taiwan财务管理_lecture3(ch3)(PPT 35页)

,Irwin/McGraw-Hill,Chapter3,FundamentalsofCorporateFinanceThirdEdition,TheTimeValueofMoney,BrealeyMyersMarcusslidesbyMatthewWill,Irwin/McGraw-Hill,TheMcGraw-HillCompanies,Inc.,2001,TopicsCovered,FutureValuesPresentValuesMultipleCashFlowsPerpetuitiesandAnnuitiesInflation&TimeValueEffectiveAnnualInterestRate,FutureValues,FutureValue-Amounttowhichaninvestmentwillgrowafterearninginterest.CompoundInterest-Interestearnedoninterest.SimpleInterest-Interestearnedonlyontheoriginalinvestment.,FutureValues,FutureValueof$100=FV,FutureValues,Example-FVWhatisthefuturevalueof$100ifinterestiscompoundedannuallyatarateof6%forfiveyears?,FutureValues,Example-FVWhatisthefuturevalueof$100ifinterestiscompoundedannuallyatarateof6%forfiveyears?,FutureValueswithCompounding,InterestRates,ManhattanIslandSale,PeterMinuitboughtManhattanIslandfor$24in1626.Wasthisagooddeal?,Toanswer,determine$24isworthintheyear2000,compoundedat8%.,FYI-ThevalueofManhattanIslandlandiswellbelowthisfigure.,PresentValues,PresentValueValuetodayofafuturecashflow.,DiscountRateInterestrateusedtocomputepresentvaluesoffuturecashflows.,DiscountFactorPresentvalueofa$1futurepayment.,PresentValues,PresentValues,ExampleYoujustboughtanewcomputerfor$3,000.Thepaymenttermsare2yearssameascash.Ifyoucanearn8%onyourmoney,howmuchmoneyshouldyousetasidetodayinordertomakethepaymentwhendueintwoyears?,PresentValues,DiscountFactor=DF=PVof$1DiscountFactorscanbeusedtocomputethepresentvalueofanycashflow.,ThePVformulahasmanyapplications.Givenanyvariablesintheequation,youcansolvefortheremainingvariable.,TimeValueofMoney(applications),ValueofFreeCreditImpliedInterestRatesInternalRateofReturnTimenecessarytoaccumulatefunds,TimeValueofMoney(applications),PVofMultipleCashFlows,ExampleYourautodealergivesyouthechoicetopay$15,500cashnow,ormakethreepayments:$8,000nowand$4,000attheendofthefollowingtwoyears.Ifyourcostofmoneyis8%,whichdoyouprefer?,PVofMultipleCashFlows,PVscanbeaddedtogethertoevaluatemultiplecashflows.,Perpetuities&Annuities,PerpetuityAstreamoflevelcashpaymentsthatneverends.AnnuityEquallyspacedlevelstreamofcashflowsforalimitedperiodoftime.,Perpetuities&Annuities,PVofPerpetuityFormulaC=cashpaymentr=interestrate,Perpetuities&Annuities,Example-PerpetuityInordertocreateanendowment,whichpays$100,000peryear,forever,howmuchmoneymustbesetasidetodayintherateofinterestis10%?,Perpetuities&Annuities,Example-continuedIfthefirstperpetuitypaymentwillnotbereceiveduntilthreeyearsfromtoday,howmuchmoneyneedstobesetasidetoday?,Perpetuities&Annuities,PVofAnnuityFormulaC=cashpaymentr=interestratet=Numberofyearscashpaymentisreceived,Perpetuities&Annuities,PVAnnuityFactor(PVAF)-Thepresentvalueof$1ayearforeachoftyears.,Perpetuities&Annuities,Example-AnnuityYouarepurchasingacar.Youarescheduledtomake3annualinstallmentsof$4,000peryear.Givenarateofinterestof10%,whatisthepriceyouarepayingforthecar(i.e.whatisthePV)?,Perpetuities&Annuities,ApplicationsValueofpaymentsImpliedinterestrateforanannuityCalculationofperiodicpaymentsMortgagepaymentAnnualincomefromaninvestmentpayoutFutureValueofannualpayments,Perpetuities&Annuities,Example-FutureValueofannualpaymentsYouplantosave$4,000everyyearfor20yearsandthenretire.Givena10%rateofinterest,whatwillbetheFVofyourretirementaccount?,Inflation,Inflation-Rateatwhichpricesasawholeareincreasing.NominalInterestRate-Rateatwhichmoneyinvestedgrows.RealInterestRate-Rateatwhichthepurchasingpowerofaninvestmentincreases.,Inflation,approximationformula,Inflation,ExampleIftheinterestrateononeyeargovt.bondsis5.0%andtheinflationrateis2.2%,whatistherealinterestrate?,SavingsBond,EffectiveInterestRates,AnnualPercentageRate-Interestratethatisannualizedusingsimpleinterest.,EffectiveAnnualInterestRate-Interestratethatisannualizedusingcompoundinterest.,EffectiveInterestRates,exampleGivenamonthlyrateof1%,whatistheEffectiveAnnualRate(EAR)?WhatistheAnnualPercentageRate(APR)?,基本財務數學摘要,現值與未來值年金（Annuity）的未來值和現值貸款常數（mortgageconstant）與沉入基金因子（sinkingfundfactor）,現值與未來值,現值與未來值之關係FVn=PV(1+r)nFVn=PV(1+r/m)nmEffectiveAnnualYield(EAY)EAY=(1+r/m)m-1未來值因子：FV(r/m,nm)=(1+r/m)nm現值因子：PV(r/m,nm)=1/(1+r/m)nm,年金的未來值和現值（I）