Suppose that a company’s ROE is 25 percent and its retention rate is 60 percent. According to the expression for the sustainable growth rate, the dividends should grow at g = b × ROE = 0.60 × 25 percent = 15 percent.

To demonstrate the working of the expression, suppose that, in the year just ended, a company began with shareholders’ equity of \($1\),000,000, earned \($250\),000 net income, and paid dividends of \($100\),000. The company begins the next year with \($1\),000,000 +

0.60(\($250\),000) = \($1\),000,000 + \($150\),000 = \($1\),150,000 of shareholders’ equity. No additions to equity are made from the sale of additional shares.

If the company again earns 25 percent on equity, net income will be 0.25 × \($1\),150,000

= \($287\),500, which is a \($287\),500 − \($250\),000 = \($37\),500 or a \($37\),500/\($250\),000 = 0.15 percent increase from the prior year level. The company retains 60 percent of earnings, 60 percent × \($287\),500 = \($172\),500, and pays out the other 40 percent, 40 percent ×

\($287\),500 = \($115\),000 as dividends. Dividends for the company grew from \($100\),000 to \($115\),000, which is exactly a 15 percent growth rate. With the company continuing to earn 25 percent each year on the 60% of earnings that is reinvested in the company, dividends would continue to grow at 15 percent.