Question

A company with earnings per share of $5 has decided to plowback 50 percent of its future earnings into new investments. The reinvestments generate an expected return of 20 percent. If the opportunity cost of capital is 20 percent, at what rate are dividends expected to grow?

Answer 1

Dividends are expected to grow at a rate of 10 percent annually for a company that plows back half of its earnings at a return equal to the opportunity cost of capital at 20 percent.

Step-by-step explanation:

The question seeks to determine at what rate dividends are expected to grow given that a company with earnings per share (EPS) of $5 decides to plow back 50 percent of its earnings and the reinvestments yield an expected return of 20 percent. As the company is reinvesting at the opportunity cost of capital, which is also 20 percent, the growth rate of dividends can be determined using the formula for sustainable growth rate (SGR): SGR = Retention Ratio * Return on Equity (ROE).

Since the company is retaining 50 percent of earnings and the ROE is equal to the return on reinvestments (20 percent), the expected growth rate of dividends would be 0.5 * 0.2 = 0.1 or 10 percent. The rate at which dividends are expected to grow for this company is therefore 10 percent annually.