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Sustainable Growth Rate

Hi guys,

I have a question on the sustainable growth rate. 

The following definitions are provided in Wiley:

ROE = Net Income / Average Equity

Retention Ratio = (Net Income Attributed to Common Shareholders - Common Dividends) / Net Income Attributed to Common Shareholders

I’m presuming that Net Income Attributed to Common Shareholders = Net Income - Preferred Dividends

If the above are true, why does ROE * RR give us a sustainable growth rate? The numerator of ROE (Net Income) and denominator of RR (Net Income - Preferred Dividends) are different. 

Thanks

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I wouldn’t think about it so much in algebraic terms, instead think in common sense terms. Your Retention ratio is the % of income that you retain (ie, reinvest back into the business). The ROE is the the return you generate from your equity invested. So when you multiply the % that you reinvested back into the business by the return that you get on your overall equity invested, you have the rate that your income will grow at. Does that make sense?