Question

J. Ross and Sons Inc. has a target capital structure that calls for 40 percent debt, 10 percent preferred stock, and 50 percent common equity. Ross' common stock currently sells for $40 per share. The firm recently paid a dividend of $2 per share on its common stock, and investors expect the dividend to grow indefinitely at a constant rate of 10 percent per year. J. Ross's cost of retained earnings is closest to: a. ​15.50 percent b. ​12.20 percent c. ​16.34 percent d. ​10.42 percent

Answer 1

The cost of retained earnings is 15.50%

Step-by-step explanation:

The cost of retained earnings is the cost of equity capital to the firm. We will use the dividend discount model equation to calculate the cost of retained earnings.

The constant growth model of DDM is used to calculate the price of a stock whose dividends are expected to grow at a constant rate every year. The formula for price today under this model is,

P0 = D0 * (1+g) / (r - g)

Where,

• D0 * (1+g) which is the dividend expected for the next period of D1
• r is the cost of equity
• g is the growth rate in dividends

As we already have the price today, the D0 and the growth rate, we can plug in these variables in the equation to calculate the cost of retained earnings.

40 = 2 * (1+0.1) / (r - 0.1)

40 * (r - 0.1) = 2.2

40r - 4 = 2.2

40r = 2.2 + 4

r = 6.2 / 40

r = 0.155 or 15.5%