博迪投资学第九版 Investment Chap014 习题答案.docx

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