The Whirlwind Co. just paid an annual dividend of $3 a share. The firm expects to pay dividends forever and to increase the dividend by 5 percent annually. What is the current value of this stock if the required return is 9 percent?

The current value of the stock is $78.75

Explanation:

The constant growth model of DDM will be used to calculate the price of the stock as its dividends are expected to grow at a constant rate forever. The formula for price under this model is,

P0 = D1 / r - g

Where,

D1 is the dividend expected for the next period r is the required rate of return g is the growth rate in dividends

P0 = 3 * (1+0.05) / (0.09 - 0.05)

P0 = $78.75

Stock price is $78.75

Explanation:

The formula for computing the stock price is given below:

stock price=Do * (1+g) / r-g

Do is the dividend that has just been paid at $3

g is the dividend growth rate at 5%

rate of return r is the expected return on the share at 9%

stock price=$3 * (1+5%) / (9%-5%)

=$78.75

A rational investor would only pay $78.75 for the stock of the company considering the fact that the dividend grows at 5% per year and the return on stock is 9%