Margin is not markup
Buy something for 100 and sell it for 150. Your markup is 50%. Your margin is 33.3%. Both describe the same transaction, and neither is wrong.
The trouble starts when a supplier quotes one and a retailer applies the other. That mistake always runs in the same direction — you undercharge — and it survives for years because the price still looks profitable.
Two denominators, one profit
Markup is profit divided by cost. Margin is profit divided by selling price. The profit is the same number in both; only what you divide it by changes.
Because the selling price is always larger than the cost, margin is always the smaller percentage. A 50% markup on a cost of 100 gives a price of 150 and a profit of 50 — which is 50% of the cost and 33.3% of the price.
To actually reach a 50% margin on that item you need a price of 200, which is a 100% markup. You have to double the cost, not add half to it.
Cost 100, price 150, profit 50
Markup = 50 / 100 = 50%
Margin = 50 / 150 = 33.3%
For a 50% margin the price is 200 (a 100% markup)
Work it out: Profit Margin Calculator →
The gap widens as the numbers climb
At small percentages the two are close enough to confuse without much damage: a 5% markup is a 4.8% margin. At larger ones they diverge sharply.
A 100% markup is a 50% margin. A 300% markup is a 75% margin. And the asymmetry is fundamental rather than incidental — margin can never reach 100%, because that would mean the item cost nothing, whereas markup has no upper limit at all.
That is the tell for which one someone means. If a figure over 100% is being quoted, it can only be markup.
Work it out: Markup Calculator →
Discounts do not add up either
The same shape of error appears on the way down. Thirty per cent off, then a further twenty, is not fifty per cent off. The second discount comes off the already reduced price.
On a 120 item: 30% off leaves 84, and 20% off that leaves 67.20. The saving is 52.80, which is 44% of the original — six points less than the 50% it appears to be.
The quick way to handle any single discount is to multiply rather than subtract. Twenty per cent off means paying eighty per cent, so multiply by 0.8. Stack them by multiplying: 0.7 times 0.8 is 0.56, so you pay 56% and save 44%.
120, less 30% = 84.00
84, less 20% = 67.20
Saved 52.80 = 44% off, not 50%
Shortcut: 0.7 x 0.8 = 0.56 -> pay 56%
Work it out: Discount Calculator →
Break-even depends on what you call fixed
Break-even is fixed costs divided by contribution per unit, where contribution is the price less the variable cost — what each sale puts towards the overheads. At 24,000 of fixed costs, a price of 45 and a variable cost of 18, contribution is 27 and break-even is 889 units.
The arithmetic is trivial. The judgement is in the classification, and it depends entirely on the horizon you are looking at. Rent is fixed over a month and negotiable over a year. Staff are fixed over a notice period and variable over a planning cycle. Neither answer is wrong; they answer different questions.
Anyone quoting a break-even figure should say which assumption they made. A number produced under one classification and read under another is a number that will be wrong when it matters.
Work it out: Break-Even Calculator →
Return on investment needs a time period
A 50% return sounds good until you learn it took six years. ROI on its own is a ratio with no time in it, which makes it close to meaningless for comparing anything.
Turning it into an annualised figure is what makes two investments comparable, and the annualised version of a large-sounding total is often unremarkable. That is not a reason to distrust ROI so much as a reason never to quote it without the period attached.
The other thing it hides is what was actually included in the cost. Return on an investment that quietly omitted the staff time is a different number from one that counted it, and both will be presented with the same confidence.
Questions
What is the difference between margin and markup?
Markup is profit divided by cost; margin is profit divided by selling price. Same profit, different denominator — so margin is always the smaller percentage.
What markup gives a 50% margin?
100% — you have to double the cost. A 50% markup only produces a 33.3% margin.
Can margin be over 100%?
No. That would mean the item cost nothing. Markup has no ceiling, so any percentage above 100 can only be a markup.
Is 30% off then 20% off the same as 50% off?
No — it is 44% off, because the second discount applies to the already reduced price. Multiply the remainders: 0.7 times 0.8 is 0.56, so you pay 56%.
How do I work out break-even?
Fixed costs divided by contribution per unit, where contribution is price less variable cost. The hard part is deciding what counts as fixed, which depends on the time horizon.
Why is ROI misleading on its own?
Because it contains no time. A 50% return over one year and over six years are the same ROI and completely different investments. Always annualise before comparing.