Corporate Finance 第7版 答案Ch004Word格式文档下载.docx

Corporate Finance 第7版 答案Ch004Word格式文档下载.docx

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PV（C10）=C10/（1+r）10

=$2,000/（1.08）10

=$926.39

Sincethepresentvalueofthecashflowoccurringtodayishigherthanthepresentvalueofthecashflowoccurringinyear10,youshouldtakethe$1,000now.

4.4Sincethebondhasnointerimcouponpayments,itspresentvalueissimplythepresentvalueofthe$1,000thatwillbereceivedin25years.Notethatthepriceofabondisthepresentvalueofitscashflows.

P0=PV（C25）

=C25/（1+r）25

=$1,000/（1.10）25

=$92.30

Thepriceofthebondis$92.30.

4.5Thefuturevalue,FV,ofthefirm’sinvestmentmustequalthe$1.5millionpensionliability.

FV=C0（1+r）27

Tosolvefortheinitialinvestment,C0,discountthefuturepensionliability（$1,500,000）back27yearsateightpercent,（1.08）27.

$1,500,000/（1.08）27=C0

=$187,780.23

Thefirmmustinvest$187,708.23todaytobeabletomakethe$1.5millionpayment.

4.6Thedecisioninvolvescomparingthepresentvalue,PV,ofeachoption.ChoosetheoptionwiththehighestPV.

a.Atadiscountrateofzero,thefuturevalueandpresentvalueofacashflowarealwaysthesame.ThereisnoneedtodiscountthetwochoicestocalculatethePV.

PV（Alternative1）=$10,000,000

PV（Alternative2）=$20,000,000

ChooseAlternative2sinceitsPV,$20,000,000,isgreaterthanthatofAlternative1,$10,000,000.

b.Discountthecashflowsat10percent.DiscountAlternative1backoneyearandAlternative2,fiveyears.

PV（Alternative1）=C/（1+r）

=$10,000,000/（1.10）1

=$9,090,909.10

PV（Alternative2）=$20,000,000/（1.10）5

=$12,418,426.46

ChooseAlternative2sinceitsPV,$12,418,426.46,isgreaterthanthatofAlternative1,$9,090,909.10.

c.Discountthecashflowsat20percent.DiscountAlternative1backoneyearandAlternative2,fiveyears.

=$10,000,000/（1.20）1

=$8,333,333.33

PV（Alternative2）=$20,000,000/（1.20）5

=$8,037,551.44

ChooseAlternative1sinceitsPV,$8,333,333.33,isgreaterthanthatofAlternative2,$8,037,551.44.

d.YouareindifferentwhenthePVsofthetwoalternativesareequal.

Alternative1,discountedatr=Alternative2,discountedatr

$10,000,000/（1+r）1=$20,000,000/（1+r）5

Solveforthediscountrate,r,atwhichthetwoalternativesareequallyattractive.

[1/（1+r）1]（1+r）5=$20,000,000/$10,000,000

（1+r）4=2

1+r=1.18921

r=0.18921=18.921%

Thetwoalternativesareequallyattractivewhendiscountedat18.921percent.

4.7Thedecisioninvolvescomparingthepresentvalue,PV,ofeachoffer.ChoosetheofferwiththehighestPV.

SincetheSmiths’paymentoccursimmediately,itspresentvaluedoesnotneedtobeadjusted.

PV（Smith）=$115,000

TheJoneses’offeroccursthreeyearsfromtoday.Therefore,thepaymentmustbediscountedbackthreeperiodsat10percent.

PV（Jones）=C3/（1+r）3

=$150,000/（1.10）3

=$112,697.22

SincethePVoftheJoneses’offer,$112,697.22,islessthantheSmiths’offer,$115,000,youshouldchoosetheSmiths’offer.

4.8a.Sincethebondhasnointerimcouponpayments,itspresentvalueissimplythepresent

valueofthe$1,000thatwillbereceivedin20years.Notethatthepriceofthebondisthispresentvalue.

P0=PV（C20）

=C20/（1+r）20

=$1,000/（1.08）20

=$214.55

Thecurrentpriceofthebondis$214.55.

b.Tofindthebond’sprice10yearsfromtoday,findthefuturevalueofthecurrentprice.

P10=FV10

=C0（1+r）10

=$214.55（1.08）10

=$463.20

Thebond’sprice10yearsfromtodaywillbe$463.20.

c.Tofindthebond’sprice15yearsfromtoday,findthefuturevalueofthecurrentprice.

P15=FV15

=C0（1+r）15

=$214.55（1.08）15

=$680.59

Thebond’sprice15yearsfromtodaywillbe$680.59.

4.9AnnWoodhousewouldbewillingtopaythepresentvalueofitsresalevalue.

PV=$5,000,000/（1.12）10

=$1,609,866.18

Themostshewouldbewillingtopayforthepropertyis$1,609,866.18.

4.10a.Comparethecostoftheinvestmenttothepresentvalueofthecashinflows.Youshould

maketheinvestmentonlyifthepresentvalueofthecashinflowsisgreaterthanthecostoftheinvestment.Sincetheinvestmentoccurstoday（year0）,itdoesnotneedtobediscounted.

PV（Investment）=$900,000

PV（CashInflows）=$120,000/（1.12）+$250,000/（1.12）2+$800,000/（1.12）3

=$875,865.52

SincethePVofthecashinflows,$875,865.52,islessthanthecostoftheinvestment,$900,000,youshouldnotmaketheinvestment.

b.Thenetpresentvalue,NPV,isthepresentvalueofthecashinflowsminusthecostoftheinvestment.

NPV=PV（CashInflows）–CostofInvestment

=$875,865.52–$900,000

=-$24,134.48

TheNPVis-$24,134.48.

c.CalculatethePVofthecashinflows,discountedat11percent,minusthecostoftheinvestment.IftheNPVispositive,youshouldinvest.IftheNPVisnegative,youshouldnotinvest.

=$120,000/（1.11）+$250,000/（1.11）2+$800,000/（1.11）3–$900,000

=-$4,033.18

SincetheNPVisstillnegative,-$4,033.18,youshouldnotmaketheinvestment.

4.11CalculatetheNPVofthemachine.PurchasethemachineifithasapositiveNPV.DonotpurchasethemachineifithasanegativeNPV.

Sincetheinitialinvestmentoccurstoday（year0）,itdoesnotneedtobediscounted.

PV（Investment）=-$340,000

Discounttheannualrevenuesat10percent.

PV（Revenues）=$100,000/（1.10）+$100,000/（1.10）2+$100,000/（1.10）3+$100,000/（1.10）4+$100,000/（1.10）5

=$379,078.68

Sincethemaintenancecostsoccuratthebeginningofeachyear,thefirstpaymentisnotdiscounted.Eachyearthereafter,themaintenancecostisdiscountedatanannualrateof10percent.

PV（Maintenance）=-$10,000-$10,000/（1.10）-$10,000/（1.10）2-$10,000/（1.10）3–

$10,000/（1.10）4

=-$41,698.65

NPV=PV（Investment）+PV（CashFlows）+PV（Maintenance）

=-$340,000+$379,078.68-$41,698.65

=-$2,619.97

SincetheNPVisnegative,-$2,619.97,youshouldnotbuythemachine.

TofindtheNPVofthemachinewhentherelevantdiscountrateisninepercent,repeattheabovecalculations,withadiscountrateofninepercent.

Discounttheannualrevenuesatninepercent.

PV（Revenues）=$100,000/（1.09）+$100,000/（1.09）2+$100,000/（1.09）3+$100,000/（1.09）4+$100,000/（1.09）5

=$388,965.13

Sincethemaintenancecostsoccuratthebeginningofeachyear,thefirstpaymentisnotdiscounted.Eachyearthereafter,themaintenancecostisdiscountedatanannualrateofninepercent.

PV（Maintenance）=-$10,000-$10,000/（1.09）-$10,000/（1.09）2-$10,000/（1.09）3–

$10,000/（1.09）4

=-$42,397.20

=-$340,000+$388,965.13-$42,397.20

=$6,567.93

SincetheNPVispositive,$6,567.93,youshouldbuythemachine.

4.12a.TheNPVofthecontractisthePVoftheitem’srevenueminusitscost.

PV（Revenue）=C5/（1+r）5

=$90,000/（1.10）5

=$55,882.92

NPV=PV（Revenue）–Cost

=$55,882.92-$60,000

=-$4,117.08

TheNPVoftheitemis-$4,117.08.

b.Thefirmwillbreakevenwhentheitem’sNPVisequaltozero.

NPV=PV（Revenues）–Cost

=C5/（1+r）5–Cost

$0=$90,000/（1+r）5-$60,000

r=0.08447=8.447%

Thefirmwillbreakevenontheitemwithan8.447percentdiscountrate.

4.13ComparethePVofyouraunt’sofferwithyourroommate’soffer.ChoosetheofferwiththehighestPV.ThePVofyouraunt’sofferisthesumofherpaymenttoyouandthebenefitfromowningthecaranadditionalyear.

PV（Aunt）=PV（Trade-In）+PV（BenefitofOwnership）

=$3,000/（1.12）+$1,000/（1.12）

=$3,571.43

Sinceyourroommate’sofferoccurstoday（year0）,itdoesnotneedtobediscounted.

PV（Roommate）=$3,500

SincethePVofyouraunt’soffer,$3,571.43,ishigherthanyourroommate’soffer,$3,500,youshouldacceptyouraunt’soffer.

4.14Thecostofthecar12yearsfromtodaywillbe$80,000.Tofindtherateofinterestsuchthatyour$10,000investmentwillpayforthecar,settheFVofyourinvestmentequalto$80,000.

FV=C0（1+r）12

$80,000=$10,000（1+r）12

Solvefortheinterestrate,r.

8=（1+r）12

0.18921=r

Theinterestraterequiredis18.921%.

4.15Thedepositattheendofthefirstyearwillearninterestforsixyears,fromtheendofyear1totheendofyear7.

FV=$1,000（1.12）6

=$1,973.82

Thedepositattheendofthesecondyearwillearninterestforfiveyears.

FV=$1,000（1.12）5

=$1,762.34

Thedepo