Final answer:
To calculate the fair price of the stock, we need to calculate the present value of the future dividends and the present value of the future reinvestments. By using the dividend payout ratio and the expected return on reinvestments, we can calculate the dividend growth rate. With the given values, we can calculate the present value of dividends and the present value of reinvestments. Adding these values together will give us the fair price of the stock.
Step-by-step explanation:
To determine the fair price of the stock, we need to calculate the present value of the future dividends and the present value of the future reinvestments. The dividend payout ratio is given as 0.7, which means that 70% of the earnings will be paid out as dividends. The remaining 30% will be reinvested in projects with an expected return of 9%. Let's calculate the present value of the dividends first:
Present Value of Dividends = Dividends / (Required Rate of Return - Dividend Growth Rate)
The dividend growth rate can be calculated as the product of the dividend payout ratio and the expected return on reinvestments:
Dividend Growth Rate = (1 - Payout Ratio) * Reinvestment Return Rate
Substituting the given values, we get:
Dividend Growth Rate = (1 - 0.7) * 0.09 = 0.027
Next, we calculate the present value of dividends:
Present Value of Dividends = 5.79 * 0.7 / (0.149 - 0.027) = 5.79 * 0.7 / 0.122 = 5.79 * 5.7377 = 33.1845
Next, we calculate the present value of the reinvestments:
Present Value of Reinvestments = (1 - Payout Ratio) / (Required Rate of Return - Reinvestment Return Rate) = 0.3 / (0.149 - 0.09) = 0.3 / 0.059 = 5.0847
Finally, we add the present values of dividends and reinvestments to get the fair price of the stock:
Fair Price of Stock = Present Value of Dividends + Present Value of Reinvestments = 33.1845 + 5.0847 = 38.2692
Rounding to the nearest penny, the fair price of the stock today is $38.27.