Interest Rates and Security Prices Problem Set
1. Western Enterprises' bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon rate is 9 percent. The bonds have a yield to maturity of 7 percent. What is the current market price of these bonds?
2. Calculate the fair present value of the following bonds, all of which have a 10 percent coupon rate (paid semiannually), face value of $1,000, and a required rate of return of 8 percent.
a. The bond has 10 years remaining to maturity.
b. The bond has 15 years remaining to maturity.
c. The bond has 20 years remaining to maturity.
d. What do your answers to parts (a) through (c) say about the relation between time to maturity and present values?
3. Compute the stock valuation in the following cases.
a. Financial analysts forecast Safeco Corp. (SAF) growth for the future to be 10 percent. Safeco's recent dividend was $1.20. What is the fair present value of Safeco stock if the required rate of return is 12 percent?
b. A stock you are evaluating just paid an annual dividend of $2.50. Dividends have grown at a constant rate of 1.5 percent over the last 15 years and you expect this to continue.
i. If the required rate of return on the stock is 12 percent, what is its fair present value?
ii. If the required rate of return on the stock is 15 percent, what should the fair value be four years from today?
c. A stock you are evaluating is expected to experience supernormal growth in dividends of 8 percent over the next six years. Following this period, dividends are expected to grow at a constant rate of 3 percent. The stock paid a dividend of $5.50 last year and the required rate of return on the stock is 10 percent. Calculate the stock's fair present value.
4. A bond has a par value of $1000 and a coupon rate of 8%, which is paid annually. The maturity of the bond is four years and the coupon payments are reinvested at the current rates listed below. The required rate of return is 6 percent. What is the bonds duration?
|
Year
|
Rate
|
|
1
|
4%
|
|
2
|
3%
|
|
3
|
5%
|
|
4
|
6%
|
5. What is the duration of a five-year, $1,000 Treasury bond with a 10 percent semiannual coupon selling at par? Selling with a yield to maturity of 12 percent? 14 percent? What can you conclude about the relationship between duration and yield to maturity? Plot the relationship. Why does this relationship exist?
6. MLK Bank has an asset portfolio that consists of $100 million of 30-year, 8 percent coupon, $1,000 bonds that sell at par.
a. What will be the bonds' new prices if market yields change immediately by ± 0.10 percent? What will be the new prices if market yields change immediately by ± 2.00 percent?
b. The duration of these bonds is 12.1608 years. What are the predicted bond prices in each of the four cases using the duration rule? What is the amount of error between the duration prediction and the actual market values?