Question

A stock will pay dividends of $2, $6, and $10 over the next

three years, and then increase dividends at a rate of 5%
afterwards. Its required rate of return is 17%. What is the value
of the stock?

Answer 1

The value of the stock is $93.59

Step-by-step explanation:

To find the value of the stock, we need to calculate the present value of the future dividends and the future price of the stock. The formula to calculate the present value of dividends is:

PV = D1 / (1+r) + D2 / ((1+r)^2) + D3 / ((1+r)^3) + ...

Where PV is the present value, D1, D2, D3 are the future dividends, r is the required rate of return. Using this formula, the present value of the dividends would be:

PV = 2 / (1+0.17) + 6 / ((1+0.17)^2) + 10 / ((1+0.17)^3) = $14.64

To calculate the future price of the stock, we need to use the constant growth formula:

P = D4 / (r - g)

Where P is the future price of the stock, D4 is the next dividend after three years, r is the required rate of return, and g is the growth rate of dividends. The growth rate is given as 5%. Using this formula, the future price of the stock would be:

P = 10 / (0.17 - 0.05) = $78.95

Finally, to find the value of the stock, we need to sum up the present value of dividends and the future price of the stock:

Value of the stock = PV + P = $14.64 + $78.95 = $93.59