corporate finance Chap006new.docx
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corporate finance Chap006new.docx
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corporatefinanceChap006new
SolutionstoChapter6
ValuingBonds
1.a.Couponrate=6%,whichremainsunchanged.Thecouponpaymentsarefixedat$60peryear.
b.Whenthemarketyieldincreases,thebondpricewillfall.Thecashflowsarediscountedatahigherrate.
c.Atalowerprice,thebond’syieldtomaturitywillbehigher.Thehigheryieldtomaturityforthebondiscommensuratewiththehigheryieldsavailableintherestofthebondmarket.
d.Currentyield=couponrate/bondprice
Asthecouponrateremainsthesameandthebondpricedecreases,thecurrentyieldincreases.
Esttime:
01–05
2.Whenthebondissellingatadiscount,$970inthiscase,theyieldtomaturityisgreaterthan8%.Weknowthatiftheyieldtomaturitywere8%,thebondwouldsellatpar.Atapricebelowpar,theyieldtomaturityexceedsthecouponrate.
Esttime:
01–05
3.Couponpayment=0.08$1,000=$80
Currentyield=$80/bondprice=0.06
Therefore:
Bondprice=$80/0.06=$1,333.33
Esttime:
01–05
4.Couponrate=$80/$1,000=0.080=8.0%
Tocomputetheyieldtomaturity,usetrialanderrortosolveforrinthefollowingequation:
r=9.119%
Usingafinancialcalculator,computetheyieldtomaturitybyentering
n=6,PV=()950,FV=1,000,PMT=80;computei=9.119%.
Verifythesolutionasfollows:
(differenceduetorounding)
Esttime:
01–05
5.Inorderforthebondtosellatpar,thecouponratemustequaltheyieldtomaturity.SinceCircularbondsyield9.119%,thismustbethecouponrate.
Esttime:
01–05
6.a.Currentyield=coupon/price=$80/$1,100=0.0727=7.27%
b.Tocomputetheyieldtomaturity,usetrialanderrortosolveforrinthefollowingequation:
r=6.3662%
Usingafinancialcalculator,computetheyieldtomaturitybyentering
n=8,PV=()1,100,FV=1,000,PMT=80;computei=6.3662%.
Esttime:
01–05
7.Whenthebondissellingatfacevalue,itsyieldtomaturityequalsitscouponrate.Thisfirm’sbondsaresellingatayieldtomaturityof9.25%.Sothecouponrateonthenewbondsmustbe9.25%iftheyaretosellatfacevalue.
Esttime:
01–05
8.Thebondpaysacouponof8.75%,whichmeansannualinterestis$87.50.Thebondissellingfor14419/32=$1,445.9375.Therefore,thecurrentyieldis$87.50/$1445.9375=6.05%.
Thecurrentyieldexceedstheyieldtomaturityonthebondbecausethebondissellingatapremium.Atmaturitytheholderofthebondwillreceiveonlythe$1,000facevalue,reducingthetotalreturnoninvestment.
Esttime:
01–05
9.Bond1:
Year1:
Year2:
Usingafinancialcalculator:
Year1:
PMT=80,FV=1,000,i=10%,n=10;computePV0=$877.11.
Year2:
PMT=80,FV=1,000,i=10%,n=9;computePV1=$884.82.
Rateofreturn=
Bond2:
Year1:
Year2:
Usingafinancialcalculator:
Year1:
PMT=120,FV=1,000,i=10%,n=10;computePV0=$1,122.89.
Year2:
PMT=120,FV=1,000,i=10%,n=9;computePV1=$1,115.18.
Rateofreturn=
Bothbondsprovidethesamerateofreturn.
Esttime:
01–05
10.a.Ifyieldtomaturity=8%,pricewillbe$1,000.
b.Rateofreturn=
c.Realreturn=
1=
Esttime:
01–05
11.a.Withaparvalueof$1,000andacouponrateof8%,thebondholderreceives$80peryear.
b.
c.Iftheyieldtomaturityis6%,thebondwillsellfor:
Esttime:
01–05
12.a.Tocomputetheyieldtomaturity,usetrialanderrortosolveforrinthefollowingequation:
r=8.971%
Usingafinancialcalculator,computetheyieldtomaturitybyentering
n=30,PV=()900,FV=1,000,PMT=80;computei=8.971%.
Verifythesolutionasfollows:
(differenceduetorounding)
b.Sincethebondissellingforfacevalue,theyieldtomaturity=8.000%.
c.Tocomputetheyieldtomaturity,usetrialanderrortosolveforrinthefollowingequation:
r=7.180%
Usingafinancialcalculator,computetheyieldtomaturitybyentering
n=30,PV=()1,100,FV=1,000,PMT=80;computei=7.180%.
Verifythesolutionasfollows:
(differenceduetorounding)
Esttime:
06–10
13.a.Tocomputetheyieldtomaturity,usetrialanderrortosolveforrinthefollowingequation:
r=4.483%
Usingafinancialcalculator,computetheyieldtomaturitybyentering
n=60,PV=()900,FV=1,000,PMT=40;computei=4.483%.
Verifythesolutionasfollows:
(differenceduetorounding)
Therefore,theannualizedbondequivalentyieldtomaturityis:
4.483%2=8.966%
b.Sincethebondissellingforfacevalue,thesemiannualyield=4%.
Therefore,theannualizedbondequivalentyieldtomaturityis4%2=8%.
c.Tocomputetheyieldtomaturity,usetrialanderrortosolveforrinthefollowingequation:
r=3.592%
Usingafinancialcalculator,computetheyieldtomaturitybyentering
n=60,PV=()1,100,FV=1,000,PMT=40;computei=3.592%.
Verifythesolutionasfollows:
(differenceduetorounding)
Therefore,theannualizedbondequivalentyieldtomaturityis:
3.592%2=7.184%
Esttime:
06–10
14.Ineachcase,wesolvethefollowingequationforthemissingvariable:
Price=$1,000/(1+y)maturity
Price
Maturity(Years)
YieldtoMaturity
$300.00
30.00
4.095%
$300.00
15.64
8.000%
$385.54
10.00
10.000%
Esttime:
01–05
15.PVofperpetuity=couponpayment/rateofreturn
PV=C/r=$60/0.06=$1,000.00
Iftherequiredrateofreturnis10%,thebondsellsfor:
PV=C/r=$60/0.10=$600.00
Esttime:
01–05
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.
Esttime:
01–05
17.SolvethefollowingequationforPMT:
PMT=$80.00
Usingafinancialcalculator,computetheannualpaymentbyentering
n=9,PV=()1,065.15,FV=1,000,i=7;computePMT=$80.00.
Sincetheannualpaymentis$80,thecouponrateis8%.
Esttime:
01–05
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%.
Esttime:
06–10
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=
Esttime:
01–05
20.
Rateofreturn=
Esttime:
01–05
21.a.,b.
PriceofEachBondatDifferentYieldstoMaturity
MaturityofBond
Yield
4Years
8Years
30Years
7%
$1,033.87
$1,059.71
$1,124.09
8%
$1,000.00
$1,000.00
$1,000.00
9%
$967.60
$944.65
$897.26
c.Thetableshowsthatpricesoflonger-termbondsaremoresensitivetochangesininterestrates.
Esttime:
06–10
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%
Esttime:
01–05
23.Theoriginalpriceofthebondiscomputedasfollows:
After1year,thematurityofthebondwillbe29years,anditspricewillbe:
Thecapitallossonthebondis$74.07.Therateofreturnistherefore:
($40$74.07)/$627.73=0.0543=5.43%
Esttime:
06–10
24.Thebond’syieldtomaturitywillincreasefrom7.5%to7.8%whentheperceiveddefaultriskincreases.Thebondpricewillfall:
Initialprice=
Newprice=
Esttime:
01–05
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%
Esttime:
01–05
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=
Realrateofreturn=
c.Nominalrateofreturn=
Realrateofreturn=
d.Nominalrateofreturn=
Realrateofreturn=
Esttime:
06–10
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
Esttime:
06–10
28.Thecouponbondwillfallfromaninitialpriceof$1,000(whenyieldt
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