Chapter Seventeen Capital Budgeting for the Levered Firm.docx

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