Variable Growth A fast growing firm recently paid a dividend of $1.00 per share. The dividend is expected to increase at a 25 percent rate for the next 3 years. Afterwards, a more stable 8 percent growth rate can be assumed. If a 10 percent discount rate is appropriate for this stock, what is its value?

Question

Quizplus · Accepted Answer

We can use the dividend discount model to find the stock's value:

D1 = D0 x (1+g)^1 = $1.00 x (1+0.25)^1 = $1.25
D2 = D1 x (1+g)^1 = $1.25 x (1+0.25)^1 = $1.56
D3 = D2 x (1+g)^1 = $1.56 x (1+0.25)^1 = $1.95

After the third year, we can use the Gordon growth model to find the terminal value of the stock:

D4 = D3 x (1+g) / (r-g) = $1.95 x (1+0.08) / (0.10-0.08) = $54.15
So the stock's value today is:
PV = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^3 = $1.13 + $1.26 + $1.34 + $38.40 = $41.13

Therefore, the closest answer choice is C) $83.13.

Variable Growth a Fast Growing Firm Recently Paid a Dividend