RW7eCh14.docx

RW7eCh14.docx

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RW7eCh14

CHAPTER14

COSTOFCAPITAL

LearningObjectives

LO1Howtodetermineafirm’scostofequitycapital.

LO2Howtodetermineafirm’scostofdebt.

LO3Howtodetermineafirm’soverallcostofcapital.

LO4Howtocorrectlyincludeflotationcostsincapitalbudgetingprojects.

LO5Someofthepitfallsassociatedwithafirm’soverallcostofcapitalandwhattodoaboutthem.

AnswerstoConceptsReviewandCriticalThinkingQuestions

1.（LO3）Itistheminimumrateofreturnthefirmmustearnoverallonitsexistingassets.Ifitearnsmorethanthis,valueiscreated.

2.（LO3）Bookvaluesfordebtarelikelytobemuchclosertomarketvaluesthanareequitybookvalues.

3.（LO5）No.Thecostofcapitaldependsontheriskoftheproject,notthesourceofthemoney.

4.（LO3）Interestexpenseistax-deductible.Thereisnodifferencebetweenpretaxandaftertaxequitycosts.

5.（LO1）TheprimaryadvantageoftheDCFmodelisitssimplicity.Themethodisdisadvantagedinthat

（1）themodelisapplicableonlytofirmsthatactuallypaydividends;manydonot;

（2）evenifafirmdoespaydividends,theDCFmodelrequiresaconstantdividendgrowthrateforever;（3）theestimatedcostofequityfromthismethodisverysensitivetochangesing,whichisaveryuncertainparameter;and（4）themodeldoesnotexplicitlyconsiderrisk,althoughriskisimplicitlyconsideredtotheextentthatthemarkethasimpoundedtherelevantriskofthestockintoitsmarketprice.Whilethesharepriceandmostrecentdividendcanbeobservedinthemarket,thedividendgrowthratemustbeestimated.Twocommonmethodsofestimatinggaretouseanalysts’earningsandpayoutforecastsortodeterminesomeappropriateaveragehistoricalgfromthefirm’savailabledata.

6.（LO1）TwoprimaryadvantagesoftheSMLapproacharethatthemodelexplicitlyincorporatestherelevantriskofthestockandthemethodismorewidelyapplicablethanisthedividenddiscountmodelmodel,sincetheSMLdoesn’tmakeanyassumptionsaboutthefirm’sdividends.TheprimarydisadvantagesoftheSMLmethodare

（1）threeparameters（therisk-freerate,theexpectedreturnonthemarket,andbeta）mustbeestimated,and

（2）themethodessentiallyuseshistoricalinformationtoestimatetheseparameters.Therisk-freerateisusuallyestimatedtobetheyieldonveryshortmaturityT-billsandis,hence,observable;themarketriskpremiumisusuallyestimatedfromhistoricalriskpremiumsand,hence,isnotobservable.Thestockbeta,whichisunobservable,isusuallyestimatedeitherbydeterminingsomeaveragehistoricalbetafromthefirmandthemarket’sreturndata,orbyusingbetaestimatesprovidedbyanalystsandinvestmentfirms.

7.（LO2）Theappropriateaftertaxcostofdebttothecompanyistheinterestrateitwouldhavetopayifitweretoissuenewdebttoday.Hence,iftheYTMonoutstandingbondsofthecompanyisobserved,thecompanyhasanaccurateestimateofitscostofdebt.Ifthedebtisprivately-placed,thefirmcouldstillestimateitscostofdebtby

（1）lookingatthecostofdebtforsimilarfirmsinsimilarriskclasses,

（2）lookingattheaveragedebtcostforfirmswiththesamecreditrating（assumingthefirm’sprivatedebtisrated）,or（3）consultinganalystsandinvestmentbankers.Evenifthedebtispubliclytraded,anadditionalcomplicationiswhenthefirmhasmorethanoneissueoutstanding;theseissuesrarelyhavethesameyieldbecausenotwoissuesareevercompletelyhomogeneous.

8.（LO5）

a.Thisonlyconsidersthedividendyieldcomponentoftherequiredreturnonequity.

b.Thisisthecurrentyieldonly,notthepromisedyieldtomaturity.Inaddition,itisbasedonthebookvalueoftheliability,anditignorestaxes.

c.Equityisinherentlymoreriskythandebt（except,perhaps,intheunusualcasewhereafirm’sassetshaveanegativebeta）.Forthisreason,thecostofequityexceedsthecostofdebt.Iftaxesareconsideredinthiscase,itcanbeseenthatatreasonabletaxrates,thecostofequitydoesexceedthecostofdebt.

9.（LO5）RSup=.12+.75（.08）=.1800or18.00%

Bothshouldproceed.Theappropriatediscountratedoesnotdependonwhichcompanyisinvesting;itdependsontheriskoftheproject.SinceSuperiorisinthebusiness,itisclosertoapureplay.Therefore,itscostofcapitalshouldbeused.Withan18%costofcapital,theprojecthasanNPVof$1millionregardlessofwhotakesit.

10.（LO5）Ifthedifferentoperatingdivisionswereinmuchdifferentriskclasses,thenseparatecostofcapitalfiguresshouldbeusedforthedifferentdivisions;theuseofasingle,overallcostofcapitalwouldbeinappropriate.Ifthesinglehurdleratewereused,riskierdivisionswouldtendtoreceivemorefundsforinvestmentprojects,sincetheirreturnwouldexceedthehurdleratedespitethefactthattheymayactuallyplotbelowtheSMLand,hence,beunprofitableprojectsonarisk-adjustedbasis.Thetypicalproblemencounteredinestimatingthecostofcapitalforadivisionisthatitrarelyhasitsownsecuritiestradedonthemarket,soitisdifficulttoobservethemarket’svaluationoftheriskofthedivision.Twotypicalwaysaroundthisaretouseapureplayproxyforthedivision,ortousesubjectiveadjustmentsoftheoverallfirmhurdleratebasedontheperceivedriskofthedivision.

SolutionstoQuestionsandProblems

NOTE:

Allendofchapterproblemsweresolvedusingaspreadsheet.Manyproblemsrequiremultiplesteps.Duetospaceandreadabilityconstraints,whentheseintermediatestepsareincludedinthissolutionsmanual,roundingmayappeartohaveoccurred.However,thefinalanswerforeachproblemisfoundwithoutroundingduringanystepintheproblem.

Basic

1.（LO1）Withtheinformationgiven,wecanfindthecostofequityusingthedividendgrowthmodel.Usingthismodel,thecostofequityis:

RE=[$2.40（1.055）/$52]+.055=.1037or10.37%

2.（LO1）HerewehaveinformationtocalculatethecostofequityusingtheCAPM.Thecostofequityis:

RE=.053+1.05（.12–.053）=.1234or12.34%

3.（LO1）WehavetheinformationavailabletocalculatethecostofequityusingtheCAPMandthedividendgrowthmodel.UsingtheCAPM,wefind:

RE=.05+0.85（.08）=.1180or11.80%

Andusingthedividendgrowthmodel,thecostofequityis

RE=[$1.60（1.06）/$37]+.06=.1058or10.58%

Bothestimatesofthecostofequityseemreasonable.Ifwerememberthehistoricalreturnonlargecapitalizationstocks,theestimatefromtheCAPMmodelisabouttwopercenthigherthanaverage,andtheestimatefromthedividendgrowthmodelisaboutonepercenthigherthanthehistoricalaverage,sowecannotdefinitivelysayoneoftheestimatesisincorrect.Giventhis,wewillusetheaverageofthetwo,so:

RE=（.1180+.1058）/2=.1119or11.19%

4.（LO1）Tousethedividendgrowthmodel,wefirstneedtofindthegrowthrateindividends.So,theincreaseindividendseachyearwas:

g1=（$1.12–1.05）/$1.05=.0667or6.67%

g2=（$1.19–1.12）/$1.12=.0625or6.25%

g3=（$1.30–1.19）/$1.19=.0924or9.24%

g4=（$1.43–1.30）/$1.30=.1000or10.00%

So,theaveragearithmeticgrowthrateindividendswas:

g=（.0667+.0625+.0924+.1000）/4=.0804or8.04%

Usingthisgrowthrateinthedividendgrowthmodel,wefindthecostofequityis:

RE=[$1.43（1.0804）/$45.00]+.0804=.1147or11.47%

Calculatingthegeometricgrowthrateindividends,wefind:

$1.43=$1.05（1+g）4

g=.0803or8.03%

Thecostofequityusingthegeometricdividendgrowthrateis:

RE=[$1.43（1.0803）/$45.00]+.0803=.1146or11.46%

5.（LO1）Thecostofpreferredstockisthedividendpaymentdividedbytheprice,so:

RP=$6/$96=.0625or6.25%

6.（LO2）ThepretaxcostofdebtistheYTMofthecompany’sbonds,so:

P0=$1,070=$35（PVIFAR%,30）+$1,000（PVIFR%,30）

R=3.137%

YTM=2×3.137%=6.27%

Andtheaftertaxcostofdebtis:

RD=.0627（1–.35）=.0408or4.08%

7.（LO2）

a.ThepretaxcostofdebtistheYTMofthecompany’sbonds,so:

P0=$950=$40（PVIFAR%,46）+$1,000（PVIFR%,46）

R=4.249%

YTM=2×4.249%=8.50%

b.Theaftertaxcostofdebtis:

RD=.0850（1–.35）=.0552or5.52%

c.Theafter-taxrateismorerelevantbecausethatistheactualcosttothecompany.

8.（LO2）Thebookvalueofdebtisthetotalparvalueofalloutstandingdebt,so:

BVD=$80,000,000+35,000,000=$115,000,000

Tofindthemarketvalueofdebt,wefindthepriceofthebondsandmultiplybythenumberofbonds.Alternatively,wecanmultiplythepricequoteofthebondtimestheparvalueofthebonds.Doingso,wefind:

MVD=.95（$80,000,000）+.61（$35,000,000）

MVD=$76,000,000+21,350,000

MVD=$97,350,000

TheYTMofthezerocouponbondsis:

PZ=$610=$1,000（PVIFR%,14）

R=3.594%

YTM=2×3.594%=7.19%

So,theaftertaxcostofthezerocouponbondsis:

RZ=.0719（1–.35）=.0467or4.67%

Theaftertaxcostofdebtforthecompanyistheweightedaverageoftheaftertaxcostofdebtforalloutstandingbondissues.Weneedtousethemarketvalueweightsofthebonds.Thetotalaftertaxcostofdebtforthecompanyis:

RD=.0552（$76/$97.35）+.0467（$21.35/$97.35）=.0534or5.34%

9.（LO3）

a.UsingtheequationtocalculatetheWACC,wefind:

WACC=.60（.14）+.05（.06）+.35（.08）（1–.35）=.1052or10.52%

b.Sinceinterestistaxdeductibleanddividendsarenot,wemustlookattheafter-taxcostofdebt,whichis:

.08（1–.35）=.0520or5.20%

Hence,onanafter-taxbasis,debtischeaperthanthepreferredstock.

10.（LO3）Hereweneedtousethedebt-equityratiotocalculatetheWACC.Doingso,wefind:

WACC=.15（1/1.65）+.09（.65/1.65）（1–.35）=.1140or11.40%

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