Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall1Chapter4:

在時(shí)間上配置資源ObjectiveExplaintheconceptofcompoundinganddiscountingandtoprovideexamplesofreallifeapplicationsCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall2Note:本章ppt并不像其他章按照課本內(nèi)容初次學(xué)習(xí)貨幣時(shí)間價(jià)值的學(xué)生需要2-3倍的基本訓(xùn)練本ppt刪去了約170張附加練習(xí)，但會(huì)將完整版發(fā)給大家，供需要的同學(xué)使用Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall3Introduction:TimeValueofMoney(TVM)今天的20元比明天的20元更有價(jià)值，因?yàn)椋篴bankwouldpayinterestonthe$20 inflationmakestomorrows$20lessvaluablethantoday’suncertaintyofreceivingtomorrow’s$20【人的時(shí)間偏好】Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall44.1復(fù)利CompoundingAssumethattheinterestrateis10%p.a.Whatthismeansisthatifyouinvest$1foroneyear,youhavebeenpromised$1*(1+10/100)or$1.10nextyearInvesting$1foryetanotheryearpromisestoproduce1.10*(1+10/100)or$1.21in2-yearsCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall5ValueofInvesting$1Continuinginthismanneryouwillfindthatthefollowingamountswillbeearned:Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall6GeneralizingthemethodGeneralizingthemethodrequiressomedefinitions.Letibetheinterestratenbe一次性（lumpsum）投資持續(xù)的期數(shù)PVbe現(xiàn)值（thepresentvalue）

FVbe未來值（thefuturevalue）Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall7FutureValueandCompoundInterestCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall8FutureValueofaLumpSumCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall9Example:FutureValueofaLumpSumYourbankoffersaCDwithaninterestrateof3%fora5yearinvestment.Youwishtoinvest$1,500for5years,howmuchwillyourinvestmentbeworth?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall10

RULEOF72

一筆投資在價(jià)值上翻倍所需年數(shù)為72除以年利率的100倍。DoublingTime= 72

InterestRate*100Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall11PresentValueofaLumpSumCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall12Example:PresentValueofaLumpSumYouhavebeenoffered$40,000foryourprintingbusiness,payablein2years.Giventherisk,yourequireareturnof8%.Whatisthepresentvalueoftheoffer?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall13LumpSumsFormulaeYouhavesolvedapresentvalueandafuturevalueofalumpsum.Thereremainstwoothervariablesthatmaybesolvedforinterest,inumberofperiods,nCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall14SolvingLumpSumCashFlowforInterestRateCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall15Example:InterestRateonaLumpSumInvestmentIfyouinvest$15,000fortenyears,youreceive$30,000.Whatisyourannualreturn?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall16SolvingLumpSumCashFlowforNumberofPeriodsCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall174.2TheFrequencyofCompoundingYouhaveacreditcardthatcarriesarateofinterestof18%peryearcompoundedmonthly.Whatistheinterestratecompoundedannually?Thatis,ifyouborrowed$1withthecard,whatwouldyouoweattheendofayear?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall18TheFrequencyofCompoundingWhenarateisexpressedintermsofamacroperiodcompoundedwithadifferentmicroperiod,thenitisanominalorannualpercentagerate(APR)Ifmacroperiod=microperiodthentherateisreferredtoasatherealoreffectiveratebasedonthatperiodCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall19TheFrequencyofCompoundingAssumemmicroperiodsinamacroperiodandanominalratekpermacroperiodcompoundedmicro-periodically.Thatistheeffectiverateisk/mpermicroperiod.Invest$1foronemacroperiodtoobtain$1*(1+k/m)m,producinganeffectiverateoverthemacroperiodof($1*(1+k/m)m-$1)/$1=(1+k/m)m-1Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall20CreditCardIfthecreditcardpaysanAPRof18%peryearcompoundedmonthly.The(real)monthlyrateis18%/12=1.5%sotherealannualrateis(1+0.015)12-1=19.56%ThetwoequalAPRwithdifferentfrequencyofcompoundinghavedifferenteffectiveannualrates:Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall21EffectiveAnnualRatesofanAPRof18%Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall22TheFrequencyofCompoundingNotethatasthefrequencyofcompoundingincreases,sodoestheannualeffectiverateWhatoccursasthefrequencyofcompoundingrisestoinfinity?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall23TheFrequencyofCompoundingTheeffectiveannualratethat’sequivalenttoanannualpercentagerateof18%isthene0.18-1=19.72%Moreprecisionshowsthatmovingfromdailycompoundingtocontinuouscompoundinggains0.53ofonebasispointCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall24TheFrequencyofCompoundingAbankdeterminesthatitneedsaneffectiverateof12%oncarloanstomediumriskborrowersWhatannualpercentageratesmayitoffer?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall25TheFrequencyofCompoundingCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall26TheFrequencyofCompoundingCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall27TheFrequencyofCompoundingManylendersandborrowersdonothaveaclearunderstandingofAPRs,butinstitutionallendersandborrowersdoInstitutionsarethereforeabletoextractafewbasispointsfromconsumers,butwhybother?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall28TheFrequencyofCompoundingFinancialintermediariesprofitfromdifferencesinthelendingandborrowingrates.Overheads(日常管理費(fèi)用),badloansandcompetitionresultsinanarrowmargin.SmallrategainsthereforeresultinalargeincreasesininstitutionalprofitsInthelongterm,ill-informedconsumerslosebecauseofcompoundingCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall294.5MultipleCashFlowsTimeLinesFutureValueofaStreamofCashFlowPresentValueofaStreamofCashFlowsInvestingwithMultipleCashFlowsCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall30TimeLineCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall31PresentValueofMultipleCashFlows

（利率10%）Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall324.6Annuities（年金）Financialanalystsuseseveralannuitieswithdifferingassumptionsaboutthefirstpayment.Wewillexaminejusttwo:regularannuity（普通年金）withitsfirstcoupon（付款）oneperiodfromnow,annuitydue（即期年金）withitsfirstcoupontoday,Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall33CashFlowDiagramofAnnuitiesCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall34年金公式的基本原理asequenceofequallyspacedidenticalcashflowsisacommonoccurrence,soautomationpaysoffatypicalannuityisamortgagewhichmayhave360monthlypayments,alotofworkforusingelementarymethodsCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall35AssumptionsRegularAnnuitythefirstcashflowwilloccurexactlyoneperiodformnowallsubsequentcashflowsareseparatedbyexactlyoneperiodallperiodsareofequallengththetermstructureofinterestisflatallcashflowshavethesame(nominal)valueCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall36AnnuityFormulaNotationPV=thepresentvalueoftheannuityi=interestratetobeearnedoverthelifeoftheannuityn=thenumberofpaymentspmt=theperiodicpaymentCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall37DerivationofPVofAnnuityFormula:Algebra.1of5Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall38DerivationofPVofAnnuityFormula:Algebra.2of5Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall39DerivationofPVofAnnuityFormula:Algebra.3of5Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall40DerivationofPVofAnnuityFormula:Algebra.4of5Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall41DerivationofPVofAnnuityFormula:Algebra.5of5Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall42PVofAnnuityFormulaCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall43PVAnnuityFormula:PaymentCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall44PVAnnuityFormula:NumberofPaymentsCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall45PVAnnuityFormula:ReturnThereisnotranscendentalsolution（超越解）tothePVofanannuityequationintermsoftheinterestrate【以利息率為未知數(shù)的方程】.StudentsinterestedinthereasonwhyarereferredtoGaloisTheory,2nd.EdI.Stewart.Studentswithastrongersenseoffashionare“seen”carryingMichioKuga’spoison-ivy-green-coloredbook“GaloisDream.”Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall46AnnuityFormula:PVAnnuityDueCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall47DerivationofFVofAnnuityFormula:AlgebraCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall48FVAnnuityFormula:PaymentCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall49FVAnnuityFormula:NumberofPaymentsCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall50FVAnnuityFormula:ReturnThereisnotranscendentalsolutionNumericalmethodshavetobeemployedCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall514.7PerpetualAnnuities（永續(xù)年金）Recalltheannuityformula:Letn->infinitywithi>0:Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall52GrowingAnnuitiesGrowingannuitiessolvethesuper-normalgrowthproblemTheyareoftenmoreappropriateinday-to-daysituationsthanannuitiesCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall534.8LoanAmortization（分期償還）:Mortgageearlyrepaymentpermittedatanytimeduringmortgage’s360monthlypaymentsmarketinterestratesmayfluctuate,buttheloan’srateisaconstant1/2%permonththemortgagerequires10%equityand“threepoints”assumea$500,000housepriceCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall54Mortgage:ThepaymentWewillexaminethisproblemusingafinancialcalculatorThefirstquantitytodetermineistheamountoftheloanandthepointsCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall55CalculatorSolutionThisisthemonthlyrepaymentCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall56OutstandingBalance（未償余額）asaFunctionofTimeThefollowinggraphsillustratethatintheearlyyears,monthlypaymentaremostlyinterest.Inlatteryears,thepaymentsaremostlyprincipleRecallthatonlytheinterestportionistax-deductible,sothetaxshelterdecaysCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall57Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall58Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall594.9ExchangeRatesandTimeValueofMoney

Youareconsideringthechoice:Investing$10,000indollar-denominatedbondsoffering10%/yearInvesting$10,000inyen-denominatedbondsoffering3%/yearAssumeanexchangerateof0.01Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall60$10,000$11,000￥1,000,000￥1,030,000￥Time10%$/$(direct)0.01$/￥3%￥/￥?$/￥U.S.A.JapanCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall61ExchangeRateDiagramReviewofthediagramindicatesthatyouwillendtheyearwitheither$11,000or￥1,030,000Ifthe$priceoftheyenrisesby8%/yearthentheyear-endexchangeratewillbe$0.0108/￥Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall62$10,000$11,124$11,000￥1,000,000￥1,030,000￥Time10%$/$(direct)0.01$/￥3%￥/￥0.0108$/￥U.S.A.JapanCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall63InterpretationandAnotherScenarioInthecaseofthe$priceof￥risingby8%yougain$124onyourinvestmentNow,ifthe$priceof￥risesby6%,theexchangerateinoneyearwillbe$0.0106Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall64$10,000$10,918￥$11,000￥1,000,000￥1,030,000￥Time10%$/$(direct)0.01$/￥3%￥/￥0.0106$/￥U.S.A.JapanCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall65InterpretationInthiscase,youwilllose$82byinvestingintheJapanesebondIfyoudivideproceedsoftheUSinvestmentbythoseoftheJapaneseinvestment,youobtaintheexchangerateatwhichyouareindifferent$11,000/￥1,030,000=0.1068$/￥Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall66$10,000$11,000￥$11,000￥1,000,000￥1,030,000￥Time10%$/$(direct)0.01$/￥3%￥/￥0.01068$/￥U.S.A.JapanCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall67ConclusionIftheyenpriceactuallyrisesbymorethan6.8%duringthecomingyearthentheyenbondisabetterinvestmentCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall68FinancialDecisioninanInternationalContextInternationalcurrencyinvestorsborrowandlendinTheirowncurrencyThecurrencyofcountrieswithwhichtheydobusinessbutwishtohedgeCurrenciesthatappeartoofferabetterdealExchangeratefluctuationscanresultinunexpectedgainsandlossesCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall69ComputingNPVinDifferentCurrenciesInanytime-value-of-moneycalculation,thecashflowsandinterestratesmustbedenominatedinthesamecurrencyUSAprojectUrequiresaninvestmentof$10,000,asdoesaJapaneseprojectJ.Ugenerates$6,000/yearfor5years,andprojectJgenerates￥575,000/yearfor5yearsTheUSinterestis6%,theJapaneseinterestis4%,andthecurrentexchangerateis0.01Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall70SolutionUsingyourfinancialcalculatorDeterminethepresentvalueofUin$bydiscountingthe5paymentsat6%,andsubtracttheinitialinvestmentof$10,000DeterminethepresentvalueofJin￥bydiscountingthe5paymentsat4%,andsubtracttheinitialinvestmentof￥1,000,000Obtain$15,274&￥1,5599,798respectivelyCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall71SolutionConvertthe￥1,5599,798to$usingthecurrentexchangeratetoobtain$15,600TheJapaneseNPVof￥of$15,600ishigherthantheUSANPVor$15,274,soinvestintheJapaneseprojectCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall724.10InflationandDiscountedCashFlowAnalysisWewillusethenotationIntherateofinterestinnominaltermsIrtherateofinterestinrealtermsRtherateofinflationFromchapter2wehavetherelationshipCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall73IllustrationWhatistherealrateofinterestifthenominalrateis8%andinflationis5%?TherealrateorreturndeterminesthespendingpowerofyoursavingsThenominalvalueofyourwealthisonlyasimportantasitspurchasingpowerCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall74InvestinginInflation-protectedCD’sYouhavedecidedtoinvest$10,000forthenext12-months.YouareofferedtwochoicesAnominalCDpayinga8%returnArealCDpaying3%+inflationrateIfyouanticipatetheinflationbeingBelow5%investinthenominalsecurityAbove5%investintherealsecurityEqualto5%investineitherCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall75WhyDebtors（債務(wù)人）GainFromUnanticipatedInflation

Youborrow$10,000at8%interest.Thetoday’sspendingpoweroftherepaymentis$10,000*1.08/(1+inflation)Iftheactualinflationistheexpected6%,thentherealcostoftheloanintoday’smoneyis$10,188.68Iftheactualinflationis10%,thentheloan’srealcost(intoday’svalues)is$9,818.18UnexpectedinflationbenefitsborrowerCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall76InflationandPresentValue

一個(gè)經(jīng)常遇到的情況是需要決定為一定時(shí)間后的某個(gè)目標(biāo)應(yīng)每期儲(chǔ)蓄多少問題是未來的購買目標(biāo)的價(jià)格在上漲（因通貨膨脹）用“實(shí)際”（實(shí)際價(jià)值、實(shí)際利率）方法解決此問題Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall77InflationandSavingsPlansAnquestionisHowmuchmustIsaveeachyearinordertoachieveasavingsgoal?Wewillreusetheboatproblem,butwiththeassumptionthattheboateriswillingtowait8-years,butwishestominimizeannual(inflationadjusted)paymentsCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall784.11TaxesandInvestmentDecisionsRule:Investsoastomaximizeyourafter-taxrateofreturnThisisnotatallthesamethingas Minimizethetaxyoupay(False)Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall79Chapter4:

在時(shí)間上配置資源ObjectiveExplaintheconceptofcompoundinganddiscountingandtoprovideexamplesofreallifeapplicationsCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall80Note:本章ppt并不像其他章按照課本內(nèi)容初次學(xué)習(xí)貨幣時(shí)間價(jià)值的學(xué)生需要2-3倍的基本訓(xùn)練本ppt刪去了約170張附加練習(xí)，但會(huì)將完整版發(fā)給大家，供需要的同學(xué)使用Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall81Introduction:TimeValueofMoney(TVM)今天的20元比明天的20元更有價(jià)值，因?yàn)椋篴bankwouldpayinterestonthe$20 inflationmakestomorrows$20lessvaluablethantoday’suncertaintyofreceivingtomorrow’s$20【人的時(shí)間偏好】Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall824.1復(fù)利CompoundingAssumethattheinterestrateis10%p.a.Whatthismeansisthatifyouinvest$1foroneyear,youhavebeenpromised$1*(1+10/100)or$1.10nextyearInvesting$1foryetanotheryearpromisestoproduce1.10*(1+10/100)or$1.21in2-yearsCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall83ValueofInvesting$1Continuinginthismanneryouwillfindthatthefollowingamountswillbeearned:Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall84GeneralizingthemethodGeneralizingthemethodrequiressomedefinitions.Letibetheinterestratenbe一次性（lumpsum）投資持續(xù)的期數(shù)PVbe現(xiàn)值（thepresentvalue）

FVbe未來值（thefuturevalue）Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall85FutureValueandCompoundInterestCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall86FutureValueofaLumpSumCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall87Example:FutureValueofaLumpSumYourbankoffersaCDwithaninterestrateof3%fora5yearinvestment.Youwishtoinvest$1,500for5years,howmuchwillyourinvestmentbeworth?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall88

RULEOF72

一筆投資在價(jià)值上翻倍所需年數(shù)為72除以年利率的100倍。DoublingTime= 72

InterestRate*100Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall89PresentValueofaLumpSumCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall90Example:PresentValueofaLumpSumYouhavebeenoffered$40,000foryourprintingbusiness,payablein2years.Giventherisk,yourequireareturnof8%.Whatisthepresentvalueoftheoffer?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall91LumpSumsFormulaeYouhavesolvedapresentvalueandafuturevalueofalumpsum.Thereremainstwoothervariablesthatmaybesolvedforinterest,inumberofperiods,nCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall92SolvingLumpSumCashFlowforInterestRateCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall93Example:InterestRateonaLumpSumInvestmentIfyouinvest$15,000fortenyears,youreceive$30,000.Whatisyourannualreturn?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall94SolvingLumpSumCashFlowforNumberofPeriodsCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall954.2TheFrequencyofCompoundingYouhaveacreditcardthatcarriesarateofinterestof18%peryearcompoundedmonthly.Whatistheinterestratecompoundedannually?Thatis,ifyouborrowed$1withthecard,whatwouldyouoweattheendofayear?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall96TheFrequencyofCompoundingWhenarateisexpressedintermsofamacroperiodcompoundedwithadifferentmicroperiod,thenitisanominalorannualpercentagerate(APR)Ifmacroperiod=microperiodthentherateisreferredtoasatherealoreffectiveratebasedonthatperiodCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall97TheFrequencyofCompoundingAssumemmicroperiodsinamacroperiodandanominalratekpermacroperiodcompoundedmicro-periodically.Thatistheeffectiverateisk/mpermicroperiod.Invest$1foronemacroperiodtoobtain$1*(1+k/m)m,producinganeffectiverateoverthemacroperiodof($1*(1+k/m)m-$1)/$1=(1+k/m)m-1Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall98CreditCardIfthecreditcardpaysanAPRof18%peryearcompoundedmonthly.The(real)monthlyrateis18%/12=1.5%sotherealannualrateis(1+0.015)12-1=19.56%ThetwoequalAPRwithdifferentfrequencyofcompoundinghavedifferenteffectiveannualrates:Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall99EffectiveAnnualRatesofanAPRof18%Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall100TheFrequencyofCompoundingNotethatasthefrequencyofcompoundingincreases,sodoestheannualeffectiverateWhatoccursasthefrequencyofcompoundingrisestoinfinity?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall101TheFrequencyofCompoundingTheeffectiveannualratethat’sequivalenttoanannualpercentagerateof18%isthene0.18-1=19.72%Moreprecisionshowsthatmovingfromdailycompoundingtocontinuouscompoundinggains0.53ofonebasispointCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall102TheFrequencyofCompoundingAbankdeterminesthatitneedsaneffectiverateof12%oncarloanstomediumriskborrowersWhatannualpercentageratesmayitoffer?Copyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall103TheFrequencyofCompoundingCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall104TheFrequencyofCompoundingCopyright?2009PearsonEducaCopyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall105TheFrequencyofCompoundingManylendersandborrowersdonothaveaclearunderstandingofAPRs,butinstitutionallendersandborrowersdoInstitutionsarethereforeabletoextractafewbasispoints