Two of the most common metrics you'll come across when you read companies' earnings announcements, annual reports, or analyst reports are earnings per share and return on equity. What are they, and what is the difference between them?

What are earnings per share?
There's not a lot of mystery here; the name pretty well says it all. Earnings per share (or EPS) is the dollar amount of earnings attributable to each one of the company's shares.

The calculation of a company's earnings per share is straightforward:

Earnings per share = Net income / Number of shares outstanding during reporting period

EPS is expressed in dollars per share (or whatever the reporting currency is). In practice, we use the weighted average number of shares outstanding during the reporting period (the number of shares outstanding is liable to change during a reporting period because of buybacks and/or stock offerings).

Note that EPS can be negative if the company has realized a net loss rather than a net profit.

What is return on equity?
Return on equity (ROE) is a key measure of how profitably a company employs its shareholders' equity.

ROE is equal to the dollar amount of profits per dollar of shareholders' equity, expressed on a percentage basis (as befits a return):

Return on equity = Net income / Average shareholders' equity for the period

We use average shareholders' equity for the same reason we use the weighted average number of shares outstanding in calculating EPS: Shareholders' equity is not constant; it changes over the course of a reporting period.

What are the differences between earnings per share and return on equity?
This may sound surprising, but earnings per share tells us essentially nothing about a company's profitability beyond whether it has been profitable or loss-making during the period in question (i.e., is the earnings-per-share figure positive or negative?).

Yes, profits have been scaled to a per-share basis, but companies authorize an arbitrary number of shares and issue shares at their discretion.

As a result, there is absolutely no uniformity in the number of shares between companies, and the difference can be an order of magnitude or more. For example, during the third quarter 2015, Netflix's weighted average number of shares outstanding was 437.6 million (diluted); during the same period, AT&T's was 5.94 billion.

To repeat: There is no comparability between earnings per share of different companies.

For a single company, you will at least need a historical earnings-per-share series to start coming up with EPS growth rates, which is more interesting.

In combination with other metrics, EPS can produce some interesting things, too. For example, if you have the stock price in addition to EPS, you can derive the price-to-earnings ratio.

There are two clues that return on equity is a more versatile, more powerful metric than earnings per share:

1. It's a percentage, not an absolute dollar amount.
2. It is derived using a number from the income statement (net income) and another from the balance sheet (stockholders' equity).

Contrary to EPS, return on equity is a measure of profitability: It measures how profitably the company is able to put shareholders' equity to work.

Note, however, that ROE doesn't reflect only operating profitability. ROE also reflects a financing decision: How much, if at all, did the company leverage its shareholders' equity to achieve its profits? Indeed, a company's assets are typically financed through some combination of equity and debt.

Thus, return on equity can be used for comparisons between companies and for a single company (versus its own history), as JPMorgan does here in its 2014 Annual Report:

Source: Company filings.

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