The same profit, three answers
Buy something for 100 and sell it for 150. The profit is 50, and every one of these statements is true: the markup is 50%, because 50 is half of the cost; the margin is 33.3%, because 50 is a third of the selling price; and the return on investment — if the 100 was the only money committed — is also 50%, because the gain is half of the amount invested.
The numbers differ because the denominators differ. Markup divides by the cost, margin divides by the price, and ROI divides by the investment. None of them is wrong; using one while a decision needs another is what goes wrong. A pricing meeting that says “we need a 40% margin” and a supplier negotiation that says “we need a 40% markup” are asking for prices about 19% apart.
Margin and markup, converted
The two are locked together by the relationship markup = margin ÷ (1 − margin), and margin = markup ÷ (1 + markup). That means there is no such thing as a “40% margin” in a spreadsheet that is expecting markup — the same words describe different prices. The table below is generated by the same functions the calculators run:
| Margin | Equivalent markup | Cost | Price |
|---|---|---|---|
| 10% | 11.11% | 100.00 | 111.11 |
| 20% | 25.00% | 100.00 | 125.00 |
| 25% | 33.33% | 100.00 | 133.33 |
| 33.33% | 50.00% | 100.00 | 150.00 |
| 50% | 100.00% | 100.00 | 200.00 |
| 75% | 300.00% | 100.00 | 400.00 |
The distortion grows as the numbers get larger. At 10% the two figures are close enough to be confused harmlessly; at 75% the markup is four times the margin. This is why the error survives in small businesses for years — it only becomes expensive once margins are high or volumes are large.
Which one a decision needs
Pricing from cost needs markup: cost × (1 + markup) gives the price that achieves it. Judging profitability needs margin: profit ÷ price tells you what share of every sales pound is left after the cost of the goods. Comparing investments needs ROI, because the capital committed is the thing being compared, not the price of a unit.
A shop that prices everything at a 50% markup has a 33.3% margin, so only a third of each sale is left to cover rent, wages and tax. If the owner budgets as if the margin were 50%, every fixed cost is under-provided for by a third. The mirror error — quoting markup as margin — prices too high and loses volume; quoting margin as markup prices too low and gives the margin away. Both come from the same word being used for two ratios.
ROI adds the dimension of time
ROI is profit over investment, and its weakness is that it has no time dimension at all. Investing 10,000 and receiving 13,000 is a 30% ROI whether it took one year or eight. Spreading the return into a constant annual rate — the compound annual growth rate, CAGR — is what makes two investments comparable:
| Invested | Final | Held | Total ROI | CAGR |
|---|---|---|---|---|
| 10,000 | 13,000 | 1 year | +30.0% | +30.00% |
| 10,000 | 13,000 | 3 years | +30.0% | +9.14% |
| 10,000 | 13,000 | 8 years | +30.0% | +3.33% |
| 10,000 | 8,000 | 2 years | −20.0% | −10.56% |
The eight-year row is the one that changes decisions. A 30% gain sounds like a success until it is spread over nearly a decade at 3.3% a year — below the rate on a savings account in many periods, and before inflation. The calculation is (final ÷ initial)^(1 ÷ years) − 1; the exponent is years, so a six-month holding period is 0.5, not 6.
ROI also assumes the money stayed invested for the whole period and that nothing was added or removed. If cash flowed in or out, the honest measure is IRR/XIRR, which works from dated cash flows. Presenting a CAGR computed on a position that changed size as if it were an IRR is a common way to flatter a fund with steady contributions.
Break-even is a different question again
Margin and markup describe a unit; break-even describes the volume at which fixed costs are covered. The bridge between them is the contribution per unit — price minus variable cost. Fixed costs of 5,000, a price of 40 and a variable cost of 25 give a contribution of 15 and a break-even of 333.3 units, rounded up to 334 because a third of a sale is not a thing you can make. The corresponding revenue is 334 × 40 = 13,360.
That number is not the same as the margin, and it is not a profit forecast. It assumes the price and the variable cost hold across the whole range, that fixed costs really are fixed, and that the market will buy 334 units. A business can have a healthy margin and still fail because its break-even volume is above what the market will buy; a low-margin business can thrive on volume. The two ratios answer different questions and both are needed.
Commission: the denominator is the contract
Commission is a percentage of a base, and the base is where disputes live. Twelve thousand of sales at 7% pays 840 if the base is revenue, but only 420 if the base is a 50% gross profit — the same headline rate, half the money. Agreements also vary on whether tax, shipping, discounts and returns are inside the base. Before comparing two commission offers, convert both to “what do I keep on a typical sale”; the percentage alone is not comparable.
The four numbers on one page
| Question | Ratio | Denominator | Tool |
|---|---|---|---|
| What share of the price is profit? | Margin | Selling price | Profit margin calculator |
| What do I add to cost to reach a price? | Markup | Cost | Markup calculator |
| What did the invested capital return? | ROI / CAGR | Amount invested | ROI calculator |
| How many units cover fixed costs? | Break-even | Contribution per unit | Break-even calculator |
Mistakes that survive because the arithmetic is right
- Quoting markup as margin. A 50% markup is a 33.3% margin; reporting it as margin overstates profitability by half at that level.
- Comparing ROI across different holding periods. The total is not comparable; the annualised figure is.
- Using break-even as a profit target. Break-even means zero profit — it is the floor, not the goal.
- Forgetting that margin is before overheads. Gross margin pays for rent, salaries and tax; a 40% gross margin is not a 40% net margin.
- Averaging percentages. The average of a 50% margin and a 10% margin is not the margin of the combined business unless the revenues are equal.