Expecting a period of intense growth and has decided to retain more of its earnings to help finance that growth. As a result, it is going to reduce its annual dividend by 10% a year for the next three years. After that, it will maintain a constant dividend of $.70 a share. Last month, the company paid $1.80 per share. What is the value of this stock if the required rate of return is 13%

The price of the stock is $7.216

Explanation:

The price of the stock will be calculate the using the two stage dividend Gordon growth model. In the first stage, the dividend is falling a constant percentage for 3 years. After that the growth rate is zero. Thus the formula for the price of such a stock will be,

P0 = D1 / (1+r)  +  D2 / (1+r)²  +  D3 / (1+r)³ + [D4 / r] / (1+r)^4

P0 = [1.8 * (1-0.1)] / (1+0.13) + [1.8 * (1-0.1)²] / (1+0.13)² + [1.8 * (1-0.1)³] / (1+0.13)³ + (0.7 / 0.13) / (1+0.13)^3

P0 = $7.216