Chapter Seventeen Capital Budgeting for the Levered Firm.docx
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Chapter Seventeen Capital Budgeting for the Levered Firm.docx
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ChapterSeventeenCapitalBudgetingfortheLeveredFirm
ChapterSeventeenCapitalBudgetingfortheLeveredFirm
CorporateFinanceRoss?
?
Westerfield?
?
Jaffe
SixthEdition
17
ChapterSeventeen
CapitalBudgetingfortheLeveredFirm
Preparedby
GadyJacoby
UniversityofManitoba
and
SebouhAintablian
AmericanUniversityofBeirut
Prospectus
Recallthattherearethreequestionsincorporatefinance.
Thefirstregardswhatlong-terminvestmentsthefirmshouldmake(thecapitalbudgetingquestion).
Thesecondregardstheuseofdebt(thecapitalstructurequestion).
Thischapteristhenexusofthesequestions.
ChapterOutline
17.1AdjustedPresentValueApproach
17.2FlowstoEquityApproach
17.3WeightedAverageCostofCapitalMethod
17.4AComparisonoftheAPV,FTE,andWACCApproaches
17.5CapitalBudgetingforProjectsthatareNotScale-Enhancing
17.6APVExample
17.7BetaandLeverage
17.8SummaryandConclusions
17.1AdjustedPresentValueApproach
Thevalueofaprojecttothefirmcanbethoughtofasthevalueoftheprojecttoanunleveredfirm(NPV)plusthepresentvalueofthefinancingsideeffects(NPVF):
Therearefoursideeffectsoffinancing:
TheTaxSubsidytoDebt
TheCostsofIssuingNewSecurities
TheCostsofFinancialDistress
SubsidiestoDebtFinancing
APVExample
ConsideraprojectofthePearsonCompany,thetimingandsizeoftheincrementalafter-taxcashflowsforanall-equityfirmare:
01234
-$1,000$125$250$375$500
Theunleveredcostofequityisr0=10%:
Theprojectwouldberejectedbyanall-equityfirm:
NPV<0.
APVExample(continued)
Now,imaginethatthefirmfinancestheprojectwith$600ofdebtatrB=8%.
Pearson’staxrateis40%,sotheyhaveaninteresttaxshieldworthTCBrB=.40×$600×.08=$19.20eachyear.
Thenetpresentvalueoftheprojectunderleverageis:
So,Pearsonshouldaccepttheprojectwithdebt.
APVExample(continued)
NotethattherearetwowaystocalculatetheNPVoftheloan.Previously,wecalculatedthePVoftheinteresttaxshields.Now,let’scalculatetheactualNPVoftheloan:
Whichisthesameanswerasbefore.
17.2FlowstoEquityApproach
Discountthecashflowfromtheprojecttotheequityholdersoftheleveredfirmatthecostofleveredequitycapital,rS.
TherearethreestepsintheFTEApproach:
StepOne:
Calculatetheleveredcashflows
StepTwo:
CalculaterS.
StepThree:
ValuationoftheleveredcashflowsatrS.
StepOne:
LeveredCashFlowsforPearson
Sincethefirmisusing$600ofdebt,theequityholdersonlyhavetocomeupwith$400oftheinitial$1,000.
Thus,CF0=-$400
Eachperiod,theequityholdersmustpayinterestexpense.Theafter-taxcostoftheinterestisB×rB×(1-TC)=$600×.08×(1-.40)=$28.80
01234
-$400
$221.20
CF2=$250-28.80
$346.20
CF3=$375-28.80
-$128.80
CF4=$500-28.80-600
CF1=$125-28.80
$96.20
StepTwo:
CalculaterSforPearson
Tocalculatethedebt-to-equityratio,B/S,startwiththedebttovalueratio.Notethatthevalueoftheprojectis
B=$600whenV=$1,007.09soS=$407.09.
StepThree:
ValuationforPearson
DiscountthecashflowstoequityholdersatrS=11.77%
01234
-$400$96.20$221.20$346.20-$128.80
17.3WACCMethodforPearson
Tofindthevalueoftheproject,discounttheunleveredcashflowsattheweightedaveragecostofcapital.
SupposePearsonInc.targetdebttoequityratiois1.50.
ValuationforPearsonusingWACC
Tofindthevalueoftheproject,discounttheunleveredcashflowsattheweightedaveragecostofcapital
17.4AComparisonoftheAPV,FTE,andWACCApproaches
Allthreeapproachesattemptthesametask:
valuationinthepresenceofdebtfinancing.
Guidelines:
UseWACCorFTEifthefirm’stargetdebt-to-valueratioappliestotheprojectoverthelifeoftheproject.
UsetheAPViftheproject’slevelofdebtisknownoverthelifeoftheproject.
Intherealworld,theWACCisthemostwidelyusedapproachbyfar.
Summary:
APV,FTE,andWACC
APVWACCFTE
InitialInvestmentAllAllEquityPortion
CashFlowsUCFUCFLCF
DiscountRatesr0rWACCrS
PVoffinancingeffectsYesNoNo
Whichapproachisbest?
UseAPVwhenthelevelofdebtisconstant
UseWACCandFTEwhenthedebtratioisconstant
Ascale-enhancingprojectisonewheretheprojectissimilartothoseoftheexistingfirm.
Intherealworld,executiveswouldmaketheassumptionthatthebusinessriskofthenon-scale-enhancingprojectwouldbeaboutequaltothebusinessriskoffirmsalreadyinthebusiness.
Noexactformulaexistsforthis.Someexecutivesmightselectadiscountrateslightlyhigherontheassumptionthatthenewprojectissomewhatriskiersinceitisanewentrant.
17.5CapitalBudgetingforProjectsthat
areNotScale-Enhancing
17.5CapitalBudgetingforProjectsthatareNotScale-Enhancing:
Anexample
World-WideEnterprises(WWE)isplanningtoenterintoanewlineofbusiness(widgetindustry)
AmericanWidgets(AW)isafirminthewidgetindustry.
WWEhasaD/Eof1/3,AWhasaD/Eof2/3.
BorrowingrateforWWEis10%
BorrowingrateforAWis8%
Given:
Marketriskpremium=8.5%,Rf=8%,Tc=40%
WhatistheappropriatediscountrateforWWEtouseforitswidgetventure?
17.5CapitalBudgetingforProjectsthatareNotScale-Enhancing:
Anexample
Afourstepproceduretocalculatediscountrates:
DeterminingAW’scostofEquityCapital(rs)
DeterminingAW’sHypotheticalAll-EquityCostofCapital.(r0)
DeterminingrsforWWE’sWidgetVenture
DeterminingrWACCforWWE’sWidgetVenture.
STEP1:
DeterminingAW’scostofEquityCapital(rs)
STEP2:
DeterminingAW’sHypotheticalAll-
EquityCostofCapital.(r0)
STEP3:
DeterminingrsforWWE’sWidgetVenture
AssumingthatthebusinessriskofWWEandAW
arethesame,
NOTE:
rs(WWE)<rs(AW)becauseD/E(WWE)<D/E(AW)
STEP4:
DeterminingrWACCforWWE’sWidget
Venture.
17.6APVExample:
WorldwideTrousers,Inc.isconsideringa$5millionexpansionoftheirexistingbusiness.
Theinitialexpensewillbedepreciatedstraight-lineoverfiveyearstozerosalvagevalue
Thepretaxsalvagevalueinyear5willbe$500,000.
Theprojectwillgeneratepretaxearningsof$1,500,000peryear,andnotchangetherisklevelofthefirm.
Thefirmcanobtainafive-year$3,000,000loanat12.5%topartiallyfinancetheproject.
Iftheprojectwerefinancedwithallequity,thecostofcapitalwouldbe18%.Thecorporatetaxrateis34%,andtherisk-freerateis4%.
Theprojectwillrequirea$100,000investmentinnetworkingcapital.?
CalculatetheAPV.
17.6APVExample:
Cost
Thecostoftheprojectisnot$5,000,000.
Wemustincludetheroundtripinandoutofnetworkingcapitalandtheafter-taxsalvagevalue.
Let’sworkourwaythroughthefourtermsinthisequation:
NWCisriskless,sowediscountitatrf.Salvagevalueshouldhavethesameriskastherestofthefirm’sassets,soweuser0.
17.6APVExample:
PVunleveredproject
ThePVunleveredprojectisthepresentvalueoftheunleveredcashflowsdiscountedattheunleveredcostofcapital,18%.
Turningourattentiontothesecondterm,
17.6APVExample:
PVdepreciationtaxshield
ThePVdepreciationtaxshieldisthepresentvalueofthetaxsavingsduetodepreciationdiscountedattheriskfreerate,atrf=4%
Turningourattentiontothethirdterm,
17.6APVExample:
PVinteresttaxshield
ThePVinteresttaxshieldisthepresentvalueofthetaxsavingsduetointerestexpensediscountedatthefirmsdebtrate,atrD=12.5%
Turningourattentiontothelastterm,
17.6APVExample:
Addingitallup
SincetheprojecthasapositiveAPV,itlookslikeago.
Let’saddthefourtermsinthisequation:
17.7BetaandLeverage
Recallthatanassetbetawouldbeoftheform:
17.7BetaandLeverage:
NoCorp.Taxes
Inaworldwithoutcorporatetaxes,andwithrisklesscorporatedebt,itcanbeshownthattherelationshipbetweenthebetaoftheunleveredfirmandthebetaofleveredequityis:
Inaworldwithoutcorporatetaxes,andwithriskycorporatedebt,itcanbeshownthattherelationshipbetweenthebetaoftheunleveredfirmandthebetaofleveredequityis:
17.7BetaandLeverage:
withCorp.Taxes
Inaworldwithcorporatetaxes,andrisklessdebt,itcanbeshownthattherelationshipbetweenthebetaoftheunleveredfirmandthebetaofleveredequityis:
Sincemustbemorethan1fora
leveredfirm,itfollowsthat
17.7BetaandLeverage:
withCorp.Taxes
Ifthebetaofthedebtisnon-zero,then:
17.8SummaryandConclusions
TheAPVformulacanbewrittenas:
TheFTEformulacanbewrittenas:
TheWACCformulacanbewrittenas
17.8SummaryandConclusions(cont.)
UsetheWACCorFTEifthefirm'stargetdebttovalueratioappliestotheprojectoveritslife.
5TheAPVmethodisusedifthelevelofdebtisknownovertheproject’slife.
6Thebetaoftheequityofthefirmispositivelyrelatedtotheleverageofthefirm.
Appendix17-A:
TheAPVapproachtoValuingLeveragedBuyouts(LBOs)
AnLBOistheacquisitionbyasmallgroupofinvestorsofapublicorprivatecompanyfinancedprimarilywithdebt.
InanLBO,theequityinvestorsareexpectedtopayoffoutstandingprincipalaccordingtoaspecifictimetable.
Theownersknowthatthefirm’sdebt-to-equityratiowillfallandcanforecastthedollaramountofdebtneededtofinancefutureoperations.
Underthesecircumstances,theAPVapproachismorepracticalthantheWACCapproachbecausethecapitalstructureischanging.
TheAPVApproachtoValuingLBOs:
TheRJRNabiscoBuyout
In1988,theCEOofthefirmannouncedabidof$75persharetotakethefirmprivateinamanagementbuyout.
Anotherbidof
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