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Copyright©2009PearsonEducation,Inc.
PublishingasPrenticeHall1Chapter4:
在时间上配置资源ObjectiveExplaintheconceptofcompoundinganddiscountingandtoprovideexamplesofreallifeapplicationsCopyright©2009PearsonEducaCopyright©2009PearsonEducation,Inc.
PublishingasPrenticeHall2Note:本章ppt并不像其他章按照课本内容初次学习货币时间价值的学生需要2-3倍的基本训练本ppt删去了约170张附加练习，但会将完整版发给大家，供需要的同学使用Copyright©2009PearsonEducaCopyright©2009PearsonEducation,Inc.
PublishingasPrenticeHall3Introduction:TimeValueofMoney(TVM)今天的20元比明天的20元更有价值，因为：abankwouldpayinterestonthe$20 inflationmakestomorrows$20lessvaluablethantoday’suncertaintyofreceivingtomorrow’s$20【人的时间偏好】Copyright©2009PearsonEducaCopyright©2009PearsonEducation,Inc.
PublishingasPrenticeHall44.1复利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）投资持续的期数PVbe现值（thepresentvalue）
FVbe未来值（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
一笔投资在价值上翻倍所需年数为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(日常管理费用),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【以利息率为未知数的方程】.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（永续年金）Recalltheannuityformula:Letn->infinitywithi>0:Copyright©2009PearsonEducaCopyright©2009PearsonEducation,Inc.
PublishingasPrenticeHall52GrowingAnnuitiesGrowingannuitiessolvethesuper-normalgrowthproblemTheyareoftenmoreappropriateinday-to-daysituationsthanannuitiesCopyright©2009PearsonEducaCopyright©2009PearsonEducation,Inc.
PublishingasPrenticeHall534.8LoanAmortization（分期偿还）:Mortgageearlyrepaymentpermittedatanytimeduringmortgage’s360monthlypaymentsmarketinterestratesmayfluctuate,buttheloan’srateisaconstant1/2%permonththemortgagerequires10%equityand“threepoints”assumea$500,000housepriceCopyright©2009PearsonEducaCopyright©2009PearsonEducation,Inc.
PublishingasPrenticeHall54Mortgage:ThepaymentWewillexaminethisproblemusingafinancialcalculatorThefirstquantitytodetermineistheamountoftheloanandthepointsCopyright©2009PearsonEducaCopyright©2009PearsonEducation,Inc.
PublishingasPrenticeHall55CalculatorSolutionThisisthemonthlyrepaymentCopyright©2009PearsonEducaCopyright©2009PearsonEducation,Inc.
PublishingasPrenticeHall56OutstandingBalance（未偿余额）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（债务人）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
一个经常遇到的情况是需要决定为一定时间后的某个目标应每期储蓄多少问题是未来的购买目标的价格在上涨（因通货膨胀）用“实际”（实际价值、实际利率）方法解决此问题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:
在时间上配置资源ObjectiveExplaintheconceptofcompoundinganddiscountingandtoprovideexamplesofreallifeapplicationsCopyright©2009PearsonEducaCopyright©2009PearsonEducation,Inc.
PublishingasPrenticeHall80Note:本章ppt并不像其他章按照课本内容初次学习货币时间价值的学生需要2-3倍的基本训练本ppt删去了约170张附加练习，但会将完整版发给大家，供需要的同学使用Copyright©2009PearsonEducaCopyright©2009PearsonEducation,Inc.
PublishingasPrenticeHall81Introduction:TimeValueofMoney(TVM)今天的20元比明天的20元更有价值，因为：abankwouldpayinterestonthe$20 inflationmakestomorrows$20lessvaluablethantoday’suncertaintyofreceivingtomorrow’s$20【人的时间偏好】Copyright©2009PearsonEducaCopyright©2009PearsonEducation,Inc.
PublishingasPrenticeHall824.1复利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）投资持续的期数PVbe现值（thepresentvalue）
FVbe未来值（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
一笔投资在价值上翻倍所需年数为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
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