Question

Gentleman Gym just paid its annual dividend of $2 per share, and it is widely expected that the dividend will increase by 4% per year ndefinitely.

a. What price should the stock sell at if the discount rate is 12%. Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
b. What price should the stock sell at if the discount rate is 8%. Note: Do not round intermediate calculations. Round your answer to 2 decimal places.

Answer 1

The price of the stock can be calculated using the present value formula. For a discount rate of 12%, the stock should sell at $25, and for a discount rate of 8%, the stock should sell at $50.

Step-by-step explanation:

To calculate the price of the stock, we can use the formula for the present value of an infinite series of dividends:

P = D / (r - g)

Where P is the price of the stock, D is the dividend per share, r is the discount rate, and g is the growth rate of the dividends.

a. For a discount rate of 12% and a dividend of $2 per share, the price of the stock would be:

P = $2 / (0.12 - 0.04) = $2 / 0.08 = $25

Therefore, the stock should sell at $25.

b. For a discount rate of 8% and a dividend of $2 per share, the price of the stock would be:

P = $2 / (0.08 - 0.04) = $2 / 0.04 = $50

Therefore, the stock should sell at $50.