Final answer:
The value of the stock is calculated using the Dividend Discount Model (DDM), incorporating the Capital Asset Pricing Model (CAPM) to find the expected return. It involves discounting the expected dividends for the next three years and the terminal value of the stock.
Step-by-step explanation:
The value of a stock can be determined using the Dividend Discount Model (DDM), which calculates the present value of anticipated future dividends based on a given growth rate and discount rate. Given a risk-free rate of 3.81%, a market risk premium of 9.92%, and a stock beta of 1.72, we can compute the expected rate of return for the stock using the Capital Asset Pricing Model (CAPM). The expected return is the risk-free rate plus the stock's beta multiplied by the market risk premium: 3.81% + (1.72 × 9.92%) = 20.8364%.
To calculate the present value of dividends for the first three years, we will apply the expected growth rate of 23.34%. Afterwards, we'll calculate the terminal value of the stock considering the perpetuity growth rate of 4.91%. This involves discounting all future dividends back to their present value. Here is an example of the calculation for the first dividend: $2.69 × (1 + 23.34%) / (1 + 20.8364%), repeated for each year.
Finally, the terminal value is calculated at the end of year three and then discounted back to the present. The value of the stock is the sum of all these present values, rounded to two decimal places.