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Tocomputetheyieldtomaturity,usetrialanderrortosolveforrinthefollowingequation:
r=9.119%
Usingafinancialcalculator,computetheyieldtomaturitybyentering
n=6,PV=（）950,FV=1,000,PMT=80;
computei=9.119%.
Verifythesolutionasfollows:
（differenceduetorounding）
5.Inorderforthebondtosellatpar,thecouponratemustequaltheyieldtomaturity.SinceCircularbondsyield9.119%,thismustbethecouponrate.
6.a.Currentyield=coupon/price=$80/$1,100=0.0727=7.27%
b.Tocomputetheyieldtomaturity,usetrialanderrortosolveforrinthefollowingequation:
r=6.3662%
n=8,PV=（）1,100,FV=1,000,PMT=80;
computei=6.3662%.
7.Whenthebondissellingatfacevalue,itsyieldtomaturityequalsitscouponrate.Thisfirm’sbondsaresellingatayieldtomaturityof9.25%.Sothecouponrateonthenewbondsmustbe9.25%iftheyaretosellatfacevalue.
8.Thebondpaysacouponof8.75%,whichmeansannualinterestis$87.50.Thebondissellingfor14419/32=$1,445.9375.Therefore,thecurrentyieldis$87.50/$1445.9375=6.05%.
Thecurrentyieldexceedstheyieldtomaturityonthebondbecausethebondissellingatapremium.Atmaturitytheholderofthebondwillreceiveonlythe$1,000facevalue,reducingthetotalreturnoninvestment.
9.Bond1:
Year1:
Year2:
Usingafinancialcalculator:
PMT=80,FV=1,000,i=10%,n=10;
computePV0=$877.11.
PMT=80,FV=1,000,i=10%,n=9;
computePV1=$884.82.
Rateofreturn=
Bond2:
PMT=120,FV=1,000,i=10%,n=10;
computePV0=$1,122.89.
PMT=120,FV=1,000,i=10%,n=9;
computePV1=$1,115.18.
Bothbondsprovidethesamerateofreturn.
10.a.Ifyieldtomaturity=8%,pricewillbe$1,000.
b.Rateofreturn=
c.Realreturn=
1=
11.a.Withaparvalueof$1,000andacouponrateof8%,thebondholderreceives$80peryear.
b.
c.Iftheyieldtomaturityis6%,thebondwillsellfor:
12.a.Tocomputetheyieldtomaturity,usetrialanderrortosolveforrinthefollowingequation:
r=8.971%
n=30,PV=（）900,FV=1,000,PMT=80;
computei=8.971%.
b.Sincethebondissellingforfacevalue,theyieldtomaturity=8.000%.
c.Tocomputetheyieldtomaturity,usetrialanderrortosolveforrinthefollowingequation:
r=7.180%
n=30,PV=（）1,100,FV=1,000,PMT=80;
computei=7.180%.
06–10
13.a.Tocomputetheyieldtomaturity,usetrialanderrortosolveforrinthefollowingequation:
r=4.483%
n=60,PV=（）900,FV=1,000,PMT=40;
computei=4.483%.
Therefore,theannualizedbondequivalentyieldtomaturityis:
4.483%2=8.966%
b.Sincethebondissellingforfacevalue,thesemiannualyield=4%.
Therefore,theannualizedbondequivalentyieldtomaturityis4%2=8%.
c.Tocomputetheyieldtomaturity,usetrialanderrortosolveforrinthefollowingequation:
r=3.592%
n=60,PV=（）1,100,FV=1,000,PMT=40;
computei=3.592%.
3.592%2=7.184%
14.Ineachcase,wesolvethefollowingequationforthemissingvariable:
Price=$1,000/（1+y）maturity
Price
Maturity（Years）
YieldtoMaturity
$300.00
30.00
4.095%
15.64
8.000%
$385.54
10.00
10.000%
15.PVofperpetuity=couponpayment/rateofreturn
PV=C/r=$60/0.06=$1,000.00
Iftherequiredrateofreturnis10%,thebondsellsfor:
PV=C/r=$60/0.10=$600.00
16.Currentyield=0.098375,sobondpricecanbesolvedfromthefollowing:
$90/price=0.098375price=$914.87
Tocomputetheremainingmaturity,solvefortinthefollowingequation:
t=20.0
Usingafinancialcalculator,computetheremainingmaturitybyentering
PV=（）914.87,FV=1,000,PMT=90,i=10;
computen=20.0years.
17.SolvethefollowingequationforPMT:
PMT=$80.00
Usingafinancialcalculator,computetheannualpaymentbyentering
n=9,PV=（）1,065.15,FV=1,000,i=7;
computePMT=$80.00.
Sincetheannualpaymentis$80,thecouponrateis8%.
18.a.Thecouponratemustbe7%becausethebondswereissuedatfacevaluewithayieldtomaturityof7%.Nowthepriceis:
b.Theinvestorspay$641.01forthebond.Theyexpecttoreceivethepromisedcouponsplus$800atmaturity.Wecalculatetheyieldtomaturitybasedontheseexpectationsbysolvingthefollowingequationforr:
r=12.87%
Usingafinancialcalculator,entern=8,PV=（）641.01,FV=800,PMT=70;
thencomputei=12.87%.
19.a.Atapriceof$1,200andremainingmaturityof9years,findthebond’syieldtomaturitybysolvingforrinthefollowingequation:
r=5.165%
Usingafinancialcalculator,entern=9,PV=（）1,200,FV=1,000,PMT=80;
thencomputei=5.165%.
b.Rateofreturn=
20.
21.a.,b.
PriceofEachBondatDifferentYieldstoMaturity
MaturityofBond
Yield
4Years
8Years
30Years
7%
$1,033.87
$1,059.71
$1,124.09
8%
$1,000.00
9%
$967.60
$944.65
$897.26
c.Thetableshowsthatpricesoflonger-termbondsaremoresensitivetochangesininterestrates.
22.Thepriceofthebondattheendoftheyeardependsontheinterestrateatthattime.With1yearuntilmaturity,thebondpricewillbe$1,080/（1+r）.
a.Price=$1,080/1.06=$1,018.87
Rateofreturn=[$80+（$1,018.87$1,000）]/$1,000=0.0989=9.89%
b.Price=$1,080/1.08=$1,000.00
Rateofreturn=[$80+（$1,000$1,000）]/$1,000=0.0800=8.00%
c.Price=$1,080/1.10=$981.82
Rateofreturn=[$80+（$981.82$1,000）]/$1,000=0.0618=6.18%
23.Theoriginalpriceofthebondiscomputedasfollows:
After1year,thematurityofthebondwillbe29years,anditspricewillbe:
Thecapitallossonthebondis$74.07.Therateofreturnistherefore:
（$40$74.07）/$627.73=0.0543=5.43%
24.Thebond’syieldtomaturitywillincreasefrom7.5%to7.8%whentheperceiveddefaultriskincreases.Thebondpricewillfall:
Initialprice=
Newprice=
25.Thenominalrateofreturnis7%（$70/$1,000）.
Therealrateofreturnis[1.07/（1+inflation）]1.
a.1.07/1.021=0.0392=4.902%
b.1.07/1.041=0.0192=2.885%
c.1.07/1.061=0.009434=0.9434%
d.1.07/1.081=0.00926=0.926%
26.Theprincipalvalueofthebondwillincreasebytheinflationrate,andsincethecouponis4%oftheprincipal,thecouponwillalsoincreasealongwiththegenerallevelofprices.Thetotalcashflowprovidedbythebondwillbe:
1,000（1+inflationrate）+couponrate1,000（1+inflationrate）
Sincethebondispurchasedforfacevalue,or$1,000,totaldollarnominalreturnisthereforetheincreaseintheprincipalduetotheinflationindexing,pluscouponincome:
Income=（$1,000inflationrate）+[couponrate$1,000（1+inflationrate）]
Finally:
Nominalrateofreturn=income/$1,000
a.Nominalrateofreturn=
Realrateofreturn=
b.Nominalrateofreturn=
c.Nominalrateofreturn=
d.Nominalrateofreturn=
27.
First-YearCashFlow
Second-YearCashFlow
a.
$401.02=$40.80
$1,0401.022=$1,082.016
b.
$401.04=$41.60
$1,0401.042=$1,124.864
c.
$401.06=$42.40
$1,0401.062=$1,168.544
d.
$401.08=$43.20
$1,0401.082=$1,213.056
28.Thecouponbondwillfallfromaninitialpriceof$1,000（whenyieldt
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