Chapter6FormulasDiscountedCashFlowValuation McGraw Hill Irwin Copyright 2013byTheMcGraw HillCompanies Inc Allrightsreserved KeyConceptsandSkills BeabletocomputethefuturevalueofmultiplecashflowsBeabletocomputethepresentvalueofmultiplecashflowsBeabletocomputeloanpaymentsBeabletofindtheinterestrateonaloanUnderstandhowinterestratesarequotedUnderstandhowloansareamortizedorpaidoff 6F 2 ChapterOutline FutureandPresentValuesofMultipleCashFlowsValuingLevelCashFlows AnnuitiesandPerpetuitiesComparingRates TheEffectofCompoundingLoanTypesandLoanAmortization 6F 3 MultipleCashFlows FVExample6 1 Findthevalueatyear3ofeachcashflowandaddthemtogetherToday year0 FV 7000 1 08 3 8 817 98Year1 FV 4 000 1 08 2 4 665 60Year2 FV 4 000 1 08 4 320Year3 value 4 000Totalvaluein3years 8 817 98 4 665 60 4 320 4 000 21 803 58Valueatyear4 21 803 58 1 08 23 547 87 6F 4 MultipleCashFlows FVExample2 Supposeyouinvest 500inamutualfundtodayand 600inoneyear Ifthefundpays9 annually howmuchwillyouhaveintwoyears FV 500 1 09 2 600 1 09 1 248 05 6F 5 MultipleCashFlows Example2Continued Howmuchwillyouhavein5yearsifyoumakenofurtherdeposits Firstway FV 500 1 09 5 600 1 09 4 1 616 26Secondway usevalueatyear2 FV 1 248 05 1 09 3 1 616 26 6F 6 MultipleCashFlows FVExample3 Supposeyouplantodeposit 100intoanaccountinoneyearand 300intotheaccountinthreeyears Howmuchwillbeintheaccountinfiveyearsiftheinterestrateis8 FV 100 1 08 4 300 1 08 2 136 05 349 92 485 97 6F 7 MultipleCashFlows PVExample6 3 FindthePVofeachcashflowsandaddthemYear1CF 200 1 12 1 178 57Year2CF 400 1 12 2 318 88Year3CF 600 1 12 3 427 07Year4CF 800 1 12 4 508 41TotalPV 178 57 318 88 427 07 508 41 1 432 93 6F 8 Example6 3Timeline 6F 9 MultipleCashFlowsUsingaSpreadsheet YoucanusethePVorFVfunctionsinExceltofindthepresentvalueorfuturevalueofasetofcashflowsSettingthedataupishalfthebattle ifitissetupproperly thenyoucanjustcopytheformulasClickontheExceliconforanexample 6F 10 MultipleCashFlows PVAnotherExample Youareconsideringaninvestmentthatwillpayyou 1 000inoneyear 2 000intwoyearsand 3000inthreeyears Ifyouwanttoearn10 onyourmoney howmuchwouldyoubewillingtopay PV 1000 1 1 1 909 09PV 2000 1 1 2 1 652 89PV 3000 1 1 3 2 253 94PV 909 09 1 652 89 2 253 94 4 815 92 6F 11 MultipleUnevenCashFlowsUsingtheCalculator AnotherwaytousethefinancialcalculatorforunevencashflowsistousethecashflowkeysPressCFandenterthecashflowsbeginningwithyear0 Youhavetopressthe Enter keyforeachcashflowUsethedownarrowkeytomovetothenextcashflowThe F isthenumberoftimesagivencashflowoccursinconsecutiveperiodsUsetheNPVkeytocomputethepresentvaluebyenteringtheinterestrateforI pressingthedownarrowandthencomputeClearthecashflowkeysbypressingCFandthen2ndCLRWork 6F 12 Decisions Decisions Yourbrokercallsyouandtellsyouthathehasthisgreatinvestmentopportunity Ifyouinvest 100today youwillreceive 40inoneyearand 75intwoyears Ifyourequirea15 returnoninvestmentsofthisrisk shouldyoutaketheinvestment UsetheCFkeystocomputethevalueoftheinvestmentCF CF0 0 C01 40 F01 1 C02 75 F02 1NPV I 15 CPTNPV 91 49No thebrokerischargingmorethanyouwouldbewillingtopay 6F 13 SavingForRetirement Youareofferedtheopportunitytoputsomemoneyawayforretirement Youwillreceivefiveannualpaymentsof 25 000eachbeginningin40years Howmuchwouldyoubewillingtoinvesttodayifyoudesireaninterestrateof12 Usecashflowkeys CF CF0 0 C01 0 F01 39 C02 25 000 F02 5 NPV I 12 CPTNPV 1 084 71 6F 14 SavingForRetirementTimeline 012 394041424344 000 025K25K25K25K25K Noticethattheyear0cashflow 0 CF0 0 Thecashflowsinyears1 39are0 C01 0 F01 39 Thecashflowsinyears40 44are25 000 C02 25 000 F02 5 6F 15 QuickQuiz PartI Supposeyouarelookingatthefollowingpossiblecashflows Year1CF 100 Years2and3CFs 200 Years4and5CFs 300 Therequireddiscountrateis7 Whatisthevalueofthecashflowsatyear5 Whatisthevalueofthecashflowstoday Whatisthevalueofthecashflowsatyear3 6F 16 AnnuitiesandPerpetuitiesDefined Annuity finiteseriesofequalpaymentsthatoccuratregularintervalsIfthefirstpaymentoccursattheendoftheperiod itiscalledanordinaryannuityIfthefirstpaymentoccursatthebeginningoftheperiod itiscalledanannuityduePerpetuity infiniteseriesofequalpayments 6F 17 AnnuitiesandPerpetuitiesBasicFormulas Perpetuity PV C rAnnuities 6F 18 AnnuitiesandtheCalculator YoucanusethePMTkeyonthecalculatorfortheequalpaymentThesignconventionstillholdsOrdinaryannuityversusannuitydueYoucanswitchyourcalculatorbetweenthetwotypesbyusingthe2ndBGN2ndSetontheTIBA IIPlusIfyousee BGN or Begin inthedisplayofyourcalculator youhaveitsetforanannuitydueMostproblemsareordinaryannuities 6F 19 Annuity Example6 5 YouborrowmoneyTODAYsoyouneedtocomputethepresentvalue 48N 1I Y 632PMT CPTPV 23 999 54 24 000 Formula 6F 20 Annuity SweepstakesExample SupposeyouwinthePublishersClearinghouse 10millionsweepstakes Themoneyispaidinequalannualinstallmentsof 333 333 33over30years Iftheappropriatediscountrateis5 howmuchisthesweepstakesactuallyworthtoday PV 333 333 33 1 1 1 0530 05 5 124 150 29 6F 21 BuyingaHouse Youarereadytobuyahouse andyouhave 20 000foradownpaymentandclosingcosts Closingcostsareestimated