Corporate Finance RWJ版第7版第六章答案.docx

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）-