投資項目效益評價

投資項目效益評價2024/3/28投資項目效益評價AdvancedTopicsinCapitalBudgetingI.WhatisCapitalBudgeting? Capital=FixedAssetsusedinproduction/service;Budgeting=Plandetailingprojectedcashinflowsandoutflowsduringsomefutureperiod,thus“CapitalBudgeting”outlinestheplannedexpendituresonfixedassets. 1.Multi-conceptsforCapitalBudgeting

(1)CapitalInvestmentAnalysis&Decision (2)EconomicEvaluationofInvestmentProjects (3)TechnologicalEconomics (4)InvestmentFeasibilityStudy 2.AFormalDefinitionofCapitalBudgeting

Capitalbudgetingisafiledoffinanceconcernedwithcostandbenefit,andreturnandriskderivedfrominvestmentprojectundertakenbyafirm.

Thecapitalbudgetingisaprocedureincludeasetofsystematictechniquesdealingwithhowtoevaluateandselectinvestmentprojectsundercertaintyoruncertainty.投資項目效益評價廈門大學管理學院吳世農MarketResearchInvestmentSources&CostCBAExpendituresofCapitals

MarketingStrategyCosts&IncomeRProfitsStatementRisk&InvestmentAnalysisDManagementAssets&BalanceLiabilitiesSheetProductionFinanceCashInflow&CashflowRepaymentOpportunityStudyCashOutflowStatementAnalysisPreliminaryDiscussionFeasibilityDiscussionFinalProposalsStudyReport

Exhibit1:DiagramSuggestedforInvestmentProject’sFeasibilityStudyinFirms

投資項目效益評價廈門大學管理學院吳世農

TechnologicalMacroeconomicFeasibilityFeasibilityFinancialImplementationOperationFeasibility

Social/CulturalEnvironmentalFeasibilityFeasibility

ComprehensiveReviewPost-FeasibilityReportAssessment

Exhibit1(Continuos):DiagramSuggestedforInvestmentProject’sFeasibilityStudyinFirms

投資項目效益評價AdvancedTopicsinCapitalBudgetingII.ConflictsbetweenNPVandIRRforMutuallyExclusiveProjects 1.SizeEffectofInvestmentOutlayonNPVandIRR (1)Conflict——WhichMaximizesShareholder’sWealth?Supposethattherearetwoprojects,AandB,n=1,K=10%,theirinvestmentoutlaysandNCFarepresentedinthefollowingtable.

ProjectI0NCF1NPV(k=10%)IRRPVIA5,0008,0002,27360%45.46%B50,00075,00018,18250%36.36%

BothprojectsareacceptableduetotheirpositivevaluesofNPV,however,giventhatthetwoprojectsaremutuallyexclusive,whichoneispreferred?Also,becausethesizeofinvestmentoutlaysforAandBaredifferent.ByNPV,AisbetterthanB;byIRR(orPVI)BisoverA.ThiscaseistypicalasaconflictraisedfromdecisioncriteriabyNPVorbyIRR?投資項目效益評價廈門大學吳世農 (2)SolutionSinceK=10%isassumedtobefixed,wecansolvethisconflictbycreatingadifferentialproject(B-A),ifthedifferentialprojectyieldsapositiveNPV,itisobviousthatBisbetterthanAbecausenotonlyapartofBwillcreateaNPVequaltoNPVA,butalsocreateapositiveNPVforthedifferentialproject(B-A).Thus,wecreateadifferentialproject(B-A),andthencalculateitsNPVandIRRNPV(B-A)=[(75000-8000)/(1+10%)]-(50000-5000)=$15909[(75000-8000)/(1+IRR(B-A))]=(50000-5000),IRR(B-A)=48.8%Nodoubt,theresultsabovesuggeststhattheinvestorsofthefirmwillbebetteroffifprojectBisaccepted.

投資項目效益評價AdvancedTopicsinCapitalBudgeting 2.TrendEffectofNCFonNPVandIRR(1)Conflict——WhichOneisaSoundingDecisionRule?Supposetherearetwomutuallyexclusiveprojects,AandB,thefollowinggraphsshowthatthetrendofA’sNCFsandthetrendofB’sNCFsaredifferent.Obviously,graph1statesthatA’sNCFsarealwayslargerthanB’sNCFsovertheperiods,thus,NPVA>NPVB;graph2statesfortheearlierperiodsA’sNCFsarelargerthanB’sNCFs,thusNPVA>NPVB,butforthelaterperiods(afterK*)A’sNCFsaresmallerthanB’sNCFs,thusNPVA<NPVB.NPVGraph1NPVGraph2

BANPVA

>NPV

BBA

NPVA

<NPV

B

NPVA

=NPV

B

KNPVA

<NPV

BKkIRRB<IRRAk*IRRA<IRRB

投資項目效益評價廈門大學吳世農 Forgraph1,projectAwillbechosenforinvestmentwhileprojectbewillbegivenup.Thedecisionisclear.Forgraph2,itishardtosaywhichoneisbetter.Thequestioncannotbeanswereduntilwedoafurtherstudy.(2)SolutionToillustratethecaseshowningraph2,thefollowingtablecontainsnecessaryinformationformakingtheaccept/rejectdecision. ProjectI0NCF1NCF2NPV(K=10%)IRRNPV(K=20%)A10001000310165.324.8%48.6B10002001200173.620%0Toanswerthequestionforthecaseofgraph2,wehastocreateadifferentialproject(B-A),weregardthedifferenceofB’sNCFandA’NCFinthefirstyear(NCF1B-NCF1A)asI1,whichisanegativevalue(orcashoutflow).AlsowetreatedthedifferenceofB’sNCFandA’NCFinthesecondyear(NCF2B-NCF1A)asNCF1,whichisapositivevalue(orcashinflow).Thusthedifferentialproject’sNPVandIRRcanbeshownasfollows:投資項目效益評價AdvancedTopicsinCapitalBudgeting NPV(B-A)=[890/(1+10%)]-800=$9.1[890/(1+IRR(B-A))]-800;IRR(B-A)=11.23%Bythecalculationsabove,itsuggeststhatprojectBisbetterthanprojectA。 3.SignEffectofNCFsonNPVandIRR (1)Conflict——WhichOneisApplicable?Weonediscussedaclassificationofcashflows:conventionalNCFandnon-conventionalNCF,therationalbehindthisclassificationistoidentifyapplicabilityofcapitalbudgetingtechniques,particularlyforNPVandIRR.Ifaproject’sstreamofestimatedNCFschangessignmorethanonce,thestreamofNCFsisnon-conventional.Inthiscase,IRRisnotapplicablebecauseitcanresultinmultipleratesofreturn!Why?AsimpleanswertothisquestionisthatifthestreamofNCFschangessignmorethanonetime,mathematically,solvingtheequationofIRRwillresultsinmorethanonesolutions——MultipleRatesofReturns.投資項目效益評價廈門大學吳世農 Geometrically,themultipleratesofreturncanbeshowninthefollowinggraph.

NPV0K SomeStudiesshowthatcashflowsofinvestmentprojectswerehighlyassociatedwitheconomicenvironment,marketcompetition,managementabilityandmanyothers.Inpractice,itiscommonthatNCFchangessignmanytimesduringitsentirelifeastheinfluentialfactorschange.Thus,IRRisineffectivetothecaseofnon-conventionalcashflows.投資項目效益評價AdvancedTopicsinCapitalBudgeting (2)SolutionOil-wellPumpInvestmentisatypicalcaseincapitalbudgetingtoshowtheproblemofmultipleratesofreturnifIRRisemployedtoevaluatethisproject’sIRR.Aoilcompanyistryingtodecidewhetherornottoinstallahigh-speedpumponanoil-wellwhichisalreadyinoperation.Thepumpwillcost$1,600toinstall.Thepumpwill,forthefirstyear,generate$10,000moreoilthanthepumpusednow,butforthesecondyearthenewpumpwillgenerate$10,000lessoilbecausethewellhasbeendepleted.Shouldtheoilcompanyinstallthehigh-speedpimp?Wesummarizetheestimatedincrementalcashflowsandpresenttheminthefollowingtable.Year012NCF-1,60010,000-10,000(a)ConfusingSolutionResultedfromIRR1600=[10000/(1+IRR)1]+[-10000/(1+IRR)2][-1600/(1+IRR)]+[10000/(1+IRR)1]+[-10000/(1+IRR)2]=0投資項目效益評價廈門大學吳世農 BecausethisequationshowsthatNCFchangeitssignfrom“+”to“-”onetime,thesolutiontothisequationproducestwoalternativeresults:IRR=25%IRR=400%Obviously,theresultsareconfusingandhardtointerpreted.NPV

IRR=25%IRR=400%1000500 100 200 300 400 500 K(%)-500-1000-1500投資項目效益評價AdvancedTopicsinCapitalBudgeting

(b)AlternativeSolutionOfferedbyTeichrow(1964)

TeichrowthoughttheOil-wellPumpInvestmentinadifferentway——addthecashflowsoftwoadjacentperiods(period0andperiod1)togetherbyalogicallyeconomicwaytomakeNCF’ssignchangetoconventional.Assumeputmoneyintotheinvestmenttwice:$-1600atthetimeoftheinitialinvestment,and$-10000inthesecondtimeperiod.Theprojectcanbethoughtofaslending+$10000at10%(costofcapital)tothefirminthefirsttimeperiod.So,thefirst,thefirminvests$-1600nowandexpectstoearntheIRRattheendofthefirstperiod,thatis1600(1+IRR)投資項目效益評價廈門大學吳世農 Inthesecondperiod,thedifferencebetweenthisresult1600(1+IRR)andtheamountofmoney(+10000),whichtheprojectlendstothefirmat10%,istheamountborrowedat10%,thefuturevalueofthisdifferenceattheendofthesecondtimeperiodis[10000-1600(1+IRR)](1+10%)Thus,wecanestablishannewequationtosolveIRR[10000-1600(1+IRR)](1+10%)=$10000IRR=-43.18%Thisanswersuggeststhatheprojectmustberejected. (c)SimpleSolutionResultedfromNPVNPV=[10000/(1+10%)1]+[-10000/(1+10%)2]-1600=466.41-1600=$-1133.59ThissolutionprovidedbyNPVsuggeststhatthisprojectmustberejected,thisisconsistentwiththeconclusionbyTeichrow’s.

投資項目效益評價AdvancedTopicsinCapitalBudgetingIII.CapitalBudgetingwithInflation 1.InflationEffectonCostofCapitalInflationmustconsideredincapitalbudgetingsinceinvestorswillincorporatedexpectationaboutinflationintotheirrequiredrateofreturn.Infact,NominalRateofReturn,whichweusuallysee,consistsofrealrateofreturnandinflationrate.NominalRateofReturn(Kn)isarealrateofreturn(K)plusinflationrate(f),butwecannotsimplyaddthesetwocomponentstogether,nominalrateofreturnislagerthanaresultfromanadditionofKandi.Moreprecisely,(1+Kn)=(1+K)(1+f)Kn=K+f+Kf

2.CapitalBudgetingbyNPVunderInflation(1)CashInflowsandOutflowsGrowwiththeSameInflationRateNPV=[NCFi(1+f)i/(1+K)i(1+f)i

]-I0

[NCFi/(1+K+f)i

]-I0投資項目效益評價廈門大學吳世農 Thus,iftheinflationisreflectedinboththecashflowsandintherequiredrateofreturn,theresultingNPVwillbefreeofinflationbias. (2)DifferentInflationonCashInflowsandOutflows

[CIFi(1+f1)i-COFi(1+f2)i](1-T)+DepreciationTNPV=

-I0

[(1+K)i(1+f)i

]whereCIF=cashinflows;COF=cashoutflows;

f1andf2=inflationratesforCIFandCOF,respectively;f=averageinflationrate;T=taxrate.

投資項目效益評價AdvancedTopicsinCapitalBudgetingIV.CapitalBudgetingforProjectswithUnequalLives 1.MutuallyExclusiveProjectswithDifferentLives (1)ProblemRaisedfromtheAssumptiononEqualLifeUsually,capitalbudgetingassumesthatallmutuallyexclusiveprojectshavethesamelife(andscale).Inpractice,thisassumptionmanynotbehold.Giventhatasetofmutuallyexclusiveprojectshavedifferentlives,howtoevaluateandcomparingtheirNPVs?Supposethattherearetwomutuallyexclusiveprojects,AandB,K=10%andtheirNCFsarepresentedinthefollowingtable.Year0123nNPV(K=10%)ProjectA-1000600600241ProjectB-1000400400475350

Bycalculation,NPVA=41;NPVB=50.WillbeprojectBbetterthanprojectA?No,Infact,theyarenotcomparable!投資項目效益評價廈門大學吳世農 (2)SolutionTomakeprojectAandprojectBcomparable,itisreasonabletoassumethatprojectAandprojectBcanbereplicatedataconstantscale.Thus,projectAshouldbesuperiortoprojectBbecauseitrecoverscashflowsfaster.How?Inordertocompareprojectswithunequallives,weneedtoassumethattheprojectscanbereplicatedatconstantscaleandcomputetheNPVofinfinitestreamofconstantreplications.Bydoingso,wefinallyhavethefollowingformulatocomputeNPVforprojectAandprojectB,assumingthatbothAandBarereplicatedatconstantscaleforever.(1+K)n

NPV(n,)=NPN(n)(1+K)n-1ByemployingtheformulaabovetoprojectAandprojectB,wefindthatNPVA(n,)=$236NPVB(n,)=$202TheresultssuggestthatprojectAissuperiortoprojectB,thus,thefirmmustacceptprojectAinsteadofprojectB!投資項目效益評價AdvancedTopicsinCapitalBudgeting 2.ImportantNotices (1)ReasonableJudgementonReplicationSimpleNPVrule,ifmisused,alsocanleadtowrongdecision.Formutuallyexclusiveprojectswithunequallives,correctusageofsimpleNPVdependsonwhetherornottheprojectscanbereasonablyassumedtobereplicable.(2)ImplicationofNPVwithInfiniteReplicationatConstantScaleInfiniteReplicationatConstantScaleimpliesthattheprojectswillberepeatedataconstantscaleeverynyears.Suchanimplicationisapplicabletosomecasesinpracticesuchasforestryoperation,X’mastreeplantingandharvesting,raisingpigsorchickens,andsoon. (3)AProblemRemainedUnsolved——DurationWemaytrytofindoutanoptimallife——durationofaproject.Thisoptimalproblemcanbesolvedwithdifferentcriteria:(a)UsethesimpleNPVrule;(b)UsetheIRRrule;(c)UseNPVrulewithconstantscalereplication.投資項目效益評價廈門大學吳世農Forthesameproblem,youmayfindthatthesolutionsfromthethreeapproacheswillyielddifferentanswers.However,akeytoachievingthecorrectansweristomaximizeNPVofastreamofprojectsreplicatedatconstantscale.投資項目效益評價AdvancedTopicsinCapitalBudgetingV.CapitalBudgetingUnderUncertainty1.ExpectedNPVandVarianceofNPV (1)NCFiwithprobabilityDistribution Inmanycasesinpractice,afirmisfacedwithaninvestmentprojectwhichNCFsareuncertain,foreachperiodofnperiods,theremaybemorethanonepossiblevaluesofNCFassociatedwithprobabilities。 TodetermineNPVunderuncertainty,itisnecessarytoidentifywhetherNCFsineachperiodareindependentordependent.(a)IndependentNCFi

IfNCFineachPeriodisindependenttoeachothers,then,thentheexpectedNCFineachperiodwillbeequalanaveragedNCF,andtheexpectedNPVofaprojectwillbeequaltoacumulativesumfromtheaverageofdiscountedexpectedNCFofeachperiodminusI0.Similarly,wecancalculateavarianceofNCFforeachperiodandavarianceofaproject.投資項目效益評價廈門大學吳世農

YearStateNCFijPij=(Probability)

ExpectedNCF

11500080%2600020%520021800070%21000030%5900311000080%2900020%9800411000060%21200040%10800

Forexample,afirmwillinvest$300,000milliontoproduceGreen-battery,K=10,n=4,andtheproject’sNCFsareindependentoneperiodtoothers,aspresentedinabovetable.ExpectedNCFi

ExpectedNPV=E(NPV)=

------------------------I0

(1+K)n

投資項目效益評價AdvancedTopicsinCapitalBudgeting(a)DependentNCFi

DependentNCFiisdefinedasNCFinoneperiodwillinfluenceNCFinnextperiod,orhowmuchNCFinthenextperiodiswillberelatedwithNCFinthepreviousperiod.Forexample,Afirmwantstoinvest$1000milliontoproduceauto-glass,theequipmentofprojectisexpectedtohave3-yearlife,K=10%.Aftertheprojectisinoperation,NCFsappearinthefirstyear,thesecondyear,…,thefifthyeararedifferent,inaddition,ineachyear,theremaybemanyvaluesofNCFassociatedwithprobabilities.ThefollowinggraphpresentsasituationwhereNCFisarandomvariableandtheNCFinoneperiodisdependenttoNCFinotherperiod.投資項目效益評價廈門大學吳世農

Auto-glassProject’sNCFsandProbabilityDistribution($million)Period1Period2Period31200(60%)1200(50%)NCF3

1000(60%)NCF21000(40%)900(70%)NCF11000(50%)NCF3

600(30%)3000(50%)2500(60%)NCF3

2000(40%)NCF22600(50%)2200(50%)2200(40%)NCF3

2000(50%)

投資項目效益評價AdvancedTopicsinCapitalBudgeting (2)ExpectedNPVandVarianceforDependentNCFs Supposethataprojectneedsaninvestmentoutlay$10000,n=2,K=10%.TheprojectisriskyanditsNCFsareuncertain.Thefollowingtableindicatestheproject’sNCFsandprobabilitiesassociatedwithNCFs. Obviously,inthefirstperiod,itispossiblefortheprojecttohaveeitherNCF=$7000with90%probabilityorNCF=$2000with10%probability.Inthesecondperiod,giventhatstate1inthefirstperiodhappens,itispossiblefortheprojecttohaveeitherNCF=$10000with70%probabilityorNCF=$9000with30%probability;giventhatstate2inthefirstperiodhappens,itispossiblefortheprojecttohaveeitherNCF=$2000with50%probabilityorNCF=$1000with50%probability.Thequestionsisthatundersuchauncertainty,whatisexpectedNPVanditsrisk(standarddeviation)?

PeriodStateNCFProbabilityPeriodStateNCFProbability11000070%1700090%2900030%121200050%2200010%2100050%投資項目效益評價廈門大學吳世農 (a)FindpossiblecombinationsofNCFsCombinationofNCFsProbabilityforCombination$7000,$10000(90%)(70%)=63%$7000,$9000(90%)(30%)=27%$2000,$2000(10%)(50%)=5%$2000,$1000(10%)(50%)=5%Total100% (b)DeterminepossibleNPVforeachcombinationStateNPVjProbability1-1000+7000(0.909)+10000(0.826)=46240.632-1000+7000(0.909)+9000(0.826)=37970.273-1000+2000(0.909)+2000(0.826)=-65300.054-1000+2000(0.909)+1000(0.826)=-73560.05Total1.00 (c)ComputeExpectedNPVandVarianceE(NPV)=4623(63%)+3797(27%)+(-6530)(5%)+(-7356)(5%)=$3242S(NPV)=[(NPVj-3242)2Probability]1/2=$3254

投資項目效益評價AdvancedTopicsinCapitalBudgetingVI.ProjectAbandonment 1.WhytoAbandonaProject? (1)EconomicEnvironment(2)MarketCompetition (3)Product-ConsumptionCycle(4)TechnologicalChanges (5)ManagementTeam (6)WrongEstimationinCapitalBudgetingSales

TestGrowthMatureDeclinet投資項目效益評價廈門大學吳世農 2.WhentoAbandonaProject?

(1)ProjectAbandonmentUnderCertaintySupposethatafirminvests$10000inaproject,K=10%,n=5.Thefollowingtablecontainstheproject’sdataformakingtheaccept/rejectdecisionandtheabandonmentdecision.

Year12 3 4 5NCF50004000300020001000Salvage(F)70005000300010000 (a)Istheprojectacceptable?NPV=5000(0.909)+4000(0.826)+3000(0.751)+2000(0.683)+1000(0.683)-10000=$2089>0,sotheprojectshouldbeaccepted! (b)Shouldbetheprojectbeabandonedafteritsoperation?Yes,becausetheproject’sNCFsrendtodeclineyearbyyear!(c)Whentoabandontheproject?ThefirmshouldabandontheprojectwhentheNPVismaximized!ThefollowingCalculationshowMax(NPV)appearswhenn=3.Why?投資項目效益評價AdvancedTopicsinCapitalBudgeting (c-1)NPVfor5-yearOperation:NPV=5000(0.909)+4000(0.826)+3000(0.751)+2000(0.683)+1000(0.621)-10000=$2089(c-2)NPVfor4-yearOperation:NPV=5000(0.909)+4000(0.826)+3000(0.751)+2000(0.683)+1000(0.683)--10000=$2157(c-3)NPVfor3-yearOperation:NPV=5000(0.909)+4000(0.826)+3000(0.751)+3000(0.751)-10000=$2355=Max(NPV)

(c-4)NPVfor2-yearOperation:NPV=5000(0.909)+4000(0.826)+5000(0.826)-10000=$1979(c-5)NPVfor1-yearOperation:NPV=