You are reading the 2026 curriculum (exams up to November 2026). Sitting in February 2027 or later? Go to the 2027 Equities guide.
Operating profitability and working capital
Classify costs as fixed or variable to see how profit reacts to sales: operating profit = Q × (P − VC) − FC, where VC is variable cost, and the more fixed costs, the higher the degree of operating leverage. Track gross, EBITDA (earnings before interest, taxes, depreciation, and amortization) and operating margins, and use the cash conversion cycle, days sales outstanding plus days inventory outstanding minus days payables outstanding (DSO + DIO − DPO), to see how much cash working capital absorbs.
Before this: Revenue drivers and pricing power, Working Capital and Liquidity, Financial Analysis Techniques
On the exam
- Evaluate a company’s operating profitability and working capital using key measures
Evaluate a company's operating profitability and working capital using key measures. Expect: contribution margin, operating profit, degree of operating leverage, margins, days ratios and the cash conversion cycle.
How deeply to learn each part
- Know the idea
- Understand it in general. It frames other topics, but you will not calculate with it.
- Use it
- Understand it well enough to solve a question with it. Recognize when it applies.
- Memorize
- Learn it by heart. The exam will not give it to you.
You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.
You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.
How do you classify a company’s costs?
Operating costs can be sorted three ways, and each answers a different question. By behavior with output, a cost is fixed or variable. By nature, it is what the cost is. By function, it is what the cost is for. Operating costs are most of what a company spends, and they depend mainly on its business model and size.
- By behavior with output Memorize the one that drives operating leverage
- Variable Memorize materials, merchandise, per-unit labor
- Fixed Memorize salaried staff, depreciation, rent, software
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- By nature Use it what the cost is
- Employee pay, raw materials, office supplies
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- By function Use it what the cost is for
- Cost of sales, selling and marketing, general and administrative, R&D
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The behavior split is the one that matters for risk. Variable costs rise and fall with output (materials, merchandise, per-unit labor). Fixed costs do not move with output within a normal range (salaried staff, depreciation, rent, software, insurance). Accounting groupings do not always match intuition: research and development is expensed as an operating cost though economically it is an investment, and interest is a financing cost, not an operating one.
Companies rarely disclose fixed and variable costs, so analysts estimate them. That is easier in industries that report unit costs and volumes, such as energy and airlines.
How do fixed costs create operating leverage?
Memorize
Operating profit is what the units earn after their own costs, less everything that does not change with units.
Here is units sold, price per unit, variable cost per unit and total fixed operating costs. The part in brackets is the contribution margin : what each unit contributes toward fixed costs and profit.
For a firm to profit, the contribution margin must be positive and high enough to cover . Break-even volume is .
The more of the cost base is fixed, the more profit swings when sales move. The degree of operating leverage (DOL) measures that sensitivity.
A company sells 20 million units at 0.90 each. Variable cost is 0.50 per unit and fixed operating costs are 5.00 million. Its operating profit, in millions, is closest to:
20 × (0.90 − 0.50) − 5.00 = 3.00
Operating profit (millions)3.00
- 20×(0.9−0.5)−5=
- 0.9ENTER0.5−20×5−
ENTER enter (on the HP, puts the number on the stack)
A company's total contribution (units × (price − variable cost)) is 8.00 million and its operating profit is 3.00 million. Its degree of operating leverage is closest to:
8.00 ÷ 3.00 = 2.6667
Degree of operating leverage2.6667
- 8÷3=
- 8ENTER3÷
ENTER enter (on the HP, puts the number on the stack)
A company's degree of operating leverage is 2.667. If sales change by 10.00%, operating profit changes by closest to:
2.667 × 10.00% = 26.67%
Change in operating profit26.67%
- 2.667×10=in percent
- 2.667ENTER10×in percent
ENTER enter (on the HP, puts the number on the stack)
More fixed costs means a higher DOL: profit rises faster in good years and falls faster in bad ones. A firm raises its leverage by swapping variable costs for fixed ones, for example by automating work that used to be paid per unit.
Exam tip Two-step questions are common. Find DOL from the numbers first, then multiply it by the sales change: 2.8 × −5% = −14%.
Try this 0 of 3
- From the worked example, sell 10% more bottles and compare the profit change with DOL
- Move fixed costs to 10.0 and read DOL at 20 million bottles
- Make the cash conversion cycle negative
Price stays USD 0.90 a bottle. Total cost at 20 million bottles stays USD 15.0m, so moving cost into fixed lowers the variable cost per bottle to USD 0.50.
- Operating profit
- Revenue
- Total cost
- Fixed cost
A 10% rise in volume lifts operating profit from 3.00 to 3.80, or 26.7% (DOL 2.67 × 10%).
Show working
Variable cost per bottle = (15.0 − 5.0) ÷ 20 = 0.50. Contribution margin per bottle = 0.90 − 0.50 = 0.40.
Total contribution = 20m × 0.40 = 8. Operating profit = Q × (P − VC) − FC = 8 − 5 = 3.
DOL = total contribution ÷ operating profit = 8 ÷ 3 = 2.67.
Check: at 22m bottles, profit = 22 × 0.4 − 5 = 3.8; 3.8 ÷ 3 − 1 = 26.7%, which is 2.67 × 10%.
Breakeven = fixed costs ÷ contribution per bottle = 5 ÷ 0.4 = 12.5 million bottles.
- 0.9−0.5=×20=STO1total contribution 8
- −5=STO2operating profit 3
- RCL1÷RCL2=DOL 2.6667
- 5÷0.4=breakeven 12.5 million bottles
STO store · RCL recall a stored number
- 0.9ENTER0.5−20×STO1total contribution 8
- 5−STO2operating profit 3
- RCL1RCL2÷DOL 2.6667
- 5ENTER0.4÷breakeven 12.5 million bottles
ENTER enter (on the HP, puts the number on the stack) · STO store · RCL recall a stored number
What do the margins show?
Three margins read down the income statement, each stopping at a different cost line, the last at earnings before interest and taxes (EBIT). Compare them over time and with peers, and ask which cost explains the change.
- Minus cost of sales = gross profit Memorize gross margin; mostly variable costs
- Minus operating expenses excl. D&A = EBITDA Memorize EBITDA margin; selling, G&A, R&D mostly fixed
- Minus D&A = operating profit (EBIT) Memorize operating margin; before interest and tax
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Gross margin ignores everything below cost of sales. EBITDA margin adds selling, administrative and research costs but leaves out depreciation and amortization. Operating margin is after depreciation and amortization and before interest and tax.
How much cash does working capital absorb?
Memorize
Customers owe the company, stock sits in the warehouse, and suppliers are owed. The days measures turn each balance into how long it lasts, and the cash conversion cycle adds them up.
- Days sales outstanding Memorize receivables ÷ revenue × 365
- Days of inventory on hand Memorize inventory ÷ cost of sales × 365
- Days payables outstanding Memorize payables ÷ cost of sales × 365
- Cash conversion cycle Memorize DSO + DIO − DPO
- Net working capital Use it receivables + inventory − payables, as % of sales
Days sales outstanding is how long customers take to pay. Days of inventory on hand (also written DOH) is how long stock sits before it is sold. Days payables outstanding is how long the company takes to pay its suppliers.
The cash conversion cycle is the days between paying suppliers and collecting from customers. A short or negative cycle means suppliers finance the business. A lengthening cycle ties up cash and can signal slow collections or unsold stock.
Alongside the days, analysts track net working capital , receivables plus inventory minus payables, as a share of sales.
A company has a balance of 1.50 against an annual flow of 18.00 (the flow that matches the balance). On a 365-day basis, the days ratio is closest to:
1.50 ÷ 18.00 × 365 = 30.4167
Days (365 basis)30.4167
- 1.5÷18×365=
- 1.5ENTER18÷365×
ENTER enter (on the HP, puts the number on the stack)
A company has days sales outstanding of 30.4167, days of inventory on hand of 43.8 and days payables outstanding of 36.5. Its cash conversion cycle, in days, is closest to:
30.4167 + 43.8 − 36.5 = 37.7167
Cash conversion cycle, days37.7167
- 30.4167+43.8−36.5=
- 30.4167ENTER43.8+36.5−
ENTER enter (on the HP, puts the number on the stack)
Go deeper Why gross margin approximates contribution margin
Contribution margin per unit is price less variable cost per unit. If cost of sales is mostly variable and other operating costs are mostly fixed, then revenue minus cost of sales is close to total contribution, and gross margin is close to the contribution margin as a share of price. The approximation fails when cost of sales includes fixed items such as factory depreciation, or when selling costs include variable commissions. The notes to the financial statements show how costs are made up.
Go deeper Scale, scope and negative working capital
Economies of scale are falling costs per unit as output grows, usually because fixed costs are spread over more units (a variable-cost firm can also gain scale by bargaining harder with suppliers). Economies of scope are falling costs per unit as the number of product lines grows, because lines share costs. Both show up as improving margins as the company grows. Separately, some businesses run negative working capital: customers pay up front (subscriptions, ticketing) before suppliers are paid, so growth releases cash rather than absorbing it. That is a strength only if it comes from bargaining power rather than from stretching suppliers because the company cannot pay.
Memorize this
MemorizeCost structure and leverage
| Item | Formula | Note |
|---|---|---|
| Operating profit | Q × (P − VC) − FC | Q units, P price, VC per unit, FC total |
| Contribution margin | P − VC | per unit, before fixed costs |
| DOL | %Δ operating profit ÷ %Δ sales | or total contribution ÷ operating profit |
| More fixed costs | higher DOL | bigger gains in good years, bigger losses in bad |
Memory hook Contribution is what a unit gives toward the bills; operating profit is what is left after all the bills.
Know it cold Break-even units = FC ÷ (P − VC). Change in profit ≈ DOL × change in sales.
MemorizeMargins and days
| Measure | Numerator | Denominator |
|---|---|---|
| Gross margin | revenue − cost of sales | revenue |
| EBITDA margin | gross profit − opex excl. D&A | revenue |
| Operating margin | EBITDA − D&A = EBIT | revenue |
| DSO | receivables × 365 | revenue |
| DIO | inventory × 365 | cost of sales |
| DPO | payables × 365 | cost of sales |
Memory hook Receivables come from sales, so revenue. Inventory and payables come from buying, so cost of sales.
Know it cold CCC = DSO + DIO − DPO. Add what ties cash up, subtract what suppliers fund. Shorter frees cash.
- By behavior with output Memorize the one that drives operating leverage
- Variable Memorize materials, merchandise, per-unit labor
- Fixed Memorize salaried staff, depreciation, rent, software
-
- By nature Use it what the cost is
- Employee pay, raw materials, office supplies
-
- By function Use it what the cost is for
- Cost of sales, selling and marketing, general and administrative, R&D
-
- Minus cost of sales = gross profit Memorize gross margin; mostly variable costs
- Minus operating expenses excl. D&A = EBITDA Memorize EBITDA margin; selling, G&A, R&D mostly fixed
- Minus D&A = operating profit (EBIT) Memorize operating margin; before interest and tax
-
- Days sales outstanding Memorize receivables ÷ revenue × 365
- Days of inventory on hand Memorize inventory ÷ cost of sales × 365
- Days payables outstanding Memorize payables ÷ cost of sales × 365
- Cash conversion cycle Memorize DSO + DIO − DPO
- Net working capital Use it receivables + inventory − payables, as % of sales
Quick example
A firm sells 2.0 million units at 12 with variable cost of 7 and fixed costs of 6.0 million. 2.0 × (12 − 7) − 6.0 = 4.0 million.
- 2×(12−7)−6= 4
- 12ENTER7−2×6− 4
ENTER enter (on the HP, puts the number on the stack)
Quick example
Price 12, variable cost 7. 12 − 7 = 5 per unit toward fixed costs and profit.
- 12−7= 5
- 12ENTER7− 5
ENTER enter (on the HP, puts the number on the stack)
Quick example
Sales rise 8% and operating profit rises 20%. 20 ÷ 8 = 2.5. A 2.5 DOL means each 1% change in sales moves operating profit about 2.5%.
- 20÷8= 2.5
- 20ENTER8÷ 2.5
ENTER enter (on the HP, puts the number on the stack)
Quick example
Total contribution 10.0, operating profit 4.0. 10.0 ÷ 4.0 = 2.5. Needs no second year of data.
- 10÷4= 2.5
- 10ENTER4÷ 2.5
ENTER enter (on the HP, puts the number on the stack)
Quick example
Revenue 500, cost of sales 320. (500 − 320) ÷ 500 = 36.0%.
- 500−320=÷500= 0.36
- 500ENTER320−500÷ 0.36
ENTER enter (on the HP, puts the number on the stack)
Quick example
Gross profit 180, operating expenses excluding D&A 85, revenue 500. EBITDA = 95, so 95 ÷ 500 = 19.0%.
- 180−85=÷500= 0.19
- 180ENTER85−500÷ 0.19
ENTER enter (on the HP, puts the number on the stack)
Quick example
EBITDA 95, depreciation and amortization 30, revenue 500. EBIT (earnings before interest and taxes) is 65, so 65 ÷ 500 = 13.0%.
- 95−30=÷500= 0.13
- 95ENTER30−500÷ 0.13
ENTER enter (on the HP, puts the number on the stack)
Quick example
Receivables 40, revenue 480. 40 ÷ 480 × 365 = 30.4 days.
- 40÷480×365= 30.42
- 40ENTER480÷365× 30.42
ENTER enter (on the HP, puts the number on the stack)
Quick example
Inventory 55, cost of sales 330. 55 ÷ 330 × 365 = 60.8 days. Cost of sales, not revenue.
- 55÷330×365= 60.83
- 55ENTER330÷365× 60.83
ENTER enter (on the HP, puts the number on the stack)
Quick example
Payables 33, cost of sales 330. 33 ÷ 330 × 365 = 36.5 days.
- 33÷330×365= 36.5
- 33ENTER330÷365× 36.5
ENTER enter (on the HP, puts the number on the stack)
Quick example
DSO 32, DIO 58, DPO 40. 32 + 58 − 40 = 50 days. Negative means suppliers fund the business.
- 32+58−40= 50
- 32ENTER58+40− 50
ENTER enter (on the HP, puts the number on the stack)
Quick example
Receivables 40, inventory 55, payables 33, revenue 480. 62 ÷ 480 = 12.9% of sales.
- 40+55−33=÷480= 0.1292
- 40ENTER55+33−480÷ 0.1292
ENTER enter (on the HP, puts the number on the stack)
How it is asked
-
Operating profit from price, cost and units
P 40, VC 26, 100,000 units, FC 0.9 million. Operating profit?
Contribution 14 × 100,000 = 1.4m; less 0.9m = 0.5m. The trap is 1.4m (forgetting fixed costs).
-
Two-step: DOL then a sales change
From the prior numbers, sales fall 5%. Change in operating profit?
DOL = 1.4 ÷ 0.5 = 2.8; 2.8 × −5% = −14%.
-
Cash conversion cycle
DSO 30, DIO 25, DPO 70.
30 + 25 − 70 = −15 days. Adding DPO (125) is the trap.
-
Which margin moved
Prices stable, gross margin down, operating margin unchanged.
Cost of sales rose as a share of revenue while other operating costs fell. Interest is below EBIT.
Exam traps
- Using revenue instead of cost of sales for inventory days and payables days. Only receivables go with revenue.
- Adding DPO in the cash conversion cycle. Payables are supplier financing, so they are subtracted.
- Confusing contribution margin (P − VC, before fixed costs) with operating profit (after fixed costs).
- Reading DOL as a fixed property of the firm. It changes with output and falls as volume rises above break-even.
- Using EBIT margin when asked about gross margin: each margin stops at a different cost line.
Checkpoint
4 exam-style questions. About 90 seconds each.
1A company sells 500,000 units at CHF 24 with variable costs of CHF 15 per unit and fixed operating costs of CHF 3.0 million. If unit sales rise 10%, operating profit will rise by closest to:
2A company's days sales outstanding are 45, its days of inventory on hand 60 and its days payables outstanding 50. Its cash conversion cycle is closest to:
3A company has revenue of EUR 600 million, cost of sales of EUR 420 million and inventory of EUR 70 million. Its days of inventory on hand are closest to:
4A company's prices are stable but its gross margin falls while its operating margin is unchanged. The most likely explanation is that:
Key takeaways
- Operating profit = Q × (P − VC) − FC; DOL = %Δ operating profit ÷ %Δ sales.
- More fixed costs, more operating leverage: bigger swings both ways.
- Margins: gross, EBITDA, operating (EBIT). Read trends and peers, and ask which cost moved.
- CCC = DSO + DIO − DPO; shorter frees cash.
Quick example
A firm sells 2.0 million units at 12 with variable cost of 7 and fixed costs of 6.0 million. 2.0 × (12 − 7) − 6.0 = 4.0 million.
- 2×(12−7)−6= 4
- 12ENTER7−2×6− 4
ENTER enter (on the HP, puts the number on the stack)
Quick example
Price 12, variable cost 7. 12 − 7 = 5 per unit toward fixed costs and profit.
- 12−7= 5
- 12ENTER7− 5
ENTER enter (on the HP, puts the number on the stack)
Quick example
Sales rise 8% and operating profit rises 20%. 20 ÷ 8 = 2.5. A 2.5 DOL means each 1% change in sales moves operating profit about 2.5%.
- 20÷8= 2.5
- 20ENTER8÷ 2.5
ENTER enter (on the HP, puts the number on the stack)
Quick example
Total contribution 10.0, operating profit 4.0. 10.0 ÷ 4.0 = 2.5. Needs no second year of data.
- 10÷4= 2.5
- 10ENTER4÷ 2.5
ENTER enter (on the HP, puts the number on the stack)
Quick example
Revenue 500, cost of sales 320. (500 − 320) ÷ 500 = 36.0%.
- 500−320=÷500= 0.36
- 500ENTER320−500÷ 0.36
ENTER enter (on the HP, puts the number on the stack)
Quick example
Gross profit 180, operating expenses excluding D&A 85, revenue 500. EBITDA = 95, so 95 ÷ 500 = 19.0%.
- 180−85=÷500= 0.19
- 180ENTER85−500÷ 0.19
ENTER enter (on the HP, puts the number on the stack)
Quick example
EBITDA 95, depreciation and amortization 30, revenue 500. EBIT (earnings before interest and taxes) is 65, so 65 ÷ 500 = 13.0%.
- 95−30=÷500= 0.13
- 95ENTER30−500÷ 0.13
ENTER enter (on the HP, puts the number on the stack)
Quick example
Receivables 40, revenue 480. 40 ÷ 480 × 365 = 30.4 days.
- 40÷480×365= 30.42
- 40ENTER480÷365× 30.42
ENTER enter (on the HP, puts the number on the stack)
Quick example
Inventory 55, cost of sales 330. 55 ÷ 330 × 365 = 60.8 days. Cost of sales, not revenue.
- 55÷330×365= 60.83
- 55ENTER330÷365× 60.83
ENTER enter (on the HP, puts the number on the stack)
Quick example
Payables 33, cost of sales 330. 33 ÷ 330 × 365 = 36.5 days.
- 33÷330×365= 36.5
- 33ENTER330÷365× 36.5
ENTER enter (on the HP, puts the number on the stack)
Quick example
DSO 32, DIO 58, DPO 40. 32 + 58 − 40 = 50 days. Negative means suppliers fund the business.
- 32+58−40= 50
- 32ENTER58+40− 50
ENTER enter (on the HP, puts the number on the stack)
Quick example
Receivables 40, inventory 55, payables 33, revenue 480. 62 ÷ 480 = 12.9% of sales.
- 40+55−33=÷480= 0.1292
- 40ENTER55+33−480÷ 0.1292
ENTER enter (on the HP, puts the number on the stack)
Questions about this lesson?
Where this comes back
- Capital investments and capital structure Company Analysis: Past and Present
- Company Analysis: Forecasting Equity Investments
Questions candidates ask
What is the degree of operating leverage?
The percentage change in operating profit divided by the percentage change in sales. A DOL of 3 means a 10% rise in sales lifts operating profit about 30%.
How do you calculate the cash conversion cycle?
Days sales outstanding plus days of inventory on hand minus days payables outstanding.
What is contribution margin?
Price minus variable cost per unit: what each unit contributes toward fixed costs and profit.
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