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InterestRatesandBondValuation Chapter8 Copyright 2010bytheMcGraw HillCompanies Inc Allrightsreserved McGraw Hill Irwin KeyConceptsandSkills KnowtheimportantbondfeaturesandbondtypesUnderstandbondvaluesandwhytheyfluctuateUnderstandbondratingsandwhattheymeanUnderstandtheimpactofinflationoninterestratesUnderstandthetermstructureofinterestratesandthedeterminantsofbondyields ChapterOutline 8 1BondsandBondValuation8 2GovernmentandCorporateBonds8 3BondMarkets8 4InflationandInterestRates8 5DeterminantsofBondYields 8 1BondsandBondValuation Abondisalegallybindingagreementbetweenaborrowerandalenderthatspecifiesthe Par face valueCouponrateCouponpaymentMaturityDateTheyieldtomaturityistherequiredmarketinterestrateonthebond BondValuation PrimaryPrinciple Valueoffinancialsecurities PVofexpectedfuturecashflowsBondvalueis therefore determinedbythepresentvalueofthecouponpaymentsandparvalue Interestratesareinverselyrelatedtopresent i e bond values TheBond PricingEquation BondExample ConsideraU S governmentbondwithas63 8 couponthatexpiresinDecember2013 TheParValueofthebondis 1 000 Couponpaymentsaremadesemiannually June30andDecember31forthisparticularbond Sincethecouponrateis63 8 thepaymentis 31 875 OnJanuary1 2009thesizeandtimingofcashflowsare BondExample OnJanuary1 2009 therequiredyieldis5 Thecurrentvalueis BondExample Calculator PMT I Y FV PV N PV 31 875 2 5 1 000 1 060 17 10 Findthepresentvalue asofJanuary1 2009 ofa63 8 couponbondwithsemi annualpayments andamaturitydateofDecember2013iftheYTMis5 BondExample Nowassumethattherequiredyieldis11 Howdoesthischangethebond sprice YTMandBondValue 800 1000 1100 1200 1300 0 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 0 1 DiscountRate BondValue WhentheYTM coupon thebondtradesatapremium WhentheYTM coupon thebondtradesatpar WhentheYTM coupon thebondtradesatadiscount BondConcepts Bondpricesandmarketinterestratesmoveinoppositedirections Whencouponrate YTM price parvalueWhencouponrate YTM price parvalue premiumbond Whencouponrate YTM price parvalue discountbond InterestRateRisk PriceRiskChangeinpriceduetochangesininterestratesLong termbondshavemorepriceriskthanshort termbondsLowcouponratebondshavemorepriceriskthanhighcouponratebonds ReinvestmentRateRiskUncertaintyconcerningratesatwhichcashflowscanbereinvestedShort termbondshavemorereinvestmentrateriskthanlong termbonds Highcouponratebondshavemorereinvestmentrateriskthanlowcouponratebonds MaturityandBondPriceVolatility Considertwootherwiseidenticalbonds Thelong maturitybondwillhavemuchmorevolatilitywithrespecttochangesinthediscountrate CouponRatesandBondPrices Considertwootherwiseidenticalbonds Thelow couponbondwillhavemuchmorevolatilitywithrespecttochangesinthediscountrate HighCouponBond LowCouponBond ComputingYieldtoMaturity Yieldtomaturityistherateimpliedbythecurrentbondprice FindingtheYTMrequirestrialanderrorifyoudonothaveafinancialcalculatorandissimilartotheprocessforfindingrwithanannuity Ifyouhaveafinancialcalculator enterN PV PMT andFV rememberingthesignconvention PMTandFVneedtohavethesamesign PVtheoppositesign YTMwithAnnualCoupons Considerabondwitha10 annualcouponrate 15yearstomaturity andaparvalueof 1 000 Thecurrentpriceis 928 09 Willtheyieldbemoreorlessthan10 N 15 PV 928 09 FV 1 000 PMT 100CPTI Y 11 YTMwithSemiannualCoupons Supposeabondwitha10 couponrateandsemiannualcouponshasafacevalueof 1 000 20yearstomaturity andissellingfor 1 197 93 IstheYTMmoreorlessthan10 Whatisthesemi annualcouponpayment Howmanyperiodsarethere N 40 PV 1 197 93 PMT 50 FV 1 000 CPTI Y 4 IsthistheYTM YTM 4 2 8 CurrentYieldvs YieldtoMaturity CurrentYield annualcoupon priceYieldtomaturity currentyield capitalgainsyieldExample 10 couponbond withsemi annualcoupons facevalueof1 000 20yearstomaturity 1 197 93priceCurrentyield 100 1197 93 0835 8 35 Priceinoneyear assumingnochangeinYTM 1 193 68Capitalgainyield 1193 68 1197 93 1197 93 0035 35 YTM 8 35 35 8 whichisthesameYTMcomputedearlier BondPricingTheorems Bondsofsimilarrisk andmaturity willbepricedtoyieldaboutthesamereturn regardlessofthecouponrate Ifyouknowthepriceofonebond youcanestimateitsYTMandusethattofindthepriceofthesecondbond Thisisausefulconceptthatcanbetransferredtovaluingassetsotherthanbonds ZeroCouponBonds Makenoperiodicinterestpayments couponrate 0 TheentireyieldtomaturitycomesfromthedifferencebetweenthepurchasepriceandtheparvalueCannotsellformorethanparvalueSometimescalledzeroes deepdiscountbonds ororiginalissuediscountbonds OIDs TreasuryBillsandprincipal onlyTreasurystripsaregoodexamplesofzeroes PureDiscountBonds Informationneededforvaluingpurediscountbonds Timetomaturity T Maturitydate today sdateFacevalue F Discountrate r Presentvalueofapurediscountbondattime0 PureDiscountBonds Example Findthevalueofa15 yearzero couponbondwitha 1 000parvalueandaYTMof12 BondPricingwithaSpreadsheet Therearespecificformulasforfindingbondpricesandyieldsonaspreadsheet PRICE Settlement Maturity Rate Yld Redemption Frequency Basis YIELD Settlement Maturity Rate Pr Redemption Frequency Basis SettlementandmaturityneedtobeactualdatesTheredemptionandPrneedtogivenas ofparvalueClickontheExceliconforanexample 8 2GovernmentandCorporateBonds TreasurySecuritiesFederalgovernmentdebtT bills purediscountbondswithoriginalmaturitylessthanoneyearT notes coupondebtwithoriginalmaturitybetweenoneandtenyearsT bonds coupondebtwithoriginalmaturitygreaterthantenyearsMunicipalSecuritiesDebtofstateandlocalgovernmentsVaryingdegreesofdefaultrisk ratedsimilartocorporatedebtInterestreceivedistax exemptatthefederallevel After taxYields Ataxablebondhasayieldof8 andamunicipalbondhasayieldof6 Ifyouareina40 taxbracket whichbonddoyouprefer 8 1 4 4 8 Theafter taxreturnonthecorporatebondis4 8 comparedtoa6 returnonthemunicipalAtwhattaxratewouldyoubeindifferentbetweenthetwobonds 8 1 T 6 T 25 CorporateBonds GreaterdefaultriskrelativetogovernmentbondsThepromisedyield YTM maybehigherthantheexpectedreturnduetothisaddeddefaultrisk BondRatings InvestmentQuality HighGradeMoody sAaaandS PAAA capacitytopayisextremelystrongMoody sAaandS PAA capacitytopayisverystrongMediumGradeMoody sAandS PA capacitytopayisstrong butmoresusceptibletochangesincircumstancesMoody sBaaandS PBBB capacitytopayisadequate adverseconditionswillhavemoreimpactonthefirm sabilitytopay BondRatings Speculative LowGradeMoody sBaandBS PBBandBConsideredspeculativewithrespecttocapacitytopay VeryLowGradeMoody sCS PC DHighlyuncertainrepaymentand inmanycases alreadyindefault withprincipalandinterestinarrears 8 3BondMarkets Primarilyover the countertransactionswithdealersconnectedelectronicallyExtremelylargenumberofbondissues butgenerallylowdailyvolumeinsingleissuesMakesgettingup to datepricesdifficult particularlyonasmallcompanyormunicipalissuesTreasurysecuritiesareanexception TreasuryQuotations 8Nov25132 23132 24 125 14Whatisthecouponrateonthebond Whendoesthebondmature Whatisthebidprice Whatdoesthismean Whatistheaskprice Whatdoesthismean Howmuchdidthepricechangefromthepreviousday Whatistheyieldbasedontheaskprice CleanversusDirtyPrices Cleanprice quotedpriceDirtyprice priceactuallypaid quotedpriceplusaccruedinterestExample ConsiderT bondinpreviousslide assumetodayisJuly15 2009Numberofdayssincelastcoupon 61Numberofdaysinthecouponperiod 184Accruedinterest 61 184 04 1 000 13 26Prices basedonask Cleanprice 1 327 50Dirtyprice 1 327 50 13 26 1 340 76So youwouldactuallypay 1 340 76forthebond 8 4InflationandInterestRates Realrateofinterest changeinpurchasingpowerNominalrateofinterest quotedrateofinterest changeinpurchasingpowerandinflationTheexantenominalrateofinterestincludesourdesiredrealrateofreturnplusanadjustmentforexpectedinflation RealversusNominalRates 1 R 1 r 1 h whereR nominalrater realrateh expectedinflationrateApproximationR r h Inflation LinkedBonds MostgovernmentbondsfaceinflationriskTIPS TreasuryInflation ProtectedSecurities however eliminatethisriskbyprovidingpromisedpaymentsspecifiedinreal ratherthannominal terms TheFisherEffect Example Ifwerequirea10 realreturnandweexpectinflationtobe8 whatisthenominalrate R 1 1 1 08 1 188 18 8 Approximation R 10 8 18 Becausetherealreturnandexpectedinflationarerelativelyhigh thereisasignificantdifferencebetweentheactualFisherEffectandtheapproximation 8 5DeterminantsofBondYields Termstr

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