Margin × turnover × leverage, and why ROE beats ROA

Why is ROE almost double ROA?

Tamarack’s ROA is 12.97 % and its ROE is 24.00 %. The same 480 of income sits on top of both; the gap is entirely the denominator. Assets of 3,700 were financed by only 2,000 of equity — the other 1,700 came from suppliers, accrued liabilities and the bank. The shareholders put up 54 % of the money and keep 100 % of the profit after interest. That is leverage, and the DuPont identity shows exactly how much of ROE it explains.

The DuPont decomposition

Multiply and divide ROE by revenue and by average assets, and it splits into three factors that each mean something:

$$\text{ROE}=\underset{\text{net margin}}{\underbrace{\frac{\text{NI}}{\text{Revenue}}}}\times \underset{\text{asset turnover}}{\underbrace{\frac{\text{Revenue}}{\text{Avg assets}}}}\times \underset{\text{leverage}}{\underbrace{\frac{\text{Avg assets}}{\text{Avg equity}}}}$$

For Tamarack 2025:

Net margin       480 ÷ 4,800   = 10.00 %
Asset turnover   4,800 ÷ 3,700 = 1.297
Leverage         3,700 ÷ 2,000 = 1.85

ROE = 0.1000 × 1.297 × 1.85   = 24.0 %  ✓

The first two factors multiply to ROA (0.1000 × 1.297 = 12.97 %). The third — the equity multiplier — is what turns 12.97 % into 24.0 %. When ROE changes between years, the decomposition tells you whether the company sold at better margins, worked its assets harder, or simply borrowed more.

The leverage ratios

Three ratios measure how much of the balance sheet the lenders own and how comfortably the company services them. This course computes debt-to-equity and the debt ratio on total liabilities (some analysts use interest-bearing debt only — state your definition when you use one):

$$\text{Debt-to-equity}=\frac{\text{Total liabilities}}{\text{Total equity}}=\frac{1,800}{2,200}=0.818$$

$$\text{Debt ratio}=\frac{\text{Total liabilities}}{\text{Total assets}}=\frac{1,800}{4,000}=45.0\%$$

$$\text{Times interest earned}=\frac{\text{EBIT}}{\text{Interest expense}}=\frac{720}{80}=9.0$$

These are point-in-time solvency measures, so they use closing balances, not averages — the lender wants to know what stands behind the loan today. Times interest earned uses EBIT, income before the interest it is covering; using net income would deduct the interest first and understate the cover.

Leverage cuts both ways

Leverage raises ROE only when the assets earn more than the borrowed money costs. Tamarack’s assets return 12.97 %; its 80 of interest on 1,800 of liabilities is about 4.4 % before tax and about 3.3 % after the 25 % tax shield. Every dollar borrowed at 4 % and invested at 13 % leaves the difference for the shareholders — that is the whole of the ROE-over-ROA gap.

Now run the same arithmetic in a bad year. Suppose a company has 4,000 of assets financed by 2,800 of liabilities and 1,200 of equity (debt-to-equity 2.33, debt ratio 70 %) and EBIT falls to 720 against interest of 200: times interest earned is 3.6, and a further 30 % fall in EBIT would leave it barely covering interest. If ROA drops below the cost of debt, leverage works in reverse — each borrowed dollar loses money for the shareholders, and ROE falls below ROA. Interest is fixed; the profit it is paid from is not. That asymmetry is why lenders write the covenants of lesson 9.4.