4.2 Returns and DuPont Analysis

Return on Equity, Assets, and Invested Capital

Margins tell you how many cents of profit sit on each sales dollar. Return ratios tell you how much profit you earned on the capital tied up to produce those sales. CFI's Financial Analysis Fundamentals treats three returns as the core set: return on equity (ROE), return on assets (ROA), and return on invested capital (ROIC).

Harbor Year 3 stocks used in this section:

ROE = Net income / Equity. Using ending equity: 10,500,000 / 42,000,000 = 25.0%. Using average equity (35,700,000 + 42,000,000) / 2 = 38,850,000, ROE = 10,500,000 / 38,850,000 = 27.0%. CFI classroom examples often use ending balances so the identity is easy to audit in a common-size pack. Average equity is more accurate when the book-value stock moved a lot during the year — Harbor's retained earnings rose by net income $10.5 million minus dividends $4.2 million = $6.3 million. This chapter's DuPont walk uses ending 25% so every factor multiplies back to one number you can tick.

ROA = Net income / Assets = 10,500,000 / 70,000,000 = 15.0%. ROA uses the same numerator as ROE but a larger denominator, so it is always lower than ROE when the company has liabilities. ROA is not operating return: the numerator is after interest, and the denominator includes cash, operating assets, and any non-operating items on the balance sheet.

ROIC = NOPAT / Invested capital.

NOPAT (net operating profit after tax) = EBIT × (1 − tax rate) = 16,000,000 × (1 − 0.25) = $12,000,000. NOPAT is the after-tax operating profit as if the firm had no debt. It is not net income.

Invested capital can be built from either side of the balance sheet:

• Financing side: Equity + interest-bearing debt − excess cash = 42,000,000 + 20,000,000 − 4,000,000 = $58,000,000
• Operating side: Operating net working capital + net PP&E + other operating assets (excluding excess cash)

Both sides equal $58 million for Harbor if the residual operating assets are consistent. ROIC = 12,000,000 / 58,000,000 = 20.7%.

ROE 25%, ROIC 20.7%, and ROA 15% are three different questions. ROE asks what residual owners earned on book equity. ROIC asks what the operations earned on the capital providers actually have tied up, after tax but before the financing mix. ROA sits in between and is the least clean of the three because NI is levered while assets are not. Later in the FMVA core you compare ROIC to WACC. That test is capital-structure-neutral. Comparing WACC to ROE is a mismatch: ROE is a levered return, WACC is a blended cost.

Exam trap: putting net income in the ROIC numerator, or putting total assets in the ROIC denominator. Either error re-imports capital structure into a ratio whose point is to strip it out.

Three-Step DuPont Analysis

CFI decomposes ROE so you can see why it is 25%, not just that it is 25%. The three-step DuPont identity is:

ROE = Net profit margin × Asset turnover × Equity multiplier

ROE = (Net income / Revenue) × (Revenue / Assets) × (Assets / Equity)

Harbor Year 3, ending balances:

Check the intermediate: NPM × AT = 0.13125 × 1.14286 = 0.150 = 15%, which is ROA. Then ROA × EM = 0.15 × 1.667 = 25% = ROE. If the product does not equal standalone ROE, a balance-sheet total or a share of NI is wrong. That is an audit check, not a display trick.

Read the three factors as three levers:

1. Profitability (NPM): cents of net income per sales dollar — gross margin, opex, interest, and tax all live here.
2. Efficiency (AT): sales generated per dollar of assets — working-capital tightness and fixed-asset utilization live here.
3. Leverage (EM): assets held per dollar of equity — debt and other liabilities live here.

Two firms can print the same 25% ROE with opposite economics. A software firm might pair a 20% net margin with 1.0× turnover and 1.25× leverage. A grocer might pair a 2.5% net margin with 5.0× turnover and 2.0× leverage. Same ROE, different risk. The FMVA skill is to split the 25% before you call it quality.

Five-Step DuPont Analysis

The five-step (extended) DuPont does not add a new theory. It splits net profit margin into operating margin, the cost of debt, and tax:

ROE = Tax burden × Interest burden × EBIT margin × Asset turnover × Equity multiplier

ROE = (NI / EBT) × (EBT / EBIT) × (EBIT / Revenue) × (Revenue / Assets) × (Assets / Equity)

Harbor:

Tax burden × interest burden × EBIT margin = 0.750 × 0.875 × 0.200 = 0.13125, which is net margin. The last two factors are the same as three-step DuPont. The five-step is worth doing when ROE moved and you need to know whether operations, interest, or tax did the work.

Worked contrast: suppose next year EBIT margin stays 20%, turnover and leverage stay put, but the tax rate rises to 30%. Tax burden falls to 0.70. Net margin becomes 0.70 × 0.875 × 0.20 = 12.25%, and ROE falls to 12.25% × 1.143 × 1.667 = 23.3%. Nothing in the factory changed. Five-step DuPont points at tax, not at SG&A.

Exam trap: writing five-step DuPont as ROE = NPM × AT × EM × tax rate × interest rate. The tax and interest rates are not the factors. The factors are the burdens NI/EBT and EBT/EBIT, which are complements of those rates, not the rates themselves. A 25% tax rate is a 75% tax burden.

Some textbooks insert a four-step that keeps EBT/Revenue as a single pretax margin. That is valid algebra (interest burden × EBIT margin = EBT/Revenue). It is not the five-step. If a question asks for five factors, split pretax margin into EBIT margin and interest burden.

The Pyramid of Ratios

CFI's Financial Analysis Fundamentals organizes the ratio set as a pyramid, not as a flat glossary. The point of the pyramid is diagnostic order: start at ROE, then drop one layer at a time until you find the line that moved.

Apex: ROE.

Layer 2 — the three-step DuPont drivers:

• Profitability: net profit margin
• Efficiency: asset turnover
• Leverage: equity multiplier (assets / equity)

Layer 3 — the operating, working-capital, and financing ratios that feed each driver:

• Under NPM: gross margin, SG&A%, D&A%, EBIT margin, interest coverage, effective tax rate
• Under asset turnover: receivable days, inventory days, payable days, and fixed-asset turnover (revenue / net PP&E)
• Under the equity multiplier: debt / equity, debt / assets, and the mix of operating liabilities versus interest-bearing debt

Working-capital day counts and coverage ratios get their own chapter next. They still belong on the pyramid now so you do not treat DuPont as three isolated formulas. If ROE fell because asset turnover fell, the next question is whether inventory days stretched, not whether the tax rate moved.

A practical walk on Harbor:

1. ROE is 25%.
2. NPM is 13.1% (healthy), AT is only 1.14× (capital intensive), EM is 1.67× (moderate leverage).
3. The 1.14× turnover is the place to zoom in: $48 million of net PP&E against $80 million of revenue is 1.67× fixed-asset turnover, and the rest of the asset base is working capital and cash. Improving ROE without adding debt means either raising the 40% gross margin / 20% EBIT margin, or sweating $70 million of assets harder — not automatically drawing the revolver so EM rises.

That last sentence is the pyramid's warning. Leverage is the fastest way to lift ROE and the least informative about operations.

How Leverage Inflates ROE

The equity multiplier Assets / Equity is greater than 1 whenever the firm has liabilities. Interest-bearing debt is the part that can inflate ROE relative to the unlevered return — and can deflate it when operations weaken.

Hold operating assets and EBIT constant and compare an all-equity twin with Harbor's capital structure. Tax rate 25%.

Harbor's net income is lower ($10.5 million versus $12.0 million). ROE is higher because the equity base shrank by more than NI shrank. Pre-tax cost of debt = 2,000,000 / 20,000,000 = 10%. After-tax cost of debt = 10% × (1 − 0.25) = 7.5%. Harbor's unlevered-style operating return is above 7.5%, so the extra assets funded by debt earn more than they cost, and the residual accrues to a thinner equity slice.

Now drop EBIT to $4,000,000 and keep interest at $2,000,000:

Leverage now hurts ROE. Interest is contractual. EBIT is not. If EBIT fell to $1,000,000, Harbor's EBT would be negative $1,000,000 and levered ROE would go negative while the unlevered twin still earned a small positive return. That is magnification, not alchemy.

Related traps:

• A debt-funded share repurchase raises EM and can lift ROE with no change in EBIT margin or turnover. DuPont will show the leverage factor doing the work. That is not operating improvement.
• Operating liabilities (payables, accrued expenses) also raise Assets/Equity, but they do not carry an interest charge. They improve ROE partly by shrinking net working capital, which is an efficiency story as much as a financing story. Do not call every EM increase financial leverage.
• ROIC is the check. Harbor's ROIC of 20.7% is the operating result after tax. If management praises a 25% ROE, ask what the equity multiplier did, then look at ROIC.

Exam Traps on Return Ratios

1. Using average assets in ROA and ending equity in ROE in the same DuPont product — the identity will not tick.
2. Computing ROE as EBIT / Equity (mixing an unlevered numerator with a levered denominator).
3. Computing ROIC as NI / (Debt + Equity) — NI is after interest, so you double-count the cost of debt: once in the numerator, once by leaving debt in the denominator.
4. Treating a rising ROE as proof of a better business when the only moving DuPont factor was EM.
5. Forgetting that a tax-rate cut raises the tax burden factor (NI/EBT) and therefore ROE even if EBIT is unchanged.

On the FMVA final, Finance is about a quarter of estimated weight and Financial Analysis Fundamentals is a required core course. The tested move is not reciting the three-step formula. It is using the pyramid: ROE moved; which of NPM, AT, and EM moved; and whether leverage is hiding a weaker operating return.