Finance-chapter-8-课后答案

8-1SolutionstoChapter8NetPresentValueandOtherInvestmentCriteria1.NPVA=–$200+[$80annuityfactor(11%,4periods)]=–20.48$(1.11)0.1110.111$80$2004NPVB=–$200+[$100annuityfactor(11%,3periods)]=–37.44$(1.11)0.1110.111$100$2003Bothprojectsareworthpursuing.2.ChooseProjectA,theprojectwiththehigherNPV.3.NPVA=–$200+[$80annuityfactor(16%,4periods)]=–85.23$(1.16)0.1610.161$80$2004NPVB=–$200+[$100annuityfactor(16%,3periods)]=–59.24$(1.16)0.1610.161$100$2003Therefore,youshouldnowchooseprojectB.4.IRRA=Discountrate(r)whichisthesolutiontothefollowingequation:200$r)(1r1r1$804r=IRRA=21.86%IRRB=Discountrate(r)whichisthesolutiontothefollowingequation:200$r)(1r1r1$1003r=IRRB=23.38%8-25.No.EventhoughprojectBhasthehigherIRR,itsNPVislowerthanthatofprojectAwhenthediscountrateislower(asinProblem1)andhigherwhenthediscountrateishigher(asinProblem3).ThisexampleshowsthattheprojectwiththehigherIRRisnotnecessarilybetter.TheIRRofeachprojectisfixed,butasthediscountrateincreases,projectBbecomesrelativelymoreattractivecomparedtoprojectA.ThisisbecauseB’scashflowscomeearlier,sothepresentvalueofthesecashflowsdecreaseslessrapidlywhenthediscountrateincreases.6.Theprofitabilityindexesareasfollows:ProjectA:$48.20/$200=0.2410ProjectB:$44.37/$200=0.2219Inthiscase,withequalinitialinvestments,boththeprofitabilityindexandNPVgiveprojectsthesameranking.Thisisanunusualcase,however,sinceitisrarefortheinitialinvestmentstobeequal.7.ProjectAhasapaybackperiodof:$200/$80=2.5yearsProjectBhasapaybackperiodof2years.8.No.Despiteitslongerpaybackperiod,ProjectAmaystillbethepreferredproject,forexample,whenthediscountrateis11%(asinProblems1and2).Asinproblem5,youshouldnotethatthepaybackperiodforeachprojectisfixed,buttheNPVchangesasthediscountratechanges.TheprojectwiththeshorterpaybackperiodneednothavethehigherNPV.9.NPV=$3,000+[$800annuityfactor(10%,6years)]=–21.484$(1.10)0.1010.101$800$3,0006Atthe10%discountrate,theprojectisworthpursuing.IRR=Discountrate(r)whichisthesolutiontothefollowingequation:000,3$r)(1r1r1$8006r=IRR=15.34%YoucansolveforIRRusingafinancialcalculatorbyentering:PV=()3000;n=6;FV=0;PMT=800;andthencomputei.SincetheIRRis15.34%,thisisthehighestdiscountratebeforeprojectNPVturnsnegative.8-310.Paybackperiod=$2,500/$600=4.167yearsThisislessthanthecutoff,sothefirmwouldaccepttheproject.r=2%NPV=$2,500+[$600annuityfactor(2%,6years)]=–86.860$(1.02)0.0210.021$600$2,5006r=12%NPV=$2,500+[$600annuityfactor(12%,6years)]=–16.33$(1.12)0.1210.121$600$2,5006Ifr=2%,theprojectshouldbepursued;atr=12%,itshouldnotbe.11.38.680,2$09.1000,5$09.1000,5$09.1000,3$09.1000,3$000,10$NPV432Profitabilityindex=NPV/Investment=0.268012.NPV=$2.2billion+[$0.3billionannuityfactor(r,15years)][$0.9billion/(1+r)15]–1515r)(1billion9.0$r)(1r1r1billion$0.3billion$2.2r=5%NPV=$2.2billion+$2.681billion=$0.481billionr=18%NPV=$2.2billion+$1.452billion=$0.748billion13.IRRA=Discountrate(r)whichisthesolutiontothefollowingequation:000,30$r)(1r1r1$21,0002r=IRRA=25.69%IRRB=Discountrate(r)whichisthesolutiontothefollowingequation:000,50$r)(1r1r1$33,0002r=IRRB=20.69%TheIRRofprojectAis25.69%,andthatofBis20.69%.However,projectBhasthehigherNPVandthereforeispreferred.TheincrementalcashflowsofBoverAare:$20,000attime0;+$12,000attimes1and2.TheNPVoftheincrementalcashflows(discountedat10%)is$826.45,whichispositiveandequaltothedifferenceintherespectiveprojectNPVs.8-414.70.197$)12.1(000,11$12.1000,4$000,5$NPV2BecausetheNPVisnegative,youshouldrejecttheoffer.YoushouldrejecttheofferdespitethefactthattheIRRexceedsthediscountrate.Thisisa‘borrowingtype’projectwithpositivecashflowsfollowedbynegativecashflows.AhighIRRinthesecasesisnotattractive:Youdon’twanttoborrowatahighinterestrate.15.a.r=0%NPV=–$6,750+$4,500+$18,000=$15,750r=50%NPV=250,4$50.1000,18$50.1500,4$750,6$2r=100%NPV=0$00.2000,18$00.2500,4$750,6$2b.IRR=100%,thediscountrateatwhichNPV=0.16.09.029,2$12.1500,8$12.1500,7$000,10$NPV32SincetheNPVispositive,theprojectshouldbeaccepted.Alternatively,youcancomputetheIRRbysolvingforr,usingtrial-and-error,inthefollowingequation:0)r1(500,8$r)1(500,7$000,10$32IRR=20.61%SincetheIRRoftheprojectisgreaterthantherequiredrateofreturnof12%,theprojectshouldbeaccepted.17.NPV9%=–$20,000+[$4,000annuityfactor(9%,8periods)]=–28.139,2$(1.09)0.0910.091$4,000$20,0008NPV14%=–$20,000+[$4,000annuityfactor(14%,8periods)]=–54.444,1$(1.14)0.1410.141$4,000$20,00088-5IRR=Discountrate(r)whichisthesolutiontothefollowingequation:000,20$r)(1r1r1$4,0008r=IRR=11.81%[Usingafinancialcalculatior,enter:PV=()20,000;PMT=4000;FV=0;n=8,andcomputei.]Theprojectwillberejectedforanydiscountrateabovethisrate.18.a.Thepresentvalueofthesavingsis:$1,000/rr=0.08PV=$12,500andNPV=–$10,000+$12,500=$2,500r=0.10PV=$10,000andNPV=–$10,000+$10,000=$0b.IRR=0.10=10%Atthisdiscountrate,NPV=$0c.Paybackperiod=10years19.a.NPVforeachofthetwoprojects,atvariousdiscou