Example Showing g = b X ROE.
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. Its ROE is 25 percent and its retention rate is 60 percent. ‘The company begins the next year with $1,150,000 of shareholders’ equity because it retained $150,000. There are no additions to equity from an increase in shares outstanding.
If the company again earns 25 percent on equity in the next year, net income will be $287,500, which is a 15 percent increase. The increase in earnings is $287,500 $250,000 = $37,500. This is 15 percent above the previous year’s earnings of $250,000. The company retains 60 percent of earnings (60% X $287,500 = $172,500) and pays out the other 40 percent (40% X $287,500 =
$1 15,000) as dividends.
The formula for the dividend growth rate is g = b X ROE, which is g = 0.60 X 25% = 15%. Notice that dividends for the company grew from $100,000 to $1 15,000, which is exactly a 15 percent growth rate.