FM11 Ch 06 Test Bank
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CHAPTER 6 BONDS AND THEIR VALUATION (Difficulty: E = Easy, M = Medium, and T = Tough)
True-False Easy: Discounted cash flows 1
.
Answer: b
Diff: E
The mar market val value of any any real or fin financ ancial ass asset, inc includi uding stoc tocks, bonds, or art work, may be found by determining future cash flows and then discounting them back to the present. a. True b. Fals e
Issuing bonds 2
.
Answer: b
Diff: E
If a firm firm rais raises es capi capita tal l by by sel selli ling ng new new bon bonds ds, , the the buye buyer r is call called ed the the "issu "issuing ing firm, firm," " and and the coupo coupon n rate rate is gene general rally ly set set equa equal l to the the required rate. a. True b. Fals e
Interest rate risk 3
.
Answer: b
Diff: E
A 20-y 20-yea ear r orig origin inal al mat matur urit ity y bond bond wit with h 1 yea year r left left to to matu maturi rity ty has has mor more e interest rate risk than a 10-year original maturity bond with 1 year left to maturity. (Assume that the bonds have equal default risk and equal coupon rates.) a. True b. Fals e
Interest rate risk 4
.
Answer: b
Diff: E
Beca Becaus use e shor shortt-te term rm int inter eres est t rate rates s are are much much mor more e vola volati tile le tha than n long long-t -ter erm m rates, you would, in the real world, be subject to much more interest rate risk if you purchased a 30-day bond than if you bought a 30-year bond. a. True b. Fals e
Bond prices and interest rates 5
.
Answer: a
Di D iff: E
For bonds, price sensitivity to a given change in interest rates generally increases as years remaining to maturity increases. a. True b. Fals e
Chapter 6 - Page 1
Mortgage bond 6
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Answer: a
Diff: E
Typi Typica call lly, y, debe debent ntur ures es have have high higher er inte intere rest st rate rates s than than mort mortga gage ge bond bonds s prim primar aril ily y beca becaus use e the the mort mortga gage ge bond bonds s are are back backed ed by asse assets ts whil while e debentures are unsecured. a. True b. Fals e
Debt coupon rate 7
.
Answer: a
Diff: E
Othe Other r thin things gs equ equal al, , a firm firm wil will l have have to to pay pay a high higher er cou coupo pon n rate rate on on a subordinated debenture than on a second mortgage bond. a. True b. Fals e
Call provision 8
.
Answer: b
Diff: E
A call call pro provi visi sion on giv gives es bon bondh dhol olde ders rs the the rig right ht to to dema demand nd, , or "cal "call l for, for," " repayment repayment of a bond. bond. Typically, Typically, calls are exercised exercised if interest interest rates rates rise, rise, becau because se when when rates rates rise rise the bond bondhol holder der can can get get the princ princip ipal al amount back and reinvest it elsewhere at higher rates. a. True b. Fals e
Sinking fund 9
.
Answer: a
Diff: E
Many Many bon bond d inde indent ntur ures es all allow ow the the com compa pany ny to to acqu acquir ire e bond bonds s for for a sink sinkin ing g fund fund eith either er by purc purcha hasi sing ng bond bonds s in the the mark market et or by a lott lotter ery y administered by the trustee for the purchase of a percentage of the issue through a call at face value. a. True b. Fals e
Zero coupon bond
.
10
Answer: b
Diff: E
A zero zero cou coupo pon n bond bond is is a bond bond tha that t pays pays no no inte intere rest st and and is is offe offere red d (and (and subs subseq eque uent ntly ly sell sells) s) at par, par, ther theref efor ore e prov provid idin ing g comp compen ensa sati tion on to investors in the form of capital appreciation. a. True b. Fals e
Floating rate debt
.
11
Answer: a
Diff: E
The motivation for floating rate bonds arose out of the costly experience of the early 1980s when inflation pushed interest rates to very very high high level levels s causi causing ng shar sharp p declin declines es in the prices prices of longlong-te term rm bonds. a. True b. Fals e
Chapter 6 - Page 2
Mortgage bond 6
.
Answer: a
Diff: E
Typi Typica call lly, y, debe debent ntur ures es have have high higher er inte intere rest st rate rates s than than mort mortga gage ge bond bonds s prim primar aril ily y beca becaus use e the the mort mortga gage ge bond bonds s are are back backed ed by asse assets ts whil while e debentures are unsecured. a. True b. Fals e
Debt coupon rate 7
.
Answer: a
Diff: E
Othe Other r thin things gs equ equal al, , a firm firm wil will l have have to to pay pay a high higher er cou coupo pon n rate rate on on a subordinated debenture than on a second mortgage bond. a. True b. Fals e
Call provision 8
.
Answer: b
Diff: E
A call call pro provi visi sion on giv gives es bon bondh dhol olde ders rs the the rig right ht to to dema demand nd, , or "cal "call l for, for," " repayment repayment of a bond. bond. Typically, Typically, calls are exercised exercised if interest interest rates rates rise, rise, becau because se when when rates rates rise rise the bond bondhol holder der can can get get the princ princip ipal al amount back and reinvest it elsewhere at higher rates. a. True b. Fals e
Sinking fund 9
.
Answer: a
Diff: E
Many Many bon bond d inde indent ntur ures es all allow ow the the com compa pany ny to to acqu acquir ire e bond bonds s for for a sink sinkin ing g fund fund eith either er by purc purcha hasi sing ng bond bonds s in the the mark market et or by a lott lotter ery y administered by the trustee for the purchase of a percentage of the issue through a call at face value. a. True b. Fals e
Zero coupon bond
.
10
Answer: b
Diff: E
A zero zero cou coupo pon n bond bond is is a bond bond tha that t pays pays no no inte intere rest st and and is is offe offere red d (and (and subs subseq eque uent ntly ly sell sells) s) at par, par, ther theref efor ore e prov provid idin ing g comp compen ensa sati tion on to investors in the form of capital appreciation. a. True b. Fals e
Floating rate debt
.
11
Answer: a
Diff: E
The motivation for floating rate bonds arose out of the costly experience of the early 1980s when inflation pushed interest rates to very very high high level levels s causi causing ng shar sharp p declin declines es in the prices prices of longlong-te term rm bonds. a. True b. Fals e
Chapter 6 - Page 2
Junk bond
.
12
Answer: a
Diff: E
A junk junk bon bond d is a hig high h risk risk, , high high yie yield ld deb debt t inst instru rume ment nt typ typic ical ally ly use used d to finance a leveraged buyout or a merger, or to provide financing to a company of questionable financial strength. a. True b. Fals e
Bond ratings and required returns
.
13
Answer: a
Diff: E
Ther There e is an inve invers rse e rela relati tion onsh ship ip betw betwee een n bond bond rati rating ngs s and the the requ requir ired ed return on on a bond. bond. The required required return return is lowest lowest for for AAA-rated AAA-rated bonds, bonds, and required returns increase as the ratings get lower. a. True b. Fals e
Medium: Bond value
.
14
Answer: a
Diff: M
If the the req required rat rate of re return on a bon bond is greater than its coupon interest rate (and rd remains above the coupon rate), the market value of that bond will always be below its par value until the bond matures, at which which time its market market value value will will equal equal its its par par value value. . (Accr (Accrue ued d interest between interest payment dates should not be considered when answering this question.) a. True b. Fals e
Bond value - annual payment
.
15
Answer: a
Di Diff: M
You You have have just just noti notice ced d in the the finan financi cial al page pages s of the the local local news newspa pape per r that you can can buy a $1,000 $1,000 par value value bond for $800. If the coupon coupon rate is 10 percent, with annual interest payments, payments, and there are 10 years to matur maturity ity, , you shoul should d make make the the purch purchase ase if your your requi require red d retur return n on investments of this type is 12 percent. a. True b. Fals e
Prices and interest rates
.
16
Answer: a
Diff: M
The The pric prices es of of highhigh-co coup upon on bond bonds s tend tend to be be less less sensi sensiti tive ve to to a give given n change in interest rates than low-coupon bonds, other things equal and held constant. a. True b. Fals e
Chapter 6 - Page 3
Bond premiums and discounts
.
17
Answer: a
Di Diff: M
A bond bond wit with h a $100 $100 ann annua ual l inte intere rest st pay payme ment nt wit with h five five yea years rs to to matu maturi rity ty (not expected to default) would sell for a premium if interest rates were below 9 percent and would sell for a discount if interest rates were greater than 11 percent. a. True b. Fals e
Callable bond
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18
Answer: b
Diff: M
A bond bond tha that t is cal calla labl ble e has has a chan chance ce of of bein being g reti retire red d earl earlie ier r than than its its state stated d term term to maturit maturity. y. There Therefo fore, re, if the yield yield curve curve is upwar upward d slopi sloping, ng, an outst outstan andin ding g calla callabl ble e bond bond shoul should d have have a lowe lower r yield yield to maturity than an otherwise identical noncallable bond. a. True b. Fals e
Indexed bond
.
19
Answer: b
Diff: M
An indexe indexed d bond bond has has its its value value tied tied to an infla inflatio tion n index index. . As infla inflati tion on increases increases the value of the bond increases and the issuer is responsible responsible for for the the accu accumu mula late ted d valu value e whic which h may may beco become me much much grea greate ter r than than the the original face value. a. True b. Fals e
Income bond
.
20
Answer: b
Diff: M
Inco ncome bonds pay intere erest only when the amount unt of the intere erest is actually earned by the the company. company. Thus, these these securities securities cannot cannot bankrupt bankrupt a company and this makes them safer than regular bonds. a. True b. Fals e
Restrictive covenants
.
21
Answer: a
Diff: M
Restr Restrict ictiv ive e cove covena nants nts are are desig designed ned so as as to prot protect ect both both the the bon bondho dhold lder er and the issuer even though they may constrain the actions of the firm's managers. Such covenants are contained in the bond's indenture. a. True b. Fals e
Sinking fund
.
22
Answer: b
Diff: M
You are are co consi nsideri ering two two bon bonds. ds. Both are are rat rated dou doub ble A (AA (AA), bot both mature in 20 years, both have a 10 percent coupon, and both are offered to you at their their $1,000 $1,000 par value. However, Bond X has a sinking fund while Bond Bond Y does not. This is probably probably not an equilibr equilibrium ium situation, situation, as Bond X, which has the sinking fund, would generally be expected to have a higher yield than Bond Y. a. True b. Fals e
Chapter 6 - Page 4
Floating rate debt
.
23
Answer: b
Diff: M
Floa Floati ting ng rate rate debt debt is adva advant ntag ageo eous us to inve invest stor ors s beca becaus use e the the inte intere rest st rate moves moves up if market market rates rates rise. Floating Floating rate debt debt shifts interest interest rate risk to companies and thus has no advantages for issuers. a. True b. Fals e
Bond ratings
.
24
Answer: a
Diff: M
A fir firm wit with a low bo bond rat rating ing fac faces a mor more seve sever re pen penalty whe when the Security Market Line (SML) is relatively steep than when it is not so steep. a. True b. Fals e
Multiple Choice: Conceptual Easy: Interest rates 25
.
a. b. c. d. e. .
Diff: E
longe longer; r; smalle smaller. r. short shorter er; ; large larger. r. longe longer; r; greate greater. r. short shorter er; ; smalle smaller. r. Answers Answers c and d are correct. correct.
Interest rate and reinvestment risk 26
Answer: e
One One of the the bas basic ic rel relat atio ions nshi hips ps in in inte intere rest st rat rate e theo theory ry is is that that, , othe other r thin things gs held held cons consta tant nt, , for for a give given n chan change ge in the the requ requir ired ed rate rate of return, the the time to maturity, the the change in price.
Answer: e
Diff: E
Whic Which h of of the the foll follow owin ing g sta state teme ment nts s is is mos most t cor corre rect ct? ? a. All All else else equal equal, , longlong-ter term m bonds bonds have have more more inte interes rest t rate rate risk risk than than short term bonds. b. All else equal, equal, higher higher coupon bonds bonds have more more reinvestment reinvestment risk risk than low coupon bonds. c. All else equal, equal, short-term short-term bonds bonds have more more reinvestment reinvestment risk than than do long-term bonds. d. Stateme Statements nts a and and c are are correct correct. . e. All of of the statements statements above above are are correct. correct.
Callable bond
.
27
Answer: a
Diff: E
Whic Which h of the the fol follo lowi wing ng eve event nts s woul would d make make it it more more lik likel ely y that that a com compa pany ny would choose to call its outstanding callable bonds? a. b. c. d. e.
A reductio reduction n in market market interes interest t rates. rates. The compan company's y's bonds bonds are downg downgrade raded. d. An incre increase ase in the call call premi premium. um. Answers Answers a and b are correct. correct. Answers Answers a, b, and and c are are correc correct. t. Chapter 6 - Page 5
Call provision
.
28
higher than lower than the same as either higher or lower, depending on the level of call premium, than unrelated to
Bond coupon rate
.
Diff: E
Sinking fund. Restrictive covenant. Call provision. Change in rating from Aa to Aaa. None of the answers above (all may reduce the required coupon rate).
Bond concepts
.
Answer: c
All of the following m ay serve t o reduce the coupon rate that would otherwise be required on a bond issued at par, except a a. b. c. d. e.
30
Diff: E
Other things held constant, if a bond indenture contains a call provision, the yield to maturity that would exist without such a call provision will generally be _________________ the YTM with it. a. b. c. d. e.
29
Answer: b
Answer: a
Diff: E
Which of the following statements is most correct? a. All else equal, if a bond’s yield to maturity increases, its price will fall. b. All else equal, if a bond’s yield to maturity increases, its current yield will fall. c. If a bond’s yield to maturity exceeds the coupon rate, the bond will sell at a premium over par. d. All of the answers above are correct. e. None of the answers above is correct.
Bond concepts
.
31
Answer: c
Diff: E
Which of the following statements is most correct? a. If a bond’s yield to maturity exceeds its annual coupon, then the bond will be trading at a premium. b. If interest rates increase, the relative price change of a 10-year coupon bond will be greater than the relative price change of a 10year zero coupon bond. c. If a coupon bond is selling at par, its current yield equals its yield to maturity. d. Both a and c are correct. e. None of the answers above is correct.
Chapter 6 - Page 6
Bond concepts
.
32
Answer: e
Diff: E
A 10-year corporate bond has an annual coupon payment of 9 percent. The bond is currently selling at par ($1,000). Which of the following statements is most correct? a. The bond’s yield to maturity is 9 percent. b. The bond’s current yield is 9 percent. c. If the bond’s yield to maturity remains constant, the bond’s price will remain at par. d. Both answers a and c are correct. e. All of the answers above are correct.
Sinking fund
.
33
Answer: e
Diff: E
Which of the following statements is most correct? a. Sinking fund provisions do not require companies to retire their debt; they only establish “targets” for the company to reduce its debt over time. b. Sinking fund provisions sometimes work to the detriment of bondholders – particularly if interest rates have declined over time. c. If interest rates have increased since the time a company issues bonds with a sinking fund provision, the company is more likely to retire the bonds by buying them back in the open market, as opposed to calling them in at the sinking fund call price. d. Statements a and b are correct. e. Statements b and c are correct.
Sinking fund provision
.
34
Answer: d
Diff: E
Which of the following statements is most correct? a. Retiring bonds under a sinking fund provision is similar to calling bonds under a call provision in the sense that bonds are repurchased by the issuer prior to maturity. b. Under a sinking fund, bonds will be purchased on the open market by the issuer when the bonds are selling at a premium and bonds will be called in for redemption when the bonds are selling at a discount. c. The sinking fund provision makes a debt issue less risky to the investor. d. Both statements a and c are correct. e. All of the statements above are correct.
Types of debt
.
35
Answer: e
Diff: E
Which of the following statements is most correct? a. Junk bonds typically have a lower yield to maturity relative to investment grade bonds. b. A debenture is a secured bond which is backed by some or all of the firm’s fixed assets. c. Subordinated debt has less default risk than senior debt. d. All of the statements above are correct. e. None of the statements above is correct.
Chapter 6 - Page 7
Medium: Bond yield
.
36
Answer: b
Diff: M
Which of the following statements is most correct? a. Rising inflation makes the actual yield to maturity on a bond greater than the quoted yield to maturity which is based on market prices. b. The yield to maturity for a coupon bond that sells at its par value consists entirely of an interest yield; it has a zero expected capital gains yield. c. On an expected yield basis, the expected capital gains yield will always be positive because an investor would not purchase a bond with an expected capital loss. d. The market value of a bond will always approach its par value as its maturity date approaches. This holds true even if the firm enters bankruptcy. e. All of the statements above are false.
Bond yield
.
37
Answer: c
Diff: M
Which of the following statements is most correct? a. The current yield on Bond A exceeds the current yield on Bond B; therefore, Bond A must have a higher yield to maturity than Bond B. b. If a bond is selling at a discount, the yield to call is a better measure of return than the yield to maturity. c. If a coupon bond is selling at par, its current yield equals its yield to maturity. d. Both a and b are correct. e. Both b and c are correct.
Price risk 38
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A 10-year bond with a 10 percent coupon. An 8-year bond with a 9 percent coupon. A 10-year zero coupon bond. A 1-year bond with a 15 percent coupon. A 3-year bond with a 10 percent coupon.
Price risk
.
Diff: M
Assume that all interest rates in the economy decline from 10 percent to 9 percent. Which of the following bonds will have the largest percentage increase in price? a. b. c. d. e.
39
Answer: c
Answer: c
Diff: M
Which of the following has the greatest price risk? a. A 10-year, $1,000 face value, 10 percent coupon bond with semiannual interest payments. b. A 10-year, $1,000 face value, 10 percent coupon bond with annual interest payments. c. A 10-year, $1,000 face value, zero coupon bond. d. A 10-year $100 annuity. e. All of the above have the same price risk since they all mature in 10 years.
Chapter 6 - Page 8
Price risk
.
40
Answer: c
A A A A A
1-year bond with an 8 percent coupon. 1-year zero-coupon bond. 10-year zero-coupon bond. 10-year bond with an 8 percent coupon. 10-year bond with a 12 percent coupon.
Price risk
.
Answer: a
A A A A A
10-year zero coupon bond. 10-year bond with a 10 percent semiannual coupon. 10-year bond with a 10 percent annual coupon. 5-year zero coupon bond. 5-year bond with a 12 percent annual coupon.
Bond concepts
.
Diff: M
If interest rates fall from 8 percent to 7 percent, which of the following bonds will have the largest percentage increase in its value? a. b. c. d. e.
42
If the yield to maturity decreased 1 percentage point, which of the following bonds would have the largest percentage increase in value? a. b. c. d. e.
41
Diff: M
Answer: e
Diff: M
Which of the following statements is most correct? a. Other things held constant, a callable bond would have a lower required rate of return than a noncallable bond. b. Other things held constant, a corporation would rather issue noncallable bonds than callable bonds. c. Reinvestment rate risk is worse from a typical investor's standpoint than interest rate risk. d. If a 10-year, $1,000 par, zero coupon bond were issued at a price which gave investors a 10 percent rate of return, and if interest rates then dropped to the point where rd = YTM = 5%, we could be sure that the bond would sell at a premium over its $1,000 par value. e. If a 10-year, $1,000 par, zero coupon bond were issued at a price which gave investors a 10 percent rate of return, and if interest rates then dropped to the point where rd = YTM = 5%, we could be sure that the bond would sell at a discount below its $1,000 par value.
Bond concepts
.
43
Answer: d
Diff: M
Which of the following statements is most correct? a. The market value of a bond will always approach its par value as its maturity date approaches, provided the issuer of the bond does not go bankrupt. b. If the Federal Reserve unexpectedly announces that it expects inflation to increase, then we would probably observe an immediate increase in bond prices. c. The total yield on a bond is derived from interest payments and changes in the price of the bond. d. Statements a and c are correct. e. All of the statements above are correct.
Chapter 6 - Page 9
Bond concepts
.
44
Answer: b
Diff: M
Which of the following statements is most correct? a. If a bond is selling for a premium, this implies that the bond’s yield to maturity exceeds its coupon rate. b. If a coupon bond is selling at par, its current yield equals its yield to maturity. c. If rates fall after its issue, a zero coupon bond could trade for an amount above its par value. d. Statements b and c are correct. e. None of the statements above is correct.
Bond concepts
.
45
Answer: b
Diff: M
Which of the following statements is most correct? a. All else equal, a bond that has a coupon rate of 10 percent will sell at a discount if the required return for a bond of similar risk is 8 percent. b. The price of a discount bond will increase over time, assuming that the bond’s yield to maturity remains constant over time. c. The total return on a bond for a given year consists only of the coupon interest payments received. d. Both b and c are correct. e. All of the statements above are correct.
Bond concepts
.
46
Answer: e
Diff: M
Which of the following statements is most correct? a. All else equal, a bond that has a coupon rate of 10 percent will sell at a discount if the required return for a bond of similar risk is 8 percent. b. Debentures generally have a higher yield to maturity relative to mortgage bonds. c. If there are two bonds with equal maturity and credit risk, the bond which is callable will have a higher yield to maturity than the bond which is noncallable. d. Answers a and c are correct. e. Answers b and c are correct.
Bond concepts
.
47
Answer: d
Diff: M
A 10-year bond has a 10 percent annual coupon and a yield to maturity of 12 percent. The bond can be called in 5 years at a call price of $1,050 and the bond’s face value is $1,000. Which of the following statements is most correct? a. b. c. d. e.
The bond’s current yield is greater than 10 percent. The bond’s yield to call is less than 12 percent. The bond is selling at a price below par. Both answers a and c are correct. None of the above answers is correct.
Chapter 6 - Page 10
Callable bond
.
48
Answer: d
Diff: M
Which of the following statements is most correct? a. Distant cash flows are generally riskier than near-term cash flows. Further, a 20-year bond that is callable after 5 years will have an expected life that is probably shorter, and certainly no longer, than an otherwise similar noncallable 20-year bond. Therefore, investors should require a lower rate of return on the callable bond than on the noncallable bond, assuming other characteristics are similar. b. A noncallable 20-year bond will generally have an expected life that is equal to or greater than that of an otherwise identical callable 20-year bond. Moreover, the interest rate risk faced by investors is greater the longer the maturity of a bond. Therefore, callable bonds expose investors to less interest rate risk than noncallable bonds, other things held constant. c. Statements a and b are correct. d. Statements a and b are false.
Callable bond
.
49
Answer: b
Diff: M
Which of the following statements is most correct? a. A callable 10-year, 10 percent bond should sell at a higher price than an otherwise similar noncallable bond. b. Two bonds have the same maturity and the same coupon rate. However, one is callable and the other is not. The difference in prices between the bonds will be greater if the current market interest rate is below the coupon rate than if it is above the coupon rate. c. Two bonds have the same maturity and the same coupon rate. However, one is callable and the other is not. The difference in prices between the bonds will be greater if the current market interest rate is above the coupon rate than if it is below the coupon rate. d. The actual life of a callable bond will be equal to or less than the actual life of a noncallable bond with the same maturity date. Therefore, if the yield curve is upward sloping, the required rate of return will be lower on the callable bond. e. Corporate treasurers dislike issuing callable bonds because these bonds may require the company to raise additional funds earlier than would be true if noncallable bonds with the same maturity were used.
Chapter 6 - Page 11
Types of debt
.
50
Answer: c
Diff: M
A company is planning to raise $1,000,000 to finance a new plant. Which of the following statements is most correct? a. If debt is used to raise the million dollars, the cost of the debt would be lower if the debt is in the form of a fixed rate bond rather than a floating rate bond. b. If debt is used to raise the million dollars, the cost of the debt would be lower if the debt is in the form of a bond rather than a term loan. c. If debt is used to raise the million dollars, but $500,000 is raised as a first mortgage bond on the new plant and $500,000 as debentures, the interest rate on the first mortgage bond would be lower than it would be if the entire $1 million were raised by selling first mortgage bonds. d. The company would be especially anxious to have a call provision included in the indenture if its management thinks that interest rates are almost certain to rise in the foreseeable future. e. All of the statements above are false.
Miscellaneous concepts
.
51
Answer: b
Diff: M
Which of the following statements is most correct? a. A firm with a sinking fund payment coming due would generally choose to buy back bonds in the open market, if the price of the bond exceeds the sinking fund call price. b. Income bonds pay interest only when the amount of the interest is actually earned by the company. Thus, these securities cannot bankrupt a company and this makes them safer to investors than regular bonds. c. One disadvantage of zero coupon bonds is that issuing firms cannot realize the tax savings from issuing debt until the bonds mature. d. Other things held constant, callable bonds should have a lower yield to maturity than noncallable bonds. e. All of the above statements are false.
Miscellaneous concepts
.
52
Answer: b
Diff: M
Which of the following statements is most correct? a. A 10-year 10 percent coupon bond has less reinvestment rate risk than a 10-year 5 percent coupon bond (assuming all else equal). b. The total return on a bond for a given year arises from both the coupon interest payments received for the year and the change in the value of the bond from the beginning to the end of the year. c. The price of a 20-year 10 percent bond is less sensitive to changes in interest rates (i.e., has lower interest rate price risk) than the price of a 5-year 10 percent bond. d. A $1,000 bond with $100 annual interest payments with five years to maturity (not expected to default) would sell for a discount if interest rates were below 9 percent and would sell for a premium if interest rates were greater than 11 percent. e. Answers a, b, and c are correct statements.
Chapter 6 - Page 12
Miscellaneous concepts
.
53
Answer: e
Diff: M
Which of the following statements is most correct? a. All else equal, a 1-year bond will have a higher (i.e., better) bond rating than a 20-year bond. b. A 20-year bond with semiannual interest payments has higher price risk (i.e., interest rate risk) than a 5-year bond with semiannual interest payments. c. 10-year zero coupon bonds have higher reinvestment rate risk than 10-year, 10 percent coupon bonds. d. If a callable bond is trading at a premium, then you would expect to earn the yield-to-maturity. e. Statements a and b are correct.
Interest rate risk
.
54
A A A A A
7 percent coupon bond which matures in 12 years. 9 percent coupon bond which matures in 10 years. 12 percent coupon bond which matures in 7 years. 7 percent coupon bond which matures in 9 years. 10 percent coupon bond which matures in 10 years.
Interest rate risk
.
Diff: M
15-year zero coupon Treasury bond. 12-year Treasury bond with a 10 percent annual coupon. 15-year Treasury bond with a 12 percent annual coupon. 2-year zero coupon Treasury bond. 2-year Treasury bond with a 15 percent annual coupon.
Current yield and yield to maturity
.
Answer: a
All treasury securities have a yield to maturity of 7 percent--so the yield curve is flat. If the yield to maturity on all Treasuries were to decline to 6 percent, which of the following bonds would have the largest percentage increase in price? a. b. c. d. e.
56
Diff: M
Which of the following Treasury bonds will have the largest amount of interest rate risk (price risk)? a. b. c. d. e.
55
Answer: a
Answer: e
Diff: M
Which of the following statements is most correct? a. If a bond sells for less than par, then its yield to maturity is less than its coupon rate. b. If a bond sells at par, then its current yield will be less than its yield to maturity. c. Assuming that both bonds are held to maturity and are of equal risk, a bond selling for more than par with ten years to maturity will have a lower current yield and higher capital gain relative to a bond that sells at par. d. Answers a and c are correct. e. None of the answers above is correct.
Chapter 6 - Page 13
Current yield and yield to maturity
.
57
Answer: a
Diff: M
You just purchased a 10-year corporate bond that has an annual coupon of 10 percent. The bond sells at a premium above par. Which of the following statements is most correct? a. The bond’s yield to maturity is less than 10 percent. b. The bond’s current yield is greater than 10 percent. c. If the bond’s yield to maturity stays constant, the bond’s price will be the same one year from now. d. Statements a and c are correct. e. None of the answers above is correct.
Corporate bonds and default risk
.
58
Answer: c
Diff: M
Which of the following statements is most correct? a. The expected return on corporate bonds will generally exceed the yield to maturity. b. If a company increases its debt ratio, this is likely to reduce the default premium on its existing bonds. c. All else equal, senior debt will generally have a lower yield to maturity than subordinated debt. d. Answers a and c are correct. e. None of the answers above is correct.
Default risk
.
59
Answer: b
Diff: M
Which of the following statements is most correct? a. If a company increases its debt ratio, this is likely to reduce the default premium on its existing bonds. b. All else equal, senior debt has less default risk than subordinated debt. c. An indenture is a bond that is less risky than a subordinated debenture. d. Statements a and c are correct. e. All of the answers above are correct.
Default risk
.
60
Answer: d
Diff: M
Which of the following statements is most correct? a. The expected return on a corporate bond is always less than its promised return when the probability of default is greater than zero. b. All else equal, secured debt is considered to be less risky than unsecured debt. c. An indenture is a bond that is less risky than a subordinated debenture. d. Both a and b are correct. e. All of the answers above are correct.
Chapter 6 - Page 14
Sinking funds and default risk
.
61
Answer: d
Diff: M
Which of the following statements is correct? a. If a company is retiring bonds for sinking fund purposes it will buy back bonds on the open market when the coupon rate is less than the market interest rate. b. A bond sinking fund would be good for investors if interest rates have declined after issuance and the investor’s bonds get called. c. Mortgage bonds have less default risk than debentures. d. Both a and c are correct. e. All of the statements above are correct.
Tough: Bond yields and prices
.
62
Answer: b
Diff: T
Which of the following statements is most correct? a. If a bond's yield to maturity exceeds its coupon rate, the bond's current yield must also exceed its coupon rate. b. If a bond's yield to maturity exceeds its coupon rate, the bond's price must be less than its maturity value. c. If two bonds have the same maturity, the same yield to maturity, and the same level of risk, the bonds should sell for the same price regardless of the bond's coupon rate. d. Answers b and c are correct. e. None of the answers above is correct.
Bond concepts
.
63
Answer: b
Which of the following is true about bonds? In all statements, assume other things are held constant. not
Diff: T
of the
a. Price sensitivity, that is, the change in price due to a given change in the required rate of return, increases as a bond's maturity increases. b. For a given bond of any maturity, a given percentage point increase in the interest rate (rd) causes a larger dollar capital loss than the capital gain stemming from an identical decrease in the interest rate. c. For any given maturity, a given percentage point increase in the interest rate causes a smaller dollar capital loss than the capital gain stemming from an identical decrease in the interest rate. d. From a borrower's point of view, interest paid on bonds is taxdeductible. e. A 20-year zero coupon bond has less reinvestment rate risk than a 20-year coupon bond.
Chapter 6 - Page 15
Bond concepts
.
64
Answer: e
Diff: T
Which of the following statements is most correct? a. All else equal, an increase in interest rates will have a greater effect on the prices of long-term bonds than it will on the prices of short-term bonds. b. All else equal, an increase in interest rates will have a greater effect on higher-coupon bonds than it will have on lower-coupon bonds. c. An increase in interest rates will have a greater effect on a zero coupon bond with 10 years maturity than it will have on a 9-year bond with a 10 percent annual coupon. d. All of the statements above are correct. e. Answers a and c are correct.
Interest vs. reinvestment rate risk
.
65
Answer: c
Diff: T
Which of the following statements is most correct? a. A 10-year bond would have more interest rate risk than a 5-year bond, but all 10-year bonds have the same interest rate risk. b. A 10-year bond would have more reinvestment rate risk than a 5-year bond, but all 10-year bonds have the same reinvestment rate risk. c. If their maturities were the same, a 5 percent coupon bond would have more interest rate risk than a 10 percent coupon bond. d. If their maturities were the same, a 5 percent coupon bond would have less interest rate risk than a 10 percent coupon bond. e. Zero coupon bonds have more interest rate risk than any other type bond, even perpetuities.
Bond indenture
.
66
Answer: d
Diff: T
Listed below are some provisions that are often contained in bond indentures: 1. 2. 3. 4. 5. 6.
Fixed assets The bond may The bond may The bond may The bond may The bond may
may be used as security. be subordinated to other classes of debt. be made convertible. have a sinking fund. have a call provision. have restrictive covenants in its indenture.
Which of the above provisions, each viewed alone, would tend to reduce the yield to maturity investors would otherwise require on a newly issued bond? a. b. c. d. e.
1, 1, 1, 1, 1,
2, 2, 3, 3, 4,
3, 3, 4, 4, 6
Chapter 6 - Page 16
4, 5, 6 4, 6 5, 6 6
Weighted average cost of debt
.
67
Answer: e
Diff: T
Suppose a new company decides to raise its initial $200 million of capital as $100 million of common equity and $100 million of long-term debt. By an iron-clad provision in its charter, the company can never borrow any more money. Which of the following statements is most correct? a. If the debt were raised by issuing $50 million of debentures and $50 million of first mortgage bonds, we could be absolutely certain that the firm's total interest expense would be lower than if the debt were raised by issuing $100 million of debentures. b. If the debt were raised by issuing $50 million of debentures and $50 million of first mortgage bonds, we could be absolutely certain that the firm's total interest expense would be lower than if the debt were raised by issuing $100 million of first mortgage bonds. c. The higher the percentage of total debt represented by debentures, the greater the risk of, and hence the interest rate on, the debentures. d. The higher the percentage of total debt represented by mortgage bonds, the riskier both types of bonds will be, and, consequently, the higher the firm’s total dollar interest charges will be. e. In this situation, we cannot tell for sure how, or whether, the firm's total interest expense on the $100 million of debt would be affected by the mix of debentures versus first mortgage bonds. Interest rates on the two types of bonds would vary as their percentages were changed, but the result might well be such that the firm's total interest charges would not be affected materially by the mix between the two.
Multiple Choice: Problems Easy: Bond value - semiannual payment
.
68
Answer: c
Diff: E
Assume that you wish to purchase a bond with a 30-year maturity, an annual coupon rate of 10 percent, a face value of $1,000, and semiannual interest payments. If you require a 9 percent nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond? a. b. c. d. e.
$905.35 $1,102.74 $1,103.19 $1,106.76 $1,149.63
Chapter 6 - Page 17
Yield to maturity
.
69
Answer: b
Diff: E
A bond has an annual 8 percent coupon rate, a maturity of 10 years, a face value of $1,000, and makes semiannual payments. If the price is $934.96, what is the annual nominal yield to maturity on the bond? a. 8% b. 9% c. 10% d. 11% e. 12%
Return on a bond
.
70
Answer: b
Diff: E
A bond has an annual 11 percent coupon rate, an annual interest payment of $110, a maturity of 20 years, a face value of $1,000, and makes annual payments. It has a yield to maturity of 8.83 percent. If the price is $1,200, what rate of return will an investor expect to receive during the next year? a. -0.33% b. 8.83% c. 9.17% d. 11.00% e. None of the above
Bond value - semiannual payment
.
71
$ 826.31 $1,086.15 $ 957.50 $1,431.49 $1,124.62
Bond value - semiannual payment
.
Diff: E
You intend to purchase a 10-year, $1,000 face value bond that pays interest of $60 every 6 months. If your nominal annual required rate of return is 10 percent with semiannual compounding, how much should you be willing to pay for this bond? a. b. c. d. e.
72
Answer: e
Answer: d
Diff: E
Assume that you wish to purchase a 20-year bond that has a maturity value of $1,000 and makes semiannual interest payments of $40. If you require a 10 percent nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond? a. b. c. d. e.
$619 $674 $761 $828 $902
Chapter 6 - Page 18
Bond value - quarterly payment
.
73
a. b. c. d. e. .
Diff: E
$ 941.36 $1,051.25 $1,115.57 $1,391.00 $ 825.49
Current yield 74
Answer: c
A $1,000 par value bond pays interest of $35 each quarter and will mature in 10 years. If your nominal annual required rate of return is 12 percent with quarterly compounding, how much should you be willing to pay for this bond?
Consider a $1,000 par value bond bond pays interest annually. maturity. What is the current required return on the bond is 10
Answer: b
Diff: E
with a 7 percent annual coupon. The There are 9 years remaining until yield on the bond assuming that the percent?
a. 10.00% b. 8.46% c. 7.00% d. 8.52% e. 8.37% Risk premium on bonds
.
75
Answer: c
Diff: E
Rollincoast Incorporated issued BBB bonds two years ago that provided a yield to maturity of 11.5 percent. Long-term risk-free government bonds were yielding 8.7 percent at that time. The current risk premium on BBB bonds versus government bonds is half what it was two years ago. If the risk-free long-term governments are currently yielding 7.8 percent, then at what rate should Rollincoast expect to issue new bonds? a. 7.8% b. 8.7% c. 9.2% d. 10.2% e. 12.9%
Chapter 6 - Page 19
Medium: Bond value - annual payment
.
76
$538.21 $426.73 $384.84 $266.88 $249.98
Bond value - annual payment
.
Diff: M
You are the owner of 100 bonds issued by Euler, Ltd. These bonds have 8 years remaining to maturity, an annual coupon payment of $80, and a par value of $1,000. Unfortunately, Euler is on the brink of bankruptcy. The creditors, including yourself, have agreed to a postponement of the next 4 interest payments (otherwise, the next interest payment would have been due in 1 year). The remaining interest payments, for Years 5 through 8, will be made as scheduled. The postponed payments will accrue interest at an annual rate of 6 percent, and they will then be paid as a lump sum at maturity 8 years hence. The required rate of return on these bonds, considering their substantial risk, is now 28 percent. What is the present value of each bond? a. b. c. d. e.
77
Answer: d
Answer: a
Diff: M
Marie Snell recently inherited some bonds (face value $100,000) from her father, and soon thereafter she became engaged to Sam Spade, a University of Florida marketing graduate. Sam wants Marie to cash in the bonds so the two of them can use the money to "live like royalty" for two years in Monte Carlo. The 2 percent annual coupon bonds mature on January 1, 2024, and it is now January 1, 2004. Interest on these bonds is paid annually on December 31 of each year, and new annual coupon bonds with similar risk and maturity are currently yielding 12 percent. If Marie sells her bonds now and puts the proceeds into an account which pays 10 percent compounded annually, what would be the largest equal annual amounts she could withdraw for two years, beginning today (i.e., two payments, the first payment today and the second payment one year from today)? a. b. c. d. e.
$13,255 $29,708 $12,654 $25,305 $14,580
Chapter 6 - Page 20
Bond value - semiannual payment
.
78
a. b. c. d. e. .
Diff: M
2,400 2,596 3,000 5,000 4,275
Bond value - semiannual payment
.
Answer: b
JRJ Corporation recently issued 10-year bonds at a price of $1,000. These bonds pay $60 in interest each six months. Their price has remained stable since they were issued, i.e., they still sell for $1,000. Due to additional financing needs, the firm wishes to issue new bonds that would have a maturity of 10 years, a par value of $1,000, and pay $40 in interest every six months. If both bonds have the same yield, how many new bonds must JRJ issue to raise $2,000,000 cash? a. b. c. d. e.
80
Diff: M
$1,273 $1,000 $7,783 $ 550 $ 450
Bond value - semiannual payment 79
Answer: d
Due to a number of lawsuits related to toxic wastes, a major chemical manufacturer has recently experienced a market reevaluation. The firm has a bond issue outstanding with 15 years to maturity and a coupon rate of 8 percent, with interest paid semiannually. The required nominal rate on this debt has now risen to 16 percent. What is the current value of this bond?
Answer: d
Diff: M
Assume that you are considering the purchase of a $1,000 par value bond that pays interest of $70 each six months and has 10 years to go before it matures. If you buy this bond, you expect to hold it for 5 years and then to sell it in the market. You (and other investors) currently require a nominal annual rate of 16 percent, but you expect the market to require a nominal rate of only 12 percent when you sell the bond due to a general decline in interest rates. How much should you be willing to pay for this bond? a. b. c. d. e.
$ 842.00 $1,115.81 $1,359.26 $ 966.99 $ 731.85
Chapter 6 - Page 21
Bond value - quarterly payment
.
81
a. b. c. d. e. .
Diff: M
$ 800 $ 926 $1,025 $1,216 $ 981
Market value of bonds
.
Answer: b
Your client has been offered a 5-year, $1,000 par value bond with a 10 percent coupon. Interest on this bond is paid quarterly. If your client is to earn a nominal rate of return of 12 percent, compounded quarterly, how much should she pay for the bond? a. b. c. d. e.
83
Diff: M
$ 821.92 $1,207.57 $ 986.43 $1,120.71 $1,358.24
Bond value - quarterly payment 82
Answer: b
Assume that a 15-year, $1,000 face value bond pays interest of $37.50 every 3 months. If you require a nominal annual rate of return of 12 percent, with quarterly compounding, how much should you be willing to pay for this bond? (Hint: The PVIFA and PVIF for 3 percent, 60 periods are 27.6748 and 0.1697, respectively.)
Answer: a
Diff: M
In order to accurately assess the capital structure of a firm, it is necessary to convert its balance sheet figures to a market value basis. KJM Corporation's balance sheet as of today, January 1, 2004, is as follows: Long-term debt (bonds, at par) Preferred stock Common stock ($10 par) Retained earnings Total debt and equity
$10,000,000 2,000,000 10,000,000 4,000,000 $26,000,000
The bonds have a 4 percent coupon rate, payable semiannually, and a par value of $1,000. They mature on January 1, 2014. The yield to maturity is 12 percent, so the bonds now sell below par. What is the current market value of the firm's debt? a. b. c. d. e.
$5,412,000 $5,480,000 $2,531,000 $7,706,000 $7,056,000
Chapter 6 - Page 22
Future value of bond
.
84
a. b. c. d. e. .
Diff: M
8% 6% 4% 2% 0%
Bond coupon rate
.
Answer: c
Cold Boxes Ltd. has 100 bonds outstanding (maturity value = $1,000). The nominal required rate of return on these bonds is currently 10 percent, and interest is paid semiannually. The bonds mature in 5 years, and their current market value is $768 per bond. What is the annual coupon interest rate? a. b. c. d. e.
86
Diff: M
$1,000 $1,064 $1,097 $1,100 $1,150
Bond coupon rate 85
Answer: c
You just purchased a 15-year bond with an 11 percent annual coupon. The bond has a face value of $1,000 and a current yield of 10 percent. Assuming that the yield to maturity of 9.7072 percent remains constant, what will be the price of the bond 1 year from now?
Answer: d
Diff: M
The current price of a 10-year, $1,000 par value bond is $1,158.91. Interest on this bond is paid every six months, and the nominal annual yield is 14 percent. Given these facts, what is the annual coupon rate on this bond? a. b. c. d. e.
10% 12% 14% 17% 21%
Chapter 6 - Page 23
Tough: Bond value
.
87
$242.26 $281.69 $578.31 $362.44 $813.69
Bond sinking fund payment
.
Diff: T
Recently, Ohio Hospitals Inc. filed for bankruptcy. The firm was reorganized as American Hospitals Inc., and the court permitted a new indenture on an outstanding bond issue to be put into effect. The issue has 10 years to maturity and a coupon rate of 10 percent, paid annually. The new agreement allows the firm to pay no interest for 5 years. Then, interest payments will be resumed for the next 5 years. Finally, at maturity (Year 10), the principal plus the interest that was not paid during the first 5 years will be paid. However, no interest will be paid on the deferred interest. If the required annual return is 20 percent, what should the bonds sell for in the market today? a. b. c. d. e.
88
Answer: d
Answer: d
Diff: T
GP&L sold $1,000,000 of 12 percent, 30-year, semiannual payment bonds 15 years ago. The bonds are not callable, but they do have a sinking fund which requires GP&L to redeem 5 percent of the original face value of the issue each year ($50,000), beginning in Year 11. To date, 25 percent of the issue has been retired. The company can either call bonds at par for sinking fund purposes or purchase bonds on the open market, spending sufficient money to redeem 5 percent of the original face value each year. If the nominal yield to maturity (15 years remaining) on the bonds is currently 14 percent, what is the least amount of money GP&L must put up to satisfy the sinking fund provision? a. b. c. d. e.
$43,856 $50,000 $37,500 $43,796 $39,422
Chapter 6 - Page 24
Financial Calculator Section Multiple Choice: Problems Easy: Bond value - semiannual payment
.
89
a. b. c. d. e. .
Diff: E
$ 784.27 $ 781.99 $1,259.38 $1,000.00 $ 739.19
Yield to maturity
.
Answer: b
A bond with a $1,000 face value and an 8 percent annual coupon pays interest semiannually. The bond will mature in 15 years. The nominal yield to maturity is 11 percent. What is the price of the bond today? a. b. c. d. e.
91
Diff: E
$ 634.86 $1,064.18 $1,065.04 $1,078.23 $1,094.56
Bond value - semiannual payment 90
Answer: c
A corporate bond with a $1,000 face value pays a $50 coupon every six months. The bond will mature in ten years, and has a nominal yield to maturity of 9 percent. What is the price of the bond?
Answer: a
Diff: E
Palmer Products has outstanding bonds with an annual 8 percent coupon. The bonds have a par value of $1,000 and a price of $865. The bonds will mature in 11 years. What is the yield to maturity on the bonds? a. 10.09% b. 11.13% c. 9.25% d. 8.00% e. 9.89%
YTM and YTC
.
92
Answer: e
Diff: E
A corporate bond matures in 14 years. The bond has an 8 percent semiannual coupon and a par value of $1,000. The bond is callable in five years at a call price of $1,050. The price of the bond today is $1,075. What are the bond’s yield to maturity and yield to call? a. b. c. d. e.
YTM YTM YTM YTM YTM
= 14.29%; YTC = 14.09% = 3.57%; YTC = 3.52% = 7.14%; YTC = 7.34% = 6.64%; YTC = 4.78% = 7.14%; YTC = 7.05%
Chapter 6 - Page 25
Current yield
.
93
Answer: d
Diff: E
A 12-year bond pays an annual coupon of 8.5 percent. The bond has a yield to maturity of 9.5 percent and a par value of $1,000. What is the bond’s current yield? a. 6.36% b. 2.15% c. 8.95% d. 9.14% e. 10.21%
Current yield and yield to maturity
.
94
Answer: b
a. b. c. d. e.
Current Current Current Current Current
yield yield yield yield yield
= = = = =
8.00%; 8.12%; 8.20%; 8.12%; 8.12%;
yield yield yield yield yield
to to to to to
Yield on semiannual bond
.
95
Diff: E
A bond matures in 12 years, and pays an 8 percent annual coupon. The bond has a face value of $1,000, and currently sells for $985. What is the bond’s current yield and yield to maturity? maturity maturity maturity maturity maturity
= = = = =
7.92%. 8.20%. 8.37%. 8.37%. 7.92%. Answer: c
Diff: E
A corporate bond has a face value of $1,000, and pays a $50 coupon every six months (i.e., the bond has a 10 percent semiannual coupon). The bond matures in 12 years and sells at a price of $1,080. What is the bond’s nominal yield to maturity? a. 8.28% b. 8.65% c. 8.90% d. 9.31% e. 10.78%
Yield to maturity and bond value--annual
.
96
Answer: d
Diff: E
A 20-year bond with a par value of $1,000 has a 9 percent annual coupon. The bond currently sells for $925. If the bond’s yield to maturity remains at its current rate, what will be the price of the bond 5 years from now? a. b. c. d. e.
$ 966.79 $ 831.35 $1,090.00 $ 933.09 $ 925.00
Chapter 6 - Page 26
Medium: Bond value - semiannual payment
.
97
$ $ $ $ $
898.64 736.86 854.27 941.09 964.23
Call price
.
Diff: M
$ 379.27 $1,025.00 $1,048.34 $1,036.77 $1,136.78
Yield to call
.
Answer: c
Kennedy Gas Works has bonds which mature in 10 years, and have a face value of $1,000. The bonds have a 10 percent quarterly coupon (i.e., the nominal coupon rate is 10 percent). The bonds may be called in five years. The bonds have a nominal yield to maturity of 8 percent and a yield to call of 7.5 percent. What is the call price on the bonds? a. b. c. d. e.
99
Diff: M
An 8 percent annual coupon, noncallable bond has ten years until it matures and a yield to maturity of 9.1 percent. What should be the price of a 10-year noncallable bond of equal risk which pays an 8 percent semiannual coupon? Assume both bonds have a par value of $1,000. a. b. c. d. e.
98
Answer: d
Answer: b
Hood Corporation recently issued 20-year bonds. The bonds rate of 8 percent and pay interest semiannually. Also, callable in 6 years at a call price equal to 115 percent The par value of the bonds is $1,000. If the yield to percent, what is the yield to call?
Diff: M
have a coupon the bonds are of par value. maturity is 7
a. 8.33% b. 7.75% c. 9.89% d. 10.00% e. 7.00%
Yield to call
Answer: d
Diff: M
Chapter 6 - Page 27
.
100
A 12-year bond with a 10 percent semiannual coupon and a $1,000 par value has a nominal yield to maturity of 9 percent. The bond can be called in five years at a call price of $1,050. What is the bond's nominal yield to call? a. b. c. d. e.
4.50% 8.25% 8.88% 8.98% 9.00%
Yield to call
.
101
A corporate maturity of ten years. What is the a. b. c. d. e.
.
Diff: M
8.43% 8.50% 8.58% 8.65% 9.00%
Yield to call 102
Answer: c
bond with an 11 percent semiannual coupon has a yield to 9 percent. The bond matures in 20 years but is callable in The maturity value is $1,000. The call price is $1,055. bond's yield to call?
Answer: a
Diff: M
A corporate bond which matures in 12 years, pays a 9 percent annual coupon, has a face value of $1,000, and a yield to maturity of 7.5 percent. The bond can first be called four years from now. The call price is $1,050. What is the bond’s yield to call? a. 6.73% b. 7.10% c. 7.50% d. 11.86% e. 13.45%
Yield to call
.
103
Answer: b
Diff: M
A bond that matures in 11 years has an annual coupon rate of 8 percent with interest paid annually. The bond’s face value is $1,000 and its yield to maturity is 7.5 percent. The bond can be called 3 years from now at a price of $1,060. What is the bond’s nominal yield to call? a. b. c. d. e.
9.82% 8.41% 8.54% 8.38% 7.86%
Chapter 6 - Page 28
Yield to call
.
104
Answer: b
Diff: M
McGriff Motors has bonds outstanding which will mature in 12 years. The bonds pay a 12 percent semiannual coupon and have a face value of $1,000 (i.e., the bonds pay a $60 coupon every six months). The bonds currently have a yield to maturity of 10 percent. The bonds are callable in 8 years and have a call price of $1,050. What are the bonds' yield to call? a. 8.89% b. 9.89% c. 9.94% d. 10.00% e. 12.00%
After-tax yield to call
.
105
5.52% 5.90% 6.60% 7.07% 9.52%
Yield to maturity
.
Diff: M
5.97% 6.30% 6.75% 6.95% 7.10%
Interest payments remaining
.
Answer: d
A 15-year bond with a 10 percent semiannual coupon has a par value of $1,000. The bond may be called after 10 years at a call price of $1,050. The bond has a nominal yield to call of 6.5 percent. What is the bond's yield to maturity, stated on a nominal, or annual basis? a. b. c. d. e.
107
Diff: M
A company is issuing $1,000 bonds at par value. The coupon rate (and yield to maturity) on the bonds is 8 percent (with annual payments) and the bonds will mature in 10 years. The bonds can be called at a call premium of 5 percent above face value after 3 years. What is the after-tax yield to call for an investor with a 31 percent tax rate? a. b. c. d. e.
106
Answer: c
Answer: b
Diff: M
You have just been offered a $1,000 par value bond for $847.88. The coupon rate is 8 percent, payable annually, and annual interest rates on new issues of the same degree of risk are 10 percent. You want to know how many more interest payments you will receive, but the party selling the bond cannot remember. Can you determine how many interest payments remain? a. b. c. d. e.
14 15 12 20 10
Chapter 6 - Page 29
Current yield and capital gains yield
.
108
a. b. c. d. e.
Current Current Current Current None of
yield = 8.50%, capital gains yield = 9.35%, capital gains yield = 9.35%, capital gains yield = 10.00%, capital gains the answers above is correct.
Bond value
.
109
Answer: c
Diff: M
Meade Corporation bonds mature in 6 years and have a yield to maturity of 8.5 percent. The par value of the bonds is $1,000. The bonds have a 10 percent coupon rate and pay interest on a semiannual basis. What are the current yield and capital gains yield on the bonds for this year? (Assume that interest rates do not change over the course of the year). yield yield yield yield
= = = =
1.50% 0.65% -0.85% 0.00% Answer: e
Diff: M
A 6-year bond which pays 8 percent interest semiannually sells at par ($1,000). Another 6-year bond of equal risk pays 8 percent interest annually. Both bonds are non-callable and have a face value of $1,000. What is the price of the bond which pays annual interest? a. b. c. d. e.
$689.08 $712.05 $980.43 $986.72 $992.64
Tough: Bond value
.
110
Answer: d
Diff: T
Assume that McDonald's and Burger King have similar $1,000 par value bond issues outstanding. The bonds are equally risky. The Burger King bond has an annual coupon rate of 8 percent and matures 20 years from today. The McDonald's bond has a coupon rate of 8 percent, with interest paid semiannually , and it also matures in 20 years. If the nominal required rate of return, rd, is 12 percent, semiannual basis, for both bonds, what is the difference in current market prices of the two bonds? a. b. c. d. e.
No difference. $ 2.20 $ 3.77 $17.53 $ 6.28
Chapter 6 - Page 30
Bond value and effective annual rate
.
111
Answer: b
Diff: T
You are considering investing in a security that matures in 10 years with a par value of $1,000. During the first five years, the security has an 8 percent coupon with quarterly payments (i.e., you receive $20 a quarter for the first 20 quarters). During the remaining five years the security has a 10 percent coupon with quarterly payments (i.e., you receive $25 a quarter for the second 20 quarters). After 10 years (40 quarters) you receive the par value. Another 10-year bond has an 8 percent semiannual coupon (i.e., coupon payment is $40 every six months). This bond is selling at par value, $1,000. This bond has the same risk as the security you thinking of purchasing. Given this information, what should be price of the security you are considering purchasing? a. b. c. d. e.
$ 898.65 $1,060.72 $1,037.61 $ 943.22 $1,145.89
Bond coupon payment
.
112
Diff: T
$120.00 $ 37.12 $ 56.42 $ 29.68 $ 11.16
Bonds with differential payments
.
Answer: b
Fish & Chips Inc. has two bond issues outstanding, and both sell for $701.22. The first issue has an annual coupon rate of 8 percent and 20 years to maturity. The second has an identical yield to maturity as the first bond, but only 5 years until maturity. Both issues pay interest annually. What is the annual interest payment on the second issue? a. b. c. d. e.
113
the its are the
Answer: c
Diff: T
Semiannual payment bonds with the same risk (Aaa) and maturity (20 years) as your company's bonds have a nominal (not EAR) yield of 9 percent. Your company's treasurer is thinking of issuing at par some $1,000 par value, 20-year, quarterly payment bonds. She has asked you to determine what quarterly interest payment, in dollars, the company would have to set in order to provide the same effective annual rate (EAR) as those on the 20-year, semiannual payment bonds. What would the quarterly interest payment be, in dollars? a. b. c. d. e.
$45.00 $25.00 $22.25 $27.50 $23.00
Chapter 6 - Page 31
CHAPTER 6 ANSWERS AND SOLUTIONS
Chapter 6 - Page 32
1.
Discounted cash flows
Answer: b
Diff: E
2.
Issuing bonds
Answer: b
Diff: E
3.
Interest rate risk
Answer: b
Diff: E
4.
Interest rate risk
Answer: b
Diff: E
5.
Bond prices and interest rates
Answer: a
Diff: E
6.
Mortgage bond
Answer: a
Diff: E
7.
Debt coupon rate
Answer: a
Diff: E
8.
Call provision
Answer: b
Diff: E
9.
Sinking fund
Answer: a
Diff: E
10.
Zero coupon bond
Answer: b
Diff: E
11.
Floating rate debt
Answer: a
Diff: E
12.
Junk bond
Answer: a
Diff: E
13.
Bond ratings and required returns
Answer: a
Diff: E
14.
Bond value
Answer: a
Diff: M
15.
Bond value - annual payment
Answer: a
Diff: M
Time Line: 0
1 2 3 9 10 Years 12% ├────────┼─────────┼─────────┼──────···─────┼──────────┤ PMT = 100 100 100 100 100 PV = ? FV = 1,000
Numerical solution: VB = $100(PVIFA12%,10 ) + $1,000(PVIF12%,10 ) = $100((1- 1/1.1210)/0.12) + $1,000(1/1.1210) = $100(5.6502) + $1,000(0.3220) = $887.02. Thus, the value is significantly higher than the market price and the bond should be purchased.
1 16
Financial calculator solution: Inputs: N = 10; I = 12; PMT = 100; FV = 1,000.
Output: PV = -$887.00.
.
Prices and interest rates
Answer: a
Diff: M
17.
Bond premiums and discounts
Answer: a
Diff: M
18.
Callable bond
Answer: b
Diff: M
19.
Indexed bond
Answer: b
Diff: M
20.
Income bond
Answer: b
Diff: M
21.
Restrictive covenants
Answer: a
Diff: M
22.
Sinking fund
Answer: b
Diff: M
23.
Floating rate debt
Answer: b
Diff: M
24.
Bond ratings
Answer: a
Diff: M
25.
Interest rates
Answer: e
Diff: E
26.
Interest rate and reinvestment risk
Answer: e
Diff: E
Statements a, b, c, and d are all correct. 27.
2 28
Callable bond
Therefore, the answer is e. Answer: a
Diff: E
Statement a is correct; the other statements are false. A bond downgrade generally raises the cost of issuing new debt. Therefore, the callable bonds would not be called. If the call premium (the cost paid in excess of par) increases, the cost of calling debt increases; therefore, callable bonds would not be called.
.
Call provision
Answer: b
Diff: E
29.
Bond coupon rate
Answer: c
Diff: E
30.
Bond concepts
Answer: a
Diff: E
Statement a is correct; the other statements are false. A bond's price and YTM are negatively related. If a bond's YTM is greater than its coupon rate, it will sell at a discount. 31.
Bond concepts
Answer: c
Diff: E
Statement c is correct; the other statements are false. If a bond’s YTM > annual coupon, then it will trade at a discount. If interest rates increase, the 10-year zero coupon bond’s price change is greater than the 10-year coupon bond’s. 32
. Bond concepts
Answer: e
Diff: E
All the statements are true; therefore, the correct statement is e. Since the bond is selling at par, its YTM = coupon rate. The current yield is calculated as $90/$1,000 = 9%. If YTM = coupon rate, the bond will sell at par. So, if the bond’s YTM remains constant the bond’s price will remain at par. 33.
Sinking fund
Answer: e
Diff: E
Statement a is false; sinking funds require companies to retire a certain portion of their debt annually. Statement b is true; if interest rates have declined, companies will call the bonds and investors will have to reinvest at lower rates. Statement c is true; if interest rates have risen (causing bond prices to fall) the company will buy bonds back in the open market. Statements b and c are true; therefore, statement e is the correct choice. 34.
Sinking fund provision
Answer: d
Diff: E
Statements a and c are correct; therefore, statement d is the correct choice. Bonds will be purchased on the open market when they are selling at a
discount and will be called for redemption when the price of the bonds exceeds the redemption price. 35.
Types of debt
Answer: e
Diff: E
Statement e is correct; the others are false. Junk bonds have a higher yield to maturity relative to investment grade bonds. A debenture is an unsecured bond, while subordinated debt has greater default risk than senior debt. 36.
Bond yield
Answer: b
Diff: M
37.
Bond yield
Answer: c
Diff: M
Statement c is correct; the other statements are false. By definition, if a coupon bond is selling at par its current yield will equal its yield to maturity. If we let Bond A be a 5-year, 12% coupon bond that sells at par, its current yield equals its YTM which equals 12%. If we let Bond B be a 5year, 10% coupon bond (in a 12% interest rate environment) the bond will sell for $927.90. Its current yield equals 10.78% ($100/$927.90), but its yield to maturity equals 12%. The YTC is a better measure of return than the YTM if the bond is selling at a premium. 38.
Price risk
Answer: c
Diff: M
Statement c is correct; the other statements are incorrect. Long-term, lowcoupon bonds are most affected by changes in interest rates; therefore, of the bonds listed the 10-year zero coupon bond will have the largest percentage increase in price. 39.
Price risk
Answer: c
Diff: M
The correct answer is c; the other statements are false. Zero coupon bonds have greater price risk than either of the coupon bonds or the annuity. 40.
Price risk
Answer: c
Diff: M
The correct answer is c; the other statements are false. All other things equal, a zero coupon bond will experience a larger percentage change in value for a given change in interest rates than will a coupon-bearing bond. Further, bonds with long remaining lives experience greater percentage changes in value than do bonds with short remaining lives. Thus, the 10-year zero coupon bond has the largest percentage increase in value. 41.
Price risk
Answer: a
Diff: M
Statement a is correct. All other things equal, a zero coupon bond will experience a larger percentage change in value for a given change in interest rates than will a coupon-bearing bond. Further, bonds with long remaining lives experience greater percentage changes in value than do bonds with short remaining lives. Thus, the 10-year zero coupon bond has the largest percentage increase in value. 42.
43
Bond concepts
Answer: e
Diff: M
The correct answer is e; the other statements are false. A zero coupon bond will always sell at a discount below par, provided interest rates are above zero, which they always are.
.
Bond concepts
Answer: d
Diff: M
Statements a and c are correct; therefore, statement d is the correct choice. If inflation were to increase, interest rates would rise, thus bond prices would fall. 44.
Bond concepts
Answer: b
Diff: M
Statement b is correct; the other statements are false. If a bond is selling at a premium, the YTM would be less than the coupon rate. In addition, as long as interest rates are greater than zero, zeros should never trade above par. 45.
Bond concepts
Answer: b
Diff: M
Statement b is correct; the other statements are false. If a bond’s coupon rate > than the required rate, the bond will sell at a premium. A bond’s total return also includes a capital gains component that represents the change in the price of the bond over a given year. 4 46 .
Bond concepts
Answer: e
Diff: M
47.
Bond concepts
Answer: d
Diff: M
Statements a and c are correct; therefore, statement d is the appropriate choice. Statement a is correct. From the information given, we can solve for the price of the bond = $887. Current yield = $100/$887 = 11.274%. Statement b is incorrect; since the bond is selling at a discount its YTC > YTM. The YTC = 14.05%. Statement c is correct. From the information given, since the coupon rate < YTM we know the bond is selling at a discount. VB = $887.00. 48.
Callable bond
Answer: d
Diff: M
49.
Callable bond
Answer: b
Diff: M
Statement b is correct; the other statements are false. The bonds' prices would differ substantially only if investors think a call is likely, in which case investors would have to give up a high coupon bond. Calls are most likely if the current market rate is well below the coupon rate. Note that if the current rate is above the coupon rate, the bond won't be called. 50.
Types of debt
Answer: c
Diff: M
51.
Miscellaneous concepts
Answer: b
Diff: M
Statement b is correct; the other statements are false. Firms prefer the less expensive option of calling the bonds--which in this case is the sinking fund call price. Interest expense accrues for tax purposes on zero coupon bonds, so firms can realize the tax savings from issuing debt. Callable bonds will sell for a higher yield than noncallable bonds, if all other things are held constant. 52.
Miscellaneous concepts
Answer: b
Diff: M
53.
Miscellaneous concepts
Answer: e
Diff: M
Statements a and b are both correct; therefore statement e is the correct choice. Low coupon bonds have less reinvestment rate risk than high coupon
bonds. If the bond is trading at a premium, then its coupon rate is high in relation to current interest rates. The issuer would be likely to call the bond and issue new bonds at the lower current interest rate. Thus, we would expect to earn the yield to call. 54.
Interest rate risk
Answer: a
Diff: M
Statement a is correct. The longer the maturity and the lower the coupon of a bond, the more sensitive it is to interest rate price risk. The bond in answer a has a maturity greater than or equal to and a coupon less than or equal to all the other bonds. 55.
5 56 .
Interest rate risk
Answer: a
Diff: M
The correct answer is a. The bond with the smallest coupon and longest maturity will be most sensitive to changes in interest rates. Current yield and yield to maturity
Answer: e
Diff: M
Statement e is the correct choice. If a bond sells for less than par, then its yield to maturity will exceed its coupon rate. If a bond sells at par, then its current yield, yield to maturity, and coupon rate are all the same. The bond selling for more than par will have a lower current yield than a bond selling at par. However, the bond selling for more than par will have a negative capital gain (i.e., a capital loss) while the bond selling at par will have no capital gain. 5 57 .
Current yield and yield to maturity
Answer: a
Diff: M
Statement a is correct; the other statements are false. If the bond sells for a premium, this implies that the YTM must be less than the coupon rate. As a bond approaches maturity, its price will move toward the par value. 58.
Corporate bonds and default risk
Answer: c
Diff: M
Statement c is the correct choice; the other statements are false. The expected return may be greater than, less than, or equal to the yield to maturity. If a company increases its debt ratio, the default risk premium on its existing bonds will increase. 59.
Default risk
Answer: b
Diff: M
60.
Default risk
Answer: d
Diff: M
Statements a and b are correct; therefore, statement d is the correct choice. An indenture is not a bond, it is a legal contract spelling out the rights of investors and issuers. 61.
Sinking funds and default risk
Answer: d
Diff: M
Statements a and c are correct; therefore, statement d is the correct choice. When the coupon rate is below the market rate, then the price is below par, so the firm will buy back its bonds on the open market. If interest rates have declined after the issuance of a bond, then the bond has a coupon rate higher than the going market interest rate. Therefore, investors are being paid a higher rate than current interest rates and they would prefer to keep the bonds to receive a higher return.
62.
Bond yields and prices
Answer: b
Diff: T
Statement b is correct. If a bond's YTM exceeds its coupon rate, then, by definition, the bond sells at a discount. Thus, the bond's price is less than its maturity value. Statement a is false. Consider zero coupon bonds. A zero coupon bond's YTM exceeds its coupon rate (which is equal to zero); however, its current yield is equal to zero which is equal to its coupon rate. Statement c is false; a bond's value is determined by its cash flows: coupon payments plus principal. If the 2 bonds have different coupon payments, their prices would have to be different in order for them to have the same YTM. 63.
Bond concepts
Answer: b
Diff: T
64.
Bond concepts
Answer: e
Diff: T
Statements a and c are correct; therefore, Statement e is the correct choice. The longer the maturity of a bond, the greater the impact an increase in interest rates will have on the bond's price. Statement b is false. To see this, assume interest rates increase from 7 percent to 10 percent. Evaluate the change in the prices of a 10-year, 5 percent coupon bond and a 10-year, 12 percent coupon bond. The 5 percent coupon bond's price decreases by 19.4 percent, while the 12 percent coupon bond's price decreases by only 16.9 percent. Statement c is correct. To see this, evaluate a 10-year, zero coupon bond and a 9-year, 10 percent annual coupon bond at 2 different interest rates, say 7 percent and 10 percent. The zero coupon bond's price decreases by 24.16 percent, while the 9-year, 10 percent coupon bond's price decreases by only 16.33 percent. 65.
Interest vs. reinvestment rate risk
Answer: c
Diff: T
Statement c is correct. For example, assume these coupon bonds have 10 years until maturity and the current interest rate is 12 percent. The 5 percent coupon bond's value is $604.48, while the 10 percent coupon bond's value is $887.00. Thus, the lower-coupon bond has more interest rate risk than the higher-coupon bond. The lower the coupon, the greater the percentage of the cash flow that will come in the later years (from the maturity value), hence, the greater the impact of interest rate changes. Statement a is false--as we demonstrated above. Statement b is false--shorter-term bonds have more reinvestment rate risk than longer-term bonds because the principal payment must be reinvested sooner on the shorter-term bond. Statement d is false--as we demonstrated earlier. Statement e is false because perpetuities have no maturity date; therefore, they have more interest rate risk than zero coupon bonds. The longer a security's maturity, the greater its interest rate risk. 66.
Bond indenture
Answer: d
Diff: T
Weighted average cost of debt
Answer: e
Diff: T
6 67 .
r d% e.g. Part A represents 50% debentures and 50% mortgage bonds
Debentures
WACD
Mortgage A
0
50%
100%
Percentage of total issue as mortgage bonds
1. Company can't lower its total cost of the $100 million of debt very much if any by the mix of debentures and mortgage bonds. 2. Debentures' risk rises as mortgage debt rises. 3. Mortgage bonds' risk rises as more mortgage bonds are issued. 4. So, the "WACD" will likely remain fairly stable. 68.
Bond value - semiannual payment
Answer: c
Diff: E
Time Line: 0
4.5%
|
1
| 50
2 | 50
3 | 50
4 | 50
60 . .
PV = ?
| 50 FV = 1,000
6-month Periods
Numerical solution: VB = $50((1- 1/1.04560)/0.045) + $1,000(1/1.04560) = $50(20.6380) + $1,000(0.071289) = $1,103.19≈ $1,103. Financial calculator solution: Inputs: N = 60; I = 4.5; PMT = 50; FV = 1,000. Output: PV = -$1,103.19; VB ≈ $1,103. 69.
70.
Yield to maturity
Answer: b
Enter N = 20 PV = -934.96, PMT = 40, and FV = 1000. the annual rate is 9%.
Solve for I = 4.5%.
Return on a bond
Diff: E
Answer: b Diff: E
So
The bond has a current yield of 9.17% = $110/$1200. Next year’s projected price is $1,196.02 (N=19, I=8.83, PMT=110, FV=1000), for a capital gains return of –0.33%. The total return is 9.17% - 0.33% = 8.84% ≈ 8.83%, which is the yield to maturity.
71.
Bond value - semiannual payment
Answer: e
Diff: E
Time Line: 0
5%
| PV = ?
1
2
| PMT = 60
| 60
20 . .
| 60 FV = 1,000
6-month periods
Numerical solution: VB = $60(PVIFA5%,20) + $1,000(PVIF5%,20) = $60((1- 1/1.0520)/0.05) + $1,000(1/1.0520) = $60(12.4622) + $1,000(0.3769) = $1,124.63. Financial calculator solution: Inputs: N = 20; I = 5; PMT = 60; FV = 1,000. Output: PV = -$1,124.62; VB = $1,124.62.
72.
Bond value - semiannual payment
Answer: d
Diff: E
Time Line: 0
5%
|
1 | 40
2 | 40
3 | 40
4 | 40
40 . .
| 40 FV = 1,000
PV = ?
6-month Periods
Numerical solution: VB = $40((1- 1/1.0540)/0.05) + $1,000(1/1.0540) = $40(17.1591) + $1,000(0.1420) = $828.36 ≈ $828. Financial calculator solution: Inputs: N = 40; I = 5; PMT = 40; FV = 1,000. Output: PV = -$828.41; VB ≈ $828. 73.
Bond value - quarterly payment
Answer: c
Diff: E
Time Line: 0 |
3%
1
2
3
4
|
|
|
|
35
35
PMT = 35 35 PV = ?
40 · ·
Numerical solution: VB = $35((1- 1/1.0340)/0.03) + $1,000(1/1.0340) = $35(23.1148) + $1,000(0.3066) = $1,115.62. Financial calculator solution: Inputs: N = 40; I = 3; PMT = 35; FV = 1,000. Output: PV = -$1,115.57; VB = $1,115.57.
| 35 FV = 1,000
Quarters
74.
Current yield
Answer: b
Diff: E
Numerical solution: VB = $70((1- 1/1.109)/0.10) + $1,000(1/1.109) = $70(5.7590) + $1,000(0.4241) = $403.13 + $424.10 = $827.23. Financial calculator solution: N = 9, I = 10, PMT = 70, FV = 1,000, and solve for PV = ? = -$827.23. Current yield = $70/$827.23 = 8.46%. 75.
Risk premium on bonds
Answer: c
Calculate the previous risk premium,
RPBBB = 11.5% - 8.7% = 2.8%. New RPBBB = 2.8%/2 = 1.4%. Calculate new YTM on BBB bonds:
76.
RPBBB,
and new RPBBB:
YTMBBB = 7.8% + 1.4% = 9.2%.
Bond value - annual payment
Time Line: 0 1 28%
2
3
| | | | Deferred PMTs earn 6% 80 80 80
Diff: E
Answer: d
4
5
6
7
|
| 80
| 80 6% 6% 6% 6%
| 80
80
VB = ? FVDeferred
PMTs
Diff: M
8 Years
| 80 101.00 107.06 113.48 120.29 + Interest = 441.83 FVPar = 1,000.00
Numerical solution: Find the compounded value at Year 8 of the postponed interest payments
FVDeferred interest = $80(1.06)7 + $80(1.06)6 + $80(1.06)5 + $80(1.06)4 = $441.83 payable at t = 8. Now find the value of the bond considering all cash flows
VB = $80(1/1.28)5 + $80(1/1.28)6 + $80(1/1.28)7 + $80(1/1.28)8 + $1,000(1/1.28)8 + $441.83(1/1.28)8 = $266.86. Financial calculator solution: Calculate FV of deferred interest
Inputs: CF0 = 0; CF1 = 80; Nj = 4; CF2 = 0; Nj = 4; I = 6. Output: NFV = $441.828. Calculate V which is the B, interest, and maturity value
PV
of
scheduled
interest,
deferred
accrued
Inputs: CF0 = 0; CF1 = 0; Nj = 4; CF2 = 80; Nj = 3; CF3 = 1,521.83; I = 28. Output: NPV = $266.88; VB = $266.88. Differences in numerical and financial rounding of interest rate table figures.
calculator
solutions
are
due
to
7 77
.
Bond value - annual payment
Time Line: 1/1/02 0
12%
|
1
Answer: a
Diff: M
1/1/2022 20 Years
2 . . .
| | 2,000 2,000
| 2,000 FV = 100,000
VB = ?
Numerical solution: Calculate PV of the bonds Step 1 VB = $2,000(PVIFA12%,20 ) + $100,000(PVIF12%,20 ) = $2,000((1- 1/1.1220)/0.12) + $100,000(1/1.1220) = $2,000(7.4694) + $100,000(0.1037) = $25,308.80. Calculate the equal payments of the annuity due. Step 2 PMT = =
$25,308.80 ( PVIFA10%,2 )(1.10) $25,308.80 (1.7355)(1.10)
=
$25,308.80 2 ((1 - 1/1.10 )/0.10) (1.10)
= $13,257.27.
Financial calculator solution: Calculate the PV of the bonds
Inputs: N = 20; I = 12; PMT = 2,000; FV = 100,000. Output: PV = -$25,305.56. Calculate equal annuity due payments BEGIN mode Inputs: N = 2; I = 10; PV = -25,305.56; FV = 0. Output: PMT = $13,255.29 ≈ $13,255. 78.
Bond value - semiannual payment
Time Line: 0
8%
1
|
VB
| PMT = 40 = ?
Numerical solution:
Answer: d
2 | 40
30 6-month ·· ·
| 40 FV = 1,000
Periods
Diff: M
VB = $40(PVIFA8%,30) + $1,000(PVIF8%,30) = $40((1- 1/1.0230)/0.02) + $1,000(1/1.0230) = $40(11.2578) + $1,000(0.0994) = $549.71 ≈ $550. Financial calculator solution: Inputs: N = 30; I = 8; PMT = 40; FV = 1,000. Output: PV = -$549.69; VB = $549.69 ≈ $550.
79.
Bond value - semiannual payment
Time Line: 0 | VB-Old VB-New
6%
1
Answer: b
2
| | PMT = 60 60 = 1,000 PMT = 40 40 = ?
Diff: M
20 6-month . . .
| Periods 60 FV = 1,000 40 FV = 1,000
Numerical solution: Since the old bond issue sold at its maturity (or par) value, and still sells at par, its yield (and the yield on the new issue) must be 6 percent semiannually. The new bonds will be offered at a discount: VB = $40(PVIFA6%,20) + $1,000(PVIF6%,20) = $40((1- 1/1.0620)/0.06) + $1,000(1/1.0620) = $40(11.4699) + $1,000(0.3118) = $770.60. Number of bonds = $2,000,000/$770.60 = 2,595.38 ≈ 2,596. Financial calculator solution: Inputs: N = 20; I = 6; PMT = 40; FV = 1,000. Output: PV = -$770.60; VB = $770.60. Number of bonds: $2,000,000/$770.60 ≈ 2,596 bonds.* *Rounded up to next whole bond. 80.
Bond value - semiannual payment Answer: d Time Line: 0 rd/2 = 8% 1 2 10 6-month . . . TL1 | | | | Periods PMT = 70 70 70 VB = ? FV = VB5 = 1,073.61
TL2
10 rd/2 = 6% 11 | | PMT = 70 VB5 = ?
Maturity 20 6-month
12 | 70
. . .
| Periods 70 FV = 1,000
Numerical solution: VB5 = $70(PVIFA6%,10) + $1,000(PVIF6%,10) = $70((1- 1/1.0610)/0.06) + $1,000(1.0610) = $70(7.3601) + $1,000(0.5584) = $1,073.61. VB = $70(PVIFA8%,10) + $1,073.61(PVIF8%,10)
Diff: M
= $70((1- 1/1.0810)/0.08) + $1,073.61(1.0810) = $70(6.7101) + $1,073.61(0.4632) = $967.00. Financial calculator solution:
Solve for V B at Time = 5 (V 5) with 5 years to maturity
Inputs: N = 10; I = 6; PMT = 70; FV = 1,000.
Output: PV = -$1,073.60.
B5
Solve for V B at Time = 0, assuming sale at
= $1,073.60.
Inputs: N = 10; I = 8; PMT = 70; FV = 1,073.60. Output: PV = -$966.99; VB = $966.99.
81.
Bond value - quarterly payment
Time Line: 0
VB
3% 1 | | PMT = 37.5 = ?
2
3
| | 37.5 37.5
Answer: b
4
Diff: M
60 Quarters
| · · · 37.5
| 37.5 FV = 1,000
Numerical solution: (PVIFA and PVIF are given in the VB = $37.50(PVIFA3%,60) + $1,000(PVIF3%,60) = $37.50(27.6748) + $1,000(0.1697) = $1,207.51.
problem.)
Financial calculator solution: Inputs: N = 60; I = 3; PMT = 37.50; FV = 1,000. Output: PV = -$1,207.57; VB = $1,207.57. Numerical solution differs from calculator solution due to interest factor rounding. Note:
82.
Bond value - quarterly payment
Time Line: 0 3% |
1
2
| PMT = 25
| 25
3 | 25
Answer: b
4 | 25
Diff: M
20 Quarters . . .
| 25 FV = 1,000
VB = ?
Numerical solution: VB = $25(PVIFA3%,20) + $1,000(PVIF3%,20) = $25((1- 1/1.0320)/0.03) + $1,000(1/1.0320) = $25(14.8775) + $1,000(0.5537) = $925.64 ≈ $926. Financial calculator solution: Inputs: N = 20; I = 3; PMT = 25; FV = 1,000. Output: PV = -$925.61; VB ≈ $926.
83.
Market value of bonds
Time Line: 1/1/04 0 6% |
Answer: a
1
2
| PMT = 20
| 20
VB = ?
Numerical solution:
1/1/2014 20 6-month . . .
| Periods 20 FV = 1,000
Diff: M
VB
= $20(PVIFA6%,20) + $1,000(PVIF6%,20) = $20((1- 1/1.0620)/0.06) + $1,000(1/1.0620) = $20(11.4699) + $1,000(0.3118) = $541.20 per bond.
Since there are 10,000 bonds outstanding $541.20(10,000) = $5.412 million.
the
total
value
of debt is
Financial calculator solution: Inputs: N = 20; I = 6; PMT = 20; FV = 1,000. Output: PV = -$541.20; VB = $541.20. 84.
Future value of bond
Answer: c
Diff: M
The YTM = Current yield + Capital Gain Thus: Capital gain = YTM - Current yield = 9.7072% - 10% = -0.2928%. The price in 1 year = Price now
×
(1 + CG%).
Price now: Current yield = Annual coupon/Price Thus: Price = Annual coupon/Current yield = $110/0.10 = $1,100. Price in one year = $1,100 × (1 + CG%) = $1,100 × (1 - 0.002928) (Remember to express the = $1,096.78 ≈ $1,097. capital gain as a decimal.) 85.
Bond coupon rate
Answer: c
Time Line: 0 rd/2 = 5% 1 | | PMT = ? VB = 768
2
3
| PMT
| PMT
4
Diff: M
10 6-month ...
| PMT
| Periods PMT FV = 1,000
Numerical solution: $768 = PMT/2(PVIFA5%,10) + $1,000(PVIF5%,10) = PMT/2((1- 1/1.0510)/0.05) + $1,000(1/1.0510) = PMT/2(7.7217) + $1,000(0.6139) 154.10 = PMT/2(7.7217) PMT/2 = $19.96 ≈ $20 PMT ≈ $40 and coupon rate ≈ 4%. Financial calculator solution: Inputs: N = 10; I = 5; PV = -768; FV = 1,000. Output: PMT = $19.955 (semiannual PMT). Annual coupon rate = PMT × 2/M = $19.955 × 2/1,000 = 3.99% 86.
Bond coupon rate
Time Line: 0 rd/2 = 7% |
4%.
Answer: d
1
2
|
|
PMT = ? VB = 1,158.91
≈
PMT
Diff: M
20 6-month . . . .
|
PMT FV = 1,000
Numerical solution: $1,158.91 = PMT(PVIFA7%,20) + $1,000(PVIF7%,20) = PMT((1- 1/1.0720)/0.07) + $1,000(1/1.0720) = PMT(10.5940) + $1,000(0.2584) PMT = $900.51/10.5940 = $85. Annual coupon rate = (2)($85)/$1,000 = 17%.
Periods
Financial calculator solution: Inputs: N = 20; I = 7; PV = -1,158.91; FV = 1,000. Output: PMT = $85.00 (semiannual PMT). Annual coupon rate = $85(2)/$1,000 = 17.0%. 87.
Bond value
Answer: d
Diff: T
Time Line: 0
1 rd = 20% | | 100 | |
2
3
4
|
|
|
100 | |
100 | |
100 | |
5
6
|
|
100 | |
10 ...
100
Yrs
| 100
i = 0%
500
Deferred payments accruing no interest VB= ?
FV = 1,000
Numerical solution: 10 $1,500 $100 PVbond = ∑ + t t (1 + r ) t = 6 (1 + r ) VB = $100(PVIFA20%,10 - PVIFA20%,5) + $1,500(PVIF20%,10 ) = $100([(1- 1/1.210)/0.2]– [(1- 1/1.25)/0.2]) + $1,500(1/1.210) = $100(4.1925 - 2.9906) + $1,500(0.1615) = $120.19 + $242.25 = $362.44. Financial calculator solution: Method 1. Cash flows:
Inputs: Output:
CF0 = 0; CF1 = 0; Nj = 5; CF2 = 100; Nj = 4; CF5 = 1,600; I = 20. NPV = $362.44. VB = $362.44.
Method 2. Time value discounting: (Calculate V B as of Year 5, V 5)
Inputs: N = 5; I = 20; PMT = 100; FV = 1,500. Output: PV5 = -$901.878. Calculate V B or PV of V 5
Inputs: N = 5; I = 20; FV = 901.878. Output: PV = -$362.44. VB = $362.44.
88.
Bond sinking fund payment
Answer: d
Diff: T
The company must call 5 percent or $50,000 face value each year. It could call at par and spend $50,000 or buy on the open market. Since the interest rate is higher than the coupon rate (14% vs. 12%), the bonds will sell at a discount, so open market purchases should be used. Time Line: 0 1 7% | | PV = ? PMT = 60
2 | 60
30 . . .
| 60 FV = 1,000
6-month Periods
Numerical solution: VB = $60(PVIFA7%,30) + $1,000(PVIF7%,30) = $60((1- 1/1.0730)/0.07) + $1,000(1/1.0730) = $60(12.4090) + $1,000(0.1314) = $744.54 + $131.40 = $875.94. The company would have to buy $50,000/1,000 = 50 bonds at $875.94 each = $43,797 ≈ $43,796.
Financial calculator solution: Inputs: N = 30; I = 7; PMT = 60; FV = 1,000. Output: PV = -$875.91. The company would have to buy 50 bonds at $875.91 each = $43,795.50 $43,796. 89.
9 90 .
Bond value - semiannual payment
Answer: c
Diff: E
Answer: b
Diff: E
Answer: a
Diff: E
≈
N = 10 × 2 = 20 I = 9/2 = 4.5 PMT = 50 FV = 1,000 Solve for PV = -$1,065.04. Bond value - semiannual payment
N = 15 × 2 = 30 I/YR = 11/2 = 5.5 PMT = 1,000 × 0.08/2 = 40 FV = 1,000 Solve for PV = -$781.99. 91.
Yield to maturity
Enter N = 11, PV = -865, PMT = 80, and FV = 1000. ≈ 10.09%. 92.
93.
YTM and YTC
Solve for I/YR = 10.0868% Answer: e
Diff: E
To calculate YTM: N = 28, PV = -1075, PMT = 40, and FV = 1000. I/YR = 3.57% × 2 = 7.14%.
Solve for
To calculate YTC: N = 10, PV = -1075, I/YR = 3.52% × 2 = 7.05%.
Solve for
PMT = 40, and FV = 1050.
Current yield
Answer: d
Diff: E
Current yield = Annual coupon payment/Current price.
94.
9 95 .
Step 1
Find the price of the bond: 1000. Solve for PV = $930.
Step 2
Calculate the current yield:
Current yield and yield to maturity
N = 12, I/YR = 9.5, PMT = 85, and FV = CY = $85/$930 = 9.14%. Answer: b
Diff: E
Answer: c
Diff: E
N = 12 PV = -985 PMT = 80 FV = 1,000 Solve for I/YR (YTM) = 8.20%. Current yield is calculated as: $80/$985 = 8.12%. Yield on semiannual bond
N = 12
×
2 = 24
96.
9 97 .
PV = -1,080 PMT = 50 FV = 1,000 Solve for I = 4.4508%
× 2 = 8.9016%. Yield to maturity and bond value--annual
Answer: d
Diff: E
Step 1
Find the YTM. N = 20; PV = -925; PMT = 90; FV = 1000; and solve for I = YTM. I = 9.8733%.
Step 2
Solve for P5. In 5 years, there will be 15 years left until maturity, so the price at t = 5 is: N = 15; I/YR = 9.8733; PMT = 90; FV = 1000; and solve for PV. PV = $933.09.
Bond value - semiannual payment
Answer: d
Diff: M
The 8% annual coupon bond’s YTM is 9.1%. The effective annual rate (EAR) is 9.1% because the bond is an annual bond. Now, we need to find the nominal rate for the semiannual bond which has the same EAR, so we can calculate its price. EAR% = 9.1 P/YR = 2 Solve for NOM% = 8.9019%. An equally risky 8% semiannual coupon bond has the same EAR. Now, solve for the semiannual bond’s price. N = 2 × 10 = 20, I/YR = 8.9019/2 = 4.4510, PMT = 80/2 = 40, FV = 1,000, and solve for PV = $941.09. 98 .
9 99 .
1 100 .
Call price
Answer: c
Diff: M
First, solve for the price of the bond today as follows: N = 10 × 4 = 40, I = 8/4 = 2, PMT = 100/4 = 25, and FV = 1,000; thus, solve for PV = -$1,136.78. Now, the call price can be solved for as follows: N = 5 × 4 = 20, I = 7.5/4 = 1.875, PV = -1,136.78, PMT = 25; thus, solve for FV = $1,048.34. Yield to call
Answer: b
Diff: M
First, calculate the price of the bond as follows: N = 20 × 2 = 40, I = 7/2 = 3.5, PMT = 8%/2 × 1,000 = 40, FV = 1,000, and solve for PV = ? = $1,106.78. Now, we can calculate the YTC as follows, recognizing that the bond can be called in 6 years at a call price of 115% × 1,000 = 1,150: N = 6 × 2 = 12, PV = -1,106.78, PMT = 40, FV = 1,150, and solve for I = ? = 3.8758% × 2 = 7.75%. Yield to call
Find the current price of the bond using the YTM: N = 12 × 2 = 24 I = 9/2 = 4.5 PMT = 100/2 = 50 FV = 1,000 Solve for PV = -1,072.48. Solve for the YTC: N = 5 × 2 = 10
Answer: d
Diff: M
1 101 .
PV = -1,072.48 PMT = 50 FV = 1,050 I = 4.4915% × 2 = 8.9829%
≈
8.98%.
Yield to call
Answer: c
Diff: M
First calculate the price of the bond. N = 2 × 20 = 40, I/YR = 9/2 = 4.5, PMT = 110/2 = 55, FV = 1,000, and solve for PV = -$1,184.02.
1 102
.
Now, solve for the YTC: N = 2 × 10 = 20, PV = -1,184.02, PMT = 55, FV = 1,055, and solve for I/YR 4.29% × 2 = 8.58%.
Yield to call
Answer: a
Diff: M
Answer: b
Diff: M
=
First get the price based on the YTM: N = 12 I = 7.5 PMT = 90 FV = 1,000 Solve for PV = -$1,116.03.
1 103 .
Now solve for the YTC: N = 4 PV = -1,116.03 PMT = 90 FV = 1,050 I = 6.7263% ≈ 6.73%. Yield to call
The price of the bond today is found as N = 11, I = 7.5, PMT = 80, FV = 1,000 and PV = ? = -$1,036.58. Solve for the yield to call as follows: N = 3, PV = -1,036.58, PMT = 80, FV = 1,060, and solve for I = ? = 8.41%. 104.
Yield to call
First we need to find the price of the bond: N = 12 × 2 = 24 I = 10/2 = 5 PMT = 60 FV = 1,000 Solve for PV = -$1,137.99. Now use the price of the bond to figure the YTC: N = 8 × 2 = 16 PV = -1,137.99 PMT = 60 FV = 1,050
Answer: b
Diff: M
1 105 .
Solve for I = 4.9441%
×
2 = 9.8883%
≈
9.89%.
After-tax yield to call
Answer: c
Diff: M
First, find the call price on the bonds, Call price = 1.05 × $1,000 = $1,050. Now, we know the bonds will pay 0.08 × $1,000 = $80 per year and, if called, will last for 3 years. Then, solve for yield to call: N = 3, PV = -1,000, PMT = 80, FV = 1,050, and solve for I/YR = 9.5176%. Finally, find the after-tax YTC = YTC × (1 - Tax rate) = 9.5176% × (1 - 0.31) = 6.5672% ≈ 6.60%.
1 106 .
Yield to maturity
Answer: d
Diff: M
a. First find what the bond is selling for today based on the information given about its call feature: N = 10(2) = 20; I = 6.5/2 = 3.25; PMT = 100/2 = 50; FV = 1,050. Solve for PV = -$1,280.81 = Current price. b. Use this current price solution to solve for the YTM: N = 15(2) = 30; PV = -1,280.81; PMT = 100/2 = 50; FV = 1,000. Solve for I = 3.4775%.
1 107 .
c. Since this is a semiannual rate, multiply it by 2 to solve for the nominal, annual YTM: YTM = 3.4775%(2) = 6.955% ≈ 6.95%. Interest payments remaining
Time Line: 0 1 10% | | PMT = 80 VB = 847.88
1 108 .
2 | 80
n = ?
Answer: b
Diff: M
Answer: c
Diff: M
Years
. . .
| 80 FV = 1,000
Financial calculator solution: Inputs: I = 10; PV = -$847.88; PMT = 80; FV = 1,000. Output: N = 15 years. Current yield and capital gains yield
First, calculate the price of the bond as follows: N = 6 × 2 = 12, I = 8.5/2 = 4.25, PMT = 10%/2 × 1,000 = 50, FV = 1,000, and PV = ? = $1,069.3780. The current yield (CY) is then $100/$1,069.3780 = 9.35%. Recognizing that the CY and capital gains yield (CG) constitute the total return (YTM) on the bond or CY + CG = YTM, solve for CG in the following equation 9.35% + CG = 8.5%, CG = -0.85%. 109.
Bond value
Answer: e
Diff: M
The semiannual bond selling at par has a nominal yield to maturity equal to its annual coupon rate (you can check this). Thus the nominal YTM for the semiannual bond is 8%. To convert this to an effective annual rate for the annual bond:
NOM% = 8 P/YR = 2 Solve for EFF% = 8.16%. We can now value the annual bond using this rate, as the nominal rate is the same as the effective rate when compounding is done annually. Thus;
1 110 .
N = 6 I = 8.16 PMT = 80 FV = 1,000 Solve for PV = -$992.64. Bond value
Answer: d
Time Line: 0 12.36% TLBK
|
1
2
3
| PMT = 80
| 80
| 80
VBK = ? 0
2 6% 1 TLMcD | | | PMT = 40 40 VMcD = ?
3 | 40
4
38
| . . . | 40 40
20
Diff: T
Years
. . .
| 80 FV = 1,000
39
40
| | 40 40 FV = 1,000
6-month Periods
Financial calculator solution: Burger King V B Calculate EAR to apply to Burger King bonds using interest rate conversion feature, and calculate the value, V , of Burger King bonds: BK
Inputs: P/YR = 2; NOM% = 12. Output: EFF% = EAR = 12.36%. Inputs: N = 20; I = 12.36; PMT = 80; FV = 1,000. Output: PV = -$681.54. McDonalds V B
Inputs: N = 40; I = 6; PMT = 40; FV = 1,000.
Output: PV = $699.07.
Calculate the difference between the two bonds' PVs
Difference: VB(McD) - VB(BK) = 699.07 - 681.54 = $17.53. 111.
Bond value and effective annual rate
Answer: b
Diff: T
Since the securities are of equal risk, they must have the same effective rate. Since the comparable 10-year bond is selling at par, its nominal yield is 8 percent, the same as its coupon rate. Because it is a semiannual coupon bond, its effective rate is 8.16 percent. Using your calculator, enter NOM% = 8; P/YR = 2; and solve for EFF%. (Don't forget to change back to P/YR = 1.) So, since the bond you are considering purchasing has quarterly payments, its nominal rate is calculated as follows: EFF% = 8.16; P/YR = 4; and solve for NOM%. NOM% = 7.9216%. To determine the bond's price you must use the cash flow register because the payment amount changes. CF0 = 0, CF1 = 20; Nj = 20; CF2 = 25; Nj = 19; CF3 = 1025; I = 7.9216/4 = 1.9804; solve for NPV. NPV = $1,060.72. 1 112 .
Bond coupon payment
Answer: b
Diff: T
Time Line: 0 1 rd = ? TL1 | | VB1 = 701.22 PMT = 80
0 rd = 12% 1 TL2 | | VB2 = 701.22 PMT = ?
2
20
| 80
. . .
2
3
| PMT
| PMT
Years
| 80 FV = 1,000 4
5
Years
| | PMT PMT FV = 1,000
Financial calculator solution: Calculate YTM or r d for first issue
Inputs: N = 20; PV = -701.22; PMT = 80; FV = 1,000.
Output: I = 12%.
Calculate PMT on second issue using 12% = r d = YTM
Inputs: N = 5; I = 12; PV = -701.22; FV = 1,000. Output: PMT = $37.116 ≈ $37.12.
1 113
.
Bonds with differential payments
Time Line: Semiannual 0 rd/2 | CFs -1,000
Answer: c
1
2
3
| PMT = ?
| PMT
| PMT
= 4.5%
Quarterly 0 rd/4 = 2.225% 1 2 | | | CFs -1,000 PMT = ? PMT
3 | PMT
4 | PMT
4
40 6-month
| ... | Periods PMT PMT FV = 1,000 5 | PMT
6 80 Qtrs. | ... | PMT PMT FV = 1,000
Numerical solution: Solve for the EAR of 9% nominal compounded Step 1 EARS = (1 + 0.09/2)2 - 1 = 0.09203. Step 2
Step 3
Diff: T
semiannually.
Solve for r Nom of 9.203% EAR but with quarterly compounding.
1 + EAR = (1 + rNOM/4)4 = 1.09203. rNom/4 = periodic rate = 0.02225.
rNom = 0.02225
×
4 = 0.08901.
Calculate the quarterly payment using the periodic rate.
Multiply 0.02225
×
$1,000 = $22.25 = quarterly payment.
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