博迪投资学第九版 Investment Chap014 习题答案.docx
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博迪投资学第九版 Investment Chap014 习题答案.docx
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博迪投资学第九版InvestmentChap014习题答案
CHAPTER14:
BONDPRICESANDYIELDS
PROBLEMSETS
1.a)Catastrophebond–Abondthatallowstheissuertotransfer“catastropherisk”fromthefirmtothecapitalmarkets.Investorsinthesebondsreceiveacompensationfortakingontheriskintheformofhighercouponrates.Intheeventofacatastrophe,thebondholderswillgiveupallorpartoftheirinvestments.“Disaster”canbedefinedbytotalinsuredlossesorbycriteriasuchaswindspeedinahurricaneorRichterlevelinanearthquake.
b)Eurobond–Abondthatisdenominatedinonecurrency,usuallythatoftheissuer,butsoldinothernationalmarkets.
c)Zero-couponbond–Abondthatmakesnocouponpayments.Investorsreceiveparvalueatthematuritydatebutreceivenointerestpaymentsuntilthen.Thesebondsareissuedatpricesbelowparvalue,andtheinvestor’sreturncomesfromthedifferencebetweenissuepriceandthepaymentofparvalueatmaturity.
d)Samuraibond–Yen-dominatedbondssoldinJapanbynon-Japaneseissuers.
e)Junkbond–Abondwithalowcreditratingduetoitshighdefaultrisk.Theyarealsoknownashigh-yieldbonds.
f)Convertiblebond–Abondthatgivesthebondholdersanoptiontoexchangethebondforaspecifiednumberofsharesofcommonstockofthefirm.
g)Serialbonds–Bondsissuedwithstaggeredmaturitydates.Asbondsmaturesequentially,theprincipalrepaymentburdenforthefirmisspreadovertime.
h)Equipmentobligationbond–Acollateralizedbondinwhichthecollateralisequipmentownedbythefirm.Ifthefirmdefaultsonthebond,thebondholderswouldreceivetheequipment.
i)Originalissuediscountbond–Abondissuedatadiscounttothefacevalue.
j)Indexedbond–Abondthatmakespaymentsthataretiedtoageneralpriceindexorthepriceofaparticularcommodity.
k)Callablebond–Abondwhichallowstheissuertorepurchasethebondataspecifiedcallpricebeforethematuritydate.
l)Puttablebond–Abondwhichallowsthebondholdertosellbackthebondataspecifiedputpricebeforethematuritydate.
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%
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
Pre-taxincome
$37.06
$80.00
$90.74
Pre-taxrateofreturn
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
Pre-taxincome
$80.74
$145.15
$161.26
Pre-taxrateofreturn
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%couponbondwasissuedatparandthatthedecreaseinpricewhenthebondissoldatyearendistreatedasacapitallossandthereforeisnottreatedasanoffsettoordinaryincome.
**Incomputingtaxesforthezerocouponbond,$37.06istaxedasordinaryincome(seepart(b));theremainderofthepriceincreaseistaxedasacapitalgain.
11.a.Onafinancialcalculator,enterthefollowing:
n=40;FV=1000;PV=–950;PMT=40
Youwillfindthattheyieldtomaturityonasemi-annualbasisis4.26%.Thisimpliesabondequivalentyieldtomaturityequalto:
4.26%*2=8.52%
Effectiveannualyieldtomaturity=(1.0426)2–1=0.0870=8.70%
b.Sincethebondissellingatpar,theyieldtomaturityonasemi-annualbasisisthesameasthesemi-annualcouponrate,i.e.,4%.Thebondequivalentyieldtomaturityis8%.
Effectiveannualyieldtomaturity=(1.04)2–1=0.0816=8.16%
c.KeepingotherinputsunchangedbutsettingPV=–1050,wefindabondequivalentyieldtomaturityof7.52%,or3.76%onasemi-annualbasis.
Effectiveannualyieldtomaturity=(1.0376)2–1=0.0766=7.66%
12.Sincethebondpaymentsarenowmadeannuallyinsteadofsemi-annually,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%
Theyieldscomputedinthiscasearelowerthantheyieldscalculatedwithsemi-annualpayments.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
Ifthemarketinterestrateremains4%perhalfyear,pricesixmonthsfromnowis:
[$50×Annuityfactor(4%,5)]+[$1,000×PVfactor(4%,5)]=$1,044.52
b.Rateofreturn
15.Thereportedbondpriceis:
1002/32percentofpar=$1,000.625
However,15dayshavepassedsincethelastsemiannualcouponwaspaid,so:
accruedinterest=$35*(15/182)=$2.885
Theinvoicepriceisthereportedpriceplusaccruedinterest:
$1,003.51
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,5.952%annually.Withalowercallprice,theyieldtocallislower.
c.Yieldtocallis3.031%semiannually,6.062%annually.
[n=4;PV=−1124.72;FV=1100;PMT=40]
22.Thestatedyieldtomaturity,basedonpromisedpayments,eq
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