How return on equity (ROE) works

Return on equity is one division:

$$ROE = \frac{\text{Net income}}{\text{Equity}}$$

Net income is what is left after interest and tax. Book equity is the residual claim on the balance sheet, not market capitalisation. Divide one by the other and you have a rate of return on that residual, printed in percentage points: 15, not 0.15.

On $15,000,000 of net income against $100,000,000 of equity, ROE is 15 percent. The shareholders' book claim earned 15 cents on the dollar this period.

The ROE calculator on this page is that one division. ROIC divides NOPAT by invested capital instead. NOPAT is before interest. Invested capital includes the debt. ROE puts the financing in both the numerator (interest already deducted) and the denominator (equity only). That is why a recapitalisation can lift ROE without the operations having improved.

Keep net income at $15,000,000 and cut equity to $75,000,000. ROE rises to 20 percent. Profit did not rise. The book claim it is measured against shrank.

Borrowing to buy back equity, or simply running a more borrowed sheet, does this. The operations can be unchanged. ROE still prints a higher rate. That is financial leverage sitting inside the ratio, which is why a rise in ROE is not, on its own, an operating improvement.

The third sheet runs the other way. Net income is $8,000,000 on the original $100,000,000 of equity. ROE is 8 percent. The denominator did not move. The profit after interest did: a higher coupon, a worse year, or both. Coverage of that coupon is a different ratio, on how interest coverage works.

Compare ROE with ROIC on the same year before calling the rise an operating improvement. The pair is laid out on ROE against ROIC.

The DuPont identity writes the same ROE as three pieces that have to multiply back to it:

$$ROE = \text{Net margin} \times \text{Asset turnover} \times \text{Equity multiplier}$$

Net margin is net income over sales. Asset turnover is sales over assets. The equity multiplier is assets over equity, which is the third leverage ratio on a balance sheet. A high ROE can come from a wider margin, from assets that turn over faster, or from nothing more than a larger multiplier.

This page does not split a teaching sheet into those three, because the ROE calculator takes net income and equity only. The identity is here so a 20 percent ROE on the second sheet is not read as a 20 percent operating result. Equity fell from $100,000,000 to $75,000,000. That is the multiplier moving, or the residual shrinking, which is the same fact.

The four families on financial ratios explained put ROE in profitability and the equity multiplier in leverage ratios. They are two readings of one sheet, not two companies.

It is not ROIC, not a market-value return, and not a full DuPont model with sales and assets typed in. Book equity of zero or negative makes the ratio unusable, the way negative earnings make P/E unusable. This calculator will not print a rate in that case.

Compare ROE with the cost of equity, and ROIC with WACC, rather than mixing the pairs. Fifteen percent on the teaching sheet is $15,000,000 over $100,000,000. The second sheet is the same profit on $75,000,000 of equity. The third is $8,000,000 on the original equity. This is educational material, not financial advice.