财务管理Chap.ppt

财务管理Chap.ppt

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2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.IntroductiontoValuation:

TheTimeValueofMoneyChapterFiveMcGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.1ChapterOutlineFutureValueandCompoundingPresentValueandDiscountingMoreonPresentandFutureValuesMcGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.2BasicDefinitionsPresentValueearliermoneyonatimelineFutureValuelatermoneyonatimelineInterestrate“exchangerate”betweenearliermoneyandlatermoneyDiscountrateCostofcapitalOpportunitycostofcapitalRequiredreturnMcGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.3FutureValuesSupposeyouinvest$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=1102.50McGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.4FutureValues:

GeneralFormulaFV=PV（1+r）tFV=futurevaluePV=presentvaluer=periodinterestrate,expressedasadecimalT=numberofperiodsFuturevalueinterestfactor=（1+r）tMcGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.5EffectsofCompoundingSimpleinterestCompoundinterestConsiderthepreviousexampleFVwithsimpleinterest=1000+50+50=1100FVwithcompoundinterest=1102.50Theextra2.50comesfromtheinterestof.05（50）=2.50earnedonthefirstinterestpaymentMcGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.6McGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.7FutureValuesExample2Supposeyouinvestthe$1000fromthepreviousexamplefor5years.Howmuchwouldyouhave?

FV=1000（1.05）5=1276.3Theeffectofcompoundingissmallforasmallnumberofperiods,butincreasesasthenumberofperiodsincreases.（Simpleinterestwouldhaveafuturevalueof$1250,foradifferenceof$26.3）McGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.8FutureValuesExample3Supposeyouhadarelativedeposit$10at5.5%interest200yearsago.Howmuchwouldtheinvestmentbeworthtoday?

FV=10（1.055）200=447,189.84Whatistheeffectofcompounding?

Simpleinterest=10+200（10）（.055）=210.55Compoundingadded$446,979.29tothevalueoftheinvestmentMcGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.9PresentValuesHowmuchdoIhavetoinvesttodaytohavesomeamountinthefuture?

FV=PV（1+r）tRearrangetosolveforPV=FV/（1+r）tWhenwetalkaboutdiscounting,wemeanfindingthepresentvalueofsomefutureamount.Whenwetalkaboutthe“value”ofsomething,wearetalkingaboutthepresentvalueunlesswespecificallyindicatethatwewantthefuturevalue.McGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.10PresentValueOnePeriodExampleSupposeyouneed$10,000inoneyearforthedownpaymentonanewcar.Ifyoucanearn7%annually,howmuchdoyouneedtoinvesttoday?

PV=10,000/（1.07）1=9345.79McGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.11PresentValuesExample2Youwanttobeginsavingforyoudaughterscollegeeducationandyouestimatethatshewillneed$150,000in17years.Ifyoufeelconfidentthatyoucanearn8%peryear,howmuchdoyouneedtoinvesttoday?

PV=150,000/（1.08）17=40,540.34McGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.12PresentValuesExample3Yourparentssetupatrustfundforyou10yearsagothatisnowworth$19,671.51.Ifthefundearned7%peryear,howmuchdidyourparentsinvest?

PV=?

McGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.13PresentValueImportantRelationshipIForagiveninterestratethelongerthetimeperiod,thelowerthepresentvalueWhatisthepresentvalueof$500tobereceivedin5years?

10years?

Thediscountrateis10%5years:

PV=500/（1.1）5=310.4610years:

PV=500/（1.1）10=192.77McGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.14PresentValueImportantRelationshipIIForagiventimeperiodthehighertheinterestrate,thesmallerthepresentvalueWhatisthepresentvalueof$500receivedin5yearsiftheinterestrateis10%?

15%?

Rate=10%:

PV=500/（1.1）5=310.46Rate=15%;PV=500/（1.15）5=248.58McGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.15TheBasicPVEquationPV=FV/（1+r）tTherearefourpartstothisequationPV,FV,randtIfweknowanythree,wecansolveforthefourthMcGraw-Hill/IrwinMcGraw-Hill/Irwin2003TheMcGraw-HillCompanies,Inc.Allrightsreserved.5.16DiscountRateOftenwewillwanttoknowwhattheimpliedinte