第四章净现值

ChapterOutline,4.1TheOne-PeriodCase4.2TheMultiperiodCase4.3CompoundingPeriods4.4Simplifications4.5WhatIsaFirmWorth?4.6SummaryandConclusions,4.1TheOne-PeriodCase:FutureValue,Ifyouweretoinvest$10,000at5-percentinterestforoneyear,yourinvestmentwouldgrowto$10,500$500wouldbeinterest($10,000.05)$10,000istheprincipalrepayment($10,0001)$10,500isthetotaldue.Itcanbecalculatedas:$10,500=$10,000(1.05).ThetotalamountdueattheendoftheinvestmentiscalltheFutureValue(FV).,4.1TheOne-PeriodCase:FutureValue,Intheone-periodcase,theformulaforFVcanbewrittenas:FV=C1(1+r)WhereC1iscashflowatdate1andristheappropriateinterestrate.,4.1TheOne-PeriodCase:PresentValue,Ifyouweretobepromised$10,000dueinoneyearwheninterestratesareat5-percent,yourinvestmentbeworth$9,523.81intodaysdollars.,Theamountthataborrowerwouldneedtosetasidetodaytotoabletomeetthepromisedpaymentof$10,000inoneyeariscallthePresentValue(PV)of$10,000.,Notethat$10,000=$9,523.81(1.05).,4.1TheOne-PeriodCase:PresentValue,Intheone-periodcase,theformulaforPVcanbewrittenas:,WhereC1iscashflowatdate1andristheappropriateinterestrate.,4.1TheOne-PeriodCase:NetPresentValue,TheNetPresentValue(NPV)ofaninvestmentisthepresentvalueoftheexpectedcashflows,lessthecostoftheinvestment.Supposeaninvestmentthatpromisestopay$10,000inoneyearisofferedforsalefor$9,500.Yourinterestrateis5%.Shouldyoubuy?,Yes!,4.1TheOne-PeriodCase:NetPresentValue,Intheone-periodcase,theformulaforNPVcanbewrittenas:,IfwehadnotundertakenthepositiveNPVprojectconsideredonthelastslide,andinsteadinvestedour$9,500elsewhereat5-percent,ourFVwouldbelessthanthe$10,000theinvestmentpromisedandwewouldbeunambiguouslyworseoffinFVtermsaswell:$9,500(1.05)=$9,975$1.10+5$1.10.40=$3.30Thisisduetocompounding.,FutureValueandCompounding,PresentValueandCompounding,Howmuchwouldaninvestorhavetosetasidetodayinordertohave$20,000fiveyearsfromnowifthecurrentrateis15%?,$20,000,PV,HowLongistheWait?,Ifwedeposit$5,000todayinanaccountpaying10%,howlongdoesittaketogrowto$10,000?,Assumethetotalcostofacollegeeducationwillbe$50,000whenyourchildenterscollegein12years.Youhave$5,000toinvesttoday.Whatrateofinterestmustyouearnonyourinvestmenttocoverthecostofyourchildseducation?About21.15%.,WhatRateIsEnough?,4.3CompoundingPeriods,CompoundinganinvestmentmtimesayearforTyearsprovidesforfuturevalueofwealth:,Forexample,ifyouinvest$50for3yearsat12%compoundedsemi-annually,yourinvestmentwillgrowto,EffectiveAnnualInterestRates,Areasonablequestiontoaskintheaboveexampleiswhatistheeffectiveannualrateofinterestonthatinvestment?,TheEffectiveAnnualInterestRate(EAR)istheannualratethatwouldgiveusthesameend-of-investmentwealthafter3years:,EffectiveAnnualInterestRates(continued),So,investingat12.36%compoundedannuallyisthesameasinvestingat12%compoundedsemiannually.,ContinuousCompounding(Advanced),Thegeneralformulaforthefuturevalueofaninvestmentcompoundedcontinuouslyovermanyperiodscanbewrittenas:FV=C0erTWhereC0iscashflowatdate0,risthestatedannualinterestrate,Tisthenumberofperiodsoverwhichthecashisinvested,andeisatranscendentalnumberapproximatelyequalto2.718.exisakeyonyourcalculator.,4.4Simplifications,PerpetuityAconstantstreamofcashflowsthatlastsforever.GrowingperpetuityAstreamofcashflowsthatgrowsataconstantrateforever.AnnuityAstreamofconstantcashflowsthatlastsforafixednumberofperiods.GrowingannuityAstreamofcashflowsthatgrowsataconstantrateforafixednumberofperiods.,Perpetuity,Aconstantstreamofcashflowsthatlastsforever.,Theformulaforthepresentvalueofaperpetuityis:,Perpetuity:Example,WhatisthevalueofaBritishconsolthatpromisestopay15eachyear,everyyearuntilthesunturnsintoaredgiantandburnstheplanettoacrisp?Theinterestrateis10-percent.,GrowingPerpetuity,Agrowingstreamofcashflowsthatlastsforever.,Theformulaforthepresentvalueofagrowingperpetuityis:,GrowingPerpetuity:Example,Theexpecteddividendnextyearis$1.30anddividendsareexpectedtogrowat5%forever.Ifthediscountrateis10%,whatisthevalueofthispromiseddividendstream?,Annuity,Aconstantstreamofcashflowswithafixedmaturity.,Theformulaforthepresentvalueofanannuityis:,Annuity:Example,Ifyoucanafforda$400monthlycarpayment,howmuchcarcanyouaffordifinterestratesare7%on36-monthloans?,GrowingAnnuity,Agrowingstreamofcashflowswithafixedmaturity.,Theformulaforthepresentvalueofagrowingannuity:,GrowingAnnuity,Adefined-benefitretirementplanofferstopay$20,000peryearfor40yearsandincreasetheannualpaymentby3-percenteachyear.Whatisthepresentvalueatretirementifthediscountrateis10-percent?,4.5WhatIsaFirmWorth?,Conceptually,afirmshouldbeworththepresentvalueofthefirmscashflows.Thetrickypartisdeterminingthesize,timingandriskofthosecashflows.,4.6SummaryandConclusions,Twobasicconcepts,futurevalueandpresentvalueareintroducedinthischapter.Interestratesarecommonlyexpressedonanannualbasis,butsemi-annual,quarterly,monthlyandevencontinuouslycompoundedinterestratearrangementsexist.Theformulaforthenetpresentvalueofaninvestmentthatpays$CforNperiodsis:,4.6SummaryandConclusions(continued),Wepresentedfoursimplifyingformulae:,HowdoyougettoCarnegieHall?,Practice,practice,practice.ItseasytowatchOlymp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