• Problems 6 – 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 existProblems 10 – Calculate the yield to maturity on the following bonds.

  Problems 22 – 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. (a) If the required rate of return on the stock is 12 percent, what is its fair present value? (b) If the required rate of return on the stock is 15 percent, what is its expected price four years from today?

  Problems 30 – Consider the following two banks: Bank 1 has assets composed solely of a 10-year, 12 percent coupon, $1 million loan with a 12 percent yield to maturity. It is financed with a 10-year, 10 percent coupon, $1 million CD with a 10 percent yield to maturity. Bank 2 has assets composed solely of a 7-year, 12 percent, zero-coupon bond with a current value of $894,006.20 and a maturity value of $1,976,362.88. It is financed by a 10-year, 8.275 percent coupon, $1,000,000 face value CD with a yield to maturity of 10 percent.

1. If interest rates rise by 1 percent (100 basis points), how do the values of the assets and liabilities of each bank change?
2. What accounts for the differences between the two banks’ accounts?

• Problems 32 – 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?

SOLUTION 

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?

Five-year Treasury Bond:

Par value = $1,000, Coupon rate = 10%, Semiannual payments, R = 10%, Maturity = 5 years

   t             CFt                    DFt                     CFt x DFt            CFt x DFt x t

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