FAR · Financial reporting · 8 practice questions
DuPont ROE: Find the Margin, Turnover, or Leverage Driver
DuPont ROE equals net profit margin × asset turnover × equity multiplier. Below: a worked comparison isolates each changing factor to show which one drove the ROE increase.
Try one first
Hint
Break ROE into margin × turnover × equity multiplier, compute each component for both years, and compare how much each component's change contributes to the ROE difference.
Answer D. Compute the DuPont components. Year 1: margin = 70/1,000 = 7%, turnover = 1,000/500 = 2.0, equity multiplier = 500/300 ≈ 1.667 ⇒ ROE ≈ 0.07×2×1.667 = 23.33%. Year 2: margin = 88/1,100 = 8%, turnover = 2.0, equity multiplier = 550/220 = 2.5 ⇒ ROE = 0.08×2×2.5 = 40.00% (increase ≈ 16.67 percentage points). Using an average-based decomposition, the margin change accounts for only ≈4.17 pp, turnover 0 pp, and the equity multiplier ≈12.50 pp of the ROE rise, so higher financial leverage was the principal driver.
Why not A: This is tempting because margin rose from 7% to 8%, but that change explains only a small portion (about 4.17 percentage points using an average-based split) of the ≈16.67-point ROE increase, so it was not the main driver.
Why not B: This tempts because sales increased, but sales and assets rose proportionally (1,000→1,100 and 500→550), so asset turnover stayed at 2.0 and contributed essentially nothing to the ROE change.
Why not C: ROA did increase (14% → 16%), and ROE = ROA × equity multiplier makes this tempting, but the ROA gain was modest (≈2 percentage points) and cannot explain the much larger ROE increase, the substantial rise in the equity multiplier amplified ROE.
Worked example
Orion Co. reports these annual amounts. Year 1: sales $24,000; net income $1,200; average assets $12,000; average equity $6,000. Year 2: sales $24,000; net income $1,440; average assets $12,000; average equity $4,000. Which DuPont component primarily drove the ROE increase? Isolate each component's effect using Year 1 values for the other two.
| 1 | Net profit marginYear 1: $1,200 ÷ $24,000 = 5%; Year 2: $1,440 ÷ $24,000 = 6%; change: (6% ÷ 5%) - 1 | 5% to 6%; up 20% |
| 2 | Asset turnoverBoth years: $24,000 ÷ $12,000 | 2.0; unchanged |
| 3 | Equity multiplierYear 1: $12,000 ÷ $6,000 = 2.0; Year 2: $12,000 ÷ $4,000 = 3.0; change: (3.0 ÷ 2.0) - 1 | 2.0 to 3.0; up 50% |
| 4 | ROE in each yearYear 1: 5% × 2.0 × 2.0 = 20%; Year 2: 6% × 2.0 × 3.0 = 36% | 20% to 36%; up 16 percentage points |
| 5 | Isolated margin effect(6% - 5%) × 2.0 × 2.0 | +4 percentage points |
| 6 | Isolated leverage effect5% × 2.0 × (3.0 - 2.0) | +10 percentage points |
Higher financial leverage was the primary driver of the ROE increase from 20% to 36%. Margin improved, but turnover did not change.
Check: At Year 1 levels, leverage adds 10 ROE percentage points versus margin's 4, so leverage is the larger driver.
Key points
- Use the balance basis given: averages when specified, year-end amounts when explicitly required.
- Margin × turnover equals ROA; leverage can lift ROE even when ROA is flat or falling.
- Component changes multiply, so isolated effects do not necessarily add to the total ROE change.
How the exam traps you
- Sales increased, so asset turnover must have improved. Divide sales by assets. Proportional growth in both leaves turnover unchanged.
- Equity fell, so leverage must be the biggest driver. Calculate the equity multiplier and compare its percentage change with changes in margin and turnover.
- Opposite changes in margin and turnover cancel each other. Multiply the new components. Opposite changes do not automatically cancel.
Question 2
| Year 1 | Year 2 | |
|---|---|---|
| Sales | $1,000 | $1,200 |
| Net income | $60 | $84 |
| Total assets | $500 | $600 |
| Total equity | $300 | |
Hint
Compute margin, turnover, and leverage for each year, then model the effect of changing one component at a time (holding the others constant) to see which component moves ROE most.
Answer C. Compute DuPont components. Year 1: margin = 60/1,000 = 6%; turnover = 1,000/500 = 2.0; leverage = 500/300 ≈ 1.667 → ROE = 6% × 2.0 × 1.667 = 20%. Year 2: margin = 84/1,200 = 7%; turnover = 1,200/600 = 2.0; leverage = 600/280 ≈ 2.143 → ROE = 7% × 2.0 × 2.143 = 30%. Holding other components at Year‑1 levels, the margin change raises ROE by about 3.33 percentage points while the leverage change raises ROE by about 5.71 percentage points, so increased financial leverage is the single largest contributor.
Why not A: Tempting because margin rose from 6% to 7%, but that isolated change increases ROE by only ≈3.33 percentage points, less than the effect from the leverage change. The larger absolute ROE impact came from increased financial leverage.
Why not B: Asset turnover remained constant at 2.0 in both years (1,000/500 and 1,200/600), so turnover did not drive the ROE change.
Why not D: While both margin and leverage increased and thus both contributed, they did not contribute equally, the leverage increase had the larger numeric effect on ROE.
Question 3
Hint
Compute each company's ROA (net income ÷ total assets), then consider how assets are financed (assets relative to equity) when comparing ROE.
Answer A. Both companies have ROA = 10% (Company X: 50/500; Company Y: 100/1000). Company X's equity multiplier is 500/250 = 2.0, while Company Y's is 1000/900 ≈ 1.11, so Company X's ROE ≈ 20% versus Company Y's ≈ 11.1%. The higher ROE for Company X is therefore explained primarily by greater financial leverage.
Why not B: This is tempting because Company X has a higher profit margin (50/400 = 12.5% vs 100/2000 = 5%), but it is wrong because Company X actually has lower asset turnover (400/500 = 0.8 vs 2000/1000 = 2.0). The primary driver of X's higher ROE is higher leverage, not higher turnover.
Why not C: Candidates may focus on Y's higher asset turnover, but higher turnover alone doesn't guarantee higher ROA. Y's much lower profit margin offsets its turnover advantage so both firms end up with the same ROA (10%).
Why not D: This overstates certainty. Future ROE depends on profit margins and financing structure as well as turnover; Y's low equity multiplier and low margin mean higher sales/turnover today do not ensure higher ROE.
Question 4
Hint
Use the DuPont decomposition: ROE = (Net income/Sales) × (Sales/Assets) × (Assets/Equity). Compute each component for Year 1 and Year 2 and compare which changed most.
Answer C. Compute the DuPont components: profit margin = Net income/Sales = 400/5,000 = 8% (Year 1) and 480/6,000 = 8% (Year 2). Asset turnover = Sales/Assets = 5,000/8,000 = 0.625 (Year 1) and 6,000/9,600 = 0.625 (Year 2). Equity multiplier = Assets/Equity rose from 8,000/3,200 = 2.5 to 9,600/2,400 = 4.0; since margin and turnover were unchanged, the higher equity multiplier (increased financial leverage after issuing debt and repurchasing shares) is the primary driver of the higher ROE.
Why not A: This distractor lures candidates who notice higher sales, but asset turnover was identical both years (5,000/8,000 = 6,000/9,600 = 0.625), so improved asset efficiency did not explain the change.
Why not B: This is tempting because net income rose in absolute dollars, but profit margin stayed the same (400/5,000 = 480/6,000 = 8%), so an improved margin did not cause the ROE increase.
Why not D: Repurchases can boost ROE by reducing equity, but the stem specifies the repurchase was funded from newly issued long-term debt, which increased liabilities and the equity multiplier (leverage). Therefore the primary cause was increased financial leverage, not a cash-funded repurchase.
Question 5
Hint
Calculate profit margin, asset turnover, and equity multiplier for each year (DuPont components) and compare their absolute changes; the component with the largest positive change is the primary driver of the ROE increase.
Answer B. Compute the DuPont components. Year 1: PM = 100/2000 = 5%, AT = 2000/1000 = 2.0, EM = 1000/500 = 2.0 → ROE = 0.05*2*2 = 20%. Year 2: PM = 168/2400 = 7.0%, AT = 2400/1400 ≈ 1.714, EM = 1400/560 = 2.5 → ROE ≈ 0.07*1.714*2.5 = 30%. Holding AT and EM constant, the margin increase explains about +8 percentage points; the higher equity multiplier adds ≈+5 points; the drop in turnover subtracts ≈-2.9 points. Thus margin is the primary driver, with leverage secondary.
Why not A: Although the equity multiplier rose from 2.0 to 2.5 (which increases ROE), numerically the profit margin increase (from 5% to 7%) produces a larger absolute rise in ROE when other components are held constant, so leverage is not the primary driver.
Why not C: Asset turnover actually fell (from 2.0 to ≈1.714), so turnover did not drive ROE upward and in fact partially offset the gain, sales growth alone does not guarantee improved turnover.
Why not D: ROE depends on the product of margin, turnover, and leverage, not sales alone; here the components changed unequally, margin and leverage increased while turnover decreased, so contributions were not roughly equal.
Question 6
Hint
Compare which items actually changed between years (NI, sales, assets, equity). Check ROA = NI/Assets and ROE = NI/Equity to see which component moved.
Answer D. Net income and total assets are unchanged, so ROA = NI/Assets = 200/2,000 = 10% in both years. ROE rose because the equity denominator fell from $800 to $600 while NI stayed constant (200/800 = 25%; 200/600 ≈ 33.3%). The $200 increase in long-term debt with the reduced equity reflects higher financial leverage, which magnified ROE.
Why not A: This distractor tempts because better margins increase net income and can raise ROE. It fails here because the stem shows net income is unchanged between years, so operating margin did not improve and cannot explain the ROE increase.
Why not B: This distractor is plausible since higher asset turnover raises ROA and thus ROE via DuPont. It fails because sales and total assets are unchanged, so asset turnover (sales/assets) did not change and cannot be the cause.
Why not C: Accounting-policy changes can alter reported net income and thus ROE, which makes this superficially attractive. It is incorrect here because the stem explicitly reports net income is the same in both years, so an accounting change did not drive the observed ROE increase, the smaller equity base did.
Question 7
Hint
Compute ROE for each year using ROE = net profit margin × asset turnover × equity multiplier, then compare the two results; pay attention to which component actually changed.
Answer C. Use the DuPont identity: ROE = net profit margin × asset turnover × equity multiplier. Year 1: 8.0% × 1.0 × 2.0 = 16.0%. Year 2: 6.0% × 1.4 × 2.0 = 16.8%. With the equity multiplier unchanged, the rise in asset turnover more than offsets the lower margin, so ROE increases slightly to 16.8%.
Why not A: Tempting because candidates may assume the opposite effects cancel each other; this reasoning glosses over the multiplicative nature of DuPont. It fails because the actual multiplication yields 16.8% in Year 2, so the changes do not perfectly offset.
Why not B: Tempting because a lower net profit margin commonly reduces ROE; this option reflects the error of applying the new margin but ignoring the higher asset turnover. It fails because the correct Year 2 calculation is 6.0% × 1.4 × 2.0 = 16.8%, not 12.0% (12.0% would result from using the old turnover of 1.0).
Why not D: Tempting because higher asset turnover can substantially increase ROE and some may mistakenly leave the margin at 8.0%. It fails because the stem specifies the margin fell to 6.0% and the equity multiplier is unchanged; using the stated Year 2 figures yields 16.8%, not 22.4% (22.4% would result from keeping the 8.0% margin with turnover 1.4).
Question 8
Hint
Compare profit margin, asset turnover, and the equity multiplier (DuPont decomposition) between the two years to see which component movements explain the ROE change.
Answer D. ROE = Net income / Equity: Year 1 = 80/400 = 20.0%; Year 2 = 84/380 ≈ 22.1%. DuPont decomposition shows profit margin fell (80/1,000 = 8.00% → 84/1,100 ≈ 7.64%), asset turnover rose (1,000/800 = 1.25 → 1,100/850 ≈ 1.29), and the equity multiplier increased (800/400 = 2.00 → 850/380 ≈ 2.24). The combined effect of higher turnover and greater leverage more than offset the slight margin decline, producing the higher ROE.
Why not A: Tempting because net income rose, but ROE depends on net income relative to equity and on efficiency. Profit margin actually decreased while asset turnover and the equity multiplier increased, so the net‑income rise alone does not explain the ROE change.
Why not B: Plausible if one assumes improved profitability, but the data show profit margin fell (8.00% → about 7.64%). Margin did not drive the ROE increase.
Why not C: Attractive because equity fell (400 → 380), which raises leverage, but asset turnover also improved and profit margin declined. The ROE increase is due to the combined effect of higher turnover and higher leverage, not leverage alone.
Common questions
How do you calculate DuPont ROE?
Multiply net income ÷ sales, sales ÷ average total assets, and average total assets ÷ average equity. The factors cancel to net income ÷ average equity.
How do you identify the main driver of a change in ROE?
Calculate all three components for each year and compare their percentage changes. To isolate a driver's effect, change only that component and hold the other two at their starting values.
Can ROE increase while ROA decreases?
Yes. A large enough increase in the equity multiplier can more than offset a lower ROA.
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