Stable Corporation currently pays a dividend of $0.50 a share. The firm's dividends are expected to grow at a constant rate of 10% indefinitely. If investors require a 15% return on
Stable's stock, at what price should it sell?

Question

Quizplus · Accepted Answer

To calculate the price, we use the constant growth dividend discount model: 
Price = Dividend / (Required rate of return - Dividend growth rate)
Plugging in the given values, 
Price = $0.50 / (0.15 - 0.10)
Price = $0.50 / 0.05
Price = $10.00
However, since the question asks for the price at which the stock should sell, we use the dividend growth rate to calculate the future dividend and add it to the current dividend to get the expected dividend next year. 
Expected dividend next year = $0.50 * (1 + 0.10) = $0.55
Price = Expected dividend next year / (Required rate of return - Dividend growth rate)
Price = $0.55 / (0.15 - 0.10)
Price = $0.55 / 0.05
Price = $11.00
Therefore, the stock should sell at $11.00 per share. Using the dividend discount model, we can find the price of the stock. The formula is:

Price = Dividend / (Required Rate of Return - Dividend Growth Rate)

Plugging in the given values:

Price = 0.5 / (0.15 - 0.1)
Price = 0.5 / 0.05
Price = $10.00

However, this is the price for the current year's dividend. We need to calculate the price for the next year's expected dividend:

Next year's expected dividend = Current dividend * (1 + growth rate)
Next year's expected dividend = $0.50 * (1 + 0.1)
Next year's expected dividend = $0.55

Now using the same formula with the next year's expected dividend:

Price = $0.55 / (0.15 - 0.1)
Price = $0.55 / 0.05
Price = $11.00

Therefore, the stock should sell for $11.00 to provide a 15% return to investors. So, the best choice is C) $11.00.

Stable Corporation Currently Pays a Dividend of $0