CHAPTER17CapitalBudgetingfor

theLeveredFirm0ProspectusRecallthattherearethreequestionsincorporatefinance.Thefirstregardswhatlong-terminvestmentsthefirmshouldmake(thecapitalbudgetingquestion).Thesecondregardstheuseofdebt(thecapitalstructurequestion).Thischapterconsidersthenexusofthesequestions.1ChapterOutline17.1AdjustedPresentValueApproach17.2FlowstoEquityApproach17.3WeightedAverageCostofCapitalMethod17.4AComparisonoftheAPV,FTE,andWACCApproaches17.5CapitalBudgetingWhentheDiscountRateMustBeEstimated17.6APVExample17.7BetaandLeverage17.8SummaryandConclusions217.1AdjustedPresentValueApproachAPV=NPV+NPVFThevalueofaprojecttothefirmcanbethoughtofasthevalueoftheprojecttoanunleveredfirm(NPV)plusthepresentvalueofthefinancingsideeffects(NPVF):Therearefoursideeffectsoffinancing:TheTaxSubsidytoDebtTheCostsofIssuingNewSecuritiesTheCostsofFinancialDistressSubsidiestoDebtFinancing3APVExample0 1 2 3 4

–$1,000 $125 $250 $375 $500Theunleveredcostofequityisr0=10%:Theprojectwouldberejectedbyanall-equityfirm:NPV<0.ConsideraprojectofthePearsonCompany,thetimingandsizeoftheincrementalafter-taxcashflowsforanall-equityfirmare:4APVExampleTheprojectwouldberejectedbyanall-equityfirm:NPV<0.CF2CF1F2F1CF01$1251–$56.50

–$1,000$250INPV10CF4CF3F4F31$3751$5005APVExample(continued)Now,imaginethatthefirmfinancestheprojectwith$600ofdebtatrB=8%.Pearson’staxrateis40%,sotheyhaveaninteresttaxshieldworthTCBrB=.40×$600×.08=$19.20eachyear.Thenetpresentvalueoftheprojectunderleverageis:APV=NPV+NPVdebttaxshieldSo,Pearsonshouldaccepttheprojectwithdebt.6APVExample(continued)NotethattherearetwowaystocalculatetheNPVoftheloan.Previously,wecalculatedthePVoftheinteresttaxshields.Now,let’scalculatetheactualNPVoftheloan:Whichisthesameanswerasbefore.APV=NPV+NPVF7TwoWaystoFindtheNPVoftheloan:NPVoftheloan:CF2CF1F2F1CF03–$28.80=1$63.59$600–$628.80INPV8PVoftheinteresttaxshields.

CF1F1CF04$63.59$0INPV8$19.20=.40×$600×.08

$600×.08×(1–.40)817.2FlowstoEquityApproachDiscountthecashflowfromtheprojecttotheequityholdersoftheleveredfirmatthecostofleveredequitycapital,rS.TherearethreestepsintheFTEApproach:StepOne:CalculatetheleveredcashflowsStepTwo:CalculaterS.StepThree:ValuationoftheleveredcashflowsatrS.9StepOne:LeveredCashFlowsforPearsonSincethefirmisusing$600ofdebt,theequityholdersonlyhavetocomeupwith$400oftheinitial$1,000.Thus,CF0=–$400Eachperiod,theequityholdersmustpayinterestexpense.Theafter-taxcostoftheinterestisB×rB×(1–TC)=$600×.08×(1–.40)=$28.800 1 2 3 4–$400 $221.20CF2=$250–

28.80$346.20CF3=$375–

28.80–$128.80CF4=$500–

28.80–

600CF1=$125–

28.80$96.2010StepTwo:CalculaterSforPearsonB=$600whenV=$1,007.09soS=$407.09.P

V=$943.50+$63.59=$1,007.09BSBVTocalculatethedebttoequityratio,,startwith11StepThree:ValuationforPearsonDiscountthecashflowstoequityholdersatrS=11.77%

01234–$400$96.20$221.20$346.20–$128.8012StepThree:ValuationforPearsonCF2CF1CF0$96.20$28.56

–$400$221.20INPV11.77%CF4CF3$346.20–$128.20DiscountthecashflowstoequityholdersatrS=11.77%01234–$400$96.20$221.20$346.20–$128.801317.3WACCMethodforPearsonTofindthevalueoftheproject,discounttheunleveredcashflowsattheweightedaveragecostofcapital.SupposePearson’stargetdebttoequityratiois1.5014ValuationforPearsonusingWACCTofindthevalueoftheproject,discounttheunleveredcashflowsattheweightedaveragecostofcapitalNPV7.58%=$6.6815ValuationforPearsonusingWACCCF2CF1CF0$125$6.68

–$1,000$250INPV7.58%CF4CF3$375$500Discounttheunleveredcashflowsattheweightedaveragecostofcapital01234–$1,000$125$250$375$5001617.4AComparisonoftheAPV,FTE,

andWACCApproachesAllthreeapproachesattemptthesametask:valuationinthepresenceofdebtfinancing.Guidelines:UseWACCorFTEifthefirm’stargetdebt-to-valueratioappliestotheprojectoverthelifeoftheproject.UsetheAPViftheproject’slevelofdebtisknownoverthelifeoftheproject.Intherealworld,theWACCisthemostwidelyusedbyfar.17Summary:APV,FTE,andWACC

APV WACC FTEInitialInvestment All All EquityPortionCashFlows UCF UCF LCFDiscountRates r0 rWACC rSPVoffinancingeffects Yes No NoWhichapproachisbest?UseAPVwhenthelevelofdebtisconstantUseWACCandFTEwhenthedebtratioisconstantWACCisbyfarthemostcommonFTEisareasonablechoiceforahighlyleveredfirm1817.5CapitalBudgetingWhentheDiscountRateMustBeEstimatedAscale-enhancingprojectisonewheretheprojectissimilartothoseoftheexistingfirm.Intherealworld,executiveswouldmaketheassumptionthatthebusinessriskofthenon-scale-enhancingprojectwouldbeaboutequaltothebusinessriskoffirmsalreadyinthebusiness.Noexactformulaexistsforthis.Someexecutivesmightselectadiscountrateslightlyhigherontheassumptionthatthenewprojectissomewhatriskiersinceitisanewentrant.1917.6APVExample:WorldwideTrousers,Inc.isconsideringreplacinga$5millionpieceofequipment.Theinitialexpensewillbedepreciatedstraight-linetozerosalvagevalueover5years;thepretaxsalvagevalueinyear5willbe$500,000.Theprojectwillgeneratepretaxsavingsof$1,500,000peryear,andnotchangetherisklevelofthefirm.Thefirmcanobtaina5-year$3,000,000loanat12.5%topartiallyfinancetheproject.Iftheprojectwerefinancedwithallequity,thecostofcapitalwouldbe18%.Thecorporatetaxrateis34%,andtherisk-freerateis4%.Theprojectwillrequirea$100,000investmentinnetworkingcapital.

CalculatetheAPV.2017.6APVExample:CostThecostoftheprojectisnot$5,000,000.Wemustincludetheroundtripinandoutofnetworkingcapitalandtheafter-taxsalvagevalue.Let’sworkourwaythroughthefourtermsinthisequation:NWCisriskless,sowediscountitatrf.Salvagevalueshouldhavethesameriskastherestofthefirm’sassets,soweuser0.+PV

depreciationtaxshield+PV

interesttaxshieldPV

unleveredprojectAPV=–Cost+2117.6APVExample:PVunleveredprojectisthepresentvalueoftheunleveredcashflowsdiscountedattheunleveredcostofcapital,18%.Turningourattentiontothesecondterm,+PV

depreciationtaxshield+PV

interesttaxshieldPV

unleveredprojectAPV=–$4,873,561.25+PV

unleveredproject2217.6APVExample:PVdepreciationtaxshieldistheisthepresentvalueofthetaxsavingsduetodepreciationdiscountedattheriskfreerate:rf=4%Turningourattentiontothethirdterm,PV

depreciationtaxshield+PV

depreciationtaxshield+PV

interesttaxshield$3,095,899APV=–$4,873,561.25+PV

depreciationtaxshield2317.6APVExample:PVinteresttaxshieldisthepresentvalueofthetaxsavingsduetointerestexpensediscountedatthefirm’sdebtrate:rD=12.5%Turningourattentiontothelastterm,PV

interesttaxshield+$1,513,619+PV

interesttaxshield$3,095,899APV=–$4,873,561.25+2417.6APVExample:AddingitallupSincetheprojecthasapositiveAPV,itlookslikeago.Let’saddthefourtermsinthisequation:APV=

–$4,873,561.25+$3,095,899+$1,513,619+$453,972.46APV=$189,930+PV

depreciationtaxshield+PV

interesttaxshieldPV

unleveredprojectAPV=–Cost+2517.7BetaandLeverageRecallthatanassetbetawouldbeoftheform:2617.7BetaandLeverage:NoCorp.TaxesInaworldwithoutcorporatetaxes,andwithrisklesscorporatedebt,(bDebt=0)itcanbeshownthattherelationshipbetweenthebetaoftheunleveredfirmandthebetaofleveredequityis:Inaworldwithoutcorporatetaxes,andwithriskycorporatedebt,itcanbeshownthattherelationshipbetweenthebetaoftheunleveredfirmandthebetaofleveredequityis:2717.7BetaandLeverage:withCorp.TaxesInaworldwithcorporatetaxes,andrisklessdebt,itcanbeshownthattherelationshipbetweenthebetaoftheunleveredfirmandthebetaofleveredequityis: Since mustbemorethan1foraleveredfirm,itfollowsthatbEquity>bUnleveredfirm.2817.7BetaandLeverage:

withCorp.TaxesIfthebetaofthedebtisnon-zero,then:2917.8SummaryandConclusionsTheAPVformulacanbewrittenas:TheFTEformulacanbewrittenas:TheWACCformulacanbewrittenas3017.8SummaryandConclusionsUsetheWACCorFTEifthefirm'stargetdebttovalueratioappliestotheprojectoveritslife.WACCisthemostcommonlyusedbyfar.FTEhasappealforafirmdeeplyindebt.TheAPVmethodisusedifthelevelofdebtisknownovertheproject’slife.TheAPVmethodisfrequentlyusedforspecialsituationslikeinterestsubsidies,LBOs,andleases.Thebetaoftheequityofthefirmispositivelyrelatedtotheleverageofthefirm.31Example:HamilosWorldwide HamilosWorldwideisconsideringa$5millionexpansionoftheirexistingbusiness.Theinitialexpensewillbedepreciatedstraight-lineover5yearstozerosalvagevalue;thepretaxsalvagevalueinyear5willbe$500,000.Theprojectwillgeneratepretaxgrossearningsof$1,500,000peryear,andnotchangetherisklevelofthefirm.Hamiloscanobtaina5-year12.5%loantopartiallyfinancetheproject.Flotationcostsare1%oftheproceeds.Ifundertaken,thisprojectshouldmaintainatargetD/Eratioof1.50.Iftheprojectwerefinancedwithallequity,thecostofcapitalwouldbe18%.Thecorporatetaxrateis30%,andtherisk-freerateis6%.Theprojectwillrequirea$100,000investmentinnetworkingcapital.32HamilosWorldwideUsingWACCUsingtheWACCmethodology,commentonthedesirabilityofthisproject.

33HamilosWorldwideUsingWACCUsingtheWACCmethodology,commentonthedesirabilityofthisproject.

34HamilosWorldwideUsingAPVUsingtheAPVmethodology,commentonthedesirabilityofthisproject.

Firstsomepreliminaries:Thefirmwantstofinancetheprojectsuchthatthedebt-equityratio=1.5.Thisimpliesadebt-to-valueratioof3/5:

35HamilosWorldwideUsingAPVSo,let’sfind

STEPONE:+PV

depreciationtaxshield+PV

interesttaxshieldPV

unleveredproject=PV

unleveredproject–PV

flotationcostsPV

unleveredprojectandborrow3/5ofthatvalue.36HamilosWorldwideUsingAPVPV

unleveredprojectSt=15UCFt(1+r0)t=PV

depreciation=taxshieldSt=15D×TC(1+rf)t+PV

depreciationtaxshield+PV

interesttaxshieldPV

leveredproject=PV

unleveredproject–PV

flotationcosts37HamilosWorldwideUsingAPVRecallthatthedollaramountofdebtdependsonthePVject+PV

depreciationtaxshield+PV

interesttaxshieldPV

leveredproject=PV

unleveredproject–PV

flotationcostsPV

interesttaxshieldSt=15=TC×rD×(1+rD)t×

PV

unleveredproject35PV

interesttaxshieldSt=15=TC×rD×D(1+rD)tD

=35×PV

unleveredproject38HamilosWorldwideUsingAPV+PV

depreciationtaxshield+PV

interesttaxshieldPV

leveredproject=PV

unleveredproject–PV

flotationcostsD

=35×PV

unleveredprojectWeneedtoborrow

D*suchthat:Ourpre-taxflotationcostsareonepercentofD*

D*

×(1–.01)

=35×PVunleveredprojectprojectD*=10.9935

PVunlevered××0.01×D*

=0.010.9935

PVunleveredproject××39AdigressiononfloatationcostsOhbytheway,flotationcostsaredeductible.Sothepresentvalueoftheafter-taxflotationcostsarePVflotationcosts=0.010.9935

PVunleveredproject××–(1–

TC)×40HamilosWorldwideUsingAPV+PV

depreciationtaxshieldPV

leveredproject=PV

unleveredprojectSt=15UCFt(1+r0)t=St=15D×TC(1+rf)t++PV

interesttaxshieldSt=15+TC×rD×(1+rD)t×

PV

unleveredproject35–PV

flotationcosts0.010.9935

PVunleveredproject××–(1–

TC)×41HamilosWorldwideUsingAPV+PV

depreciationtaxshieldPV

leveredproject=PV

unleveredproject+PV

interesttaxshield–PV

flotationcosts42HamilosWorldwideUsingAPV+PV

depreciationtaxshieldPV

leveredproject=PV

unleveredproject=$3,283,529.57PVleveredprojec