SolutionsCh78.docx

SolutionsCh78.docx

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SolutionsCh78

ANSWERSTOEND-OF-CHAPTERQUESTIONS:

Chapter7

7-1Yes,thestatementistrue.

7-2False.Short-termbondpricesarelesssensitivethanlong-termbondpricestointerestratechangesbecausefundsinvestedinshort-termbondscanbereinvestedatthenewinterestratesoonerthanfundstiedupinlong-termbonds.

7-3ThepriceofthebondwillfallanditsYTMwillriseifinterestratesrise.Ifthebondstillhasalongtermtomaturity,itsYTMwillreflectlong-termrates.Ofcourse,thebond’spricewillbelessaffectedbyachangeininterestratesifithasbeenoutstandingalongtimeandmaturesshortly.Whilethisistrue,itshouldbenotedthattheYTMwillincreaseonlyforbuyerswhopurchasethebondafterthechangeininterestratesandnotforbuyerswhopurchasedprevioustothechange.

Ifthebondispurchasedandheldtomaturity,thebondholder’sYTMwillnotchange,regardlessofwhathappenstointerestrates.

7-4Ifinterestratesdeclinesignificantly,thevaluesofcallablebondswillnotrisebyasmuchasthoseofbondswithoutthecallprovision.Itislikelythatthebondswouldbecalledbytheissuerbeforematurity,sothattheissuercantakeadvantageofthenew,lowerrates.

7-5Fromthecorporation’sviewpoint,oneimportantfactorinestablishingasinkingfundisthatitsownbondsgenerallyhaveahigheryieldthandogovernmentbonds;hence,thecompanysavesmoreinterestbyretiringitsownbondsthanitcouldearnbybuyinggovernmentbonds.Thisfactorcausesfirmstofavorthesecondprocedure.Investorsalsowouldprefertheannualretirementprocedureiftheythoughtthatinterestratesweremorelikelytorisethantofall,buttheywouldpreferthegovernmentbondpurchaseprogramiftheythoughtrateswerelikelytofall.Inaddition,bondholdersrecognizethat,underthegovernmentbondpurchasescheme,eachbondholderwouldbeentitledtoagivenamountofcashfromtheliquidationofthesinkingfundifthefirmshouldgointodefault,whereasundertheannualretirementplan,someoftheholderswouldreceiveacashbenefitwhileotherswouldbenefitonlyindirectlyfromthefactthattherewouldbefewerbondsoutstanding.

Onbalance,investorsseemtohavelittlereasonforchoosingonemethodovertheother,whiletheannualretirementmethodisclearlymorebeneficialtothefirm.Theconsequencehasbeenapronouncedtrendtowardannualretirementandawayfromtheaccumulationscheme.

7-6a.Ifabond’spriceincreases,itsYTMdecreases.

b.Ifacompany’sbondsaredowngradedbytheratingagencies,itsYTMincreases.

c.Ifachangeinthebankruptcycodemadeitmoredifficultforbondholderstoreceivepaymentsintheeventafirmdeclaredbankruptcy,thenthebond’sYTMwouldincrease.

d.Iftheeconomyenteredarecession,thenthepossibilityofafirmdefaultingonitsbondwouldincrease;consequently,itsYTMwouldincrease.

e.Ifabondweretobecomesubordinatedtoanotherdebtissue,thenthebond’sYTMwouldincrease.

7-7Asaninvestorwithashortinvestmenthorizon,Iwouldviewthe20-yearTreasurysecurityasbeingmoreriskythanthe1-yearTreasurysecurity.IfIboughtthe20-yearsecurity,Iwouldbearaconsiderableamountofinterestraterisk.Sincemyinvestmenthorizonisonlyoneyear,Iwouldhavetosellthe20-yearsecurityoneyearfromnow,andthepriceIwouldreceiveforitwoulddependonwhathappenedtointerestratesduringthatyear.However,ifIpurchasedthe1-yearsecurityIwouldbeassuredofreceivingmyprincipalattheendofthatoneyear,whichisthe1-yearTreasury’smaturitydate.

SOLUTIONSTOEND-OF-CHAPTERPROBLEMS

7-1Withyourfinancialcalculator,enterthefollowing:

N=10;I=YTM=9%;PMT=0.081,000=80;FV=1000;PV=VB=?

PV=$935.82.

7-2Withyourfinancialcalculator,enterthefollowingtofindYTM:

N=102=20;PV=-1100;PMT=0.08/21,000=40;FV=1000;I=YTM=?

YTM=3.31%2=6.62%.

Withyourfinancialcalculator,enterthefollowingtofindYTC:

N=52=10;PV=-1100;PMT=0.08/21,000=40;FV=1050;I=YTC=?

YTC=3.24%2=6.49%.

7-3Theproblemasksyoutofindthepriceofabond,giventhefollowingfacts:

N=16;I=8.5/2=4.25;PMT=45;FV=1000.

Withafinancialcalculator,solveforPV=$1,028.60.

7-4VB=$985;M=$1,000;Int=0.07$1,000=$70.

a.Currentyield=Annualinterest/Currentpriceofbond

=$70/$985.00

=7.11%.

b.N=10;PV=-985;PMT=70;FV=1000;YTM=?

SolveforI=YTM=7.2157%7.22%.

c.N=7;I=7.2157;PMT=70;FV=1000;PV=?

SolveforVB=PV=$988.46.

7-5a.1.5%:

BondL:

InputN=15,I=5,PMT=100,FV=1000,PV=?

PV=$1,518.98.

BondS:

ChangeN=1,PV=?

PV=$1,047.62.

2.8%:

BondL:

FromBondSinputs,changeN=15andI=8,PV=?

PV=$1,171.19.

BondS:

ChangeN=1,PV=?

PV=$1,018.52.

3.12%:

BondL:

FromBondSinputs,changeN=15andI=12,PV=?

PV=$863.78.

BondS:

ChangeN=1,PV=?

PV=$982.14.

b.Thinkaboutabondthatmaturesinonemonth.Itspresentvalueisinfluencedprimarilybythematurityvalue,whichwillbereceivedinonlyonemonth.Evenifinterestratesdouble,thepriceofthebondwillstillbecloseto$1,000.A1-yearbond’svaluewouldfluctuatemorethantheone-monthbond’svaluebecauseofthedifferenceinthetimingofreceipts.However,itsvaluewouldstillbefairlycloseto$1,000evenifinterestratesdoubled.Along-termbondpayingsemiannualcoupons,ontheotherhand,willbedominatedbydistantreceipts,receiptsthataremultipliedby1/（1+kd/2）t,andifkdincreases,thesemultiplierswilldecreasesignificantly.Anotherwaytoviewthisproblemisfromanopportunitypointofview.A1-monthbondcanbereinvestedatthenewrateveryquickly,andhencetheopportunitytoinvestatthisnewrateisnotlost;however,thelong-termbondlocksinsubnormalreturnsforalongperiodoftime.

7-6a.VB=

M=$1,000.I=0.09（$1,000）=$90.

1.VB=$829:

InputN=4,PV=-829,PMT=90,FV=1000,I=?

I=14.99%.

2.VB=$1,104:

ChangePV=-1104,I=?

I=6.00%.

b.Yes.Atapriceof$829,theyieldtomaturity,15percent,isgreaterthanyourrequiredrateofreturnof12percent.Ifyourrequiredrateofreturnwere12percent,youshouldbewillingtobuythebondatanypricebelow$908.88.

7-7Therateofreturnisapproximately15.03percent,foundwithacalculatorusingthefollowinginputs:

N=6;PV=-1000;PMT=140;FV=1090;I=?

SolveforI=15.03%.

7-8a.Usingafinancialcalculator,inputthefollowing:

N=20,PV=-1100,PMT=60,FV=1000,andsolveforI=5.1849%.

However,thisisaperiodicrate.Thenominalannualrate=5.1849%

（2）=10.3699%10.37%.

b.Thecurrentyield=$120/$1,100=10.91%.

c.YTM=CurrentYield+CapitalGains（Loss）Yield

10.37%=10.91%+CapitalLossYield

-0.54%=CapitalLossYield.

d.Usingafinancialcalculator,inputthefollowing:

N=8,PV=-1100,PMT=60,FV=1060,andsolveforI=5.0748%.

However,thisisaperiodicrate.Thenominalannualrate=5.0748%

（2）=10.1495%10.15%.

7-9TheproblemasksyoutosolvefortheYTM,giventhefollowingfacts:

N=5,PMT=80,andFV=1000.InordertosolveforIweneedPV.

However,youarealsogiventhatthecurrentyieldisequalto8.21%.Giventhisinformation,wecanfindPV.

Currentyield=Annualinterest/Currentprice

0.0821=$80/PV

PV=$80/0.0821=$974.42.

Now,solvefortheYTMwithafinancialcalculator:

N=5,PV=-974.42,PMT=80,andFV=1000.SolveforI=YTM=8.65%.

7-10Theproblemasksyoutosolveforthecurrentyield,giventhefollowingfacts:

N=14,I=10.5883/2=5.29415,PV=-1020,andFV=1000.InordertosolveforthecurrentyieldweneedtofindPMT.Withafinancialcalculator,wefindPMT=$55.00.However,becausethebondisasemiannualcouponbondthisamountneedstobemultipliedby2toobtaintheannualinterestpayment:

$55.00

（2）=$110.00.Finally,findthecurrentyieldasfollows:

Currentyield=Annualinterest/Currentprice=$110/$1,020=10.78%.

7-11Thebondissellingatalargepremium,whichmeansthatitscouponrateismuchhigherthanthegoingrateofinterest.Therefore,thebondislikelytobecalled--itismorelikelytobecalledthantoremainoutstandinguntilitmatures.Thus,itwillprobablyprovideareturnequaltotheYTCratherthantheYTM.So,thereisnopointincalculatingtheYTM--justcalculatetheYTC.Enterthesevalues:

N=10,PV=-1353.54,PMT=70,FV=1050,andthensolveforI.

Theperiodicrateis3.2366percent,sothenominalYTCis23.2366%=6.4733%6.47%.Thiswouldbeclosetothegoingrate,anditisaboutwhatthefirmwouldhavetopayonnewbonds.

7-12a.TofindtheYTM:

N=10,PV=-1175,PMT=110,FV=1000

I=YTM=8.35%.

b.TofindtheYTC,ifcalledinYear5:

N=5,PV=-1175,PMT=110,FV=1090

I=YTC=8.13%.

c.Thebondsaresellingatapremiumwhichindicatesthatinterestrateshavefallensincethebondswereoriginallyissued.Assumingthatinterestratesdonotchangefromthepresentlevel,investorswouldexpecttoearntheyieldtocall.（NotethattheYTCislessthantheYTM.）

d.Similarlyfromabove,YTCcanbefound,ifcalledineachsubsequentyear.

IfcalledinYear6:

N=6,PV=-1175,PMT=110,FV=1080

I=YTM=8.27%.

IfcalledinYear7:

N=7,PV=-1175,PMT=110,FV=1070

I=YTM=8.37%.

IfcalledinYear8:

N=8,PV=-1175,PMT=110,FV=1060

I=YTM=8.46%.

IfcalledinYear9:

N=9,PV=-1175,PMT=110,FV=1050

I=YTM=8.53%.

Accordingtothesecalculations,thelatestinvestorsmightexpectacallofthebondsisinYear6.ThisisthelastyearthattheexpectedYTCwillbeless