Question

You are evaluating the purchase of Cool Toys, Inc. common stock that just paid a dividend of $1.80. You expect the dividend to grow at a rate of 12%, indefinitely. You estimate that a required rate of return of 17.5% will be adequate compensation for this investment. Assuming that your analysis is correct, what is the most that you would be willing to pay for the common stock if you were to purchase it today?

Answer 1

Using the Gordon Growth Model and assuming a 12% dividend growth rate and a required rate of return of 17.5%, the maximum price you would be willing to pay for a share of Cool Toys, Inc. is $36.65.

Step-by-step explanation:

To determine the maximum price you would be willing to pay for a share of Cool Toys, Inc., you can use the Gordon Growth Model (also known as the Dividend Discount Model). This model helps in calculating the present value of an infinite stream of future dividends that are expected to grow at a constant rate. Since the dividend has just been paid, the value of the stock today (P0) can be calculated using the formula P0 = D1 / (r - g), where D1 is the dividend next year, 'r' is the required rate of return, and 'g' is the growth rate of the dividend.

In this case, the dividend next year (D1) would be the recent dividend of $1.80 increased by the growth rate of 12%, so D1 = $1.80 * (1 + 0.12) = $2.016. The required rate of return is 17.5%, or 0.175 in decimal form, and the growth rate is 12%, or 0.12 in decimal form.

Applying these values to the formula gives us P0 = $2.016 / (0.175 - 0.12) = $2.016 / 0.055 = $36.65. Therefore, based on your analysis and assuming a 12% growth rate and a 17.5% required rate of return, the most you would be willing to pay for a share of Cool Toys, Inc. is $36.65.