Corporate Finance RWJ版第7版第六章答案.docx
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CorporateFinanceRWJ版第7版第六章答案
Chapter6:
SomeAlternativeInvestmentRules
6.1a.Thepaybackperiodisthetimethatittakesforthecumulativeundiscountedcashinflows
toequaltheinitialinvestment.
ProjectA:
CumulativeUndiscountedCashFlowsYear1=$4,000=$4,000
CumulativeUndiscountedCashFlowsYear2=$4,000+$3,500=$7,500
Paybackperiod=2
ProjectAhasapaybackperiodoftwoyears.
ProjectB:
CumulativeUndiscountedCashFlowsYear1=$2,500=$2,500
CumulativeUndiscountedCashFlowsYear2=$2,500+$1,200=$3,700
CumulativeUndiscountedCashFlowsYear3=$2,500+$1,200+$3,000=$6,700
ProjectB’scumulativeundiscountedcashflowsexceedtheinitialinvestmentof$5,000bytheendofyear3.Manycompaniesanalyzethepaybackperiodinwholeyears.ThepaybackperiodforprojectBis3years.
ProjectBhasapaybackperiodofthreeyears.
Companiescancalculateamoreprecisevalueusingfractionalyears.Tocalculatethefractionalpaybackperiod,findthefractionofyear3’scashflowsthatisneededforthecompanytohavecumulativeundiscountedcashflowsof$5,000.Dividethedifferencebetweentheinitialinvestmentandthecumulativeundiscountedcashflowsasofyear2bytheundiscountedcashflowofyear3.
Paybackperiod=2+($5,000-$3,700)/$3,000
=2.43
SinceprojectAhasashorterpaybackperiodthanprojectBhas,thecompanyshouldchooseprojectA.
b.Discounteachproject’scashflowsat15percent.ChoosetheprojectwiththehighestNPV.
ProjectA=-$7,500+$4,000/(1.15)+$3,500/(1.15)2+$1,500/(1.15)3
=-$388.96
ProjectB=-$5,000+$2,500/(1.15)+$1,200/(1.15)2+$3,000/(1.15)3
=$53.83
ThefirmshouldchooseProjectBsinceithasahigherNPVthanProjectAhas.
6.2a.Findthepaybackperiodfortheproject.Sincethecashinflowsareconstant,
dividetheinitialinvestmentbytheannualcashinflowtodeterminethepaybackperiod.
PaybackPeriod=InitialInvestment/AnnualCashInflow
=$1,000,000/$150,000
=6.67
Thepaybackperiodis6.67years.Sincethepaybackperiodisshorterthanthecutoffperiodoftenyears,theprojectshouldbeaccepted.
b.Findthenumberofyearsneededforthediscountedcashinflowstoequaltheinitialinvestmentof$1million.Applytheannuityformula,discountedat10percent,tofindtheapproximatediscountedpaybackperiod.TheapproximatediscountedpaybackperiodistheyearinwhichthePVoftheinitialinvestmentissurpassed.
Sincethediscountedpaybackperiodwillalwaysbegreaterthantheundiscountedpaybackperiodwhentherearepositivecashinflows,starttheapproximationatyear7.
CumulativeDiscountedCashFlowsYear7=$150,000A70.1=$730,262.82
CumulativeDiscountedCashFlowsYear8=$150,000A80.1=$800,238.93
CumulativeDiscountedCashFlowsYear9=$150,000A90.1=$863,853.57
CumulativeDiscountedCashFlowsYear10=$150,000A100.1=$921,685.07
CumulativeDiscountedCashFlowsYear11=$150,000A110.1=$974,259.15
CumulativeDiscountedCashFlowsYear12=$150,000A120.1=$1,022,053.77
Thecumulativediscountedcashflowsexceedtheinitialinvestmentof$1,000,000bytheendofyear12.Manycompaniesanalyzethepaybackperiodinwholeyears.Thepaybackperiodfortheprojectis12years.
Thediscountedpaybackperiodis12years.
c.Applytheperpetuityformula,discountedat10percent,tocalculatethePVoftheannualcashinflows.
NPV=-$1,000,000+$150,000/0.1
=$500,000
TheNPVoftheprojectis$500,000.
6.3a.Theaverageaccountingreturnistheaverageprojectearningsaftertaxes,dividedbythe
averagebookvalue,oraveragenetinvestment,ofthemachineduringitslife.Thebookvalueofthemachineisthegrossinvestmentminustheaccumulateddepreciation.
AverageBookValue=(BookValue0+BookValue1+BookValue2+BookValue3+BookValue4+BookValue5)/(EconomicLife)
=($16,000+$12,000+$8,000+$4,000+$0)/(5years)
=$8,000
AverageProjectEarnings=$4,500
Dividetheaverageprojectearningsbytheaveragebookvalueofthemachinetocalculatetheaverageaccountingreturn.
AverageAccountingReturn=AverageProjectEarnings/AverageBookValue
=$4,500/$8,000
=0.5625
=56.25%
Theaverageaccountingreturnis56.25%.
b.1.Theaverageaccountingreturnusesaccountingdataratherthannetcashflows.
2.Theaverageaccountingreturnusesanarbitraryfirmstandardasthedecisionrule.Thefirmstandardisarbitrarybecauseitdoesnotnecessarilyrelatetoamarketrateofreturn.
3.Theaverageaccountingreturndoesnotconsiderthetimingofcashflows.Hence,itdoesnotconsiderthetimevalueofmoney.
6.4Determinetheaveragebookvalueoftheinvestment.Thebookvalueisthegrossinvestmentminusaccumulateddepreciation.
Purchase
Year1
Year2
Year3
Year4
Year0
GrossInvestment
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
$2,000,000
Less:
AccumulatedDepreciation
0
400,000
800,000
1,200,000
1,600,000
2,000,000
NetInvestment
$2,000,000
$1,600,000
$1,200,000
$800,000
$400,000
$0
AverageBookValue=($2,000,000+$1,600,000+$1,200,000+$800,000
+$400,000+$0)/(6)
=$1,000,000
Next,calculateaverageannualnetincome.
NetIncomeYear1=$100,000
NetIncomeYear2=$100,000(1.07)=$107,000
NetIncomeYear3=$100,000(1.07)2=$114,490
NetIncomeYear4=$100,000(1.07)3=$122,504
NetIncomeYear5=$100,000(1.07)4=$131,080
AverageNetIncome=($100,000+$107,000+$114,490+$122,504+$131,080)/5
=$115,015
Theaverageaccountingreturnistheaveragenetincomedividedbytheaveragebookvalue.
AverageAccountingReturn=AverageNetIncome/AverageBookValue
=$115,015/$1,000,000
=0.115
=11.5%
Sincethemachine’saverageaccountingreturn,11.5%,isbelowthecompany’scutoffof20%,themachineshouldnotbepurchased.
6.5Firstdeterminetheaveragebookvalueoftheproject.Thebookvalueisthegrossinvestmentminusaccumulateddepreciation.
PurchaseDate
Year1
Year2
Year3
GrossInvestment
$8,000
$8,000
$8,000
$8,000
Less:
AccumulatedDepreciation
0
4,000
6,500
8,000
NetInvestment
$8,000
$4,000
$1,500
$0
AverageBookValue=($8,000+$4,000+$1,500+$0)/(4years)
=$3,375
Remembertousetheafter-taxaveragenetincomewhencalculatingtheaverageaccountingreturn.
AverageAfter-taxNetIncome=(1–Tc)AnnualPre-taxNetIncome
=(1–0.25)$2,000
=$1,500
Theaverageaccountingreturnistheaverageafter-taxnetincomedividedbytheaveragebookvalue.
AverageAccountingReturn=$1,500/$3,375
=0.44
=44%
Theaverageaccountingreturnofthemachineis44%.
6.6TheinternalrateofreturnisthediscountrateatwhichtheNPVoftheproject’scashflowsequalszero.Settheproject’scashflows,discountedattheinternalrateofreturn(IRR),equaltozero.SolvefortheIRR.
IRR(ProjectA)=C0+C1/(1+IRR)+C2/(1+IRR)2
0=-$3,000+$2,500/(1+IRR)+$1,000/(1+IRR)2
IRR=0.1289
IRR(ProjectB)=C0+C1/(1+IRR)+C2/(1+IRR)2
0=-$6,000+$5,000/(1+IRR)+$1,000/(1+IRR)2
IRR=0.1289
NotethatsinceProjectB’scashflowsaretwotimesthoseofProjectA,theIRR’sofbothprojectsarethesame.
TheIRRofbothProjectAandProjectBis12.89%.
6.7a.TheinternalrateofreturnisthediscountrateatwhichtheNPVoftheproject’scash
flowsequalzero.Settheproject’scashflows,discountedattheinternalrateofreturn(IRR),equaltozero.SolvefortheIRR.
IRR=C0+C1/(1+IRR)+C2/(1+IRR)2+C3/(1+IRR)3
0=-$8,000+$4,000/(1+IRR)+$3,000/(1+IRR)2+$2,000/(1+IRR)3
IRR=0.0693
TheIRRis6.93%.
b.No.Aninvesting-typeprojectisonewithanegativeinitialcashoutflowandpositivefuturecashinflows.OneacceptsaprojectwhentheIRRisgreaterthanthediscountrate.Similarly,onerejectstheprojectwhentheIRRislessthanthediscountrate.TheprojectshouldnotbeacceptedbecausetheIRR(6.93%)islessthanthediscountrate(8%).
6.8Settheproject’scashflows,discountedattheinternalrateofreturn(IRR),equaltozero.SolvefortheIRR.
IRR(ProjectA)=C0+C1/(1+IRR)+C2/(1+IRR)2+C3/(1+IRR)3
0=-$2,000+$2,000/(1+IRR)+$8,000/(1+IRR)2+$8,000/(1+IRR)3
IRR=1.88
IRR(ProjectB)=C0+C1/(1+IRR)+C2/(1+IRR)2+C3/(1+IRR)3
0=-$1,500+$500/(1+IRR)+$1,000/(1+IRR)2+$1,500/(1+IRR)3
IRR=0.362
TheIRRforProjectAis188%andtheIRRforProjectBis36.2%.
6.9a.Settheproject’scashflows,discountedattheinternalrateofreturn(IRR),equaltozero.
SolvefortheIRR.
IRR=C0+C1/(1+IRR)+C2/(1+IRR)2+C3/(1+IRR)3+C4/(1+IRR)4
0=$5,000-$2,500/(1+IRR)-$2,000/(1+IRR)2-$1,000/(1+IRR)3
-$1,000/(1+IRR)4
IRR=0.1399
TheIRRis13.99%.
b.Thisproblemdiffersfrompreviousonesbecausetheinitialcashflowispositiveandallfuturecashflowsarenegative.Inotherwords,thisisafinancing-typeprojectwhilepreviousprojectswereinvesting-typeprojects.Forfinancingsituations,accepttheprojectwhentheIRRislessthanthediscountrate.RejecttheprojectwhentheIRRisgreaterthanthediscountrate.
IRR=13.99%
DiscountRate=10%
IRR>DiscountRate
RejecttheofferwhenthediscountrateislessthantheIRR.
c.IRR=13.99%
DiscountRate=20%
IRR AccepttheofferwhenthediscountrateisgreaterthantheIRR. d.CalculatetheNPVwhenthediscountrateis10percent. NPV=$5,000-$2,500/(1.1)-
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