罗斯公司理财Chpt004ppt课件.ppt

CorporateFinanceRoss Westerfield Jaffe SixthEdition 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 10 000 1 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 81intoday sdollars Theamountthataborrowerwouldneedtosetasidetodaytobeabletomeetthepromisedpaymentof 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 10 000 4 2TheMultiperiodCase FutureValue Thegeneralformulaforthefuturevalueofaninvestmentovermanyperiodscanbewrittenas FV C0 1 r TWhereC0iscashflowatdate0 ristheappropriateinterestrate andTisthenumberofperiodsoverwhichthecashisinvested 4 2TheMultiperiodCase FutureValue SupposethatJayRitterinvestedintheinitialpublicofferingoftheModiglianicompany Modiglianipaysacurrentdividendof 1 10 whichisexpectedtogrowat40 percentperyearforthenextfiveyears Whatwillthedividendbeinfiveyears FV C0 1 r T 5 92 1 10 1 40 5 FutureValueandCompounding Noticethatthedividendinyearfive 5 92 isconsiderablyhigherthanthesumoftheoriginaldividendplusfiveincreasesof40 percentontheoriginal 1 10dividend 5 92 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 Whatrateofinterestmustyouearnonyourinvestmenttocoverthecostofyourchild seducation 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 C0 erTWhereC0iscashflowatdate0 risthestatedannualinterestrate Tisthenumberofperiodsoverwhichthecashisinvested andeisatranscendentalnumberapproximatelyequalto2 718 exisakeyonyourcalculator 4 4Simplifications PerpetuityAconstantstreamofcashflowsthatlastsforever GrowingperpetuityAstreamofcashflowsthatgrowsataconstantrateforever AnnuityAstreamofconstantcashflowsthatlastsforafixednumberofperiods GrowingannuityAstreamofcashflowsthatgrowsataconstantrateforafixednumberofperiods Perpetuity Aconstantstreamofcashflowsthatlastsforever Theformulaforthepresentvalueofaperpetuityis Perpetuity Example WhatisthevalueofaBritishConsolthatpromisestopay 15eachyear 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 afirmshouldbeworththepresentvalueofthefirm scashflows Thetrickypartisdeterminingthesize timingandriskofthosecashflows 4 6SummaryandConclusions Twobasicconcepts futurevalueandpresentvalueareintroducedinthischapter Interestratesarecommonlyexpressedonanannualbasis butsemi annual quarterly monthlyandevencontinuouslycompoundedinterestratearrangementsexist Theformulaforthenetpresentvalueofaninvestmentthatpays CforNperiodsis 4 6SummaryandConclusions continued Wepresentedfoursimplifyingformulae HowdoyougettoCarnegieHall Practice practice practice It seasytowatchOlympicgymnastsandconv