BondValuationandTermStructureofInterestRatesFall20031DefinitionandFeaturesofBondsAbondisanIOU.Abondrepresentsaloanmadebyinvestorstotheissuer.

Theissuerpromisesto:MakecouponpaymentsuntilmaturityPaythefacevalueatmaturityCouponrateCurrentyieldFall20032DefinitionandFeaturesofBondsBondissuersFederalgovernmentPrivateCorporationsGovernmentagencies(intheUS)MunicipalgovernmentsDefaultFall20033ValuingaBond:AnExampleIfabondhasfiveyearstomaturity,an$80annualcoupon,anda$1000facevalue,itscashflowswouldlooklikethis: Time 0 1 2 3 4 5 Coupons $80 $80 $80 $80 $80 FaceValue $1000 MarketPricetoday=?Howmuchisthisbondworth?Couponrate?Currentyield?Fall20034ValuingaBond:AnExample(Cont’d)Ifthegoingrateonbondslikethisoneis10%,thenthisbondhasamarketvalueof$924.18.Alternatively,Fall20035ValuingaBond:AnotherExampleAssumeyouhavethefollowinginformation. Seagramsbondshavea$1000facevalue. Thepromisedannualcouponis$100. Thebondsmaturein20years.Whatisthebond’svalueifthemarket’srequiredreturnonsimilarbondsis10%?Whatarethecouponrateandcurrentyield?Whatiftherateofreturnis8%?Whatiftherateofreturnis12%?Fall20036BondValuation:ASummaryBondValue=PresentValueoftheCoupons +PresentValueoftheFaceValue Iftheinterestrateisconstant, BondValue =C

[1-1/(1+r)t]/r

+F

1/(1+r)t

where: C=Couponpaideachperiod

r=Rateperperiod

t=Numberofperiods

F=Bond’sfacevalue

Fall20037BondValuation:ASummary(Cont’d)SometerminologyP0(C)<Fsellatadiscount.P0(C)=F

sellatpar.P0(C)>F

sellatapremium.InverserelationbetweenbondpricesandinterestratesResultsforconstantinterestratesIfC/F>r,thenP0(C)>F.IfC/F=r,thenP0(C)=F.IfC/F<r,thenP0(C)<FFall20038HoldingPeriodReturnsofBondsDollarreturnsfromholdingabondforacertainperiodCouponincomeCapitalgain/lossOne-periodholdingperiodreturnFall20039CouponBondValuation:AnotherExampleConsidera2yearU.S.TreasuryNotewithannualcouponrateof8%(couponpaidsemiannually)andfacevalue$1000.Supposethebondyieldis10%.WhatisthefairpriceforyoutobuytheT-Notetoday?Theproperdiscountrateis5%persixmonths

Fall200310CouponBondValuation:AnotherExample(cont’d)Supposeyoudecidetosellitrightafteryoureceivethe1stcouponwhenthebondyielddropsto6%perannum.WhatisyourHPR?Bondpricein6months=40A0.033+1000/1.033=$1028.29HPR =(40+1028.29-964.54)/964.54 =10.76%Currentyield=40/964.54=4.15%,Capitalgainyield=(1028.29-964.54)/964.54=6.61%Fall200311PureDiscountBondsSinglepaymentatthematurity.Alsocalledzero-couponbonds,orzeros.Thepriceofazero-couponbondwithfacevalueFisAcoupon-bearingbondcanberegardedasaportfolioofpure-discountbonds.Fall200312Non-constantInterestRates

andBondPricingInterestratesofdifferentmaturitiesaredifferentingeneral.Shouldwediscountthecashflowsoccurredatdifferentpointsoftimebythesamediscountrates?Fall200313Non-constantInterestRates

andBondPricingIfweknowthediscountratesforcashflowsofdifferentpointsoftimeinthefuture,acouponbondispricedas,Eachcouponasapure-discountbondFall200314TermStructureofInterestRatesTherelationshipbetweenlevelofinterestratesandtimetomaturity.Graphicalrepresentationoftermstructureofinterestratestimetomaturityonx-axisspotratesony-axisPlotspotratesofallmaturities=>zeroyieldcurve.Fall200315TermStructureofInterestRatesAzeroyieldcurveisagraphicalrepresentationofthetermstructureofinterestratesEachpointonthezeroyieldcurvecorrespondstoaspotratewhichistheappropriatediscountrateonlyforcashflowsoccurredatthatpointoftime.Atanytime,thereisonlyonezeroyieldcurve.Allpointsonazeroyieldcurvearewithrespecttoperiodsstartingfromthesametime.Fall200316BondValuationwithNon-FlatTermStructures:AnExampleSupposeyouaregiventhefollowingtermstructureofinterestratesWhatarethepricesof1-,2-,and3-yearpurediscountbondswith$100principal?Supposethatthereisa3-year6%annualcouponbondwithfacevalueof$1000.Whatisthebondprice?Fall200317BondValuationwithNon-FlatTermStructures:AnExample(Cont’d)Purediscountbondprices:1-yearbondprice=$100/(1.04)=$96.152-yearbondprice=$100/(1.05)2=$90.703-yearbondprice=$100/(1.055)3=$85.163-year6%annualcouponbondOrmoredirectlyQ.If,intheexample,pure-discountbondpricesaregiven,canyoucalculatethespotrates?Fall200318YieldtoMaturity(YTM)therateofreturnthatmakesthemarketpriceofthebondequaltothepresentvalueofitsfuturecashflows,i.e.,thenumberythatsolvesYTMusedasdiscountrateYTMisdifferentfromspotratesWhenisYTM=r?Fall200319YieldtoMaturity(YTM):AnExampleQ. Atwo-year10%annualcouponbondwithfacevalueof$1000.r1=8%,r2=10%.WhatistheYTMofthebond?A. First,solveforthebondpriceSecond,solvefortheYTM,yFall200320FindingYieldtoMaturityIngeneral,YTMcanbefoundonlybytrialanderrorAnexample:A5-yearannualbondissellingfor$924.18.Thecouponrateis8%andthefacevalueis$1000.WhatistheYTMofthebond? Try8%,P=1000Try9%:P=$961.10Try10%:P=$924.18

Fall200321PropertiesofYieldtoMaturityIfthetermstructureofinterestratesisflat(constant),thenYTM=r.Ingeneral,YTMisacomplicatedaverageofinterestrates.Spotratesaremarket-wide.YTMisbondspecific:yieldsonbondswithdifferentcouponscannotbecompared.Eg.Considera2-year2%couponbondunderthesametermstructureasinSlide20.YTM=9.98%Fall200322PropertiesofYieldtoMaturityYTMdoesnotguaranteerealizedrateofreturn.Sellbondbeforematurity=>subjecttointerestrateriskReinvestmentofcoupon=>unknownrateofretunYieldtomaturitydoesnotprovidereliableestimatesofthetimevalueofmoney.Fall200323BondPriceSensitivitytoYTM4%6%8%10%12%14%16%$1,800$1,600$1,400$1,200$1,000$800$600BondpriceYieldtomaturity,YTMCoupon=$100

20yearstomaturity

$1,000facevalueKeyInsight:BondpricesandYTMsareinverselyrelated.copyright?2002McGraw-HillRyerson,LtdFall200324InterestRateRiskandTimetoMaturity(Figure7.2)copyright?2002McGraw-HillRyerson,LtdFall200325ACoupleofFactsGiventwobondsidenticalbutformaturity,thepriceofthelonger-termbondwillchangemore(inpercentageterms)thanthatoftheshorter-termbond,foragivenchangeinmarketinterestrates.Giventwobondsidenticalbutforcoupon,thepriceof thelower-couponbondwillchangemore(inpercentageterms)thanthatofthehigher-couponbond,foragivenchangeinmarketinterestrates.Fall200326ComponentsofTermStructureofInterestRatesFall200327ComponentsofTermStructureofInterestRatesFall200328InflationandReturnsWhatisthedifferencebetweenarealreturnandanominalreturn?Howcanweconvertfromonetotheother?Example: Supposewehave$1000,andDietCokecosts$2.00persixpack.Wecanbuy500sixpacks.Nowsupposetherateofinflationis5%,sothatthepricerisesto$2.10inoneyear.Weinvestthe$1000anditgrowsto$1100inoneyear.What’sourreturnindollars?Insixpacks?Fall200329InflationandReturns(continued)A.

Ourreturnintermsofdollarsis ($1,100-$1,000)/$1,000=$100/$1,000=.10.

ReturnintermsofSixpacks. Wecanbuy$1,100/$2.10=523.81sixpacks,soourreturnis (523.81-500)/500=23.81/500=4.76%Fall200330InflationandReturns(continued)Realversusnominalreturns: Yournominalreturnisthepercentagechangeintheamountofmoneyyouhave. Yourrealreturnisthepercentagechangeintheamountofstuffyoucanactuallybuy.Fall200331InflationandReturns(concluded)FisherEffect.1+R=(1+r)(1+h) where R = thenominalreturn r = therealreturn h = theinflationrateFromtheexample,therealreturnis4.76%;thenominalreturnis10%,andtheinflationrateis5%:(1+R)=1.10(1+r)(1+h)=1.0476x1.05=1.10Fall200332U.S.InterestRates:1800-1997Fall200333CorporateBondsvs.

GovernmentBondsOnlyconsidergovernmentbondssofarDefault-freeHighlyliquidCorporatebondsSubjecttodefaultriskLessliquidContainmorefeaturesFall200334FeaturesofaMay

DepartmentStoresBondTerm

ExplanationAmountofissue$200millionThecompanyissued$200millionworthofbonds.Dateofissue8/4/94Thebondsweresoldon8/4/94.Maturity8/1/24Theprincipalwillbepaid30yearsaftertheissuedate.FaceValue$1,000Thedenominationofthebondsis$1,000.Annualcoupon8.375Eachbondholderwillreceive$83.75perbondperyear(8.375%oftheOfferprice100Theofferpricewillbe100%ofthe$1,000facevalueperbond.Fall200335FeaturesofaMayDepartment

StoresBond(concluded)TermExplanationCouponpaymentdates2/1,8/1Couponsof$83.75/2=$41.875willbepaidonthesedates.SecurityNoneThebondsaredebentures.SinkingfundAnnualbeginning8/1/05Thefirmwillmakeannualpaymentstowardthesinkingfund.CallprovisionNotcallablebefore8/1/04Thebondshaveadeferredcallfeature(SeeAppendix7ConCanadapluscalls.)Callprice104.188initially,decliningto100After8/1/04,thecompanycanbuybackthebondsfor$1,041.88perbond,decliningto$1,000on8/1/14.RatingMoody’sA2ThisisoneofMoody’shigherratings.Thebondshavealowprobabilityofdefault.Fall200336TheBondIndentureThebondindentureisathree-partycontractbetweenthebondissuer,thebondholders,andthetrustee.Thetrusteeishiredbytheissuertoprotectthebondholders’interests.Whatdoyouthinkwouldhappenifanissuerrefusedtohireatrustee?Fall200337TheBondIndentureTheindentureincludesThebasictermsofthebondissueThetotalamountofbondsissuedAdescriptionofthesecurityTherepaymentarrangementsThecallprovisionsDetailsoftheprotectivecovenantsFall200338BondRatings

Investment-QualityBondRatings

HighGradeMediumGradeMoody’sAaaAaABaaDBRS(S&P)AAAAAABBBLowQuality,speculative,and/or“Junk”LowGradeVeryLowGradeMoody’sBaBCaaCaCDDBRS(S&P)BBBCCCCCCDFall200339BondRatingsandDefaultProbabilitiesSource:Moody’sInvestorService,Specialcomments,January2000Fall200340BondRatingsandDefaultProbabilitiesRatingTransitionRates,1970-2001;5-YearHorizonAveragesRatingto:AaaAaABaaBaBCaa-CDefaultWRAaa55.9823.284.950.490.490.160.090.1314.43Aa4.5151.9823.303.580.940.280.010.2815.12RatingA0.268.1558.3413.652.950.750.140.4415.33from:Baa0.231.6115.8147.099.562.420.301.6321.35Ba0.090.252.9012.6133.0310.600.678.1831.66B0.050.070.532.9213.2530.401.5819.5531.64Caa-C0.000.000.00616.1841.9025.90Source:Moody’sInvestorService,Specialcomments,February2002Fall200341FactorsAffectingBondYieldsKeyIssue: Whatfactorsaffectobservedbondyields?T