Ratio Toolkit I: Profitability & DuPont

Phase 2 — Financial Statement Analysis & Quality of Earnings · Week 18 · ~20 hours (one immersive week)

You can already read the statements. You can hand-spread a 10-K and an Indian annual report, trace net income into retained earnings and the cash-flow statement, and navigate every note. The work now is to judge what you read, and the first family of judgments answers one question: is the engine any good?

The margin stack (gross, EBITDA, operating, net) answers that question one layer at a time. Most of the skill is knowing which costs live between the layers. ROA and ROE answer it against the money employed, once you carry the conventions professionals actually use. DuPont decomposition in its 3-step and 5-step forms turns a single ROE number into a readable story about how a business earns.

All of Phase 1 stands behind this, especially the multi-step P&L and the equity build, plus the full-filing capstone. Next week's survival and velocity ratios complete the toolkit, and the returns-on-capital work that follows fixes these deliberately blunt capital measures with proper ROIC. Every ratio here serves Question 2 of the five questions: is it a good business?

From this week your company-of-the-week teardown carries a standing ratio pass: margin stack plus DuPont on five years of numbers, every week, forever.

Learning objectives

By the end of the week you can:

1. Compute the four-layer margin stack (gross, EBITDA, operating (EBIT), and net margin) from either a US function-of-expense P&L or an Indian Schedule III nature-of-expense P&L, and name precisely which costs live between each pair of layers.
2. Explain what each margin layer isolates (product economics, the pre-capital-charge operating engine, full operating discipline, the all-in residual) and diagnose a business model from its margin signature alone.
3. Compute ROA and ROE with exact formulas and full convention discipline: average balances, parent-only numerator and denominator, preferred-dividend adjustment, and the ROA variants that neutralize financing.
4. Derive the 3-step DuPont identity algebraically (ROE = net margin × asset turnover × financial leverage) and decompose any company's ROE into its three levers.
5. Derive and run the 5-step DuPont (tax burden × interest burden × operating margin × asset turnover × leverage), and interpret each factor, including what a falling interest burden or an unusually high tax-burden factor is telling you.
6. Contrast a margin-led and a turnover-led route to the same ROE (Hindustan Unilever versus Walmart) and read strategy directly off the decomposition.
7. Use the leverage identity ROE = R + (R − i) × D/E to show exactly when debt inflates ROE, when it destroys it, and why two identical ROEs can carry very different risk.
8. State what profitability ratios cannot see (capital intensity, cash conversion, equity-base games, one-offs, cycle position) and name the module that supplies each missing lens.

Prerequisites & connections

Builds on. M1.02 (the multi-step income statement: the margin stack is that statement read as a ladder), M1.03 (the equity build, including non-controlling interest: ROE's denominator) and M1.05 (the three-statement linkage: you will pull D&A from the cash-flow statement when the P&L hides it). Then M1.07 (depreciation and amortization: the wedge between EBITDA and EBIT), M1.08 (leases: the EBITDA comparability trap returns here), M1.09 (NCI and SBC conventions) and M1.10 (filings navigation and non-GAAP policing: "adjusted EBITDA" games start in this week's territory).

Feeds forward. M2.02 gives the financial-leverage factor its full treatment (coverage, net debt, when leverage is survivable) and adds the velocity ratios that explain the turnover factor. M2.03 repairs the bluntest instruments here: total assets and total equity become NOPAT over invested capital, and ROIC replaces ROE as the master test of business quality. M2.04 asks whether the profits you measure here are backed by cash (CFO/NI). M2.05 disciplines every comparison you will be tempted to make this week (time-series, peers, common-size, segments). M2.06–2.08 weaponize the stack: a gross margin that rises while inventory balloons, or a net margin propped by "other income," are forensic tripwires, and M2.06 to 2.08 also handle the deliberately dishonest cases. In Phase 3, margins and ROE drive the multiples (P/B is a function of ROE; EV/EBITDA inherits every EBITDA trap you learn here). In Phase 4, persistent margins and returns become the numerical proof of moats.

Core teaching content

4.0 The question this module answers: and the one it defers

Every business is a machine that turns capital into sales and sales into profit. Profitability ratios measure the second conversion. Of each rupee or dollar of revenue, how much survives each layer of cost? That's a question about return on sales. But Question 2 of the spine, is this a good business, comes down in the end to return on capital. What does the machine earn on the money trapped inside it? You'll build both here, in their first, deliberately simple forms. Margins measure return on sales. ROA and ROE measure return on capital, and DuPont is the bridge that shows how one becomes the other.

Hold one caution from the start. ROA and ROE use total assets and shareholders' equity straight off the balance sheet. Those are accurate but blunt measures, and they count idle cash and acquired goodwill along with every accounting accident of history. ROIC sharpens them later. Learn the blunt tools first anyway. You'll use them within the first ten minutes of every teardown you ever run, because they need no adjustments.

4.6 What good looks like, by business type

Numbers first, then the rule that organizes them. All bands are analyst rules-of-thumb for healthy incumbents at mid-cycle. Calibrate to sub-segment, geography and cycle. Each band is a question generator, never a grade sheet:

The table teaches three lessons that last. First, margin is a strategy variable. Walmart's 2.9% net margin isn't "worse" than HUL's 16.6%. It's a different machine producing a comparable ROE. Ranking across industries by margin is a category error, while ranking within a peer set is analysis. Second, each archetype has its own way of failing. Margin-led models die by gross-margin erosion, turnover-led ones by velocity loss and leverage-led ones by the cost of debt, and the decomposition tells you which vital sign to monitor. Third, banks and NBFCs fall outside this toolkit entirely. Leverage of 8 to 12× is their business model and interest is their raw material. Their instruments are NIM, ROA above 1%, and regulatory capital, which you'll meet in Phase 5. Treat them as the standing exception. Next week's liquidity ratios will do the same.

Where do you find live benchmarks instead of memorized bands? Damodaran's data library (pages.stern.nyu.edu) publishes margins by sector and ROE by sector, updated each January. Pull the current tables. Don't trust any book's frozen numbers, this one's included.

4.8 The capability card: what each ratio sees and cannot see

You'll reuse this table in every teardown. It turns the week's mastery outcome, "explain what each ratio can and cannot see", into something you can check yourself against:

The toolkit's job, this week and forever, is to generate questions faster than the market does. On its own it never hands you a verdict.

Common mistakes & how experts think differently

1. Ranking companies by net margin across industries. The beginner sees Walmart's 2.9% and calls it a bad business; the expert sees a turnover-led machine compounding at 20%+ ROE for decades. Margin is a strategy variable. The only cross-industry profitability verdict that means anything is return on capital versus its cost, and even that has to wait for ROIC's cleaner measurement.
2. Ending balances in return ratios. Dividing a year's profit by the year-end balance sheet understates every fast grower and flatters every shrinking company. Use averages. State the convention once and apply it everywhere. Break the rule knowingly, and only when screening for the freshest deterioration.
3. Comparing gross margins across presentation regimes. A US retailer whose COGS excludes depreciation, a Schedule III filer whose COGS you must assemble from three lines, and an IFRS filer presenting by nature are not comparable off the face. Rebuild the stack to one convention before comparing anything (P2 drills this).
4. Treating EBITDA as cash flow. EBITDA ignores capex, working capital, interest, and tax, the four places cash actually goes. It's a comparison and covenant tool. The tooth-fairy question is the permanent antidote, and the cash-quality work later in this phase supplies the real cash measures.
5. Including other income in operating margin or EBITDA. Treasury income on a cash pile isn't the business model, and Indian "total income" presentation makes the slip easy. Compute operating layers off revenue from operations. Let the 5-step's top-down EBIT carry other income only when you know it's there.
6. Celebrating ROE without decomposing it. A 24% ROE at 3.2× leverage and thin coverage is a different animal from 24% at 1.4×. Faced with any ROE, the expert asks by reflex which lever produced it. Next come whether it's durable and whether it was chosen or forced. The three-factor multiplication takes twenty seconds, so there's no reason to skip it.
7. Mixing claimants. The usual slips are consolidated net income over parent equity, forgetting preferred dividends (US GAAP), and adjusting for preference dividends already inside finance costs (Ind AS). Match numerator and denominator to the same owners, every time.
8. Reading one year. A cyclical's peak-year 25% ROE, a margin held up by one year of slashed advertising, a tax-holiday net margin. All of them evaporate under a 5 to 10 year series. Experts default to the decade view (screener.in and stockanalysis.com make it a ten-second habit) and treat any single-year ratio as a hypothesis.
9. Forgetting that the leverage factor isn't all debt. Assets ÷ equity counts payables, deferred revenue and provisions. Those liabilities are free, and often a strength (HUL's supplier float). The expert mentally splits the leverage factor into financial debt and operating float before judging it, and next week formalizes the split.
10. Stopping at the ratio. The beginner computes ROE = 20.2% and writes it down. The expert writes the sentence it implies ("HUL converts brand-driven pricing power into a fully-funded 20% return without leverage; the number to watch is gross margin"), because a ratio that hasn't become a sentence about the business hasn't been analyzed yet.

Worked examples

WE1: Infosys: a high-ROE, low-leverage signature, with a cash-pile drag (India)

Figures illustrative, modeled on ~FY24/FY25 consolidated scale, pull the actual annual report (infosys.com or BSE/NSE): revenue ₹1,55,000 cr; net profit ₹26,000 cr; average total assets ₹1,32,000 cr; average equity ₹85,000 cr; cash and liquid investments ~₹40,000 cr earning ~₹2,500 cr after tax.

Step 1: the three factors. Net margin = 26,000 ÷ 1,55,000 = 16.8%. Asset turnover = 1,55,000 ÷ 1,32,000 = 1.17×. Financial leverage = 1,32,000 ÷ 85,000 = 1.55×.

Step 2: multiply and verify. 0.168 × 1.17 × 1.55 = 0.306 → ROE ≈ 30.6%. Direct check: 26,000 ÷ 85,000 = 30.6%. ROA = 26,000 ÷ 1,32,000 = 19.7%.

Step 3: read it. A 30% ROE at only 1.55× leverage is the quality signature. Infosys carries no borrowings to speak of, so the leverage factor is payables, unearned revenue and other operating liabilities, the free kind. And the reported numbers understate the engine, because roughly 30% of the balance sheet is treasury earning treasury returns. Strip it out crudely. Operating assets are 1,32,000 − 40,000 = 92,000 and operating profit is 26,000 − 2,500 = 23,500, so the operating return on operating assets is 23,500 ÷ 92,000 = 25.5%, against the blended 19.7% ROA. The business is better than its blended ratios. The cash pile is a capital-allocation question, not an operating one. That strip is a hand-sketch of what ROIC does properly with invested capital.

WE2: Apple: when ROE stops measuring the business (US)

Figures illustrative, modeled on ~FY24 scale, pull the 10-K from EDGAR: revenue $390bn; EBIT (top-down; net interest ≈ 0) $123.5bn; EBT $123.5bn; net income $94bn; average total assets $360bn; average equity $60bn.

Step 1: the five factors. Tax burden = 94 ÷ 123.5 = 0.761. Interest burden = 123.5 ÷ 123.5 = 1.00. Operating margin = 123.5 ÷ 390 = 31.7%. Turnover = 390 ÷ 360 = 1.08×. Leverage = 360 ÷ 60 = 6.0×.

Step 2: multiply. 0.761 × 1.00 × 0.317 × 1.08 × 6.0 ≈ 1.57 → ROE ≈ 157%. Direct: 94 ÷ 60 = 157%.

Step 3: read it, carefully. A 157% ROE doesn't mean Apple is seven times better than HUL. The 6× leverage factor isn't distress, since the interest burden is 1.00. It's a decade of buybacks that shrank book equity from ~$134bn (2017) toward ~$57bn while returning far more than earnings each year. Equity is a management-chosen residual. Apple chose to make it small, and ROE mechanically exploded. The elite parts are in the other factors: a 31.7% operating margin at 1.08× turnover, on hardware scale. When the denominator is a policy choice, ROE stops ranking businesses. This decomposition makes the case for ROIC better than any lecture could. Starbucks and Domino's are the limit case. Their equity is negative and their ROE undefined, yet the business is fine.

WE3: Meera Distribution vs Kanchan Speciality: same ROE, opposite fragilities (synthetic)

Two synthetic Indian companies, both ₹ cr, both ROE = 18%, both leverage 2.0×:

Stress 1, a price war that shaves 100bp off net margin. Meera: 1.0% × 4.5 × 2.0 = 9.0%, ROE halves. Kanchan: 11.0% × 0.75 × 2.0 = 16.5%, barely dented. Thin-margin, high-velocity models live one price war from mediocrity, so their moat must defend price.

Stress 2, both must add ₹500 cr of revenue. At constant turnover, Meera needs 500 ÷ 4.5 = ₹111 cr of new assets, ₹56 cr of it equity at 2× leverage. Kanchan needs 500 ÷ 0.75 = ₹667 cr of new assets, ₹333 cr of it equity. Kanchan's growth consumes six times the capital per rupee of new sales, so its moat must defend returns on large reinvestment.

Identical ROEs can hide opposite risk profiles and opposite growth economics. The headline won't tell you which stress test each must pass or what its moat must protect. The decomposition will. You'll hear "Same number, different machine: what breaks each?" in every case exam from here to Phase 8.

WE4: Rajhans Polymers: ROE rises while the business rots (synthetic, 5-step)

Synthetic Indian mid-cap, ₹ cr. Year 1: revenue 2,000; EBIT 300; interest 30; EBT 270; tax 81; NI 189; average assets 1,600; average equity 800. Year 3: revenue 2,400; EBIT 288; interest 96; EBT 192; tax 24 (a one-off MAT-credit year); NI 168; average assets 2,000; average equity 640 (a debt-funded buyback shrank it).

The direct checks give 189 ÷ 800 = 23.6% and 168 ÷ 640 = 26.25%. The headline says progress, with ROE up 2.6 points. The factors say decay. Operating margin is down 300bp, turnover is down, the creditors' toll on EBIT has tripled, and the "improvement" rests on a tax one-off plus a leverage jump. Reprice the tax burden at a normal 0.75 and Year 3 ROE is 0.75 × 0.667 × 0.12 × 1.2 × 3.125 = 22.5%. That's below Year 1, on triple the financing risk. The three-step would show margin down and leverage up. Only the five-step shows the interest and tax layers carrying the result. When the headline holds steady or rises while the engine weakens and financing grows, the forensic work on shenanigans treats it as a hunting ground.

WE5: Bharat Grid Utilities: a leverage-led ROE, read five ways (synthetic, India)

This is a synthetic Indian power-transmission utility (₹ cr), the leverage-led archetype from the 4.6 table, to set beside HUL's margin-led and Walmart's turnover-led machines. A regulated asset base throws off a fat operating margin but turns over slowly, and the balance sheet is deliberately debt-heavy. One year: revenue 24,000; EBIT (top-down) 6,000; interest 2,400; EBT 3,600; tax 900 (25%); net income 2,700; average total assets 60,000 (of which ₹45,000 cr is borrowing); average equity 15,000.

Step 1: the five factors. Tax burden = 2,700 ÷ 3,600 = 0.750. Interest burden = 3,600 ÷ 6,000 = 0.600. Operating margin = 6,000 ÷ 24,000 = 25.0%. Asset turnover = 24,000 ÷ 60,000 = 0.40×. Financial leverage = 60,000 ÷ 15,000 = 4.0×.

Step 2: multiply and verify. 0.750 × 0.600 × 0.250 × 0.40 × 4.0 = 0.180 → ROE = 18.0%. Direct: 2,700 ÷ 15,000 = 18.0%. As a self-check, the first three factors collapse to net margin, and 0.750 × 0.600 × 0.250 = 0.1125 = 2,700 ÷ 24,000.

Step 3: cross-check with the leverage identity. NOPAT = EBIT × (1 − 0.25) = 4,500, so the after-tax operating return on assets R = 4,500 ÷ 60,000 = 7.5%. The after-tax cost of debt is i = 2,400 × 0.75 ÷ 45,000 = 4.0%, and D/E = 45,000 ÷ 15,000 = 3.0. Then ROE = R + (R − i) × D/E = 7.5 + (7.5 − 4.0) × 3.0 = 7.5 + 10.5 = 18.0%. It's the same number, reached by a completely independent road (the identity from 4.7).

Step 4: read it. Don't be seduced by the 25% operating margin. At 0.40× turnover the after-tax engine returns just 7.5% on assets, and plain ROA is a mere 4.5% (2,700 ÷ 60,000). The 18% ROE is manufactured almost entirely by the 4.0× leverage. Three of every four rupees of assets are borrowed, and creditors already intercept 40 paise of every operating rupee (interest burden 0.600). That isn't distress. It's the regulated-utility model working as designed, and it's fine for as long as the allowed return holds and coverage stays comfortable. Whether it does is a survival question for next week, and no profitability ratio can answer it. So the vital sign here is neither gross margin (HUL) nor turns (Walmart). It's the cost and availability of debt. A 200bp rise in refinancing rates would do more damage to this ROE than almost any operating slip. Same three-factor arithmetic, a third kind of machine.

WE6: Summit Toolworks vs Cascade Machine: why plain ROA misleads (synthetic, US)

Two synthetic US machine-tool makers with the identical operating business (revenue $2,000m, EBIT $300m, average total assets $2,000m, tax 25%) financed differently. Summit Toolworks is all-equity, and Cascade Machine carries $800m of debt at 6%. Watch what each return measure says about two firms that are, at the operating level, twins.

Step 1: the plain-ROA lie. Plain ROA rates Summit (11.25%) a better asset user than Cascade (9.45%), yet the two run the same assets to the same $300m of EBIT. The gap is pure capital structure. Plain ROA puts an after-interest profit over assets that debt helped finance, so it docks Cascade for borrowing. That's the inconsistency behind convention 4 in 4.3.

Step 2: repair it two ways. Add back Cascade's after-tax interest: (189 + 48 × 0.75) ÷ 2,000 = (189 + 36) ÷ 2,000 = 11.25%, now equal to Summit. Or ignore financing and tax altogether: operating ROA = 300 ÷ 2,000 = 15.0% for both. The twins are revealed as twins.

Step 3: read the ROE, and the spread. ROE is supposed to reflect financing, and it does. Cascade's 15.75% beats Summit's 11.25% because the borrowed $800m works at an after-tax operating return of 11.25% while costing only 4.5% after tax. That 6.75-point spread lands on a thinner equity base. The leverage identity confirms it: 11.25 + (11.25 − 4.5) × (800 ÷ 1,200) = 15.75%. So use plain ROA only for one company's own time series. To rank two companies with different debt, use adjusted or operating ROA. And the distance between a firm's adjusted ROA and its ROE is its leverage story, told at a glance.

Practice set

All companies are synthetic unless named, and figures are in ₹ cr unless stated. P1 to P3 are guided and P4 to P8 independent. P9 to P12 are timed. Each problem is followed straight away by its full solution. Work it first, then check. Use a 25% tax rate and 365-day year unless stated.

P1 (guided). The stack from a US-style P&L. Bluegrass Beverages ($m): revenue 2,400; cost of sales 1,392 (includes $60m of depreciation); SG&A 480 (includes $36m of amortization); R&D 72; interest expense 36; other income 12; tax rate 25%. Compute the gross, EBITDA, operating (EBIT), and net margins; then compute top-down EBIT and reconcile it to operating EBIT.

Solution. Gross profit = 2,400 − 1,392 = 1,008 → gross margin = 42.0%. Operating EBIT = 1,008 − 480 − 72 = 456 → operating margin = 19.0%. Total D&A = 60 + 36 = 96. It's embedded in COGS and SG&A, so on a real 10-K you'd pull it from the cash-flow statement. EBITDA = 456 + 96 = 552 → EBITDA margin = 23.0%. PBT = 456 + 12 − 36 = 432, tax = 108 and NI = 324 → net margin = 13.5%. Top-down EBIT = PBT + interest = 432 + 36 = 468 = operating EBIT 456 + other income 12. The reconciliation is the other-income line. State which EBIT you are using, always.

P2 (guided). The stack from a Schedule III P&L. Saraswati Foods (Ind AS): revenue from operations 3,000; other income 40; cost of materials consumed 1,260; purchases of stock-in-trade 300; changes in inventories of FG/WIP/stock-in-trade (60), i.e. shown as a negative because inventory rose; employee benefits 330; finance costs 45; depreciation & amortisation 105; other expenses 660. Tax 25%. Build COGS, then gross, EBITDA, EBIT, and PAT margins. Then show what happens to the EBITDA margin if you carelessly include other income.

Solution. COGS = 1,260 + 300 − 60 = 1,500 (the inventory build removes 60 of cost from this year's charge). Gross = 3,000 − 1,500 = 1,500 → gross margin = 50.0%. EBITDA = 3,000 − 1,500 − 330 − 660 = 510 → 17.0%. That's the Schedule III gift: D&A and finance costs are on the face, so EBITDA is direct. EBIT = 510 − 105 = 405 → 13.5%. PBT = 405 + 40 − 45 = 400. Tax is 100, so PAT = 300 → net margin = 10.0%. The careless version gives (510 + 40) ÷ 3,000 = 18.3%, so other income flatters the EBITDA margin by 130bp. Treasury income isn't operations. Compute operating layers off revenue from operations only.

P3 (guided). ROA and ROE with full convention discipline. Tern Logistics (consolidated, US GAAP): net income 180, of which 12 is attributable to non-controlling interests; preferred dividends paid 8. Equity attributable to parent: opening 1,050, closing 1,170. NCI: opening 100, closing 120. Total assets: opening 2,300, closing 2,700. Compute ROA, common ROE done correctly, and the sloppy ROE (consolidated NI ÷ average total equity), and state the size of the error.

Solution. Average assets = (2,300 + 2,700) ÷ 2 = 2,500 → ROA = 180 ÷ 2,500 = 7.2% (consolidated profit over consolidated assets, consistent). Correct common ROE: numerator = 180 − 12 (minority's profit) − 8 (preferred claim) = 160; denominator = average parent equity = (1,050 + 1,170) ÷ 2 = 1,110 → ROE = 160 ÷ 1,110 = 14.4%. The sloppy version is 180 ÷ [(1,150 + 1,290) ÷ 2] = 180 ÷ 1,220 = 14.75%. That's 35bp off here, but the error scales with NCI weight and preferred size, and for an NCI-heavy consolidator it can run to whole points. Match claimants, every time.

P4. Which lever moved? Verma Ceramics: Year 1, revenue 1,500, NI 120, average assets 1,000, average equity 500. Year 2, revenue 1,800, NI 126, average assets 1,000, average equity 450 (a buyback). Run the 3-step both years, attribute the ROE change to its levers (change one factor at a time, in order: margin, then turnover, then leverage), and write the two-sentence diagnosis.

Solution. Year 1: margin 120 ÷ 1,500 = 8.0%, turnover 1.5×, leverage 2.0× → ROE = 0.08 × 1.5 × 2.0 = 24.0% (check: 120 ÷ 500). Year 2: margin 126 ÷ 1,800 = 7.0%, turnover 1.8×, leverage 1,000 ÷ 450 = 2.22× → ROE = 0.07 × 1.8 × 2.222 = 28.0% (check: 126 ÷ 450). Now attribute the change, one lever at a time from Year 1's 24.0%. Moving margin from 8 to 7% alone gives 0.07 × 1.5 × 2.0 = 21.0% (−3.0 pts). Moving turnover from 1.5 to 1.8 next gives 0.07 × 1.8 × 2.0 = 25.2% (+4.2 pts). Moving leverage from 2.0 to 2.22 last gives 28.0% (+2.8 pts). Diagnosis: the company bought velocity with price, since margin fell 100bp while turnover jumped, and a buyback added leverage. ROE rose 4 points, but two-thirds of the operating gain came from a lever competitors can match tomorrow (price), and the rest from the balance sheet. Watch whether the volume holds when a peer matches the price cut.

P5. The 5-step, end to end. Halcyon Tools: revenue 5,000; EBIT (top-down) 750; interest 150; tax 150; average assets 4,000; average equity 1,600. Compute all five factors and ROE; verify directly.

Solution. EBT = 750 − 150 = 600; NI = 600 − 150 = 450. Tax burden = 450 ÷ 600 = 0.75; interest burden = 600 ÷ 750 = 0.80; operating margin = 750 ÷ 5,000 = 15.0%; turnover = 5,000 ÷ 4,000 = 1.25×; leverage = 4,000 ÷ 1,600 = 2.5×. ROE = 0.75 × 0.80 × 0.15 × 1.25 × 2.5 = 28.1%. Direct: 450 ÷ 1,600 = 28.125%, which matches. Reading it, you see a healthy engine (15% operating margin) with a fifth of EBIT going to creditors, so check coverage before you admire the 28%.

P6. Three roads to 24%. Three companies each report ROE = 24%. A: margin 3%, turnover 4.0×, leverage 2.0×. B: margin 16%, turnover 0.5×, leverage 3.0×. C: margin 8%, turnover 1.0×, leverage 3.0×, and its interest burden is 0.70. Classify each route, name the most plausible business model for each, and state which stress test each must pass before its 24% deserves respect.

Solution. Verify first. A is 0.03 × 4 × 2 = 24%, B is 0.16 × 0.5 × 3 = 24% and C is 0.08 × 1 × 3 = 24%. A, turnover-led (distribution, food retail): the test is margin durability. At 4× turns, a 150bp margin hit takes ROE to 0.015 × 4 × 2 = 12%, so half of it is gone. Its moat must defend price (cost advantage). B, margin-led, leverage-assisted (hotels, branded real assets, luxury with property): the tests are (i) what happens to the 16% margin in a downcycle and (ii) growth economics, because at 0.5× turns every rupee of new revenue needs ₹2 of assets. C, leverage-led with a mediocre engine: an 8% margin at 1× turns is an ordinary business. Creditors already intercept 30% of EBIT (burden 0.70), so the 24% is mostly borrowed. On its face C is the most fragile. Its ROE depends on credit conditions it doesn't control, and it has to pass coverage tests before the number means anything. In general, though, the decomposition doesn't rank the three. It tells you which question to ask each.

P7. The leverage identity. A company earns an after-tax operating return on assets R = 10%; its after-tax cost of debt is i = 6%. (a) Compute ROE at D/E of 0, 1.0, and 2.0. (b) Recompute all three if a downturn cuts R to 4%. (c) State the exact R at which leverage stops helping.

Solution. ROE = R + (R − i) × D/E. (a) D/E 0: 10%; D/E 1: 10 + 4 = 14%; D/E 2: 10 + 8 = 18%. (b) With R = 4%, the spread is 4 − 6 = −2: D/E 0: 4%; D/E 1: 4 − 2 = 2%; D/E 2: 4 − 4 = 0%. The levered company's shareholders earn nothing in a year the unlevered twin earns 4%. (c) Leverage is neutral at R = i = 6%. Above that, every unit of D/E adds the spread, and below it, every unit subtracts. The multiplier is symmetric. The consequences aren't, because enough bad years in a row is death.

P8. The lease border, at the margin layer. Two identical apparel retailers. Retailer P (US GAAP, store leases as operating rent): revenue 1,000; cost of sales ex-D&A 550; rent 95; other opex 210; owned-asset D&A 30; no debt. Retailer Q (Ind AS 116): same economics, so revenue 1,000; cost of sales ex-D&A 550; other opex 210; D&A 100 (30 owned + 70 right-of-use); lease interest 25. Compute each one's EBITDA margin, EBIT margin, PBT, and net margin (tax 25%); then repair the comparison with EBITDAR and state the size of the accounting mirage.

Solution. P: EBITDA = 1,000 − 550 − 95 − 210 = 145 (14.5%); EBIT = 145 − 30 = 115 (11.5%); PBT = 115; NI = 86.25 → net margin 8.6%. Q: EBITDA = 1,000 − 550 − 210 = 240 (24.0%; no rent line exists); EBIT = 240 − 100 = 140 (14.0%); PBT = 140 − 25 = 115; NI = 86.25 → net margin 8.6%. These are identical companies. Net margins agree, because economics survive at the bottom, but EBITDA margins differ by 950bp and EBIT margins by 250bp. That's pure P&L geography. To repair it, EBITDAR_P = 145 + 95 = 240 = Q's reported EBITDA. Or subtract Q's full lease cost (70 + 25 = 95) to get 145 = P. The rule: at any layer above PBT, never compare a rent-expensing reporter with a lease-capitalizing one without the repair. Next week extends the same fix to the leverage and coverage ratios.

P9 (timed, 10 min). Flat headline, moving parts. Three years of Nalanda Wires: revenue 8,000 → 8,800 → 9,680; NI 640 → 616 → 581; average assets 5,000 → 5,867 → 6,914; average equity 3,125 → 3,009 → 2,834. Run the 3-step for each year and write the three-sentence diagnosis.

Solution. Year 1: margin 8.0%, turnover 1.60×, leverage 1.60× → ROE = 20.5% (640 ÷ 3,125). Year 2: margin 7.0%, turnover 1.50×, leverage 1.95× → ROE = 20.5% (616 ÷ 3,009). Year 3: margin 6.0%, turnover 1.40×, leverage 2.44× → ROE = 20.5% (581 ÷ 2,834). Diagnosis: headline ROE is perfectly flat, and everything under it is deteriorating. Margin is down 200bp and turnover down 0.2 turns, and leverage rising from 1.6× to 2.4× plugs the whole gap. Revenue grows 10% a year while profit falls, so growth is being bought. Of all the patterns DuPont catches, this one matters most. A stable ROE doesn't mean a stable business. Decompose or be deceived.

P10 (timed, 10 min). The buyback illusion. Juhi Consumer Products: all-equity, negligible non-equity liabilities, so average assets = average equity = 1,667; NI 300. It borrows 700 at 7% pre-tax (tax 25%) and buys back 700 of stock; assets are unchanged. Compute ROE before and after, decompose what changed, verify with the leverage identity, and state what happens if NOPAT falls to 66.7 (R = 4%).

Solution. Before: ROE = 300 ÷ 1,667 = 18.0%; leverage 1.0×. After: interest = 49, after-tax cost = 36.75 → NI = 263.25 ≈ 263; equity = 1,667 − 700 = 967 → ROE = 263 ÷ 967 = 27.2%; leverage = 1,667 ÷ 967 = 1.72×; ROA falls to 263 ÷ 1,667 = 15.8%. Identity check: R = 300 ÷ 1,667 = 18%; i = 7% × 0.75 = 5.25%; D/E = 700 ÷ 967 = 0.724 → ROE = 18 + (18 − 5.25) × 0.724 = 18 + 9.2 = 27.2%, which matches. That's nine points of "improvement" with zero change in the engine. It's a purely financial rearrangement, and to be fair a rational one while R ≫ i. Now the downside. With NOPAT at 66.7, EBIT = 88.9, EBT = 88.9 − 49 = 39.9 and NI = 29.9, so ROE = 29.9 ÷ 967 = 3.1%, against 4.0% unlevered. The spread flipped, and the same lever now subtracts. Never compare ROEs across a buyback without decomposing.

P11 (timed, 5 min). Match the signature. Four stacks: (i) gross 62%, EBITDA 24%, net 16%, turnover 0.9×, leverage 1.4×. (ii) gross 14%, EBITDA 6.5%, net 2.4%, turnover 3.8×, leverage 2.2×. (iii) gross 30%, EBITDA 25%, net 16%, turnover 1.15×, leverage 1.3×, large cash balance. (iv) gross 45%, EBITDA 38%, net 8%, turnover 0.3×, leverage 3.5×. Models: grocery retail; IT services; regulated utility; branded FMCG. Match and justify in one line each.

Solution. (i) FMCG: a fat gross margin (brands price far above input cost) and a short road below it; modest turns, no real debt. (ii) grocery retail: thin at every layer, alive only through 3.8× velocity and supplier credit in the leverage factor. (iii) IT services: almost no gross-to-EBITDA drop (delivery salaries are the "COGS" and there's little else), low leverage, and the cash pile marks the sector's habit. (iv) regulated utility: a huge EBITDA margin collapsing to 8% net as depreciation and interest (0.3× turns, 3.5× leverage) consume the middle. The leverage is there by regulatory design. The giveaway is never one number. It's where the stack narrows.

P12 (timed, 5 min). The screener's 45%. A screener flags "ROE 45%" and a colleague wants to buy. List the three checks you run before the number is allowed to mean anything, each with the specific computation, and name the metric that ultimately settles business quality.

Solution. (1) Decompose the leverage factor and the equity base: assets ÷ equity, and the 5-year history of equity, because buybacks or write-offs shrinking the denominator manufacture ROE (the Apple pattern, and at the limit negative equity breaks it entirely). (2) Interrogate the numerator with the 5-step: tax burden versus the normal ~0.75, interest burden trend, and a scan for one-off gains or other income inside NI. A 0.92 tax burden or a disposal gain is borrowed glory. (3) Test persistence and cash: the 5–10 year ROE series (one great year means nothing) and CFO ÷ NI to confirm the profits are cash-backed. The settling metric is ROIC versus the cost of capital on properly measured invested capital, because total-assets-and-equity ratios can always be dressed up. Invested capital is much harder to hide from.

P13 (guided). The 5-step, built from a Schedule III P&L. Ganga Cements (synthetic, Ind AS, ₹ cr): revenue from operations 6,000; other income 120; cost of materials consumed 2,400; purchases of stock-in-trade 600; changes in inventories of FG/WIP/stock-in-trade (120), negative because inventory rose; employee benefits 900; finance costs 300; depreciation & amortisation 480; other expenses 780. Tax 25%; average assets 4,800; average equity 2,000. Assemble COGS, both EBIT constructions, then run the full 5-step DuPont and verify.

Solution. COGS = 2,400 + 600 − 120 = 2,880 (the inventory build removes 120 of cost from this year's charge, the same sign trap as P2). Gross = 6,000 − 2,880 = 3,120 → gross margin 52.0%. EBITDA (off revenue from operations, other income excluded) = 6,000 − 2,880 − 900 − 780 = 1,440; operating EBIT = 1,440 − 480 = 960 → operating margin 16.0%. PBT = 960 + 120 − 300 = 780; tax = 195; net income = 585. Top-down EBIT = PBT + finance costs = 780 + 300 = 1,080 = operating EBIT 960 + other income 120. Use this for the 5-step so the identity closes. Factors: tax burden = 585 ÷ 780 = 0.750; interest burden = 780 ÷ 1,080 = 0.722; operating margin (top-down) = 1,080 ÷ 6,000 = 18.0%; turnover = 6,000 ÷ 4,800 = 1.25×; leverage = 4,800 ÷ 2,000 = 2.40×. Product = 0.750 × 0.722 × 0.180 × 1.25 × 2.40 = 29.25%, and the direct 585 ÷ 2,000 = 29.25% matches. Here's the wrinkle from 4.5. The top-down operating margin of 18.0% is flattered by other income, since the true operating engine is 16.0%. Always state which EBIT you decomposed.

P14 (guided). Three ROAs for one company. Ridgeline Instruments (synthetic, US $m): revenue 1,600; EBIT 240; interest expense 40; tax 25%; average total assets 1,600. Compute plain, adjusted, and operating ROA; rank them and state which you would use to compare Ridgeline against a debt-free peer.

Solution. EBT = 240 − 40 = 200; tax = 50; net income = 150. Plain ROA = 150 ÷ 1,600 = 9.375%. Adjusted ROA = (150 + 40 × 0.75) ÷ 1,600 = (150 + 30) ÷ 1,600 = 11.25%. Operating ROA = 240 ÷ 1,600 = 15.0%. They rise as financing is stripped from the numerator. Plain ROA is contaminated by after-interest profit. Adjusted ROA adds back the after-tax cost of debt (the CFA convention), and operating ROA removes tax too. To compare with a debt-free peer, use adjusted or operating ROA. Plain ROA would penalize Ridgeline for a capital-structure choice that has nothing to do with operations.

P15. Margin is marketing; margin × turnover is the business. Two synthetic Indian companies, ₹ cr. Nilgiri Estates: operating margin 30%, asset turnover 0.25×. Konkan Distributors: operating margin 5%, asset turnover 3.0×. The pre-tax hurdle on assets is 12%. (a) Compute each firm's operating return on assets. (b) Which is the better business, and by how much against the hurdle? (c) State the one-sentence lesson.

Solution. (a) Operating ROA = operating margin × turnover: Nilgiri 0.30 × 0.25 = 7.5%; Konkan 0.05 × 3.0 = 15.0%. (b) Konkan. The 5%-margin distributor returns 15% pre-tax on assets and clears the 12% hurdle by 3 points, while the 30%-margin "premium" business returns only 7.5% and destroys value as it grows (4.5 points below the hurdle). (c) A margin is a fact about one sale. Only margin × turnover (ROA, and in the end ROIC versus the hurdle) is a fact about the business, so never admire a fat margin until you know the turnover it's multiplied by.

P16. Two routes to a ~30% ROE, five factors each. Compute the full 5-step for both and name the route. Ashirwad Brands (synthetic, India ₹ cr): revenue 10,000; EBIT (top-down) 2,000; interest 40; tax 25%; average assets 8,000; average equity 5,000. Summit Stores (synthetic, US $m): revenue 20,000; EBIT (top-down) 800; interest 120; tax 25%; average assets 5,000; average equity 1,700.

Solution. Ashirwad: EBT = 1,960; net income = 1,470. Tax burden 0.750; interest burden 1,960 ÷ 2,000 = 0.980; operating margin 20.0%; turnover 1.25×; leverage 1.60×. Product = 0.750 × 0.980 × 0.20 × 1.25 × 1.60 = 29.4% (direct 1,470 ÷ 5,000 agrees). Summit Stores: EBT = 680; net income = 510. Tax burden 0.750; interest burden 680 ÷ 800 = 0.850; operating margin 4.0%; turnover 4.0×; leverage ≈ 2.94×. Product = 0.750 × 0.850 × 0.04 × 4.0 × 2.941 = 30.0% (direct 510 ÷ 1,700 agrees). Ashirwad is margin-led, a 20% operating engine on a slow, barely levered balance sheet (the HUL road). Summit is turnover-led, a 4% engine forced through 4.0× turns with supplier-and-lease leverage (the Walmart road). Nearly the same ROE, opposite machines. Ashirwad's vital sign is operating margin. Summit's is turns and comparable-store sales.

P17. Reprice the tax one-off. Vidarbha Agro (synthetic, ₹ cr): reported year, net income 460; EBT 500; EBIT (top-down) 800; revenue 4,000; average assets 3,200; average equity 1,600. (a) Run the 5-step and read the interest burden. (b) A colleague capitalizes the ROE as "quality." Reprice the tax burden to a normal 0.75 and restate ROE. (c) Give your one-line verdict.

Solution. (a) Tax burden = 460 ÷ 500 = 0.920; interest burden = 500 ÷ 800 = 0.625; operating margin = 800 ÷ 4,000 = 20.0%; turnover 1.25×; leverage 2.0×. Product = 0.920 × 0.625 × 0.20 × 1.25 × 2.0 = 28.75% (direct 460 ÷ 1,600 agrees). The interest burden of 0.625 means creditors already take 37.5% of EBIT. (b) A 0.92 tax burden is a ~8% effective rate. That points to a credit, a holiday or a reversal, and none of those is a norm. At a normal 0.75 the ROE is 0.75 × 0.625 × 0.20 × 1.25 × 2.0 = 23.4%. (c) Roughly 5 points of the headline 28.75% is borrowed tax glory, and it rests on a heavily levered engine. Normalize the tax, cross-examine coverage, and confirm the profit is cash-backed before you let the word "quality" anywhere near it.

P18 (timed, 12 min, stretch). One company, top to bottom. Beltline Logistics (synthetic, US $m): revenue 5,000; cost of sales 3,500 and other operating expenses 700, both stated before depreciation; depreciation (from the cash-flow statement) 300; interest expense 100; no other income; tax 25%; average assets 4,000; average equity 1,600. In ten minutes compute (a) the full margin stack (gross, EBITDA, operating, net); (b) plain, adjusted, and operating ROA; (c) ROE; (d) the 3-step and 5-step DuPont, each verified against direct ROE; (e) a one-line diagnosis.

Solution. (a) Gross = 5,000 − 3,500 = 1,500 → 30.0%. EBITDA = 5,000 − 3,500 − 700 = 800 → 16.0%. Operating EBIT = 800 − 300 = 500 → 10.0%. EBT = 500 − 100 = 400; tax = 100; net income = 300 → net margin 6.0%. (b) Plain ROA = 300 ÷ 4,000 = 7.5%; adjusted = (300 + 100 × 0.75) ÷ 4,000 = 375 ÷ 4,000 = 9.375%; operating = 500 ÷ 4,000 = 12.5%. (c) ROE = 300 ÷ 1,600 = 18.75%. (d) 3-step: 0.06 × 1.25 × 2.5 = 18.75%, matching. 5-step: tax burden 300 ÷ 400 = 0.750, interest burden 400 ÷ 500 = 0.800, operating margin 10.0%, turnover 1.25×, leverage 2.5× → 0.750 × 0.800 × 0.10 × 1.25 × 2.5 = 18.75%, matching again. Top-down EBIT = 400 + 100 = 500 = operating EBIT, because there's no other income. (e) A middling logistics engine (30% gross, 10% operating) carried to a respectable 18.75% ROE by 1.25× turns and 2.5× leverage. The interest burden of 0.80 shows a fifth of EBIT going to creditors, so check coverage before calling the number safe. Scoring: five parts correct in 12 minutes means you're fluent. The usual failures are double-counting the 300 of depreciation in the stack and forgetting the after-tax interest add-back in adjusted ROA.

P19. PRAT, and the lever that moves in an afternoon. Konark Fasteners (synthetic, India, ₹ cr) reports a net margin of 9.0%, an asset turnover of 1.20×, financial leverage of 1.75×, and a dividend payout ratio of 45%. (a) Compute ROE and the sustainable growth rate from the PRAT factors. (b) Chinese import competition takes the net margin to 7.5% with turnover and leverage unchanged; recompute both. (c) The board wants the original sustainable growth rate back without adding debt or issuing shares. What payout ratio does that require, and what is the objection to doing it?

Solution. (a) Retention = 1 − 0.45 = 0.55. ROE = 0.09 × 1.20 × 1.75 = 18.90%; sustainable growth = 0.55 × 0.1890 = 10.40% (10.395% before rounding). (b) ROE = 0.075 × 1.20 × 1.75 = 15.75%; sustainable growth = 0.55 × 0.1575 = 8.66%, so 1.73 points of fundable growth vanished with 1.5 points of margin. (c) Solve b × 0.1575 = 0.10395 → b = 0.660, a payout of 34%. The arithmetic works. The economics may not. The payout cut buys growth out of the shareholders' pocket at a return of 15.75%, and that's worth doing only if the incremental capital actually earns it. So answer the ROIIC question first, the one the returns-on-capital work sets up. Cutting the dividend to fund reinvestment into a shrinking-margin business is how a value trap is financed.

Applied mini-project

Two roads to ROE: HUL and Walmart, from the actual filings.

You've seen both companies through illustrative numbers. Now do it for real and find out where reality complicates the clean version.

Pull two documents. (1) Hindustan Unilever's latest annual report, from the investor-relations section of hul.co.in, or the BSE/NSE filings portal. You need the standalone P&L (or consolidated, as long as you state which and stay consistent), the balance sheet, and the tax and finance-cost notes. (2) Walmart's latest 10-K from SEC EDGAR (sec.gov → company search "Walmart" → 10-K). You need the income statement, the balance sheet and the cash-flow statement (for D&A). Take three fiscal years of each. Each filing carries one comparative year, so pull one prior filing for the third.

Build (a spreadsheet, one tab per company):

1. The full margin stack, each year: gross (assemble HUL's COGS from the three Schedule III lines; note what Walmart's cost-of-sales definition includes), EBITDA (HUL: off the face, excluding other income; Walmart: EBIT + D&A from the CFS), operating EBIT, and net margin. Present both bottom-up operating EBIT and top-down EBIT = PBT + finance costs, and reconcile.
2. ROA and ROE on average balances, parent-only discipline throughout.
3. The 3-step DuPont, each year, both companies, then a one-row summary: who is margin-led, who is turnover-led, and by how much.
4. The 5-step DuPont for the latest year, both companies. Compare your tax-burden and interest-burden factors against the illustrative ones above and explain any gap (tax-rate changes, other income, NCI).
5. A sensitivity line: for each company, recompute ROE if net margin fell 100bp: who suffers more, and why (WE3 logic on real numbers)?
6. Memo (one page): tell the two routes to ROE as strategy. Say which factor moved most over your three years and what management action explains it, and name the one number you would monitor quarterly for each company. Then point to one place where the real filing surprised you against the illustrative figures. There will be one.

Rubric (self-score honestly; 0 = missing/wrong, 1 = partial, 2 = correct and defended):

Pass: ≥ 9/12, with no zero on any criterion. Keep the spreadsheet. The margin-stack and DuPont tabs become the standing "ratio pass" of your weekly company teardown from this week on, and when you reach benchmarking, this workbook grows into your benchmarking template.

Case Lab: run case CL-2.1 (The Flat-ROE Trap) in the app's Cases tab for this module: a five-year series whose headline ROE barely moves while margin, turnover, leverage, and the tax and interest burdens shift underneath; you decompose it interactively, catch what the headline hides, and write the one-number-to-monitor memo.

Reading & resources

Core texts (in the order to reach for them):

• Benjamin Graham & Spencer Meredith, The Interpretation of Financial Statements: the ratio entries in Part II, sixty pages of definitional clarity. [Paid] [Beginner]
• Pat Dorsey, The Five Rules for Successful Stock Investing, Ch. 5 ("Financial Statements Explained") and Ch. 6 ("Analyzing a Company — The Basics"): profitability and ROE analysis as a practitioner runs it, including a DuPont walkthrough. [Paid] [Beginner]
• Warren Buffett, "How Inflation Swindles the Equity Investor," Fortune, May 1977 (free online). The five ways to raise ROE: higher turnover, cheaper leverage, more leverage, lower taxes, wider margins. The 5-step DuPont written as an essay, by its best user. Read it this week. [Free] [Intermediate]
• K. R. Subramanyam, Financial Statement Analysis (11th ed.), Ch. 8, "Return on Invested Capital and Profitability Analysis": the full academic treatment of everything here, plus the bridge toward M2.03. [Paid] [Intermediate]
• Stephen Penman, Financial Statement Analysis and Security Valuation (5th ed.), the profitability-analysis chapters (Ch. 11–12): reformulation done properly; hard, and worth it after this week, not before. [Paid] [Advanced]
• White, Sondhi & Fried, The Analysis and Use of Financial Statements (3rd ed.), Ch. 4, "Foundations of Ratio and Financial Analysis." [Paid] [Advanced]
• CFA Institute, Level I reading "Financial Analysis Techniques": the standard-setter's conventions for every ratio in this week's work, including the adjusted-ROA variant. [Paid] [Intermediate]

Free courses & videos:

• Aswath Damodaran's free "Accounting 101" sessions on ratio analysis and profitability (YouTube playlist + session notes at pages.stern.nyu.edu). [Free] [Beginner]
• Damodaran's data library: the "Margins by Sector" and "ROE by Sector" tables (pages.stern.nyu.edu, updated each January) are your permanent, live source for "what good looks like" benchmarks. Never memorize a book's frozen table, including this one's. [Free] [Intermediate]
• Zerodha Varsity, Module 3 "Fundamental Analysis", the financial-ratio chapters: Indian statements, Indian conventions, gentle pace. [Free] [Beginner]
• Michael Mauboussin & Dan Callahan, "Return on Invested Capital: How to Calculate ROIC and Handle Common Issues" (Counterpoint Global, free PDF). Read just the opening pages now as the bridge to M2.03; the rest is next module's core reading. [Free] [Advanced]

Filings & datasets to pull (the module's specimens):

• HUL annual report (hul.co.in / BSE) and Walmart 10-K (SEC EDGAR) are the mini-project pair. The Infosys annual report carries the cash-pile drag of WE1, and the Apple 10-K the buyback-shrunken equity of WE2; look at the equity section's ten-year shrink. All [Free].
• screener.in (India) and stockanalysis.com (US) for ten-year margin and ROE series. Then recompute one year by hand and reconcile with the vendor's figure: their conventions (other income in EBITDA? ending or average equity?) differ, and finding the difference is the exercise. [Free] [Intermediate]

Going deeper:

• Aswath Damodaran, "Return on Capital (ROC), Return on Invested Capital (ROIC) and Return on Equity (ROE): Measurement and Implications" (working paper, free on pages.stern.nyu.edu / SSRN). The definitive catalogue of what distorts every return ratio built this week (operating leases, goodwill, surplus cash, cross-holdings, the averaging choice), and the formal bridge into M2.03's ROIC. Read it after this week's work, before M2.03. [Free] [Advanced]
• Krishna Palepu & Paul Healy, Business Analysis and Valuation, the "Profitability Analysis" chapter. It's the B-school gold standard for ROE decomposition, including the "alternative" DuPont that splits the leverage factor into operating and financial leverage and isolates net operating profit after tax. Think of it as the rigorous, reformulated version of sections 4.4 and 4.5, and the natural next step once the three- and five-step feel automatic. [Paid] [Intermediate]

The Modern Analyst's Addendum

Everything above teaches this skill from first principles, by hand. That is how you learn it, and the mastery check still tests it that way. This addendum shows how a working analyst amplifies the same skill today. It adds; it never replaces. (R1/R10)

AI-Augment this skill

{
  "skill": "The margin stack, ROA and ROE, and the three- and five-step DuPont decompositions read as strategy rather than as arithmetic",
  "use": "The arithmetic here is trivial and the reading is not, which fixes exactly where a tool helps. (1) Hand it a completed decomposition — five factors, five to ten years, two or three companies — and ask it to describe the business model each set of numbers implies, with the vital sign it would monitor. Then compare its story to yours: where you disagree is either its error or the fact that you know something the numbers do not carry, and both are worth finding out. (2) Ask it to argue the opposite case for a company whose ROE you find impressive, restricted to the decomposition you supplied — the five-step's whole purpose is to catch quality rotting under a stable headline, and an adversary generates that hypothesis faster than you will. (3) Use it to build the peer list before you build the panel, then verify every name against the filings; a wrong comparable poisons the cross-section more thoroughly than a wrong number does. (4) Ask it to name what would have to be true for a high tax burden or a rising leverage factor to be benign, and go read the tax and borrowings notes to see whether it is.",
  "tools": ["Chat assistants — Claude, ChatGPT for reading a decomposition as a strategy and for the adversarial case", "Document/PDF AI — for pulling the tax-rate reconciliation and borrowings notes that explain the burden factors", "Coding assistants — for the panel and the variance decomposition below"],
  "prompt": "Here is a five-step DuPont decomposition for <COMPANY>, ten years, and for three named peers: <PASTE TABLE>. Describe the business model each column implies and the single vital sign you would monitor for each. Then, using only these figures, make the strongest possible case that this company's ROE quality has DETERIORATED over the decade, and state what evidence in the filings would refute that case. Do not introduce any figure that is not in my table, and do not tell me the company is a good or bad investment.",
  "verify": "The identity is the check and it is free: the five factors must multiply back to net income over average equity to the last decimal, and the first three must collapse into net margin. If they do not, the EBIT is inconsistent with the EBT (use the top-down EBIT of §4.1), or averages have been mixed with point-in-time balances, or a consolidated numerator has been divided by a parent-only denominator. Every striking factor gets its source read: a 0.92 tax burden is a question answered only by the ETR reconciliation note, and a leverage factor of 3 is a question answered only by the borrowings note and M2.02's coverage tests. A model handed a decomposition will always produce a narrative; only the filing establishes whether the narrative is about this company (Guardrail 1-5).",
  "diy": "The gate is unaided: you compute the margin stack, ROA, ROE and both DuPont decompositions from a filing, verify that the factors multiply back, and read the strategy off the arithmetic on paper. Nothing in this callout is admissible in that room."
}

Modern Data Analysis

By hand first. You multiplied HUL's and Walmart's factors out by hand and read two opposite machines off the same ROE, and the gate still asks for that. Code changes the number of companies and years you can hold at once. A ratio means nothing without a comparison, and that's the central claim here, so the extra scale is what turns the lesson into practice.

Today's workflow. Build the panel once and every ratio above becomes a column: five years of income statement and balance sheet for a peer set, averaged balance-sheet terms, and the three- and five-step factors computed as products. That opens up two things you can't do by hand. The first is attributing a change in ROE to its levers with nothing left unexplained. It works because the decomposition is multiplicative. Take logs and it becomes additive, so the log change in ROE equals the sum of the log changes in the factors, with no residual and no interaction term to argue about. Take a synthetic filer whose net margin falls from 12.0% to 10.5% while turnover edges from 1.10× to 1.15× and leverage climbs from 1.60× to 2.10×. Reported ROE rises from 21.12% to 25.36%, an apparently healthy gain of 4.24 percentage points. Leverage contributes +148.7% of it and the eroding margin −73.0%. That's the warning from 4.5 about quality rotting under a stable headline, turned into a number you can put in a memo. The second is the cross-section. Standardising each factor within a true peer set turns "is 22.9% a good operating margin" into a percentile, and that's the only form in which the question has an answer.

Tools & sources (IN + US). pandas for the panel, numpy for the decompositions, matplotlib for the factor trend charts. India: the Schedule III statement of profit and loss plus the balance sheet from the annual report (BSE/NSE), where you must build EBIT yourself from the by-nature format (section 4.13 of the filings-navigation module); the tax note for the burden factor; and screener.in for the convenience series you reconcile against the filing. US: EDGAR XBRL companyfacts (Revenues, OperatingIncomeLoss, IncomeLossFromContinuingOperationsBeforeIncomeTaxes..., NetIncomeLoss, Assets, StockholdersEquity), the 10-K for the notes behind any surprising factor, and Damodaran's sector data library at pages.stern.nyu.edu for live margin-and-ROE-by-sector benchmarks instead of memorised bands.

# Synthetic filer, module's own factor shape — R3: recomputed in-session
import numpy as np
y0, y5 = (0.120, 1.10, 1.60), (0.105, 1.15, 2.10)   # margin, turnover, leverage
roe0, roe5 = np.prod(y0), np.prod(y5)                # 0.2112 -> 0.2536 (+4.24 pp)
tot = np.log(roe5 / roe0)                            # multiplicative -> additive in logs
share = [np.log(b / a) / tot for a, b in zip(y0, y5)]
print(round(roe0 * 100, 2), round(roe5 * 100, 2), [round(s * 100, 1) for s in share])
#   21.12 25.36 [-73.0, 24.3, 148.7]  -> the ROE gain is leverage, net of margin erosion
assert abs(sum(np.log(b / a) for a, b in zip(y0, y5)) - tot) < 1e-12   # exact, no residual
print(round(0.166 * 0.80 * 1.52, 4), round(0.0287 * 2.66 * 2.91, 4))   # 0.2019 0.2222

Verify. Reconcile the panel to one filing you spread by hand before you trust a single column of it (revenue, EBIT, net profit, total assets and equity for the most recent year), and log every difference with its cause. An aggregator's "standardised" EBIT for an Indian by-nature P&L embeds someone else's judgment about other income, and that judgment lands directly in your operating-margin factor. Check that balance-sheet terms are averages throughout and that the numerator's scope matches the denominator's: parent net income over parent equity, or consolidated over consolidated, never one of each. Then let the identity close. A panel whose factors do not multiply back to ROE is not a panel with a rounding issue.

Quantitative lens

Because ROE is a product of three factors, its logarithm is a sum of three terms, and that makes the cross-sectional dispersion of ROE decomposable without remainder: Var(ln ROE) = Var(ln margin) + Var(ln turnover) + Var(ln leverage) + 2Cov(ln m, ln t) + 2Cov(ln m, ln l) + 2Cov(ln t, ln l), with no approximation and nothing left over. Run it on a ten-archetype synthetic cross-section built from the midpoints of the 4.6 table above (FMCG through airlines) and the result is startling in the right way. ROE spans only 9.5% to 39.6%, yet the three lever variances sum to 662% of the variance in ln ROE, and the covariance terms subtract 562% of it. The correlation between log margin and log turnover is −0.58, and between log margin and log leverage −0.73.

Think about what that means. The levers vary enormously across business models (net margin from 2% to 22.5%, turnover from 0.35× to 4.5×), and they cancel, almost completely, because of how the business models are built. Competition doesn't equalise margins. It equalises returns, by pushing high-margin businesses toward capital intensity and low-margin businesses toward velocity. So "same destination, opposite roads" is more than a phrase about two companies. It's a measurable property of the whole cross-section, and it's the reason ranking companies across industries by margin is a category error while ranking within a peer set is analysis.

The limits matter. This is a decomposition, and it isn't a causal model. It tells you where dispersion comes from, never why. And it certainly doesn't say leverage is safe just because leverage explains little of the variance. The archetype cross-section above is synthetic and built from the course's own mid-cycle bands, so its percentages illustrate the structure. They aren't measurements of a real universe. Run it on your own panel and the magnitudes will move, though the cancellation won't disappear. Logs also require positive factors, so loss-makers drop out of the arithmetic entirely, and that biases any real sample toward survivors. A single cyclical peak inside a five-year window will also dominate a variance term without meaning anything at all.

Do it in code: build the peer panel, compute the exact variance decomposition and the pairwise correlations of the log factors, then regress log ROE on the three log levers within a sector and note that the coefficients are all exactly one. The fit itself is dull. The covariance structure it conceals is the interesting output. See G1/QM1.02 and G2/DA1.05.

Where this goes next: galaxy cross-links

• G2 · DA1.02 Pandas Data Wrangling: the five-year, multi-company DuPont panel as a tidy frame, which is what makes every comparison in M2.05 a groupby instead of an afternoon.
• G2 · DA1.05 Statistics in Code: cross-sectional standardisation, percentile ranks and the covariance arithmetic above, done properly rather than by eye.
• G1 · QM1.02 Hypothesis Testing & Regression: whether a company's operating margin is genuinely above its peer set or merely in the upper half of a small, noisy sample, and how much of a factor's movement is mean reversion.
• G3 · CN5.01 Business Model Teardown: the consulting-side reading of the same arithmetic: a margin-led and a turnover-led machine are different businesses with different failure modes, and this is where that becomes a structured teardown rather than a ratio.

Teach it back & journal

Feynman prompt. Write a one-page explainer for a smart 15-year-old titled "The jeweller, the vegetable seller, and the cousin with a loan." The jeweller turns her ₹100 of savings into ₹20 of profit by selling one necklace a year at a huge markup. The vegetable seller turns his ₹100 into the same ₹20 by earning fifty paise on a crate, three hundred mornings a year. The cousin earns ₹20 on ₹100 too, but ₹60 of his stall was paid for with a borrowed ₹60 he must repay whatever happens. Explain why all three "earn 20%," why they are completely different businesses, what could ruin each one, and which you would rather own for twenty years. Only in the last paragraph may you use the words margin, turnover, leverage, and ROE. Attach each to the person it describes.

Journal prompt. Run DuPont on your own consulting practice. Your "net margin" is what survives of each project fee after delivery costs; your "asset turnover" is how intensively your one real asset (your time) is utilized and billed; your "leverage" is other people's time (associates, subcontractors) billed out above their cost. Which lever does your practice actually pull today? Which lever do the giant consulting firms pull (think about why partners want pyramids of juniors)? Write down the one lever you could realistically move this year, what moving it would cost, and what this exercise teaches you about why you should never again read a company's ROE without asking which lever, and who chose it.

This module's flashcards and mastery quiz are wired into the app: see the node's Quiz and Reviews.