Corporate Finance 第7版 答案Ch017.docx

Corporate Finance 第7版 答案Ch017.docx

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CorporateFinance第7版答案Ch017

Chapter17:

ValuationandCapitalBudgetingfortheLeveredFirm

17.1a.ThemaximumpricethatHertzshouldbewillingtopayforthefleetofcarswithall-equityfunding

isthepricethatmakestheNPVofthetransactionequaltozero.

NPV=-PurchasePrice+PV[（1-TC）（EarningsBeforeTaxesandDepreciation）]+

PV（DepreciationTaxShield）

LetPequalthepurchasepriceofthefleet.

NPV=-P+（1-0.34）（$100,000）A50.10+（0.34）（P/5）A50.10

SettheNPVequaltozero.

0=-P+（1-0.34）（$100,000）A50.10+（0.34）（P/5）A50.10

P=$250,191.93+（P）（0.34/5）A50.10

P=$250,191.93+0.2578P

0.7422P=$250,191.93

P=$337,095

Therefore,themostthatHertzshouldbewillingtopayforthefleetofcarswithall-equityfundingis$337,095.

b.Theadjustedpresentvalue（APV）ofaprojectequalsthenetpresentvalueoftheprojectifitwerefundedcompletelybyequityplusthenetpresentvalueofanyfinancingsideeffects.InHertz’scase,theNPVoffinancingsideeffectsequalstheafter-taxpresentvalueofthecashflowsresultingfromthefirm’sdebt.

APV=NPV（All-Equity）+NPV（FinancingSideEffects）

NPV（All-Equity）

NPV=-PurchasePrice+PV[（1-TC）（EarningsBeforeTaxesandDepreciation）]+

PV（DepreciationTaxShield）

Hertzpaid$325,000forthefleetofcars.Becausethisfleetwillbefullydepreciatedoverfiveyearsusingthestraight-linemethod,annualdepreciationexpenseequals$65,000（=$325,000/5）.

NPV=-$325,000+（1-0.34）（$100,000）A50.10+（0.34）（$65,000）A50.10

=$8,968

NPV（FinancingSideEffects）

Thenetpresentvalueoffinancingsideeffectsequalstheafter-taxpresentvalueofcashflowsresultingfromthefirm’sdebt.

NPV（FinancingSideEffects）=Proceeds–After-TaxPV（InterestPayments）–PV（PrincipalPayments）

Givenaknownlevelofdebt,debtcashflowsshouldbediscountedatthepre-taxcostofdebt（rB）,8%.

NPV（FinancingSideEffects）=$200,000–（1–0.34）（0.08）（$200,000）A50.08–[$200,000/（1.08）5]

=$21,720

APV

APV=NPV（All-Equity）+NPV（FinancingSideEffects）

=$8,968+$21,720

=$30,688

Therefore,ifHertzuses$200,000offive-year,8%debttofundthe$325,000purchase,theAdjustedPresentValue（APV）oftheprojectis$30,688.

17.2Theadjustedpresentvalueofaprojectequalsthenetpresentvalueoftheprojectunderall-equityfinancingplusthenetpresentvalueofanyfinancingsideeffects.InGemini’scase,theNPVoffinancingsideeffectsequalstheafter-taxpresentvalueofthecashflowsresultingfromthefirm’sdebt.

APV=NPV（All-Equity）+NPV（FinancingSideEffects）

NPV（All-Equity）

NPV=-InitialInvestment+PV[（1-TC）（EarningsBeforeTaxesandDepreciation）]+

PV（DepreciationTaxShield）

Sincetheinitialinvestmentof$2.1millionwillbefullydepreciatedoverthreeyearsusingthestraight-linemethod,annualdepreciationexpenseequals$700,000（=$2,100,000/3）.

NPV=-$2,100,000+（1-0.30）（$900,000）A30.18+（0.30）（$700,000）A30.18

=-$273,611

NPV（FinancingSideEffects）

Thenetpresentvalueoffinancingsideeffectsequalstheafter-taxpresentvalueofcashflowsresultingfromthefirm’sdebt.

NPV（FinancingSideEffects）=Proceeds,netofflotationcosts–After-TaxPV（InterestPayments）–PV（PrincipalPayments）+PV（FlotationCostTaxShield）

Givenaknownlevelofdebt,debtcashflowsshouldbediscountedatthepre-taxcostofdebt（rB）,12.5%.Since$21,000inflotationcostswillbeamortizedoverthethree-yearlifeoftheloan,$7,000=（$21,000/3）offlotationcostswillbeexpensedperyear.

NPV（FinancingSideEffects）=（$2,100,000-$21,000）–（1–0.30）（0.125）（$2,100,000）A30.125–

[$2,100,000/（1.125）3]+（0.30）（$7,000）A30.125

=$171,532

APV

APV=NPV（All-Equity）+NPV（FinancingSideEffects）

=-$273,611+$171,532

=-$102,079

Sincetheadjustedpresentvalue（APV）oftheprojectisnegative,Geminishouldnotundertaketheproject.

17.3Theadjustedpresentvalueofaprojectequalsthenetpresentvalueoftheprojectunderall-equityfinancingplusthenetpresentvalueofanyfinancingsideeffects.

AccordingtoModigliani-MillerPropositionIIwithcorporatetaxes:

rS=r0+（B/S）（r0–rB）（1–TC）

wherer0=therequiredreturnontheequityofanunleveredfirm

rS=therequiredreturnontheequityofaleveredfirm

rB=thepre-taxcostofdebt

TC=thecorporatetaxrate

B/S=thefirm’sdebt-to-equityratio

Inthisproblem:

rS=0.18

rB=0.10

TC=0.40

B/S=0.25

SolveforMVP’sunleveredcostofcapital（r0）:

rS=r0+（B/S）（r0–rb）（1–TC）

0.18=r0+（0.25）（r0–0.10）（1–0.40）

r0=0.17

ThecostofMVP’sunleveredequityis17%.

APV=NPV（All-Equity）+NPV（FinancingSideEffects）

NPV（All-Equity）

NPV=PV（UnleveredCashFlows）

=-$15,000,000+$4,000,000/1.17+$8,000,000/（1.17）2+$9,000,000/（1.17）3

=-$117,753

NPV（FinancingSideEffects）

Thenetpresentvalueoffinancingsideeffectsequalstheafter-taxpresentvalueofcashflowsresultingfromthefirm’sdebt.

NPV（FinancingSideEffects）=Proceeds–After-TaxPV（InterestPayments）–PV（Principal

Payments）

Givenaknownlevelofdebt,debtcashflowsshouldbediscountedatthepre-taxcostofdebt（rB）,10%.

NPV（FinancingSideEffects）=$6,000,000–（1–0.40）（0.10）（$6,000,000）/（1.10）–

$2,000,000/（1.10）–（1–0.40）（0.10）（$4,000,000）/（1.10）2–

$2,000,000/（1.10）2–（1–0.40）（0.10）（$2,000,000）/（1.10）3–

$2,000,000/（1.10）3

=$410,518

APV

APV=NPV（All-Equity）+NPV（FinancingSideEffects）

=-$117,753+$410,518

=$292,765

Sincetheadjustedpresentvalue（APV）oftheprojectispositive,MVPshouldproceedwiththeexpansion.

17.4Theadjustedpresentvalueofaprojectequalsthenetpresentvalueoftheprojectunderall-equityfinancingplusthenetpresentvalueofanyfinancingsideeffects.Inthejointventure’scase,theNPVoffinancingsideeffectsequalstheafter-taxpresentvalueofcashflowsresultingfromthefirms’debt.

APV=NPV（All-Equity）+NPV（FinancingSideEffects）

NPV（All-Equity）

NPV=-InitialInvestment+PV[（1–TC）（EarningsBeforeInterest,Taxes,andDepreciation）]+PV（DepreciationTaxShield）

Sincetheinitialinvestmentof$20millionwillbefullydepreciatedoverfiveyearsusingthestraight-linemethod,annualdepreciationexpenseequals$4,000,000（=$20,000,000/5）.

NPV=-$20,000,000+[（1-0.25）（$3,000,000）A200.12]+（0.25）（$4,000,000）A50.12

=$411,024

NPV（FinancingSideEffects）

TheNPVoffinancingsideeffectsequalstheafter-taxpresentvalueofcashflowsresultingfromthefirms’debt.

Givenaknownlevelofdebt,debtcashflowsshouldbediscountedatthepre-taxcostofdebt（rB）,10%.

NPV（FinancingSideEffects）=Proceeds–After-taxPV（InterestPayments）–PV（Principal

Repayments）

=$10,000,000–（1–0.25）（0.05）（$10,000,000）A150.09–

[$10,000,000/（（1.09）15]

=$4,231,861

APV

APV=NPV（All-Equity）+NPV（FinancingSideEffects）

=$411,024+$4,231,861

=$4,642,885

TheAdjustedPresentValue（APV）oftheprojectis$4,642,885.

17.5a.Inordertovalueafirm’sequityusingtheFlow-to-Equityapproach,discountthecashflowsavailabletoequityholdersatthecostofthefirm’sleveredequity（rS）.

Sincethiscashflowwillremainthesameforever,thepresentvalueofcashflowsavailabletothefirm’sequityholdersisaperpetuityof$493,830,discountedat21%.

PV（Flows-to-Equity）=$493,830/0.21

=$2,351,571

ThevalueofMilanoPizzaClub’sequityis$2,351,571.

b.Thevalueofafirmisequaltothesumofthemarketvaluesofitsdebtandequity.

VL=B+S

ThemarketvalueofMilanoPizzaClub’sequity（S）is$2,351,571（seeparta）.

Theproblemstatesthatthefirmhasadebt-to-equityratioof30%,whichcanbewrittenalgebraicallyas:

B/S=0.30

SinceS=$2,351,571:

B/$2,351,571=0.30

B=$705,471

ThemarketvalueofMilanoPizzaClub’sdebtis$705,471,andthevalueofthefirmis$3,057,042（=$705,471+$2,351,571）.

ThevalueofMilanoPizzaClubis$3,057,042.

17.6a.Inordertodeterminethecostofthefirm’sdebt（rB）,solveforthediscountratethatmakesthe

presentvalueofthebond’sfuturecashflowsequaltothebond’scurrentprice.

SinceWWI’sone-year,$1,000parvaluebondscarrya7%coupon,bondholderswillreceiveapaymentof$1,070=[$1,000+（0.07）（$1,000）]inoneyear.

$972.73=$1,070/（1+rB）

rB=0.10

Therefore,thecostofWWI’sdebtis10%.

b.UsetheCapitalAssetPricingModeltofindthereturnonWWI’sunleveredequity（r0）.

AccordingtotheCapitalAssetPricingModel:

r0=rf+βUnlevered（rm–rf）

wherer0=thecostofafirm’sunleveredequity

rf=therisk-freerate

rm=theexpectedreturnonthemarketportfolio

βUnlevered=thefirm’sbetaunderall-equityfinancing

Inthisproblem:

rf=0.08

rm=0.16

βUnlevered=0.9

r0=rf+βUnlevered（rm–rf）

=0.08+0.9（0.16-0.08）

=0.152

ThecostofWWI’sunleveredequityis15.2%.

Next,findthecostofWWI’sleveredequity.

AccordingtoModigliani-MillerPropositionIIwithcorporatetaxes

rS=r0+（B/S）（r0–rB）（1–TC）

wherer0=thecostofafirm’sunleveredequity

rS=thecostofafirm’sleveredequity

rB=thepre-taxcostofdebt

TC=thecorporatetaxrate

B/S=thefirm’stargetdebt-to-equityratio

Inthisproblem:

r0=0.152

rB=0.10

TC=0.34

B/S=0.50

ThecostofWWI’sleveredequityis:

rS=r0+（B/S）（r0–rB）（1–TC）

=0.152+（0.50）（0.152-0.10）（1–0.34）

=0.1692

ThecostofWWI’sleveredequityis