发布时间 : 星期四 文章兹维博迪金融学第二版试题库08TB更新完毕开始阅读
12. Eisenstein Corporation plans to raise $100,000,000 in funds by issuing zero-coupon $1,000 par value
bonds with a 30-year maturity. Assuming that Eisenstein Corporation is able to issue these bonds at an after-tax cost of debt of 11%, how many bonds must Eisenstein Corporation issue?
Answer: First, calculate the price of an Eisenstein bond:
n i = YTM PV FV PMT Result 30 11 ? 1,000 0 PV = $43.68
The corporation wants to raise $100,000,000, so it must issue the following number of bonds: $100,000,000/$43.68 = 2,289,377 bonds
13. Currently, an Eisenstein bond trades at $1,050 per bond and has a coupon rate of 10%. Assuming the
bond matures at a $1,000 value, and the required rate of return is 9.5%, in how many years does an Eisenstein bond mature?
Answer:
n i = YTM PV FV PMT Result ? 9.5 –1,050 1,000 0 n = 33
14. Compute the current price of Walsingham bonds based on the following information. Walsingham
bonds have a $1,000 par value, 26 years remaining until maturity, a 13 percent coupon rate, and a current yield to maturity of 11 percent per year.
Answer:
n i = YTM PV FV PMT Result 26 11 ? 1,000 0 PV = $1,169.69
15. Health & US Corporation is a major pharmaceutical firm that has recently experienced a market
reevaluation. Currently, the firm has a bond issue outstanding with 18 years to maturity and a coupon rate of 9 percent, with interest paid annually. The required rate of return of this debt issue has risen to 15 percent. Calculate the current price of this bond.
Answer:
n i = YTM PV FV PMT Result 18 15 ? 1,000 90 PV = $632.32
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16. Calculate the coupon rate, current yield, and the yield to maturity for a bond that has $1,000 par value,
pays a coupon of $85 annually, matures in 20 years, and has a current price of $985.25.
Answer:
Coupon rate = 85/1,000 = 8.5% per year Current yield = coupon/price = 85/985.25 = 8.63%
For yield to maturity:
n i = YTM PV FV PMT Result 20 ? –985.25 1,000 85 YTM = 8.66%
17. Suppose you buy a 20-year pure discount bond with a face value of $1,000 and a yield of 7% per year.
A day later, market interest rates rise to 8% and so does the yield of your bond. What is the
proportional change in the price of your bond? What is the elasticity of the bond price to the change in the yield?
Answer:
n i = YTM PV FV PMT Result 20 7 ? 1,000 0 PV = $258.42
n i = YTM PV FV PMT Result 20 8 ? 1,000 0 PV = $214.55
The price of the bond decreased by $43.87, so the proportional decline in price is $43.87/$258.42 = 16.98%.
Elasticity is % change in price over % change in YTM, or –16.98%/14.29% = –1.19.
18. As of today, January 1, 2009, Flanders Corporation is holding $10,000,000 in long-term debt at par
bonds. The bonds have a par value of $1,000, mature on January 1, 2019, and pay a 5 percent coupon. Calculate the current market value of Flanders’ debt, if the yield to maturity is 7 percent.
Answer: Total number of bonds = $10,000,000/$1,000 = 10,000 bonds
n i PV FV PMT Result 10 7 ? 1,000 50 PV = $859.50
The current market value = $859.50 x 10,000 = $8,578,800
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Longer Problems
1. Consider the purchase of a 30-year pure discount bond with a face value of $1,000 and a yield of 7%
per year. A week later the market interest rate rises to 8% and o does the yield on your bond. Calculate the proportional change in the price of the bond. What basic principle in valuation of known cash flows does this illustrate? Answer: n i PV FV Result 30 7 ? $1,000 PV = $131.37 n i PV FV Result 30 8 ? $1,000 PV = $99.38
The price drops by $31.99, so a rise of 1% in market interest rates results in a $31.99/$131.37 = 24.35% drop in the price of the bond. The general principle illustrates is that a change in market interest rates causes a change in the opposite direction in the market value of the bonds.
2. Suppose our want to know the price of a 15-year 8% coupon bond which pays interest annually. The
face value of the bond is $1,000. (a) You have been told the yield to maturity is 9%. What is the price? Assume coupons are
paid annually.
(b) What is the price if coupons are paid semi-annually and the yield to maturity is 9% per
year?
Answer: (a) If coupons are paid annually: n i PV FV PMT Result 15 9 ? $1,000 $80 PV = $919.39 (b) If coupons are paid semi-annually: n i PV FV PMT Result 30 4.5 ? $1,000 $40 PV = $918.56
3. A media report recently stated that prices of 30-year treasury bonds increased substantially because
inflation was falling and the Federal Reserve was not expected to increase interest rates. How would you describe this interpretation using discounted cash flow techniques? Answer:
Inflation is a component of i, the required return on bonds, so when inflation decreases, i decreases and bond prices rise.
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4. Suppose you want to know the price of a 10-year 7% coupon bond which pays interest annually. The
face value of the bond is $1,000. (a) What is the price of this bond if the yield to maturity is 8%? (b) What is the current yield of this coupon bond? (c) What is the price of this bond if coupons are paid semi-annually and the yield to maturity
is 8%?
Answer: a. n i PV FV PMT Result 10 8 ? $1,000 $70 PV = $932.90 b. Current yield = coupon/price = 70/932.9 = 7.5% c. n i PV FV PMT Result 20 4 ? $1,000 $35 PV = $932.05
5. Suppose you buy a 30-year pure discount bond with a face value of $1,000 and a yield of 9% per year.
A day later, market interest rates fall to 8% and so does the yield of your bond. What is the
proportional change in the price of your bond? What is the elasticity of the bond price to the change in the yield?
Answer:
n i = YTM PV FV PMT Result 30 9 ? 1,000 0 PV = $75.37
n i = YTM PV FV PMT Result 30 8 ? 1,000 0 PV = $99.38
The price of the bond decreased by $24.01, so the proportional increase in price is $24.01/$75.37 = 31.86%.
Elasticity is % change in price over % change in YTM, or 31.86%/–11.11% = –2.87.
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