatetaxrateislowered. b. TheFederalReservetightenscredit. c. Thefirmusesmoredebt;thatis,itincreases itsdebt/assetsratio. d. Thedividendpayoutratioisincreased. e. Thefirmdoublestheamountofcapitalitraises duringtheyear. f. Thefirmexpandsintoariskynewarea. 0or+ + 0or+ + 0or+ + + 0 + 0 0 0 + + 0 + + +
g. Thefirmmergeswithanotherfirmwhoseearnings arecountercyclicalbothtothoseofthefirstfirmand tothestockmarket. h. Thestockmarketfallsdrastically,andthefirmsstock fallsalongwiththerest. i. j. Investorsbecomemoreriskaverse. Thefirmisanelectricutilitywithalargeinvestmentin nuclearplants.Severalstatesproposeabanon nuclearpowergeneration. 102 + + + 0 + + + + +
Anincreaseintheriskfreeratewillincreasethecostofdebt.RememberfromChapter6,r=rRF+ DRP+LP+MRP.Thus,ifrRFincreasessodoesr(thecostofdebt).Similarly,iftheriskfreerate increasessodoesthecostofequity.FromtheCAPMequation,rs=rRF+(rMrRF)b.Consequently, ifrRFincreasesrswillincreasetoo.
103
Eachfirmhasanoptimalcapitalstructure,definedasthatmixofdebt,preferred,andcommon
Chapter10:TheCostofCapital
AnswersandSolutions
245
equity that causes its stock price to be maximized. A valuemaximizing firm will determine its optimalcapitalstructure,useitasatarget,andthenraisenewcapitalinamannerdesignedto keeptheactualcapitalstructureontargetovertime. Thetargetproportionsofdebt,preferred stock,andcommonequity,alongwiththecostsofthosecomponents,areusedtocalculatethe firmsweightedaveragecostofcapital,WACC. Theweightscouldbebasedeitherontheaccountingvaluesshownonthefirmsbalancesheet (bookvalues)oronthemarketvaluesofthedifferentsecurities.Theoretically,theweightsshould bebasedonmarketvalues,butifafirmsbookvalueweightsarereasonablyclosetoitsmarket value weights, book value weights can be used as a proxy for market value weights. Consequently,targetmarketvalueweightsshouldbeusedintheWACCequation. 104 Ingeneral,failingtoadjustfordifferencesinriskwouldleadthefirmtoaccepttoomanyrisky projectsandrejecttoomanysafeones.Overtime,thefirmwouldbecomemorerisky,itsWACC wouldincrease,anditsshareholdervaluewouldsuffer. The cost of capital for averagerisk projects would be the firms cost of capital, 10%. A somewhathighercostwouldbeusedformoreriskyprojects,andalowercostwouldbeusedfor lessriskyones. Forexample,wemightuse12%formoreriskyprojectsand9%forlessrisky projects.Thesechoicesarearbitrary. 105 Thecost ofretained earningsislowerthanthecostofnewcommon equity; therefore, ifnew commonstockhadtobeissuedthenthefirmsWACCwouldincrease. ThecalculatedWACCdoesdependonthesizeofthecapitalbudget.Afirmcalculatesits retainedearningsbreakpoint(andanyothercapitalbreakpointsforadditionaldebtandpreferred). ThisR/Ebreakpointrepresentstheamountofcapitalraisedbeyondwhichnewcommonstock must beissued.Thus, acapitalbudgetsmaller thanthisbreakpoint would usethelower cost retainedearningsandthusalowerWACC.Acapitalbudgetgreaterthanthisbreakpointwoulduse thehighercostofnewequityandthusahigherWACC. DividendpolicyhasasignificantimpactontheWACC.TheR/Ebreakpointiscalculatedasthe additiontoretainedearningsdividedbytheequityfraction.Thehigherthefirmsdividendpayout, thesmallertheadditiontoretainedearningsandthelowertheR/Ebreakpoint.(Thatis,thefirms WACCwillincreaseatasmallercapitalbudget.)
246
AnswersandSolutions
Chapter10:TheCostofCapital
SolutionstoEndOfChapterProblems
101 102
rd(1T)=0.12(0.65)=7.80%. Pp=$47.50;Dp=$3.80;rp=? rp = Dp Pp = $3.80 =8%. $47.50
103
40%Debt;60%Commonequity;rd=9%;T=40%;WACC=9.96%;rs=? WACC =(wd)(rd)(1T)+(wc)(rs) 0.0996 =(0.4)(0.09)(10.4)+(0.6)rs 0.0996 =0.0216+0.6rs 0.078 =0.6rs rs =13%.
104
P0=$30;D1=$3.00;g=5%;rs=? a. rs= D1 $3.00 +g= +0.05=15%. P0 $30.00
b. F=10%;re=? re= D1 $3.00 +g = +0.05 P0 (1 F) $30(1 0.10) =
$3.00 +0.05=16.11%. $27.00
105 WACC.
ProjectsA,B,C,D,andEwouldbeacceptedsinceeachprojectsreturnisgreaterthanthefirms
106
a. rs=
D1 $2.14 +g= +7%=9.3%+7%=16.3%. P0 $23
b. rs =rRF+(rMrRF)b Chapter10:TheCostofCapital AnswersandSolutions 247
=9%+(13%9%)1.6=9%+(4%)1.6=9%+6.4%=15.4%. c. rs=Bondrate+Riskpremium=12%+4%=16%. d. Sinceyouhaveequalconfidenceintheinputsusedforthethreeapproaches,anaverageof thethreemethodologiesprobablywouldbewarranted. rs= 16.3% + 15.4% + 16% =15.9%. 3 D1 +g P0 $3.18 +0.06 $36
107
a. rs = =
=14.83%. b. F=($36.00$32.40)/$36.00=$3.60/$36.00=10%. c. re=D1/[P0(1F)]+g=$3.18/$32.40+6%=9.81%+6%=15.81%. 108 Debt=40%,Commonequity=60%. P0=$22.50,D0=$2.00,D1=$2.00(1.07)=$2.14,g=7%. rs= D1 $2.14 +g= +7%=16.51%. P0 $22.50
WACC =(0.4)(0.12)(10.4)+(0.6)(0.1651) =0.0288+0.0991=12.79%. 109 CapitalSources Longtermdebt CommonEquity Amount $1,152 1,728 $2,880 CapitalStructureWeight 40.0% 60.0 % 100.0
WACC =wdrd(1T)+wcrs=0.4(0.13)(0.6)+0.6(0.16) =0.0312+0.0960=12.72%. 1010 Iftheinvestmentrequires$5.9million,thatmeansthatitrequires$3.54million(60%)ofcommon equityand$2.36million(40%)ofdebt. Inthisscenario,thefirmwouldexhaustits$2millionof
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AnswersandSolutions
Chapter10:TheCostofCapital
retainedearningsandbeforcedtoraisenewstockatacostof15%. Needing$2.36millionin debt,thefirmcouldgetbyraisingdebtatonly10%.Therefore,itsweightedaveragecostofcapital is:WACC=0.4(10%)(10.4)+0.6(15%)=11.4%. 1011 rs =D1/P0+g=$2(1.07)/$24.75+7% =8.65%+7%=15.65%. WACC=wd(rd)(1T)+wc(rs);wc=1wd. 13.95% =wd(11%)(10.35)+(1wd)(15.65%) 0.1395 =0.0715wd+0.15650.1565wd 0.017 =0.085wd wd =0.20=20%. 1012 a. rd=10%,rd(1T)=10%(0.6)=6%. D/A=45%;D0=$2;g=4%;P0=$20;T=40%. ProjectA:Rateofreturn=13%. ProjectB:Rateofreturn=10%. rs=$2(1.04)/$20+4%=14.40%. b. WACC=0.45(6%)+0.55(14.40%)=10.62%. c. SincethefirmsWACCis10.62%andeachoftheprojectsisequallyriskyandasriskyasthe firmsotherassets,MECshouldacceptProjectA.Itsrateofreturnisgreaterthanthefirms WACC.ProjectBshouldnotbeaccepted,sinceitsrateofreturnislessthanMECsWACC. 1013 Ifthefirm'sdividendyieldis5%anditsstockpriceis$46.75,thenextexpectedannualdividend canbecalculated. Dividendyield =D1/P0 5% =D1/$46.75 D1 =$2.3375. Next,thefirm'scostofnewcommonstockcanbedeterminedfromtheDCFapproachforthecost ofequity.
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AnswersandSolutions
249
re =D1/[P0(1F)]+g =$2.3375/[$46.75(10.05)]+0.12 =17.26%. $100( 0.11) $11 = =11.94%. $92.15 $92.15
1014
rp=
1015
a. ExaminingtheDCFapproachtothecostofretainedearnings,theexpectedgrowthratecanbe determinedfromthecostofcommonequity,price,andexpecteddividend.However,first,this problemrequiresthattheformulaforWACCbeusedtodeterminethecostofcommonequity. WACC =wd(rd)(1T)+wc(rs) 13.0% =0.4(10%)(10.4)+0.6(rs) 10.6% =0.6rs rs =0.17667or17.67%. Fromthecostofcommonequity,theexpectedgrowthratecannowbedetermined. rs =D1/P0+g 0.17667 =$3/$35+g g =0.090952or9.10%. b. Fromtheformulaforthelongrungrowthrate: g 0.090952 0.090952 0.496104 Div.payoutratio =(1Div.payoutratio) ROE=(1Div.payoutratio) (NI/Equity) =(1Div.payoutratio) ($1,100million/$6,000million) =(1Div.payoutratio) 0.1833333 =(1Div.payoutratio) =0.503896or50.39%.
1016
a. Withafinancialcalculator,inputN=5,PV=4.42,PMT=0,FV=6.50,andthensolvefor I/YR=g=8.02% 8%. b. D1=D0(1+g)=$2.60(1.08)=$2.81. c. rs=D1/P0+g=$2.81/$36.00+8%=15.81%.
1017
a.
rs =
D1 +g P0 Chapter10:TheCostofCapital
250
AnswersandSolutions
0.09 =
$3.60 +g $60.00
0.09 =0.06+g g =3%. b. CurrentEPS Less:Dividendspershare Retainedearningspershare Rateofreturn IncreaseinEPS Plus:CurrentEPS NextyearsEPS $5.400 3.600 $1.800 0.090 $0.162 5.400 $5.562
Alternatively,EPS1=EPS0(1+g)=$5.40(1.03)=$5.562.
1018
a. rd(1T)=0.10(10.3)=7%. rp=$5/$49=10.2%. rs=$3.50/$36+6%=15.72%. b. WACC: Component Debt[0.10(1T)] Preferredstock Commonstock Weight 0.15 0.10 0.75 Aftertax Cost 7.00% 10.20 15.72 Weighted Cost 1.05% 1.02 11.79 WACC = % 13.86 =
c. Projects1and2willbeacceptedsincetheirratesofreturnexceedtheWACC.
Chapter10:TheCostofCapital
AnswersandSolutions
251
1019
a. If all project decisions are independent, the firm should accept all projects whose returns exceedtheirriskadjustedcostsofcapital. Theappropriatecostsofcapitalaresummarized below: Project A B C D E F G H Required Investment $4million 5million 3million 2million 6million 5million 6million 3million Rateof Return 14.0% 1.5 9.5 9.0 12.5 12.5 7.0 11.5 Costof Capital 12% 12 8 10 12 10 8 8
Therefore,ZiegeshouldacceptprojectsA,C,E,F,andH. b. Withonly$13milliontoinvestinitscapitalbudget,Ziegemustchoosethebestcombinationof ProjectsA,C,E,F,andH.Collectively,theprojectswouldaccountforaninvestmentof$21 million, sonaturallynotalltheseprojectsmaybeaccepted. Lookingattheexcessreturn createdbytheprojects(rateofreturnminusthecostofcapital),weseethattheexcessreturns forProjectsA,C,E,F,andHare2%,1.5%,0.5%,2.5%,and3.5%.Thefirmshouldaccept theprojectswhichprovidethegreatestexcessreturns.Bythatrationale,thefirstprojecttobe eliminatedfromconsiderationisProjectE.Thisbringsthetotalinvestmentrequireddownto $15million,thereforeonemoreprojectmustbeeliminated.Thenextlowestexcessreturnis ProjectC. Therefore,Ziege'soptimalcapitalbudgetconsistsofProjectsA,F,andH,andit amountsto$12million. c. SinceProjectsA,F,andHarealreadyacceptedprojects,wemustadjustthecostsofcapital fortheothertwovalueproducingprojects(CandE). Required Investment $3million 6million Rateof Return 9.5% 12.5 Costof Capital 8% + 1% = 9% 12% + 1% = 13%
Project C E
Ifnewcapitalmustbeissued,ProjectEceasestobeanacceptableproject. Ontheother hand,ProjectC'sexpectedrateofreturnstillexceedstheriskadjustedcostofcapitaleven afterraisingadditionalcapital.Hence,Ziege'snewcapitalbudgetshouldconsistofProjectsA, C,F,andHandrequires$15millionofcapital,so$3millionofadditionalcapitalmustbe raised.
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AnswersandSolutions
Chapter10:TheCostofCapital
1020
a. Aftertaxcostofnewdebt:rd(1T)=0.09(10.4)=5.4%. Costofcommonequity:Calculategasfollows: Withafinancialcalculator,inputN=9,PV=3.90,PMT=0,FV=7.80,andthensolvefor I/YR=g=8.01% 8%. rs= D1 ( 0.55)($ 7.80) $4.29 +g= +0.08= +0.08=0.146=14.6%. P0 $65.00 $65.00
b. WACCcalculation: Component Debt[0.09(1T)] Commonequity(RE) Weight 0.40 0.60 Aftertax Cost 5.4% 14.6 Weighted Cost 2.16% 8.76 WACC = % 10.92 Thesolutiontothisproblemisnotprovidedtostudentsatthebackoftheirtext.Instructorscan =
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AnswersandSolutions
253
Comprehensive/SpreadsheetProblem
NotetoInstructors: accesstheExcelfileonthetextbooksWebsiteortheInstructorsResourceCD. 1021 a. INPUT DATA EPS P0 Pp Dp D0 g B-T rd Skye's beta Market risk premium, rM - rRF Risk free rate, rRF Tax rate Flotation cost for common $3.20 $55.00 $30.00 $3.30 $2.10 9% 10% 1.516 5.0% 6.0% 35% 10%
Cost of debt B-T rd 10% x (1 T) 65% = A-T rd 6.50%
Cost of preferred stock Dp $3.30 / Pp $30.00 = rp 11.00%
Cost of common equity from retained earnings D1 $2.29 / P0 $55.00 + g 9% = rs 13.16%
Cost of common equity from new common stock D0 (1 + g) $2.29 / P0 (1 F) $49.50 + g 9% = re 13.62%
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Comprehensive/SpreadsheetProblem
Chapter10:TheCostofCapital
b.
rs rs
= =
rRF
+
b * RPM = 7.58% = 13.58%
6.0%
c.
re
=
rs 13.58%
+ +
Differential 0.46%
=
14.04%
d.
WACC using retained earnings wd wp wc 29.3% 6.1% 64.6% 100.0% wd A-T rd + 1.90% wp rp 0.67% +
Notethatweusedthecapitalstructurebasedon longtermcapitalascalculatedabove.
wc r s 8.64% = WACC 11.22%
WACC using new common stock wd wp wc 29.3% 6.1% 64.6% 100.0% wd A-T rd + 1.90% wp rp 0.67% + wc re 8.94% =
Notethatweusedtheaverageofthe2 methodsusedtocalculaters.
WACC 11.51%
Notethatweusedtheaverageofthe2 methodsusedtocalculaters. Skye'sWACCwillbe11.22%solongasitfinanceswithdebt,preferredstock,andcommon equityraisedasretainedearnings. Ifitexpandssorapidlythatitusesupallofitsretained earningsandmustissuenewcommonstockwithacostof13.83%(averageofDCFand CAPMestimates),thenitsWACCwillincreaseto11.51%.
Chapter10:TheCostofCapital
Comprehensive/SpreadsheetProblem
255
256
Comprehensive/SpreadsheetProblem
Chapter10:TheCostofCapital
IntegratedCase
1022
ColemanTechnologiesInc. CostofCapital
ColemanTechnologiesisconsideringamajorexpansionprogramthathasbeen proposed by the companys information technology group. Before proceeding withtheexpansion,thecompanymustestimateitscostofcapital. Assumethat youareanassistanttoJerryLehman,thefinancialvicepresident.Yourfirsttask is to estimate Colemans cost of capital. Lehman has provided you with the followingdata,whichhebelievesmayberelevanttoyourtask: 1. 2. Thefirmstaxrateis40%. The current price of Colemans 12% coupon, semiannual payment, noncallablebondswith15yearsremainingtomaturityis$1,153.72.Coleman doesnotuseshortterminterestbearingdebtonapermanentbasis. New bondswouldbeprivatelyplacedwithnoflotationcost. 3. The current price of the firms 10%, $100 par value, quarterly dividend, perpetualpreferredstockis$111.10. 4. Colemans common stock is currently selling for $50 per share. Its last dividend(D0)was$4.19,anddividendsareexpectedtogrowataconstantrate of5%intheforeseeablefuture.Colemansbetais1.2,theyieldonTbondsis 7%,andthemarketriskpremiumisestimatedtobe6%.Forthebondyield
Chapter10:TheCostofCapital IntegratedCase 257
plusriskpremiumapproach,thefirmusesariskpremiumof4%. 5. Colemanstargetcapitalstructureis30%debt,10%preferredstock,and60% commonequity. Tostructurethetasksomewhat,Lehmanhasaskedyoutoanswerthefollowing questions. A. (1) What sources of capital should be included when you estimate ColemansWACC? Answer: [Show S101 through S103 here.] The WACC is used primarily for making longterm capital investment decisions, i.e., for capital budgeting.Thus,theWACCshouldincludethetypesofcapitalusedto payforlongtermassets,andthisistypicallylongtermdebt,preferred stock (if used), and common stock. Shortterm sources of capital consist of (1) spontaneous, noninterestbearing liabilities such as accounts payable and accrued liabilities and (2) shortterm interest bearingdebt,suchasnotespayable.Ifthefirmusesshortterminterest bearingdebttoacquirefixedassetsratherthanjusttofinanceworking capital needs, then the WACC should include a shortterm debt component. Noninterestbearing debt is generally not included in the cost of capital estimate because these funds are netted out when determininginvestmentneeds,thatis,netoperatingratherthangross operatingworkingcapitalisincludedincapitalexpenditures.
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IntegratedCase
Chapter10:TheCostofCapital
A.
(2)
Shouldthecomponentcostsbefiguredonabeforetaxoranaftertax basis?
Answer:
[Show S104 here.] Stockholders are concerned primarily with those corporatecashflowsthatareavailablefortheiruse,namely,thosecash flowsavailabletopaydividendsorforreinvestment. Sincedividends arepaidfromandreinvestmentismadewithaftertaxdollars,allcash flow and rate of return calculations should be done on an aftertax basis.
A.
(3)
Should the costs be historical (embedded) costs or new (marginal) costs?
Answer:
[Show S105 and S106 here.] In financial management, the cost of capital is used primarily to make decisions that involve raising new capital.Thus,therelevantcomponentcostsaretodaysmarginalcosts ratherthanhistoricalcosts.
B.
WhatisthemarketinterestrateonColemansdebtanditscomponent costofdebt?
Answer:
[ShowS107throughS109here.]Colemans12%bondwith15yearsto maturityiscurrentlysellingfor$1,153.72.Thus,itsyieldtomaturityis 10%: 0 1 2 3 29 30
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Chapter10:TheCostofCapital
IntegratedCase
| 1,153.72
| 60
| 60
| 60
| 60
| 60 1,000
EnterN=30,PV=1153.72,PMT=60,andFV=1000,andthenpress theI/YRbuttontofindrd/2=I/YR=5.0%. Sincethisisasemiannual rate,multiplyby2tofindtheannualrate,rd=10%,thepretaxcostof debt. Sinceinterestistaxdeductible,UncleSam,ineffect,payspartof thecost,andColemansrelevantcomponentcostofdebtistheafter taxcost: rd(1T)=10.0%(10.40)=10.0%(0.60)=6.0%.
OptionalQuestion
Shouldyouusethenominalcostofdebtortheeffectiveannualcost? Answer: Our10%pretaxestimateisthenominalcostofdebt.Sincethefirms debthassemiannualcoupons,itseffectiveannualrateis10.25%: (1.05)21.0=1.10251.0=0.1025=10.25%. However,nominalratesaregenerallyused.Thereasonisthatthecost of capital is used in capital budgeting, and capital budgeting cash flowsaregenerallyassumedtooccuratyearend. Therefore,using nominalratesmakesthetreatmentofthecapitalbudgetingdiscount rateandcashflowsconsistent.
260 IntegratedCase Chapter10:TheCostofCapital
C.
(1)
Whatisthefirmscostofpreferredstock? [ShowS1010andS1011here.]Sincethepreferredissueisperpetual, itscostisestimatedasfollows: rp= Dp Pp = 0 . 1 ($ 100 ) $ 10 = =0.090=9.0%. $ 111 . 10 $ 111 . 10
Answer:
Note (1) that since preferreddividends are not tax deductible to the issuer,thereisnoneedforataxadjustment,and(2)thatwecouldhave estimatedtheeffectiveannualcostofthepreferred,butasinthecase ofdebt,thenominalcostisgenerallyused. C. (2) Colemanspreferredstockisriskiertoinvestorsthanitsdebt,yetthe preferredsyieldtoinvestorsislowerthantheyieldtomaturityonthe debt.Doesthissuggestthatyouhavemadeamistake?(Hint:Think abouttaxes.) Answer: [Show S1012 and S1013 here.] Corporate investors own most preferred stock, because 70% of preferred dividends received by corporations are nontaxable. Therefore, preferred often has a lower beforetaxyieldthanthebeforetaxyieldondebtissuedbythesame company.Note,though,thattheaftertaxyieldtoacorporateinvestor andtheaftertaxcosttotheissuerarehigheronpreferredstockthan ondebt.
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D.
(1)
Whyisthereacostassociatedwithretainedearnings? [ShowS1014throughS1016here.]Colemansearningscaneitherbe retainedandreinvestedinthebusinessorpaidoutasdividends. If earningsareretained,Colemansshareholdersforgotheopportunityto receivecashandtoreinvestitinstocks,bonds,realestate,andthelike. Thus,Colemanshouldearnonitsretainedearningsatleastasmuchas itsstockholdersthemselvescouldearnonalternativeinvestmentsof equivalentrisk. Further,thecompanysstockholderscouldinvestin Colemansowncommonstock,wheretheycouldexpecttoearnrs.We concludethatretainedearningshaveanopportunitycostthatisequal tors,therateofreturninvestorsexpectonthefirmscommonstock.
Answer:
D.
(2)
WhatisColemansestimatedcostofcommonequityusingtheCAPM approach?
Answer:
[Show S1017 here.] The CAPM estimate for Colemans cost of commonequityis14.2%: rs =rRF+(rMrRF)b =7.0%+(6.0%)1.2=7.0%+7.2%=14.2%.
E.
What is the estimated cost of common equity using the DCF approach?
Answer:
262
[Show S1018 through S1020 here.] Since Coleman is a constant
Chapter10:TheCostofCapital
IntegratedCase
growthstock,theconstantgrowthmodelcanbeused: rs = s = r = D 0 ( 1 + g) $ 4 . 19 ( 1 . 05 ) D1 + + 0 . 05 = P0 + g P0 $ 50 $ 4 . 40 +0.05=0.088+0.05=8.8%+5.0%=13.8%. $ 50
F.
WhatisthebondyieldplusriskpremiumestimateforColemanscost ofcommonequity?
Answer:
[ShowS1021here.]Thebondyieldplusriskpremiumestimateis14%: rs=Bondyield+Riskpremium=10.0%+4.0%=14.0%. Note that the risk premium required in this method is difficult to estimate,sothisapproachonlyprovidesaballparkestimateofrs.Itis useful,though,asacheckontheDCFandCAPMestimates,whichcan, undercertaincircumstances,produceunreasonableestimates.
G. Answer:
Whatisyourfinalestimateforrs? [ShowS1022here.]Thefollowingtablesummarizesthersestimates: Method CAPM DCF rd+rp Average Estimate 14.2% 13.8 14.0 % 14.0
Atthispoint,considerablejudgmentisrequired.Ifamethodisdeemed tobeinferiorduetothequalityofitsinputs,thenitmightbegiven
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IntegratedCase
263
little weight or evendisregarded. In our example,though, the three methodsproducedrelativelycloseresults,sowedecidedtousethe average,14%,asourestimateforColemanscostofcommonequity. H. Explain in words why new common stock has a higher cost than retainedearnings. Answer: [ShowS1023here.]Thecompanyisraisingmoneyinordertomakean investment.Themoneyhasacost,andthiscostisbasedprimarilyon theinvestorsrequiredrateofreturn,consideringriskandalternative investment opportunities. So, the new investment must provide a returnatleastequaltotheinvestorsopportunitycost. Ifthecompanyraisescapitalbysellingstock,thecompanydoesnt receive all of the money that investors contribute. For example, if investors put up $100,000, and if they expect a 15% return on that $100,000,then$15,000ofprofitsmustbegenerated.Butifflotationcosts are20%($20,000),thenthe company will receive only $80,000 of the $100,000investorscontribute.That$80,000mustthenproducea$15,000 profit,ora$15/$80=18.75%rateofreturnversusa15%returnonequity raisedasretainedearnings. I. (1) What are two approaches that can be used to adjust for flotation costs? Answer:
264
The first approach is to include the flotation costs as part of the
Chapter10:TheCostofCapital
IntegratedCase
projectsupfrontcost.Thisreducestheprojectsestimatedreturn.The second approach is to adjust the cost of capital to include flotation costs.Thisismostcommonlydonebyincorporatingflotationcostsin theDCFmodel. I. (2) Colemanestimatesthatifitissuesnewcommonstock,theflotation costwillbe15%. Colemanincorporatestheflotationcostsintothe DCFapproach.Whatistheestimatedcostofnewlyissuedcommon stock,consideringtheflotationcost? Answer: [ShowS1024andS1025here.] re = = = D 0 ( 1 + g) +g P0 ( 1 F) $ 4 . 19 ( 1 . 05 ) +5.0% $ 50 ( 1 0 . 15 ) $ 4 . 40 +5.0%=15.35%. $ 42 . 50
J.
What is Colemans overall, or weighted average, cost of capital (WACC)?Ignoreflotationcosts.
Answer:
[ShowS1026here.]ColemansWACCis11.1%. CapitalStructure Weights 0.3 0.1 0.6 AT Component Costs 6% 9 14
=
Product 1.8% 0.9 8.4
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265
1.0
WACC = % 11.1
WACC =wdrd(1T)+wprp+wcrs =0.3(10%)(0.6)+0.1(9%)+0.6(14%) =1.8%+0.9%+8.4%=11.1%. K. Answer: WhatfactorsinfluenceColemanscompositeWACC? [ShowS1027here.]Therearefactorsthatthefirmcannotcontroland thosethattheycancontrolthatinfluenceWACC. Factorsthefirmcannotcontrol: Interestrates Taxrates Factorsthefirmcancontrol: Capitalstructurepolicy Dividendpolicy Investmentpolicy L. ShouldthecompanyusethecompositeWACCasthehurdleratefor eachofitsprojects?Explain. Answer: [ShowS1028here.]No.ThecompositeWACCreflectstheriskofan average project undertaken by the firm. Therefore, the WACC only represents the hurdle rate for a typical project with average risk. Differentprojectshavedifferentrisks. TheprojectsWACCshouldbe adjustedtoreflecttheprojectsrisk.
266 IntegratedCase Chapter10:TheCostofCapital
Marketconditions