A7X Corp. just paid a dividend of $1.90 per share. The dividends are expected to grow at 22 percent for the next eight years and then level off to a growth rate of 6 percent indefinitely. If the required return is 13 percent, what is the price of the stock today?
To calculate the price of a stock using the dividend growth model, we need to use the following formula:
Price = Dividend / (Required Return - Dividend Growth Rate)
In this case, the dividend is expected to grow at 22 percent for the next eight years and then level off to a growth rate of 6 percent indefinitely. The required return is 13 percent.
Let's break down the calculation step by step:
Step 1: Calculate the dividend growth rate during the initial growth period.
During the initial eight years, the dividend is expected to grow at 22 percent.
Dividend Growth Rate = 22% = 0.22
Step 2: Calculate the dividend growth rate during the stable growth period.
After the initial growth period, the dividend is expected to grow at a constant rate of 6 percent.
Dividend Growth Rate (Stable) = 6% = 0.06
Step 3: Calculate the price of the stock today.
Using the formula mentioned earlier, we can calculate the price of the stock today:
Price = Dividend / (Required Return - Dividend Growth Rate)
To calculate the dividend, we start with the dividend paid per share today and then compound it with the growth rate during the initial growth period.
Dividend = $1.90
Next, let's calculate the present value of the dividends during the stable growth period using the formula for the present value of a growing perpetuity:
Present Value of Dividends (Stable) = Dividend / (Required Return - Dividend Growth Rate (Stable))
Dividend = $1.90
Required Return = 13%
Dividend Growth Rate (Stable) = 6% = 0.06
Present Value of Dividends (Stable) = $1.90 / (0.13 - 0.06) = $1.90 / 0.07
Now, we have the present value of dividends for the stable growth period. We need to calculate the present value of the dividends during the initial growth period.
To calculate that, we use the formula for the present value of a growing annuity:
Present Value of Dividends (Initial Growth) = Dividend × [((1 + Dividend Growth Rate) ^ Number of Periods) - 1] / (Required Return - Dividend Growth Rate) × (1 + Required Return) ^ (-Number of Periods)
Dividend = $1.90
Required Return = 13%
Dividend Growth Rate = 22% = 0.22
Number of Periods = 8
Present Value of Dividends (Initial Growth) = $1.90 × [((1 + 0.22) ^ 8) - 1] / (0.13 - 0.22) × (1 + 0.13) ^ (-8)
Finally, we can calculate the price of the stock today by summing up the two present values of dividends:
Price = Present Value of Dividends (Initial Growth) + Present Value of Dividends (Stable)
After calculating these values, you will have the price of the stock today.