Question

A company has just paid a $2 per share dividend. The dividends are expected to grow by 24% a year for 8 years. The growth rate in dividends thereafter is expected to stabilize at 4% a year. The appropriate annual discount rate for the company’s stock is 12%.

a. What is the company’s current equilibrium stock price?

b. What is the company’s expected stock price in 20 years?

Answer 1

Part (a)

D1 = D0 x (1 + g) = 2 x (1 + 24%) = 2.48

PV of a growing annuity

1+0) PV =- 1- r - g 1+r)

Hence, present value of dividend over 8 years = 2.48 / (12% - 24%) x [1 - (1 + 24%)⁸ / (1 + 12%)⁸] =  25.99

Dividend in 9th year = D0 x (1 + g)⁸ x (1 + g_t) = 2 x (1 + 24%)⁸ x (1 + 4%) = 11.63

Terminal value of dividends at the end of year 8, TV = D9 / (r - g_t) = 11.63 / (12% - 4%) = 145.33

Hence, the company’s current equilibrium stock price = PV of dividends as growing annuity over 8 years + PV of TV = 25.99 + 145.33 x (1 + r)^-t = 25.99 + 145.33 x (1 + 12%)^-8 = $  84.68

Part (b)

D21 = D0 x (1 + g)⁸ x (1 + g_t)¹³ = 2 x (1 + 24%)⁸ x (1 + 4%)¹³ = 18.61

Hence, the company’s expected stock price in 20 years = D21 / (r - g_t) = 18.61 / (12% - 4%) = 232.67