财务管理Chap.ppt
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财务管理Chap.ppt
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IntroductiontoValuation:
TheTimeValueofMoney,ChapterFive,ChapterOutline,FutureValueandCompoundingPresentValueandDiscountingMoreonPresentandFutureValues,BasicDefinitions,PresentValueearliermoneyonatimelineFutureValuelatermoneyonatimelineInterestrate“exchangerate”betweenearliermoneyandlatermoneyDiscountrateCostofcapitalOpportunitycostofcapitalRequiredreturn,FutureValues,Supposeyouinvest$1000foroneyearat5%peryear.Whatisthefuturevalueinoneyear?
Interest=1000(.05)=50Valueinoneyear=principal+interest=1000+50=1050FutureValue(FV)=1000(1+.05)=1050Supposeyouleavethemoneyinforanotheryear.Howmuchwillyouhavetwoyearsfromnow?
FV=1000(1.05)(1.05)=1000(1.05)2=1102.50,FutureValues:
GeneralFormula,FV=PV(1+r)tFV=futurevaluePV=presentvaluer=periodinterestrate,expressedasadecimalT=numberofperiodsFuturevalueinterestfactor=(1+r)t,EffectsofCompounding,SimpleinterestCompoundinterestConsiderthepreviousexampleFVwithsimpleinterest=1000+50+50=1100FVwithcompoundinterest=1102.50Theextra2.50comesfromtheinterestof.05(50)=2.50earnedonthefirstinterestpayment,FutureValuesExample2,Supposeyouinvestthe$1000fromthepreviousexamplefor5years.Howmuchwouldyouhave?
FV=1000(1.05)5=1276.3Theeffectofcompoundingissmallforasmallnumberofperiods,butincreasesasthenumberofperiodsincreases.(Simpleinterestwouldhaveafuturevalueof$1250,foradifferenceof$26.3),FutureValuesExample3,Supposeyouhadarelativedeposit$10at5.5%interest200yearsago.Howmuchwouldtheinvestmentbeworthtoday?
FV=10(1.055)200=447,189.84Whatistheeffectofcompounding?
Simpleinterest=10+200(10)(.055)=210.55Compoundingadded$446,979.29tothevalueoftheinvestment,PresentValues,HowmuchdoIhavetoinvesttodaytohavesomeamountinthefuture?
FV=PV(1+r)tRearrangetosolveforPV=FV/(1+r)tWhenwetalkaboutdiscounting,wemeanfindingthepresentvalueofsomefutureamount.Whenwetalkaboutthe“value”ofsomething,wearetalkingaboutthepresentvalueunlesswespecificallyindicatethatwewantthefuturevalue.,PresentValueOnePeriodExample,Supposeyouneed$10,000inoneyearforthedownpaymentonanewcar.Ifyoucanearn7%annually,howmuchdoyouneedtoinvesttoday?
PV=10,000/(1.07)1=9345.79,PresentValuesExample2,Youwanttobeginsavingforyoudaughterscollegeeducationandyouestimatethatshewillneed$150,000in17years.Ifyoufeelconfidentthatyoucanearn8%peryear,howmuchdoyouneedtoinvesttoday?
PV=150,000/(1.08)17=40,540.34,PresentValuesExample3,Yourparentssetupatrustfundforyou10yearsagothatisnowworth$19,671.51.Ifthefundearned7%peryear,howmuchdidyourparentsinvest?
PV=?
PresentValueImportantRelationshipI,Foragiveninterestratethelongerthetimeperiod,thelowerthepresentvalueWhatisthepresentvalueof$500tobereceivedin5years?
10years?
Thediscountrateis10%5years:
PV=500/(1.1)5=310.4610years:
PV=500/(1.1)10=192.77,PresentValueImportantRelationshipII,Foragiventimeperiodthehighertheinterestrate,thesmallerthepresentvalueWhatisthepresentvalueof$500receivedin5yearsiftheinterestrateis10%?
15%?
Rate=10%:
PV=500/(1.1)5=310.46Rate=15%;PV=500/(1.15)5=248.58,TheBasicPVEquation,PV=FV/(1+r)tTherearefourpartstothisequationPV,FV,randtIfweknowanythree,wecansolveforthefourth,DiscountRate,OftenwewillwanttoknowwhattheimpliedinterestrateisinaninvestmentRearrangethebasicPVequationandsolveforrFV=PV(1+r)tr=(FV/PV)1/t1Ifyouareusingformulas,youwillwanttomakeuseofboththeyxandthe1/xkeys,DiscountRateExample1,Youarelookingataninvestmentthatwillpay$1200in5yearsifyouinvest$1000today.Whatistheimpliedrateofinterest?
r=(1200/1000)1/51=.03714=3.714%,DiscountRateExample2,Supposeyouareofferedaninvestmentthatwillallowyoutodoubleyourmoneyin6years.Youhave$10,000toinvest.Whatistheimpliedrateofinterest?
DiscountRateExample3,Supposeyouhavea1-yearoldsonandyouwanttoprovide$75,000in17yearstowardshiscollegeeducation.Youcurrentlyhave$5000toinvest.Whatinterestratemustyouearntohavethe$75,000whenyouneedit?
FindingtheNumberofPeriods,StartwithbasicequationandsolvefortFV=PV(1+r)tt=ln(FV/PV)/ln(1+r),NumberofPeriodsExample1,Youwanttopurchaseanewcarandyouarewillingtopay$20,000.Ifyoucaninvestat10%peryearandyoucurrentlyhave$15,000,howlongwillitbebeforeyouhaveenoughmoneytopaycashforthecar?
t=ln(20,000/15,000)/ln(1.1)=3.02years,NumberofPeriodsExample2,Supposeyouwanttobuyanewhouse.Youcurrentlyhave$15,000andyoufigureyouneedtohavea10%downpaymentplusanadditional5%inclosingcosts.Ifthetypeofhouseyouwantcostsabout$150,000andyoucanearn7%peryear,howlongwillitbebeforeyouhaveenoughmoneyforthedownpaymentandclosingcosts?
Table5.4,
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