Corporate Finance RWJ版第7版第五章 答案.docx
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CorporateFinanceRWJ版第7版第五章答案
Chapter5:
HowtoValueBondsandStocks
5.1Thepresentvalueofanypurediscountbondisitsfacevaluediscountedbacktothepresent.
a.PV=F/(1+r)10
=$1,000/(1.05)10
=$613.91
b.PV=$1,000/(1.10)10
=$385.54
c.PV=$1,000/(1.15)10
=$247.19
5.2First,findtheamountofthesemiannualcouponpayment.
SemiannualCouponPayment=AnnualCouponPayment/2
=(0.08$1,000)/2
=$40
a.Sincethestatedannualinterestrateiscompoundedsemiannually,simplydividethisratebytwoinordertocalculatethesemiannualinterestrate.
SemiannualInterestRate=0.08/2
=0.04
Thebondhas40couponpayments(=20years2paymentsperyear).ApplytheannuityformulatocalculatethePVofthe40couponpayments.Inaddition,the$1,000paymentatmaturitymustbediscountedback40periods.
P=CATr+F/(1+r)40
=$40A400.04+$1,000/(1.04)40
=$1,000
Thepriceofthebondis$1,000.Noticethatwheneverthecouponrateandthemarketratearethesame,thebondispricedatpar.Thatis,itsmarketvalueisequaltoitsfacevalue.
b.SemiannualInterestRate=0.10/2
=0.05
P=$40A400.05+$1,000/(1.05)40
=$828.41
Thepriceofthebondis$828.41.Noticethatwheneverthecouponrateisbelowthemarketrate,thebondispricedbelowpar.
c.SemiannualInterestRate=0.06/2
=0.03
P=$40A400.03+$1,000/(1.03)40
=$1,231.15
Thepriceofthebondis$1,231.15.Noticethatwheneverthecouponrateisabovethemarketrate,thebondispricedabovepar.
5.3Sincethepaymentsoccursemiannually,discountthematthesemiannualinterestrate.Converttheeffectiveannualyield(EAY)toasemiannualinterestrate.
SemiannualInterestRate=(1+EAY)1/T–1
=(1.12)1/2–1
=0.0583
a.Calculatethesemiannualcouponpayment.
SemiannualCouponPayment=AnnualCouponPayment/2
=(0.08$1,000)/2
=$40
ApplytheannuityformulatocalculatethePVofthe40couponpayments(=20years2paymentsperyear).Inaddition,the$1,000paymentatmaturitymustbediscountedback40periods.Theappropriatediscountrateisthesemiannualinterestrate.
P=CATr+F/(1+r)40
=$40A400.0583+$1,000/(1.0583)40
=$718.65
Thepriceofthebondis$718.65.
b.Calculatethesemiannualcouponpayment.
SemiannualCouponPayment=(0.10$1,000)/2
=$50
ApplytheannuityformulatocalculatethePVofthe30couponpayments(=15years2paymentsperyear).Inaddition,the$1,000paymentatmaturitymustbediscountedback30periods.Theappropriatediscountrateisthesemiannualinterestrate.
P=$50A300.0583+$1,000/(1.0583)30
=$883.64
Thepriceofthebondis$883.64.
5.4First,calculatethesemiannualinterestrate.
SemiannualInterestRate=(1+EAY)1/T–1
=(1.10)1/2–1
=0.04881
Next,findthesemiannualcouponpayment.
SemiannualCouponPayment=(0.08$1,000)/2
=$40
Thebondhas40payments(=20years2paymentsperyear).ApplytheannuityformulatofindthePVofthecouponpayments.Inaddition,discountthe$1,000paymentatmaturityback40periods.Theappropriatediscountrateisthesemiannualinterestrate.
P=CATr+F/(1+r)40
=$40A400.04881+$1,000/(1.04881)40
=$846.33
Thepriceofthebondis$846.33.
5.5First,calculatethesemiannualinterestrate.
SemiannualInterestRate=0.10/2
=0.05
SetthepriceofthebondequaltothesumofthePVofthe30semiannualcouponpayments(=15years2paymentsperyear)andthePVofthepaymentatmaturity.ThePVofthesemiannualcouponpaymentsshouldbeexpressedasanannuity.SolveforC,thesemiannualcouponpayment.
P=CATr+F/(1+r)30
$923.14=CA300.05+$1,000/(1.05)30
[$923.14–$1,000/(1.05)30]/A300.05=C
$45=C
Tofindthecouponrateonthebond,setthesemiannualcouponpayment,$45,equaltotheproductofthecouponrateandfacevalueofthebond,dividedbytwo.
SemiannualCouponPayment=(CouponRateFaceValue)/2
$45=(CouponRate$1,000)/2
$90=CouponRate$1,000
$90/$1,000=CouponRate
0.09=CouponRate
Theannualcouponrateis9percent.
5.6a.Themarketinterestrateandthecouponrateareequalbecausethebondisselling
atpar.Sincethefacevalueofthebondis$1,000andthesemiannualcouponpaymentis$60,thesemiannualcouponrateissixpercent(=$60/$1,000).Thus,thesemiannualinterestrateisalsosixpercent.Calculatetheyield,expressedasaneffectiveannualyield,bycompoundingthesemiannualinterestrateovertwoperiods.
Yield=(1+r)2–1
=(1.06)2–1
=0.1236
Theyieldis0.1236.
b.YouarewillingtopayapriceequaltothePVofthebond’spayments.TofindthePVofthe12couponpayments,applytheannuityformula,discountedatthesemiannualrateofreturn.Also,discountthe$1,000paymentmadeatmaturitybacktothepresent.Thediscountrate,r,isthesameascalculatedinpart(a).
P=CATr+F/(1+r)12
=$30A120.06+$1,000/(1.06)12
=$748.49
Thepriceofthebondis$748.49.
c.Ifthefive-yearbondpays$40insemiannualpaymentsandispricedatpar,thesemiannualrateofreturnwillbedifferentfromthatinpart(a).Sincethefacevalueofthebondis$1,000andthesemiannualcouponpaymentis$40,thesemiannualinterestrateisfourpercent(=$40/$1,000).Tocalculatethepriceofthebond,applytheannuityformula,discountedatthesemiannualinterestrate.Inaddition,discountthe$1,000paymentmadeatmaturityback12periods.
P=CATr+F/(1+r)12
=$30A120.04+$1,000/(1.04)12
=$906.15
Thepriceofthebondis$906.15.
5.7a.Sincethecouponratesofthebondsareequaltothemarketinterestrate,thebondsare
pricedatfacevalue.Bothbondshavefacevaluesof$1,000.
PA=$1,000
PB=$1,000
b.Discountthecashflowsofthebondsat12percent.Sincethecouponratesofbothbondsarelessthanthemarketinterestrate,thebondswillbepricedatadiscount.
PA=$100A200.12+$1,000/(1.12)20
=$850.61
PB=$100A100.12+$1,000/(1.12)10
=$887.00
c.Discountthecashflowsofthebondsateightpercent.Sincethecouponratesofbothbondsaregreaterthanthemarketinterestrate,thebondswillbepricedatapremium.
PA=$100A200.08+$1,000/(1.08)20
=$1,196.36
PB=$100A100.08+$1,000/(1.08)10
=$1,134.20
5.8a.Thepricesoflong-termbondsshouldfall.ThepriceofanybondisthePVofthecash
flowsassociatedwiththebond.Astheinterestrateincreases,thePVofthosecashflowsfalls.Thiscanbeeasilyseenbylookingataone-year,purediscountbond.
P=$1,000/(1+i)
Asiincreases,thedenominator,(1+i),rises,thusreducingthevalueofthenumerator($1,000).Thepriceofthebonddecreases.
b.Theeffectonstocksisnotasclear-cutastheeffectonbonds.Thenominalinterestrateisafunctionofboththerealinterestrate,r,andtheinflationrate,i.e.,
(1+i)=(1+r)(1+Inflation)
Fromthisrelationshipitiseasytoconcludethat,asinflationrises,thenominalinterestrate,i,rises.However,stockpricesareafunctionofdividendsandfuturepricesaswellastheinterestrate.Thosedividendsandfuturepricesaredeterminedbytheearningpowerofthefirm.Inflationmayincreaseordecreasefirmearnings.Thus,ariseininterestrateshasanuncertaineffectonthegenerallevelofstockprices.
5.9SetthepriceofthebondequaltothePVofitscashflows,discountedattheyieldtomaturity,r.Solveforr.
a.P=CATr+F/(1+r)20
$1,200=$80A20r+$1,000/(1+r)20
r=0.0622
Theyieldtomaturityis6.22percent.
b.$950=$80A10r+$1,000/(1+r)10
r=0.0877
Theyieldtomaturityis8.77percent.
5.10Theappropriatediscountrateisthesemiannualinterestratebecausethebondmakessemiannualpayments.Thus,calculatetheappropriatesemiannualinterestrateforbothbondsAandB.
SemiannualInterestRate=0.12/2
=0.06
a.ThepriceofBondAisthesumofthePVsofeachofitscashflowstreams.ApplythedelayedannuityformulatocalculatethePVofthe16paymentsof$2,000thatbegininyear7aswellastocalculatethePVofthe12paymentsof$2,500thatbegininyear15.Becausethepaymentsaremadesemiannually,thedelayedannuitiesbegininperiods13and29,respectively.ApplyingtheannuityformulawillyieldthePVofastreamasofoneperiodpriortoitsfirstpayment.Thus,applyingtheannuityformulawillyieldthePVofthestreamsasofperiods12and28,respectively.TofindthePVasoftoday(year0)discountthosestreamsback12and28periods,respectively.Also,discountthepaymentmadeatmaturityback40periods.
PA=CATr/(1+r)12+CATr/(1+r)28+F/(1+r)40
=$2,000A160.06/(1.06)12+$2,500A120.06/(1.06)28+$40,000/(1.06)40
=$18,033.86
ThepriceofBondAis$18,033.86.
b.DiscountBondB’sfacevalueback40periodsatthesemiannualinterestrate.
PB=$40,000/(1.06)40
=$3,888.89
ThepriceofBondBis$3,888.89.
5.11a.True.ThebondwiththeshortestmaturityistheATT51/8,whichmaturesin2003.
Itsclosingpriceis100,or100percentofthe$1,000facevalue.
b.True.Thecouponrateofthebondmaturingin2018isninepercent.Thecouponpaymentis$90(=$1,0000.09).
c.True.ThepriceofthebondonFebruary10,2002was1073/8.Sincethatpricemarkeda1/8declinefromthedaybefore,thepriceonFebruary9,2002was1074/8,or$1,075.
d.False.Thecurrentyieldistheannualcouponpaymentdividedbythepriceofthebond.FortheAT&Tbondmaturingin2002,thecurrentyieldis6.84percent(=$
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