1、Chapter6:SomeAlternativeInvestmentRulesConceptQuestions-Chapter66.2*ListtheproblemsofthepaybackperiodruleItdoesnottakeintoaccountthetimevalueofmoney.Itignorespaymentsafterthepaybackperiod.Thecutoffperiodisarbitrary.*Whataresomeadvantages?Itissimpletoimplement.Itmayhelpincontrollingandevaluatingmanag

2、ers.6.4*WhatarethethreestepsincalculatingAAR?Determineaveragenetincome.DetermineaverageinvestmentDivideaveragenetincomebyaverageinvestment.*WhataresomeflawswiththeAARapproach?Itusesaccountingfigures.Ittakesnoaccountoftiming.Thecutoffperiodisarbitrary.*HowdoesonecalculatetheIRRofaproject?Usingeithert

3、rial-and-errororafinancialcalculator,onefindsthediscountratethatproducesanNPVofzero.?Whatisthedifferencebetweenindependentprojectsandmutuallyexclusiveprojects?Anindependentprojectisonewhoseacceptaneedoesnotaffecttheacceptaneeofanother.Amutuallyexclusiveproject,ontheotherhandisonewhoseacceptaneeprecl

4、udestheacceptaneeofanother.*WhataretwoproblemswiththeIRRapproachthatapplytobothindependentandmutuallyexclusiveprojects?Thedecisionruledependsonwhetheroneisinvestingoffinancing.Multipleratesofreturnarepossible.*Whataretwoadditionalproblemsapplyingonlytomutuallyexclusiveprojects?TheIRRapproachignoresi

5、ssuesofscale.TheIRRapproachdoesnotaccommodatethetimingofthecashflowsproperly.6.7?Howdoesonecalculateaprojectsprofitabilityindex?Dividethepresentvalueofthecashflowssubsequenttotheinitialinvestmentbytheinitialinvestment.*Howistheprofitabilityindexappliedtoindependentprojects,mutuallyexclusiveprojects,

6、andsituationsofcapitalrationing?Withindependentprojects,accepttheprojectifthePIisgreaterthan1.0andrejectiflessthan1.0.Withmutuallyexclusiveprojects,useincrementalanalysis,subtractingthecashflowsofproject2fromproject1.FindthePI.IfthePIisgreaterthan1.0,acceptproject1.Iflessthan1.0,acceptproject2.Incap

7、italrationing,thefirmshouldsimplyranktheprojectsaccordingtotheirrespectivePlsandaccepttheprojectswiththehighestPls,subjecttothebudgetconstrain.AnswerstoEnd-of-ChapterProblemsQUESTIONSANDPROBLEMSThePaybackPeriodRuleFujiSoftware,Inc.,hasthefollowingprojects.YearProjectAProjectB0_$7,500_$5,00014,0002,5

8、0023,5001,20031,5003,000SupposeFujiscutoffpaybackperiodistwoyears.Whichofthesetwoprojectsshouldbechosen?SupposeFujiusestheNPVruletorankthesetwoprojects.Iftheappropriatediscountrateis15percent,whichprojectshouldbechosen?a.PaybackperiodofProjectA=1+($7,500-$4,000)/$3,500=2yearsPaybackperiodofProjectB=

9、2+($5,000-$2,500-$1,200)/$3,000=2.43yearsProjectAshouldbechosen.b.NPVa=-$7,500+$4,000/1.15+$3,500/1.152+$1,500/1.153=-$388.96NPVb=-$5,000+$2,500/1.15+$1,200/1.152+$3,000/1.153=$53.83ProjectBshouldbechosen.SupposePeachPavingCompanyinvests$1milliontodayonanewconstructionproject.Theprojectwillgeneratea

10、nnualcashflowsof$150,000inperpetuity.Theappropriateannualdiscountratefortheprojectis10percent.Whatisthepaybackperiodfortheproject?IfthePeachPavingCompanydesirestohavea10-yearpaybackperiod,shouldtheprojectbeadopted?Whatisthediscountedpaybackperiodfortheproject?c.WhatistheNPVoftheproject?6.2a.Paybackp

11、eriod=6+$1,000,000-($150,0006)/$150,000=6.67yearsYes,theprojectshouldbeadopted.11$150,000.-.0.10=$974,25912Thediscountedpaybackperiod=11+($1,000,000-$974,259)/($150,000/1.1)=11.54yearsNPV=-$1,000,000+$150,000/0.10=$500,000TheAverageAccountingReturn6.3Theannual,end-of-year,book-investmentaccountsfort

12、hemachinewhosepurchaseyourfirmisconsideringareshownbelow.PurchaseYearYearYearYearDate1234Grossinvestment$16,000$16,000$16,000$16,000$16,000Less:accumulateddepreciation04_,0_0_08_,0_0_01_2_,0_0_0_1_6_,_0_0_0Netinvestment$16,000$12,000$8,000$4,000$0Ifyourfirmpurchasesthismachine,youcanexpectittogenera

13、te,onaverage,$4,500peryearinadditionalnetincome.a.Whatistheaverageaccountingreturnforthismachine?b.Whatthreeflawsareinherentinthisdecisionrule?6.3a.AverageInvestment:($16,000+$12,000+$8,000+$4,000+0)/5=$8,000Averageaccountingreturn:$4,500/$8,000=0.5625=56.25%b.1.AARdoesnotconsiderthetimingofthecashf

14、lows,henceitdoesnotconsiderthetimevalueofmoney.AARusesanarbitraryfirmstandardasthedecisionrule.AARusesaccountingdataratherthannetcashflows.6.4WesternPrintingCo.hasanopportunitytopurchasea$2millionnewprintingmachine.Ithasaneconomiclifeoffiveyearsandwillbeworthlessafterthattime.Thisnewinvestmentisexpe

15、ctedtogenerateanannualnetincomeof$100,000oneyearfromtodayandtheincomestreamwillgrowat7percentperyearsubsequently.Thecompanyadoptsastraight-linedepreciationmethod(i.e.,equalamountsofdepreciationineachyear).Whatistheaverageaccountingreturnoftheinvestment? Supposing Western PrintingsAARcutoffis20percen

16、t,shouldthemachinebepurchased?AverageInvestment=($2,000,000+0)/2=$1,000,0005Averagenetincome=$100,000(1+g)-1/g/5=$100,000A(1.075-1/0.07/5=$115,014.78AAR=$115,014.78/$1,000,000=11.50%No,sincethemachinesAARislessthanthefirmscutoffAAR.NokiaGrouphasinvested$8,000inahigh-techproject.Thiscostisdepreciated

17、onanacceleratedbasisthatyields$4,000,$2,500,$1,500ofdepreciation,respectively,duringitsthree-yeareconomiclife.Theprojectisexpectedtoproduceincomebeforetaxof$2,000eachyearduringitseconomiclife.Ifthetaxrateis25%,whatistheprojectsaverageaccountingreturn(AAR)?44.44%50.23%66.67%70.00%82.21%TheInternalRat

18、eofReturnaComputetheinternalrateofreturnonprojectswiththefollowingcashflows.CashFlows($)YearProjectAProjectB0_3,000_6,00012,5005,00021,0002,000PI=$40,000A7.15/$160,000=1.04SincethePIexceedsoneaccepttheproject.CPC,Inc.,hasaprojectwiththefollowingcashflows.YearCashFlows($)0_8,00014,00023,00032,000Comp

19、utetheinternalrateofreturnontheproject.Supposetheappropriatediscountrateis8percent.ShouldtheprojectbeadoptedbyCPC?TheIRRisthediscountrateatwhichtheNPV=0.-$3,000+$2,500/(1+IRRa)+$1,000/(1+IRRa)2=0Bytrialanderror,IRRA=12.87%SinceprojectBscashflowsaretwotimesofthoseofprojectA,theBlRRRRA=12.87%Computeth

20、einternalrateofreturnforthecashflowsofthefollowingtwoprojects.CashFlows($)TimeAB0_2,000_1,50012,00050028,0001,0003_8,0001,500a.Solvexbytrialanderror:23-$4,000+$2,000/(1+x)+$1,500/(1+x)+$1,000/(1+x)3=0 x=6.93%b.No,sincetheIRR(6.93%)islessthanthediscountrateof8%.Supposeyouareoffered$5,000todayandoblig

21、atedtomakescheduledpaymentsasfollows:YearCashFlows($)05,0001_2,5002_2,0003_1,0004_1,000WhatistheIRRsofthisoffer?Iftheappropriatediscountrateis10percent,shouldyouacceptthisoffer?Iftheappropriatediscountrateis20percent,shouldyouacceptthisoffer?Chapter6SomeAlternativeInvestmentRules165Whatisthecorrespo

22、ndingNPVoftheprojectiftheappropriatediscountratesare10percentand20percent,respectively?ArethechoicesundertheNPVruleconsistentwiththoseoftheIRRrule?6.9FindtheIRRsofprojectAanalytically.SincetheIRRisthediscountratethatmakestheNPVequaltozero,thefollowingequationmusthold.-$200+$200/(1+r)+$800/(1+r)2-$80

23、0/(1+r)3=02$200-1+1/(1+r)-$800/(1+r)2-1+1/(1+r)=0-1+1/(1+r)$200-$800/(1+r)2=0Forthisequationtohold,either-1+1/(1+r)=0or$200-$800/(1+r)2=0.Solveeachofthesefactorsfortherthatwouldcausethefactortoequalzero.TheresultingratesarethetwoIRRsforprojectA.Theyareeitherr=0%orr=100%.Note:Byinspectionyoushouldhav

24、eknownthatoneoftheIRRsofprojectAiszero.Noticethatthesumoftheun-discountedcashflowsforprojectAiszero.Thus,notdiscountingthecashflowswouldyieldazeroNPV.Thediscountratewhichistantamounttonotdiscountingiszero.Here are some of the interactions used to find the IRR by trial and error. Sophisticated calcul

25、ators can compute this rate without all of the tedium involved in the trial-and-error method.2323NPVNPV= -$150 + $50 / 1.3 + $100 / 1.3= -$150 + $50 / 1.4 + $100 / 1.4+ $150 / 1.3 3 = + $150 / 1$.415.391=/ 1.37 2NPV+ $150 / 1.37 3 = -$1.89= -$150 + $50 / 1.36 + $100 / 1.3623 NPV+ $150 / 1.3623 NPV=

26、-$150 + $50 / 1.36194 + $100 / 1.36194NPVNPV= $0.0010= -$150 + $50 / 1.36195 + $100 / 1.36195= -$0.0013= -$150 + $50 / 1.361944 + $100 / 1.361944= $0.0000906+ $50 / 1.37 + $1003 = $0.462 + $150 / 1.36194 32 + $150 / 1.36195 32 + $150 / 1.361944 3Thus,theIRRisapproximately36.1944%.AstheChiefFinancial

27、OfficeroftheOrientExpress,youareofferedthefollowingtwomutuallyexclusiveprojects.YearProjectAProjectB0_$5,000_$100,00013,50065,00023,50065,000WhataretheIRRsofthesetwoprojects?IfyouaretoldonlytheIRRsoftheprojects,whichwouldyouchoose?Whatdidyouignorewhenyoumadeyourchoiceinpart(b)?Howcantheproblembereme

28、died?ComputetheincrementalIRRfortheprojects.Basedonyouranswertopart(e),whichprojectshouldyouchoose?Supposeyouhavedeterminedthattheappropriatediscountratefortheseprojectsis15percent.AccordingtotheNPVrule,whichofthesetwoprojectsshouldbeadopted?6.10a.Solverintheequation:$5,000-$2,500/(1+r)-$2,000/(1+r)

29、2-$1,000/(1+r)3-$1,000/(1+r)4=0Bytrialanderror,IRR=r=13.99%b.Sincethisproblemisthecaseoffinancing,accepttheprojectiftheIRRislessthantherequiredrateofreturn.IRR=13.99%10%Rejecttheoffer.c.IRR=13.99%20%Accepttheoffer.d.Whenr=10%:NPV=$5,000-$2,500/1.1-$2,000/1.12-$1,000/1.13-$1,000/1.14=-$359.95Whenr=20

30、%:NPV=$5,000-$2,500/1.2-$2,000/1.22-$1,000/1.23-$1,000/1.24=$466.82Yes,theyareconsistentwiththechoicesoftheIRRrulesincethesignsofthecashflowschangeonlyonce.6.11Considertwostreamsofcashflows,AandB.CashflowAconsistsof$5,000startingthreeyearsfromtodayandgrowingat4percentinperpetuity.CashflowBconsistsof

31、_$6,000startingtwoyearsfromtodayandcontinuinginperpetuity.Assumetheappropriatediscountrateis12percent.Whatisthepresentvalueofeachstream?WhatistheIRRofaprojectC,whichisacombinationofprojectsAandB;thatis,C_A_B?Ifitisassumedthatthediscountrateisalwayspositive,whatistherulerelatedtoIRRforassessingprojec

32、tCthatwouldcorrespondtotheNPVrule?6.11a.ProjectA:NPV=-$5,000+$3,500/(1+r)+$3,500/(1+r)2=0IRR=r=25.69%ProjectB:2NPV=-$100,000+$65,000/(1+r)+$65,000/(1+r)=0IRR=r=19.43%ChooseprojectAbecauseithasahigherIRR.Thedifferenceinscaleisignored.ApplytheincrementalIRRmethod.e.CoCiC2B-A-$95,000$61,500$61,5002f.If

33、thediscountrateislessthan19.09%,chooseprojectB.Otherwise,chooseprojectA.g.NPVa=-$5,000+$3,500/1.15+$3,500/1.152=$689.98NPVb=-$100,000+$65,000/1.15+$65,000/1.152=$5,671.08ChooseprojectB.6.12 Project A involves an investment of $1 million, and project B involves an investment of $2 million. Both proje

34、cts have a uni que in ter nal rate of return of 20 perce nt. Is the followi ng stateme nt true or false? Expla in your an swer.For any discou nt rate betwee n 0 perce nt and 20 perce nt, i nclusive, project B has an NPV twice as great as that of project A.6.12 a. PVa = $5,000 / (0.12 - 0.04)/ 1.122

35、= $49,824.61b.PVb = (-$6,000 / 0.12) / 1.12 = -$44,642.86The IRR for project C must solve$5,000 / (x - 0.04) / (1 + x) 2 + (-$6,000 / x) / (1 + x) = 0 $5,000 / (x - 0.04) - $6,000 (1 + x) / x = 0 25 x2 + 3.17 x - 1 =0 x = -3.17 - (110.0489)0.5 / 50 or -3.17 + (110.0489)0.5 / 50 The releva nt positiv

36、e rootis IRR = x = 0.1464 = 14.64%c. To arrive at the appropriate decision rule, we must graph the NPV as a function of the discount rate. At a discount rate of 14.64% the NPV is zero. To determine if the graph is upward or dow nward slop ing, check the NPV at ano ther disco unt rate. At a discount

37、rate of 10% the NPV is $14,325.07 = $68,870.52 - $54,545.54. Thus, the graph of the NPV is dow nward slop ing. From the discussi on in the text, if an NPV graph is dow nward slop ing, the project is an in vesti ng project. The correct decisi on rule for an in vest ing project is to accept the projec

38、t if the disco unt rate is below 14.64%.NPV$14,325.0710%14 64%The Profitability In dex6.13 Suppose the following two mutually exclusive investment opportunities are available to the DeAngelo Firm. The appropriate discou nt rate is 10 perce nt.Year Project Alpha Project Beta0 _$500 _$2,0001 _300 _300

39、2 700 1,8003 600 1,700What is the NPV of project alpha and project beta?Which project would you recomme nd for the DeAn gelo Firm?6.13 Gen erally, the stateme nt is false. If the cash flows of project B occur early and the cash flows ofproject A occur late, the n for a low disco unt rate the NPV of

40、A can exceed the NPV of B. Examples are easy to con struct.CiIRR NPV 0%A:B:-$1,000,000-2,000,000$0$1,440,0000.202,400,00000.20$440,000400,000Inoneparticularcase,thestatementistrueforequallyriskyprojects.IfthelivesofthetwoprojectsareequalandineverytimeperiodthecashflowsoftheprojectBaretwicethecashflo

41、wsofprojectA,thentheNPVofprojectBwillbetwiceasgreatastheNPVofprojectAforanydiscountratebetween0%and20%.Thefirmforwhichyouworkmustchoosebetweenthefollowingtwomutuallyexclusiveprojects.Theappropriatediscountratefortheprojectsis10percent.ProfitabilityC0C1C2IndexNPVA_$1,000$1,000$5001.32$322B_5005004001

42、.57285ThefirmchosetoundertakeA.Ataluncheonforshareholders,themanagerofapensionfundthatownsasubstantialamountofthefirmsstockasksyouwhythefirmchoseprojectAinsteadofprojectBwhenBismoreprofitable.Howwouldyoujustifyyourfirmsaction?Arethereanycircumstancesunderwhichthepensionfundmanagersargumentcouldbecor

43、rect?a.NPV-=$756.57-$500=$256.57NPVp=$2,492.11-$2,000=$492.11b.Chooseprojectbeta.ThetreasurerofDavids,Inc.,hasprojectedthecashflowsofprojectsA,B,andCasfollows.Supposetherelevantdiscountrateis12percentayear.YearProjectAProjectBProjectC0_$100,000_$200,000_$100,000170,000130,00075,000270,000130,00060,0

44、00Computetheprofitabilityindicesforeachofthethreeprojects.ComputetheNPVsforeachofthethreeprojects.Supposethesethreeprojectsareindependent.WhichprojectsshouldDavidsacceptbasedontheprofitabilityindexrule?Supposethesethreeprojectsaremutuallyexclusive.WhichprojectshouldDavidsacceptbasedontheprofitabilit

45、yindexrule?SupposeDavidsbudgetfortheseprojectsis$300,000.Theprojectsarenotdivisible.WhichprojectsshouldDavidsaccept?AlthoughtheprofitabilityindexishigherforprojectBthanforprojectA,theNPVistheincreaseinthevalueofthecompanythatwilloccurifaparticularprojectisundertaken.Thus,theprojectwiththehigherNPVsh

46、ouldbechosenbecauseitincreasesthevalueofthefirmthemost.Onlyinthecaseofcapitalrationingcouldthepensionfundmanagerbecorrect.Billplanstoopenaself-servegroomingcenterinastorefront.Thegroomingequipmentwillcost$160,000.Billexpectstheafter-taxcashinflowstobe$40,000annuallyforsevenyears,afterwhichheplanstos

47、craptheequipmentandretiretothebeachesofJamaica.Assumetherequiredreturnis15%.WhatistheprojectsPI?Shoulditbeaccepted?ComparisonofInvestmentRulesa.PIa=($70,000/1.12+$70,000/1.122)/$100,000=1.183PIb=($130,000/1.12+$130,000/1.122)/$200,000=1.099PIC=($75,000/1.12+$60,000/1.122)/$100,000=1.148NPVA=-$100,00

48、0+$118,303.57=$18,303.57NPVb=-$200,000+$219,706.63=$19,706.63NPVc=-$100,000+$114,795.92=$14,795.92AcceptallthreeprojectsbecausePIsofallthethreeprojectsaregreaterthanone.BasedonthePIrule,projectCcanbeeliminatedbecauseitsPIislessthantheoneofprojectA,whilebothhavethesameamountoftheinvestment.Wecancompu

49、tethePIoftheincrementalcashflowsbetweenthetwoprojects,ProjectC。CiC2PIB-A$00,000$60,000$60,0001.014WeshouldtakeprojectBsincethePIoftheincrementalcashflowsisgreaterthanone.ProjectBhasthehighestNPV,whileAhasthenexthighestNPV.TakebothprojectsAandB.6.17Defineeachofthefollowinginvestmentrules.Inyourdefini

50、tionstatethecriteriaforacceptingorrejectinganinvestmentundereachrule.PaybackperiodAverageaccountingreturnInternalrateofreturnProfitabilityindexNetpresentvaluea.Thepaybackperiodisthetimeittakestorecouptheinitialinvestmentofaproject.Acceptanyprojectthathasapaybackperiodthatisequaltoorshorterthanthecom

51、panysstandardpaybackperiod.Rejectallotherprojects.s sta ndard.Theaverageaccountingreturn(AAR)isdefinedasAverageprojectearningsAveragebookvalueoftheinvestment.AcceptprojectsforwhichtheAARisequaltoorgreaterthanthefirmRejectallotherprojects.Theinternalrateofreturn(IRR)isthediscountratewhichmakesthenetp

52、resentvalue(NPV)oftheprojectzero.Theaccept/rejectcriteriais:IfC00andallfuturecashflowsarepositive,accepttheprojectifIRR-discountrate.IfC00andallfuturecashflowsarepositive,rejecttheprojectifIRR0andallfuturecashflowsarenegative,accepttheprojectifIRR-discountrate.IfC00andallfuturecashflowsarenegative,r

53、ejecttheprojectifIRRdiscountrate.Iftheprojecthascashflowsthatalternateinsign,thereislikelytobemorethanonepositiveIRR.Inthatsituation,thereisnovalidIRRaccept/rejectrule.Theprofitabilityindex(PI)isdefinedas:(Thepresentvalueofthecashflowssubsequenttotheinitialinvestmentvestment)Acceptanyprojectforwhich

54、theprofitabilityindexisequaltoorgreaterthanone.Rejectprojectforwhichthatisnottrue.Thenetpresentvalue(NPV)isthesumofthepresentvaluesofallprojectcashflows.AcceptthoseprojectswithNPVswhichareequaltoorgreaterthanzero.RejectsproposalswithnegativeNPVs.Considerthefollowingcashflowsoftwomutuallyexclusivepro

55、jectsforChineseDailyNews.NewSundayNewSaturdayYearEarlyEditionLateEdition0_$1,200_$2,10016001,00025509003450800Basedonthepaybackperiodrule,whichprojectshouldbechosen?Supposethereisnocorporatetaxandthecashflowsaboveareincomebeforethedepreciation.Thefirmusesastraight-linedepreciationmethod(i.e.,equalam

56、ountsofdepreciationineachyear).Whatistheaverageaccountingreturnforeachofthesetwoprojects?WhichprojecthasagreaterIRR?BasedontheincrementalIRRrule,whichprojectshouldbechosen?a.6.18LetprojectArepresentNewSundayEarlyEdition;andletprojectBrepresentNewSaturdayLateEdition.PaybackperiodofprojectA=2+($1,200-

57、$1,150)/$450=2.11yearsPaybackperiodofprojectB=2+($2,100-$1,900)/$800=2.25yearsBasedonthepaybackperiodrule,youshouldchooseprojectA.ProjectA:Averageinvestment=($1,200+$0)/2=$600Depreciation=$400/yearAverageincome=($600-$400)+($550-$400)+($450-$400)/3=$133.33AAR=$133.33/$600=22.22%ProjectB:Averageinves

58、tment=($2,100+$0)/2=$1,050Depreciation=$700/yearAverageincome=($1,000-$700)+($900-$700)+($800-$700)/3=$200AAR=$200/$1,050=19.05%IRRofprojectA:-$1,200+$600/(1+r)+$550/(1+r)123+$450/(1+r)4=0B-A-$900$400$350$350-$900+$400/(1+r)+$350/(1+r)2+$350/(1+r)3=0IncrementalIRR=r=11.02%Iftherequiredrateofreturnis

59、greaterthan11.02%,thenchooseprojectA.Iftherequiredrateofreturnislessthan11.02%,thenchooseprojectB.6.19Considerthefollowingcashflowsontwomutuallyexclusiveprojectsthatrequireanannualreturnof15percent.WorkinginthefinancialplanningdepartmentfortheBahamasRecreationCorp.,youaretryingtocomparedifferentinve

60、stmentcriteriatoarriveatasensiblechoiceofthesetwoprojects.DeepwaterNewSubmarineYearFishingRide0_$600,000_$1,800,0002270,0001,000,0003350,000700,0004300,000900,000Basedonthediscountedpaybackperiodrule,whichprojectshouldbechosen?IfyourdecisionruleistoaccepttheprojectwithagreaterIRR,whichprojectshouldy