Chapter 4 The Time Value of Money

Chapter4TheTimeValueofMoneyFundamentalsofCorporateFinance2TopicsCovered★FutureValuesandCompoundInterestPresentValuesMultipleCashFlowsLevelCashFlowsPerpetuitiesandAnnuitiesInflation&TimeValueEffectiveAnnualInterestRateFundamentalsofCorporateFinance3FutureValuesFutureValue-Amounttowhichaninvestmentwillgrowafterearninginterest.CompoundInterest-Interestearnedoninterest.SimpleInterest-Interestearnedonlyontheoriginalinvestment.FundamentalsofCorporateFinance4FutureValuesExample-SimpleInterestInterestearnedatarateof6%forfiveyearsonaprincipalbalanceof$100.InterestEarnedPerYear=100x.06=$6FundamentalsofCorporateFinance5Example-SimpleInterestInterestearnedatarateof6%forfiveyearsonaprincipalbalanceof$100.TodayFutureYears12345InterestEarnedValue100FutureValues61066112611861246130ValueattheendofYear5=$130FundamentalsofCorporateFinance6FutureValuesExample-CompoundInterestInterestearnedatarateof6%forfiveyearsonthepreviousyear’sbalance.InterestEarnedPerYear=PriorYearBalancex.06FundamentalsofCorporateFinance7Example-CompoundInterestInterestearnedatarateof6%forfiveyearsonthepreviousyear’sbalance.TodayFutureYears12345InterestEarnedValue100FutureValues61066.36112.366.74119.107.15126.257.57133.82ValueattheendofYear5=$133.82FundamentalsofCorporateFinance8FutureValuesFutureValueof$100=FVFutureValueInterestFactor=FVIFFVrt$100()1FundamentalsofCorporateFinance9FutureValuesFVrt$100()1Example-FVWhatisthefuturevalueof$100ifinterestiscompoundedannuallyatarateof6%forfiveyears?82.133$)06.1(100$5FVFundamentalsofCorporateFinance1001000200030004000500060007000024681012141618202224262830NumberofYearsFVof$1000%5%10%15%FutureValueswithCompoundingInterestRatesFundamentalsofCorporateFinance11ManhattanIslandSalePeterMinuitboughtManhattanIslandfor$24in1626.Wasthisagooddeal?trillionFV57.120$)08.1(24$380Toanswer,determine$24isworthintheyear2006,compoundedat8%.FYI-ThevalueofManhattanIslandlandiswellbelowthisfigure.FundamentalsofCorporateFinance12PresentValuesPresentValueValuetodayofafuturecashflow.DiscountRateInterestrateusedtocomputepresentvaluesoffuturecashflows.DiscountFactorPresentvalueofa$1futurepayment.FundamentalsofCorporateFinance13PresentValuesPresentValue=PVPV=FutureValueaftertperiods(1+r)tFundamentalsofCorporateFinance14PresentValuesExampleYoujustboughtanewcomputerfor$3,000.Thepaymenttermsare2yearssameascash.Ifyoucanearn8%onyourmoney,howmuchmoneyshouldyousetasidetodayinordertomakethepaymentwhendueintwoyears?572,2$2)08.1(3000PVFundamentalsofCorporateFinance15PresentValuesPresentValueInterestFactor=PVIF=DiscountFactor=DF=PVof$1DiscountFactorscanbeusedtocomputethepresentvalueofanycashflow.DFrt11()FundamentalsofCorporateFinance16ThePVformulahasmanyapplications.Givenanyvariablesintheequation,youcansolvefortheremainingvariable.PVFVrt11()TimeValueofMoney(applications)FundamentalsofCorporateFinance1702040608010012001234567891011121314151617181920NumberofYearsPVof$1005%10%15%PresentValueswithCompoundingInterestRatesFundamentalsofCorporateFinance18Intheexpression,PV=FV(1+r)t,whenthePV,FV,andtareknown,(1+r)maybesolvedmathematically.Thediscountratecalculatedisalsocalledtheannualinterestrate,growthrate,andinternalrateofreturn,dependingonthesituation.FindingtheInterestRateFundamentalsofCorporateFinance19MultipleCashFlowsFutureValueofMultipleCashFlowsAccumulatingafuturesumviaunequal,periodicpaymentsentailsacombinationofaseriesofsinglefuturevaluecashflows.PresentValueofMultipleCashFlowsCalculatingthepresentvalueofaunequalseriesoffuturecashflowsisdeterminedbysummingthepresentvaluesofeachdiscountedsinglefuturecashflow.....)1()1(2211rCrCFVPVCrCr112211()()....FundamentalsofCorporateFinance20PVofMultipleCashFlowsExampleYourautodealergivesyouthechoicetopay$15,500cashnow,ormakethreepayments:$8,000nowand$4,000attheendofthefollowingtwoyears.Ifyourcostofmoneyis8%,whichdoyouprefer?$15,133.06PVTotal36.429,370.703,38,000.0021)08.1(000,42)08.1(000,41paymentImmediatePVPVFundamentalsofCorporateFinance21PerpetuitiesPerpetuityAstreamoflevelcashpaymentsthatneverends.FundamentalsofCorporateFinance22Perpetuities—Astreamoflevelcashpaymentsthatneverends.—PVofPerpetuityFormulaPVCrFundamentalsofCorporateFinance23PerpetuitiesExample-PerpetuityInordertocreateanendowment,whichpays$100,000peryear,forever,howmuchmoneymustbesetasidetodayintherateofinterestis10%?PV10000010000000,.$1,,FundamentalsofCorporateFinance24AnnuitiesAnannuityisanequallyspaced,levelstreamofcashflows,suchas$4,000peryearforthreeyears.Ifcashflowsoccurattheendofeachperiod,itiscalledanordinaryannuity.Ifcashflowsoccuratthebeginningofeachperiod,itiscalledanannuitydue.FundamentalsofCorporateFinance25PresentValueofAnnuitiesFundamentalsofCorporateFinance26PresentValueofAnnuitiesThepresentvalueofannuityisthedifferencebetweenthePVofthecashflowsinperpetuitylessthePVofthecashflowsbeyondtherelevantannuityperiod.FundamentalsofCorporateFinance27PresentValueofAnnuitiesPVofOrdinaryAnnuityC=cashpaymentr=interestratet=NumberofyearscashpaymentisreceivedPVAnnuityFactor(PVAF)PVCrrrt