Return on Equity

Builds onNet Profit Margin — if this page feels steep, start there.

ROE = \frac{\text{Net income}}{\text{Average shareholders' equity}}

$NI$: net income: the year's profit belonging to shareholders
$E_{begin}, E_{end}$: shareholders' equity at the start and end of the year
$\bar{E}$: average equity — the owners' capital that was actually at work during the year
$ROE$: the compounding rate of the owners' stake: profit per dollar of equity

Why it must be true

Shareholders put capital into the business; ROE measures what the business did with it — cents of profit per dollar of owners' money per year. It is the number that makes companies comparable to every other use of the same capital: a 15% ROE business is compounding its owners' stake faster than a 7% one, whatever the industries.

The denominator uses average equity because the income was earned across the whole year while equity is measured at instants: profit earned in March worked with the January capital base, not December's. Averaging the two endpoints is the honest middle.

The derivation

The owners' claim on the year's earnings, over the owners' capital at work:

ROE = \frac{NI}{\bar{E}}, \qquad \bar{E} = \frac{E_{begin} + E_{end}}{2}

Why it deserves decomposition: multiply and divide by revenue and assets and it factors into DuPont's three levers,

ROE = \underbrace{\frac{NI}{Rev}}_{margin} \times \underbrace{\frac{Rev}{Assets}}_{turnover} \times \underbrace{\frac{Assets}{E}}_{leverage}

— which is why ROE is where profitability analysis starts, not where it ends.

When to reach for it

Measuring how productively a company employs shareholders' capital, or comparing capital efficiency across firms and against required returns.

Listen for

“return on (average) equity”“net income … shareholders' equity”“how efficiently management uses owners' capital”“book value grew by …”

Back-of-the-envelope

Estimate it in your head first — then the calculator only confirms.

≈
Lead digits: NI 84 on equity ~560 → 84/56 = 1.5 → 15%. Two digits of division are enough to pick the answer.
≈
Averaging moves the answer toward the SMALLER endpoint's ratio: if equity grew during the year, average-equity ROE sits above the ending-equity version. Know which direction the distractor errs.
≈
Context: mature US large-caps cluster around 10–20%. A computed ROE of 60% with ordinary inputs means a units slip (millions vs thousands) or ending-vs-average mix-up.

Traps in applying it

✗Using ending equity instead of the average — flatters or punishes depending on the year's direction.
✗Comparing high-ROE firms without checking leverage: borrowing shrinks the denominator and inflates ROE while adding risk (DuPont exposes this).
✗Using total equity when preferred shareholders exist — common-shareholder ROE wants net income minus preferred dividends over common equity.

Limits & criticisms

ROE is blind to how the return was manufactured: a mediocre business plus heavy debt posts the same ROE as an excellent unlevered one — until a bad year, when leverage runs the movie in reverse. Buybacks and write-offs shrink book equity and mechanically inflate ROE with no operating change, and book equity itself drifts far from economic value for asset-light firms. Always read it alongside the DuPont decomposition.

Where it came from

ROE became the executive scorecard through the DuPont Corporation's planning system (circa 1919), spread to General Motors, and never left: Warren Buffett has called consistently high ROE the single best evidence of a durable business, and bank regulators watch it as the driver of capital formation. Every screener, annual report and MBA case builds on it — usually in DuPont's decomposed form, to see whether the return comes from operations or from borrowed money.

One identity, 1 questions

The exam can hide any variable. Each face below is the same equation solved for a different unknown — drill them separately.

Owners' compounding rate

ROE = \frac{NI}{(E_{begin}+E_{end})/2}

The scorecard face: profit per dollar of owners' capital — the rate at which the shareholders' stake compounds if earnings are retained.

Drill this face →

On the BA II Plus

Worked example: From the statements: net income $135.00m; equity $375.00m opening, $825.00m closing. Compute ROE on average equity.

1.375 [+] 825 [=] [÷] 2 [=]average equity at work
2.[STO] 1 135 [÷] [RCL] 1 [=]net income over it (decimal)

→ 22.5%

Where it leads

Master this and the following come almost for free:

DuPont Decomposition (3-Way)Sustainable Growth Rate

Drill this formula Back to the library