Sample Problems - Chapter 7 1. Which of the following statements is most correct?
a. Bond prices and interest rates move in the same direction, i.e., if interest rates rise, so will bond prices.
b. The market price of a discount bond will approach the bond's par value as the maturity date approaches. Barring changes in the probability of default, there is no way the value of the bond can fail to increase each year as the time to maturity approaches.
c. The "current yield" on a noncallable discount bond will normally exceed the bond's yield to maturity.
d. The "current yield" on a noncallable discount bond will normally exceed the bond's coupon interest rate.
e. All of the statements above are false. 2. If the yield to maturity decreased 1 percentage point, which of the following bonds would have the largest percentage increase in value? a. A 1-year bond with an 8 percent coupon.
b. A 1-year zero-coupon bond.
c. A 10-year zero-coupon bond.
d. A 10-year bond with an 8 percent coupon.
e. A 10-year bond with a 12 percent coupon. 3. Which of the following statements is most correct? a. The discount or premium on a bond can be expressed as the difference between the coupon payment on an old bond, which originally sold at par, and the coupon payment on a new bond, selling at par, where the difference in payments is discounted at the new market rate.
b. The price of a coupon bond is determined primarily by the number of years to maturity.
c. On a coupon paying bond, the final interest payment is made one period before maturity and then, at maturity, the bond's face value is paid as the final payment.
d. The actual capital gains yield for a one-year holding period on a bond can never be greater than the current yield on the bond.
e. All of the statements above are false. 4. 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 they expect 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.

5. 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. 6. 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. 7. Which of the following types of debt protect a bondholder against an increase in interest rates? a. Floating rate debt.
b. Bonds that are redeemable ("putable") at par at the bondholders' option.
c. Bonds with call provisions.
d. All of the answers above.
e. Only answers a and b above. 8. 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.

9. 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. 10. 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. 11. Which of the following statements is most correct? a. The expected return on corporate bonds will generally exceed the yield to maturity.
b. Firms that are in financial distress are forced to declare bankruptcy.
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. 12. 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, 2018, and it is now January 1, 1998. 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. $13,255
b. $29,708
c. $12,654
d. $25,305
e. $14,580 13. 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. 2,400
b. 2,596
c. 3,000
d. 5,000
e. 4,275 14. Assume that you own a hundred $1,000 par value bonds, with a total face value of $100,000. These bonds have a 4 percent coupon, pay interest semiannually, and have 5 years remaining until they mature. New bonds with the same risk and maturity provide yields to maturity of 14 percent. You are considering selling your bonds and depositing the proceeds in a savings account which pays interest at a rate of 6 percent, annual compounding. If you do make the transaction, you will liquidate the savings account by making 5 equal withdrawals, the first coming 1 year from now. What will be the amount of each annual withdrawal? a. $12,940
b. $15,403
c. $24,860
d. $29,425
e. $64,880 15. 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. $ 898.64
b. $ 736.86
c. $ 854.27
d. $ 941.15
e. $ 964.23 16. 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. 9.82%
b. 8.41%
c. 8.54%
d. 8.38%
e. 7.86% 17. 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. 5.52%
b. 5.90%
c. 6.60%
d. 7.07%
e. 9.52% 18. 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. 5.97%
b. 6.30%
c. 6.75%
d. 6.95%
e. 7.10% 19. Trickle Corporation's 12 percent coupon rate, semiannual payment, $1,000 par value bonds which mature in 25 years, are callable at a price of $1,080 five years from now. The bonds currently sell for $1,230.51 in the market, and the yield curve is flat. Assuming that the yield curve is expected to remain flat, what is Trickle's most likely before-tax cost of debt if it issues new bonds today? a. 4.78%
b. 6.46%
c. 7.70%
d. 9.56%
e. 12.92% 20. 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).

a. Current yield = 8.50%, capital gains yield = 1.50%
b. Current yield = 9.35%, capital gains yield = 0.65%
c. Current yield = 9.35%, capital gains yield = -0.85%
d. Current yield = 10.00%, capital gains yield = 0.00%
e. None of the answers above is correct.

ANSWER KEY 1. d. The "current yield" on a noncallable discount bond will normally exceed the bond's coupon interest rate.
Discount bonds 2. c. A 10-year zero-coupon bond.
Price risk
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. 3. a. The discount or premium on a bond can be expressed as the difference between the coupon payment on an old bond, which originally sold at par, and the coupon payment on a new bond, selling at par, where the difference in payments is discounted at the new market rate.
Bond concepts 4. d. Statements a and c are correct.
Bond concepts 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. 5. b. If a coupon bond is selling at par, its current yield equals its yield to maturity.
Bond concepts 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. 6. 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.
Callable bond 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. 7. e. Only answers a and b above.
Types of debt 8. 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.
Types of debt 9. e. None of the answers above is correct.
Current yield and yield to maturity 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. 10. a. The bond's yield to maturity is less than 10 percent.
Current yield and yield to maturity 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. 11. c. All else equal, senior debt will generally have a lower yield to maturity than subordinated debt.
Corporate bonds and default risk 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. Firms in financial distress may or may not eventually declare bankruptcy, i.e., they may recover. 12. a. $13,255 Bond value - annual payment Time line: 1/1/98 1/1/2018 0 12% 1 2 20 Years TL ³ÄÄÄÄÄÄijÄÄÄÄÄÄijÄÄÄÄÄÄÄúúúÄÄÄÄÄÄij 2,000 2,000 2,000 VB = ? FV = 100,000 0 10% 1 2 TLŽ ³ÄÄÄÄÄÄÄÄÄijÄÄÄÄÄÄÄÄÄij PMT = ? PMT FV = 0 VB = 25,305.56 Tabular solution: Step 1 Calculate PV of the bonds VB = $2,000(PVIFAŽ%,Ž™) + $100,000(PVIFŽ%,Ž™) = $2,000(7.4694) + $100,000(0.1037) = $25,308.80. Step 2 Calculate the equal payments of the annuity due $25,308.80 $25,308.80 PMT = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ = ÄÄÄÄÄÄÄÄÄÄÄÄÄ = $13,257.27. (PVIFA™%,Ž)(1.10) (1.7355)(1.10) Financial calculator solution: Calculate the PV of the bonds Inputs: N = 20; I = 12; PMT = 2,000; FV = 100,000. Outpue: 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. 13. b. 2,596
Bond value - semiannual payment Time line: 0 6% 1 2 20 6-month ³ÄÄÄÄÄijÄÄÄÄÄijÄÄÄÄÄÄúúúÄÄÄÄÄij Periods PMT = 60 60 60
VB-Old = 1,000 FV = 1,000 PMT = 40 40 40
VB-New = ? FV = 1,000 Tabular 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(PVIFA•%,Ž™) + $1,000(PVIF•%,Ž™) = $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. 14. b. $15,403 Annuity payments Time lines: 0 kd/2 = 7% 1 2 10 6-month TL ³ÄÄÄÄÄÄÄÄÄÄijÄÄÄÄÄÄÄÄÄÄijÄÄÄÄÄÄÄÄúúúÄÄÄÄÄÄÄij Periods 2,000 2,000 2,000 Vbonds = ? = 64,877.20 FV = 100,000 0 i = 6 1 2 3 4 5 Years TLŽ ³ÄÄÄÄÄÄijÄÄÄÄÄÄijÄÄÄÄÄÄijÄÄÄÄÄÄijÄÄÄÄÄÄij PMT = ? PMT PMT PMT PMT PV = 64,877.20 FV = 0 Tabular solution: Vbonds = $2,000(PVIFA–%,™) + $100,000(PVIF–%,™) = $2,000(7.0236) + $100,000(0.5083) = $64,877.20. $64,877.20 $64,877.20 PMT = ÄÄÄÄÄÄÄÄÄÄ = ÄÄÄÄÄÄÄÄÄÄ = $15,401.48 ÷ $15,403. PVIFA•%,” 4.2124 Financial calculator solution: Calculate PV of bonds Inputs: N = 10; I = 7; PMT = 2,000; FV = 100,000. Output: PV = -$64,882.09. Calculate annuity payment Inputs: N = 5; I = 6; PV = -64,882.09; FV = 0. Output: PMT = $15,402.77 ÷ $15,403. Note: Difference between financial calculator and tabular solutions due to rounding of tabular interest factors. 15. d. $ 941.15
Bond value - semiannual payment 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.
EFF% = 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 x 10 = 20, I/YR = 8.9010/2 = 4.4505, PMT = 80/2 = 40, FV = 1,000, and solve for PV = $941.15. 16. b. 8.41%
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%. 17. c. 6.60%
After-tax yield to call First, find the call price on the bonds, Call price = 1.05 x $1,000 = $1,050. Now, we know the bonds will pay 0.08 x $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 x (1 - Tax rate) = 9.5176% x (1 - 0.31) = 6.5672% ÷ 6.60%. 18. d. 6.95%
Yield to maturity 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%. 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%. 19. c. 7.70%
Cost of debt Time line: 0 i = ? 1 2 3 4 5 10 50 6-month ³ÄÄÄÄÄÄÄÄÄÄÄijÄÄÄÄÄijÄÄÄÄijÄÄÄÄÄijÄÄÄÄÄijÄÄúúúÄijÄÄúúúÄÄij Periods
VB = 1,230.51 60 60 60 60 60 60 60 Call price = 5 = 1,080 FV = 1,000
Calculate the nominal yield to call: The bonds are selling at a premium because the coupon rate is above the market rate. Under the expectation of a flat yield curve, the bonds will most likely be called so that the firm can issue new, cheaper bonds. The FV is the call price and the period is 5 years or 10 semiannual periods.
Financial calculator solution:
Inputs: N = 10; PV = -1,230.51; PMT = 60; FV = 1,080.
Output: I = 3.85 periodic rate (semiannual).
The nominal annual rate equals 2 x 3.85% = 7.70%. Thus, the before-tax cost of debt is 7.70%. 20. c. Current yield = 9.35%, capital gains yield = -0.85%
Current yield and capital gains yield
First, calculate the price of the bond as follows: N = 6 x 2 = 12, I = 8.5/2 = 4.25, PMT = 10%/2 x 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 9.35% + CG = 8.5% for CG = -0.85%.