Dividend Growth Rate, Retention Rate, and ROE Analysis

Return on equity is net income divided by shareholder's equity. A fine ratio, and simple enough. But suppose you want to make it bigger.

Not just for the complexity, but to start breaking ROE down into pieces so that you can see the drivers behind it. One way is to start with ROA, or net income over assets. What would this need to be multiplied by in order to end up with ROE?

No. That would give you a meaningless value with squared assets on the bottom.

Yes! That's the idea. Line those two up, and assets cancel out to make ROE. $$\displaystyle \mbox{ROE} = \frac{\mbox{Net Income}}{\mbox{Total Assets}} \times \frac{\mbox{Total Assets}}{\mbox{Shareholders' Equity}} $$ So ROE is affected by both ROA and the equity multiplier, which is essentially a leverage measure.

Not quite. That would leave you with equity over assets, not ROE.

But think bigger. ROA can be further broken down, so that ROE is the product of profit margin, turnover, and the equity multiplier. $$\displaystyle \mbox{ROE} = \frac{\mbox{Net Income}}{\mbox{Sales}} \times \frac{\mbox{Sales}}{\mbox{Total Assets}} \times \frac{\mbox{Total Assets}}{\mbox{Shareholders' Equity}} $$ This is the DuPont model of ROE. How many of these ratios would boost a positive ROE if they increased?

Absolutely. Profit margin and asset turnover are both "good" things which will increase ROE. The equity multiplier of assets over equity is a leverage measure, so higher leverage means _magnified_ ROE, for better or worse. As long as ROE is positive, leverage is for the better.

Not quite. Consider just the fact that these ratios are all multiplied to arrive at ROE.

No. More than that.

Once you have ROE broken up into bits, recall that the sustainable growth rate is just ROE multiplied by the retention ratio. One way to think of the retention ratio is just the net income that is _not_ paid out in dividends, divided by net income. So adding that ratio in for _b_, you have a nice, large expression for the sustainable growth rate. $$\displaystyle g = \frac{\mbox{Net Income - Dividends}}{\mbox{Net Income}} \times \frac{\mbox{Net Income}}{\mbox{Sales}} \times \frac{\mbox{Sales}}{\mbox{Total Assets}} \times \frac{\mbox{Total Assets}}{\mbox{Shareholders' Equity}} $$ That's big. It's also called the PRAT model, since you have (not in this order) __P__rofit margin, __R__etention rate, __A__sset turnover, and __T__ for financial leverage, perhaps because the letter looks like a lever on a fulcrum.

For example, suppose that a firm has ROA of 10%, pays 40% of earnings to shareholders, and assets are comprised of 30% debt and 70% equity. This is enough to calculate the growth rate. Why do you think that profit margin isn't included here?

When calculating a growth rate using these parts, beginning equity is sometimes used since retained earnings aren't available for reinvestment until the end of the period. Average assets are commonly used in calculation of ROE. Obviously these choices will affect the estimate.

Yes! ROA can be decomposed to the product of profit margin and total asset turnover. Those are the "P" and "A" in PRAT, so profit margin is in there. The "R" is the 60% retention rate, since 40% is the payout ratio, and the "T" is assets over equity. Since assets are 70% equity, this is just 1 over 70%. The growth rate in this example can then be calculated. $$\displaystyle g = b \times ROA \times \frac{A}{E} = 0.60 \times 0.10 \times \frac{1}{0.70} = 0.0857 $$

No. The retention rate just uses net income and dividends.

No, it is. Profit margin is the "P" in PRAT, so it's definitely in there somewhere.

As with any sustainable growth rate, its constituent parts should be estimated with caution as well. To say that _g_ is forever can suggest that these pieces are also forever, and that's a big claim. Competition, technological change, and many other fundamental forces will act to reduce growth rates that are well above average.

To summarize: [[summary]]

Equity over assets

Assets over equity

Equity over net income

Just one

Two of them

All three of them

Profit margin is part of ROA

Profit margin is included in the retention rate

Profit margin isn't related to the sustainable growth rate

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