公司理财（第6版）（上下册）课件 第7章　投资决策法则

CorporateFinanceSixthEditionChapter7InvestmentDecisionRulesCopyright©2024,2021,2018PearsonEducation,Inc.AllRightsReservedChapterOutline7.1

NPVandStand-AloneProjects7.2

TheInternalRateofReturnRule7.3

ThePaybackRule7.4

ChoosingbetweenProjects7.5

ProjectSelectionwithResourceConstraintsLearningObjectives(1of2)Definenetpresentvalue,paybackperiod,internalrateofreturn,profitabilityindex,andincrementalIRR.Describedecisionrulesforeachofthetoolsinobjective1,forbothstand-aloneandmutuallyexclusiveprojects.Givencashflows,computetheNPV,paybackperiod,internalrateofreturn,andprofitabilityindexforagivenproject,andtheincrementalIRRforapairofprojects.LearningObjectives(2of2)Compareeachofthecapitalbudgetingtoolsabove,andtellwhyNPValwaysgivesthecorrectdecision.DiscussthereasonsIRRcangiveaflaweddecision.Describesituationsinwhichprofitabilityindexcannotbeusedtomakeadecision.7.1NPVandStand-AloneProjectsConsideratake-it-or-leave-itinvestmentdecisioninvolvingasingle,stand-aloneprojectforFredrick’sFeedandFarm(FFF).Theprojectcosts$250millionandisexpectedtogeneratecashflowsof$35millionperyear,startingattheendofthefirstyearandlastingforever.ApplyingtheNPVRuleTheNPVoftheprojectiscalculatedas:TheNPVisdependentonthediscountrateFigure7.1NPVofFredrick’sFertilizerProjectIfFFF’scostofcapitalis10%,theNPVis$100million,andtheyshouldundertaketheinvestmentAlternativeRulesVersustheNPVRuleSometimesalternativeinvestmentrulesmaygivethesameanswerastheNPVrule,butatothertimestheymaydisagreeWhentherulesconflict,theNPVdecisionruleshouldbefollowed7.2TheInternalRateofReturnRule(1of2)InternalRateofReturn(IRR)InvestmentRuleTakeanyinvestmentwheretheIRRexceedsthecostofcapitalTurndownanyinvestmentwhoseIRRislessthanthecostofcapital7.2TheInternalRateofReturnRule(2of2)TheIRRInvestmentRulewillgivethesameanswerastheNPVruleinmany,butnotall,situationsIngeneral,theIRRruleworksforastand-aloneprojectifalloftheproject’snegativecashflowsprecedeitspositivecashflowsInFigure7.1,wheneverthecostofcapitalisbelowtheIRRof14%,theprojecthasapositiveNPV,andyoushouldundertaketheinvestmentApplyingtheIRRRuleInothercases,theIRRrulemaydisagreewiththeNPVruleandthusbeincorrectSituationswheretheIRRruleandNPVrulemaybeinconflict:DelayedInvestmentsNonexistentIRRMultipleIRRsPitfall1:DelayedInvestments(1of3)AssumeyouhavejustretiredastheCEOofasuccessfulcompany.Amajorpublisherhasofferedyouabookdeal.Thepublisherwillpayyou$1millionupfrontifyouagreetowriteabookaboutyourexperiences.Youestimatethatitwilltakethreeyearstowritethebook.Thetimeyouspendwritingwillcauseyoutogiveupspeakingengagementsamountingto$500,000peryear.Youestimateyouropportunitycosttobe10%.Pitfall1:DelayedInvestments(2of3)Shouldyouacceptthedeal?CalculatetheIRRBlankNPERRATEPVPMTFVExcelFormulaGiven3Blank1,000,000Negative500,0000BlankSolvefor1blank23.38%BlankBlankBlankEqualsrateleftparenthesis3comma500000comma1000000comma0rightparenthesis.TheIRRisgreaterthanthecostofcapitalThus,theIRRruleindicatesyoushouldacceptthedealFinancialCalculatorSolutionPitfall1:DelayedInvestments(3of3)Shouldyouacceptthedeal?SincetheNPVisnegative,theNPVruleindicatesyoushouldrejectthedealFigure7.2NPVofStar’s$1MillionBookDealWhenthebenefitsofaninvestmentoccurbeforethecosts,theNPVisanincreasingfunctionofthediscountratePitfall2:MultipleIRRs(1of4)SupposeStarinformsthepublisherthatitneedstosweetenthedealbeforehewillacceptitThepublisheroffers$550,000advanceand$1,000,000infouryearswhenthebookispublishedShouldheacceptorrejectthenewoffer?Pitfall2:MultipleIRRs(2of4)ThecashflowswouldnowlooklikeTheNPViscalculatedasPitfall2:MultipleIRRs(3of4)BysettingtheNPVequaltozeroandsolvingforr,wefindtheIRRInthiscase,therearetwoIRRs:7.164%and33.673%BecausethereismorethanoneIRR,theIRRrulecannotbeappliedFigure7.3NPVofStar’sBookDealwithRoyaltiesPitfall2:MultipleIRRs(4of4)AsseeninFigure7.3,between7.164%and33.673%,thebookdealhasanegativeNPV.Sinceyouropportunitycostofcapitalis10%,youshouldrejectthedeal.Pitfall3:NonexistentIRRFinally,Starisabletogetthepublishertoincreasehisadvanceto$750,000,inadditiontothe$1millionwhenthebookispublishedinfouryearsWiththesecashflows,noIRRexists;thereisnodiscountratethatmakesNPVequaltozeroFigure7.4NPVofStar’sFinalOfferNoIRRexistsbecausetheNPVispositiveforallvaluesofthediscountrate.ThustheIRRrulecannotbeused.CommonMistakeIRRVersustheIRRRuleWhiletheIRRrulehasshortcomingsformakinginvestmentdecisions,theIRRitselfremainsusefulIRRmeasurestheaveragereturnoftheinvestmentandthesensitivityoftheNPVtoanyestimationerrorinthecostofcapitalTextbookExample7.1(1of2)ProblemwiththeIRRRuleProblemConsiderprojectswiththefollowingcashflows:Project012ANegative375Negative300900BNegative22,22250,000Negative28,000C400400Negative1,056DNegative4,30010,000Negative6,000WhichoftheseprojectshaveanIRRcloseto20%?ForwhichoftheseprojectsistheIRRrulevalid?TextbookExample7.1(2of2)SolutionWeplottheNPVprofileforeachprojectinFigure7.5fromtheNPVprofiles,wecanseethatprojectsA,B,andCeachhaveanIRRofapproximately20%,whichprojectDhasnoIRR.NotealsothatprojectBhasanotherIRRof5%.TheIRRruleisvalidonlyiftheprojecthasapositiveNPVforeverydiscountratebelowtheIRR.Thus,theIRRruleisonlyvalidforprojectA.thisprojectistheonlyoneforwhichallthenegativecashflowsprecedethepositiveones.NPVProfilesforExample7.1WhiletheIRRRuleworksforprojectA,itfailsforeachoftheotherprojectsAlternativeExample7.1(1of3)ProblemConsiderthefollowingprojects:CashFlowProject01231($200,000)$50,000$75,000$125,0002($250,000)$675,000($225,000)($250,000)3$500,000($300,000)($200,000)($100,000)Estimateeachproject’sIRRbygraphingtheNPVprofileforeach.AlternativeExample7.1(2of3)SolutionAlternativeExample7.1(3of3)Solution(continued)TheNPVprofileforProject1crossesthehorizontalaxisatabout10%.TheNPVprofileforProject2crossesthehorizontalaxisatabout14%and100%.TheNPVprofileforProject3crossesthehorizontalaxisatabout12%.7.3ThePaybackRule(1of2)ThepaybackperiodisamountoftimeittakestorecoverorpaybacktheinitialinvestmentIfthepaybackperiodislessthanapre-specifiedlengthoftime,youaccepttheprojectOtherwise,yourejecttheprojectThepaybackruleisusedbymanycompaniesbecauseofitssimplicityTextbookExample7.2(1of2)ThePaybackRuleProblemAssumeFredrick’srequiresallprojectstohaveapaybackperiodoffiveyearsorless.Wouldthefirmundertakethefertilizerprojectunderthisrule?TextbookExample7.2(2of2)SolutionRecallthattheprojectrequiresaninitialinvestmentof$250million,andwillgenerate$35millionperyear.Thesumofthecashflowsfromyear1toyear5ismillion,whichwillnotcovertheinitialinvestmentof$250million.Infact,itwillnotbeuntilyear8thattheinitialinvestmentwillbepaidbackBecausethepaybackperiodforthisprojectexceedsfiveyears,Fredrick’swillrejecttheproject.AlternativeExample7.2(1of2)ProblemProjectsA,B,andCeachhaveanexpectedlifeoffiveyears.Giventheinitialcostandannualcashflowinformationbelow,whatisthepaybackperiodforeachproject?BlankABCCost$80$120$150CashFlow$25$30$35AlternativeExample7.2(2of2)SolutionPaybackAProjectBProjectCThePaybackRule(2of2)PitfallsIgnorestheproject’scostofcapitalandtimevalueofmoneyIgnorescashflowsafterthepaybackperiodReliesonanadhocdecisioncriterion7.4ChoosingbetweenProjectsMutuallyExclusiveProjectsWhenyoumustchooseonlyoneprojectamongseveralpossibleprojects,thechoiceismutuallyexclusiveNPVRuleSelecttheprojectwiththehighestNPVIRRRuleSelectingtheprojectwiththehighestIRRmayleadtomistakesTextbookExample7.3(1of2)NPVandMutuallyExclusiveProjectsProblemAsmallcommercialpropertyisforsalenearyouruniversity.Givenitslocation,youbelieveastudent–orientedbusinesswouldbeverysuccessfulthere.Youhaveresearchedseveralpossibilitiesandcomeupwiththefollowingcashflowestimates(includingthecostofpurchasingtheproperty).Whichinvestmentshouldyouchoose?ProjectInitialInvestmentFirst-YearCashFlowGrowthRateCostofCapitalBookstore$300,000$63,0003.0percent.8%Coffeeshop$400,000$80,0003.0percent.8%Musicstore$400,000$104,0000.0percent.8%Electronicstore$400,000$100,0003.0percent.11%TextbookExample7.3(2of2)SolutionAssumingeachbusinesslastsindefinitely,wecancomputethepresentvalueofthecashflowsfromeachasaconstantgrowthperpetuity.TheNPVofeachprojectisThus,allofthealternativeshaveapositiveNPV.But,becausewecanonlychooseone,thecoffeeshopisthebestalternative.AlternativeExample7.3(1of2)ProblemAventurecapitalistisconsideringinvestinginseveralprojects.Youhaveresearchedseveralpossibilitiesforherandcomeupwiththefollowingcashflowestimates.Whichinvestmentshouldyourecommendfortheventurecapitalisttochoose?ProjectInitialInvestmentFirst-YearCashFlowGrowthRateCostofCapitalDatingApp$250,000$55,0004%7%GreenEnergy$350,000$75,0004%8%WaterPurification$400,000$120,0005%8%“Smart”Clothes$500,000$125,0008%12%AlternativeExample7.3(2of2)SolutionAssumingeachbusinesslastsindefinitely,wecancomputethepresentvalueofthecashflowsfromeachasaconstantgrowthperpetuity.TheNPVofeachprojectisThus,allofthealternativeshaveapositiveNPV.But,becausewecanonlychooseone,theclothingstoreisthebestalternative.IRRRuleandMutuallyExclusiveInvestments(1of4)DifferencesinScaleIfaproject’ssizeisdoubled,itsNPVwilldoubleThisisnotthecasewithIRRThus,theIRRrulecannotbeusedtocompareprojectsofdifferentscalesIRRRuleandMutuallyExclusiveInvestments(2of4)DifferencesinScaleConsidertwooftheprojectsfromExample7.3BlankBookstoreCoffeeshopInitialInvestment$300,000$400,000Cashflowsubscriptyear1baseline.$363,000$80,000AnnualGrowthRate3%3%Costofcapital8%8%IRR24%23%NPV$960,000$1,200,000IRRRuleandMutuallyExclusiveInvestments(3of4)TimingofCashFlowsAnotherproblemwiththeIRRisthatitcanbeaffectedbychangingthetimingofthecashflows,evenwhenthescaleisthesameIRRisareturn,butthedollarvalueofearningagivenreturndependsonhowlongthereturnisearnedConsideragainthecoffeeshopandthemusicstoreinvestmentinExample7.3BothhavethesameinitialscaleandthesamehorizonThecoffeeshophasalowerIRR,butahigherNPVbecauseofitshighergrowthrateIRRRuleandMutuallyExclusiveInvestments(4of4)DifferencesinRiskAnIRRthatisattractiveforasafeprojectneednotbeattractiveforariskierprojectConsidertheinvestmentintheelectronicsstorefromExample7.3TheIRRishigherthanthoseoftheotherinvestmentopportunities,yettheNPVisthelowestThehighercostofcapitalmeansahigherIRRisnecessarytomaketheprojectattractiveTheIncrementalIRRRule(1of2)IncrementalIRRInvestmentRuleApplytheIRRruletothedifferencebetweenthecashflowsofthetwomutuallyexclusivealternatives(theincrementtothecashflowsofoneinvestmentovertheother)TextbookExample7.4(1of4)UsingtheIncrementalIRRtoCompareAlternativesProblemYourfirmisconsideringoverhaulingitsproductionplant.Theengineeringteamhascomeupwithtwoproposals,oneforaminoroverhaulandoneforamajoroverhaul.Thetwooptionshavethefollowingcashflows(inmillionsofdollars):Proposal0123MajoroverhaulNegative10666MinoroverhaulNegative50252525WhatistheIRRofeachproposal?WhatistheincrementalIR

R?Ifthecostofcapitalforbothoftheseprojectsis12%,whatshouldyourfirmdo?TextbookExample7.4(2of4)SolutionWecancomputetheIRRofeachproposalusingtheannuitycalculator.Fortheminoroverhaul,theIRRis36.3%:BlankNPERRATEPVPMTFVExcelFormulaGiven3BlankNegative1060BlankSolveforrateBlank36.3%BlankBlankBlankEqualsRATEleftparenthesis3comma6commanegative10comma0rightparenthesis.Forthemajoroverhaul,theIRRis23.4%:BlankNPERRATEPVPMTFVExcelFormulaGiven3BlankNegative50250BlankSolveforrateBlank23.4%BlankBlankBlankEqualsRATEleftparenthesis3comma25commanegative50comma0rightparenthesis.TextbookExample7.4(3of4)Whichprojectisbest?Becausetheprojectshavedifferentscales,wecannotcomparetheirIRRsdirectly.TocomputetheincrementalIRRofswitchingfromtheminoroverhaultothemajoroverhaul,wefirstcomputetheincrementalcashflows:Proposal0123MajoroverhaulNegative50252525Less:MinoroverhaulNegativeleftparenthesisnegative10rightparenthesisNegative6Negative6Negative6IncrementalcashflowNegative40191919TextbookExample7.4(4of4)ThesecashflowshaveanIRRofBlankNPERRATEPVPMTFVExcelFormulaGiven3BlankNegative40190BlankSolveforRateblank20.0percent.BlankBlankBlankEqualsRATEleftparenthesis3comma19commanegative40comma0rightparenthesis.BecausetheincrementalIRRexceedsthe12%costofcapital,switchingtothemajoroverhaullooksattractive(i.e.,itslargerscaleissufficienttomakeupforitslowerIRR).WecancheckthisresultusingFigure7.5,whichshowstheNPVprofilesforeachproject.Atthe12%costofcapital,theNPVofthemajoroverhauldoesindeedexceedthatoftheminoroverhaul,despiteitslowerIRR.NotealsothattheincrementalIRRdeterminesthecrossoverpointoftheNPVprofiles,thediscountrateforwhichthebestprojectchoiceswitchesfromthemajoroverhaultominorone.Figure7.5ComparisonofMinorandMajorOverhaulsInExample7.4,wecanseethatdespiteitslowerIRR,themajoroverhaulhasahigherNPVatthecostofcapitalof12%.TheincrementalIRRof20%isthecrossoverpointatwhichtheoptimaldecisionchanges.AlternativeExample7.4(1of5)ProblemSupposeyourfirmisconsideringtwodifferentprojects,onethatlastsoneyearandanotherthatlastsfiveyears.Thecashflowsforthetwoprojectslooklikethis:WhatistheIRRofeachproposal?WhatistheincrementalIRR?Ifyourfirm’scostofcapitalis10%,whatshouldyoudo?AlternativeExample7.4(2of5)SolutionWecancomputetheIRRofProjectLusingtheannuitycalculator:BlankNPERRATEPVPMTFVExcelformulaGiven5BlankNegative1000200BlankSolveforrateblank14.87%BlankBlankBlankEqualsRATEleftparenthesis5comma0commanegative100comma200rightparenthesis.AlternativeExample7.4(3of5)SolutionWecancomputetheIRRofProjectSusingtheannuitycalculator:BlankNPERRATEPVPMTFVExcelformulaGiven1BlankNegative1000125BlankSolveforrateblank25%BlankBlankBlankEqualsRATEleftparenthesis1comma0commanegative100comma125rightparenthesis.AlternativeExample7.4(4of5)SolutionWecancalculatetheincrementalIRRthisway:Project012345LNegative100BlankBlankBlankBlank200SNegative100125BlankBlankBlankBlankDifference0Negative125BlankBlankBlank200BlankNPERRATEPVPMTFVExcelformulaGiven4BlankNegative1250200BlankSolveforrateBlank12.47%BlankBlankBlankEqualsRATEleftparenthesis4comma0commanegative125comma200rightparenthesis.AlternativeExample7.4(5of5)SolutionBecausethe12.47%incrementalIRRisbiggerthanthecostofcapitalof10%,thelong-termprojectisbetterthantheshort-termproject,eventhoughtheshort-termprojecthasahigherIRR.TheIncrementalIRRRule(2of2)ShortcomingsoftheIncrementalIRRRuleTheincrementalIRRmaynotexistMultipleincrementalIRRscouldexistThefactthattheIRRexceedsthecostofcapitalforbothprojectsdoesnotimplythateitherprojecthasapositiveNPVWhenindividualprojectshavedifferentcostsofcapital,itisnotobviouswhichcostofcapitaltheincrementalIRRshouldbecomparedto7.5ProjectSelectionwithResourceConstraintsEvaluationofProjectswithDifferentResourceConstraintsConsiderthreepossibleprojectswitha$100millionbudgetconstraint:Table7.1PossibleProjectsfora$100MillionBudgetProjectNPV($millions)InitialInvestment($millions)ProfitabilityIndexNPV/InvestmentOne.1101001.1Two.70501.4Three.60501.2ProfitabilityIndexTheprofitabilityindexcanbeusedtoidentifytheoptimalcombinationofprojectstoundertakeFromTable7.1,wecanseeitisbettertotakeprojectsandtogetherandforgoprojectTextbookExample7.5(1of3)ProfitabilityIndexwithaHumanResourceConstraintProblemYourdivisionatNetIt,alargernetworkingcompany,hasputtogetheraprojectproposaltodevelopanewhomenetworkingrouter.TheexceptedNPVoftheprojectis$17.7million,andtheprojectwillrequire50softwareengineers.NetIthasatotalof190engineersavailable,andtherouterprojectmustcompetewiththefollowingotherprojectsfortheseengineers:ProjectNPV($millions)EngineeringHeadcountRouter17.750ProjectA22.747ProjectB8.144ProjectC14.0.40ProjectD11.561ProjectE20.658ProjectF12.932Total107.5332HowshouldNetItprioritizetheseprojects?TextbookExample7.5(2of3)SolutionThegoalistomaximizethetotalNPVwecancreatewith190engineers(atmost).WecomputetheprofitabilityindexforeachprojectusingEngineeringHeadcountinthedenominator,andthensortprojectsbasedontheindex:ProjectNPV($millions)EngineeringHeadcount(EHC)ProfitabilityIndex(NPVperEHC)CumulativeEHCRequiredProjectA22.7470.483.47ProjectF12.9320.403.79ProjectE20.6580.355.137Router17.7500.354.187ProjectC14.0.400.350.BlankProjectD11.5610.189.BlankProjectB8.1440.184.BlankTextbookExample7.5(3of3)Wenowassigntheresourcetotheprojectsindescendingorderaccordingtotheprofitabilityindex.Thefinalcolumnshowsthecumulativeuseoftheresourceaseachprojectistakenonuntiltheresourceisusedup.TomaximizeNPVwithintheconstraintof190engineers.NetItshouldchoosethefirstfourprojectsonthelist.Thereisnoothercombinationofprojectsthatwillcreatemorevaluewithoutusingmoreengineersthanwehave.Note,however,thattheresourceconstraintforcesNetIttoforgothreeotherwisevaluableprojects(C,D,andB)withatotalNPVof$3.36million.AlternativeExample7.5(1of3)ProblemSupposeyourfirmhasthefollowingfivepositiveNPVprojectstochoosefrom.However,thereisnotenoughmanufacturingspaceinyourplanttoselectalloftheprojects.Useprofitabilityindextochooseamongtheprojects,giventhatyouonlyhave100,000squarefeetofunusedspace.ProjectNPVSquarefeetneededProject1100,00040,000Project288,00030,000Project380,00038,000Project450,00024,000Project512,0001,000Total330,000133,000AlternativeExample7.5(2of3)SolutionComputethePIforeachproject.ProjectNPVSquarefeetneededProfitabilityIndex(NPV/Sq.Ft)Project1100,00040,0002.5Project288,00030,0002.93Project380,00038,0002.10Project450,00024,0002.08Project512,0001,00012point0Total330,000133,000BlankAlternativeExample7.5(3of3)SolutionRankorderthembyPIandseehow