What will one share of S&P common stock be worth ten years from now if the applicable discount rate is 8 percent?

Question

S&P Enterprises will pay an annual dividend of $2.08 a share on its common stock next year. Last week, the company paid a dividend of $2.00 a share. The company adheres to a constant rate of growth dividend policy. What will one share of S&P common stock be worth ten years from now if the applicable discount rate is 8 percent?

Answer 1

There are at least 2 ways you could approach this problem:

1) value the stock at t=0, which is today and then grow the price until t=10, growth is proportional to the dividend growth rate in this case

2) grow the dividend to period 11 and apply the appropriate form of the Gordon Growth Model (GGM) to value the stock at time=10.

Briefly, the GGM:

P_t = [D_t * (1+g)]/(k_e-g) = D_t+1/(r_e-g)

P_t= price at time t

D_t= dividend at time t

D_t+1= dividend one period ahead of time t

g= growth rate of dividend (here equal to [2.08/2]-1)

r_e= required return on equity (discount rate for this problem)

First, the dividend growth rate is found as (2.08/2)-1 = 0.04.

1) P₀=D_t+1/(r_e-g) = 2.08/(.08-.04) = 52 = price today, t=0

Next, send it forward at the dividend growth rate:

P₁₀= P₀*(1+g)¹⁰= 52*1.04¹⁰= 76.97 USD is the price at 10 periods from today

2) D₁₁= D₀*(1+g)¹¹= 2*1.04¹¹= 3.08 is the dividend at time =11 years from today so we can then value the stock at time = 10 years from today.

P₁₀= D₁₁/(r_e-g)= 3.08/(.08-.04) = 76.97 USD price of stock at time =10 years from today.

The key to solving the problem is remembering that any asset should be valued on the basis of its expected future cash flows. This reminds us that we need the dividend in time 1 (and beyond) to value the stock at time =0 or that we need the dividend at time = 11(and beyond) to value the stock at time =10 (depending which way you conceptualize the problem). With constant growth and required rate of return, we can treat this as the sum of an infinite series.

Hope this helps!