公司理财CapitalInvestmentDecisions(2)

CorporateFinance2-0©ProfessorHo-MouWuCapitalInvestmentDecisions2.1NetPresentValue2.2ProjectValuationinaRisklessWorldFisher’sPrinciple2.3PresentValueandCompounding2.4PresentValuewithSpecialCashFlows(RWJCh3,4)CorporateFinance2-1©ProfessorHo-MouWuInvestmentDecisionExample1:Supposeaninvestmentthatpromisestopay$10,000inoneyearisofferedforsalefor$9,500.Yourinterestrateis5%.Shouldyoubuy?•Ifyouweretobepromised$10,000dueinoneyearwheninterestratesareat5-percent,yourinvestmentbeworth$9,523.81intoday’sdollars.CorporateFinance2-2©ProfessorHo-MouWu2.1NetPresentValue:FVandPV•Theamountthataborrowerwouldneedtosetasidetodaytotoabletomeetthepromisedpaymentof$10,000inoneyeariscallthePresentValue(PV)of$10,000.Notethat$10,000=$9,523.81×(1.05).•Ifyouweretoinvest$10,000at5-percentinterestforoneyear,yourinvestmentwouldgrowto$10,500:$10,500=$10,000×(1.05).ThetotalamountdueattheendoftheinvestmentiscalltheFutureValue(FV).CorporateFinance2-3©ProfessorHo-MouWuNetPresentValue•TheNetPresentValue(NPV)ofaninvestmentisthepresentvalueoftheexpectedcashflows,lessthecostoftheinvestment.:SoyoushouldInvest.BacktoExample1:CorporateFinance2-4©ProfessorHo-MouWuNetPresentValueastheInvestmentCriterionIntheone-periodcase,theformulaforNPVcanbewrittenas:IfwehadnotundertakenthepositiveNPVprojectconsideredonthelastslide,andinsteadinvestedour$9,500elsewhereat5-percent,ourFVwouldbelessthanthe$10,000thatinvestmentpromisedandwewouldbeunambiguouslyworseoffinFVtermsaswell:$9,500×(1.05)=$9,975$10,000.,whereiscashflowatdate1CorporateFinance2-5©ProfessorHo-MouWu2.2ProjectEvaluationinaRisklessWorldC0C0C1C1Y1=1.2mY0=1mSaver(lending)BSpender(borrowing)AY)r1(YY)Y(PV1011+rslope=-(1+r)WhydoweuseNPVastheinvestmentcriterion?AssumePerfectCapitalMarketandTwoPeriodCorporateFinance2-6©ProfessorHo-MouWu(I)Saving(Financing)DecisionCorporateFinance2-7©ProfessorHo-MouWuUsePVtoCheckFeasibilityofConsumptionplanExample2:IstheconsumptionplanC0＝0.9mandC1＝1.325mfeasible?UsethePVformulatoevaluateit.Ifr＝10%,0.9＋＝2.105＝PV(C)＞1＋＝2.091＝PV(Y):notfeasibleIfr＝20%,0.9＋＝2.004＝PV(C)＞1＋＝2.000＝PV(Y):notfeasibleIfr＝30%,0.9＋＝1.919＝PV(C)＜1＋＝1.923＝PV(Y):feasible!CorporateFinance2-8©ProfessorHo-MouWu(Ⅱ)InvestmentOpportunitiesCorporateFinance2-9©ProfessorHo-MouWuCorporateInvestmentDecision-MakingConsumptionatt+1PositiveNPVprojectsshifttheshareholder’sopportunitysetout,whichisunambiguouslygood.AllshareholdersagreeontheirpreferenceforpositiveNPVprojects,whethertheyareborrowersorlenders.CorporateFinance2-10©ProfessorHo-MouWu(Ⅲ)InvestmentOpportunitieswithFinancialMarketsFinancialmarketspresentsaving/borrowingopportunities,asrepresentedbythedottedstraightline.Supposethecompany(farm)choosesD,itsownerscanthenusefinancialmarketsforsavingorborrowing.Bothinvestorsarehappierthanin(Ⅱ),butDisnottheoptimalinvestmentplanyet.C0BADEC1slope=-(1+r)PV(D)CorporateFinance2-11©ProfessorHo-MouWuProjectValuationinaRisklessWorldC0A’DEslope=-(1+r)PV(Y)C1B’Y*Y1Y0Y*istheoptimalinvestmentplan,whichistheonethatmaximizesNPV(Y)＝PV(Y)－EorPV(Y).Perfectcapitalmarket(borrowingrate＝lendingrate)isassumed.CorporateFinance2-12©ProfessorHo-MouWuCorporateInvestmentDecision-Making•Inreality,shareholdersdonotvoteoneveryinvestmentdecisionfacedbyafirmandthemanagersoffirmsneeddecisionrulestooperateby.•AllshareholdersofafirmwillbemadebetteroffifmanagersfollowtheNPVrule—undertakepositiveNPVprojectsandrejectnegativeNPVprojects.CorporateFinance2-13©ProfessorHo-MouWuOptimalInvestmentPlanNetPresentValueNPV＝＝PV(Y)－ETherefore,thebestinvestmentplanistheonethatmaximizesNPV(Y);andthebestinvestmentplanisindependentofinvestors’preferences.PV＝NPV＝＝CorporateFinance2-14©ProfessorHo-MouWuFisher’sSeparationPrincipleGivenperfectcapitalmarketandcertainty,theoptimalinvestmentplanistheonethatmaximizesthenetpresentvalueofavailableproductionplans,withoutregardtotheindividuals’subjectivepreferencesthatenterintotheirconsumption/savingdecisions.(IrvingFisher)Thisisthebasisforusingthepresentvalueastheevaluationcriterion.SeparationofinvestmentandfinancingdecisionsSeparationofownershipandmanagement.CorporateFinance2-15©ProfessorHo-MouWuWhydoweuseNPVorPVasinvestmentcriterionCorporateFinance2-16©ProfessorHo-MouWuNPVasInvestmentCriterionCorporateFinance2-17©ProfessorHo-MouWu2.3PresentValueandCompounding•Howmuchwouldaninvestorhavetosetasidetodayinordertohave$20,000fiveyearsfromnowifthecurrentrateis15%?012345$20,000PVCorporateFinance2-18©ProfessorHo-MouWuHowLongistheWait?Example5:Ifwedeposit$5,000todayinanaccountpaying10%,howlongdoesittaketogrowto$10,000?CorporateFinance2-19©ProfessorHo-MouWuExample6:Assumethetotalcostofacollegeeducationwillbe$50,000whenyourchildenterscollegein12years.Youhave$5,000toinvesttoday.Whatrateofinterestmustyouearnonyourinvestmenttocoverthecostofyourchild’seducation?WhatRateIsEnough?CorporateFinance2-20©ProfessorHo-MouWu2.4PVwithSpecialCashFlows•Perpetuity–Aconstantstreamofcashflowsthatlastsforever.•Growingperpetuity–Astreamofcashflowsthatgrowsataconstantrateforever.•Annuity–Astreamofconstantcashflowsthatlastsforafixednumberofperiods.•Growingannuity–Astrea