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InterestRatesandBondValuationChapter8Copyright?2010bytheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinInterestRatesandBondValuat0KeyConceptsandSkillsKnowtheimportantbondfeaturesandbondtypesUnderstandbondvaluesandwhytheyfluctuateUnderstandbondratingsandwhattheymeanUnderstandtheimpactofinflationoninterestratesUnderstandthetermstructureofinterestratesandthedeterminantsofbondyieldsKeyConceptsandSkillsKnowth1ChapterOutline8.1 BondsandBondValuation8.2 GovernmentandCorporateBonds8.3 BondMarkets8.4 InflationandInterestRates8.5 DeterminantsofBondYieldsChapterOutline8.1 Bondsand28.1BondsandBondValuationAbondisalegallybindingagreementbetweenaborrowerandalenderthatspecifiesthe:Par(face)valueCouponrateCouponpaymentMaturityDateTheyieldtomaturityistherequiredmarketinterestrateonthebond.8.1BondsandBondValuationA3BondValuationPrimaryPrinciple:Valueoffinancialsecurities=PVofexpectedfuturecashflowsBondvalueis,therefore,determinedbythepresentvalueofthecouponpaymentsandparvalue.Interestratesareinverselyrelatedtopresent(i.e.,bond)values.BondValuationPrimaryPrincip4TheBond-PricingEquationTheBond-PricingEquation5BondExampleConsideraU.S.governmentbondwithas63/8%couponthatexpiresinDecember2013.TheParValueofthebondis$1,000.Couponpaymentsaremadesemiannually(June30andDecember31forthisparticularbond).Sincethecouponrateis63/8%,thepaymentis$31.875.OnJanuary1,2009thesizeandtimingofcashflowsare:BondExampleConsideraU.S.go6BondExampleOnJanuary1,2009,therequiredyieldis5%.Thecurrentvalueis:BondExampleOnJanuary1,20097BondExample:CalculatorPMTI/YFVPVNPV31.875=2.51,000–

1,060.17101,000×0.063752Findthepresentvalue(asofJanuary1,2009),ofa63/8%couponbondwithsemi-annualpayments,andamaturitydateofDecember2013iftheYTMis5%.BondExample:CalculatorPMTI/Y8BondExampleNowassumethattherequiredyieldis11%.Howdoesthischangethebond’sprice?BondExampleNowassumethatth9YTMandBondValue800100011001200130000.010.020.030.040.050.060.070.080.090.1DiscountRateBondValue63/8WhentheYTM<coupon,thebondtradesatapremium.WhentheYTM=coupon,thebondtradesatpar.WhentheYTM>coupon,thebondtradesatadiscount.YTMandBondValue80010001100110BondConceptsBondpricesandmarketinterestratesmoveinoppositedirections.Whencouponrate=YTM,price=parvalueWhencouponrate>YTM,price>parvalue(premiumbond)Whencouponrate<YTM,price<parvalue(discountbond)BondConceptsBondpricesandm11InterestRateRiskPriceRiskChangeinpriceduetochangesininterestratesLong-termbondshavemorepriceriskthanshort-termbondsLowcouponratebondshavemorepriceriskthanhighcouponratebonds.ReinvestmentRateRiskUncertaintyconcerningratesatwhichcashflowscanbereinvestedShort-termbondshavemorereinvestmentrateriskthanlong-termbonds.Highcouponratebondshavemorereinvestmentrateriskthanlowcouponratebonds.InterestRateRiskPriceRisk12MaturityandBondPriceVolatilityCConsidertwootherwiseidenticalbonds.Thelong-maturitybondwillhavemuchmorevolatilitywithrespecttochangesinthediscountrate.DiscountRateBondValueParShortMaturityBondLongMaturityBondMaturityandBondPriceVolati13CouponRatesandBondPricesConsidertwootherwiseidenticalbonds.Thelow-couponbondwillhavemuchmorevolatilitywithrespecttochangesinthediscountrate.DiscountRateBondValueHighCouponBondLowCouponBondParCCouponRatesandBondPricesCo14ComputingYieldtoMaturityYieldtomaturityistherateimpliedbythecurrentbondprice.FindingtheYTMrequirestrialanderrorifyoudonothaveafinancialcalculatorandissimilartotheprocessforfindingrwithanannuity.Ifyouhaveafinancialcalculator,enterN,PV,PMT,andFV,rememberingthesignconvention(PMTandFVneedtohavethesamesign,PVtheoppositesign).ComputingYieldtoMaturityYie15YTMwithAnnualCouponsConsiderabondwitha10%annualcouponrate,15yearstomaturity,andaparvalueof$1,000.Thecurrentpriceis$928.09.Willtheyieldbemoreorlessthan10%?N=15;PV=-928.09;FV=1,000;PMT=100CPTI/Y=11%YTMwithAnnualCouponsConside16YTMwithSemiannualCouponsSupposeabondwitha10%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%YTMwithSemiannualCouponsSup17CurrentYieldvs.YieldtoMaturityCurrentYield=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%,whichisthesameYTMcomputedearlierCurrentYieldvs.YieldtoMat18BondPricingTheoremsBondsofsimilarrisk(andmaturity)willbepricedtoyieldaboutthesamereturn,regardlessofthecouponrate.Ifyouknowthepriceofonebond,youcanestimateitsYTMandusethattofindthepriceofthesecondbond.Thisisausefulconceptthatcanbetransferredtovaluingassetsotherthanbonds.BondPricingTheoremsBondsof19ZeroCouponBondsMakenoperiodicinterestpayments(couponrate=0%)TheentireyieldtomaturitycomesfromthedifferencebetweenthepurchasepriceandtheparvalueCannotsellformorethanparvalueSometimescalledzeroes,deepdiscountbonds,ororiginalissuediscountbonds(OIDs)TreasuryBillsandprincipal-onlyTreasurystripsaregoodexamplesofzeroesZeroCouponBondsMakenoperio20PureDiscountBondsInformationneededforvaluingpurediscountbonds:Timetomaturity(T)=Maturitydate-today’sdateFacevalue(F)Discountrate(r)Presentvalueofapurediscountbondattime0:PureDiscountBondsInformation21PureDiscountBonds:ExampleFindthevalueofa15-yearzero-couponbondwitha$1,000parvalueandaYTMof12%.PureDiscountBonds:ExampleFi22BondPricingwithaSpreadsheetTherearespecificformulasforfindingbondpricesandyieldsonaspreadsheet.PRICE(Settlement,Maturity,Rate,Yld,Redemption,Frequency,Basis)YIELD(Settlement,Maturity,Rate,Pr,Redemption,Frequency,Basis)SettlementandmaturityneedtobeactualdatesTheredemptionandPrneedtogivenas%ofparvalueClickontheExceliconforanexample.BondPricingwithaSpreadshee238.2GovernmentandCorporateBondsTreasurySecuritiesFederalgovernmentdebtT-bills–purediscountbondswithoriginalmaturitylessthanoneyearT-notes–coupondebtwithoriginalmaturitybetweenoneandtenyearsT-bonds–coupondebtwithoriginalmaturitygreaterthantenyearsMunicipalSecuritiesDebtofstateandlocalgovernmentsVaryingdegreesofdefaultrisk,ratedsimilartocorporatedebtInterestreceivedistax-exemptatthefederallevel8.2GovernmentandCorporateB24After-taxYieldsAtaxablebondhasayieldof8%,andamunicipalbondhasayieldof6%.Ifyouareina40%taxbracket,whichbonddoyouprefer?8%(1-.4)=4.8%Theafter-taxreturnonthecorporatebondis4.8%,comparedtoa6%returnonthemunicipalAtwhattaxratewouldyoubeindifferentbetweenthetwobonds?8%(1–T)=6%T=25%After-taxYieldsAtaxablebond25CorporateBondsGreaterdefaultriskrelativetogovernmentbondsThepromisedyield(YTM)maybehigherthantheexpectedreturnduetothisaddeddefaultriskCorporateBondsGreaterdefault26BondRatings–InvestmentQualityHighGradeMoody’sAaaandS&PAAA–capacitytopayisextremelystrongMoody’sAaandS&PAA–capacitytopayisverystrongMediumGradeMoody’sAandS&PA–capacitytopayisstrong,butmoresusceptibletochangesincircumstancesMoody’sBaaandS&PBBB–capacitytopayisadequate,adverseconditionswillhavemoreimpactonthefirm’sabilitytopayBondRatings–InvestmentQual27BondRatings-SpeculativeLowGradeMoody’sBaandBS&PBBandBConsideredspeculativewithrespecttocapacitytopay.VeryLowGradeMoody’sCS&PC&DHighlyuncertainrepaymentand,inmanycases,alreadyindefault,withprincipalandinterestinarrears.BondRatings-SpeculativeLow288.3BondMarketsPrimarilyover-the-countertransactionswithdealersconnectedelectronicallyExtremelylargenumberofbondissues,butgenerallylowdailyvolumeinsingleissuesMakesgettingup-to-datepricesdifficult,particularlyonasmallcompanyormunicipalissuesTreasurysecuritiesareanexception8.3BondMarketsPrimarilyover29TreasuryQuotations8Nov25 132:23 132:24 -12 5.14Whatisthecouponrateonthebond?Whendoesthebondmature?Whatisthebidprice?Whatdoesthismean?Whatistheaskprice?Whatdoesthismean?Howmuchdidthepricechangefromthepreviousday?Whatistheyieldbasedontheaskprice?TreasuryQuotations8Nov25 30CleanversusDirtyPricesCleanprice: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.CleanversusDirtyPricesClean318.4InflationandInterestRatesRealrateofinterest–changeinpurchasingpowerNominalrateofinterest–quotedrateofinterest,changeinpurchasingpowerandinflationTheexantenominalrateofinterestincludesourdesiredrealrateofreturnplusanadjustmentforexpectedinflation.8.4InflationandInterestRat32RealversusNominalRates(1+R)=(1+r)(1+h),whereR=nominalrater=realrateh=expectedinflationrateApproximationR=r+hRealversusNominalRates(1+33Inflation-LinkedBondsMostgovernmentbondsfaceinflationriskTIPS(TreasuryInflation-ProtectedSecurities),however,eliminatethisriskbyprovidingpromisedpaymentsspecifiedinreal,ratherthannominal,termsInflation-LinkedBondsMostgov34TheFisherEffect:ExampleIfwerequirea10%realreturnandweexpectinflationtobe8%,whatisthenominalrate?R=(1.1)(1.08)–1=.188=18.8%Approximation:R=10%+8%=18%Becausetherealreturnandexpectedinflationarerelativelyhigh,thereisasignificantdifferencebetweentheactualFisherEffectandtheapproximation.TheFisherEffect:ExampleIfw358.5DeterminantsofBondYieldsTermstructureistherelationshipbetweentimetomaturityandyields,allelseequal.Itisimportanttorecognizethatwepullouttheeffectofdefaultrisk,differentcoupons,etc.Yieldcurve–graphicalrepresentationofthetermstructureNormal–upward-sloping,long-termyieldsarehigherthanshort-termyieldsInverted–downward-sloping,long-termyieldsarelowerthanshort-termyields8.5DeterminantsofBondYield36FactorsAffectingRequiredReturnDefaultriskpremium–rememberbondratingsTaxabilitypremium–remembermunicipalversustaxableLiquiditypremium–bondsthathavemorefrequenttradingwillgenerallyhavelowerrequiredreturns(rememberbid-askspreads)Anythingelsethataffectstheriskofthecashflowstothebondholderswillaffecttherequiredreturns.FactorsAffectingRequiredRet37QuickQuizHowdoyoufindthevalueofabond,andwhydobondpriceschange?Whatarebondratings,andwhyaretheyimportant?Howdoesinflationaffectinterestrates?Whatisthetermstructureofinterestrates?Whatfactorsdeterminetherequiredreturnonbonds?QuickQuizHowdoyoufindthe38InterestRatesandBondValuationChapter8Copyright?2010bytheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinInterestRatesandBondValuat39KeyConceptsandSkillsKnowtheimportantbondfeaturesandbondtypesUnderstandbondvaluesandwhytheyfluctuateUnderstandbondratingsandwhattheymeanUnderstandtheimpactofinflationoninterestratesUnderstandthetermstructureofinterestratesandthedeterminantsofbondyieldsKeyConceptsandSkillsKnowth40ChapterOutline8.1 BondsandBondValuation8.2 GovernmentandCorporateBonds8.3 BondMarkets8.4 InflationandInterestRates8.5 DeterminantsofBondYieldsChapterOutline8.1 Bondsand418.1BondsandBondValuationAbondisalegallybindingagreementbetweenaborrowerandalenderthatspecifiesthe:Par(face)valueCouponrateCouponpaymentMaturityDateTheyieldtomaturityistherequiredmarketinterestrateonthebond.8.1BondsandBondValuationA42BondValuationPrimaryPrinciple:Valueoffinancialsecurities=PVofexpectedfuturecashflowsBondvalueis,therefore,determinedbythepresentvalueofthecouponpaymentsandparvalue.Interestratesareinverselyrelatedtopresent(i.e.,bond)values.BondValuationPrimaryPrincip43TheBond-PricingEquationTheBond-PricingEquation44BondExampleConsideraU.S.governmentbondwithas63/8%couponthatexpiresinDecember2013.TheParValueofthebondis$1,000.Couponpaymentsaremadesemiannually(June30andDecember31forthisparticularbond).Sincethecouponrateis63/8%,thepaymentis$31.875.OnJanuary1,2009thesizeandtimingofcashflowsare:BondExampleConsideraU.S.go45BondExampleOnJanuary1,2009,therequiredyieldis5%.Thecurrentvalueis:BondExampleOnJanuary1,200946BondExample:CalculatorPMTI/YFVPVNPV31.875=2.51,000–

1,060.17101,000×0.063752Findthepresentvalue(asofJanuary1,2009),ofa63/8%couponbondwithsemi-annualpayments,andamaturitydateofDecember2013iftheYTMis5%.BondExample:CalculatorPMTI/Y47BondExampleNowassumethattherequiredyieldis11%.Howdoesthischangethebond’sprice?BondExampleNowassumethatth48YTMandBondValue800100011001200130000.010.020.030.040.050.060.070.080.090.1DiscountRateBondValue63/8WhentheYTM<coupon,thebondtradesatapremium.WhentheYTM=coupon,thebondtradesatpar.WhentheYTM>coupon,thebondtradesatadiscount.YTMandBondValue80010001100149BondConceptsBondpricesandmarketinterestratesmoveinoppositedirections.Whencouponrate=YTM,price=parvalueWhencouponrate>YTM,price>parvalue(premiumbond)Whencouponrate<YTM,price<parvalue(discountbond)BondConceptsBondpricesandm50InterestRateRiskPriceRiskChangeinpriceduetochangesininterestratesLong-termbondshavemorepriceriskthanshort-termbondsLowcouponratebondshavemorepriceriskthanhighcouponratebonds.ReinvestmentRateRiskUncertaintyconcerningratesatwhichcashflowscanbereinvestedShort-termbondshavemorereinvestmentrateriskthanlong-termbonds.Highcouponratebondshavemorereinvestmentrateriskthanlowcouponratebonds.InterestRateRiskPriceRisk51MaturityandBondPriceVolatilityCConsidertwootherwiseidenticalbonds.Thelong-maturitybondwillhavemuchmorevolatilitywithrespecttochangesinthediscountrate.DiscountRateBondValueParShortMaturityBondLongMaturityBondMaturityandBondPriceVolati52CouponRatesandBondPricesConsidertwootherwiseidenticalbonds.Thelow-couponbondwillhavemuchmorevolatilitywithrespecttochangesinthediscountrate.DiscountRateBondValueHighCouponBondLowCouponBondParCCouponRatesandBondPricesCo53ComputingYieldtoMaturityYieldtomaturityistherateimpliedbythecurrentbondprice.FindingtheYTMrequirestrialanderrorifyoudonothaveafinancialcalculatorandissimilartotheprocessforfindingrwithanannuity.Ifyouhaveafinancialcalculator,enterN,PV,PMT,andFV,rememberingthesignconvention(PMTandFVneedtohavethesamesign,PVtheoppositesign).ComputingYieldtoMaturityYie54YTMwithAnnualCouponsConsiderabondwitha10%annualcouponrate,15yearstomaturity,andaparvalueof$1,000.Thecurrentpriceis$928.09.Willtheyieldbemoreorlessthan10%?N=15;PV=-928.09;FV=1,000;PMT=100CPTI/Y=11%YTMwithAnnualCouponsConside55YTMwithSemiannualCouponsSupposeabondwitha10%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%YTMwithSemiannualCouponsSup56CurrentYieldvs.YieldtoMaturityCurrentYield=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%,whichisthesameYTMcomputedearlierCurrentYieldvs.YieldtoMat57BondPricingTheoremsBondsofsimilarrisk(andmaturity)willbepricedtoyieldaboutthesamereturn,regardlessofthecouponrate.Ifyouknowthepriceofonebond,youcanestimateitsYTMandusethattofindthepriceofthesecondbond.Thisisausefulconceptthatcanbetransferredtovaluingassetsotherthanbonds.BondPricingTheoremsBondsof58ZeroCouponBondsMakenoperiodicinterestpayments(couponrate=0%)TheentireyieldtomaturitycomesfromthedifferencebetweenthepurchasepriceandtheparvalueCannotsellformorethanparvalueSometimescalledzeroes,deepdiscountbonds,ororiginalissuediscountbonds(OIDs)TreasuryBillsandprincipal-onlyTreasurystripsaregoodexamplesofzeroesZeroCouponBondsMakenoperio59PureDiscountBondsInformationneededforvaluingpurediscountbonds:Timetomaturity(T)=Maturitydate-today’sdateFacevalue(F)Discountrate(r)Presentvalueofapurediscountbondattime0:PureDiscountBondsInformation60PureDiscountBonds:ExampleFindthevalueofa15-yearzero-couponbondwitha$1,000parvalueandaYTMof12%.PureDiscountBonds:ExampleFi61BondPricingwithaSpreadsheetTherearespecificformulasforfindingbondpricesandyieldsonaspreadsheet.PRICE(Settlement,Maturity,Rate,Yld,Redemption,Frequency,Basis)YIELD(Settlement,Maturity,Rate,Pr,Redemption,Frequency,Basis)SettlementandmaturityneedtobeactualdatesTheredemptionandPrneedtogivenas%ofparvalueClickontheExceliconforanexample.BondPricingwithaSpreadshee628.2GovernmentandCorporateBondsTreasurySecuritiesFederalgovernmentdebtT-bills–purediscountbondswithoriginalmaturitylessthanoneyearT-notes–coupondebtwithoriginalmaturitybetweenoneandtenyearsT-bonds–coupondebtwithoriginalmaturitygreaterthantenyearsMunicipalSecuritiesDebtofstateandlocalgovernmentsVaryingdegreesofdefaultrisk,ratedsimilartocorporatedebtInterestreceivedistax-exemptatthefederallevel8.2GovernmentandCorporateB63After-taxYieldsAtaxablebondhasayieldof8%,andamunicipalbondhasayieldof6%.Ifyouareina40%taxbracket,whichbonddoyouprefer?8%(1-.4)=4.8%Theafter-taxreturnonthecorporatebondis4.8%,comparedtoa6%returnonthemunicipalAtwhattaxratewouldyoubeindifferentbetweenthetwobonds?8%(1–T)=6%T=25%After-taxYieldsAtaxablebond64CorporateBondsGreaterdefaultriskrelativetogovernmentbondsThepromisedyield(YTM)maybehigherthantheexpectedreturnduetothisaddeddefaultriskCorporateBondsGreaterdefault65BondRatings–InvestmentQualityHighGradeMoody’sAaaandS&PAAA–capacitytopayisextremelystrongMoody’sAaandS&PAA–capacitytopayisverystrongMediumGradeMoody’sAandS&PA–capacitytopayisstrong,butmoresusceptibletochangesincircumstancesMoody’sBaaandS&PBBB–capacitytopayisadequate,adverseconditionswillhavemoreimpactonthefirm’sabilitytopayBondRatings–InvestmentQual66BondRatings-SpeculativeLowGradeMoody’sBaandBS&PBBandBConsideredspeculativewithrespecttocapacitytopay.VeryLowGradeMoody’sCS&PC&DHighlyuncertainrepaymentand,inmanycases,alreadyindefault,withprincipalandinterestinarrears.BondRatings-SpeculativeLow678.3BondMarketsPrimarilyover-the-countertransactionswithdealersconnectedelectronicallyExtremelylargenumberofbondissues,butgenerallylowdailyvolumeinsingleissuesMakesgettingup-to-datepricesdifficult,particularlyonasmallcompanyormunicipalissuesTreasurysecuritiesareanexception8.3BondMarketsPrimarilyover68TreasuryQuotations8Nov25 132:23 132:24 -12 5.14Whatisthecouponrateonthebond?Whendoesthebondmature?Whatisthebidprice?Whatdoesthismean?Whatistheaskprice?Whatdoesthismean?Howmuchdidthepricechangefromthepreviousday?Whatistheyieldbasedontheaskprice?TreasuryQuotations8Nov25 69CleanversusDirtyPricesCleanprice:quotedpriceDirtyprice:priceactuallypaid=quotedpriceplusaccruedinterestExample:ConsiderT-bondinpreviousslide,assumetodayisJuly15,2009Numberofdayssincelastcoupon=61Numberofdaysinthecouponperiod=184Accruedinterest=(61/184)(.04*1,000)=13.26Prices(basedon