投資項目管理和經濟效益評價英文版

廈門大學管理學院博士研究生課程報告八高級投資項目管理和經濟效益評價——理論、方法和實踐廈門大學管理學院吳世農AdvancedCapitalBudgeting ——Theory,Methods&ApplicationsWuShinongSchoolofManagementXiamenUniversityAdvancedTopicsinCapitalBudgetingI.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.廈門大學管理學院吳世農MarketResearchInvestmentSources&CostCBAExpendituresofCapitals

MarketingStrategyCosts&IncomeRProfitsStatementRisk&InvestmentAnalysisDManagementAssets&BalanceLiabilitiesSheetProductionFinanceCashInflow&CashflowRepaymentOpportunityStudyCashOutflowStatementAnalysisPreliminaryDiscussionFeasibilityDiscussionFinalProposalsStudyReport

Exhibit1:DiagramSuggestedforInvestmentProject’sFeasibilityStudyinFirms

廈門大學管理學院吳世農

TechnologicalMacroeconomicFeasibilityFeasibilityFinancialImplementationOperationFeasibility

Social/CulturalEnvironmentalFeasibilityFeasibility

ComprehensiveReviewPost-FeasibilityReportAssessment

Exhibit1(Continuos):DiagramSuggestedforInvestmentProject’sFeasibilityStudyinFirms

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?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.

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

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: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.廈門大學吳世農 Geometrically,themultipleratesofreturncanbeshowninthefollowinggraph.

NPV0K SomeStudiesshowthatcashflowsofinvestmentprojectswerehighlyassociatedwitheconomicenvironment,marketcompetition,managementabilityandmanyothers.Inpractice,itiscommonthatNCFchangessignmanytimesduringitsentirelifeastheinfluentialfactorschange.Thus,IRRisineffectivetothecaseofnon-conventionalcashflows.AdvancedTopicsinCapitalBudgeting(2)SolutionOil-wellPumpInvestmentisatypicalcaseincapitalbudgetingtoshowtheproblemofmultipleratesofreturnifIRRisemployedtoevaluatethisproject’’sIRR.Aoilcompanyistryingtodecidewhetherornottoinstallahigh-speedpumponanoil-wellwhichisalreadyinoperation.Thepumpwillcost$1,600toinstall.Thepumpwill,forthefirstyear,generate$10,000moreoilthanthepumpusednow,butforthesecondyearthenewpumpwillgenerate$10,000lessoilbecausethewellhasbeendepleted.Shouldtheoilcompanyinstallthehigh-speedpimp?Wesummarizetheestimatedincrementalcashflowsandpresenttheminthefollowingtable.Year012NCF-1,60010,000-10,000(a)ConfusingSolutionResultedfromIRR1600=[10000/(1+IRR)1]+[-10000/(1+IRR)2][-1600/(1+IRR)]+[10000/(1+IRR)1]+[-10000/(1+IRR)2]=0廈門大學吳世世農BecausethisequationshowsthatNCFchangeitssignfrom“+””to““-”onetime,thesolutiontothisequationproducestwoalternativeresults:IRR=25%IRR=400%Obviously,theresultsareconfusingandhardtointerpreted.NPVIRR=25%IRR=400%1000500100 200 300 400500 K(%)-500-1000-1500AdvancedTopicsinCapitalBudgeting(b)AlternativeSolutionOfferedbyTeichrow(1964)TeichrowthoughttheOil-wellPumpInvestmentinadifferentway———addthecashflowsoftwoadjacentperiods(period0andperiod1)togetherbyalogicallyeconomicwaytomakeNCF’ssignchangetoconventional.Assumeputmoneyintotheinvestmenttwice:$-1600atthetimeoftheinitialinvestment,and$-10000inthesecondtimeperiod.Theprojectcanbethoughtofaslending+$10000at10%(costofcapital)tothefirminthefirsttimeperiod.So,thefirst,thefirminvests$-1600nowandexpectstoearntheIRRattheendofthefirstperiod,thatis1600(1+IRR)廈門大學吳世世農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.AdvancedTopicsinCapitalBudgetingIII.CapitalBudgetingwithInflation1.InflationEffectonCostofCapitalInflationmustconsideredincapitalbudgetingsinceinvestorswillincorporatedexpectationaboutinflationintotheirrequiredrateofreturn.Infact,NominalRateofReturn,whichweusuallysee,consistsofrealrateofreturnandinflationrate.NominalRateofReturn(Kn)isarealrateofreturn(K)plusinflationrate(f),butwecannotsimplyaddthesetwocomponentstogether,nominalrateofreturnislagerthanaresultfromanadditionofKandi.Moreprecisely,(1+Kn)=(1+K)(1+f)Kn=K+f+Kf2.CapitalBudgetingbyNPVunderInflation(1)CashInflowsandOutflowsGrowwiththeSameInflationRateNPV=[NCFi(1+f)i/(1+K)i(1+f)i]-I0[NCFi/(1+K+f)i]-I0廈門大學吳世世農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.AdvancedTopicsinCapitalBudgetingIV.CapitalBudgetingforProjectswithUnequalLives1.MutuallyExclusiveProjectswithDifferentLives(1)ProblemRaisedfromtheAssumptiononEqualLifeUsually,capitalbudgetingassumesthatallmutuallyexclusiveprojectshavethesamelife(andscale).Inpractice,thisassumptionmanynotbehold.Giventhatasetofmutuallyexclusiveprojectshavedifferentlives,howtoevaluateandcomparingtheirNPVs?Supposethattherearetwomutuallyexclusiveprojects,AandB,K=10%andtheirNCFsarepresentedinthefollowingtable.Year0123nNPV(K=10%)Bycalculation,NPVA=41;NPVB=50.WillbeprojectBbetterthanprojectA?No,Infact,theyarenotcomparable!廈門大學吳世世農(2)SolutionTomakeprojectAandprojectBcomparable,itisreasonabletoassumethatprojectAandprojectBcanbereplicatedataconstantscale.Thus,projectAshouldbesuperiortoprojectBbecauseitrecoverscashflowsfaster.How?Inordertocompareprojectswithunequallives,weneedtoassumethattheprojectscanbereplicatedatconstantscaleandcomputetheNPVofinfinitestreamofconstantreplications.Bydoingso,wefinallyhavethefollowingformulatocomputeNPVforprojectAandprojectB,assumingthatbothAandBarereplicatedatconstantscaleforever.(1+K)nNPV(n,)=NPN(n)(1+K)n-1ByemployingtheformulaabovetoprojectAandprojectB,wefindthatNPVA(n,)=$236NPVB(n,)=$202TheresultssuggestthatprojectAissuperiortoprojectB,thus,thefirmmustacceptprojectAinsteadofprojectB!AdvancedTopicsinCapitalBudgeting2.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.廈門大學吳世世農Forthesameproblem,youmayfindthatthesolutionsfromthethreeapproacheswillyielddifferentanswers.However,akeytoachievingthecorrectansweristomaximizeNPVofastreamofprojectsreplicatedatconstantscale.AdvancedTopicsinCapitalBudgetingV.CapitalBudgetingUnderUncertainty1.ExpectedNPVandVarianceofNPV(1)NCFiwithprobabilityDistributionInmanycasesinpractice,afirmisfacedwithaninvestmentprojectwhichNCFsareuncertain,foreachperiodofnperiods,theremaybemorethanonepossiblevaluesofNCFassociatedwithprobabilities。。TodetermineNPVunderuncertainty,itisnecessarytoidentifywhetherNCFsineachperiodareindependentordependent.(a)IndependentNCFiIfNCFineachPeriodisindependenttoeachothers,then,thentheexpectedNCFineachperiodwillbeequalanaveragedNCF,andtheexpectedNPVofaprojectwillbeequaltoacumulativesumfromtheaverageofdiscountedexpectedNCFofeachperiodminusI0.Similarly,wecancalculateavarianceofNCFforeachperiodandavarianceofaproject.廈門門大大學學吳吳世世農農YearStateNCFijPij=(Probability)ExpectedNCF11500080%2600020%520021800070%21000030%5900311000080%2900020%9800411000060%21200040%10800Forexample,afirmwillinvest$300,000milliontoproduceGreen-battery,K=10,n=4,andtheproject’’sNCFsareindependentoneperiodtoothers,aspresentedinabovetable.ExpectedNCFiExpectedNPV=E(NPV)=------------------------I0(1+K)nAdvancedTopicsinCapitalBudgeting(a)DependentNCFiDependentNCFiisdefinedasNCFinoneperiodwillinfluenceNCFinnextperiod,orhowmuchNCFinthenextperiodiswillberelatedwithNCFinthepreviousperiod.Forexample,Afirmwantstoinvest$1000milliontoproduceauto-glass,theequipmentofprojectisexpectedtohave3-yearlife,K=10%.Aftertheprojectisinoperation,NCFsappearinthefirstyear,thesecondyear,……,thefifthyeararedifferent,inaddition,ineachyear,theremaybemanyvaluesofNCFassociatedwithprobabilities.ThefollowinggraphpresentsasituationwhereNCFisarandomvariableandtheNCFinoneperiodisdependenttoNCFinotherperiod.廈門門大大學學吳吳世世農農Auto-glassProject’’sNCFsandProbabilityDistribution($million)Period1Period2Period31200(60%)1200(50%)NCF31000(60%)NCF21000(40%)900(70%)NCF11000(50%)NCF3600(30%)3000(50%)2500(60%)NCF32000(40%)NCF22600(50%)2200(50%)2200(40%)NCF32000(50%)AdvancedTopicsinCapitalBudgeting(2)ExpectedNPVandVarianceforDependentNCFsSupposethataprojectneedsaninvestmentoutlay$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%廈門大大學吳吳世農農(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=$3254AdvancedTopicsinCapitalBudgetingVI.ProjectAbandonment1.WhytoAbandonaProject?(1)EconomicEnvironment(2)MarketCompetition(3)Product-ConsumptionCycle(4)TechnologicalChanges(5)ManagementTeam(6)WrongEstimationinCapitalBudgetingSalesTestGrowthMatureDeclinet廈門大大學吳吳世農農2.WhentoAbandonaProject?(1)ProjectAbandonmentUnderCertaintySupposethatafirminvests$10000inaproject,K=10%,n=5.Thefollowingtablecontainstheproject’sdataformakingtheaccept/rejectdecisionandtheabandonmentdecision.Year12345NCF50004000300020001000Salvage(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?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=5000(0.909)+7000(0.909)-10000=$908廈門大大學吳吳世農農(2)ProjectAbandonmentUnderUncertaintySupposethatafirmconsidersaprojectwhichinitialoutlayis$10000,K=10%,n=2,anditsNCFsandassociatedprobabilitieswereshownintheprevioussection(seeIV).Ifthefirmexpectedthatsalvagevalue(F)bytheendofperiod1is$3000whilenothingleftbytheendofperiod2,willthisprojectisacceptable?Ifyes,shouldbeitabandonedafteroperation?(a)Istheprojectacceptable?BycomputationfromSectionIV,E(NPV)>0,sotheprojectmustbeaccepted!E(NPV)=4623(63%)+3797(27%)+(-6530)(5%)+(-7356)(5%)=$3242S(NPV)=[(NPVj-3242)2Probability]1/2=$3254(b)WhentoAbandontheProject?Year1orYear2?(b-1):Iftheprojectisabandonedattheendofyear2,thenE(NPV)=$3242S(NPV)=$3254AdvancedTopicsinCapitalBudgeting(b-2):Iftheprojectisabandonedattheendofyear1,thenE(NPV)=4623(63%)+3797(27%)+(-5455)(5%)+(-5455)(5%)=$3392S(NPV)=[(NPVj-3392)2Probability]1/2=$2971Theresultsabovecomefromthefollowingtable:StateNPVjProbability1-1000+7000(0.909)+10000(0.826)=46240.632-1000+7000(0.909)+9000(0.826)=37970.273-1000+(2000+3000)(0.909)=-54550.054-1000+(2000+3000)(0.909)=-54550.05Total1.00(b-3)DecisionsThefirst,theresultssuggestthatabandoningtheprojectattheendofyear1showsalargerNPVandlessstandarddeviationbyacomparisontoNPVandstandarddeviationresultedfromabandoningtheprojectattheendofyear2,sotheprojectshouldbeabandonedattheendofyear1.廈門大學吳吳世農Thesecond,theprojectwillnotbeabandonedbytheendofyear1iftheNCF=$70000inthefirstyear,butwillbeabandonediftheNCF=$2000inthefirstyear.(3)OptimalProjectLifeforContinuosVariableinCapitalBudgeting(a)ContinuosVariableinCapitalBudgetingInpractice,somefirmmaybefacedwithsomecapitalbudgetingproblemswhichvariablessuchasprice,profitandcashflowarecontinuousvariables,forinstance,breweryindustry,forestsplantation,raisingchicken,andsonon.Therearetwoquestionsneededtoanswerforthesecase:(a-1)WhatisNPVforaProjectwithcontinuosvariables?(a-2):Howtodetermineanoptimallifefortheseprojects?(b)IllustrationSupposethataninvestmentinawinerywillproducethenetafter-taxprofit($perbottle)onabottleofredwinecanbeapproximatelybythefollowingequation:Profit=(3t)1/2wheret=numberofyearsheldforagingpriortosale.AdvancedTopicsinCapitalBudgetingAlso,assumethatK=10%,investmentoutlayperbottle=$1.Thus,NPVforeachbottleis:NPV=-cost+[(3t)1/2]/(1+K)t=-1+[(3t)1/2]/(1+10%)tObviously,agingthewinelongerwillincreasethenetrevenue,butalsoincreasethecapitalorcarryingcosts.Therefore,themanagementofthewinerywanttochoset*tomaximizeNPV.(c)MaximizeNPVperBottleSetd(NPV)/d(t)=0t*=1/[2Ln(1+K)]=1/[2Ln(1.1)]=5.2Years(d)AlternativeSolutionYearPrice/bottlePVPrice/bottleNPV1$1.73$1.57$0.572$2.45$2.02$1.023$3.00$2.25$1.254$3.46$2.36$1.365*$3.87$2.40$1.406$4.24$2.39$1.39AdvancedTopicsinCapitalBudgetingVII.OptimalCapitalBudgeting—MCC-IOSMethod1.MarginalCostofCapital———MCC(1)WhatisMCC?Themarginalcostofanyitemisthecostofanotheruniteofthatitem.AsdefinedinEconomics,themarginalcostoflaboristhecostofaddingonadditionalworker.TheMarginalcostofcapitaliddefinedasthecostofobtaininganotheroradditionaldollarofnewcapital.(2)CharacteristicsofMCC(a)Themarginalcostofcapitalis,infact,onetypeorspecialcaseoftheweightedaveragecostofcapital.Inotherwords,themarginalcostofcapitalcanbedeterminedbyanoptimalcapitalstructurebasedonmarketvalueandbycostsofnewcapitalsraised;(b)Intheory,themarginalcostofcapitalwillriseasmoreandmorenewcapitalisraised.ThissuggeststhatanyfirmcannotraiseanunlimitedamountofcapitalatafixedWACC.廈門大學吳吳世農(3)HowtoMeasureandDeterminetheMarginalCostofCapital?(a)Example&DataAssumethatCarsonFoodhasatargetcapitalstructurebasedonmarketvalueandotherinformationasfollows.Debt$300000030%PreferredStock100000010%CommonStock600000060%(300000shares)StockPrice=P0=$20NextExpectedDPS=D1=$1.6ConstantGrowthRate=g=7%TaxRate=T=40%CurrentInterestRateonDebt=Kd=10%FlotationCost=F=10%CurrentCostofPreferredStock=K=12%(b)CalculateKs=?Ks=(D1/P0)+g=(1.6/20)+7%=15%NotethatGordonConstantGrowthModelisapplicableduetoaconstantg!AdvancedTopicsinCapitalBudgeting(c)CalculateWACC1=?WACC1=Ka=WdKd(1-T)+WpKp+WsKs=0.3(10%)(1-40%)+0.1(12%)+0.6(15%)=1.8%+1.2%+9%=12%Notetheresultabovemeansthatthefirmwillraiseoneuniteofnewcapitalconsistingof30%ofdebt,10%ofpreferredstockand60%ofcommonequityatanaverageoroverallcost12%bythetargetcapitalstructure.(d)FromWACCtoMCC———RaisingNewCapitalFirstTimeAsmoreandmorenewcapitalisrequiredoveragiventimeperiod,thecostofdebtandthecostofequitywillbegintorise,thustheoverallcostofeachuniteofnewcapitalwillincreaseabove12%.Bythefollowingassumptions,weareabletofindoutMCCwiththeretainedearningsareusedasnewcapitalatfirst.Assumption1:CarsonFoodhastheretainedearningsonlyfromthisthisyear’’stotalearnings,andRetainingEarnings=TotalEarnings(PayoutRatio)=$840000(50%)=$420000;廈門大學吳吳世農Assumption2:thatCarsonFoodapprovedaninvestmentprojectwithcapitalexpenditureof$1million,tomaintainingthetargetcapitalstructure,thefirmhastoraise30%newdebt,10%newpreferredstockand60%newequity;Assumption3:thatthenewcommonequitywillbefirstlyraisedbytheretainingearnings;Assumption4:thecostofdebtremainsthesameas10%iftheretainedearningsareused;Thus,Ks2=[D1/P0(1-F)]+g=[1.6/20(1-10%)]+7%=15.9%Kp2=D1/P0(1-F)=2.4/20(1-10%)=13.33%MCC2=WACC2=WdKd(1-T)+WpKp+WsKs=0.3(10%)(1-40%)+0.1(13.33%)+0.6(15.9%)=1.8%+1.333%+9.5%=12.63%TheresultabovemeansthatWACC,whichisMCC,is12%solongasretainedearningsareused,butMCCwilljumpsfrom12%to12.63%assoonasCarsonuseduptheretainedearnings$420000.AdvancedTopicsinCapitalBudgeting(e)FirstBreakPointinMCCNowwealsocanfigureoutabreakpointwhichindicatesthatthetotalamountofnewcapitalCarsoncanraiseat12%(ratherthan12.63%)beforeitisforcedtosellnewcommonstock.Afterthisbreakpoint,Carsonwillhavetoraisenewcapitalbysellingnewcommonstockandtheoverallcostis12.63%ratherthan12%.BreakPoint=TotalAmountofNewCapital=X=RetainedEarnings/60%=42000/60%=$700000Theresultabovemeansthatthetotalamountofnewcapitalis$700000whichconsistsof30%fromNewDebt:700000(30%)=$210000atcostof10%10%fromPreferredS.:700000(10%)=$100000atcostof12%60%fromRetainedE.:700000(60%)=$420000atcostof15%Thus,implicationoftheresultaboveistwofold.IfCarsonUseslessthanthetotalofnewcapital$7000000,WACC=12%;IfCarsonusesmorethanthetotalofnewcapital$7000000,WACC=12.63%.廈門大學學吳世農農(f)SecondBreakPointinMCCSupposethatCarsononlycanenjoythelowinterestrate10%ifitborrow$3000000,ifCarsonwantstoborrowmoredebt,thenewdebtwillcostat12%,whiletheothersr