Final answer:
The value of the stock is calculated using a two-stage Dividend Discount Model. Initial dividends grow at 20.39% for three years before settling to a long-term growth of 4.60%. The required return is 11.16%, and the stock value is obtained by discounting forecasted dividends and terminal value back to the present.
Step-by-step explanation:
The value of the stock in question can be calculated using a Dividend Discount Model (DDM), specifically a two-stage DDM since the stock's dividends are expected to grow at different rates in the short and long term. Given that the stock just paid a dividend of $1.60 and that this dividend is expected to grow at 20.39% for three years, before settling to a long-term growth rate of 4.60%, we can calculate the present value of expected dividends for the first three years and then find the present value of all subsequent dividends, assuming perpetual growth at the lower rate after year three. The required return on the stock is 11.16%.
To value the stock, we first forecast the dividends for the first three years and discount them back to the present:
- Year 1 Dividend: $1.60 * (1 + 0.2039) = $1.92624
- Year 2 Dividend: $1.92624 * (1 + 0.2039) = $2.32022
- Year 3 Dividend: $2.32022 * (1 + 0.2039) = $2.79356
These dividends are then discounted back to the present value using the required return of 11.16%.
The terminal value of the stock at year 3, which represents the present value of all subsequent dividends growing at 4.60% in perpetuity, is calculated using the Gordon Growth Model. The formula for the terminal value is:
Terminal Value at Year 3 = Dividend at Year 4 / (required return - perpetual growth rate)
Where Dividend at Year 4 is Year 3 Dividend * (1 + perpetual growth rate).
The sum of the present value of the dividends for the first three years and the present value of the terminal value gives us the value of the stock today.