CapitalInvestmentDecisions2.1NetPresentValue2.2ProjectValuationinaRisklessWorldFisher’sPrinciple2.3PresentValueandCompounding2.4PresentValuewithSpecialCashFlows(RWJCh3,4)CapitalInvestmentDecisions2.InvestmentDecisionExample1:Supposeaninvestmentthatpromisestopay$10,000inoneyearisofferedforsalefor$9,500.Yourinterestrateis5%.Shouldyoubuy?

Ifyouweretobepromised$10,000dueinoneyearwheninterestratesareat5-percent,yourinvestmentbeworth$9,523.81intoday’sdollars.InvestmentDecisionExample1:I2.1NetPresentValue:FVandPVTheamountthataborrowerwouldneedtosetasidetodaytotoabletomeetthepromisedpaymentof$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).2.1NetPresentValue:FVandNetPresentValueTheNetPresentValue(NPV)ofaninvestmentisthepresentvalueoftheexpectedcashflows,lessthecostoftheinvestment.:SoyoushouldInvest.BacktoExample1:NetPresentValueTheNetPreseNetPresentValueastheInvestmentCriterionIntheone-periodcase,theformulaforNPVcanbewrittenas:IfwehadnotundertakenthepositiveNPVprojectconsideredonthelastslide,andinsteadinvestedour$9,500elsewhereat5-percent,ourFVwouldbelessthanthe$10,000thatinvestmentpromisedandwewouldbeunambiguouslyworseoffinFVtermsaswell:$9,500×(1.05)=$9,975<$10,000.,whereiscashflowatdate

1NetPresentValueastheInves2.2ProjectEvaluationinaRisklessWorldWhydoweuseNPVastheinvestmentcriterion?AssumePerfectCapitalMarketandTwoPeriod2.2ProjectEvaluationinaRi(I)Saving(Financing)Decision(I)Saving(Financing)DecisioUsePVtoCheckFeasibilityofConsumptionplanExample2:

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!UsePVtoCheckFeasibilityof(Ⅱ) InvestmentOpportunities(Ⅱ) InvestmentOpportunitiesCorporateInvestmentDecision?MakingConsumptionatt+1PositiveNPVprojectsshifttheshareholder’sopportunitysetout,whichisunambiguouslygood.AllshareholdersagreeontheirpreferenceforpositiveNPVprojects,whethertheyareborrowersorlenders.CorporateInvestmentDecision?(Ⅲ)InvestmentOpportunitieswithFinancialMarketsFinancialmarketspresentsaving/borrowingopportunities,asrepresentedbythedottedstraightline.Supposethecompany(farm)choosesD,its ownerscanthenusefinancialmarketsforsavingorborrowing.Bothinvestorsarehappierthanin(Ⅱ),butDisnottheoptimalinvestmentplanyet.C0BADEC1slope=-(1+r)PV(D)(Ⅲ)InvestmentOpportunitieswProjectValuationinaRisklessWorldC0A’DEslope=-(1+r)PV(Y)C1B’Y*Y1Y0Y*istheoptimalinvestmentplan,whichistheonethatmaximizesNPV(Y)＝PV(Y)－EorPV(Y).Perfectcapitalmarket(borrowingrate＝lendingrate)isassumed.ProjectValuationinaRisklesCorporateInvestmentDecision?MakingInreality,shareholdersdonotvoteoneveryinvestmentdecisionfacedbyafirmandthemanagersoffirmsneeddecisionrulestooperateby.AllshareholdersofafirmwillbemadebetteroffifmanagersfollowtheNPVrule—undertakepositiveNPVprojectsandrejectnegativeNPVprojects.CorporateInvestmentDecision?OptimalInvestmentPlanNetPresentValueNPV＝＝PV(Y)－ETherefore,thebestinvestmentplanistheonethatmaximizesNPV(Y);andthebestinvestmentplanisindependentofinvestors’preferences.PV＝NPV＝＝OptimalInvestmentPlanNetPreFisher’sSeparationPrinciple Givenperfectcapitalmarketandcertainty,theoptimalinvestmentplanistheonethatmaximizesthenetpresentvalueofavailableproductionplans,withoutregardtotheindividuals’subjectivepreferencesthatenterintotheirconsumption/savingdecisions.(IrvingFisher)Thisisthebasisforusingthepresentvalueastheevaluationcriterion.SeparationofinvestmentandfinancingdecisionsSeparationofownershipandmanagement.Fisher’sSeparationPrinciple WhydoweuseNPVorPVasinvestmentcriterionWhydoweuseNPVorPVasinvNPVasInvestmentCriterionNPVasInvestmentCriterion2.3PresentValueandCompoundingHowmuchwouldaninvestorhavetosetasidetodayinordertohave$20,000fiveyearsfromnowifthecurrentrateis15%?012345$20,000PV2.3PresentValueandCompoundHowLongistheWait?Example5:Ifwedeposit$5,000todayinanaccountpaying10%,howlongdoesittaketogrowto$10,000?HowLongistheWait?Example5Example6:Assumethetotalcostofacollegeeducationwillbe$50,000whenyourchildenterscollegein12years.Youhave$5,000toinvesttoday.Whatrateofinterestmustyouearnonyourinvestmenttocoverthecostofyourchild’seducation?WhatRateIsEnough?Example6:Assumethetotalco2.4PVwithSpecialCashFlowsPerpetuityAconstantstreamofcashflowsthatlastsforever.GrowingperpetuityAstreamofcashflowsthatgrowsataconstantrateforever.AnnuityAstreamofconstantcashflowsthatlastsforafixednumberofperiods.GrowingannuityAstreamofcashflowsthatgrowsataconstantrateforafixednumberofperiods.2.4PVwithSpecialCashFlowsPerpetuityAconstantstreamofcashflowsthatlastsforever.0…1C2C3CTheformulaforthepresentvalueofaperpetuityis:PerpetuityAconstantstreamofGrowingPerpetuityAgrowingstreamofcashflowsthatlastsforever.0…1C2C×(1+g)3C×(1+g)2Theformulaforthepresentvalueofagrowingperpetuityis:GrowingPerpetuityAgrowingstAnnuityAconstantstreamofcashflowswithafixedmaturity.01C2C3CTheformulaforthepresentvalueofanannuityis:TCAnnuityAconstantstreamofcaGrowingAnnuityAgrowingstreamofcashflowswithafixedmaturity.01CTheformulaforthepresentvalueofagrowingannuity:2C×(1+g)3C×(1+g)2T

C×(1+g)T-1GrowingAnnuityAgrowingstreaWhatIsaFirmWorth?Conceptually,afirmshouldbeworththepresentvalueofthefirm’scashflows.Thetrickypartisdeterminingthesize,timingand“risk”ofthosecashflows:wewillprobefurtherinlaterclass..WhatIsaFirmWorth?ConceptuaCapitalInvestmentDecisions2.1NetPresentValue2.2ProjectValuationinaRisklessWorldFisher’sPrinciple2.3PresentValueandCompounding2.4PresentValuewithSpecialCashFlows(RWJCh3,4)CapitalInvestmentDecisions2.InvestmentDecisionExample1:Supposeaninvestmentthatpromisestopay$10,000inoneyearisofferedforsalefor$9,500.Yourinterestrateis5%.Shouldyoubuy?

Ifyouweretobepromised$10,000dueinoneyearwheninterestratesareat5-percent,yourinvestmentbeworth$9,523.81intoday’sdollars.InvestmentDecisionExample1:I2.1NetPresentValue:FVandPVTheamountthataborrowerwouldneedtosetasidetodaytotoabletomeetthepromisedpaymentof$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).2.1NetPresentValue:FVandNetPresentValueTheNetPresentValue(NPV)ofaninvestmentisthepresentvalueoftheexpectedcashflows,lessthecostoftheinvestment.:SoyoushouldInvest.BacktoExample1:NetPresentValueTheNetPreseNetPresentValueastheInvestmentCriterionIntheone-periodcase,theformulaforNPVcanbewrittenas:IfwehadnotundertakenthepositiveNPVprojectconsideredonthelastslide,andinsteadinvestedour$9,500elsewhereat5-percent,ourFVwouldbelessthanthe$10,000thatinvestmentpromisedandwewouldbeunambiguouslyworseoffinFVtermsaswell:$9,500×(1.05)=$9,975<$10,000.,whereiscashflowatdate

1NetPresentValueastheInves2.2ProjectEvaluationinaRisklessWorldWhydoweuseNPVastheinvestmentcriterion?AssumePerfectCapitalMarketandTwoPeriod2.2ProjectEvaluationinaRi(I)Saving(Financing)Decision(I)Saving(Financing)DecisioUsePVtoCheckFeasibilityofConsumptionplanExample2:

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!UsePVtoCheckFeasibilityof(Ⅱ) InvestmentOpportunities(Ⅱ) InvestmentOpportunitiesCorporateInvestmentDecision?MakingConsumptionatt+1PositiveNPVprojectsshifttheshareholder’sopportunitysetout,whichisunambiguouslygood.AllshareholdersagreeontheirpreferenceforpositiveNPVprojects,whethertheyareborrowersorlenders.CorporateInvestmentDecision?(Ⅲ)InvestmentOpportunitieswithFinancialMarketsFinancialmarketspresentsaving/borrowingopportunities,asrepresentedbythedottedstraightline.Supposethecompany(farm)choosesD,its ownerscanthenusefinancialmarketsforsavingorborrowing.Bothinvestorsarehappierthanin(Ⅱ),butDisnottheoptimalinvestmentplanyet.C0BADEC1slope=-(1+r)PV(D)(Ⅲ)InvestmentOpportunitieswProjectValuationinaRisklessWorldC0A’DEslope=-(1+r)PV(Y)C1B’Y*Y1Y0Y*istheoptimalinvestmentplan,whichistheonethatmaximizesNPV(Y)＝PV(Y)－EorPV(Y).Perfectcapitalmarket(borrowingrate＝lendingrate)isassumed.ProjectValuationinaRisklesCorporateInvestmentDecision?MakingInreality,shareholdersdonotvoteoneveryinvestmentdecisionfacedbyafirmandthemanagersoffirmsneeddecisionrulestooperateby.AllshareholdersofafirmwillbemadebetteroffifmanagersfollowtheNPVrule—undertakepositiveNPVprojectsandrejectnegativeNPVprojects.CorporateInvestmentDecision?OptimalInvestmentPlanNetPresentValueNPV＝＝PV(Y)－ETherefore,thebestinvestmentplanistheonethatmaximizesNPV(Y);andthebestinvestmentplanisindependentofinvestors’preferences.PV＝NPV＝＝OptimalInvestmentPlanNetPreFisher’sSeparationPrinciple Givenperfectcapitalmarketandcertainty,theoptimalinvestmentplanistheonethatmaximizesthenetpresentvalueofavailableproductionplans,withoutregardtotheindividuals’subjectivepreferencesthatenterintotheirconsumption/savingdecisions.(IrvingFisher)Thisisthebasisforusingthepresentvalueastheevaluationcriterion.SeparationofinvestmentandfinancingdecisionsSeparationofownershipandmanagement.Fisher’sSeparationPrinciple WhydoweuseNPVorPVasinvestmentcriterionWhydoweuseNPVorPVasinvNPVasInvestmentCriterionNPVasInvestmentCriterion2.3PresentValueandCompoundingHowmuchwouldaninvestorhavetosetasidetodayinordertohave$20,000fiveyearsfromnowifthecurrentrateis15%?012345$20,000PV2.3PresentValueandCompoundHowLongistheWait?Example5:Ifwedeposit$5,000todayinanaccountpaying10%,howlongdoesittaketogrowto$10,000?HowLongistheWait?Example5Example6:Assumethetotalcostofacollegeeducationwillbe$50,000whenyourchildenterscollegein12years.Youhave$5,000toinvesttoday.Whatrateofinterestmustyouearnonyourinvestmenttocoverthecostofyourchild’seducation?WhatRateIsEnough?Example6:Assume