Georgia Nursery is a relatively young firm which just paid its first annual dividend of $.50 a share. Management projects dividend increases of 15 percent per year for five years followed by a constant growth rate of 5.0 percent annually. What is this stock worth today if the applicable discount rate is 10 percent?

Question

Quizplus · Accepted Answer

To solve for the current stock price, we need to use the dividend discount model:
P = D1/(1+r) + D2/(1+r)^2 + ... + D5/(1+r)^5 + D6/(r-g) * 1/(1+r)^5
where
D1 = $0.50 (first annual dividend)
g = 5%
r = 10%
We can find the value of D6 by using the constant growth model:
D6 = D5 * (1+g)/(r-g)
D6 = $1.2824
Now we can plug in the values:
P = 0.50/(1+0.10) + 0.575/(1+0.10)^2 + 0.6613/(1+0.10)^3 + 0.7605/(1+0.10)^4 + 0.8746/(1+0.10)^5 + 1.2824/(0.10-0.05) * 1/(1+0.10)^5
P = $15.98
Therefore, the best choice is C.

Georgia Nursery Is a Relatively Young Firm Which Just Paid