罗斯《公司理财》英文习题答案chap004

公司理财习题答案第四章AnswerstoEnd-of-ChapterProblemsB-49Chapter4:NetPresentValue4.1a.$1,0001.0510=$1,628.89b.$1,0001.0710=$1,967.15c.$1,0001.0520=$2,653.30d.InterestcompoundsontheInterestalreadyearned.Therefore,theinterestearnedinpartc,$1,653.30,ismorethandoubletheamountearnedinparta,$628.89.4.2a.$1,000/1.17=$513.16b.$2,000/1.1=$1,818.18c.$500/1.18=$233.254.3Youcanmakeyourdecisionbycomputingeitherthepresentvalueofthe$2,000thatyoucanreceiveintenyears,orthefuturevalueofthe$1,000thatyoucanreceivenow.Presentvalue:$2,000/1.0810=$926.39Futurevalue:$1,0001.0810=$2,158.93Eithercalculationindicatesyoushouldtakethe$1,000now.4.4Sincethisbondhasnointerimcouponpayments,itspresentvalueissimplythepresentvalueofthe$1,000thatwillbereceivedin25years.Note:Aswillbediscussedinthenextchapter,thepresentvalueofthepaymentsassociatedwithabondisthepriceofthatbond.PV=$1,000/1.125=$92.304.5PV=$1,500,000/1.0827=$187,780.234.6a.Atadiscountrateofzero,thefuturevalueandpresentvaluearealwaysthesame.Remember,FV=PV(1+r)t.Ifr=0,thentheformulareducestoFV=PV.Therefore,thevaluesoftheoptionsare$10,000and$20,000,respectively.Youshouldchoosethesecondoption.b.Optionone:$10,000/1.1=$9,090.91Optiontwo:$20,000/1.15=$12,418.43Choosethesecondoption.c.Optionone:$10,000/1.2=$8,333.33Optiontwo:$20,000/1.25=$8,037.55Choosethefirstoption.d.YouareindifferentattheratethatequatesthePVsofthetwoalternatives.Youknowthatratemustfallbetween10%and20%becausetheoptionyouwouldchoosediffersattheserates.Letrbethediscountratethatmakesyouindifferentbetweentheoptions.$10,000/(1+r)=$20,000/(1+r)5(1+r)4=$20,000/$10,000=21+r=1.18921r=0.18921=18.921%4.7PVofJoneses’offer=$150,000/(1.1)3=$112,697.22SincethePVofJoneses’offerislessthanSmiths’offer,$115,000,youshouldchooseSmiths’offer.4.8a.P0=$1,000/1.0820=$214.55b.P10=P0(1.08)10=$463.20AnswerstoEnd-of-ChapterProblemsB-50c.P15=P0(1.08)15=$680.594.9The$1,000thatyouplaceintheaccountattheendofthefirstyearwillearninterestforsixyears.The$1,000thatyouplaceintheaccountattheendofthesecondyearwillearninterestforfiveyears,etc.Thus,theaccountwillhaveabalanceof$1,000(1.12)6+$1,000(1.12)5+$1,000(1.12)4+$1,000(1.12)3=$6,714.614.10PV=$5,000,000/1.1210=$1,609,866.184.11a.Thecostofinvestmentis$900,000.PVofcashinflows=$120,000/1.12+$250,000/1.122+$800,000/1.123=$875,865.52SincethePVofcashinflowsislessthanthecostofinvestment,youshouldnotmaketheinvestment.b.NPV=-$900,000+$875,865.52=-$24,134.48c.NPV=-$900,000+$120,000/1.11+$250,000/1.112+$800,000/1.113=$-4,033.18SincetheNPVisstillnegative,youshouldnotmaketheinvestment.4.12NPV=-($340,000+$10,000)+($100,000-$10,000)/1.1+$90,000/1.12+$90,000/1.13+$90,000/1.14+$100,000/1.15=-$2,619.98SincetheNPVisnegative,youshouldnotbuyit.Iftherelevantcostofcapitalis9percent,NPV=-$350,000+$90,000/1.09+$90,000/1.092+$90,000/1.093+$90,000/1.094+$100,000/1.095=$6,567.93SincetheNPVispositive,youshouldbuyit.4.13a.Profit=PVofrevenue-Cost=NPVNPV=$90,000/1.15-$60,000=-$4,117.08No,thefirmwillnotmakeaprofit.b.FindrthatmakeszeroNPV.$90,000/(1+r)5-$60,000=$0(1+r)5=1.5r=0.08447=8.447%4.14Thefuturevalueofthedecisiontoownyourcarforoneyearisthesumofthetrade-invalueandthebenefitfromowningthecar.Therefore,thePVofthedecisiontoownthecarforoneyearis$3,000/1.12+$1,000/1.12=$3,571.43SincethePVoftheroommate’soffer,$3,500,islowerthantheaunt’soffer,youshouldacceptaunt’soffer.4.15a.$1.000(1.08)3=$1,259.71b.$1,000[1+(0.08/2)]23=$1,000(1.04)6=$1,265.32c.$1,000[1+(0.08/12)]123=$1,000(1.00667)36=$1,270.24d.$1,000e0.083=$1,271.25公司理财习题答案第四章AnswerstoEnd-of-ChapterProblemsB-51e.Thefuturevalueincreasesbecauseofthecompounding.Theaccountisearninginterestoninterest.Essentially,theinterestisaddedtotheaccountbalanceattheendofeverycompoundingperiod.Duringthenextperiod,theaccountearnsinterestonthenewbalance.Whenthecompoundingperiodshortens,thebalancethatearnsinterestisrisingfaster.4.16a.$1,000e0.125=$1,822.12b.$1,000e0.13=$1,349.86c.$1,000e0.0510=$1,648.72d.$1,000e0.078=$1,750.674.17PV=$5,000/[1+(0.1/4)]412=$1,528.364.18EffectiveannualinterestrateofBankAmerica=[1+(0.041/4)]4-1=0.0416=4.16%EffectiveannualinterestrateofBankUSA=[1+(0.0405/12)]12-1=0.0413=4.13%YoushoulddeposityourmoneyinBankAmerica.4.19Thepriceoftheconsolbondisthepresentvalueofthecouponpayments.Applytheperpetuityformulatofindthepresentvalue.PV=$120/0.15=$8004.20Quarterlyinterestrate=12%/4=3%=0.03Therefore,thepriceofthesecurity=$10/0.03=$333.334.21Thepriceattheendof19quarters(or4.75years)fromtoday=$1/(0.154)=$26.67Thecurrentprice=$26.67/[1+(.15/4)]19=$13.254.22a.$1,000/0.1=$10,000b.$500/0.1=$5,000isthevalueoneyearfromnowoftheperpetualstream.Thus,thevalueoftheperpetuityis$5,000/1.1=$4,545.45.c.$2,420/0.1=$24,200isthevaluetwoyearsfromnowoftheperpetualstream.Thus,thevalueoftheperpetuityis$24,200/1.12=$20,000.4.23Thevalueatt=8is$120/0.1=$1,200.Thus,thevalueatt=5is$1,200/1.13=$901.58.4.24P=$3(1.05)/(0.12-0.05)=$45.004.25P=$1/(0.1-0.04)=$16.674.26Thefirstcashflowwillbegenerated2yearsfromtoday.Thevalueattheendof1yearfromtoday=$200,000/(0.1-0.05)=$4,000,000.Thus,PV=$4,000,000/1.1=$3,636,363.64.4.27AzeroNPV-$10