财务管理双本PPT课件.ppt

CHAPTER3TimeValueofMoney FuturevaluePresentvalueAnnuitiesRatesofreturnAmortization 1 Timelines Showthetimingofcashflows Tickmarksoccurattheendofperiods soTime0istoday Time1istheendofthefirstperiod year month etc orthebeginningofthesecondperiod 显示现金流量的时间 刻度标记发生在周期的结束 所以时间0今天 时间1是结束的第一个时期 年 月等 或第二期的开始 CF0 CF1 CF3 CF2 0 1 2 3 i 2 Drawingtimelines 100lumpsumduein2years 3 year 100ordinaryannuity 3 Drawingtimelines Unevencashflowstream CF0 50 CF1 100 CF2 75 andCF3 50 4 Whatisthefuturevalue FV ofaninitial 100after3years ifI YR 10 FindingtheFVofacashfloworseriesofcashflowswhencompoundinterestisappliediscalledcompounding FVcanbesolvedbyusingthearithmetic financialcalculator andspreadsheetmethods 找到一个现金流或现金流序列的FV当复利应用称为复合 抗体可以通过使用算法 解决金融计算器和电子表格方法 5 SolvingforFV Thearithmeticmethod After1year FV1 PV 1 i 100 1 10 110 00After2years FV2 PV 1 i 2 100 1 10 2 121 00After3years FV3 PV 1 i 3 100 1 10 3 133 10Afternyears generalcase FVn PV 1 i n 6 SolvingforFV Thecalculatormethod SolvesthegeneralFVequation Requires4inputsintocalculator andwillsolveforthefifth SettoP YR 1andENDmode INPUTS OUTPUT N I YR PMT PV FV 3 10 0 133 10 100 7 PV 100 Whatisthepresentvalue PV of 100duein3years ifI YR 10 FindingthePVofacashfloworseriesofcashflowswhencompoundinterestisappliediscalleddiscounting thereverseofcompounding ThePVshowsthevalueofcashflowsintermsoftoday spurchasingpower 当复合息被应用时 发现现金流或现金流的一系列的现值被称为贴现 复合的反向 光伏显示现金流量的价值 在今天的购买力 0 1 2 3 10 8 SolvingforPV Thearithmeticmethod SolvethegeneralFVequationforPV PV FVn 1 i nPV FV3 1 i 3 100 1 10 3 75 13 9 SolvingforPV Thecalculatormethod SolvesthegeneralFVequationforPV ExactlylikesolvingforFV exceptwehavedifferentinputinformationandaresolvingforadifferentvariable INPUTS OUTPUT N I YR PMT PV FV 3 10 0 100 75 13 10 SolvingforN Ifsalesgrowat20 peryear howlongbeforesalesdouble SolvesthegeneralFVequationforN Sameaspreviousproblems butnowsolvingforN INPUTS OUTPUT N I YR PMT PV FV 3 8 20 0 2 1 11 Whatisthedifferencebetweenanordinaryannuityandanannuitydue 12 SolvingforFV 3 yearordinaryannuityof 100at10 100paymentsoccurattheendofeachperiod butthereisnoPV INPUTS OUTPUT N I YR PMT PV FV 3 10 100 331 0 13 SolvingforPV 3 yearordinaryannuityof 100at10 100paymentsstilloccurattheendofeachperiod butnowthereisnoFV INPUTS OUTPUT N I YR PMT PV FV 3 10 100 0 248 69 14 SolvingforFV 3 yearannuitydueof 100at10 Now 100paymentsoccuratthebeginningofeachperiod Setcalculatorto BEGIN mode INPUTS OUTPUT N I YR PMT PV FV 3 10 100 364 10 0 15 SolvingforPV 3yearannuitydueof 100at10 Again 100paymentsoccuratthebeginningofeachperiod Setcalculatorto BEGIN mode INPUTS OUTPUT N I YR PMT PV FV 3 10 100 0 273 55 16 WhatisthePVofthisunevencashflowstream 17 SolvingforPV Unevencashflowstream Inputcashflowsinthecalculator s CFLO register CF0 0CF1 100CF2 300CF3 300CF4 50EnterI YR 10 pressNPVbuttontogetNPV 530 09 HereNPV PV 18 SolvingforI Whatinterestratewouldcause 100togrowto 125 97in3years SolvesthegeneralFVequationforI INPUTS OUTPUT N I YR PMT PV FV 3 8 0 125 97 100 19 ThePowerofCompoundInterest A20 year oldstudentwantstostartsavingforretirement Sheplanstosave 3aday Everyday sheputs 3inherdrawer Attheendoftheyear sheinveststheaccumulatedsavings 1 095 inanonlinestockaccount Thestockaccounthasanexpectedannualreturnof12 Howmuchmoneywillshehavewhensheis65yearsold 20 SolvingforFV Savingsproblem Ifshebeginssavingtoday andstickstoherplan shewillhave 1 487 261 89whensheis65 INPUTS OUTPUT N I YR PMT PV FV 45 12 1095 1 487 262 0 21 SolvingforFV Savingsproblem ifyouwaituntilyouare40yearsoldtostart Ifa40 year oldinvestorbeginssavingtoday andstickstotheplan heorshewillhave 146 000 59atage65 Thisis 1 3millionlessthanifstartingatage20 Lesson Itpaystostartsavingearly INPUTS OUTPUT N I YR PMT PV FV 25 12 1095 146 001 0 22 SolvingforPMT Howmuchmustthe40 yearolddepositannuallytocatchthe20 yearold Tofindtherequiredannualcontribution enterthenumberofyearsuntilretirementandthefinalgoalof 1 487 261 89 andsolveforPMT INPUTS OUTPUT N I YR PMT PV FV 25 12 11 154 42 1 487 262 0 23 WilltheFVofalumpsumbelargerorsmallerifcompoundedmoreoften holdingthestatedI constant LARGER asthemorefrequentlycompoundingoccurs interestisearnedoninterestmoreoften Annually FV3 100 1 10 3 133 10 Semiannually FV6 100 1 05 6 134 01 24 Classificationsofinterestrates Nominalrate iNOM alsocalledthequotedorstaterate Anannualratethatignorescompoundingeffects iNOMisstatedincontracts Periodsmustalsobegiven e g 8 Quarterlyor8 Dailyinterest Periodicrate iPER amountofinterestchargedeachperiod e g monthlyorquarterly iPER iNOM m wheremisthenumberofcompoundingperiodsperyear m 4forquarterlyandm 12formonthlycompounding 25 Classificationsofinterestrates Effective orequivalent annualrate EAR EFF theannualrateofinterestactuallybeingearned takingintoaccountcompounding EFF for10 semiannualinvestmentEFF 1 iNOM m m 1 1 0 10 2 2 1 10 25 Aninvestorwouldbeindifferentbetweenaninvestmentofferinga10 25 annualreturnandoneofferinga10 annualreturn compoundedsemiannually 26 Whyisitimportanttoconsidereffectiveratesofreturn Aninvestmentwithmonthlypaymentsisdifferentfromonewithquarterlypayments MustputeachreturnonanEFF basistocompareratesofreturn MustuseEFF forcomparisons SeefollowingvaluesofEFF ratesatvariouscompoundinglevels EARANNUAL10 00 EARQUARTERLY10 38 EARMONTHLY10 47 EARDAILY 365 10 52 27 Cantheeffectiverateeverbeequaltothenominalrate Yes butonlyifannualcompoundingisused i e ifm 1 Ifm 1 EFF willalwaysbegreaterthanthenominalrate 28 Wheniseachrateused iNOMwrittenintocontracts quotedbybanksandbrokers Notusedincalculationsorshownontimelines iPERUsedincalculationsandshownontimelines Ifm 1 iNOM iPER EAR EARUsedtocomparereturnsoninvestmentswithdifferentpaymentsperyear Usedincalculationswhenannuitypaymentsdon tmatchcompoundingperiods 29 WhatistheFVof 100after3yearsunder10 semiannualcompounding Quarterlycompounding 30 What stheFVofa3 year 100annuity ifthequotedinterestrateis10 compoundedsemiannually Paymentsoccurannually butcompoundingoccursevery6months Cannotusenormalannuityvaluationtechniques 31 Method1 Compoundeachcashflow FV3 100 1 05 4 100 1 05 2 100FV3 331 80 32 Method2 Financialcalculator FindtheEARandtreatasanannuity EAR 1 0 10 2 2 1 10 25 INPUTS OUTPUT N I YR PMT PV FV 3 10 25 100 331 80 0 33 FindthePVofthis3 yearordinaryannuity Couldsolvebydiscountingeachcashflow or UsetheEARandtreatasanannuitytosolveforPV INPUTS OUTPUT N I YR PMT PV FV 3 10 25 100 0 247 59 34 Loanamortization Amortizationtablesarewidelyusedforhomemortgages autoloans businessloans retirementplans etc Financialcalculatorsandspreadsheetsaregreatforsettingupamortizationtables EXAMPLE Constructanamortizationschedulefora 1 000 10 annualrateloanwith3equalpayments 35 Step1 Findtherequiredannualpayment Allinputinformationisalreadygiven justrememberthattheFV 0becausethereasonforamortizingtheloanandmakingpaymentsistoretiretheloan INPUTS OUTPUT N I YR PMT PV FV 3 10 402 11 0 1000 36 Step2 FindtheinterestpaidinYear1 Theborrowerwilloweinterestupontheinitialbalanceattheendofthefirstyear Interesttobepaidinthefirstyearcanbefoundbymultiplyingthebeginningbalancebytheinterestrate INTt Begbalt i INT1 1 000 0 10 100 37 Step3 FindtheprincipalrepaidinYear1 Ifapaymentof 402 11wasmadeattheendofthefirstyearand 100waspaidtowardinterest theremainingvaluemustrepresenttheamountofprincipalrepaid PRIN PMT INT 402 11 100 302 11 38 Step4 FindtheendingbalanceafterYear1 Tofindthebalanceattheendoftheperiod subtracttheamountpaidtowardprincipalfromthebeginningbalance ENDBAL BEGBAL PRIN 1 000 302 11 697 89 39 Constructinganamortizationtable Repeatsteps1 4untilendofloan Interestpaiddeclineswitheachpaymentasthebalancedeclines Whatarethetaximplicationsofthis 40 Illustratinganamortizedpayment