Chapter4:

AllocatingResources OverTimeObjectiveExplaintheconceptofcompoundinganddiscountingandtoprovideexamplesofreallifeapplications1Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallNote:ThisslideshowdoesnotfollowthebookascloselyasshowsfortheotherchaptersStudentsgettingtimevalueofmoneyforthefirsttimeneedtodoubleortripleexposuretothisbasicskillTherearemanyexamplesattheendofthiscollectionorganizedintosubsectionsstartingatslide95of2632Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallIntroduction:TimeValueofMoney(TVM)

$20todayisworthmorethantheexpectationof$20tomorrowbecause:abankwouldpayinterestonthe$20 inflationmakestomorrows$20lessvaluablethantoday’suncertaintyofreceivingtomorrow’s$203Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall4.1CompoundingAssumethattheinterestrateis10%p.a.Whatthismeansisthatifyouinvest$1foroneyear,youhavebeenpromised$1*(1+10/100)or$1.10nextyearInvesting$1foryetanotheryearpromisestoproduce1.10*(1+10/100)or$1.21in2-years4Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallValueofInvesting$1Continuinginthismanneryouwillfindthatthefollowingamountswillbeearned:5Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallValueof$5InvestedMoregenerally,withaninvestmentof$5at10%weobtain6Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallGeneralizingthemethodGeneralizingthemethodrequiressomedefinitions.LetibetheinterestratenbethelifeofthelumpsuminvestmentPVbethepresentvalueFVbethefuturevalue7Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallFutureValueandCompoundInterest8Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallFutureValueofaLumpSum9Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallExample:FutureValueofaLumpSumYourbankoffersaCDwithaninterestrateof3%fora5yearinvestment.Youwishtoinvest$1,500for5years,howmuchwillyourinvestmentbeworth?10Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall

RULEOF72

Thisrulesaysthatthenumberofyearsittakesforasumofmoneytodoubleinvalue(“thedoublingtime”)isapproximatelyequaltothenumber72dividedbytheinterestrateexpressedinpercentperyearDoublingTime= 72

InterestRate11Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallHint:Roundingiscommonsense“plus”traditionItsimportanttoroundappropriatelyIna$7billionsproject,roundingmightbetothenearest$’000,000Yourcheckbookshouldberoundedto$0.01Inanaccountingsituation,anyunexpectederror,howeversmallcouldbetheresultoftwolargercompensatingerrors.Accordingly,theyneedtoberesolvedAvoidanytruncationwithinacalculation12Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallHint:AvoidanytruncationwithinacalculationEngineersstudynumericalanalysis.Infact,itissoimportant,theymaytakeseveralcourses.Fewfinancefolkhaveanyideaofcomputationaldangers.FornowyoushouldbesafeifyouAvoidremovingintermediateresultsfromyourcalculator.Storetheminamemoryregister.ThisavoidsinputandoutputcopyingerrorsLearntousethe“stack”orbracketsprovidedbyyourfinancialcalculator.YourcalculatorprobablykeepsamoreaccurateversionofdisplayednumbersinternallyInnocaseshouldyouevertruncateanintermediatecomputationunlessyoufullyunderstandtheaffectonaccuracy(Youprobablydon’t!)13Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallPresentValueofaLumpSum14Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallExample:PresentValueofaLumpSumYouhavebeenoffered$40,000foryourprintingbusiness,payablein2years.Giventherisk,yourequireareturnof8%.Whatisthepresentvalueoftheoffer?15Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallLumpSumsFormulaeYouhavesolvedapresentvalueandafuturevalueofalumpsum.Thereremainstwoothervariablesthatmaybesolvedforinterest,inumberofperiods,n16Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallSolvingLumpSumCashFlowforInterestRate17Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallExample:InterestRateonaLumpSumInvestmentIfyouinvest$15,000fortenyears,youreceive$30,000.Whatisyourannualreturn?18Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallReviewofLogarithmsThenextthreeslidesareaquickreviewoflogarithmsIknowthatyouprobablylearnedthisineighthgrade,butthoseofuswhodonotusethemfrequentlyforgetthebasicrules19Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallLogarithmsareimportantinfinancebecausegrowthisrelatedtothetheexponential,andtheexponentialistheinversefunctionofthelogarithmLogarithmsmayhavedifferentbases,butinfinanceweneedonlythenaturallogarithm,thatisthelogarithmofbasee.Theeistheirrationalnumberthatmaybeapproximatedas2.718281828.Itiseasytorememberbecauseitstartstorepeat,butdon’tbefooled,itdoesn't,anditis

irrational20Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallReviewofLogarithmsThebasicpropertiesoflogarithmsthatareusedbyfinanceare:21Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallReviewofLogarithmsThefollowingpropertiesareeasytoprovefromthelastones,andareusefulinfinance22Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallSolvingLumpSumCashFlowforNumberofPeriods23Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall4.2TheFrequencyofCompoundingYouhaveacreditcardthatcarriesarateofinterestof18%peryearcompoundedmonthly.Whatistheinterestratecompoundedannually?Thatis,ifyouborrowed$1withthecard,whatwouldyouoweattheendofayear?24Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTheFrequencyofCompounding18%peryearcompoundedmonthlyisjustcodefor18%/12=1.5%permonthAllcalculationmustbeexpressedintermsofconsistentunitsArawrateofinterestexpressedintermsofyearsandmonthsmayneverbeusedinacalculation25Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTheFrequencyofCompoundingTheannualratecompoundedmonthlyiscodeforonetwelfthofthestatedratepermonthcompoundedmonthlyTheyearisthemacroperiod,andthemonthisthemicroperiodInthiscasethereare12microperiodsinonemacroperiod26Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTheFrequencyofCompoundingWhenarateisexpressedintermsofamacroperiodcompoundedwithadifferentmicroperiod,thenitisanominalorannualpercentagerate(APR)Ifmacroperiod=microperiodthentherateisreferredtoasatherealoreffectiveratebasedonthatperiod27Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTheFrequencyofCompoundingAssumemmicroperiodsinamicroperiodandanominalratekpermacroperiodcompoundedmicro-periodically.Thatistheeffectiverateisk/mpermicroperiod.Invest$1foronemacroperiodtoobtain$1*(1+k/n)n,producinganeffectiverateoverthemacroperiodof($1*(1+k/n)n-$1)/$1=(1+k/n)n-128Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallCreditCardIfthecreditcardpaysanAPRof18%peryearcompoundedmonthly.The(real)monthlyrateis18%/12=1.5%sotherealannualrateis(1+0.015)12-1=19.56%ThetwoequalAPRwithdifferentfrequencyofcompoundinghavedifferenteffectiveannualrates:29Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallEffectiveAnnualRatesofanAPRof18%30Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTheFrequencyofCompoundingNotethatasthefrequencyofcompoundingincreases,sodoestheannualeffectiverateWhatoccursasthefrequencyofcompoundingrisestoinfinity?31Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTheFrequencyofCompoundingTheeffectiveannualratethat’sequivalenttoanannualpercentagerateof18%isthene0.18-1=19.72%Moreprecisionshowsthatmovingfromdailycompoundingtocontinuouscompoundinggains0.53ofonebasispoint32Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTheFrequencyofCompoundingAbankdeterminesthatitneedsaneffectiverateof12%oncarloanstomediumriskborrowersWhatannualpercentageratesmayitoffer?33Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTheFrequencyofCompounding34Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTheFrequencyofCompounding35Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTheFrequencyofCompoundingManylendersandborrowersdonothaveaclearunderstandingofAPRs,butinstitutionallendersandborrowersdoInstitutionsarethereforeabletoextractafewbasispointsfromconsumers,butwhybother?36Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTheFrequencyofCompoundingFinancialintermediariesprofitfromdifferencesinthelendingandborrowingrates.Overheads,badloansandcompetitionresultsinanarrowmargin.SmallrategainsthereforeresultinalargeincreasesininstitutionalprofitsInthelongterm,ill-informedconsumerslosebecauseofcompounding37Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall4.5MultipleCashFlowsTimeLinesFutureValueofaStreamofCashFlowPresentValueofaStreamofCashFlowsInvestingwithMultipleCashFlows38Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTimeLine39Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallPresentValueofMultipleCashFlows40Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall4.6AnnuitiesFinancialanalystsuseseveralannuitieswithdifferingassumptionsaboutthefirstpayment.Wewillexaminejusttwo:regularannuitywithitsfirstcoupononeperiodfromnow,(detaillook)annuityduewithitsfirstcoupontoday,(cursorylook)41Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallCashFlowDiagramofAnnuities42Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallRationaleforAnnuityFormulaasequenceofequallyspacedidenticalcashflowsisacommonoccurrence,soautomationpaysoffatypicalannuityisamortgagewhichmayhave360monthlypayments,alotofworkforusingelementarymethods43Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallAssumptionsRegularAnnuitythefirstcashflowwilloccurexactlyoneperiodformnowallsubsequentcashflowsareseparatedbyexactlyoneperiodallperiodsareofequallengththetermstructureofinterestisflatallcashflowshavethesame(nominal)valuethepresentvalueofasumofpresentvaluesisthesumofthepresentvalues44Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallAnnuityFormulaNotationPV=thepresentvalueoftheannuityi=interestratetobeearnedoverthelifeoftheannuityn=thenumberofpaymentspmt=theperiodicpayment45Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallDerivationofPVofAnnuityFormula:Algebra.1of546Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallDerivationofPVofAnnuityFormula:Algebra.2of547Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallDerivationofPVofAnnuityFormula:Algebra.3of548Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallDerivationofPVofAnnuityFormula:Algebra.4of549Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallDerivationofPVofAnnuityFormula:Algebra.5of550Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallPVofAnnuityFormula51Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallPVAnnuityFormula:Payment52Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallPVAnnuityFormula:NumberofPayments53Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallPVAnnuityFormula:ReturnThereisnotranscendentalsolutiontothePVofanannuityequationintermsoftheinterestrate.StudentsinterestedinthereasonwhyarereferredtoGaloisTheory,2nd.EdI.Stewart.Studentswithastrongersenseoffashionare“seen”carryingMichioKuga’spoison-ivy-green-coloredbook“GaloisDream.”54Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallAnnuityFormula:PVAnnuityDue55Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallDerivationofFVofAnnuityFormula:Algebra56Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallFVAnnuityFormula:Payment57Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallFVAnnuityFormula:NumberofPayments58Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallFVAnnuityFormula:ReturnThereisnotranscendentalsolutionNumericalmethodshavetobeemployed59Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall4.7PerpetualAnnuitiesRecalltheannuityformula:Letn->infinitywithi>0:60Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallGrowingAnnuitiesGrowingannuitiessolvethesuper-normalgrowthproblemTheyareoftenmoreappropriateinday-to-daysituationsthanannuities61Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall4.8LoanAmortization:Mortgageearlyrepaymentpermittedatanytimeduringmortgage’s360monthlypaymentsmarketinterestratesmayfluctuate,buttheloan’srateisaconstant1/2%permonththemortgagerequires10%equityand“threepoints”assumea$500,000houseprice62Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallMortgage:ThepaymentWewillexaminethisproblemusingafinancialcalculatorThefirstquantitytodetermineistheamountoftheloanandthepoints63Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallCalculatorSolutionThisisthemonthlyrepayment64Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallMortgage:EarlyRepaymentAssumethatthefamilyplanstosellthehouseafterexactly60payments,whatwillbetheoutstandingprinciple?65Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallMortgageRepayment:IssuesTheoutstandingprincipleisthepresentvalue(atrepaymentdate)oftheremainingpaymentsonthemortgageThereareinthiscase360-60=300remainingpayments,startingwiththeone1-monthfromnow66Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallCalculatorSolutionOutstanding@60Months67Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallSummaryofPaymentsThefamilyhasmade60payments=$2687.98*12*5=$161,878.64Theirmortgagerepayment= 450,000-418,744.61=$31,255.39Interest=payments-principlereduction=161,878.64-31,255.39=$130,623.2568Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallAvoidAddingCashFlowsFromDifferentPeriodsIntheaboveslide,webrokeoneofthecardinalrulesoffinance:Webundledthecashflowsfor5-yearsbyaddingthemtogetherThiskindofanalysiscanleadtoinappropriatefinancialdecisions,suchasearlyrepaymentofamortgage69Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallAResultofBreakingtheRuleGiventhetaxadvantagesofamortgage,andthefactitcollateralized,theirinterestratesarequitelowSomefinancialpunditsrecommendadding(say10%)tomonthlypaymentstoreducethemortgagelifeby5-to10-yearsAtyourage,investingthatextra10%inamutualfundmaybemoreappropriate70Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallAResultofBreakingtheRuleThepunditsmaketheirargumentbyadding(withoutdiscounting!)thedifferenceinthecashflowsbetweenthescenarios.Thisistypicallyahugesumofmoney,andthisiswhatis“saved”Whendiscountedappropriately,therearenosignificantsavings.Therearehugeopportunitylossesforthosewillingtoaccepttheriskofastockmutualfund71Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallOutstandingBalanceasaFunctionofTimeThefollowinggraphsillustratethatintheearlyyears,monthlypaymentaremostlyinterest.Inlatteryears,thepaymentsaremostlyprincipleRecallthatonlytheinterestportionistax-deductible,sothetaxshelterdecays72Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall73Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall74Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall75Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall76Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall4.9ExchangeRatesandTimeValueofMoney

Youareconsideringthechoice:Investing$10,000indollar-denominatedbondsoffering10%/yearInvesting$10,000inyen-denominatedbondsoffering3%/yearAssumeanexchangerateof0.0177Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall$10,000$11,000￥1,000,000￥1,030,000￥Time10%$/$(direct)0.01$/￥3%￥/￥?$/￥U.S.A.Japan78Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallExchangeRateDiagramReviewofthediagramindicatesthatyouwillendtheyearwitheither$11,000or￥1,030,000Ifthe$priceoftheyenrisesby8%/yearthentheyear-endexchangeratewillbe$0.0108/￥79Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall$10,000$11,124$11,000￥1,000,000￥1,030,000￥Time10%$/$(direct)0.01$/￥3%￥/￥0.0108$/￥U.S.A.Japan80Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallInterpretationandAnotherScenarioInthecaseofthe$priceof￥risingby8%yougain$124onyourinvestmentNow,ifthe$priceof￥risesby6%,theexchangerateinoneyearwillbe$0.010681Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall$10,000$10,918￥$11,000￥1,000,000￥1,030,000￥Time10%$/$(direct)0.01$/￥3%￥/￥0.0106$/￥U.S.A.Japan82Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallInterpretationInthiscase,youwilllose$82byinvestingintheJapanesebondIfyoudivideproceedsoftheUSinvestmentbythoseoftheJapaneseinvestment,youobtaintheexchangerateatwhichyouareindifferent$11,000/￥1,030,000=0.1068$/￥83Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall$10,000$11,000￥$11,000￥1,000,000￥1,030,000￥Time10%$/$(direct)0.01$/￥3%￥/￥0.01068$/￥U.S.A.Japan84Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallConclusionIftheyenpriceactuallyrisesbymorethan6.8%duringthecomingyearthentheyenbondisabetterinvestment85Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallFinancialDecisioninanInternationalContextInternationalcurrencyinvestorsborrowandlendinTheirowncurrencyThecurrencyofcountrieswithwhichtheydobusinessbutwishtohedgeCurrenciesthatappeartoofferabetterdealExchangeratefluctuationscanresultinunexpectedgainsandlosses86Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallComputingNPVinDifferentCurrenciesInanytime-value-of-moneycalculation,thecashflowsandinterestratesmustbedenominatedinthesamecurrencyUSAprojectUrequiresaninvestmentof$10,000,asdoesaJapaneseprojectJ.Ugenerates$6,000/yearfor5years,andprojectJgenerates￥575,000/yearfor5yearsTheUSinterestis6%,theJapaneseinterestis4%,andthecurrentexchangerateis0.0187Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallSolutionUsingyourfinancialcalculatorDeterminethepresentvalueofUin$bydiscountingthe5paymentsat6%,andsubtracttheinitialinvestmentof$10,000DeterminethepresentvalueofJin￥bydiscountingthe5paymentsat4%,andsubtracttheinitialinvestmentof￥1,000,000Obtain$15,274&￥1,5599,798respectively88Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallSolutionConvertthe￥1,5599,798to$usingthecurrentexchangeratetoobtain$15,600TheJapaneseNPVof￥of$15,600ishigherthantheUSANPVor$15,274,soinvestintheJapaneseproject89Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall4.10InflationandDiscountedCashFlowAnalysisWewillusethenotationIntherateofinterestinnominaltermsIrtherateofinterestinrealtermsRtherateofinflationFromchapter2wehavetherelationship90Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallIllustrationWhatistherealrateofinterestifthenominalrateis8%andinflationis5%?TherealrateorreturndeterminesthespendingpowerofyoursavingsThenominalvalueofyourwealthisonlyasimportantasitspurchasingpower91Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallInvestinginInflation-protectedCD’sYouhavedecidedtoinvest$10,000forthenext12-months.YouareofferedtwochoicesAnominalCDpayinga8%returnArealCDpaying3%+inflationrateIfyouanticipatetheinflationbeingBelow5%investinthenominalsecurityAbove5%investintherealsecurityEqualto5%investineither92Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallWhyDebtorsGainFromUnanticipatedInflation

Youborrow$10,000at8%interest.Thetoday’sspendingpoweroftherepaymentis$10,000*1.08/(1+inflation)Iftheactualinflationistheexpected6%,thentherealcostoftheloanintoday’smoneyis$10,188.68Iftheactualinflationis10%,thentheloan’srealcost(intoday’svalues)is$9,818.18Unexpectedinflationbenefitsborrower93Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallInflationandPresentValue

AcommonplanningsituationisdetermininghowlongittakestosaveforsomethingTheproblemisthatthethingbeingsavedforincreasesin(nominal)priceduetoinflationUsingarealapproachsolvesthisissue94Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallInflationandPresentValue

IllustrationAssumethataboatcosts$20,000todayGeneralinflationisexpectedtobe3%Attoday’svalues,youcansaveataninflationadjustedrateof$3,000/year,makingthefirstdeposit1-yearhenceYouareabletoearn12%loansatHonestJoe’sPawnEmporium

?Whenistheboatyours?95Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallBoatIllustrationContinuedSolutionTheboatisalreadyatnominalvalueToconvertthenominalratetotherealrateIreal=(Inominal-inflation)/(1+inflation)=(0.12-0.03)/1.03=8.7378641%UsingyourcalculatorN->?;I->8.7378641;PV->0;PMT->3000;FV->20000“=/-”;Result:n=5.48years,(6yearsw/change)96Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallBoatIllustrationContinuedConclusionGivenboatermakesdepositsattheendofeachyear,theboatwillnotbehersforsixyearsLookattheproblemfromanominalvantage:97Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallBoatIllustration(Nominal)98Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallInflationandSavingsPlansWehaveseenhowtocomputethenumberofyearsittakestosaveforsomethingusingbothrealandnominalmethodsAnotherimportantquestionisHowmuchmustIsaveeachyearinordertoachieveasavingsgoal?Wewillreusetheboatproblem,butwiththeassumptionthattheboateriswillingtowait8-years,butwishestominimizeannual(inflationadjusted)payments99Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall4.11TaxesandInvestmentDecisionsRule:Investsoastomaximizeyourafter-taxrateofreturnThisisnotatallthesamethingas Minimizethetaxyoupay(False)100Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallInvestinginTax-ExemptBondsIntheUSA,municipalbondsareexemptfromincometaxesUnderwhatcircumstanceswouldyoubeindifferenttoinvestinginanidenticalbondthatpaystaxifyourmarginalrateoftaxis(say)20%?101Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallAdditionalSolvedProblemsLumpSumFutureValue102Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallTheProblemYou'vereceiveda$40,000legalsettlement.Yourgreat-unclerecommendsinvestingitforretirementin27-yearsby“rollingover”one-yearcertificatesofdeposit(CDs)Yourlocalbankhas3%1-yearCDsHowmuchwillyourinvestmentbeworth?Comment.103Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallCategorizationYourcapitalgainswillbereinvested.Thereisnocash-flowfromthesettlementfor27years,sothisisalumpsumproblem.Thereissomeuncertaintyinthecashflowsbecauseinterestratearestaticforjustthefirstyear,butweassumethatitwillbe3%untilyouretireIfyouareunabletoshelteryourearnings,theIRSwillwanttheircut104Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallDataExtractionPV=$40,000i=3%(or3%*(1-marginaltaxrate)?)n=27-yearsFV=?105Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallSolutionbyEquation106Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallCalculatorSolution107Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHallCommentsYourgreatuncle'safinancialidiotGivena27-yearinvestment,youshouldeitherInvestthemoneymoreaggressivelytoaccumulatethemoneyyouneedtosurvive,orLive!Blowthemoneyonthatredconvertible!108Copyright?2009PearsonEducation,Inc.

PublishingasPrenticeHall3AdditionalSolvedProblemsLumpSumInterest