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# Return on equity

Return on equity (ROE) is a measure of how much in earnings a company generates in a time period compared to its shareholders' equity. It is typically calculated on a full-year basis (either the last fiscal year or the last four quarters).

## Expanded Definition

When capital is tied up in a business, the owners of the capital want to see a good return on that capital. Looking at profit by itself is meaningless. I mean, if a company earns $1 million in net income, that's okay. But its great if the capital invested to earn that is only$2.5 million (40% return) and terrible if the capital invested is \$25 million (4% return).

Return on investment measures how profitable the company is for the owner of the investment. In this case, return on equity measures how profitable the company is for the equity owners, a.k.a. the shareholders.

$ROE=\frac{Net\ Income}{Average\ Shareholders\ Equity}$

The "average" is taken over the time period being calculated and is equal to "the sum of the beginning equity balance and the ending equity balance, divided by two."

Return on equity is expressed as a percent and measures the return a company receives on its shareholder's equity. It is a much simpler version of return on invested capital.

In general, the market is willing to pay a higher multiple for stocks with higher ROEs.

As with every ratio, ROE should be compared to the company's industry and competitors. If American Eagle Outfitters is earning 35% ROE, that may sound great, but if the industry is earning 40% on average, then the investor should find out why American Eagle is flying lower. Contrariwise, if its competitors are earning 25%, then American Eagle may be a high flyer. However, don't invest based on just one ratio. Compare several ratios before making a decision.

### DuPont model

This breaks ROE down into several components so that one can see how changes in one area of the business changes return on equity.

$ROE = (net\ margin) * (asset\ turnover) * (equity\ multiplier)$

$ROE = \frac{net\ income}{revenue} * \frac{revenue}{total\ assets} * \frac{total\ assets}{equity}$

Return on equity grows, all else equal:

While the first two seem fairly straight forward, the third one doesn't seem to be, but it really is. If revenue-generating assets are purchased through the use of debt (not equity), then the increased amount of net income generated by that greater amount of assets will increase the return on the fixed amount of equity.

### Sustainable growth

Return on equity also ties into how much growth one can expect from a company. When a firm reinvests its net income, then it can be expected to grow. The fastest this can be expected to occur is the return on equity. This is calculated:

$Sustainable\ growth = Retention\ ratio * ROE$

$Sustainable\ growth = (1 - payout\ ratio) * ROE$

$Sustainable\ growth = (1 - \frac{total\ dividend\ paid}{net\ income}) * ROE$

### A more refined definition

Common shareholders are interested in what return the company is making on their stake. To account for this, dividends paid out to preferred shareholders should be subtracted from net income before calculating ROE. So,

$ROE=\frac{Net\ Income - Preferred\ Dividends}{Average\ Shareholders\ Equity}$