Final answer:
The value of the stock can be calculated using the Dividend Discount Model (DDM), taking into account both the high initial growth rate for the first five years and the perpetual growth rate afterward. The required rate of return is determined by the CAPM, and the Gordon Growth Model is used after the initial growth period.
Step-by-step explanation:
To calculate the value of the stock with the given information, we will use the Dividend Discount Model (DDM), which incorporates the present value of the expected dividends. This stock will have two stages of growth, a high initial growth rate for five years and then a perpetual growth rate.
The risk-free rate is 1.46%, and the market risk premium is 5.43%. Since the stock has a β (beta) of 1.27, the expected return using the Capital Asset Pricing Model (CAPM) is r = risk-free rate + β * (market risk premium). Plug in the values to get r = 1.46% + 1.27 * 5.43% = 8.33%.
The stock just paid a dividend of $2.21, which is expected to grow at 22.90% for the first five years. The present value of these dividends can be found by calculating the future dividends and discounting them back to the present value at the rate of 8.33%.
After the five-year growth period, the dividend growth rate will drop to a perpetual rate of 3.02%. Use the Gordon Growth Model for this stage, which assumes a constant growth rate forever P = D1 / (r - g), where P is the price at the end of year 5, D1 is the dividend at year 6, r is the required rate of return, and g is the perpetual growth rate. After this calculation, discount the price back to today's value using the 8.33% rate.
Once both stages are calculated and discounted, the sum of these present values will give us the total current value of the stock.