Rapid City Motors Co. expects to grow at 20% for two years. After that it expects 8% growth indefinitely. The firm recently declared a $4.00 annual dividend. Similar stocks return about 12%. How much should a share of Rapid City be worth today?

Question

Quizplus · Accepted Answer

To calculate the value of a stock using the constant growth model, we use the formula:

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

First, we need to calculate the present value of the future dividends during the two-year period of 20% growth. We can use the dividend discount model to find the present value of the dividends:

PV = D1 / (1 + r) + D2 / (1 + r)^2

Where:
D1 = the dividend for next year = $4.00 * (1 + 20%) = $4.80
D2 = the dividend for the year after = $4.80 * (1 + 20%) = $5.76
r = the required rate of return = 12%

PV = $4.80 / (1 + 0.12) + $5.76 / (1 + 0.12)^2 = $8.94

Now we can use the constant growth model to find the value of the stock today:

Price = ($4.00 * (1 + 8%)) / (0.12 - 8%) + $8.94 / (1 + 0.12)^2
Price = $132.84

Therefore, choice C is correct.