公司理财(英文版)Ch04综述课件

4-0CHAPTER4NetPresent

Value4-1ChapterOutline4.1TheOne-PeriodCase4.2TheMultiperiodCase4.3CompoundingPeriods4.4Simplifications4.5WhatIsaFirmWorth?4.6SummaryandConclusionsThisismycalculator.Thisismyfriend!4-24-34.1TheOne-PeriodCase:

FutureValueIfyouweretoinvest$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).4-44.1TheOne-PeriodCase:

FutureValueIntheone-periodcase,theformulaforFVcanbewrittenas:FV=C0×(1+r)TWhereC0iscashflowtoday(timezero)andristheappropriateinterestrate.4-54.1TheOne-PeriodCase:PresentValueIfyouweretobepromised$10,000dueinoneyearwheninterestratesareat5-percent,yourinvestmentbeworth$9,523.81intoday’sdollars.Theamountthataborrowerwouldneedtosetasidetodaytotoabletomeetthepromisedpaymentof$10,000inoneyeariscallthePresentValue(PV)of$10,000.Notethat$10,000=$9,523.81×(1.05).4-64.1TheOne-PeriodCase:

PresentValueIntheone-periodcase,theformulaforPVcanbewrittenas:WhereC1iscashflowatdate1andristheappropriateinterestrate.4-74.1TheOne-PeriodCase:

NetPresentValueTheNetPresentValue(NPV)ofaninvestmentisthepresentvalueoftheexpectedcashflows,lessthecostoftheinvestment.Supposeaninvestmentthatpromisestopay$10,000inoneyearisofferedforsalefor$9,500.Yourinterestrateis5%.Shouldyoubuy?Yes!4-84.1TheOne-PeriodCase:NetPresentValueIntheone-periodcase,theformulaforNPVcanbewrittenas:NPV=–Cost+PVIfwehadnotundertakenthepositiveNPVprojectconsideredonthelastslide,andinsteadinvestedour$9,500elsewhereat5-percent,ourFVwouldbelessthanthe$10,000theinvestmentpromisedandwewouldbeunambiguouslyworseoffinFVtermsaswell:$9,500×(1.05)=$9,975

<$10,000.4-94.2TheMultiperiodCase:

FutureValueThegeneralformulaforthefuturevalueofaninvestmentovermanyperiodscanbewrittenas:FV=C0×(1+r)TWhere C0iscashflowatdate0,ristheappropriateinterestrate,andTisthenumberofperiodsoverwhichthecashisinvested.4-104.2TheMultiperiodCase:

FutureValueSupposethatJayinvestedintheinitialpublicofferingoftheModiglianicompany.Modiglianipaysacurrentdividendof$1.10,whichisexpectedtogrowat40-percentperyearforthenextfiveyears.Whatwillthedividendbeinfiveyears?FV=C0×(1+r)T$5.92=$1.10×(1.40)54-11FutureValueandCompoundingNoticethatthedividendinyearfive,$5.92,isconsiderablyhigherthanthesumoftheoriginaldividendplusfiveincreasesof40-percentontheoriginal$1.10dividend:$5.92>$1.10+5×[$1.10×.40]=$3.30Thisisduetocompounding.4-12FutureValueandCompounding0123454-13PresentValueandCompoundingHowmuchwouldaninvestorhavetosetasidetodayinordertohave$20,000fiveyearsfromnowifthecurrentrateis15%?012345$20,000PVHowLongistheWait?Ifwedeposit$5,000todayinanaccountpaying10%,howlongdoesittaketogrowto$10,000?4-144-15Ifwedeposit$5,000todayinanaccountpaying10%,howlongdoesittaketogrowto$10,000?HowLongistheWait?WhatRateIsEnough?Assumethetotalcostofacollegeeducationwillbe$50,000whenyourchildenterscollegein12years.Youhave$5,000toinvesttoday.Whatrateofinterestmustyouearnonyourinvestmenttocoverthecostofyourchild’seducation?4-164-17Assumethetotalcostofacollegeeducationwillbe$50,000whenyourchildenterscollegein12years.Youhave$5,000toinvesttoday.Whatrateofinterestmustyouearnonyourinvestmenttocoverthecostofyourchild’seducation? About21.15%.WhatRateIsEnough?4-184.3CompoundingPeriodsCompoundinganinvestmentmtimesayearforTyearsprovidesforfuturevalueofwealth:Forexample,ifyouinvest$50for3yearsat12%compoundedsemi-annually,yourinvestmentwillgrowto4-19EffectiveAnnualInterestRatesAreasonablequestiontoaskintheaboveexampleiswhatistheeffectiveannualrateofinterestonthatinvestment?TheEffectiveAnnualInterestRate(EAR)istheannualratethatwouldgiveusthesameend-of-investmentwealthafter3years:4-20EffectiveAnnualInterestRates(continued)So,investingat12.36%compoundedannuallyisthesameasinvestingat12%compoundedsemiannually.4-21EffectiveAnnualInterestRates(continued)FindtheEffectiveAnnualRate(EAR)ofan18%APRloanthatiscompoundedmonthly.Whatwehaveisaloanwithamonthlyinterestrateof1½percent.Thisisequivalenttoaloanwithanannualinterestrateof19.56percent4-22ContinuousCompounding(Advanced)Thegeneralformulaforthefuturevalueofaninvestmentcompoundedcontinuouslyovermanyperiodscanbewrittenas:FV=C0×erTWhere C0iscashflowatdate0,risthestatedannualinterestrate,Tisthenumberofperiodsoverwhichthecashisinvested,andeisatranscendentalnumberapproximatelyequalto2.718.exisakeyonyourcalculator.4-234.4SimplificationsPerpetuityAconstantstreamofcashflowsthatlastsforever.GrowingperpetuityAstreamofcashflowsthatgrowsataconstantrateforever.AnnuityAstreamofconstantcashflowsthatlastsforafixednumberofperiods.GrowingannuityAstreamofcashflowsthatgrowsataconstantrateforafixednumberofperiods.4-24PerpetuityAconstantstreamofcashflowsthatlastsforever.0…1C2C3CTheformulaforthepresentvalueofaperpetuityis:4-25Perpetuity:ExampleWhatisthevalueofaBritishconsolthatpromisestopay£15eachyear,everyyearuntilthesunturnsintoaredgiantandburnstheplanettoacrisp?Theinterestrateis10-percent.0…1£152£153£154-26GrowingPerpetuityAgrowingstreamofcashflowsthatlastsforever.0…1C2C×(1+g)3C×(1+g)2Theformulaforthepresentvalueofagrowingperpetuityis:4-27GrowingPerpetuity:ExampleTheexpecteddividendnextyearis$1.30anddividendsareexpectedtogrowat5%forever.Ifthediscountrateis10%,whatisthevalueofthispromiseddividendstream?0…1$1.302$1.30×(1.05)3$1.30×(1.05)24-28AnnuityAconstantstreamofcashflowswithafixedmaturity.Theformulaforthepresentvalueofanannuityis:01C2C3CTC4-29AnnuityIntuitionAnannuityisvaluedasthedifferencebetweentwoperpetuities:oneperpetuitythatstartsattime1

lessaperpetuitythatstartsattimeT+101C2C3CTC4-30Annuity:ExampleIfyoucanafforda$400monthlycarpayment,howmuchcarcanyouaffordifinterestratesare7%on36-monthloans?01$4002$4003$40036$4004-31 Whatisthepresentvalueofafour-yearannuityof$100peryearthatmakesitsfirstpaymenttwoyearsfromtodayifthediscountrateis9%?

0 1 2 345$100 $100 $100$100$323.97$297.22Problem1&2Whatisthepresentvalueofafour-yearannuityof$100peryearthatmakesitsfirstpaymenttwoyearsfromtodayifthediscountrateis9%?Mr.Younghasjustwonthestatelottery,paying$50,000ayearfor20years.Heistoreceivehisfirstpaymentayearfromnow.ThestateadvertisesthatastheMillionDollar(50,000X20=1,000,000)lottery.Iftheinterestrateis8percent,whatisthetruevalueofthelottery?4909054-32Problem3Supposeyouput$30,000peryearintoyourretirementfund.Theaccountpays6percentperyear.Howmuchwillyouhavewhenyouretirein30years?2371744-33Problem3Daniellewillreceiveafouryearannuityof$500peryear,beginningatdate6.Iftheinterestrateis10percent,whatisthepresentvalueofherannuity?9844-34Problem4MsChenreceivesanannuityof$450,payableonceeverytwoyears.Theannuitystretchesoutover20years.Thefirstpayoccursatdate2,thatis,twoyearsfromtoday.Theannualinterestrateis6percent.Whatisthepresentvalueofannuity?25054-35Problem5HaroldandHelenNasharesavingforthecollegeeducationfortheirnewbornbaby,Susan.TheNashesestimatesthatcollegeexpenseswillrun$30,000peryearwhentheirdaughterreachescollegein18years.Theannualinterestrateoverthenextdecadeswillbe14percent.Howmuchmoneymusttheydepositinthebankeachyearsothattheirbabywillcompletelysupportedthroughfouryearsofcollege?14784-364-37GrowingAnnuityAgrowingstreamofcashflowswithafixedmaturity.Theformulaforthepresentvalueofagrowingannuity:01C2C×(1+g)3C×(1+g)2TC×(1+g)T-14-38PVofGrowingAnnuityYouareevaluatinganincomepropertythatisprovidingincreasingrents.Netrentisreceivedattheendofeachyear.Thefirstyear'srentisexpectedtobe$8,500andrentisexpectedtoincrease7%eachyear.Eachpaymentoccurattheendoftheyear.Whatisthepresentvalueoftheestimatedincomestreamoverthefirst5yearsifthediscountrateis12%?0 1 2 345$34,706.264-39GrowingAnnuityAdefined-benefitretirementplanofferstopay$20,000peryearfor40yearsandincreasetheannualpaymentbythree-percenteachyear.Whatisthepresentvalueatretirementifthediscountrateis10percent?01$20,0002$20,000×(1.03)40$20,000×(1.03)39Problem6Mr.ChenasecondyearMBAstudenthasjustbeenofferedajobat$80,000ayear.Heanticipateshissalaryincreasingby9percentperyearuntilherretirementin40years.Givenaninterestrate20%,whatisthepresentvalueofhislifetime?4-40LoanTypesandLoanAmortizationPurediscountsloan:Itisthesimplestformofloan.Itrepaysasingleamountattheendofthetimeinfuture.Interest-OnlyLoans:Onlypayinteresteverytimeandpayprincipalatsomepointinfuture4-41AmortizedloanTheborrowersneedtorepaypartsoftheloanamountovertime.Theprocessofprovidingforaloantobepaidoffbymakingregularprincipalreductionsiscalledamortizingtheloan.Supposeyouhavetakenacarloanamount$5000for5yearsat9%interestrate.Whatwouldtheamortizationschedule?4-42AmortizationScheduleCalculatetheannuity=C=1285Interestpaidinthefirstyear=5000x0.09=450Principalpaidinthefirstyear=1285-450=835Endingbalance=5000-835=4164,thisamountisbeginningbalanceofsecondyear4-43AmortizationScheduleYearBeginningBalanceTotalPaymentInterestPaidPrincipalPaidEndingBalance1500012854508354164241641285374911325333253128529399322614226112852041082117951179128510611790Totals6427142750004-444-454.6SummaryandConclusionsTwobasicconcepts,futurevalueandpresentvalueareintroducedinthischapter.CompoundingandDiscountingInterestratesarecommonlyexpressedonanannualbasis,butsemi-annual,quarterly,monthlyandevencontinuouslycompoundedinterestratearrangementsexist.SimplificationandAmortizationschedule4.6SummaryandConclusionsFV=C0×(1+r)T4-46NPVTheformulaforthenetpresentvalueofaninvestmentthatpays$CforNperiodsis:4-474-4