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Chapter06CapitalBudgetingTechniques資本預(yù)算方法Chapter06CapitalBudgetingTeProjectEvaluation:AlternativeMethods
PaybackPeriod(PBP投資回收期)InternalRateofReturn(IRR內(nèi)含報酬率)NetPresentValue(NPV凈現(xiàn)值)ProfitabilityIndex(PI獲利指數(shù))ProjectEvaluation:AlternatiProposedProjectDataJulieMillerisevaluatinganewprojectforherfirm,BasketWonders(BW).Shehasdeterminedthattheafter-taxcashflowsfortheprojectwillbe$10,000;$12,000;$15,000;$10,000;and$7,000,respectively,foreachoftheYears1through5.Theinitialcashoutlaywillbe$40,000.ProposedProjectDataJulieMilIndependentProjectIndependent
--Aprojectwhoseacceptance(orrejection)doesnotpreventtheacceptanceofotherprojectsunderconsideration.Forthisproject,assumethatitisindependent
ofanyotherpotentialprojectsthatBasketWondersmayundertake.IndependentProjectIndependentPaybackPeriod(PBP)PBP
istheperiodoftimerequiredforthecumulativeexpectedcashflowsfromaninvestmentprojecttoequaltheinitialcashoutflow.012345
-40K10K12K15K10K7KPaybackPeriod(PBP)PBPisthe(c)10K22K37K47K54KPaybackSolution(#1)PBP =a+(b
-c)/d =3+(40-37)/10 =3+(3)/10 =3.3Years012345
-40K10K12K15K10K7KCumulativeInflows(a)(-b)(d)(c)10K22KPaybackSolution(#2)PBP =3+(3K)/10K
=3.3YearsNote:Takeabsolutevalueoflastnegativecumulativecashflowvalue.CumulativeCashFlows
-40K10K12K15K
10K7K012345-40K-30K-18K-3K7K14KPaybackSolution(#2)PBP =3PBPAcceptanceCriterionYes!Thefirmwillreceivebacktheinitialcashoutlayinlessthan3.5years.[3.3Years<3.5YearMax.]ThemanagementofBasketWondershassetamaximumPBPof3.5yearsforprojectsofthistype.Shouldthisprojectbeaccepted?PBPAcceptanceCriterionYes!PBPStrengths
andWeaknessesStrengths:Easytouseand understand Canbeusedasa measureof liquidityWeaknesses:Doesnotaccount forTVM Doesnotconsider cashflowsbeyond thePBP
PBPStrengths
andWeaknesseInternalRateofReturn(IRR)IRRisthediscountratethatequatesthepresentvalueofthefuturenetcashflowsfromaninvestmentprojectwiththeproject’sinitialcashoutflow.CF1CF2CFn
(1+IRR)1(1+IRR)2(1+IRR)n+...++ICO=InternalRateofReturn(IRR)I$15,000$10,000$7,000
IRRSolution$10,000$12,000(1+IRR)1
(1+IRR)2Findtheinterestrate(IRR)thatcausesthediscountedcashflowstoequal$40,000.++++$40,000=(1+IRR)3
(1+IRR)4
(1+IRR)5$15,000$10,000$7IRRSolution(Try10%)$40,000= $10,000(PVIF10%,1)+$12,000(PVIF10%,2)+ $15,000(PVIF10%,3)+$10,000(PVIF10%,4)+ $7,000(PVIF10%,5)= $10,000(.909)+$12,000(.826)+ $15,000(.751)+$10,000(.683)+ $7,000(.621)= $9,090+$9,912+$11,265+ $6,830+$4,347 = $41,444 [Rateistoolow!!]IRRSolution(Try10%)$40,000IRRSolution(Try15%)$40,000= $10,000(PVIF15%,1)+$12,000(PVIF15%,2)+ $15,000(PVIF15%,3)+$10,000(PVIF15%,4)+ $7,000(PVIF15%,5)
= $10,000(.870)+$12,000(.756)+ $15,000(.658)+$10,000(.572)+ $7,000(.497)
= $8,700+$9,072+$9,870+ $5,720+$3,479 = $36,841 [Rateistoohigh!!]IRRSolution(Try15%)$40,000
.10 $41,444 .05 IRR $40,000 $4,603 .15 $36,841 ($1,444)(0.05) $4,603
IRRSolution(Interpolate)$1,444XX=X=.0157IRR=.10+.0157=.1157or11.57%X/.05=1444/4603 .10 $41,444IRRSolution(IIRRAcceptanceCriterion
No!Thefirmwillreceive11.57%foreachdollarinvestedinthisprojectatacostof13%.[IRR
<HurdleRate]
ThemanagementofBasketWondershasdeterminedthatthehurdlerateis13%forprojectsofthistype.Shouldthisprojectbeaccepted?IRRAcceptanceCriterionNo!IRRStrengths
andWeaknesses
Strengths:Accountsfor TVMConsidersall cashflowsLess subjectivityWeaknesses:Assumesallcash flowsreinvestedat theIRR Difficultieswith projectrankingsand MultipleIRRsIRRStrengths
andWeaknesseNetPresentValue(NPV)
NPVisthepresentvalueofaninvestmentproject’snetcashflowsminustheproject’sinitialcashoutflow.CF1
CF2
CFn
(1+k)1(1+k)2(1+k)n+...++-
ICONPV=NetPresentValue(NPV)NPViBasketWondershasdeterminedthattheappropriatediscountrate(k)forthisprojectis13%.$10,000
$7,000
NPVSolution$10,000
$12,000
$15,000
(1.13)1
(1.13)2
(1.13)3
+++-$40,000(1.13)4
(1.13)5NPV
=+BasketWondershasdeterminedNPVSolutionNPV= $10,000(PVIF13%,1)+$12,000(PVIF13%,2)+ $15,000(PVIF13%,3)+$10,000(PVIF13%,4)+ $7,000(PVIF13%,5)-$40,000NPV= $10,000(.885)+$12,000(.783)+ $15,000(.693)+$10,000(.613)+ $7,000(.543)-$40,000NPV= $8,850+$9,396+$10,395+ $6,130+$3,801-$40,000
= -$1,428NPVSolutionNPV= $10,000(PVINPVAcceptanceCriterion
No!TheNPVisnegative.Thismeansthattheprojectisreducingshareholderwealth.[RejectasNPV
<0]ThemanagementofBasketWondershasdeterminedthattherequiredrateis13%forprojectsofthistype.Shouldthisprojectbeaccepted?NPVAcceptanceCriterionNo!NPVStrengths
andWeaknesses
Strengths:Cashflows assumedtobe reinvestedatthe hurdlerate.AccountsforTVM.Considersall cashflows.Weaknesses:Maynotinclude managerial optionsembedded intheproject.See Chapter14.NPVStrengths
andWeaknesseNetPresentValueProfileDiscountRate(%)03691215IRRNPV13%SumofCF’sPlotNPVforeachdiscountrate.Threeofthesepointsareeasynow!NetPresentValue$000s151050-4NetPresentValueProfileDiscoProfitabilityIndex(PI)
PIistheratioofthepresentvalueofaproject’sfuturenetcashflowstotheproject’sinitialcashoutflow.CF1
CF2
CFn
(1+k)1(1+k)2(1+k)n+...++ICOPI=PI=1+[NPV/ICO
]<<OR>>Method#2:Method#1:ProfitabilityIndex(PI)PIi
PIAcceptanceCriterion
No!ThePIislessthan1.00.This meansthattheprojectisnotprofitable.[RejectasPI
<1.00]
PI =$38,572/$40,000 =.9643(Method#1,13-34)Shouldthisprojectbeaccepted?PIAcceptanceCriterionNPIStrengths
andWeaknesses
Strengths:
SameasNPVAllows comparisonof differentscale projectsWeaknesses:
SameasNPVProvidesonly relativeprofitabilityPotentialRanking ProblemsPIStrengths
andWeaknesseEvaluationSummaryBasketWondersIndependentProjectEvaluationSummaryBasketWondeOtherProjectRelationshipsMutuallyExclusive
--Aprojectwhoseacceptanceprecludestheacceptanceofoneormorealternativeprojects.Dependent--Aprojectwhoseacceptancedependsontheacceptanceofoneormoreotherprojects.OtherProjectRelationshipsMutPotentialProblems
UnderMutualExclusivityA.ScaleofInvestmentB.Cash-flowPatternC.ProjectLife
Rankingofprojectproposalsmaycreatecontradictoryresults.PotentialProblems
UnderMutA.ScaleDifferences
Compareasmall(S)andalarge(L)project.NETCASHFLOWSProjectSProjectLENDOFYEAR
0-$100-$100,000
100
2$400$156,250A.ScaleDifferencesComparScaleDifferencesCalculatethePBP,IRR,NPV10%,andPI10%.Whichprojectispreferred?Why?Project
IRR
NPV
PI
S100%$2313.31L25%$29,1321.29ScaleDifferencesCalculatetheB.CashFlowPatternLetuscompareadecreasingcash-flow(D)projectandanincreasingcash-flow(I)project.NETCASHFLOWSProjectD
ProjectIENDOFYEAR
0-$1,200-$1,200
11,000100
2500600
31001,080B.CashFlowPatternLetusco
D
23%
$1981.17
I17%
$1981.17CashFlowPattern
CalculatetheIRR,NPV10%, andPI10%.Whichprojectispreferred?Project
IRR
NPV
PI?D23%$1ExamineNPVProfilesDiscountRate(%)0510152025-2000200400600IRRNPV10%PlotNPVforeachprojectatvariousdiscountrates.NetPresentValue($)ProjectIProjectDExamineNPVProfilesDiscountRFisher’sRateofIntersectionDiscountRate($)0510152025-2000200400600NetPresentValue($)Atk<10%,Iisbest!Fisher’sRateofIntersectionAtk>10%,Disbest!Fisher’sRateofIntersectionDC.ProjectLifeDifferences
Letuscomparealonglife(X)project andashortlife(Y)project.NETCASHFLOWSProjectXProjectYENDOFYEAR
0-$1,000-$1,000
10
2,000
200
33,3750C.ProjectLifeDifferences
X50%$1,5362.54Y100%$8181.82ProjectLifeDifferencesCalculatethePBP,IRR,NPV10%,andPI10%.Whichprojectispreferred?Why?
Project
IRR
NPV
PI?XAnotherWaytoLookatThings1. Adjustcashflowstoacommonterminal yearifproject“Y”willNOTbereplaced. CompoundProjectY,Year110%for2years.Year0123CF-$1,000$0$0$2,420 Results: IRR*=34.26% NPV=$818*LowerIRRfromadjustedcash-flowstream.XisstillBest.AnotherWaytoLookatThings1ReplacingProjects withIdenticalProjects2. UseReplacementChainApproach(AppendixB)whenproject“Y”willbereplaced.0123-$1,000$2,000
-1,000$2,000
-1,000$2,000-$1,000$1,000$1,000$2,000Results: IRR=100%
NPV*
=
$2,238.17*HigherNPV,butthesameIRR.
YisBest.ReplacingProjects withIdeCapitalRationing（資本配給）CapitalRationingoccurswhenaconstraint(orbudgetceiling)isplacedonthetotalsizeofcapitalexpendituresduringaparticularperiod.（對總支出有限制）Example:JulieMillermustdeterminewhatinvestmentopportunitiestoundertakeforBasketWonders(BW).Sheislimitedtoamaximumexpenditureof$32,500onlyforthiscapitalbudgetingperiod.CapitalRationing（資本配給）CapitalAvailableProjectsforBW
ProjectICOIRRNPVPI A$
50018% $501.10 B 5,000 25 6,5002.30 C 5,000 37 5,5002.10 D 7,500 20 5,0001.67 E 12,500 26 5001.04 F 15,000 28
21,0002.40 G 17,500 19 7,5001.43 H 25,000 15 6,0001.24AvailableProjectsforBWProjChoosingbyIRRsforBW
ProjectICOIRRNPVPI C$5,000 37%
$5,5002.10 F 15,000 28
21,0002.40 E 12,500 26
5001.04 B 5,000 25 6,5002.30ProjectsC,F,andEhavethe threelargestIRRs.Theresultingincrease
inshareholderwealthis$27,000witha$32,500outlay.ChoosingbyIRRsforBWProjecChoosingbyNPVsforBW
ProjectICOIRRNPVPI F$15,000 28% $21,0002.40 G 17,500 19 7,5001.43 B 5,000 25 6,5002.30 ProjectsFandGhavethe twolargestNPVs.Theresultingincrease
inshareholderwealthis$28,500witha$32,500outlay.ChoosingbyNPVsforBWProjecChoosingbyPIsforBW
ProjectICOIRRNPVPI F $15,000 28% $21,000
2.40 B 5,000 25 6,500
2.30 C 5,000 37 5,500
2.10 D 7,500 20 5,000
1.67 G 17,500 19 7,5001.43ProjectsF,B,C,andDhavethefourlargestPIs.Theresultingincrease
inshareholderwealthis$38,000witha$32,500outlay.ChoosingbyPIsforBWProjSummaryofComparison
Method
ProjectsAccepted
ValueAddedPI F,B,C,andD$38,000NPV FandG$28,500IRR C,F,andE$27,000PIgeneratesthegreatest
increase
inshareholderwealthwhenalimitedcapitalbudgetexistsforasingleperiod.SummaryofComparisonMethod謝謝謝謝45Chapter06CapitalBudgetingTechniques資本預(yù)算方法Chapter06CapitalBudgetingTeProjectEvaluation:AlternativeMethods
PaybackPeriod(PBP投資回收期)InternalRateofReturn(IRR內(nèi)含報酬率)NetPresentValue(NPV凈現(xiàn)值)ProfitabilityIndex(PI獲利指數(shù))ProjectEvaluation:AlternatiProposedProjectDataJulieMillerisevaluatinganewprojectforherfirm,BasketWonders(BW).Shehasdeterminedthattheafter-taxcashflowsfortheprojectwillbe$10,000;$12,000;$15,000;$10,000;and$7,000,respectively,foreachoftheYears1through5.Theinitialcashoutlaywillbe$40,000.ProposedProjectDataJulieMilIndependentProjectIndependent
--Aprojectwhoseacceptance(orrejection)doesnotpreventtheacceptanceofotherprojectsunderconsideration.Forthisproject,assumethatitisindependent
ofanyotherpotentialprojectsthatBasketWondersmayundertake.IndependentProjectIndependentPaybackPeriod(PBP)PBP
istheperiodoftimerequiredforthecumulativeexpectedcashflowsfromaninvestmentprojecttoequaltheinitialcashoutflow.012345
-40K10K12K15K10K7KPaybackPeriod(PBP)PBPisthe(c)10K22K37K47K54KPaybackSolution(#1)PBP =a+(b
-c)/d =3+(40-37)/10 =3+(3)/10 =3.3Years012345
-40K10K12K15K10K7KCumulativeInflows(a)(-b)(d)(c)10K22KPaybackSolution(#2)PBP =3+(3K)/10K
=3.3YearsNote:Takeabsolutevalueoflastnegativecumulativecashflowvalue.CumulativeCashFlows
-40K10K12K15K
10K7K012345-40K-30K-18K-3K7K14KPaybackSolution(#2)PBP =3PBPAcceptanceCriterionYes!Thefirmwillreceivebacktheinitialcashoutlayinlessthan3.5years.[3.3Years<3.5YearMax.]ThemanagementofBasketWondershassetamaximumPBPof3.5yearsforprojectsofthistype.Shouldthisprojectbeaccepted?PBPAcceptanceCriterionYes!PBPStrengths
andWeaknessesStrengths:Easytouseand understand Canbeusedasa measureof liquidityWeaknesses:Doesnotaccount forTVM Doesnotconsider cashflowsbeyond thePBP
PBPStrengths
andWeaknesseInternalRateofReturn(IRR)IRRisthediscountratethatequatesthepresentvalueofthefuturenetcashflowsfromaninvestmentprojectwiththeproject’sinitialcashoutflow.CF1CF2CFn
(1+IRR)1(1+IRR)2(1+IRR)n+...++ICO=InternalRateofReturn(IRR)I$15,000$10,000$7,000
IRRSolution$10,000$12,000(1+IRR)1
(1+IRR)2Findtheinterestrate(IRR)thatcausesthediscountedcashflowstoequal$40,000.++++$40,000=(1+IRR)3
(1+IRR)4
(1+IRR)5$15,000$10,000$7IRRSolution(Try10%)$40,000= $10,000(PVIF10%,1)+$12,000(PVIF10%,2)+ $15,000(PVIF10%,3)+$10,000(PVIF10%,4)+ $7,000(PVIF10%,5)= $10,000(.909)+$12,000(.826)+ $15,000(.751)+$10,000(.683)+ $7,000(.621)= $9,090+$9,912+$11,265+ $6,830+$4,347 = $41,444 [Rateistoolow!!]IRRSolution(Try10%)$40,000IRRSolution(Try15%)$40,000= $10,000(PVIF15%,1)+$12,000(PVIF15%,2)+ $15,000(PVIF15%,3)+$10,000(PVIF15%,4)+ $7,000(PVIF15%,5)
= $10,000(.870)+$12,000(.756)+ $15,000(.658)+$10,000(.572)+ $7,000(.497)
= $8,700+$9,072+$9,870+ $5,720+$3,479 = $36,841 [Rateistoohigh!!]IRRSolution(Try15%)$40,000
.10 $41,444 .05 IRR $40,000 $4,603 .15 $36,841 ($1,444)(0.05) $4,603
IRRSolution(Interpolate)$1,444XX=X=.0157IRR=.10+.0157=.1157or11.57%X/.05=1444/4603 .10 $41,444IRRSolution(IIRRAcceptanceCriterion
No!Thefirmwillreceive11.57%foreachdollarinvestedinthisprojectatacostof13%.[IRR
<HurdleRate]
ThemanagementofBasketWondershasdeterminedthatthehurdlerateis13%forprojectsofthistype.Shouldthisprojectbeaccepted?IRRAcceptanceCriterionNo!IRRStrengths
andWeaknesses
Strengths:Accountsfor TVMConsidersall cashflowsLess subjectivityWeaknesses:Assumesallcash flowsreinvestedat theIRR Difficultieswith projectrankingsand MultipleIRRsIRRStrengths
andWeaknesseNetPresentValue(NPV)
NPVisthepresentvalueofaninvestmentproject’snetcashflowsminustheproject’sinitialcashoutflow.CF1
CF2
CFn
(1+k)1(1+k)2(1+k)n+...++-
ICONPV=NetPresentValue(NPV)NPViBasketWondershasdeterminedthattheappropriatediscountrate(k)forthisprojectis13%.$10,000
$7,000
NPVSolution$10,000
$12,000
$15,000
(1.13)1
(1.13)2
(1.13)3
+++-$40,000(1.13)4
(1.13)5NPV
=+BasketWondershasdeterminedNPVSolutionNPV= $10,000(PVIF13%,1)+$12,000(PVIF13%,2)+ $15,000(PVIF13%,3)+$10,000(PVIF13%,4)+ $7,000(PVIF13%,5)-$40,000NPV= $10,000(.885)+$12,000(.783)+ $15,000(.693)+$10,000(.613)+ $7,000(.543)-$40,000NPV= $8,850+$9,396+$10,395+ $6,130+$3,801-$40,000
= -$1,428NPVSolutionNPV= $10,000(PVINPVAcceptanceCriterion
No!TheNPVisnegative.Thismeansthattheprojectisreducingshareholderwealth.[RejectasNPV
<0]ThemanagementofBasketWondershasdeterminedthattherequiredrateis13%forprojectsofthistype.Shouldthisprojectbeaccepted?NPVAcceptanceCriterionNo!NPVStrengths
andWeaknesses
Strengths:Cashflows assumedtobe reinvestedatthe hurdlerate.AccountsforTVM.Considersall cashflows.Weaknesses:Maynotinclude managerial optionsembedded intheproject.See Chapter14.NPVStrengths
andWeaknesseNetPresentValueProfileDiscountRate(%)03691215IRRNPV13%SumofCF’sPlotNPVforeachdiscountrate.Threeofthesepointsareeasynow!NetPresentValue$000s151050-4NetPresentValueProfileDiscoProfitabilityIndex(PI)
PIistheratioofthepresentvalueofaproject’sfuturenetcashflowstotheproject’sinitialcashoutflow.CF1
CF2
CFn
(1+k)1(1+k)2(1+k)n+...++ICOPI=PI=1+[NPV/ICO
]<<OR>>Method#2:Method#1:ProfitabilityIndex(PI)PIi
PIAcceptanceCriterion
No!ThePIislessthan1.00.This meansthattheprojectisnotprofitable.[RejectasPI
<1.00]
PI =$38,572/$40,000 =.9643(Method#1,13-34)Shouldthisprojectbeaccepted?PIAcceptanceCriterionNPIStrengths
andWeaknesses
Strengths:
SameasNPVAllows comparisonof differentscale projectsWeaknesses:
SameasNPVProvidesonly relativeprofitabilityPotentialRanking ProblemsPIStrengths
andWeaknesseEvaluationSummaryBasketWondersIndependentProjectEvaluationSummaryBasketWondeOtherProjectRelationshipsMutuallyExclusive
--Aprojectwhoseacceptanceprecludestheacceptanceofoneormorealternativeprojects.Dependent--Aprojectwhoseacceptancedependsontheacceptanceofoneormoreotherprojects.OtherProjectRelationshipsMutPotentialProblems
UnderMutualExclusivityA.ScaleofInvestmentB.Cash-flowPatternC.ProjectLife
Rankingofprojectproposalsmaycreatecontradictoryresults.PotentialProblems
UnderMutA.ScaleDifferences
Compareasmall(S)andalarge(L)project.NETCASHFLOWSProjectSProjectLENDOFYEAR
0-$100-$100,000
100
2$400$156,250A.ScaleDifferencesComparScaleDifferencesCalculatethePBP,IRR,NPV10%,andPI10%.Whichprojectispreferred?Why?Project
IRR
NPV
PI
S100%$2313.31L25%$29,1321.29ScaleDifferencesCalculatetheB.CashFlowPatternLetuscompareadecreasingcash-flow(D)projectandanincreasingcash-flow(I)project.NETCASHFLOWSProjectD
ProjectIENDOFYEAR
0-$1,200-$1,200
11,000100
2500600
31001,080B.CashFlowPatternLetusco
D
23%
$1981.17
I17%
$1981.17CashFlowPattern
CalculatetheIRR,NPV10%, andPI10%.Whichprojectispreferred?Project
IRR
NPV
PI?D23%$1ExamineNPVProfilesDiscountRate(%)0510152025-2000200400600IRRNPV10%PlotNPVforeachprojectatvariousdiscountrates.NetPresentValue($)ProjectIProjectDExamineNPVProfilesDiscountRFisher’sRateofIntersectionDiscountRate($)0510152025-2000200400600NetPresentValue($)Atk<10%,Iisbest!Fisher’sRateofIntersectionAtk>10%,Disbest!Fisher’sRateofIntersectionDC.ProjectLifeDifferences
Letuscomparealonglife(X)project andashortlife(Y)project.NETCASHFLOWSProjectXProjectYENDOFYEAR
0-$1,000-$1,000
10
2,000
200
33,3750C.ProjectLifeDifferences
X50%$1,5362.54Y100%$8181.82ProjectLifeDifferencesCalculatethePBP,IRR,NPV10%,andPI10%.Whichprojectispreferred?Why?
Project
IRR
NPV
PI?XAnotherWaytoLookatThings1. Adjustcashflowstoacommonterminal yearifproject“Y”willNOTbereplaced. CompoundProjectY,Year110%for2years.Year0123CF-$1,000$0$0$2,420 Results: IRR*=34.26% NPV=$818*LowerIRRfromadjustedcash-flowstream.XisstillBest.AnotherWaytoLookatThings1ReplacingProjects withIdenticalProjects2. UseReplacem
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