Final answer:
To find the current stock price, calculate the present value of each dividend payment for the first three years and then use the Gordon Growth Model to find the present value of all perpetual dividends from year 4 onwards. Add all present values for a total that represents the current stock price.
Step-by-step explanation:
To determine the current stock price, we need to calculate the present value of the estimated dividend payments as well as the present value of all future dividends that grow at a constant rate. The dividend payments are $2.4 next year, $3.4 the year after that, and $4.1 in the third year. Thereafter, dividends will grow at a constant rate of 4% per year indefinitely. The discount rate we are using for present value calculations is 13%.
The present value (PV) of a future dividend payment is calculated by the formula PV = D / (1+r)^t, where D is the dividend payment, r is the discount rate, and t is the number of years until the payment. After finding the PV of each of the first three years of dividends, we must also calculate the present value of the perpetual dividends that begin in year 4. This can be done using the Gordon Growth Model, which assumes a perpetual growth rate: PV = D4 / (r - g), where D4 is the dividend in year 4 (calculated by $4.1 * 1.04), r is the discount rate, and g is the growth rate.
Once you have calculated the PV of each dividend payment for the first three years and the perpetual dividends starting from year 4, you add all the present values together to find the total present value of the dividends, which will be the current stock price.