Chapter 3: Q11-1B (page 360)
How can perpetuity, which has an infinite maturity, have a duration as short as 10 or 20 years?
When the present value approaches zero for cash flows in the distant future
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You will be paying $10,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%.
An a. What is the present value and duration of your obligation?
b. What maturity zero-coupon bond would immunize your obligation?
c. Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 9%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? What if rates fall to 7%?
Question: Assume that two firms issue bonds with the following characteristics. Both bonds are issued at par.
| ABC Bond | XYZ Bond | |
Issue size | 1.2 Billion | 150 Million |
Maturity | 10 Years* | 20 Years |
Coupon | 9% | 10% |
Collateral | First Mortgage | General Debenture |
Callable | Not callable | In 10 Years |
Call Price | None | 110 |
Sinking fund | None | Starting in 5 Years |
| Bond is extendable at the discretion of the bondholder for an additional 10 years. | ||
Ignoring credit quality, identify four features of these issues that might account for the lower coupon on the ABC debt. Explain.
a. Which set of conditions will result in a bond with the greatest price volatility?
(1) A high coupon and short maturity.
(2) A high coupon and a long maturity.
(3) A low coupon and a short maturity.
(4) A low coupon and a long maturity.
b. An investor who expects declining interest rates would be likely to purchase a bond that has a _____________ coupon and a _____________ term to maturity.
(1) Low, long
(2) High, short
(3) High, long
(4) Zero, long
c. With a zero-coupon bond:
(1) Duration equals the weighted-average term to maturity.
(2) Term to maturity equals duration.
(3) Weighted-average term to maturity equals the term to maturity.
(4) All of the above.
d. As compared with bonds selling at par, deep discount bonds will have:
(1) Greater reinvestment risk.
(2) Greater price volatility.
(3) Less call protection.
(4) None of the above.
Question: The current yield curve for default-free zero-coupon bonds is as follows:
Maturity (Years) | YTM |
1 | 10% |
2 | 11% |
3 | 12% |
a. What are the implied one-year forward rates?
b. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will the pure yield curve (that is, the yields to maturity on one- and two-year zero-coupon bonds) be next year?
c. If you purchase a two-year zero-coupon bond now, what is the expected total rate of return over the next year? What if you purchase a three-year zero-coupon bond?
(Hint: Compute the current and expected future prices.) Ignore taxes.
Question: A 10-year bond of a firm in severe financial distress has a coupon rate of 14% and sells for $900. The firm is currently renegotiating the debt, and it appears that the lenders will allow the firm to reduce coupon payments on the bond to one-half the originally contracted amount. The firm can handle these lower payments. What are the stated and expected yields to maturity of the bonds? The bond makes its coupon payments annually.
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