公司理财第十版Chap006-Calcppt课件.ppt

Chapter6CalculatorsDiscountedCashFlowValuation McGraw Hill Irwin Copyright 2013byTheMcGraw HillCompanies Inc Allrightsreserved KeyConceptsandSkills BeabletocomputethefuturevalueofmultiplecashflowsBeabletocomputethepresentvalueofmultiplecashflowsBeabletocomputeloanpaymentsBeabletofindtheinterestrateonaloanUnderstandhowinterestratesarequotedUnderstandhowloansareamortizedorpaidoff 6C 2 ChapterOutline FutureandPresentValuesofMultipleCashFlowsValuingLevelCashFlows AnnuitiesandPerpetuitiesComparingRates TheEffectofCompoundingLoanTypesandLoanAmortization 6C 3 MultipleCashFlows FutureValueExample6 1 Findthevalueatyear3ofeachcashflowandaddthemtogetherToday s year0 CF 3N 8I Y 7 000PV CPTFV 8817 98Year1CF 2N 8I Y 4 000PV CPTFV 4 665 60Year2CF 1N 8I Y 4 000PV CPTFV 4 320Year3CF value 4 000Totalvaluein3years 8 817 98 4 665 60 4 320 4 000 21 803 58Valueatyear4 1N 8I Y 21 803 58PV CPTFV 23 547 87 6C 4 MultipleCashFlows FVExample2 Supposeyouinvest 500inamutualfundtodayand 600inoneyear Ifthefundpays9 annually howmuchwillyouhaveintwoyears Year0CF 2N 500PV 9I Y CPTFV 594 05Year1CF 1N 600PV 9I Y CPTFV 654 00TotalFV 594 05 654 00 1 248 05 6C 5 MultipleCashFlows Example2Continued Howmuchwillyouhavein5yearsifyoumakenofurtherdeposits Firstway Year0CF 5N 500PV 9I Y CPTFV 769 31Year1CF 4N 600PV 9I Y CPTFV 846 95TotalFV 769 31 846 95 1 616 26Secondway usevalueatyear2 3N 1 248 05PV 9I Y CPTFV 1 616 26 6C 6 MultipleCashFlows FVExample3 Supposeyouplantodeposit 100intoanaccountinoneyearand 300intotheaccountinthreeyears Howmuchwillbeintheaccountinfiveyearsiftheinterestrateis8 Year1CF 4N 100PV 8I Y CPTFV 136 05Year3CF 2N 300PV 8I Y CPTFV 349 92TotalFV 136 05 349 92 485 97 6C 7 MultipleCashFlows PresentValueExample6 3 FindthePVofeachcashflowandaddthemYear1CF N 1 I Y 12 FV 200 CPTPV 178 57Year2CF N 2 I Y 12 FV 400 CPTPV 318 88Year3CF N 3 I Y 12 FV 600 CPTPV 427 07Year4CF N 4 I Y 12 FV 800 CPTPV 508 41TotalPV 178 57 318 88 427 07 508 41 1 432 93 6C 8 Example6 3Timeline 6C 9 MultipleCashFlowsUsingaSpreadsheet YoucanusethePVorFVfunctionsinExceltofindthepresentvalueorfuturevalueofasetofcashflowsSettingthedataupishalfthebattle ifitissetupproperly thenyoucanjustcopytheformulasClickontheExceliconforanexample 6C 10 MultipleCashFlows PVAnotherExample Youareconsideringaninvestmentthatwillpayyou 1 000inoneyear 2 000intwoyearsand 3 000inthreeyears Ifyouwanttoearn10 onyourmoney howmuchwouldyoubewillingtopay N 1 I Y 10 FV 1 000 CPTPV 909 09N 2 I Y 10 FV 2 000 CPTPV 1 652 89N 3 I Y 10 FV 3 000 CPTPV 2 253 94PV 909 09 1 652 89 2 253 94 4 815 93 6C 11 MultipleUnevenCashFlows UsingtheCalculator AnotherwaytousethefinancialcalculatorforunevencashflowsistousethecashflowkeysPressCFandenterthecashflowsbeginningwithyear0 Youhavetopressthe Enter keyforeachcashflowUsethedownarrowkeytomovetothenextcashflowThe F isthenumberoftimesagivencashflowoccursinconsecutiveperiodsUsetheNPVkeytocomputethepresentvaluebyenteringtheinterestrateforI pressingthedownarrow andthencomputingtheanswerClearthecashflowworksheetbypressingCFandthen2ndCLRWork 6C 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 6C 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 6C 14 SavingForRetirementTimeline 012 394041424344 000 025K25K25K25K25K Noticethattheyear0cashflow 0 CF0 0 Thecashflowsinyears1 39are0 C01 0 F01 39 Thecashflowsinyears40 44are25 000 C02 25 000 F02 5 6C 15 QuickQuiz PartI Supposeyouarelookingatthefollowingpossiblecashflows Year1CF 100 Years2and3CFs 200 Years4and5CFs 300 Therequireddiscountrateis7 Whatisthevalueofthecashflowsatyear5 Whatisthevalueofthecashflowstoday Whatisthevalueofthecashflowsatyear3 6C 16 AnnuitiesandPerpetuitiesDefined Annuity finiteseriesofequalpaymentsthatoccuratregularintervalsIfthefirstpaymentoccursattheendoftheperiod itiscalledanordinaryannuityIfthefirstpaymentoccursatthebeginningoftheperiod itiscalledanannuityduePerpetuity infiniteseriesofequalpayments 6C 17 AnnuitiesandPerpetuities BasicFormulas Perpetuity PV C rAnnuities 6C 18 AnnuitiesandtheCalculator YoucanusethePMTkeyonthecalculatorfortheequalpaymentThesignconventionstillholdsOrdinaryannuityversusannuitydueYoucanswitchyourcalculatorbetweenthetwotypesbyusingthe2ndBGN2ndSetontheTIBA IIPlusIfyousee BGN or Begin inthedisplayofyourcalculator youhaveitsetforanannuitydueMostproblemsareordinaryannuities 6C 19 Annuity Example6 5 YouborrowmoneyTODAYsoyouneedtocomputethepresentvalue 48N 1I Y 632PMT CPTPV 23 999 54 24 000 Formula 6C 20 Annuity SweepstakesExample SupposeyouwinthePublishersClearinghouse 10millionsweepstakes Themoneyispaidinequalannualend of yearinstallmentsof 333 333 33over30years Iftheappropriatediscountrateis5 howmuchisthesweepstakesactuallyworthtoday 30N 5I Y 333 333 33PMT CPTPV 5 124 150 29 6C 21 BuyingaHouse Youarereadytobuyahouse andyouhave 20 000foradownpaymentandclosingcosts Closingcostsareestimatedtobe4 oftheloanvalue Youhaveanannualsalaryof 36 000 andthebankiswillingtoallowyourmonthlymortgagepaymenttobeequalto28 ofyourmonthlyincome Theinterestrateontheloanis6 peryearwithmonthlycompounding 5 permonth fora30 yearfixedrateloan Howmuchmoneywillthebankloanyou Howmuchcanyouofferforthehouse 6C 22 BuyingaHouse Continued BankloanMonthlyincome 36 000 12 3 000Maximumpayment 28 3 000 84030 12 360N 5I Y 840PMTCPTPV 140 105TotalPriceClosingcosts 04 140 105 5 604Downpayment 20 000 5 604 14 396TotalPrice 140 105 14 396 154 501 6C 23 AnnuitiesontheSpreadsheet Example ThepresentvalueandfuturevalueformulasinaspreadsheetincludeaplaceforannuitypaymentsClickontheExcelicontoseeanexample 6C 24 QuickQuiz PartII Youknowthepaymentamountforaloan andyouwanttoknowhowmuchwasborrowed Doyoucomputeapresentvalueorafuturevalue Youwanttoreceive5 000permonthinretirement Ifyoucanearn0 75 permonthandyouexpecttoneedtheincomefor25years howmuchdoyouneedtohaveinyouraccountatretirement 6C 25 FindingthePayment Supposeyouwanttoborrow 20 000foranewcar Youcanborrowat8 peryear compoundedmonthly 8 12 66667 permonth Ifyoutakea4 yearloan whatisyourmonthlypayment 4 12 48N 20 000PV 66667I Y CPTPMT 488 26 6C 26 FindingthePaymentonaSpreadsheet AnotherTVMformulathatcanbefoundinaspreadsheetisthepaymentformulaPMT rate nper pv fv ThesamesignconventionholdsasforthePVandFVformulasClickontheExceliconforanexample 6C 27 FindingtheNumberofPayments Example6 6 Thesignconventionmatters 1 5I Y1 000PV 20PMTCPTN 93 111months 7 75yearsAndthisisonlyifyoudon tchargeanythingmoreonthecard 6C 28 FindingtheNumberofPayments AnotherExample Supposeyouborrow 2 000at5 andyouaregoingtomakeannualpaymentsof 734 42 Howlongbeforeyoupayofftheloan Signconventionmatters 5I Y2 000PV 734 42PMTCPTN 3years 6C 29 FindingtheRate Supposeyouborrow 10 000fromyourparentstobuyacar Youagreetopay 207 58permonthfor60months Whatisthemonthlyinterestrate Signconventionmatters 60N10 000PV 207 58PMTCPTI Y 75 6C 30 Annuity FindingtheRateWithoutaFinancialCalculator TrialandErrorProcessChooseaninterestrateandcomputethePVofthepaymentsbasedonthisrateComparethecomputedPVwiththeactualloanamountIfthecomputedPV loanamount thentheinterestrateistoolowIfthecomputedPV loanamount thentheinterestrateistoohighAdjusttherateandrepeattheprocessuntilthecomputedPVandtheloanamountareequal 6C 31 QuickQuiz PartIII Youwanttoreceive 5 000permonthforthenext5years Howmuchwouldyouneedtodeposittodayifyoucanearn0 75 permonth Whatmonthlyratewouldyouneedtoearnifyouonlyhave 200 000todeposit Supposeyouhave 200 000todepositandcanearn0 75 permonth Howmanymonthscouldyoureceivethe 5 000payment Howmuchcouldyoureceiveeverymonthfor5years 6C 32 FutureValuesforAnnuities Supposeyoubeginsavingforyourretirementbydepositing 2 000peryearinanIRA Iftheinterestrateis7 5 howmuchwillyouhavein40years Rememberthesignconvention 40N7 5I Y 2 000PMTCPTFV 454 513 04 6C 33 AnnuityDue Youaresavingforanewhouseandyouput 10 000peryearinanaccountpaying8 Thefirstpaymentismadetoday Howmuchwillyouhaveattheendof3years 2ndBGN2ndSet youshouldseeBGNinthedisplay 3N 10 000PMT8I YCPTFV 35 061 122ndBGN2ndSet besuretochangeitbacktoanordinaryannuity 6C 34 AnnuityDueTimeline 35 016 12 6C 35 Perpetuity Example6 7 Perpetuityformula PV C rCurrentrequiredreturn 40 1 rr 025or2 5 perquarterDividendfornewpreferred 100 C 025C 2 50perquarter 6C 36 QuickQuiz PartIV Youwanttohave 1milliontouseforretirementin35years Ifyoucanearn1 permonth howmuchdoyouneedtodepositonamonthlybasisifthefirstpaymentismadeinonemonth Whatifthefirstpaymentismadetoday Youareconsideringpreferredstockthatpaysaquarterlydividendof 1 50 Ifyourdesiredreturnis3 perquarter howmuchwouldyoubewillingtopay 6C 37 WorktheWebExample AnotheronlinefinancialcalculatorcanbefoundatMoneyChimpClickonthewebsurferandworkthefollowingexampleChoosecalculatorandthenannuityYoujustinherited 5million Ifyoucanearn6 onyourmoney howmuchcanyouwithdraweachyearforthenext40years Moneychimpassumesannuitydue Payment 313 497 81 6C 38 Table6 2 6C 39 GrowingAnnuity Agrowingstreamofcashflowswithafixedmaturity 6C 40 GrowingAnnuity Example Adefined benefitretirementplanofferstopay 20 000peryearfor40yearsandincreasetheannualpaymentbythree percenteachyear Whatisthepresentvalueatretirementifthediscountrateis10percent 6C 41 GrowingPerpetuity Agrowingstreamofcashflowsthatlastsforever 6C 42 GrowingPerpetuity Example Theexpecteddividendnextyearis 1 30 anddividendsareexpectedtogrowat5 forever Ifthediscountrateis10 whatisthevalueofthispromiseddividendstream 6C 43 EffectiveAnnualRate EAR Thisistheactualratepaid orreceived afteraccountingforcompoundingthatoccursduringtheyearIfyouwanttocomparetwoalternativeinvestmentswithdifferentcompoundingperiods youneedtocomputetheEARandusethatforcomparison 6C 44 AnnualPercentageRate ThisistheannualratethatisquotedbylawBydefinitionAPR periodratetimesthenumberofperiodsperyearConsequently togettheperiodratewerearrangetheAPRequation Periodrate APR numberofperiodsperyearYoushouldNEVERdividetheeffectiveratebythenumberofperiodsperyear itwillNOTgiveyoutheperiodrate 6C 45 ComputingAPRs WhatistheAPRifthemonthlyrateis 5 5 12 6 WhatistheAPRifthesemiannualrateis 5 5 2 1 WhatisthemonthlyrateiftheAPRis12 withmonthlycompounding 12 12 1 6C 46 ThingstoRemember YouALWAYSneedtomakesurethattheinterestrateandthetimeperiodmatch Ifyouarelookingatannualperiods youneedanannualrate Ifyouarelookingatmonthlyperiods youneedamonthlyrate IfyouhaveanAPRbasedonmonthlycompounding youhavetousemonthlyperiodsforlumpsums oradjusttheinterestrateappropriatelyifyouhavepaymentsotherthanmonthly 6C 47 ComputingEARs Example Supposeyoucanearn1 permonthon 1investedtoday WhatistheAPR 1 12 12 Howmuchareyoueffectivelyearning FV 1 1 01 12 1 1268Rate 1 1268 1 1 1268 12 68 Supposeyouputitinanotheraccountandearn3 perquarter WhatistheAPR 3 4 12 Howmuchareyoueffectivelyearning FV 1 1 03 4 1 1255Rate 1 1255 1 1 1255 12 55 6C 48 EAR Formula RememberthattheAPRisthequotedrate andmisthenumberofcompoundingperiodsperyear 6C 49 Decisions DecisionsII Youarelookingattwosavingsaccounts Onepays5 25 withdailycompounding Theotherpays5 3 withsemiannualcompounding Whichaccountshouldyouuse Firstaccount EAR 1 0525 365 365 1 5 39 Secondaccount EAR 1 053 2 2 1 5 37 Whichaccountshouldyouchooseandwhy 6C 50 Decisions DecisionsIIContinued Let sverifythechoice Supposeyouinvest 100ineachaccount Howmuchwillyouhaveineachaccountinoneyear FirstAccount 365N 5 25 365 014383562I Y 100PV CPTFV 105 39SecondAccount 2N 5 3 2 2 65I Y 100PV CPTFV 105 37Youhavemoremoneyinthefirstaccount 6C 51 ComputingAPRsfromEARs Ifyouhaveaneffectiverate howcanyoucomputetheAPR RearrangetheEARequationandyouget 6C 52 APR Example Supposeyouwanttoearnaneffectiverateof12 andyouarelookingatanaccountthatcompoundsonamonthlybasis WhatAPRmusttheypay 6C 53 ComputingPaymentswithAPRs Supposeyouwanttobuyanewcomputersystemandthestoreiswillingtoallowyoutomakemonthlypayments Theentirecomputersystemcosts 3 500 Theloanperiodisfor2years andtheinterestrateis16 9 withmonthlycompounding Whatisyourmonthlypayment 2 12 24N 16 9 12 1 408333333I Y 3 500PV CPTPMT 172 88 6C 54 FutureValueswithMonthlyCompounding Supposeyoudeposit 50amonthintoanaccountthathasanAPRof9 basedonmonthlycompounding Howmuchwillyouhaveintheaccountin35years 35 12 420N9 12 75I Y50PMTCPTFV 147 089 22 6C 55 PresentValuewithDailyCompounding Youneed 15 000in3yearsforanewcar IfyoucandepositmoneyintoanaccountthatpaysanAPRof5 5 basedondailycompounding howmuchwouldyouneedtodeposit 3 365 1 095N5 5 365 015068493I Y15 000FVCPTPV 12 718 56 6C 56 ContinuousCompounding SometimesinvestmentsorloansarefiguredbasedoncontinuouscompoundingEAR eq 1TheeisaspecialfunctiononthecalculatornormallydenotedbyexExample Whatistheeffectiveannualrateof7 compoundedcontinuously EAR e 07 1 0725or7 25 6C 57 QuickQuiz PartV WhatisthedefinitionofanAPR Whatistheeffectiveannualrate Whichrateshouldyouusetocomparealternativeinvestmentsorloans Whichratedoyouneedtouseinthetimevalueofmoneycalculations 6C 58 PureDiscountLoans Example6 12 Treasurybillsareexcellentexamplesofpurediscountloans Theprincipalamountisrepaidatsomefuturedate withoutanyperiodicinterestpayments IfaT billpromisestorepay 10 000in12monthsandthemarketinterestrateis7percent howmuchwillthebillsellforinthemarket 1N 10 000FV 7I Y CPTPV 9 345 79 6C 59 Interest OnlyLoan Example Considera5 year interest onlyloanwitha7 interestrate Theprincipalamountis 10 000 Interestispaidannually Whatwouldthestreamofcashflowsbe Years1 4 Interestpaymentsof 07 10 000 700Year5 Interest principal 10 700Thiscashflowstreamissimilartothecashflowsoncorporatebonds andwewilltalkaboutthemingreaterdetaillater 6C 60 AmortizedLoanwithFixedPrincipalPayment Example Considera 50 000 10yearloanat8 interest Theloanagreementrequiresthefirmtopay 5 000inprincipaleachyearplusinterestforthatyear ClickontheExcelicontoseetheamortizationtable 6C 61 AmortizedLoanwithFixedPayment Example EachpaymentcoverstheinterestexpenseplusreducesprincipalConsidera4yearloanwithannualpayments Theinte