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1、ChapterOutline4.1TheOne-PeriodCase4.2TheMultiperiodCase4.3CompoundingPeriods4.4Simplifications4.5WhatIsaFirmWorth?4.6SummaryandConclusions4.1TheOne-PeriodCase:FutureValueIfyouweretoinvest$10,000at5-percentinterestforoneyear,yourinvestmentwouldgrowto$10,500$
2、500wouldbeinterest($10,000×.05)$10,000istheprincipalrepayment($10,000×1)$10,500isthetotaldue.Itcanbecalculatedas:$10,500=$10,000×(1.05).ThetotalamountdueattheendoftheinvestmentiscalltheFutureValue(FV).4.1TheOne-PeriodCase:FutureValueIntheone-periodcase,thef
3、ormulaforFVcanbewrittenas:FV=C1×(1+r)WhereC1iscashflowatdate1andristheappropriateinterestrate.4.1TheOne-PeriodCase:PresentValueIfyouweretobepromised$10,000dueinoneyearwheninterestratesareat5-percent,yourinvestmentbeworth$9,523.81intoday’sdollars.Theamountth
4、ataborrowerwouldneedtosetasidetodaytotoabletomeetthepromisedpaymentof$10,000inoneyeariscallthePresentValue(PV)of$10,000.Notethat$10,000=$9,523.81×(1.05).4.1TheOne-PeriodCase:PresentValueIntheone-periodcase,theformulaforPVcanbewrittenas:WhereC1iscashflowatda
5、te1andristheappropriateinterestrate.4.1TheOne-PeriodCase:NetPresentValueTheNetPresentValue(NPV)ofaninvestmentisthepresentvalueoftheexpectedcashflows,lessthecostoftheinvestment.Supposeaninvestmentthatpromisestopay$10,000inoneyearisofferedforsalefor$9,500.You
6、rinterestrateis5%.Shouldyoubuy?Yes!4.1TheOne-PeriodCase:NetPresentValueIntheone-periodcase,theformulaforNPVcanbewrittenas:IfwehadnotundertakenthepositiveNPVprojectconsideredonthelastslide,andinsteadinvestedour$9,500elsewhereat5-percent,ourFVwouldbelessthant
7、he$10,000theinvestmentpromisedandwewouldbeunambiguouslyworseoffinFVtermsaswell:$9,500×(1.05)=$9,975<$10,000.4.2TheMultiperiodCase:FutureValueThegeneralformulaforthefuturevalueofaninvestmentovermanyperiodscanbewrittenas:FV=C0×(1+r)TWhereC0iscashflowatdate0,r
8、istheappropriateinterestrate,andTisthenumberofperiodsoverwhichthecashisinvested.4.2TheMultiperiodCase:FutureValueSupposethatJayRitterinvestedintheinitialpublicofferingoftheModiglianicompany.Modiglianip
