Return on assets and equity

In depth

The denominator must be stated

Analysts use three denominators: the opening balance, the closing balance and the average. Each has a defence. The opening balance is what the owners had committed when the year began, and investment made during the year rarely earns a full year’s profit at once; Damodaran (2007) uses it for that reason. The closing balance is the only one available for a business’s first period. The average treats the year’s resources as building up evenly. None is wrong, but they can give very different answers, and a ratio quoted without its basis can’t be compared with anything.

Net income $22,431 in every row. Total assets: opening $93,676, closing $327,883. Equity: opening $42,387, closing $62,818.

The spread is widest for ROA, because Lantern’s assets more than tripled. On opening balances the cafés’ assets aren’t in the denominator at all, although they produced much of the year’s revenue; on closing balances they count for twelve months although they were used for ten. The average sits between. For a business whose balance sheet barely changes, the three bases agree closely, which is why the choice is often ignored; for a growing or shrinking business it is the first thing to check.

First periods: Lantern’s 2026

Lantern began on 1 March 2026 with nothing; Ana’s $20,000 bought its stock that day. There is no opening balance sheet, so the course uses closing balances for 2026: ROA $27{,}387 \div 93{,}676 = 29.2\%$ and ROE $27{,}387 \div 42{,}387 = 64.6\%$. Two other reasonable choices give quite different answers. Averaging the $20,000 Ana put in on 1 March with the closing $42,387 gives an ROE of 87.8%. Annualising ten months of net income ($27{,}387 \times 12 \div 10 = 32{,}864$) gives 77.5% on closing equity; but the ten months included the fourth-quarter gift peak and no January or February, so annualising probably overstates a normal year.

A first period also has a deeper problem. The closing equity of $42,387 already includes most of the year’s profit, retained in the business, so the denominator grows with the numerator; a business that earned nothing would end its first year with only its contributed capital. Whatever you choose, say what you did and compare like with like: Lantern’s 2027 ROE on closing equity is 35.7%, the figure to set beside 2026’s 64.6%. Even that pair is not fully like-for-like: 64.6% is earned in ten months (77.5% annualised) and 35.7% in twelve.

An unpaid owner

In 2026 Ana drew no salary: she was paid only through $5,000 of dividends, which are not an expense. From 2027 she is paid $48,000 a year, an operating expense that reduces net income. The two years’ profits therefore measure different things. 2026’s profit is what was left for the owner before paying her for her work; 2027’s is after paying her a market wage.

To compare them, charge 2026 with what Ana’s work would have cost: ten months of the $48,000 salary, $40,000. Income before tax becomes $36{,}516 - 40{,}000 = -3{,}484$. At Lantern’s 25% tax rate the salary would have cut income tax by $10,000, from $9,129 to a credit of $871 (in practice, a loss to carry forward), so net income becomes $-3{,}484 \times 0.75 = -2{,}613$. Held against the reported closing balances, ROE is −6.2% and ROA −2.8%. Most of 2026’s spectacular return was Ana’s unpaid labour. Buyers and lenders looking at owner-managed businesses commonly make this adjustment, often called normalising the owner’s pay; for a company whose managers are paid market salaries it isn’t needed.

Leverage: why ROE can stay high while margins fall

Write $\overline{\text{Total assets}} \div \overline{\text{Equity}}$ as the assets each dollar of equity supports. For Lantern it rose from 2.21 at the end of 2026 to 4.01 on 2027’s averages. Equity grew by $20,431 in 2027 (net income $22,431 less a $2,000 dividend); total liabilities grew by $213,776, from $51,289 to $265,065: the lease liabilities of $173,379, the line of credit, the brewer plan and the wages and customer deposits owed by a larger business. So, carrying an extra decimal place: $29.24\% \times 2.210 = 64.6\%$ in 2026 and $10.64\% \times 4.007 = 42.6\%$ in 2027. Leverage nearly doubled and absorbed much of the fall in ROA.

Leverage raises ROE only while the business earns more on its capital than the capital costs after tax. The cleanest way to see it uses Return on invested capital (ROIC): operating profit after tax divided by the capital provided by lenders (debt, $D$) and owners (equity, $E$). If debt costs $r$ before tax and the tax rate is $t$, then, as an identity, $\text{ROE} = \text{ROIC} + (\text{ROIC} - r(1-t)) \times D \div E$. Each dollar of debt earns ROIC and costs $r(1-t)$; the difference, the spread, goes to the owners, magnified by $D \div E$. When ROIC falls below the after-tax cost of debt, the spread is negative and leverage pushes ROE below ROIC. The challenging example shows both cases.

The identity follows in three lines. Net income is what is left of EBIT after interest and tax: $\text{NI} = (\text{EBIT} - rD)(1-t)$. Since $\text{ROIC} = \text{EBIT}(1-t) \div (D+E)$, $\text{EBIT}(1-t) = \text{ROIC} \times (D+E)$, so $\text{NI} = \text{ROIC} \times (D+E) - r(1-t)D$. Divide by $E$: $\text{ROE} = \text{ROIC} + (\text{ROIC} - r(1-t)) \times D \div E$. It holds exactly when the same balances (here, averages) are used throughout and there are no non-operating items.

For Lantern in 2027, on averages: interest-bearing debt averages $(30{,}000 + 65{,}250) \div 2 = 47{,}625$ and equity 52,602.5, so $D \div E = 0.905$. Interest of $2,879 on that debt is $r = 6.05\%$, or 4.53% after tax. ROIC (below) is 24.53%, so the spread is 20.0 points and $\text{ROE} = 24.53\% + 20.00\% \times 0.905 = 42.6\%$: the same answer as net income over average equity. Leverage adds 18.1 points to Lantern’s ROE, and it does so because the business earns far more on its capital than its debt costs. (Treating the lease liabilities as debt would change both ROIC and the spread; F05 takes that up.)

Higher ROE from leverage is not free. Interest and lease payments are fixed, so the owners’ result swings more widely and the business can run out of cash in a bad year. That is why the bank analyst’s note mentions Lantern’s current ratio of 0.52 at the end of 2027 (the liquidity lesson) and why the distress-scores lesson returns to these balance sheets. ROE measures the reward; the leverage and liquidity ratios measure the risk taken to get it.

When equity is tiny or negative

ROE divides by equity, so small equity gives huge answers and negative equity gives nonsense. A business with $5,000 of equity and $50,000 of profit has an ROE of 1,000%, which says more about the denominator than about the business. If equity is negative, a profitable company shows a negative ROE and a loss-making one a positive ROE, two negatives making a positive. In either case report ROE as “not meaningful” and use ROA or ROIC instead; Damodaran (2007) gives the same advice.

Starbucks is a real example. At 29 September 2024 its balance sheet shows total assets of $31,339.3 million and total liabilities of $38,780.9 million, so shareholders’ equity is a deficit: −$7,448.9 million attributable to Starbucks. The deficit was built up by returning cash to shareholders: in fiscal 2022, for example, Starbucks repurchased $4,013.0 million of its stock and paid $2,263.3 million of dividends, together far more than its net earnings of $3,283.4 million (including noncontrolling interests, as its cash-flow statement starts). In fiscal 2024 dividends ($2,585.0 million) and repurchases ($1,266.7 million) again exceeded net earnings ($3,762.3 million), yet the deficit narrowed slightly from −$7,994.8 million a year earlier, because other items added to equity. Net earnings attributable to Starbucks were $3,760.9 million, so a mechanical ROE on average equity is $3{,}760.9 \div (-7{,}721.85) = -48.7\%$ for a company that made a large profit. Its ROA, $3{,}760.9 \div 30{,}392.4 = 12.4\%$, still means something.

Return on invested capital, in outline

ROE mixes how well the business operates with how it is financed. ROIC separates them by putting operating profit after tax, often called NOPAT, over the capital that lenders and owners provide, whatever its mix. For Lantern in 2027, before any adjustment for leases: NOPAT $32{,}787 \times 0.75 = 24{,}590$; invested capital (interest-bearing debt plus equity) averages $(72{,}387 + 128{,}068) \div 2 = 100{,}227.5$; ROIC is 24.5%. Analysts differ on the details: whether to subtract cash, whether to treat lease liabilities as debt (which also means moving the interest inside the lease cost out of operating profit), which tax rate to use. F05 develops ROIC and compares it with the Cost of capital; here it is enough to know that a business creates value for its owners when ROIC exceeds what its capital costs.

Variants you will meet

• ROA on operating profit. Net income is after interest, so ROA computed on it falls when a business borrows, even if its assets are as productive as before. Some analysts use EBIT after tax over average total assets instead: Lantern’s 2027 figure is $24{,}590 \div 210{,}779.5 = 11.7\%$ against 10.6% on net income. The course uses net income, as the ratio engine does; say which you use.
• Return on average common equity. With preferred stock, net income less preferred dividends over common equity, as above.
• Annualised quarterly returns. A quarter’s net income times four over average equity; seasonal businesses distort it, as Lantern’s ten months show.
• Market-based returns. ROE uses book equity. A shareholder who paid more than book value earns less on the price paid: F00’s market-to-book ratio links the two.