Final answer:
The growth rate of a company that pays out 31% in dividends and has a return on equity of 11% can be calculated as 7.59%, using the formula: growth rate = retention ratio × ROE.
Step-by-step explanation:
To calculate the growth rate of a company's earnings given that it pays out 31% of its earnings in dividends and has a return on equity (ROE) of 11%, we will use the retention ratio and the return on equity. The retention ratio, also known as the plowback ratio, is the percentage of earnings not paid out as dividends and hence retained for growth. In this case, it would be 100% - 31% = 69%. The growth rate can then be found by the formula growth rate = retention ratio × ROE.
To calculate the exact growth rate:
- Find the retention ratio: 100% - 31% = 69%.
- Convert the retention ratio to decimal form: 69% = 0.69.
- Multiply the retention ratio by the ROE: 0.69 × 0.11 = 0.0759 or 7.59%.
Therefore, the company's earnings growth rate would be 7.59%.