习题答案Principles of Corporate Finance第十版 Chapter2

Chapter02-HowtoCalculatePresentValues2-1CHAPTER2HowtoCalculatePresentValuesAnswerstoProblemSets1.Ifthediscountfactoris.507,then.507*1.126=$12.125/139=.8993.PV=374/(1.09)9=172.204.PV=432/1.15+137/(1.152)+797/(1.153)=376+104+524=$1,0035.FV=100*1.158=$305.906.NPV=-1,548+138/.09=-14.67(costtodayplusthepresentvalueoftheperpetuity)7.PV=4/(.14-.04)=$408.a.PV=1/.10=$10b.Sincetheperpetuitywillbeworth$10inyear7,andsincethatisroughlydoublethepresentvalue,theapproximatePVequals$5.PV=(1/.10)/(1.10)7=10/2=$5(approximately)c.Aperpetuitypaying$1startingnowwouldbeworth$10,whereasaperpetuitystartinginyear8wouldbeworthroughly$5.Thedifferencebetweenthesecashflowsisthereforeapproximately$5.PV=10–5=$5(approximately)d.PV=C/(r-g)=10,000/(.10-.05)=$200,000.9.a.PV=10,000/(1.055)=$7,835.26(assumingthecostofthecardoesnotappreciateoverthosefiveyears).b.Youneedtosetaside(12,000×6-yearannuityfactor)=12,000×4.623=Chapter02-HowtoCalculatePresentValues2-2$55,476.c.Attheendof6yearsyouwouldhave1.086×(60,476-55,476)=$7,934.10.a.FV=1,000e.12x5=1,000e.6=$1,822.12.b.PV=5e-.12x8=5e-.96=$1.914millionc.PV=C(1/r–1/rert)=2,000(1/.12–1/.12e.12x15)=$13,91211.a.FV=10,000,000x(1.06)4=12,624,770b.FV=10,000,000x(1+.06/12)(4x12)=12,704,892c.FV=10,000,000xe(4x.06)=12,712,49212.a.PV=$100/1.0110=$90.53b.PV=$100/1.1310=$29.46c.PV=$100/1.2515=$3.52d.PV=$100/1.12+$100/1.122+$100/1.123=$240.1813.a.0.905r11DF11r1=0.1050=10.50%b.0.819(1.105)1)r(11DF2222c.AF2=DF1+DF2=0.905+0.819=1.724d.PVofanannuity=C[Annuityfactoratr%fortyears]Here:$24.65=$10[AF3]AF3=2.465Chapter02-HowtoCalculatePresentValues2-3e.AF3=DF1+DF2+DF3=AF2+DF32.465=1.724+DF3DF3=0.74114.Thepresentvalueofthe10-yearstreamofcashinflowsis:6$886,739.6(1.14)0.1410.141$170,000PV10Thus:NPV=–$800,000+$886,739.66=+$86,739.66Attheendoffiveyears,thefactory’svaluewillbethepresentvalueofthefiveremaining$170,000cashflows:6$583,623.7(1.14)0.1410.141$170,000PV515.$23,696.151.12$50,0001.12$68,0001.12$80,0001.12$92,0001.12$92,0001.12$85,0001.12$80,0001.12$75,0001.12$57,0001.12$50,000$380,000(1.12)CNPV109876543210ttt016.a.LetSt=salaryinyeart301tt1t(1.08)(1.05)40,000PV3$760,662.5(1.08).05)-(.08(1.05).05)-(.08143030000,0b.PV(salary)x0.05=$38,033.13Futurevalue=$38,018.96x(1.08)30=$382,714.30Chapter02-HowtoCalculatePresentValues2-4c.$38,980.30(1.08)0.0810.081$C(1.08)0.0810.081C$r)(1r1r1CPV2020t382,714.30382,714.3017.PeriodPresentValue0400,000.001+100,000/1.12=+89,285.712+200,000/1.122=+159,438.783+300,000/1.123=+213,534.07Total=NPV=$62,258.5618.Wecanbreakthisdownintoseveraldifferentcashflows,suchthatthesumoftheseseparatecashflowsisthetotalcashflow.Then,thesumofthepresentvaluesoftheseparatecashflowsisthepresentvalueoftheentireproject.(Alldollarfiguresareinmillions.)Costoftheshipis$8millionPV=$8millionRevenueis$5millionperyear,operatingexpensesare$4million.Thus,operatingcashflowis$1millionperyearfor15years.million$8.559(1.08)0.0810.081million1$PV15Majorrefitscost$2millioneach,andwilloccurattimest=5andt=10.PV=($2million)/1.085+($2million)/1.0810=$2.288millionSaleforscrapbringsinrevenueof$1.5millionatt=15.PV=$1.5million/1.0815=$0.473millionAddingthesepresentvaluesgivesthepresentvalueoftheentireproject:NPV=$8million+$8.559million$2.288million+$0.473millionNPV=$1.256millionChapter02-HowtoCalculatePresentValues2-519.a.PV=$100,000b.PV=$180,000/1.125=$102,136.83c.PV=$11,400/0.12=$95,000d.4$107,354.2(1.12)0.1210.121$19,000PV10e.PV=$6,500/(0.120.05)=$92,857.14Prize(d)isthemostvaluablebecauseithasthehighestpresentvalue.20.Mr.Bassetisbuyingasecurityworth$20,000now.Thatisitspresentvalue.Theunknownistheannualpayment.Usingthepresentvalueofanannuityformula,wehave:$2,653.90(1.08)0.0810.081000,20$C(1.08)0.0810.081C000,20$r)(1r1r1CPV1212t21.AssumetheZhangswillputasidethesameamounteachyear.Oneapproachtosolvingthisproblemistofindthepresentvalueofthecostoftheboatandthenequatethattothepresentvalueofthemoneysaved.Fromthisequation,wecansolvefortheamounttobeputasideeachyear.PV(boat)=$20,000/(1.10)5=$12,418PV(savings)=Annualsavings5(1.10)0.1010.101BecausePV(savings)mustequalPV(boat):Annualsavings418,12$5(1.10)0.1010.101Chapter02-HowtoCalculatePresentValues2-6Annualsavings$3,276(1.10)0.1010.101$12,4185Anotherapproachistousethefuturevalueofanannuityformula:$20,0005.10)(1savingsAnnual10.1Annualsavings=$3,27622.ThefactthatKangarooAutosisoffering“freecredit”tellsuswhatthecashpaymentsare;itdoesnotchangethefactthatmoneyhastimevalue.A10%annualrateofinterestisequivalenttoamonthlyrateof0.83%:rmonthly=rannual/12=0.10/12=0.0083=0.83%ThepresentvalueofthepaymentstoKangarooAutosis:8$8,93(1.0083)0.008310.00831$300$1,00030AcarfromTurtleMotorscosts$9,000cash.Therefore,KangarooAutosoffersthebetterdeal,i.e.,thelowerpresentvalueofcost.23.TheNPVsare:at5%$25,011(1.05)$320,0001.05$100,000$170,000NPV2at10%$3,554(1.10)320,0001.10$100,000$170,000NPV2at15%$14,991