To find the current market price of the stock, calculate the present value of the dividends. The dividends will grow at 10% for the next 2 years and then grow at an annual rate of 5% to infinity. Using the present value formulas, the current market price of the stock is $112.50.
To find the current market price of the stock, we need to calculate the present value of the dividends. The dividends are expected to grow at 10% for the next 2 years, and then grow at an annual rate of 5% to infinity.
First, let's calculate the present value of the dividends for the next 2 years. We can use the formula for the present value of a growing annuity:
PV = C / (r - g) * (1 - (1 + g)⁻ⁿ)
Where PV is the present value, C is the initial dividend, r is the required rate of return, g is the growth rate, and n is the number of periods. Plugging in the values, we get:
PV = 5 / (0.10 - 0.10) * (1 - (1 + 0.10)⁻²) = 12.50
Now, let's calculate the present value of the dividends after 2 years, using the same formula:
PV = C / (r - g)
Where PV is the present value, C is the initial dividend after 2 years, r is the required rate of return, and g is the growth rate. Plugging in the values, we get:
PV = 5 / (0.10 - 0.05) = 100.00
Finally, let's add up the present values of the dividends:
Current market price = 12.50 + 100.00 = $112.50
Complete Question :
A company just paid a dividend of $5.00 per share. An investor estimates that the dividends will grow at 10% for the next 2 years. After that the dividen will grow at an annual rate of 5% to infinity. What is the current market price of the stock if the required rate of return is 10%