公司理财教学资料 chap007

Chapter7 InterestRatesandBondValuation2026/5/15ChapterOutlineBondsandBondValuationBondFeaturesBondRatingsSomeDifferentTypesofBondsBondMarketsInflationandInterestRatesDeterminantsofBondYields7-22026/5/15MarketValues($Trillion)Valueofoutstandingissues2026/5/15BondsandBondValuationAbondisalegallybindingagreementbetweenaborrowerandalenderthatspecifiesthe:Par(face)valueCouponrateCouponpaymentMaturityDateTheyieldtomaturityistherequiredmarketinterestrateonthebond.DonotconfusethecouponratewiththerequiredmarketinterestrateBondDefinitionsBondParvalue(facevalue)CouponrateCouponpaymentMaturitydateYieldorYieldtomaturity(requiredreturn,marketrate)7-52026/5/15TheBond-PricingEquationNoticethat:Thefirsttermisthepresentvalueofthecouponpayments(anannuity);and,Thesecondtermisthepresentvalueofthebond’sparvalueBond=PresentValueofCashFlowsBondValue=PVofcoupons+PVofparBondValue=PVofannuity+PVoflumpsumAsinterestratesincrease,presentvaluesdecreaseSo,asinterestratesincrease,bondpricesdecreaseandviceversa7-72026/5/15ValuingaDiscountBondwithAnnualCouponsConsiderabondwithacouponrateof10%andannualcoupons.Theparvalueis$1,000,andthebondhas5yearstomaturity.Theyieldtomaturityis11%.Whatisthevalueofthebond?Usingtheformula:B=PVofannuity+PVoflumpsumB=100[1–1/(1.11)5]/.11+1,000/(1.11)5B=369.59+593.45=963.04Usingthecalculator:N=5;I/Y=11;PMT=100;FV=1,000CPTPV=-963.047-82026/5/15ValuingaPremiumBondwithAnnualCouponsSupposeyouarereviewingabondthathasa10%annualcouponandafacevalueof$1000.Thereare20yearstomaturity,andtheyieldtomaturityis8%.Whatisthepriceofthisbond?Usingtheformula:B=PVofannuity+PVoflumpsumB=100[1–1/(1.08)20]/.08+1000/(1.08)20B=981.81+214.55=1196.36Usingthecalculator:N=20;I/Y=8;PMT=100;FV=1000CPTPV=-1,196.367-92026/5/15GraphicalRelationshipBetweenPriceandYield-to-maturity(YTM)BondPriceYield-to-maturity(YTM)7-102026/5/15BondPrices:RelationshipBetweenCouponandYieldIfYTM=couponrate,thenparvalue=bondpriceIfYTM>couponrate,thenparvalue>bondpriceWhy?ThediscountprovidesyieldabovecouponratePricebelowparvalue,calledadiscountbondIfYTM<couponrate,thenparvalue<bondpriceWhy?HighercouponratecausesvalueaboveparPriceaboveparvalue,calledapremiumbond7-112026/5/15TheBondPricingEquation7-122026/5/15Example7.1p.196Couponrate=14%,semiannualcouponsYTM=16%;Maturity=7yearsParvalue=$1,000FindpresentvaluesbasedonthepaymentperiodHowmanycouponpaymentsarethere?Whatisthesemiannualcouponpayment?Whatisthesemiannualyield?B=70[1–1/(1.08)14]/.08+1,000/(1.08)14=917.567-132026/5/15InterestRateRiskPriceRiskChangeinpriceduetochangesininterestratesLong-termbondshavemorepriceriskthanshort-termbondsLowcouponratebondshavemorepriceriskthanhighcouponratebondsReinvestmentRateRiskUncertaintyconcerningratesatwhichcashflowscanbereinvestedShort-termbondshavemorereinvestmentrateriskthanlong-termbondsHighcouponratebondshavemorereinvestmentrateriskthanlowcouponratebonds7-142026/5/15Figure7.2p.1977-152026/5/15ComputingYieldtoMaturityYieldtoMaturity(YTM)istherateimpliedbythecurrentbondpriceItisnotthecouponrate!FindingtheYTMrequirestrialanderrorifyoudonothaveafinancialcalculatorIfyouhaveafinancialcalculator,enterN,PV,PMT,andFV,rememberingthesignconvention(PMTandFVneedtohavethesamesign,PVtheoppositesign)7-162026/5/15YTMwithAnnualCouponsConsiderabondwitha10%annualcouponrate,15yearstomaturityandaparvalueof$1,000.Thecurrentpriceis$928.09.Willtheyieldbemoreorlessthan10%?N=15;PV=-928.09;FV=1,000;PMT=100CPTi=11%7-172026/5/15YTMwithSemiannualCouponsSupposeabondwitha10%couponrateandsemiannualcoupons,hasafacevalueof$1,000,20yearstomaturityandissellingfor$1,197.93.IstheYTMmoreorlessthan10%?Whatisthesemiannualcouponpayment?Howmanyperiodsarethere?N=40;PV=-1,197.93;PMT=50;FV=1,000;CPTi=4%(IsthistheYTM?)YTM=4%*2=8%7-182026/5/15Table7.17-192026/5/15CurrentYieldvs.YieldtoMaturityCurrentYield=annualcoupon/priceYieldtomaturity=currentyield+capitalgainsyieldExample:10%couponbond,withsemiannualcoupons,facevalueof1,000,20yearstomaturity,$1,197.93priceCurrentyield=100/1,197.93=.0835=8.35%Priceinoneyear,assumingnochangeinYTM=1,193.68Capitalgainyield=(1,193.68–1,197.93)/1,197.93=-.0035=-.35%YTM=8.35-.35=8%,whichisthesameYTMcomputedearlier7-202026/5/15BondPricingTheoremsBondsofsimilarrisk(andmaturity)willbepricedtoyieldaboutthesamereturn,regardlessofthecouponrateIfyouknowthepriceofonebond,youcanestimateitsYTMandusethattofindthepriceofthesecondbondThisisausefulconceptthatcanbetransferredtovaluingassetsotherthanbonds7-212026/5/15BondPriceswithaSpreadsheetThereisaspecificformulaforfindingbondpricesonaspreadsheetPRICE(Settlement,Maturity,Rate,Yld,Redemption,Frequency,Basis)YIELD(Settlement,Maturity,Rate,Pr,Redemption,Frequency,Basis)SettlementandmaturityneedtobeactualdatesTheredemptionandPrneedtobeinputas%ofparvalueClickontheExceliconforanexample7-222026/5/15Differences-DebtandEquityDebtNotanownershipinterestCreditorsdonothavevotingrightsInterestisconsideredacostofdoingbusinessandistaxdeductibleCreditorshavelegalrecourseifinterestorprincipalpaymentsaremissedExcessdebtcanleadtofinancialdistressandbankruptcyEquityOwnershipinterestCommonstockholdersvotefortheboardofdirectorsandotherissuesDividendsarenotconsideredacostofdoingbusinessandarenottaxdeductibleDividendsarenotaliabilityofthefirm,andstockholdershavenolegalrecourseifdividendsarenotpaid7-232026/5/15TheBondIndentureContractbetweenthecompanyandthebondholdersthatincludesThebasictermsofthebondsThetotalamountofbondsissuedAdescriptionofpropertyusedassecurity,ifapplicableSinkingfundprovisionsCallprovisionsDetailsofprotectivecovenants7-242026/5/15SampleBondFeaturesFeaturesofarecentPepsicobondissueindenture:BondClassificationsRegisteredvs.BearerFormsSecurityCollateral–securedbyfinancialsecuritiesMortgage–securedbyrealproperty,normallylandorbuildingsDebentures–unsecuredNotes–unsecureddebtwithoriginalmaturitylessthan10yearsSeniority7-262026/5/15BondCharacteristicsandRequiredReturnsThecouponratedependsontheriskcharacteristicsofthebondwhenissuedWhichbondswillhavethehighercoupon,allelseequal?SecureddebtversusadebentureSubordinateddebentureversusseniordebtAbondwithasinkingfundversusonewithoutAcallablebondversusanon-callablebond7-272026/5/15BondRatings–InvestmentQualityHighGradeMoody’sAaaandS&PAAA–capacitytopayisextremelystrongMoody’sAaandS&PAA–capacitytopayisverystrongMediumGradeMoody’sAandS&PA–capacitytopayisstrong,butmoresusceptibletochangesincircumstancesMoody’sBaaandS&PBBB–capacitytopayisadequate,adverseconditionswillhavemoreimpactonthefirm’sabilitytopay7-282026/5/15BondRatings-SpeculativeLowGradeMoody’sBaandBS&PBBandBConsideredpossiblethatthecapacitytopaywilldegenerate.VeryLowGradeMoody’sC(andbelow)andS&PC(andbelow)incomebondswithnointerestbeingpaid,orindefaultwithprincipalandinterestinarrears7-292026/5/15DefaultRatesvs.Rating2026/5/15GovernmentBondsTreasurySecurities=FederalgovernmentdebtT-bills–purediscountbondswithoriginalmaturityofoneyearorlessT-notes–coupondebtwithoriginalmaturitybetweenoneandtenyearsT-bonds–coupondebtwithoriginalmaturitygreaterthantenyearsMunicipalSecuritiesDebtofstateandlocalgovernmentsVaryingdegreesofdefaultrisk,ratedsimilartocorporatedebtInterestreceivedistax-exemptatthefederallevel7-312026/5/15Example7.4p.210Ataxablebondhasayieldof8%,andamunicipalbondhasayieldof6%Ifyouareina40%taxbracket,whichbonddoyouprefer?8%(1-.4)=4.8%Theafter-taxreturnonthecorporatebondis4.8%,comparedtoa6%returnonthemunicipalAtwhattaxratewouldyoubeindifferentbetweenthetwobonds?8%(1–T)=6%T=25%7-322026/5/15ZeroCouponBondsMakenoperiodicinterestpayments(couponrate=0%)Theentireyield-to-maturitycomesfromthedifferencebetweenthepurchasepriceandtheparvalueCannotsellformorethanparvalueSometimescalledzeroes,deepdiscountbonds,ororiginalissuediscountbonds(OIDs)TreasuryBillsandprincipal-onlyTreasurystripsaregoodexamplesofzeroes7-332026/5/15Floating-RateBondsCouponratefloatsdependingonsomeindexvalueExamples–adjustableratemortgagesandinflation-linkedTreasuriesThereislesspriceriskwithfloatingratebondsThecouponfloats,soitislesslikelytodiffersubstantiallyfromtheyield-to-maturityCouponsmayhavea“collar”–theratecannotgoaboveaspecified“ceiling”orbelowaspecified“floor”7-342026/5/15OtherBondTypesDisasterbondsIncomebondsConvertiblebondsPutbondsTherearemanyothertypesofprovisionsthatcanbeaddedtoabondandmanybondshaveseveralprovisions–itisimportanttorecognizehowtheseprovisionsaffectrequiredreturns7-352026/5/15BondMarketsPrimarilyover-the-countertransactionswithdealersconnectedelectronicallyExtremelylargenumberofbondissues,butgenerallylowdailyvolumeinsingleissuesMakesgettingup-to-datepricesdifficult,particularlyonsmallcompanyormunicipalissuesTreasurysecuritiesareanexception7-362026/5/15TreasuryQuotationsHighlightedquoteinFigure7.4p.2187.5Nov24137.29137.31-493.9133Whatisthecouponrateonthebond?Whendoesthebondmature?Whatisthebidprice?Whatdoesthismean?Whatistheaskprice?Whatdoesthismean?Howmuchdidthepricechangefromthepreviousday?Whatistheyield(ytm)basedontheaskprice?7-372026/5/15Cleanvs.DirtyPricesCleanprice:quotedpriceDirtyprice:priceactuallypaid=quotedpriceplusaccruedinterestExample:ConsideraT-bondwitha4%semiannualyieldandacleanpriceof$1,282.50:Numberofdayssincelastcoupon=61Numberofdaysinthecouponperiod=184Accruedinterest=(61/184)(.04*1000)=$13.26Dirtyprice=$1,282.50+$13.26=$1,295.76So,youwouldactuallypay$1,295.76forthebond7-382026/5/15InflationandInterestRatesRealrateofinterest–changeinpurchasingpowerNominalrateofinterest–quotedrateofinterest,changeinactualnumberofdollarsTheforecastnominalrateofinterestincludesourdesiredrealrateofreturnplusanadjustmentforexpectedinflation7-392026/5/15TheFisherEffectTheFisherEffectdefinestherelationshipbetweenrealrates,nominalrates,andinflation(1+R)=(1+r)(1+h),whereR=nominalrater=realrateh=expectedinflationrateApproximationR=r+h7-402026/5/15Example7.5p.220Ifwerequirea10%realreturnandweexpectinflationtobe8%,whatisthenominalrate?R=(1.1)(1.08)–1=.188=18.8%Approximation:R=10%+8%=18%Becausetherealreturnandexpectedinflationarerelativelyhigh,thereissignificantdifferencebetweentheactualFisherEffectandtheapproximation.7-412026/5/15TermStructureofInterestRatesTermstructureistherelationshipbetweentimetomaturityandyields,allelseequalItisimportanttorecognizethatwepullouttheeffectofdefaultrisk,differentcoupons,etc.Yieldcurve–graphicalrepresentationofthetermstructureNormal–upward-sloping;long-termyieldsarehigherthanshort-termyieldsInverted–downward-sloping;long-termyieldsarelowerthanshort-termyields7-422026/5/15Figure7.6–Upward-SlopingYieldCurvep.2247-43Figure7.6–Downward-SlopingYieldCurve7-44Figure7.7InsertnewFigure7.7here7-452026/5/15FactorsAffectingBondY