投资学10版习题答案14.docx
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投资学10版习题答案14
CHAPTER14:
BONDPRICESANDYIELDS
PROBLEMSETS
1.a.Catastrophebond—Abondthatallowstheissuertotransfer“catastropherisk”fromthefirmtothecapitalmarkets.Investorsinthesebondsreceiveacompensationfortakingontheriskintheformofhighercouponrates.Intheeventofacatastrophe,thebondholderswillreceiveonlypartorperhapsnoneoftheprincipalpaymentduetothematmaturity.DisastercanbedefinedbytotalinsuredlossesorbycriteriasuchaswindspeedinahurricaneorRichterlevelinanearthquake.
b.Eurobond—Abondthatisdenominatedinonecurrency,usuallythatoftheissuer,butsoldinothernationalmarkets.
c.Zero-couponbond—Abondthatmakesnocouponpayments.Investorsreceiveparvalueatthematuritydatebutreceivenointerestpaymentsuntilthen.Thesebondsareissuedatpricesbelowparvalue,andtheinvestor’sreturncomesfromthedifferencebetweenissuepriceandthepaymentofparvalueatmaturity（capitalgain）.
d.Samuraibond—Yen-dominatedbondssoldinJapanbynon-Japaneseissuers.
e.Junkbond—Abondwithalowcreditratingduetoitshighdefaultrisk;alsoknownashigh-yieldbonds.
f.Convertiblebond—Abondthatgivesthebondholdersanoptiontoexchangethebondforaspecifiednumberofsharesofcommonstockofthefirm.
g.Serialbonds—Bondsissuedwithstaggeredmaturitydates.Asbondsmaturesequentially,theprincipalrepaymentburdenforthefirmisspreadovertime.
h.Equipmentobligationbond—Acollateralizedbondforwhichthecollateralisequipmentownedbythefirm.Ifthefirmdefaultsonthebond,thebondholderswouldreceivetheequipment.
i.Originalissuediscountbond—Abondissuedatadiscounttothefacevalue.
j.Indexedbond—Abondthatmakespaymentsthataretiedtoageneralpriceindexorthepriceofaparticularcommodity.
k.Callablebond—Abondthatgivestheissuertheoptiontorepurchasethebondataspecifiedcallpricebeforethematuritydate.
l.Puttablebond—Abondthatgivesthebondholdertheoptiontosellbackthebondataspecifiedputpricebeforethematuritydate.
2.Thebondcallableat105shouldsellatalowerpricebecausethecallprovisionismorevaluabletothefirm.Therefore,itsyieldtomaturityshouldbehigher.
3.Zerocouponbondsprovidenocouponstobereinvested.Therefore,theinvestor'sproceedsfromthebondareindependentoftherateatwhichcouponscouldbereinvested（iftheywerepaid）.Thereisnoreinvestmentrateuncertaintywithzeros.
4.Abond’scouponinterestpaymentsandprincipalrepaymentarenotaffectedbychangesinmarketrates.Consequently,ifmarketratesincrease,bondinvestorsinthesecondarymarketsarenotwillingtopayasmuchforaclaimonagivenbond’sfixedinterestandprincipalpaymentsastheywouldifmarketrateswerelower.Thisrelationshipisapparentfromtheinverserelationshipbetweeninterestratesandpresentvalue.Anincreaseinthediscountrate（i.e.,themarketrate.decreasesthepresentvalueofthefuturecashflows.
5.Annualcouponrate:
4.80%→$48Couponpayments
Currentyield:
6.a.Effectiveannualratefor3-monthT-bill:
b.Effectiveannualinterestrateforcouponbondpaying5%semiannually:
.2—1=0.1025or10.25%
Thereforethecouponbondhasthehighereffectiveannualinterestrate.
7.Theeffectiveannualyieldonthesemiannualcouponbondsis8.16%.Iftheannualcouponbondsaretosellatpartheymustofferthesameyield,whichrequiresanannualcouponrateof8.16%.
8.Thebondpricewillbelower.Astimepasses,thebondprice,whichisnowaboveparvalue,willapproachpar.
9.Yieldtomaturity:
Usingafinancialcalculator,enterthefollowing:
n=3;PV=-953.10;FV=1000;PMT=80;COMPi
Thisresultsin:
YTM=9.88%
Realizedcompoundyield:
First,findthefuturevalue（FV.ofreinvestedcouponsandprincipal:
FV=（$80*1.10*.+（$80*.
Thenfindtherate（yrealized.thatmakestheFVofthepurchasepriceequalto$1,268.16:
$953.10⨯（1+yrealized.3=$1,268.16⇒yrealized=9.99%orapproximately10%
Usingafinancialcalculator,enterthefollowing:
N=3;PV=-953.10;FV=1;PMT=0;COMP%.
10.
a.
Zerocoupon
8%coupon
10%coupon
Currentprices
b.Price1yearfromnow
Priceincrease
Couponincome
Pretaxincome
Pretaxrateofreturn
8.00%
8.00%
8.00%
Taxes*
After-taxincome
After-taxrateofreturn
5.60%
5.60%
5.52%
c.Price1yearfromnow
Priceincrease
Couponincome
Pretaxincome
Pretaxrateofreturn
17.43%
14.52%
14.22%
Taxes†
After-taxincome
After-taxrateofreturn
13.14%
10.81%
10.49%
*Incomputingtaxes,weassumethatthe10%couponbondwasissuedatparandthatthedecreaseinpricewhenthebondissoldatyear-endistreatedasacapitallossandthereforeisnottreatedasanoffsettoordinaryincome.
†Incomputingtaxesforthezerocouponbond,$37.06istaxedasordinaryincome（seepart（b）;theremainderofthepriceincreaseistaxedasacapitalgain.
11.a.Onafinancialcalculator,enterthefollowing:
n=40;FV=1000;PV=–950;PMT=40
Youwillfindthattheyieldtomaturityonasemiannualbasisis4.26%.Thisimpliesabondequivalentyieldtomaturityequalto:
4.26%*2=8.52%
Effectiveannualyieldtomaturity=（1.0426）2–1=0.0870=8.70%
b.Sincethebondissellingatpar,theyieldtomaturityonasemiannualbasisisthesameasthesemiannualcouponrate,i.e.,4%.Thebondequivalentyieldtomaturityis8%.
Effectiveannualyieldtomaturity=（1.04）2–1=0.0816=8.16%
c.KeepingotherinputsunchangedbutsettingPV=–1050,wefindabondequivalentyieldtomaturityof7.52%,or3.76%onasemiannualbasis.
Effectiveannualyieldtomaturity=（1.0376）2–1=0.0766=7.66%
12.Sincethebondpaymentsarenowmadeannuallyinsteadofsemiannually,thebondequivalentyieldtomaturityisthesameastheeffectiveannualyieldtomaturity.[Onafinancialcalculator,n=20;FV=1000;PV=–price;PMT=80]
Theresultingyieldsforthethreebondsare:
BondPrice
BondEquivalentYield=
EffectiveAnnualYield
$950
8.53%
1,000
1,050
Theyieldscomputedinthiscasearelowerthantheyieldscalculatedwithsemiannualpayments.Allelseequal,bondswithannualpaymentsarelessattractivetoinvestorsbecausemoretimeelapsesbeforepaymentsarereceived.Ifthebondpriceisthesamewithannualpayments,thenthebond'syieldtomaturityislower.
13.
Price
Maturity
（years.
BondEquivalent
YTM
4.688%
14.a.Thebondpays$50every6months.Thecurrentpriceis:
[$50×Annuityfactor（4%,6）]+[$1,000×
Alternatively,PMT=$50;FV=$1,000;I=4;N=6.SolveforPV=$1,052.42.
Ifthemarketinterestrateremains4%perhalfyear,pricesixmonthsfromnowis:
[$50×Annuityfactor（4%,5）]+[$1,000×
Alternatively,PMT=$50;FV=$1,000;I=4;N=5.SolveforPV=$1,044.52.
b.Rateofreturn
15.Thereportedbondpriceis:
$1,001.250
However,15dayshavepassedsincethelastsemiannualcouponwaspaid,so:
Accruedinterest=$35*
Theinvoicepriceisthereportedpriceplusaccruedinterest:
$1,004.14
16.Iftheyieldtomaturityisgreaterthanthecurrentyield,thenthebondofferstheprospectofpriceappreciationasitapproachesitsmaturitydate.Therefore,thebondmustbesellingbelowparvalue.
17.Thecouponrateislessthan9%.Ifcoupondividedbypriceequals9%,andpriceislessthanpar,thenpricedividedbyparislessthan9%.
18.
Time
Inflation
inYearJust
Ended
ParValue
Coupon
Payment
Principal
Repayment
0
1
2%
2
3%
3
1%
Thenominalrateofreturnandrealrateofreturnonthebondineachyeararecomputedasfollows:
Nominalrateofreturn=
Realrateofreturn=
SecondYear
ThirdYear
Nominalreturn
Realreturn
Therealrateofreturnineachyearispreciselythe4%realyieldonthebond.
19.Thepricescheduleisasfollows:
Year
Remaining
Maturity（T）.
ConstantYieldValue$1,000/（1.08）T
ImputedInterest
（increaseinconstant
yieldvalue）
0（now）
20years
1
19
2
18
19
1
20
0
20.Thebondisissuedatapriceof$800.Therefore,itsyieldtomaturityis:
6.8245%
Therefore,usingtheconstantyieldmethod,wefindthatthepriceinoneyear（whenmaturityfallsto9years）willbe（atanunchangedyield..
21.a.Thebondsellsfor$1,124.72basedonthe3.5%yieldtomaturity.
[n=60;i=3.5;FV=1000;PMT=40]
Therefore,yieldtocallis3.368%semiannually,6.736%annually.
[n=10semiannualperiods;PV=–1124.72;FV=1100;PMT=40]
b.Ifthecallpricewere$1,050,wewouldsetFV=1,050andredopart（a）tofindthatyieldtocallis2.976%semiannually,5.952%annually.Withalowercallprice,theyieldtocallislower.
c.Yieldtocallis3.031%semiannually,6.062%annually.
[n=4;PV=−1124.72;FV=1100;PMT=40]
22.Thestatedyieldtomaturity,basedonpromisedpayments,equals16.075%.
[n=10;PV=–900;FV=1000;PMT=140]
Basedonexpectedreducedcouponpaymentsof$70annually,theexpectedyieldtomaturityis8.526%.
23.Thebondissellingatparvalue.Itsyieldtomaturityequalsthecouponrate,10%.Ifthefirst-yearcouponisreinvestedataninterestrateofrpercent,thentotalproceedsattheendofthesecondyearwillbe:
[$100*（1+r）]+$1,100
Therefore,realizedcompoundyieldtomaturityisafunctionofr,asshowninth
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