Bonds, returns and business math Updated November 2026

Margin vs markup

Margin and markup are the same profit measured against different bases: margin = (price - cost) / price, markup = (price - cost) / cost. A 50% markup is a 33.3% margin. To price for a target margin, divide cost by (1 - margin); for a target markup, multiply cost by (1 + markup).

Syntax

margin = (P - C) / P   markup = (P - C) / C   P = C / (1 - margin)   margin = markup / (1 + markup)

Part	What it is
`P`	Selling price
`C`	Cost of the item
`margin`	Gross margin as a share of price
`markup`	Profit as a share of cost

Examples

Cost 30, price 50
margin = 20 / 50; markup = 20 / 30

Result: Margin = 40%; markup = 66.7%

Price for a 25% margin on cost 60
60 / (1 - 0.25)

Result: P = 80.00 (markup 33.3%)

Price for a 30% markup on cost 50
50 x 1.30

Result: P = 65.00 (margin 23.1%)

Common mistakes

Adding the target margin to cost (60 x 1.25 = 75) when a 25% margin requires 60 / 0.75 = 80; the first gives only a 20% margin.
Quoting a markup as if it were a margin to a customer or in a report; markup is always the larger number for the same profit.
Forgetting that margin cannot exceed 100% while markup can be any size: a 200% markup is a 66.7% margin.

Practice Margin vs markup

These drills check your answer on live data, free, no account needed.

Price for a target marginAn item costs $10.75 to buy. What selling price gives a gross margin of 20% of the selling price?
Margin from a markupA retailer prices goods at cost plus a 20% markup. What is its gross margin as a percent of the selling price?

Questions

Is a 50% margin the same as a 50% markup?

No. A 50% margin means profit is half the price (markup 100%). A 50% markup means profit is half the cost (margin 33.3%).

How do I convert margin to markup?

markup = margin / (1 - margin). A 40% margin is a 0.4 / 0.6 = 66.7% markup.

Break-even pointBreak-even units = fixed costs / (price - variable cost per unit); break-even revenue = fixed costs / contribution margin ratio. Examples, margin of safety.
Cost of trade creditSkipping an early payment discount such as 2/10 net 30 is an expensive loan: annual cost = d / (1 - d) x 365 / extra days, about 37%. Examples, when to pay.
Holding period returnHolding period return is (ending value - beginning value + income) / beginning value. Stock and bond examples, how to annualize an HPR and common mistakes.
Depreciation methodsThree depreciation methods with worked examples on the same 10,000 asset: straight-line, double-declining balance and sum-of-the-years-digits, plus Excel.