Margin and markup are different numbers and confusing them is expensive: a 50 per cent markup is a 33 per cent margin. This calculates both from any two inputs, prices backwards from a target, and works out how many units cover your fixed costs.
Margin is profit divided by the selling price. Markup is profit divided by the cost. Buy at 100, sell at 150, and you have a 50 per cent markup but a 33.3 per cent margin. Both describe the same transaction; they just divide by different things.
The expensive mistake is applying a markup when you meant a margin. A business that wants 40 per cent margin and multiplies cost by 1.4 gets 28.6 per cent — and under-prices every single item, systematically, until someone notices.
For a target margin, divide by one minus the margin: a 40 per cent margin on a cost of 100 is 100 / 0.6 = 166.67. For a markup, multiply: 100 x 1.4 = 140. Note how far apart those two prices are for the same stated percentage.
Every unit sold contributes price minus variable cost towards the fixed costs. Divide fixed costs by that contribution and you have the units needed before anything becomes profit. The lever most people reach for is cutting fixed costs, but raising the price or shaving variable cost moves the break-even point far more, because both increase the contribution on every unit.
Margin is profit as a share of the selling price; markup is profit as a share of the cost. Buy at 100 and sell at 150 and you have a 50% markup but a 33.3% margin. Pricing as if they were the same is a common way to under-price systematically.
Divide the cost by one minus the margin, not multiply by one plus it. For a 40% margin on a cost of 100: 100 / 0.6 = 166.67. Multiplying by 1.4 gives 140, which is only a 28.6% margin.
How many units you must sell before fixed costs are covered and further sales become profit. It falls out of the contribution per unit - price minus variable cost - so raising the price or cutting variable cost moves it far more than trimming fixed costs does.
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