习题答案Principles of Corporate Finance第十版 Chapter2

习题答案PrinciplesofCorporateFinance第十版Chapter2习题答案PrinciplesofCorporateFinance第十版Chapter2习题答案PrinciplesofCorporateFinance第十版Chapter2资料仅供参考文件编号：2022年4月习题答案PrinciplesofCorporateFinance第十版Chapter2版本号：A修改号：1页次：1.0审核：批准:发布日期：CHAPTER2HowtoCalculatePresentValuesAnswerstoProblemSetsIfthediscountfactoris.507,then.507*=$1125/139=.899PV=374/9=PV=432/+137/+797/=376+104+524=$1,003FV=100*=$NPV=-1,548+138/.09=(costtodayplusthepresentvalueoftheperpetuity)PV=4/(.=$40a. PV=1/.10=$10Sincetheperpetuitywillbeworth$10inyear7,andsincethatisroughly doublethepresentvalue,theapproximatePVequals$5. PV=(1/.10)/7=10/2=$5(approximately)c. Aperpetuitypaying$1startingnowwouldbeworth$10,whereasaperpetuitystartinginyear8wouldbeworthroughly$5.Thedifferencebetweenthesecashflowsisthereforeapproximately$5.PV=10–5=$5(approximately)PV=C/(r-g)=10,000/(.=$200,000.9. a. PV=10,000/=$7,(assumingthecostofthecardoesnotappreciateoverthosefiveyears).Youneedtosetaside(12,000×6-yearannuityfactor)=12,000×=

$55,476.Attheendof6yearsyouwouldhave×(60,476-55,476)=$7,934.10. a. FV=1,=1,=$1,.11.FV=10,000,000x4=12,624,770FV=10,000,000x(1+.06/12)(4x12)=12,704,892FV=10,000,000xe=12,712,49212.a.PV=$100/=$b.PV=$100/=$c.PV=$100/=$d.PV=$100/+$100/+$100/=$13. a. r1==%b. AF2=DF1+DF2=+=PVofanannuity=C[Annuityfactoratr%fortyears]Here:$=$10[AF3]AF3=

AF3=DF1+DF2+DF3=AF2+DF3=+DF3DF3=14. Thepresentvalueofthe10-yearstreamofcashinflowsis:Thus:NPV=–$800,000+$886,=+$86,Attheendoffiveyears,thefactory’svaluewillbethepresentvalueofthefiveremaining$170,000cashflows:15. 16. a. LetSt=salaryinyeartPV(salary)x=$38,Futurevalue=$38,x30=$382,

c.17.PeriodPresentValue0400,1+100,000/=+89,2+200,000/=+159,3+300,000/=+213,Total=NPV=$62,18. Wecanbreakthisdownintoseveraldifferentcashflows,suchthatthesumoftheseseparatecashflowsisthetotalcashflow.Then,thesumofthepresentvaluesoftheseparatecashflowsisthepresentvalueoftheentireproject.(Alldollarfiguresareinmillions.)Costoftheshipis$8millionPV=$8millionRevenueis$5millionperyear,operatingexpensesare$4million.Thus,operatingcashflowis$1millionperyearfor15years.Majorrefitscost$2millioneach,andwilloccurattimest=5andt=10.PV=($2million)/+($2million)/=$millionSaleforscrapbringsinrevenueof$millionatt=15.PV=$million/=$millionAddingthesepresentvaluesgivesthepresentvalueoftheentireproject:NPV=$8million+$million$million+$millionNPV=$million

19. a. PV=$100,000b. PV=$180,000/=$102,c. PV=$11,400/=$95,000d. e. PV=$6,500/=$92,Prize(d)isthemostvaluablebecauseithasthehighestpresentvalue.20. Mr.Bassetisbuyingasecurityworth$20,000now.Thatisitspresentvalue.Theunknownistheannualpayment.Usingthepresentvalueofanannuityformula,wehave:21. AssumetheZhangswillputasidethesameamounteachyear.Oneapproachtosolvingthisproblemistofindthepresentvalueofthecostoftheboatandthenequatethattothepresentvalueofthemoneysaved.Fromthisequation,wecansolvefortheamounttobeputasideeachyear.PV(boat)=$20,000/5=$12,418PV(savings)=AnnualsavingsBecausePV(savings)mustequalPV(boat):Annualsavings

AnnualsavingsAnotherapproachistousethefuturevalueofanannuityformula:Annualsavings=$3,27622. ThefactthatKangarooAutosisoffering“freecredit”tellsuswhatthecashpaymentsare;itdoesnotchangethefactthatmoneyhastimevalue.A10%annualrateofinterestisequivalenttoamonthlyrateof%:rmonthly=rannual/12=12==%ThepresentvalueofthepaymentstoKangarooAutosis:AcarfromTurtleMotorscosts$9,000cash.Therefore,KangarooAutosoffersthebetterdeal,.,thelowerpresentvalueofcost.23. TheNPVsare:at5% at10% at15% ThefigurebelowshowsthattheprojecthaszeroNPVatabout11%.

Asacheck,NPVat11%is:24. a. Thisistheusualperpetuity,andhence:ThisisworththePVofstream(a)plustheimmediatepaymentof$100:PV=$100+$1,=$1,Thecontinuouslycompoundedequivalenttoa7%annuallycompoundedrateisapproximately%,because:=Thus:Notethatthepatternofpaymentsinpart(b)ismorevaluablethanthepatternofpaymentsinpart(c).Itispreferabletoreceivecashflowsatthestartofeveryyearthantospreadthereceiptofcashevenlyovertheyear;withtheformerpatternofpayment,youreceivethecashmorequickly.

25. a. PV=$1billion/=$billionPV=$1billion/–=$billionc. d. Thecontinuouslycompoundedequivalenttoan8%annuallycompoundedrateisapproximately%,because:=Thus:ThisresultisgreaterthantheanswerinPart(c)becausetheendowmentisnowearninginterestduringtheentireyear.26. Withannualcompounding:FV=$10020=$1,Withcontinuouscompounding:FV=$100e×20)=$2,27. Onewaytoapproachthisproblemistosolveforthepresentvalueof:(1) $100peryearfor10years,and(2) $100peryearinperpetuity,withthefirstcashflowatyear11.Ifthisisafairdeal,thesepresentvaluesmustbeequal,andthuswecansolvefortheinterestrate(r).Thepresentvalueof$100peryearfor10yearsis:Thepresentvalue,asofyear10,of$100peryearforever,withthefirstpaymentinyear11,is:PV10=$100/rAtt=0,thepresentvalueofPV10is:Equatingthesetwoexpressionsforpresentvalue,wehave:

Usingtrialanderrororalgebraicsolution,wefindthatr=%.28. Assumetheamountinvestedisonedollar.LetArepresenttheinvestmentat12%,compoundedannually.LetBrepresenttheinvestmentat%,compoundedsemiannually.LetCrepresenttheinvestmentat%,compoundedcontinuously.Afteroneyear:FVA=$1(1+1 =$FVB=$1(1+2 =$FVC=$1e1) =$Afterfiveyears:FVA=$1(1+5 =$FVB=$1(1+10 =$FVC=$1e5) =$Aftertwentyyears:FVA=$1(1+20 =$FVB=$1(1+40 =$FVC=$1e20) =$ThepreferredinvestmentisC.29. Becausethecashflowsoccureverysixmonths,wefirstneedtocalculatetheequivalentsemi-annualrate.Thus,=(1+r/2)2=>r=semi-annuallycompoundedAPR.Thereforetherateforsixmonthsis2or%:30. a. Eachinstallmentis:$9,420,713/19=$495,827b. IfERCiswillingtopay$million,then:

UsingExcelorafinancialcalculator,wefindthatr=%.31. a. b.YearBeginning-of-YearBalanceYear-endInterestonBalanceTotalYear-endPaymentAmortizationofLoanEnd-of-YearBalance1402,32,70,37,364,2364,29,70,40,323,3323,25,70,44,279,4279,22,70,47,231,5231,18,70,51,180,6180,14,70,55,124,7124,9,70,60,64,864,5,70,64,32. Thisisanannuityproblemwiththepresentvalueoftheannuityequalto$2

million(asofyourretirementdate),andtheinterestrateequalto8%with15timeperiods.Thus,yourannuallevelofexpenditure(C)isdeterminedasfollows:Withaninflationrateof4%peryear,wewillstillaccumulate$2millionasofourretirementdate.However,becausewewanttospendaconstantamountperyearinrealterms(R,constantforallt),thenominalamount(Ct)mustincreaseeachyear.Foreachyeart:R=Ct/(1+inflationrate)tTherefore:PV[allCt]=PV[allR(1+inflationrate)t]=$2,000,000

R[++...+]=$2,000,000R=$2,000,000R=$177,952Alternatively,considerthattherealrateis.Then,redoingthestepsaboveusingtherealrategivesarealcashflowequalto:ThusC1=($177,952=$185,070,C2=$192,473,etc.33. a. b. Theannuallycompoundedrateis%,sothesemiannualrateis:(1/2)–1==%Sincethepaymentsnowarrivesixmonthsearlierthanpreviously:PV=$430,×=$442,34. Inthreeyears,thebalanceinthemutualfundwillbe:FV=$1,000,000×3=$1,108,718Themonthlyshortfallwillbe:$15,000–($7,500+$1,500)=$6,000Annualwithdrawalsfromthemutualfundwillbe:$6,000×12=$72,000Assumethefirstannualwithdrawaloccursthreeyearsfromtoday,whenthebalanceinthemutualfundwillbe$1,108,718.Treatingthewithdrawalsasanannuitydue,w