The detailed solution is at the bottom. 1. Which of the following bonds would have the greatest percentage increase in v
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The detailed solution is at the bottom. 1. Which of the following bonds would have the greatest percentage increase in value if all interest rates in the economy fall by 1%? a. 10-year, zero coupon bond. b. 20-year, 10% coupon bond. c. 20-year, 5% coupon bond. d. 1-year, 10% coupon bond. *e. 20-year, zero coupon bond. 2. Which of the following bonds has the greatest price risk? a. A 10-year $100 annuity. *b. A 10-year, $1,000 face value, zero coupon bond. c. A 10-year, $1,000 face value, 10% coupon bond with annual interest payments. d. All 10-year bonds have the same price risk since they have the same maturity. e. A 10-year, $1,000 face value, 10% coupon bond with semiannual interest payments. 3. Morin Company's bonds mature in 8 years, have a par value of $1,000, and make an annual coupon interest payment of $65. The market requires an interest rate of 8.2% on these bonds. What is the bond's price? *a. $903.04 b. $925.62 c. $948.76 d. $972.48 e. $996.79 4. Adams Enterprises’ noncallable bonds currently sell for $1,120. They have a 15-year maturity, an annual coupon of $85, and a par value of $1,000. What is their yield to maturity? a. 5.84% b. 6.15% c. 6.47% d. 6.81% *e. 7.17% 5. Radoski Corporation's bonds make an annual coupon interest payment of 7.35%. The bonds have a par value of $1,000, a current price of $1,130, and mature in 12 years. What is the yield to maturity on these bonds? a. 5.52% *b. 5.82% c. 6.11%
d. 6.41% e. 6.73% 6. Sadik Inc.'s bonds currently sell for $1,180 and have a par value of $1,000. They pay a $105 annual coupon and have a 15-year maturity, but they can be called in 5 years at $1,100. What is their yield to call (YTC)? a. 6.63% b. 6.98% c. 7.35% *d. 7.74% e. 8.12% 7. Assume that you are considering the purchase of a 20-year, noncallable bond with an annual coupon rate of 9.5%. The bond has a face value of $1,000, and it makes semiannual interest payments. If you require an 8.4% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond? *a. $1,105.69 b. $1,133.34 c. $1,161.67 d. $1,190.71 e. $1,220.48 8. Grossnickle Corporation issued 20-year, noncallable, 7.5% annual coupon bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds is 5.5%. What is the current price of the bonds, given that they now have 19 years to maturity? a. $1,113.48 b. $1,142.03 c. $1,171.32 d. $1,201.35 *e. $1,232.15 9. McCue Inc.'s bonds currently sell for $1,250. They pay a $90 annual coupon, have a 25-year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. What is the difference between this bond's YTM and its YTC? (Subtract the YTC from the YTM; it is possible to get a negative answer.) *a. 2.62% b. 2.88% c. 3.17% d. 3.48% e. 3.83%
10. A 25-year, $1,000 par value bond has an 8.5% annual payment coupon. The bond currently sells for $925. If the yield to maturity remains at its current rate, what will the price be 5 years from now? a. $884.19 b. $906.86 *c. $930.11 d. $953.36 e. $977.20 11. Moerdyk Corporation's bonds have a 15-year maturity, a 7.25% semiannual coupon, and a par value of $1,000. The going interest rate (rd) is 6.20%, based on semiannual compounding. What is the bond’s price? a. $1,047.19 b. $1,074.05 *c. $1,101.58 d. $1,129.12 e. $1,157.35 12. In order to accurately assess the capital structure of a firm, it is necessary to convert its balance sheet figures from historical book values to market values. KJM Corporation's balance sheet (book values) as of today is as follows: Long-term debt (bonds, at par) Preferred stock Common stock ($10 par) Retained earnings Total debt and equity
$23,500,000 2,000,000 10,000,000 4,000,000 $39,500,000
The bonds have a 7.0% coupon rate, payable semiannually, and a par value of $1,000. They mature exactly 10 years from today. The yield to maturity is 11%, so the bonds now sell below par. What is the current market value of the firm's debt? a. $17,436,237 *b. $17,883,320 c. $18,330,403 d. $17,706,000 e. $17,898,650 13. Keenan Industries has a bond outstanding with 15 years to maturity, an 8.25% nominal coupon, semiannual payments, and a $1,000 par value. The bond has a 6.50% nominal yield to maturity, but it can be called in 6 years at a price of $1,120. What is the bond’s nominal yield to call?
a. 6.20% *b. 6.53% c. 6.85% d. 7.20% e. 7.55% 14. Kebt Corporation's Class Semi bonds have a 12-year maturity and an 8.75% coupon paid semiannually (4.375% each 6 months), and those bonds sell at their $1,000 par value. The firm's Class Ann bonds have the same risk, maturity, nominal interest rate, and par value, but these bonds pay interest annually. Neither bond is callable. At what price should the annual payment bond sell? a. $937.56 b. $961.60 *c. $986.25 d. $1,010.91 e. $1,036.18
Solution: 1.
(7-7) Price risk
CG
Answer: e
2.
(7-7) Price risk
CG
Answer: b
3.
(7-3) Bond valuation: annual
CG
Answer: a
CG
Answer: e
CG
Answer: b
N I/YR PMT FV PV 4.
(7-4) Yield to maturity N PV PMT FV I/YR
5.
8 8.2% $65 $1,000 $903.04
15 $1,120 $85 $1,000 7.17%
(7-4) Yield to maturity Coupon rate N
7.35% 12
PV = Price PMT FV = Par I/YR 6.
(7-4) Yield to call N PV PMT FV I/YR = YTC
7.
$1,130 $73.50 $1,000 5.82% = YTM CG
Answer: d
CG
Answer: a
5 $1,180 $105 $1,100 7.74%
(7-6) Bond valuation: semiannual
Par value $1,000 Coupon rate 9.5% Periods/year 2 Yrs to maturity 20 Periods = Yrs to maturity × Periods/year 40 Required rate 8.4% Periodic rate = Required rate/2 = I/YR 4.20% PMT per period = Coupon rate/2 × Par value $47.50 Maturity value = FV $1,000 PV $1,105.69 8.
(7-3) Bond valuation: annual
CG
Answer: e
CG
Answer: a
Par value = Maturity value = FV$1,000 Coupon rate 7.5% Years to maturity = N 19 Required rate = I/YR 5.5% (Coupon rate)(Par value) = PMT $75 PV $1,232.15 9.
(7-4) YTM and YTC If held to maturity: N = Maturity 25 Price = PV $1,250 PMT $90 FV = Par $1,000 I/YR = YTM 6.88% Difference: YTM – YTC =2.62%
10.
(7-5) Future annual bond value
If called in 5 years: N = Call PV PMT FV = Call Price I/YR = YTC
CG
5 $1,250 $90 $1,050 4.26%
Answer: c
First find the YTM at this time, then use the YTM with the other data to find the bond's price 5 years hence. Par value Coupon rate N PV PMT FV I/YR 11.
$1,000 8.50% 25 $925 $85 $1,000 9.28%
(7-6) Bond valuation: semiannual
Value in 5 years: N I/YR PMT FV PV
20 9.28% $85 $1,000 $930.11
CG
Answer: c
CG
Answer: b
Par value = FV $1,000 Coupon rate 7.25% Periods/year 2 Yrs to maturity 15 Periods = Years × 2 = N 30 Going annual rate = YTM = rd 6.20% Periodic rate = rd/2 = I/YR 3.10% Coupon rate × Par/2 = PMT $36.25 PV $1,101.58 12.
(7-6) Market value: semiannual Calculate the price of each bond: Coupon rate Par value = FV Yrs to maturity Periods/Yr Periods = Years × 2 = N Going annual rate = rd = YTM Periodic rate = rd/2 = I/YR Coupon rate × Par/2 = PMT Price of the bonds = PV
7.0% $1,000 10 2 20 11.0% 5.5% $35.00 $760.99
Determine the number of bonds: Book value on balance sheet $23,500,000 Par value $1,000 Number of bonds = Book value/Par value 23,500 Calculate the market value of bonds: Mkt value = PV × Number of bonds = $17,883,320
13.
(7-6) Semiannual YTM and YTC
CG
Answer: b
First, use the given data to find the bond's current price. Then use that price to find the YTC. Coupon rate 8.25% YTM 6.50% Maturity 15 Par value $1,000 Periods/year 2 Determine the bond's price: PMT/period $41.25 N 30 I/YR 3.25% FV $1,000.00 PV = Price $1,166.09 14.
(7-6) Bonds: semiannual EFF%
Yrs to call Call price Determine the bond's YTC: N PV PMT FV I/YR Nom. YTC CG
6 $1,120 12 $1,166.09 $41.25 $1,120.00 3.26% 6.53% Answer: c
These two bonds should provide the same EFF%. Therefore, we can find the EFF% for the semiannual bond and then use it as the YTM for the annual payment bond. At the calculated price, the two bonds will have YTMs with the same EFF%. Note too that the semiannual payment bond must have a higher price than the annual bond because then it receives the same cash flow, but faster. Therefore, the annual bond must sell at a price below the $1,000 par value at which the semiannual bond sells. Semiannual bond: Par value $1,000 Coupon rate=Nominal rate 8.75% Payment per period $43.75 Years to maturity 12 Periods/year 2 Total periods 24 EFF% = (1+Nom rate/2)2 − 1 =8.941% Price $1,000.00
Annual bond: Par value Coupon rate Pmt/Period Yrs to maturity Periods/year Total periods EFF% = YTM Price
$1,000 8.75% $87.50 12 1 12 8.941% $986.25