SolutionsCh78.docx
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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
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