投资学10版习题答案.docx
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投资学10版习题答案
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:
（1.05.2—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*1.12.+（$80*1.12.+$1,080=$1,268.16
Thenfindtherate（yrealized.thatmakestheFVofthepurchasepriceequalto$1,268.16:
$953.10（1+yrealized.3=$1,268.16yrealized=9.99%orapproximately10%
Usingafinancialcalculator,enterthefollowing:
N=3;PV=953.10;FV=1,268.16;PMT=0;COMPI.Answeris9.99%.
10.
a.
Zerocoupon
8%coupon
10%coupon
Currentprices
$463.19
$1,000.00
$1,134.20
b.Price1yearfromnow
$500.25
$1,000.00
$1,124.94
Priceincrease
$37.06
$0.00
−$9.26
Couponincome
$0.00
$80.00
$100.00
Pretaxincome
$37.06
$80.00
$90.74
Pretaxrateofreturn
8.00%
8.00%
8.00%
Taxes*
$11.12
$24.00
$28.15
After-taxincome
$25.94
$56.00
$62.59
After-taxrateofreturn
5.60%
5.60%
5.52%
c.Price1yearfromnow
$543.93
$1,065.15
$1,195.46
Priceincrease
$80.74
$65.15
$61.26
Couponincome
$0.00
$80.00
$100.00
Pretaxincome
$80.74
$145.15
$161.26
Pretaxrateofreturn
17.43%
14.52%
14.22%
Taxes†
$19.86
$37.03
$42.25
After-taxincome
$60.88
$108.12
$119.01
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
8.00
1,050
7.51
Theyieldscomputedinthiscasearelowerthantheyieldscalculatedwithsemiannualpayments.Allelseequal,bondswithannualpaymentsarelessattractivetoinvestorsbecausemoretimeelapsesbeforepaymentsarereceived.Ifthebondpriceisthesamewithannualpayments,thenthebond'syieldtomaturityislower.
13.
Price
Maturity
（years.
BondEquivalent
YTM
$400.00
20.00
4.688%
500.00
20.00
3.526
500.00
10.00
7.177
385.54
10.00
10.000
463.19
10.00
8.000
400.00
11.91
8.000
14.a.Thebondpays$50every6months.Thecurrentpriceis:
[$50×Annuityfactor（4%,6）]+[$1,000×PVfactor（4%,6）]=$1,052.42
Alternatively,PMT=$50;FV=$1,000;I=4;N=6.SolveforPV=$1,052.42.
Ifthemarketinterestrateremains4%perhalfyear,pricesixmonthsfromnowis:
[$50×Annuityfactor（4%,5）]+[$1,000×PVfactor（4%,5）]=$1,044.52
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*（15/182）=$2.885
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
$1,000.00
1
2%
1,020.00
$40.80
$0.00
2
3%
$1,050.60
$42.02
$0.00
3
1%
$1,061.11
$42.44
$1,061.11
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
$214.55
1
19
231.71
$17.16
2
18
250.25
18.54
19
1
925.93
20
0
1,000.00
74.07
20.Thebondisissuedatapriceof$800.Therefore,itsyieldtomaturityis:
6.8245%
Therefore,usingtheconstantyieldmethod,wefindthatthepriceinoneyear（whenmaturityfallsto9years）willbe（atanunchangedyield.$814.60,representinganincreaseof$14.60.Totaltaxableincomeis:
$40.00+$14.60=$54.60
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,5.95
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