Bonds, returns and business math Updated November 2026

Break-even point

The break-even point is the sales level at which profit is zero. In units it is fixed costs / (price - variable cost per unit), where price minus variable cost is the contribution margin per unit. In revenue it is fixed costs / contribution margin ratio. Each unit above break-even adds its contribution margin.

Syntax

BE units = FC / (P - VC)   BE revenue = FC / ((P - VC) / P)

Part	What it is
`FC`	Total fixed costs for the period
`P`	Selling price per unit
`VC`	Variable cost per unit
`P - VC`	Contribution margin per unit

Examples

FC = 50,000, price 50, variable cost 30
50,000 / (50 - 30)

Result: Break-even = 2,500 units, or 125,000 of revenue

FC = 120,000, price 25, variable cost 15
120,000 / 10

Result: 12,000 units

Revenue method: FC = 50,000, contribution margin ratio 40%
50,000 / 0.40

Result: 125,000 of revenue

Common mistakes

Dividing fixed costs by the price instead of by the contribution margin, which ignores variable costs and understates the break-even.
Including fixed costs per unit in the variable cost; fixed costs stay in the numerator as a total.
Treating a cost as fixed that actually rises with volume (step costs such as extra staff), which makes the break-even too optimistic.

Practice Break-even point

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

Break-even unitsA workshop has fixed costs of $489,000 a year. Each product sells for $12.00 and costs $4.50 in materials and labor. How many units must it sell to break even? Round up to a whole unit.
Break-even revenueA coffee shop has fixed costs of $489,000 a year. Its average sale is $12.00, with $4.50 of variable cost. What sales revenue does it need to break even? Use the contribution margin ratio and do not round to whole sales.

Questions

What is the contribution margin ratio?

(Price - variable cost) / price, the fraction of each sales unit that covers fixed costs and then profit. At price 50 and variable cost 30 it is 40%.

What is the margin of safety?

Actual or budgeted sales minus break-even sales, often as a percentage of actual sales. Selling 3,000 units with a 2,500-unit break-even gives a margin of safety of 500 units, or 16.7%.

Margin vs markupMargin is profit divided by price; markup is profit divided by cost. How to convert between them, set a price from a target margin, examples and the error.
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Payback periodPayback period is the time it takes cumulative cash inflows to equal the initial investment. Formula for even and uneven cash flows, examples, interpolation.
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.