Final answer:
To calculate the fair price for the stock, we need to calculate the present value of the future dividends and the present value of the infinite stream of future dividends. By discounting each dividend back to the present value and adding them up, we can calculate the fair price for the stock today. In this case, the fair price for the stock today is $45.79.
Step-by-step explanation:
To calculate the fair price for the stock today, we first need to calculate the present value of the future dividends. The present value of each dividend is calculated by dividing the dividend by the required rate of return and discounting it back to the present value. The formula to calculate the present value of a dividend is:
PV = D / (1 + r)^n
Where PV is the present value of the dividend, D is the dividend payment, r is the required rate of return, and n is the number of years until the dividend is received.
Using this formula, we can calculate the present value of each dividend:
PV of $2.07 = $2.07 / (1 + 0.15)^1 = $1.80
PV of $1.10 = $1.10 / (1 + 0.15)^2 = $0.86
PV of $2.49 = $2.49 / (1 + 0.15)^3 = $1.63
Next, we need to calculate the present value of the infinite stream of future dividends. The formula to calculate the present value of an infinite stream of dividends is:
PV = D / (r - g)
Where g is the constant growth rate of dividends. In this case, the growth rate is 6% per year. Using this formula, we can calculate the present value of the infinite stream of dividends:
PV = $2.49 / (0.15 - 0.06) = $41.50
Finally, we add up the present values of the dividends to get the fair price for the stock today:
Fair Price = $1.80 + $0.86 + $1.63 + $41.50 = $45.79
Therefore, the fair price for the stock today is $45.79.