Chapter-05-The-Time-Value-Of-Money-現(xiàn)代財務管理英文版課件

5TheTimeValueOfMoney?2006Thomson/South-Western15TheTimeValueOfMoney?2006IntroductionThischapterintroducestheconceptsandskillsnecessarytounderstandthetimevalueofmoneyanditsapplications.2Introduction2SimpleandCompoundInterestSimpleInterestInterestpaidontheprincipalsumonlyCompoundInterestInterestpaidontheprincipalandonpriorinterestthathasnotbeenpaidorwithdrawn3SimpleandCompoundInterestSiChapter-05--The-Time-Value-Of-Money-現(xiàn)代財務管理英文版課件Chapter-05--The-Time-Value-Of-Money-現(xiàn)代財務管理英文版課件FutureValueofaCashFlowAttheendofyearnforasumcompoundedatinterestrateiisFVn=PV0(1+i)n

FormulaInTableIinthetext,(FVIFi,n)showsthefuturevalueof$1investedfornyearsatinterestratei:FVIFi,n=(1+i)n

TableIWhenusingthetable,FVn=PV0(FVIFi,n)6FutureValueofaCashFlow77TableshaveThreeVariablesInterestfactors(IF)Timeperiods(n)Interestratesperperiod(i)Ifyouknowanytwo,youcansolvealgebraicallyforthethirdvariable.8TableshaveThreeVariablesInt99PresentValueofaCashFlowPV0=FVn

[

]

FormulaPVIFi,n= TableIIPV0=FVn(PVIFi,n)

TableII

1

(1+i)n1

(1+i)n10PresentValueofaCashFlowPV1111ExampleUsingFormulaWhatisthePVof$100oneyearfromnowwith12percentinterestcompoundedmonthly?

PV0=$100

1/(1+.12/12)(12

1)

=$100

1/(1.126825)=$100

(.88744923)=$88.7412ExampleUsingFormulaWhatistExampleUsingTableIIPV0 =FVn(PVIFi,n) =$100(.887)

FromTableII =$88.7013ExampleUsingTableII131414AnnuityAseriesofequaldollarCFsforaspecifiednumberofperiodsOrdinaryannuityiswheretheCFsoccurattheendofeachperiod.AnnuitydueiswheretheCFsoccuratthebeginningofeachperiod.15AnnuityAseriesofequaldollaFVIFAi,n= FormulaforIF

FVANn

=PMT(FVIFAi,n)

TableIIIFutureValueofanOrdinary

Annuity

(1+i)n–1

i16FVIFAi,n= FormulaforIFFut17171818PresentValueofanOrdinaryAnnuity

PVIFAi,n= Formula

PVAN0=PMT(PVIFAi,n)

TableIV1(1+i)n1–i19PresentValueofanOrdinaryA20202121AnnuityDueFutureValueofanAnnuityDueFVANDn=PMT(FVIFAi,n)(1+i)TableIIIPresentValueofanAnnuityDuePVAND0=PMT(PVIFAi,n)(1+i)TableIV

22AnnuityDueFutureValueofan232324242525OtherImportantFormulasSinkingFundPMT=FVANn/(FVIFAi,n)TableIIIPaymentsonaLoanPMT=PVAN0/(PVIFAi,n)TableIV

PresentValueofaPerpetuityPVPER0=PMT/i26OtherImportantFormulasSinkinInterestCompoundedMoreFrequentlyThanOncePerYearFutureValuem =#oftimesinterestiscompoundedn=#ofyears

nmnom0nmi1PVFV)(+=27InterestCompoundedMoreFrequInterestCompoundedMoreFrequentlyThanOncePerYearPresentValue)nmminom(1+FVnPV0=m =#oftimesinterestiscompoundedn=#ofyears

28InterestCompoundedMoreFrequCompoundingandEffectiveRatesRateofinterest