投资学10版习题答案14Word下载.docx

投资学10版习题答案14Word下载.docx

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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;

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

$1,124.94

Priceincrease

$37.06

$0.00

−$9.26

Couponincome

$80.00

$100.00

Pretaxincome

$90.74

Pretaxrateofreturn

8.00%

Taxes*

$11.12

$24.00

$28.15

After-taxincome

$25.94

$56.00

$62.59

After-taxrateofreturn

5.60%

5.52%

c.Price1yearfromnow

$543.93

$1,065.15

$1,195.46

$80.74

$65.15

$61.26

$145.15

$161.26

17.43%

14.52%

14.22%

Taxes†

$19.86

$37.03

$42.25

$60.88

$108.12

$119.01

13.14%

10.81%

10.49%

*Incomputingtaxes,weassumethatthe10%couponbondwasissuedatparandthatthedecreaseinpricewhenthebondissoldatyear-endistreatedasacapitallossandthereforeisnottreatedasanoffsettoordinaryincome.

†Incomputingtaxesforthezerocouponbond,$37.06istaxedasordinaryincome（seepart（b）;

theremainderofthepriceincreaseistaxedasacapitalgain.

11.a.Onafinancialcalculator,enterthefollowing:

n=40;

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;

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

3.526

10.00

7.177

385.54

10.000

463.19

8.000

400.00

11.91

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:

Annuityfactor（4%,5）]+[$1,000×

PVfactor（4%,5）]=$1,044.52

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

1

2%

1,020.00

$40.80

2

3%

$1,050.60

$42.02

3

1%

$1,061.11

$42.44

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

19

231.71

$17.16

18

250.25

18.54

925.93

20

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;

PMT=40]

Therefore,yieldtocallis3.368%semiannually,6.736%annually.

[n=10semiannualperiods;

PV=–1124.72;

FV=1100;

b.Ifthecallpricewere$1,050,wewouldsetFV=1,050andredopart（a）tofindthatyieldtocallis2.976%semiannually,5.952%annually.