Question

Gentleman Gym just paid its annual dividend of $3 per share, and it is widely expected that the dividend will increase by 5% per year indefinitely.
A. What price should the stock sell at? The discount rate is 15%.
B. How would your answer change if the discount rate was only 12%? Why does the answer change?

Answer 1

Answer: a. $31.5 ; b. $45.

Explanation:

A. What price should the stock sell at? The discount rate is 15%.

The dividend for the first year will be:

= $3 × (100% + 5%)

= $3 × 105%

= $3 × 1.05

= $3.15

Since Price = D1/Ke - g

Price = 3.15/0.15 - 0.05

Price = 3.15/0.10

Price = $31.5

B. How would your answer change if the discount rate was only 12%?

Price = D1/Ke - g

Price = 3.15/(0.12 - 0.05)

= 3.15/0.07

= $45

The answer changed because the discount rate has been reduced which led to the increase in the answer.