财务管理课件cha

DiscountedCashFlowValuation,Chapter5,5.1,KeyConceptsandSkills,BeabletocomputethefuturevalueofmultiplecashflowsBeabletocomputethepresentvalueofmultiplecashflowsBeabletocomputeloanpaymentsBeabletofindtheinterestrateonaloanUnderstandhowloansareamortizedorpaidoffUnderstandhowinterestratesarequoted,5.2,ChapterOutline,FutureandPresentValuesofMultipleCashFlowsValuingLevelCashFlows:AnnuitiesandPerpetuitiesComparingRates:TheEffectofCompoundingPeriodsLoanTypesandLoanAmortization,5.3,MultipleCashFlowsFVExample5.1,Findthevalueatyear3ofeachcashflowandaddthemtogether.Today(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=8817.98+4665.60+4320+4000=21,803.58Valueatyear4=21,803.58(1.08)=23,547.87,5.4,MultipleCashFlowsFVExample2,Supposeyouinvest$500inamutualfundtodayand$600inoneyear.Ifthefundpays9%annually,howmuchwillyouhaveintwoyears?FV=500(1.09)2+600(1.09)=1248.05,5.5,Example2Continued,Howmuchwillyouhavein5yearsifyoumakenofurtherdeposits?Firstway:FV=500(1.09)5+600(1.09)4=1616.26Secondwayusevalueatyear2:FV=1248.05(1.09)3=1616.26,5.6,MultipleCashFlowsFVExample3,Supposeyouplantodeposit$100intoanaccountinoneyearand$300intotheaccountinthreeyears.Howmuchwillbeintheaccountinfiveyearsiftheinterestrateis8%?FV=100(1.08)4+300(1.08)2=136.05+349.92=485.97,5.7,Example3Timeline,100,0,1,2,3,4,5,300,136.05,349.92,485.97,5.8,MultipleCashFlowsPresentValueExample5.3,FindthePVofeachcashflowandaddthemYear1CF: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=1432.93,5.9,Example5.3Timeline,5.10,MultipleCashFlowsPVAnotherExample,Youareconsideringaninvestmentthatwillpayyou$1000inoneyear,$2000intwoyearsand$3000inthreeyears.Ifyouwanttoearn10%onyourmoney,howmuchwouldyoubewillingtopay?PV=1000/(1.1)1=909.09PV=2000/(1.1)2=1652.89PV=3000/(1.1)3=2253.94PV=909.09+1652.89+2253.94=4815.93,5.11,MultipleUnevenCashFlowsUsingtheCalculator,AnotherwaytousethefinancialcalculatorforunevencashflowsisyouusethecashflowkeysTexasInstrumentsBA-IIPlusPressCFandenterthecashflowsbeginningwithyear0.Youhavetopressthe“Enter”keyforeachcashflowUsethedownarrowkeytomovetothenextcashflowThe“F”isthenumberoftimesagivencashflowoccursinconsecutiveyearsUsetheNPVkeytocomputethepresentvaluebyenteringtheinterestrateforI,pressingthedownarrowandthencomputeClearthecashflowkeysbypressingCFandthenCLRWork,5.12,Example:SpreadsheetStrategies,YoucanusethePVorFVfunctionsinExceltofindthepresentvalueorfuturevalueofasetofcashflowsSettingthedataupishalfthebattleifitissetupproperly,thenyoucanjustcopytheformulasClickontheExceliconforanexample,5.13,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=91.49Nothebrokerischargingmorethanyouwouldbewillingtopay.,5.14,SavingForRetirement,Youareofferedtheopportunitytoputsomemoneyawayforretirement.Youwillreceivefiveannualpaymentsof$25,000eachbeginningin40years.Howmuchwouldyoubewillingtoinvesttodayifyoudesireaninterestrateof12%?Usecashflowkeys:CF;CF0=0;C01=0;F01=39;C02=25000;F02=5;NPV;I=12;CPTNPV=1084.71,5.15,SavingForRetirementTimeline,012394041424344,000025K25K25K25K25K,Noticethattheyear0cashflow=0(CF0=0)Thecashflowsyears139are0(C01=0;F01=39Thecashflowsyears4044are25,000(C02=25,000;F02=5),5.16,QuickQuiz:Part1,Supposeyouarelookingatthefollowingpossiblecashflows:Year1CF=$100;Years2and3CFs=$200;Years4and5CFs=$300.Therequireddiscountrateis7%Whatisthevalueofthecashflowsatyear5?Whatisthevalueofthecashflowstoday?Whatisthevalueofthecashflowsatyear3?,5.17,AnnuitiesandPerpetuitiesDefined,AnnuityfiniteseriesofequalpaymentsthatoccuratregularintervalsIfthefirstpaymentoccursattheendoftheperiod,itiscalledanordinaryannuityIfthefirstpaymentoccursatthebeginningoftheperiod,itiscalledanannuityduePerpetuityinfiniteseriesofequalpayments,5.18,AnnuitiesandPerpetuitiesBasicFormulas,Perpetuity:PV=C/rAnnuities:,5.19,AnnuitiesandtheCalculator,YoucanusethePMTkeyonthecalculatorfortheequalpaymentThesignconventionstillholdsOrdinaryannuityversusannuitydueYoucanswitchyourcalculatorbetweenthetwotypesbyusingthe2ndBGN2ndSetontheTIBA-IIPlusIfyousee“BGN”or“Begin”inthedisplayofyourcalculator,youhaveitsetforanannuitydueMostproblemsareordinaryannuities,5.20,AnnuityExample5.5,YouborrowmoneyTODAYsoyouneedtocomputethepresentvalue.48N;1I/Y;-632PMT;CPTPV=23,999.54($24,000)Formula:,5.21,AnnuitySweepstakesExample,SupposeyouwinthePublishersClearinghouse$10millionsweepstakes.Themoneyispaidinequalannualinstallmentsof$333,333.33over30years.Iftheappropriatediscountrateis5%,howmuchisthesweepstakesactuallyworthtoday?PV=333,333.3311/1.0530/.05=5,124,150.29,5.22,BuyingaHouse,Youarereadytobuyahouseandyouhave$20,000foradownpaymentandclosingcosts.Closingcostsareestimatedtobe4%oftheloanvalue.Youhaveanannualsalaryof$36,000andthebankiswillingtoallowyourmonthlymortgagepaymenttobeequalto28%ofyourmonthlyincome.Theinterestrateontheloanis6%peryearwithmonthlycompounding(.5%permonth)fora30-yearfixedrateloan.Howmuchmoneywillthebankloanyou?Howmuchcanyouofferforthehouse?,5.23,BuyingaHouse-Continued,BankloanMonthlyincome=36,000/12=3,000Maximumpayment=.28(3,000)=840PV=84011/1.005360/.005=140,105TotalPriceClosingcosts=.04(140,105)=5,604Downpayment=20,0005604=14,396TotalPrice=140,105+14,396=154,501,5.24,Example:SpreadsheetStrategiesAnnuityPV,ThepresentvalueandfuturevalueformulasinaspreadsheetincludeaplaceforannuitypaymentsClickontheExcelicontoseeanexample,5.25,QuickQuiz:Part2,Youknowthepaymentamountforaloanandyouwanttoknowhowmuchwasborrowed.Doyoucomputeapresentvalueorafuturevalue?Youwanttoreceive5000permonthinretirement.Ifyoucanearn.75%permonthandyouexpecttoneedtheincomefor25years,howmuchdoyouneedtohaveinyouraccountatretirement?,5.26,FindingthePayment,Supposeyouwanttoborrow$20,000foranewcar.Youcanborrowat8%peryear,compoundedmonthly(8/12=.66667%permonth).Ifyoutakea4yearloan,whatisyourmonthlypayment?20,000=C11/1.006666748/.0066667C=488.26,5.27,Example:SpreadsheetStrategiesAnnuityPayment,AnotherTVMformulathatcanbefoundinaspreadsheetisthepaymentformulaPMT(rate,nper,pv,fv)ThesamesignconventionholdsasforthePVandFVformulasClickontheExceliconforanexample,5.28,FindingtheNumberofPaymentsExample5.6,Startwiththeequationandrememberyourlogs.1000=20(11/1.015t)/.015.75=11/1.015t1/1.015t=.251/.25=1.015tt=ln(1/.25)/ln(1.015)=93.111months=7.75yearsAndthisisonlyifyoudontchargeanythingmoreonthecard!,5.29,FindingtheNumberofPaymentsAnotherExample,Supposeyouborrow$2000at5%andyouaregoingtomakeannualpaymentsof$734.42.Howlongbeforeyoupayofftheloan?2000=734.42(11/1.05t)/.05.136161869=11/1.05t1/1.05t=.8638381311.157624287=1.05tt=ln(1.157624287)/ln(1.05)=3years,5.30,FindingtheRate,Supposeyouborrow$10,000fromyourparentstobuyacar.Youagreetopay$207.58permonthfor60months.Whatisthemonthlyinterestrate?Signconventionmatters!60N10,000PV-207.58PMTCPTI/Y=.75%,5.31,AnnuityFindingtheRateWithoutaFinancialCalculator,TrialandErrorProcessChooseaninterestrateandcomputethePVofthepaymentsbasedonthisrateComparethecomputedPVwiththeactualloanamountIfthecomputedPVloanamount,thentheinterestrateistoolowIfthecomputedPVloanamount,thentheinterestrateistoohighAdjusttherateandrepeattheprocessuntilthecomputedPVandtheloanamountareequal,5.32,QuickQuiz:Part3,Youwanttoreceive$5000permonthforthenext5years.Howmuchwouldyouneedtodeposittodayifyoucanearn.75%permonth?Whatmonthlyratewouldyouneedtoearnifyouonlyhave$200,000todeposit?Supposeyouhave$200,000todepositandcanearn.75%permonth.Howmanymonthscouldyoureceivethe$5000payment?Howmuchcouldyoureceiveeverymonthfor5years?,5.33,FutureValuesforAnnuities,Supposeyoubeginsavingforyourretirementbydepositing$2000peryearinanIRA.Iftheinterestrateis7.5%,howmuchwillyouhavein40years?FV=2000(1.075401)/.075=454,513.04,5.34,AnnuityDue,Youaresavingforanewhouseandyouput$10,000peryearinanaccountpaying8%.Thefirstpaymentismadetoday.Howmuchwillyouhaveattheendof3years?FV=10,000(1.0831)/.08(1.08)=35,061.12,5.35,AnnuityDueTimeline,35,016.12,5.36,Example:WorktheWeb,AnotheronlinefinancialcalculatorcanbefoundatMoneyChimpClickonthewebsurferandworkthefollowingexampleChoosecalculatorandthenannuityYoujustinherited$5million.Ifyoucanearn6%onyourmoney,howmuchcanyouwithdraweachyearforthenext40years?Datachimpassumesannuitydue!Payment=$313,497.81,5.37,PerpetuityExample5.7,Perpetuityformula:PV=C/rCurrentrequiredreturn:40=1/rr=.025or2.5%perquarterDividendfornewpreferred:100=C/.025C=2.50perquarter,5.38,Table5.2,5.39,QuickQuiz:Part4,Youwanttohave$1milliontouseforretirementin35years.Ifyoucanearn1%permonth,howmuchdoyouneedtodepositonamonthlybasisifthefirstpaymentismadeinonemonth?Whatifthefirstpaymentismadetoday?Youareconsideringpreferredstockthatpaysaquarterlydividendof$1.50.Ifyourdesiredreturnis3%perquarter,howmuchwouldyoubewillingtopay?,5.40,EffectiveAnnualRate(EAR),Thisistheactualratepaid(orreceived)afteraccountingforcompoundingthatoccursduringtheyearIfyouwanttocomparetwoalternativeinvestmentswithdifferentcompoundingperiodsyouneedtocomputetheEARandusethatforcomparison.,5.41,AnnualPercentageRate,ThisistheannualratethatisquotedbylawBydefinitionAPR=periodratetimesthenumberofperiodsperyearConsequently,togettheperiodratewerearrangetheAPRequation:Periodrate=APR/numberofperiodsperyearYoushouldNEVERdividetheeffectiveratebythenumberofperiodsperyearitwillNOTgiveyoutheperiodrate,5.42,ComputingAPRs,WhatistheAPRifthemonthlyrateis.5%?.5(12)=6%WhatistheAPRifthesemiannualrateis.5%?.5(2)=1%WhatisthemonthlyrateiftheAPRis12%withmonthlycompounding?12/12=1%CanyoudividetheaboveAPRby2togetthesemiannualrate?NO!YouneedanAPRbasedonsemiannualcompoundingtofindthesemiannualrate.,5.43,ThingstoRemember,YouALWAYSneedtomakesurethattheinterestrateandthetimeperiodmatch.Ifyouarelookingatannualperiods,youneedanannualrate.Ifyouarelookingatmonthlyperiods,youneedamonthlyrate.IfyouhaveanAPRbasedonmonthlycompounding,youhavetousemonthlyperiodsforlumpsums,oradjusttheinterestrateappropriatelyifyouhavepaymentsotherthanmonthly,5.44,ComputingEARs-Example,Supposeyoucanearn1%permonthon$1investedtoday.WhatistheAPR?1(12)=12%Howmuchareyoueffectivelyearning?FV=1(1.01)12=1.1268Rate=(1.12681)/1=.1268=12.68%Supposeifyouputitinanotheraccount,youearn3%perquarter.WhatistheAPR?3(4)=12%Howmuchareyoueffectivelyearning?FV=1(1.03)4=1.1255Rate=(1.12551)/1=.1255=12.55%,5.45,EAR-Formula,RememberthattheAPRisthequotedrate,5.46,Decisions,DecisionsII,Youarelookingattwosavingsaccounts.Onepays5.25%,withdailycompounding.Theotherpays5.3%withsemiannualcompounding.Whichaccountshouldyouuse?Firstaccount:EAR=(1+.0525/365)3651=5.39%Secondaccount:EAR=(1+.053/2)21=5.37%Whichaccountshouldyouchooseandwhy?,5.47,Decisions,DecisionsIIContinued,Letsverifythechoice.Supposeyouinvest$100ineachaccount.Howmuchwillyouhaveineachaccountinoneyear?FirstAccount:Dailyrate=.0525/365=.00014383562FV=100(1.00014383562)365=105.39SecondAccount:Semiannualrate=.0539/2=.0265FV=100(1.0265)2=105.37Youhavemoremoneyinthefirstaccount.,5.48,ComputingAPRsfromEARs,Ifyouhaveaneffectiverate,howcanyoucomputetheAPR?RearrangetheEARequationandyouget:,5.49,APR-Example,Supposeyouwanttoearnaneffectiverateof12%andyouarelookingatanaccountthatcompoundsonamonthlybasis.WhatAPRmusttheypay?,5.50,ComputingPaymentswithAPRs,Supposeyouwanttobuyanewcomputersystemandthestoreiswillingtosellittoallowyoutomakemonthlypayments.Theentirecomputersystemcosts$3500.Theloanperiodisfor2yearsandtheinterestrateis16.9%withmonthlycompounding.Whatisyourmonthlypayment?Monthlyrate=.169/12=.01408333333Numberofmonths=2(12)=243500=C11/1.01408333333)24/.01408333333C=172.88,5.51,FutureValueswithMonthlyCompounding,Supposeyoudeposit$50amonthintoanaccountthathasanAPRof9%,basedonmonthlycompounding.Howmuchwillyouhaveintheaccountin35years?Monthlyrate=.09/12=.0075Numberofmonths=35(12)=420FV=501.00754201/.0075=147,089.22,5.52,PresentValuewithDailyCompounding,Youneed$15,000in3yearsforanewcar.IfyoucandepositmoneyintoanaccountthatpaysanAPRof5.5%basedondailycompounding,howmuchwouldyouneedtodeposit?Dailyrate=.055/365=.00015068493Numberofdays=3(365)=1095FV=15,000/(1.00015068493)1095=12,718.56,5.53,QuickQuiz:Part5,WhatisthedefinitionofanAPR?Whatistheeffectiveannualrate?Whichrateshouldyouusetocomparealternativeinvestmentsorloans?Whichratedoyouneedtouseinthetimevalueofmoneycalculations?,5.54,PureDiscountLoansExample5.11,Treasurybillsareexcellentexamplesofpurediscountloans.Theprincipalamountisrepaidatsomefuturedate,withoutanyperiodicinterestpayments.IfaT-billpromisestorepay$10,000in12monthsandthemarketinterestrateis7percent,howmuchwillthebillsellforinthemarket?PV=10,000/1.07=9345.79