現(xiàn)代財務管理英文平臺

Topic7(Chapter4)

BondsandTheirValuationKeyfeaturesofbondsBondvaluationMeasuringyieldAssessingriskKeywordsBond債券Treasurybond國庫債券Corporatebond企業(yè)債券Municipalbond市政債券Foreignbond外國債券Parvalue面值Maturitydate到期日Couponpayment票面利息Couponinterestrate票面利率Floatingratebond浮動利率債券Zerocouponbond零票面利率債券Originalissuediscountedbond(OID)折價發(fā)行債券

Callprovision贖回條款Sinkingfund償債基金Convertiblebond可轉換債券Warrant認股權證Premiumbond溢價債券Discountbond折價債券Currentyield(onabond)債券的當前利率Yieldtomaturity(YTM)到期收益率Yieldtocall(YTC)贖回收益率Reinvestmentrisk再投資風險Interestraterisk利率風險

CaseRoberBalikandCarolKieferarevice-presidentsofMutualofChicagoInsuranceCompanyandco-directorsofthecompany’spensionfundmanagementdivision.Amajornewclient,theCaliforniaLeagueofCities,hasrequestedthatMutualofChicagopresentaninvestmentseminartotheMayorsoftherepresentedcities,andBalikandKiefer,whowillmaketheactualpresentation,haveaskedyoutohelpthembyansweringthefollowingquestions.BecausetheWaltDisneyCompanyoperatesinoneoftheleague’scities,youaretoworkDisneyintothepresentation.Questions：a.Whatarethekeyfeaturesofabond?b.Whatarecallprovisionandsinkingfundprovisions?Dotheseprovisionsmakebondsmoreorlessrisky?C.Howisthevalueofanyassetwhosevalueisbasedonexpectedfuturecashflowsdetermined?d.Howisthevalueofabonddetermined?Whatisthevalueofa10-year,$1,000parvaluebondwitha10percentannualcouponifitsrequiredrateofreturnis10percent?e.(1)Whatwouldbethevalueofthebonddescribedinpartdif,justafterithadbeenissued,theexpectedinflationrateroseby3percentpoints,causinginvestorstorequirea13percentreturn?Wouldwenowhaveadiscountorapremiumbond?e.(2)Whatwouldhappentothebond’svalueifinflationfell,anddeclinedto7percent?Wouldwenowhaveapremiumoradiscountbond?e.(3)Whatwouldhappentothevalueofthe10-yearbondovertimeiftherequiredrateofreturnremainedat13percent,orifitremainedat7percent?f

.(1)Whatistheyieldtomaturityona10-year,9percent,annualcoupon,$1,000parvaluebondthatsellsfor$887.00?Thatsellsfor$1,134.20?Whatdoesthefactthatabondsellsatadiscountoratapremiumtellyouabouttherelationshipbetweenandthebond’scouponrate?f.(2)Whatarethetotalreturn,thecurrentyield,andthecapitalgainsyieldforthediscountbond?g.Whatisinterestrate(orprice)risk?Whichbondhasmoreinterestraterisk,anannualpayment1-yearbondora10-yearbond?Why?h.Whatisreinvestmentraterisk?Whichhasmorereinvestmentraterisk,a1-yearbondora10-yearbond?i.Howdoestheequationforvaluingabondchangeifsemiannualpaymentsaremade?Findthevalueofa10-year,semiannualpayment,10percentcouponbondifnominal=13%.J.Supposeyoucouldbuy,for$1,000,eithera10percent,10-year,annualpaymentbondora10percent,10-year,semiannualpaymentbond,Theyareequallyrisky.Whichwouldyouprefer?If$1,000istheproperpriceforthesemiannualbond,whatistheequilibriumpricefortheannualpaymentbond?K.Supposea10-year,10percent,semiannualcouponbondwithaparvalueof$1,000iscurrentlysellingfor$1,135.90,producinganominalyieldtomaturityof8percent.However,thebondcanbecalledafter5yearforapriceof$1,050.(1)Whatisthebond’snominalyieldtocall(YTC)?(2)Ifyouboughtthisbond,doyouthinkyouwouldbemorelikelytoearntheYTMortheYTC?Why?l.Disney’sbondwereissuedwithayieldtomaturityof7.5percent.Doestheyieldtomaturityrepresentthepromisedorexpectedreturnonthebond?m.Disney’sbondswereratedAA-byS&P.Wouldyouconsiderthesebondsinvestmentgradeorjunkbonds?N.Whatfactorsdetermineacompany’sbondrating?O.Ifthisfirmweretodefaultonthebonds,wouldthecompanybeimmediatelyliquidated?Wouldthebondholdersbeassuredofreceivingalloftheirpromisedpayments?DefinetheBondBondisalong-termcontractunderwhichaborroweragreestomakepaymentsofinterestandprinciple,onspecificdates,totheholdersofthebond.TypesofBondsTreasurybondsCorporatebondsMunicipalbondsForeignbondsU.S.TreasuryYieldCurve3:08AM9/9/2009KeyFeaturesofaBond1. Parvalue:Faceamount;paid atmaturity.Assume$1,000.2. Couponinterestrate:Stated interestrate.Multiplybypar valuetogetdollarsofinterest.Generallyfixed.(More…)3. Maturity:Yearsuntilbond mustberepaid.Declines.4. Issuedate:Datewhenbond wasissued.Defaultrisk:Riskthatissuerwillnotmakeinterestorprincipalpayments.(SeeTreasury&corporatebond…)FinancialAssetValuation

PV=CF1+k

...

+CF1+k1n1221CFkn.012nkCF1CFnCF2Value...+++BondValuationThediscountrate(kd)istheopportunitycostofcapital,i.e.,theratethatcouldbeearnedonalternativeinvestmentsofequalrisk.kd=k*+IP+LP+MRP+DRPfordebtsecurities.What’sthevalueofa10-year,10%couponbondifkd=10%?

VkkBdd

$100$1,1000111010

.

.

.

+$1001+kd1001000121010%100+1,000V=?...=$90.91+...+$38.55+$385.54=$1,000.++++

10 10 1001000 N I/YR PV PMT FV -1,000Thebondconsistsofa10-year,10%annuityof$100/yearplusa$1,000lumpsumatt=10:

$614.46

385.54

$1,000.00PVannuityPVmaturityvalueValueofbond===INPUTSOUTPUT

10 13 1001000 N I/YR PV PMT FV -837.21Whenkdrises,abovethecouponrate,thebond’svaluefallsbelowpar,soitsellsatadiscount.Whatwouldhappenifexpectedinflationroseby3%,causingk=

13%?INPUTSOUTPUTWhatwouldhappenifinflationfell,andkddeclinedto7%?

10 7 1001000 N I/YR PV PMT FV -1,210.71Ifcouponrate>kd,pricerisesabovepar,andbondsellsatapremium.

INPUTSOUTPUTExampleMicroDrive’sbondswitha10percentcouponratewereoriginallyissuedatpar$1,000with15-yearmaturity.Ifremainconstantat10percent,whatwouldthevalueofthebondbeoneyearafteritwasissued?NowsupposeinterestratesintheeconomyfellaftertheAlliedBondswereissued,and,asaresult,fellbelowthecouponrate,decreasingfrom10to5percent.Assumingthatinterestratesremainconstantat5percentforthenext14years,whatwouldhappentothevalueofanMicroDrivebond?Bondsvalueatyear1andyear2aftertheywereissued:So,thebondvaluewouldfirstincreasetoitshighestvalueof$1,494.96(firstyear),andthenwoulddecreasefrom$1,469.66(Secondyear)to$1,000(thelastyear).Nowsupposeinterestratesintheeconomyhadrisenfrom10to15percentduringthefirstyearafterissue,whatwouldhappentothevalueofanMicroDrivebond?Bondsvalueatyear1andyear2aftertheywereissued:So,thebondvaluewouldfirstdecreasetoitslowestvalueof$713.78(firstyear),andthenwouldincreasefrom$720.80(Secondyear)to$1,000(thelastyear).Supposethebondwasissued20yearsagoandnowhas10yearstomaturity.Whatwouldhappentoitsvalueovertimeiftherequiredrateofreturnremainedat10%,orat13%,orat7%?MBondValue($)YearsremainingtoMaturity1,3721,2111,00083777530 25 20 15 10 5 0kd=7%.kd=13%.kd=10%.Atmaturity,thevalueofanybondmustequalitsparvalue.Thevalueofapremiumbondwoulddecreaseto$1,000.Thevalueofadiscountbondwouldincreaseto$1,000.Aparbondstaysat$1,000ifkdremainsconstant.What’s“yieldtomaturity”?YTMistherateofreturnearnedonabondheldtomaturity.Alsocalled“promisedyield.”What’stheYTMona10-year,9%annualcoupon,$1,000parvaluebondthatsellsfor$887?

9090

9001910kd=?1,000PV1...PV10PVM887Findkdthat“works”!...

10 -887 901000 N I/YR PV PMT FV 10.91

VINTkMkBdNdN

111

...

+INT1+kd

8879011000111010

kkdd

+901+kd,Findkd

+

+

+

+++++INPUTSOUTPUT

...Ifcouponrate<kd,bondsellsatadiscount.Ifcouponrate=kd,bondsellsatitsparvalue.Ifcouponrate>kd,bondsellsatapremium.Ifkdrises,pricefalls.Price=paratmaturity.FindYTMifpricewere$1,134.20.

10 -1134.2901000 N I/YR PV PMT FV 7.08Sellsatapremium.Becausecoupon=9%>kd=7.08%,bond’svalue>par.INPUTSOUTPUTHowdoesaddingacallprovisionaffectabond?Issuercanrefundifratesdecline.Thathelpstheissuerbuthurtstheinvestor.Therefore,borrowersarewillingtopaymore,andlendersrequiremore,oncallablebonds.Mostbondshaveadeferredcallandadecliningcallpremium.YieldtoCall(YTC)Ifcurrentinterestratesarewellbelowanoutstandingbond’scouponrate,thenacallablebondislikelytobecalled.Theexpectedrateofreturnonthiscalledbondisitsyieldtocall(YTC).ExampleMicroDrivebonds’parvaluewere$1,000.Theywouldpayinterestwitha10percentcouponrateduringthe15-yearslifeofthebonds,plusprinciple(generallythe$1,000parvalue)whenthebondsmature.Sincetheinterestrateintheeconomywas10percent,thosebondswereoriginallyissuedatpar.Supposetheyhadaprovisionthatpermittedthecompany,ifitdesired,tocallthebonds10yearsaftertheissuedateatapriceof$1,100.Supposefurtherthatinterestrateoftheeconomyhaddeclinedfrom10%to5%oneyearafterissuance,causingthepriceofthebondstoriseto$1,494.93.Assumingthatinterestratesremainconstantat5%forthenext14years.Question:Wouldyoubuytheoutstandingbondoneyearaftertheirissuance?

YTC=4.21%DefinitionsCurrentyield=Capitalgainsyield= =YTM=+AnnualcouponpmtCurrentpriceChangeinpriceBeginningpriceExptotalreturnExpCurryldExpcapgainsyldFindcurrentyieldandcapitalgainsyieldfora9%,10-yearbondwhenthebondsellsfor$887andYTM=10.91%.Currentyield = =0.1015=10.15%.

$90$887YTM =Currentyield+Capitalgainsyield.Capgainsyield=YTM-Currentyield =10.91%-10.15% =0.76%.CouldalsofindvaluesinYears1and2,getdifference,anddividebyvalueinYear1.Sameanswer.InterestRateRiskReinvestmentRateRiskTheRiskofaBondItistheriskofadeclineinbondvaluesduetorisinginterestrates.InterestRateRiskWhat’sinterestrate(orprice)risk?Doesa1-yearor10-year10%bondhavemorerisk?kd1-yearChange10-yearChange5%$1,048$1,38610%1,0004.8%1,00038.6%15%9564.4%74925.1%Interestraterisk:Risingkdcausesbond’spricetofall.05001,0001,5000%5%10%15%1-year10-yearkdValueOne’sexposuretointerestriskishigheronbondswithlongmaturitiesthanonthosematuringinthenearfuture.Thelongerthematurityofthebond,themoreitspricechangesinresponsetoagivenchangeininterestrates.Whatisreinvestmentraterisk?TheriskthatCFswillhavetobereinvestedinthefutureatlowerrates,reducinge.Illustration:Supposeyoujustwon$500,000playingthelottery.You’llinvestthemoneyandliveofftheinterest.Youbuya1-yearbondwithaYTMof10%.Year1e=$50,000.Atyear-endgetback$500,000toreinvest.Ifratesfallto3%,ewilldropfrom$50,000to$15,000.Hadyoubought30-yearbonds,ewouldhaveremainedconstant.Long-termbonds:Highinterestraterisk,lowreinvestmentraterisk.Short-termbonds:Lowinterestraterisk,highreinvestmentraterisk.Nothingisriskless!SemiannualBonds1. Multiplyyearsby2togetperiods=2n.2. Dividenominalrateby2togetperiodic rate=kd/2.3. DivideannualINTby2togetPMT= INT/2.

2n kd/2 OK INT/2 OK N I/YRPVPMT FV

INPUTSOUTPUT

2(10)13/2 100/2 206.5 501000 N I/YR PV PMT FV -834.72Findthevalueof10-year,10%coupon,semiannualbondifkd=13%.INPUTSOUTPUTYoucouldbuy,for$1,000,eithera10%,10-year,annualpaymentbondoranequallyrisky10%,10-yearsemiannualbond.Whichwouldyouprefer?Thesemiannualbond’sEFF%is:10.25%>10%EFF%onannualbond,sobuysemiannualbond..If$1,000istheproperpriceforthesemiannualbond,whatistheproperpricefortheannualpaymentbond?SemiannualbondhaskNom=10%,withEFF%=10.25%.ShouldearnsameEFF%onannualpaymentbond,so:INPUTSOUTPUT

1010.25 100 1000 NI/YR PV PMT FV -984.80ComparisonPrice=$1,000couponrate=10%,parvalue=$1,000semiannualbondEFF%=10.25%Price=-$984.80,couponrate=10%,parvalue=$1,000annualbondYTM=10.25%Atapriceof$984.80,theannualandsemiannualbondswouldbeinequilibrium,becauseinvestorswouldearnEFF%=10.25%oneitherbond.A10-year,10%semiannualcoupon,$1,000parvaluebondissellingfor$1,135.90withan8%yieldtomaturity.Itcanbecalledafter5yearsat$1,050.What’sthebond’snominalyieldtocall(YTC)?

10 -1135.950 1050 NI/YR PV PMTFV 3.765x2=7.53% INPUTSOUTPUTkNom=7.53%istheratebrokerswouldquote.CouldalsocalculateEFF%tocall:EFF%=(1.03765)2-1=7.672%.Thisratecouldbecomparedtomonthlymortgages,andsoon.Compare7.53%＜8%EFF%toMaturity:7.672%＜8.16%Ifyouboughtbonds,wouldyoubemorelikelytoearnYTMorYTC?Ingeneral,ifabondsellsatapremium,then(1)coupon>kd,so(2)acallislikely.So,expecttoearn:YTConpremiumbonds.YTMonpar&discountbonds.ExampleDisneyrecentlyissued100-yearbondswithaYTMof7.5%.Doestheyieldtomaturityrepresentthepromisedorexpectedreturnonthebond?Answer:Disneyrecentlyissued100-yearbondswithaYTMof7.5%--thisrepresentsthepromisedreturn.Theexpectedreturnwaslessthan7.5%whenthebondswereissued.Ifissuerdefaults,investorsreceivelessthanthepromisedreturn.Therefore,theexpectedreturnoncorporateandmunicipalbondsislessthanthepromisedreturn.QuestionDisney’sbondswereratedAA—byS&P.Wouldyouconsiderthesebondsinvestinggradeorjunkbonds?BondRatingsProvideOneMeasure

ofDefaultRiskInvestmentGradeJunkBondsMoody’sAaaAaABaaBaBCaaCS&PAAAAAABBBBBBCCCDWhatfactorsaffectdefaultriskandbondratings? FinancialperformanceDebtratioTIE,FCCratiosCurrentratios(More…)ProvisionsinthebondcontractSecuredversusunsecureddebtSeniorversussubordinateddebtGuaranteeprovisionsSinkingfundprovisionsDebtmaturity(More…)OtherfactorsEarningsstabilityRegulatoryenvironmentPotentialproductliabilityAccountingpoliciesTreasuryBondsandCorporateBonds

ManyinvestorsviewTreasurysecuritiesasasafebutboringplacetoinvesttheirfunds.Treasurysecuritiesareamongthesafestinvestments.Changesininterestratescanleadtosignificantchangesinbondvalues,particularlyforlong-termbonds.Becauseofcallanddefaultrisks,corporatebondstradeathigheryieldsthanTreasurybonds.Whenallgoeswell,corporatebondsout-performTreasurysecurities.Butwhenconcernsaboutdefaultaccelerate,corporatebondsdoworsethanTreasuries.Accountingscandalshaveincreasedcorporatebonddefaults,andthathaspushedupthespreadbetweencorporateandTreasurybon