Consider the following securities, which are assumed to be risk-free with an opportunity cost of capital (or discount rate) of 5 percent:
(1) A one-year zero-coupon bond paying $1,000.
(2) A console (i.e., a perpetuity) paying $45 per year.
(3) A stock offering a $20 dividend at the end of this year and a 3% annual rate of growth in dividend payments forever.
A. Solve for the present values of each of these assets.
B. Suppose that the discount rate increases to 8 percent. Of the securities listed above, which one will experience the largest change in price? Show your calculation and explain the intuition for your result.
C. Assume in part (A) that assets (1) and (2) sell at prices equal to their present values. What is the yield to maturity of assets (1) and (2)? In a real-world financial market would you expect the discount rate for (2) to be higher or lower than for (1)? Why?
