Retention rate * ROE

Retention rate * ROE = the growth rate for dividends for use in the Dividend discount model. Can someone intuitively explain why this is true?

Retention rate is the amount kept in retained earnings. ROE is the return on those retained earnings. So g will be the product of both.

Retained earnings can be reinvested into the company to get a return on the capital. ROE is how much the firm can return on invested equity capital

> Retention rate * ROE = the growth rate for > dividends for use in the Dividend discount model. > > Can someone intuitively explain why this is true? Assume future - dividend is a constant proportion of income - income is proportional to equity then - the dividend grows with income, - income grows with equity, and finally: - equity grows with dividends not paid out (retention) cheers

Another way to think of it is that the earnings that are not paid out as dividends (i.e. Retained earnings) end up adding to equity on the balance sheet (at the end of the current accounting period). Assuming that ROE stays constant (a big assumption in my book, but good enough for CFAI and most analysts) next periodâ€™s income will be equal to last periodâ€™s PLUS the income generated by the new equity from retained earnings. That amount of new net income will be (new equity)*ROE or (retained earnings)*ROE. To turn that into a % growth rate, divide next periodâ€™s increase in net income by current net income. That gives you: (retained earnings)*ROE/(current net income) Which can be algebraically rearranged to: (retention ratio)*ROE Because the retention ratio is (ret earnings)/(net income)

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Thank you very much , great explanation!!