Question

A company's recent dividend is $1 per share. The company expects that the dividends will grow at 10% for the next three years. After that the dividends will increase at 7% forever. Its stock beta is 1.0. Currently, the expected market return is 12%, and the risk-free rate is 7%. What is the present value of the common stock?

Answer 1

Required rate of return = Rf + beta * (Rm - Rf)
= 7% + 1 * (12% - 7%)
= 7% + 1* 5%
= 7% + 5%
= 12%

D1 = $1 * (1+10%) = $1.1
D2 = $1.1 * (1+10%) = $1.21
D3 = $1.21 * (1+10%) = $1.331
D4 = $1.331 * (1+7%) = $1.42417

P3 = D4 / (r-g)
= $1.42417 / (0.12 - 0.07)
= $1.42417 / 0.05
= $28.4834

P0 = (D1 / (1+r)) + (D2 / (1+r)^2) + (D3 / (1+r)^3) + (P3 / (1+r)^3)

= ($1.1 / (1+12%)) + ($1.21 / (1+12%)^2) + ($1.331 / (1+12%)^3) + ($28.4834 / (1+12%)^3)

= 0.9821 + 0.9646 + 0.9474 + 20.2739

= $23.17

Present value of the common stock = $23.17