Buy something for 60 and sell it for 100. You made 40. Everyone agrees on that. The disagreement starts when you turn it into a percentage.
Two denominators
Margin is the profit as a share of the price: 40 out of 100, so 40%. Markup is the profit as a share of the cost: 40 out of 60, so 66.7%. Same sale, same 40, two percentages, and the markup is always the bigger one.
markup % = (price - cost) / cost x 100
Neither is wrong. Finance people talk in margin because it lines up with the profit and loss account. Buyers talk in markup because they start from what they paid. The trouble comes when the two words are used as if they meant the same thing.
Where the money goes
Someone decides the business needs 40%. They take the cost, add 40%, and call it a price. 60 plus 40% is 84. Look at that sale from the other side: 24 profit on an 84 price is a 28.6% margin, not 40. Every line priced that way is short by more than a quarter of the profit it was meant to make, and the spreadsheet looks fine, because it says 40% in the cell.
To earn a 40% margin you divide, not multiply:
= 60 / (1 - 0.40)
= 100
The quick conversions
- Markup to margin:
margin = markup / (100 + markup). A 50% markup is a 33.3% margin. - Margin to markup:
markup = margin / (100 - margin). A 50% margin is a 100% markup, which is why "keystone" pricing, doubling the cost, gives a retailer half the ticket. - A 100% margin is impossible. It would mean the item cost nothing.
What a discount does to either one
A discount comes off the price. Your cost does not move. So the whole discount comes out of profit, and the effect is bigger than it looks. At a 30% margin, a 10% discount removes a third of the profit on that sale, and the margin after the discount is 22.2%, not 20%.
To bank the same money after a 10% discount at a 30% margin, you have to sell 50% more units. If the discount is as big as the margin, no volume gets it back: every extra sale is at or below cost.
Pick one, and put it on the wall
The fix is not a formula. It is a decision. Choose margin or markup, write which one it is next to every percentage in the business, and price from cost the right way round. The calculator below shows both numbers every time, because the day you need it is the day someone says "forty percent" and means the other one.