Chapter8:

ValuationofKnown CashFlows:BondsCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall1ObjectiveValuationoffixedincomesecuritiesExplainwhybondpriceschangeChapter8Contents8.1UsingPresentValueFormulastoValueKnownFlows8.2TheBasicBuildingBlocks:PureDiscountBonds8.3CouponBonds,CurrentYield,andYield-to-Maturity8.4ReadingBondListings8.5WhyYieldsforthesameMaturityDiffer8.6TheBehaviorofBondPricesOverTimeCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall28.1UsingPresentValueFormulastoValueKnownFlowsYouhavebeenofferedtheopportunitytopurchaseamortgage.Theremaininglifeofthemortgageis60months,withpaymentof$400.Yourrequiredrateofreturnis1.5%/month.Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall3CalculationUsingthepresentvalueofanannuityformuladiscussedinchapter4,youwillpaynomorethanCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall4FinancialCalculatorAlternatively,usingyourfinancialcalculator(remembertosetthecorrectdefaults)youobtainCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall5ChangeinRequiredRateIfyourrequiredrateofreturnincreasedto1.6%/monthCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall6UsingPresentValueFormulastoValueKnownFlowsAnincreaseintherequiredrateofreturnalwaysleadstoadecreaseinthevalueofafixedincomesecurityTheproofisveryeasyCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall7BondPricesRiseastheInterestRatesFallWritethePVofthefixedincomesecurityasthesumtermsCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall8BondPricesRiseastheInterestRatesFallIfigoesup,1+igoesup,1/(1+i)goesdownfori>-1,(1/(1+i))jgoesdownfori>0.Soifthepaymentsarepositive,thenthesummustalsogodownSimilarly,idown->PVupCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall9BondPricesRiseastheInterestRatesFallBasicprincipleinevaluatingknownflowsAchangeinmarketinterestratescausesachangeintheoppositedirectioninthemarketvaluesofallexistingcontractspromisingfixedpaymentsinthefutureCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall10NoteVolatilemarketratesimplyvolatilemarketvaluesCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall11YieldCurveAtypicalyieldcurve:Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall12Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall138.2TheBasicsBuildingBlocks:PureDiscountBondsWecanalwaysanalyzeanyfixedincomecontractintoasumofpurediscountbondsApurediscountbondisasecuritythatpromisestopayaspecifiedsinglecashpayment(facevalueorparvalue)ataspecifieddatecalleditsmaturitydateCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14PureDiscountBondsNoteThereisnocashflowassociatedwithinterestPurediscountbondsarepurchasedatadiscountfromtheirfaceorparvalueCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall15UsingPureDiscountBondstoValueotherBondsValueabondthatpaysits$100couponattheendofeachyearfor3-years,anditsparvalueof$1,000in3-yearsYouhavediscoveredthreepurediscountbonds(eachwitha$1,000parvalue)thatmaturein1,2,and3years,andthataretradingat$960,$890,and$810respectivelyCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall16FirstSolutionMethodCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall17SecondSolutionMethodCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall18ConclusionThefirstmethodusesthefactthatacouponbondisthesumofpurediscountbondsitisfastanddirectThesecondmethodfirstdeterminestheyields-to-maturityofeachdiscountbondcashflowsarethenevaluatedusingthemCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall198.3CouponBonds,CurrentYield,andYieldtoMaturityAcouponbondobligatestheissuertomakeperiodicpaymentsofinterest(calledcouponpayments)tothebondholderuntilthebondmaturesatwhichtimethefacevalueofthebondisalsopaidtothebondholderandthecontractissatisfiedCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall20CouponRateThecouponrateistheinterestrateappliedtothefacevaluetocomputethecouponpaymentAbondwithafacevalueof$1,000andacouponrateof10%paysanannualcouponof$100Atmaturity,thepaymentis$1,000+$100Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall21CashFlowsfor10%$1,000CouponBondCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall22Par,premium,andDiscountBondsAcouponbondwithitscurrentpriceequaltoitsparvalueisaparbondIfitistradingbelowparitisadiscountbondIfitistradingaboveparitisapremiumbond

(nottobeconfusedwiththeU.K.lotterybondofthesamename!)Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall238.4ReadingBondListings

TherearetraditionsforreportingyieldsandcomputingearnedinterestthatneedtobeunderstoodbeforetradingCouponbondsareoftenquotedintermsoftheannualratecompoundedsemi-annuallyT-billsareoftenquotedonadiscountbasise.g.,a1yearT-billhas364daysoutstanding,butayearhasonly360days…(itgetsnasty)Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall24ReadingBondListings

TakecarethatthefractionalpartofanumberisunderstoodIsit16ths,32nds,64ths,100thsorsomeotherconvention?Askprice:dealer’ssellingpriceBidprice:dealer’sbuyingpriceCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall258.5WhyYieldsforthesameMaturityDiffer

Thefundamentalbuildingblockofbondsisthepurediscountbond:CouponbondsmaybeviewedasaportfolioofdiscountbondsTheruleofonepriceappliestobondsthroughpurediscountbondsItisamistaketoassumethatcouponbondswiththesamelifehavethesameyield--theircouponratesdiffer,leadingtoadifferent%mixofdiscountbondsCopyright?2009PearsonEducation,Inc.PublishingasPr