Lin finds a company with return on equity of 22.4%, interest coverage of 4.5 times, and $1 million in cash. It appears profitable and able to service debt. Yet listing the payments due over the next year still reveals a shortfall.
Ratios can point to questions without guaranteeing financial health. Following one fictional company from margins to invested capital and then to payment dates shows what the attractive numbers measure—and which obligations they leave unanswered.
What you will be able to do
- Calculate three profit margins and explain the components of a change in return on equity.
- Distinguish returns on shareholder capital, operating capital, and an additional investment.
- Connect net debt, interest coverage, available cash, and debt maturities in one financial record.
Give the inputs a common basis
Yunyu Manufacturing and every amount below are independent synthetic teaching inputs, unrelated to Costco. Amounts are in units of $10,000: revenue of 1,200 means $12 million. Observe one complete year, with common shares only and no noncontrolling interests, preferred shares, leases, nonoperating investments, or other complex adjustments. Average balances are supplied; do not replace them with year-end balances.
Revenue is 1,200, cost of goods sold 720, other operating expenses 300, interest expense 40, and income tax 28, with no other gains or losses. Average assets are 1,000, average equity 500, average interest-bearing debt 400, and average cash 100.
Year-end assets, equity, debt, and cash happen to equal those averages. There are also operating payables of 100 at year-end. Cash is included in assets and is entirely accessible. This agreement between averages and closing balances is a teaching assumption, not a general accounting relationship.
For real companies, obtain the original figures, reconcile necessary adjustments, and inspect unusual items or changes in scope. Financial ratios need to be used together and interpreted in the relevant industry context. The CFA Institute's public overview identifies those connections without supplying all the particular definitions used in this exercise. [1]
What remains from each dollar of revenue?
Revenue of 1,200 less goods sold costing 720 gives gross profit of 480. Divide by revenue to obtain a 40% gross margin. Deduct the 300 operating expenses to get operating profit of 180 and an operating margin of 15%. Interest of 40 and tax of 28 then leave net income of 112, a net margin of approximately 9.33%.
These are different stages. Gross profit looks past direct merchandise or service costs; operating profit also considers operating expenses; net income reflects financing, tax, and other applicable items. The exercise lists each component so you can follow the progression. Actual reporting lines need inspection before a similar calculation.
If net margin improves while operating margin does not, investigate financing, tax, or nonoperating effects before announcing stronger pricing power. A higher gross margin may reflect product mix or lower costs. The ratio identifies a change, not its cause.
Companies may also classify costs differently, and peak-cycle margins may not persist. Compare consistent historical definitions and genuinely comparable businesses. No single gross-margin threshold can establish quality across every industry.
Is ROE higher because profit improved or equity shrank?
Here, return on equity, or ROE, is annual net income attributable to common shareholders divided by average common equity. Yunyu's 112 divided by 500 gives 22.4%. It measures accounting profit against book shareholder capital, not the shareholder's annual stock-market return. [1]
Break the ratio into three linked terms: net income divided by revenue; revenue divided by average assets; and average assets divided by average equity. The matching amounts cancel when multiplied, leaving net income divided by average equity. This is the intuition behind the three-part DuPont decomposition.
Yunyu's net margin is about 9.33%, asset turnover is 1,200 divided by 1,000, or 1.2 times, and its equity multiplier is 1,000 divided by 500, or 2. Using the unrounded margin produces 22.4%. Turnover describes revenue per unit of average assets. The equity multiplier describes the scale of assets relative to equity; interest-bearing debt is not the only liability that can affect it.
Now isolate a capital-structure scenario. Keep average assets at 1,000 and net income at 112, but reduce average equity to 400. ROE becomes 28%, without increasing revenue or operating profit. This is a demonstration of the denominator, not a forecast of earnings after borrowing or repurchasing shares. Financing costs and risks may change in reality.
When ROE rises, inspect margin, turnover, and the multiplier, then investigate why equity changed. Repurchases, losses, or accounting changes can alter that denominator. Very small or negative equity can undermine the usual interpretation. Ranking the resulting percentages would not repair it.
What return did the operating capital produce?
Financing structure influences ROE. To examine operating returns on the capital employed, you might use return on invested capital, or ROIC. State its definition first; values from different data services need not share the same adjustments.
Our numerator is net operating profit after tax, or NOPAT. Apply an assumed operating tax rate of 20% to operating profit of 180, producing 144. This is not actual net income of 112: the operating calculation has not deducted debt interest. The 20% is a teaching input, not a generally applicable tax rate.
Average invested capital is defined here as average equity of 500 plus interest-bearing debt of 400, less cash of 100. For this adjustment, assume all that cash is nonoperating and eligible for subtraction. The result is 800, and 144 divided by 800 gives ROIC of 18%.
The numerator excludes interest, while the denominator includes both debt and equity funding. That keeps the return and capital concepts aligned. In real research, explain cash eligibility and the treatment of leases, goodwill, and other items. Subtracting cash required for operations simply to reduce the denominator can overstate the calculated return.
Historical ROIC of 18% does not promise an 18% return on a new project. Suppose an additional investment of 200 is expected to produce annual incremental NOPAT of 24 once fully operational, with other effects handled in the assumptions. Its simplified incremental return is 12%.
That 12% compares one stable year's accounting profit with the investment. It does not account for the wait before full production, project life, or recovery of the invested capital. It cannot replace valuation using cash flows across periods, and it is a forward-looking scenario rather than realized performance.
If a matching cost of capital is assumed to be 10%, the 12% exceeds that reference. Cost of capital represents the return required by funding providers. The project profit, capital-cost estimate, and time to reach full operation can all be wrong; the comparison does not guarantee value creation. Detailed estimation belongs in the valuation chapters.
Where does operating money wait?
Yunyu's average receivables are 150, inventory 180, and operating payables 100. Our simplified operating working capital is 150 plus 180 minus 100, or 230, excluding cash and interest-bearing debt. This differs from the broader convention of total current assets minus current liabilities.
Slower customer payment and more inventory can tie up resources if suppliers do not offer longer terms. The balance of 230 alone cannot establish whether the amount is high. Compare business scale, seasonality, and history. An average balance is not itself a cash outflow during the year.
To inspect timing, assume all annual sales are on credit and use 365 days. Average receivables divided by credit revenue times 365 gives 45.625 days, approximately 45.63. Inventory divided by cost of goods sold times 365 gives 91.25 days. For payables, separately supplied annual credit purchases are 720: 100 divided by 720 times 365 gives about 50.69 days.
Using the unrounded values, receivable days plus inventory days minus payable days gives a cash conversion cycle of approximately 86.18 days. Purchases of 720 are independently specified; real research cannot always substitute cost of goods sold for purchases. Nor is this ratio a transaction-by-transaction calendar of actual receipts and payments.
Adjust when receivables include other businesses, sales are not entirely credit sales, or payables cover a different scope. The days can direct attention to customer, inventory, or supplier questions. They do not automatically diagnose bad management or demonstrate that cash will arrive safely.
Why 4.5 times coverage still leaves a $100,000 gap
Define net debt as interest-bearing debt of 400 less available cash of 100: 300. The calculation connects two balances but omits payment dates. Real cash also needs checking for restrictions and whether it can move between the entities holding cash and owing debt.
Interest coverage here is annual operating profit of 180 divided by interest expense of 40, giving 4.5 times. Its numerator is profit, not available cash. Its denominator is interest, not principal, leases, and all other fixed payments. Zero interest would not justify writing “infinitely safe.”
Now look twelve months forward from year-end. Of the 400 debt, principal of 120 is due; the other 280 matures later. Expected operating cash is 60, already including interest, tax, and operating working-capital changes. Capital expenditure requires another 50. Assume no dividends, repurchases, other flows, or new financing.
Cash of 100 plus operating inflow of 60 gives 160. Capital expenditure of 50 plus principal of 120 requires 170. The gap is 10, or $100,000 under our units. Do not add historical net income of 112 or NOPAT of 144 to the cash again. This is a forward stress scenario, distinct from the historical annual profit measures.
Required operating reserves could widen the gap. Investigate whether spending can be delayed, assets sold, or committed credit accessed under satisfied conditions. Until approvals, terms, and arrival dates are verified, potential refinancing is not confirmed money.
Break maturities down by month too. Annual inflows could total enough while debt falls due before customers pay. Static net debt, profit coverage, and cash dates need to be examined together; selecting the most reassuring ratio would leave the original payment problem unresolved.
Find the corresponding evidence in Costco's notes
For a real source-finding exercise, use Costco's fiscal 2025 10-K, ended August 31, 2025, as fixed C1-R retrospective material. It was not available at the original two C1 freezes. Item 8 contains statements; Note 4, Debt, includes future principal maturities. [2]
Do not assign Yunyu's 18% to Costco. Choose a question and specify inputs, averages versus closing balances, units, and adjustments. Identify which inputs need more than one main statement. Actual receivable composition, leases, and capital items can differ from our model, so read the notes before calculating.
Explain the number before ranking it
Why does ROE increasing from 22.4% to 28% not establish operating improvement? Then find the error in adding net income of 112 to cash of 100 to cover debt principal of 120 and capital expenditure of 50. Write the reasons before reading the answers.
Reference answers · reveal
Answer points: Equity shrank in the scenario while revenue and profit stayed unchanged; inspect the denominator and leverage. The cash calculation mixes historical profit with future flows. Use the supplied operating cash of 60 and retain timing and financing conditions. Net income is not another separate pot of cash.
Change collections and investment spending
Keep the forward twelve-month scenario, but delayed customer payments reduce expected operating cash from 60 to 30. Management proposes deferring 20 of the 50 capital expenditure. Assume the deferral is feasible and has no other cash consequences within the scenario. Principal due remains 120. Calculate the gap and decide whether the old 4.5-times interest coverage can replace this check.
Reference answers · reveal
Answer points: Sources are 100 plus 30, or 130. Revised uses are 30 plus 120, or 150, leaving a gap of 20. Deferral helps but does not offset all the collection deterioration. The old profit-coverage ratio cannot establish payment capacity in the new scenario. Check collections, investment commitments, and financing conditions.
Save a connected financial-ratio card
For one company, record margins, ROE components, your ROIC definition and incremental-investment assumptions, working-capital scope, net debt, and interest coverage. Include each numerator, denominator, period or date, unit, source, and adjustment. You do not need to collect every unfamiliar ratio at once.
On a second page, build the maturity cash schedule: accessible cash, operating flows, necessary investment, principal, other payments, and financing not yet committed. Change at least one collection or maturity assumption and recalculate. Identify the most consequential missing evidence.
Check whether high returns merely reflect a smaller denominator, profit has been counted as cash again, or annual totals conceal an interim gap. Obtain the relevant evidence before using a threshold to justify an allocation. The card's value is the connection between measurements, not the number of impressive ratios it contains.
Follow ratios back to operations and payment dates
Connect margins, turnover, and capital structure on consistent definitions before comparing history, peers, and the cycle. High ROE can reflect better operations or smaller equity. Historical capital returns cannot promise returns on additional investment.
Then put cash, operating changes, and maturities on a calendar. Suspend rankings when definitions differ, denominators fail, or industry structure needs another approach; financial and real-estate businesses require specialized treatment. The research task is explaining where earnings arise and where cash may run short.
References
- CFA Institute: Financial Analysis Techniques, 2026 public overview. Ratio families, DuPont analysis, and industry context; the paid reading was not reviewed. Yunyu's formulas and adjustment assumptions are specified in the exercise.
- Costco: fiscal 2025 Form 10-K, Item 8 and Note 4, Debt. Fixed retrospective evidence; real ratios require their own definitions and note checks.
Editorial status
AI-assisted draft synchronized to the accepted second-round Chinese source. See the author review for version, arithmetic, and source checks. A separate AI reviewer has completed an independent full-text review. Human financial review and target-reader testing remain pending.