Question

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 should the fair value be four years from today?

Answer 1

Answer:

a)Fair present value today = $24.17

b) Fair value 4 years from today given ke of 15% = $19.95

Explanation:

if the dividends are expected to continue growing at 1.5% till perpetuity, then the present value of the stock is represent by the present value of the dividends. This can be calculated using the contans growth model where

Present value = $\frac{D_1}{ke-g}$

Where:

D1 = the dividend expected at the end of the 1st year = D0(1+g) = 2.5(1.015)

  ke = required rate of return on the stock

 g = constant growth rate = 0.015

a)  If the required rate of return on the stock is 12%

Present value = $\frac{2.5(1.015)}{0.12-0.015}$= $24.17

b) Fair value four years from today= $\frac{D_5}{ke-g}$

where D5 =D0(1+g)^5 = 2.5(1.015)^5; ke=0.15; g=0.015

Present value = $\frac{2.5(1.015)^5}{0.15-0.015}$= $19.95