Chapter07(5)

Chapter 7Bonds and Their ValuationLearning ObjectivesAfter reading this chapter, students should be able to: List the four main classifcations of bonds and diferentiate among them. Identify the key characteristics common to all bonds. Calculate the value of a bond ith annual or semiannual interest payments. Calculate the yield to maturity, the yield to call, and the current yield on a bond. !"plain hy the market value of an outstanding f"ed#rate bond ill fall hen interest ratesrise on ne bonds of e$ual risk, or vice versa. %iferentiate beteen interest rate risk, reinvestment rate risk, and default risk. List ma&or types of corporate bonds and distinguish among them. !"plain the importance of bond ratings and list some of the criteria used to rate bonds. %iferentiate among the folloing terms:Insolvent, li$uidation, and reorgani'ation. (ead and understand the information provided on the bond market page of your nespaper.Chapter 7:Bonds and Their Valuation Learning Objectives 141Lecture Suggestions)his chapter serves to purposes.*irst, it provides important and useful information on bondsper se.+econd, it provides a good e"ample of the use of time value concepts, so it reinforcesthe topics covered in Chapter ,.-ebeginour lectureithadiscussionof thediferent types of bonds andtheircharacteristics. )henemoveontohobondvalues areestablished, hoyields aredetermined, the efects of changing interest rates on bond prices, and the riskiness inherent indiferent types of bonds.-hatecover, andtheayecoverit, canbeseenbyscanningtheslidesandIntegrated Case solution for Chapter ., hich appears at the end of this chapter solution.*orother suggestions about the lecture, please see the /Lecture +uggestions0 in Chapter ,, heree describe ho e conduct our classes.D!S O" C#$T%&:4 O' () D!S *(+,-inute periods.14/ Lecture Suggestions Chapter 7:Bonds and Their Valuationns0ers to %nd,o1,Chapter 2uestions7,1 *rom the corporation1s viepoint, one important factor in establishing a sinking fund isthat its on bonds generally have a higher yield than do government bonds2 hence, thecompany saves more interest by retiring its on bonds than it could earn by buyinggovernment bonds. )his factor causes frms to favor the second procedure. Investorsalso ould prefer the annualretirement procedure if they thought that interest rateseremorelikelytorisethantofall, but theyouldprefer thegovernment bondpurchaseprogramifthey thought rates erelikelytofall. Inaddition, bondholdersrecogni'e that, under the government bond purchase scheme, each bondholder ouldbe entitled to a given amount of cash from the li$uidation of the sinking fund if the frmshould go into default, hereas under the annual retirement plan, some of the holdersould receive a cash beneft hile others ould beneft only indirectly from the fact thatthere ould be feer bonds outstanding.3n balance, investors seem to have little reason for choosing one method over theother, hile the annual retirement method is clearly more benefcial to the frm. )heconse$uence has been a pronounced trend toard annual retirement and aay from theaccumulation scheme.7,/ 4es, the statement is true.7,3 *alse. +hort#term bond prices are less sensitive than long#term bond prices to interestrate changes because funds invested in short#term bonds can be reinvested at the neinterest rate sooner than funds tied up in long#term bonds.*or e"ample, consider to bonds, both ith a 567 annual coupon and a 85,666 parvalue. )he only diference beteen them is their maturity. 3ne bond is a 5#year bond,hile the other is a ,6#year bond. Consider the values of each at 97, 567, 597, and,67 interest rates. 5#year ,6#year 97 85,6:..;, 85,;,..6.Hond +: Change C D 5, FG D IFG D 85,6:..;,.,. >7: Hond L: *rom Hond + inputs, change C D 59 and IE4( D >, FG D I, FG D85,5.5.5=.Hond +: Change C D 5, FG D IFG D 85,65>.9,.;.Hond +: Change C D 5, FG D IFG D 8=>,.5:.144 Answers and Solutions Chapter 7:Bonds and Their Valuationb5 )hinkaboutabondthatmaturesinonemonth. Itspresentvalueisin@uencedprimarily by the maturity value, hich ill be received in only one month. !ven ifinterest rates double, the price of the bond ill still be close to 85,666. A 5#yearbond1s value ould @uctuate more than the one#month bond1s value because of thediference in the timing of receipts.Aoever, its value ould still be fairly close to85,666 even if interest rates doubled.A long#term bond paying semiannual coupons,on the other hand, ill be dominated by distant receipts, receipts that are multipliedby5EJ5KrdE,Lt, andif rdincreases, thesemultipliersill decreasesignifcantly.Another ay to vie this problem is from an opportunity point of vie.A 5#monthbond can be reinvested at the ne rate very $uickly, and hence the opportunity toinvest at this ne rate is not lost2 hoever, the long#term bond locks in subnormalreturns for a long period of time.7,4 a5 4ears to ?aturity Frice of Hond C Frice of Hond M : 85,65,..= 8;= >6.9> .5,.== :..;is 1oundtobe1+561J514( Integrated Case Chapter 7:Bonds and Their Valuationrd P C=e can tell 1ro- the bond -ust be above the 6J couponrate5=e 8no0 this because the bond is selling at a discountAand discount bonds al0a?s have rd V coupon rate5:1 the bond 0ere priced at G1A1345/+A then it 0ould beselling at a pre-iu-5:n that caseA it -ust have a !T> that isbelo0 the 6J coupon rateA because all pre-iu- bonds -usthavecouponsthate9ceedthegoinginterestrate5 Noingthrough the sa-e procedures as be1oreFplugging theappropriate values into a ;nancial calculator and thenpressing the :7!& buttonA 0e ;nd that at a price o1 G1A1345/+Ard P !T> P 75+)J5'5 */. =hat are the total returnA the current ?ieldA and the capitalgains?ield1orthediscount bondC*ssu-eitisheldto-aturit? and the co-pan? does not de1ault on it5.ns0er: DSho0S7,/+throughS7,//here5E Thecurrent ?ieldisde;ned as 1ollo0s:Current ?ield P bond the o1 price Current pa?-ent interestcoupon nnual5The capital gains ?ield is de;ned as 1ollo0s:Capital gains ?ield P price ?ear, o1 , Beginningprice s bondW in change %9pected5The total e9pected return is the su- o1 the current ?ield andthe e9pected capital gains ?ield:return total%9pected P ?ield gainscapital %9pectedeld current ?i%9pected+ 5The ter- ?ield to -aturit?A or !T>A is o1ten used in discussingbonds5 :tissi-pl?thee9pectedtotal return*assu-ingnoChapter 7:Bonds and Their Valuation Integrated Case 144de1ault ris8 and the bonds are not called.A so dr XP e9pectedtotal return P e9pected !T>5&ecall also that securities havereBuired returnsA rdA0hich depend on a nu-ber o1 1actors:&eBuired return P rd P rS T :$ T L$ T >&$ T D&$5=e 8no0 that *1. securit? -ar8ets are nor-all? in eBuilibriu-Aand */. that 1or eBuilibriu- to e9istA the e9pected returnA dr X P!T>A as seen b? the -arginal investorA -ust be eBual to thereBuired returnA rd5 :1 that eBualit? does not holdA then bu?ingandselling0ill occuruntil itdoesholdA andeBuilibriu-isestablished5There1oreA 1or the -arginal investor:dr X P !T> P rd5'or our 6J couponA 1+,?ear bond selling at a price o1 G))70ith a !T> o1 1+561JA the current ?ield is:Current ?ield P G))7G6+ P +51+1( P 1+51(J5Yno0ing the current ?ield and the total returnA 0e can ;ndthe capital gains ?ield:!T> P Current ?ield T Capital gains ?ieldandCapital gains ?ield P !T> Z Current ?ieldP 1+561J Z 1+51(J P +574J5The capital gains ?ield calculation can be chec8ed b? as8ingthis Buestion: H=hat is the e9pected value o1 the bond 1?ear 1ro-no0A assu-ing that interest rates re-ain atcurrent levelsCI This is the sa-e as as8ingA H=hat is thevalueo1 a6,?earA 6Jannual couponbondi1 its!T>*its147 Integrated Case Chapter 7:Bonds and Their ValuationreBuired rate o1 return. is 1+561JCI The ans0erA using thebond valuation 1unction o1 a calculatorA is G)635)75 =ith thisdataA 0e can no0 calculate the bond P 75+)JA 0e have thissituation:Current ?ield P G6+7G1A1345/+ P 7564JandCapital gains ?ield P 75+)J Z 7564J P ,+5)4J5Thebondprovidesacurrent ?ieldthat e9ceedsthetotalreturnA but a purchaser 0ould incur a s-all capital loss each?earA and this loss0ould e9actl?oMset the e9cess current?ield and 1orce the total return to eBual the reBuired rate5N5 =hat is interest rate *or price. ris8C=hich has -ore interestrate ris8A an annual pa?-ent 1,?ear bond or a 1+,?ear bondC=h?Cns0er: DSho0S7,/3 andS7,/4here5E :nterestrateris8A0hichiso1ten just called price ris8A is the ris8 that a bond 0ill losevalue as the result o1 an increase in interest rates5The tablebelo0gives values 1or a 1+JA annual coupon bond atdiMerent values o1 rd:Chapter 7:Bonds and Their Valuation Integrated Case 14) >aturit? rd1,!earChange 1+,!ear Change(J G1A+4) G1A3)41+ 1A+++ 1A+++1( 6(4 746 (J increase in rdcauses the value o1 the 1,?ear bond todecline b? onl? 454JA but the 1+,?ear bond declines in valueb? -ore than /(J5ThusA the 1+,?ear bond has -ore interestrate price ris85The graph above sho0s the relationship bet0een bondvalues and interest rates 1or a 1+JA annual coupon bond 0ithdiMerent -aturities5 The longer the -aturit?A the greater thechange in value 1or a given change in interest ratesA rd5#5 =hat isreinvest-ent rate ris8C =hich has -orereinvest-ent rate ris8A a 1,?ear bond or a 1+,?ear bondCns0er: DSho0 S7,/4 through S7,/7 here5E &einvest-ent rate ris8 isde;nedastheris8thatcashKo0s*interestplusprincipalrepa?-ents. 0ill have to be reinvested in the 1uture at rates146 Integrated Case Chapter 7:Bonds and Their ValuationT45)J,454JT3)54J,/(51Jlo0er than toda?5 !our inco-e0ill be G(+A+++ during the ;rst ?ear5ThenA a1ter 1 ?earA ?ou0ill receive ?our G(++A+++ 0hen the bond -aturesA and ?ou0ill then have to reinvest this a-ount5:1 rates have 1allen to3JA then ?our inco-e 0ill 1all 1ro- G(+A+++ to G1(A+++5 Onthe other handA had ?ou bought 3+,?ear bonds that ?ielded1+JA ?our inco-e 0ould have re-ained constant at G(+A+++per ?ear5 Clearl?A bu?ing bonds that have short -aturitiescarries reinvest-ent rate ris85"ote that long -aturit? bondsalso have reinvest-ent rate ris8A but the ris8 applies onl? tothe coupon pa?-entsA and not to the principal a-ount5Sincethe coupon pa?-ents are signi;cantl? less than the principala-ountA the reinvest-ent rate ris8 on a long,ter- bond issigni;cantl? less than on a short,ter- bond5Optional 2uestionSuppose a ;r- 0ill need G1++A+++ /+ ?ears 1ro- no0 to replace so-eeBuip-ent5 :t plans to -a8e /+ eBual pa?-entsA starting toda?A into aninvest-ent 1und5 :t can bu? bonds that -ature in /+ ?ears or bondsthat -ature in 1 ?ear5Both t?pes o1 bonds currentl? sell to ?ield 1+JAi5e5A rd P !T> P 1+J5The co-pan?T $>T $>T $>T $>T'V16'V1)555'V+Su- o1 'Vs P1++A+++=e have a /+,?ear annuit? due 0hose 'V P 1++A+++A 0here rd P1+J5 =e could set the calculator to HbeginningI or HdueAIinsert the 8no0n values *" P /+A rd P :7!& P 1+A $V P +A 'V P1+++++.A and then press the $>T button to ;nd the pa?-entA$>T P G1A()75/45ThusA i1 0e save G1A()75/4 per ?earA startingtoda?A and invest it to earn 1+J per ?earA 0e 0ould end up 0iththereBuiredG1++A+++5 "oteA thoughA that thiscalculationassu-es that the co-pan? can earn 1+J in each 1uture ?ear5 :1interest rates1allA it couldnot earn1+JonitsadditionaldepositsR henceA it 0ould not end up 0ith the reBuiredG1++A+++5Optional 2uestion:1theco-pan?decidestoinvestenoughrightno0toproducethe1uture G1++A+++A ho0 -uch -ust it put upCns0er: To ;nd the reBuired initial lu-p su-A 0e 0ould ;nd the $V o1G1++A+++ discounted bac8 1or /+ ?ears at 1+J: $VP171 Integrated Case Chapter 7:Bonds and Their Valuation1+JG14A)445345 :1 the co-pan? invested this a-ount no0 andearned1+JA it0ouldendup0iththereBuiredG1++A+++5"oteagainA thoughA thati1interestrates1allA theinterestreceived in each ?ear 0ill have to be reinvested to earn lessthan 1+JA and the G1++A+++ goal 0ill not be -et5Niven the 1acts as 0e have developed the-A i1 theco-pan? decides on the lu-p su- pa?-entA should it bu? 1,?ear bonds or /+,?ear bondsC "either 0ill be co-pletel? sa1einthesenseo1 assuringtheco-pan?that thereBuiredG1++A+++ 0ill be available in /+ ?earsA but is one better thanthe otherC To beginA letVBond P Su- o1 $Vs=e 0ould use this eBuation to ;nd the bondTP(+A 'VP1+++A andthenpress $Vtodeter-ine the value o1 the bond5:ts value is G1A+++5!ou could then change rd P :7!& to see 0hat happens tothe bond P /*35(4)J. P 75137J 751J5This 751J is the rate bro8ers 0ould Buote i1 ?ou as8ed aboutbu?ing the bond5!ou could also calculate the %& on the bond:%& P *15+3(4)./ Z 1 P 75/4J5Lsuall?A people in the bond business just tal8 about no-inalratesA 0hich is OY so long as allthe bonds being co-paredare on a se-iannual pa?-ent basis5=hen ?ou start -a8ingco-parisons a-ong invest-ents 0ith diMerent pa?-entpatternsA thoughA it is i-portant to convert to %&s5Y5 */. :1?ouboughtthisbondAdo?outhin8?ou0ouldbe-oreli8el? to earn the !T> or the !TCC=h?Cns0er: DSho0 S7,34 and S7,3( here5ESince the coupon rate is 1+Jversus !TC P rdP 75137JA it 0ould pa? the co-pan? to callthe bondA get rid o1 the obligation to pa? G1++ per ?ear ininterestA and sell replace-ent bonds 0hose interest 0ould beonl? G71537 per ?ear5 There1oreA i1 interest rates re-ain atthe current level until the call dateA the bond 0ill surel? becalledA so investors should e9pect to earn 75137J5:ngeneralA investors should e9pect to earn the !TC on pre-iu-bondsA but to earn the !T> on par and discount bonds5 *Bondbro8ers publish lists o1 the bonds the? have 1or saleR the?Buote !T> or !TC depending on 0hether the bond sells at apre-iu- or a discount5.Chapter 7:Bonds and Their Valuation Integrated Case 17)L5 Does the ?ield to -aturit? represent the pro-ised ore9pected return on the bondC%9plain5ns0er: DSho0 S7,34 here5EThe ?ield to -aturit? is the rate o1 returnearned on a bond i1 it is held to -aturit?5:t can be vie0ed asthe bond