Fixed costs, variable costs and the contribution
Fixed costs do not change with how much you sell in the period: rent, salaries, insurance, software subscriptions. Variable costs rise with every unit: materials, packaging, delivery, card fees. Some costs are a mixture, so you decide which side they belong on.
Each unit you sell brings in its price and costs its variable cost. What is left, price − variable cost, is the contribution. It goes first to paying the fixed costs, and once those are covered, what is left is profit. With a price of 25 and a variable cost of 10, every unit contributes 15.
How the break-even point is worked out
You break even when the contributions add up to the fixed costs. So break-even units = fixed costs ÷ contribution per unit. With fixed costs of 3,000 and a contribution of 15, that is 3,000 ÷ 15 = 200 units, and the sales are 200 × 25 = 5,000.
The sales figure can also be found without the units: fixed costs ÷ contribution margin ratio, where the ratio is the contribution as a share of the price. Here 15 ÷ 25 = 60%, and 3,000 ÷ 0.6 = 5,000.
The answer is often not a whole number. With fixed costs of 2,000, a price of 15 and a variable cost of 6, the contribution is 9 and 2,000 ÷ 9 = 222.22. You need 223 units, which is why the calculator rounds up. The sales for those 223 units are 223 × 15 = 3,345. The exact break-even sales, 2,000 ÷ 0.6 = 3,333.33, are shown too.
Profit targets, margin of safety and what moves the point
To reach a profit target, treat it as extra fixed cost: units = (fixed costs + target) ÷ contribution. A target of 2,000 on the first example needs 5,000 ÷ 15 = 333.33, so 334 units and sales of 8,350.
If you expect to sell 300 units, the profit is 300 × 15 − 3,000 = 1,500. Your margin of safety is how far sales can fall before you stop making a profit: (300 − 200) ÷ 300 = 33.33%.
- Cutting fixed costs by 10%, from 3,000 to 2,700, lowers the break-even point from 200 to 180 units.
- Raising the price from 25 to 27 lifts the contribution to 17 and lowers the point to 177 units.
- Cutting the variable cost from 10 to 8 does the same.
If you are working from percentages, the margin calculator shows how price and cost relate as a margin.
What this calculator assumes
- One product, one price. If you sell several things, use an average price and cost, or work them out together on a weighted basis.
- Costs stay in their groups. Real fixed costs can jump, for example when you need a second employee at a certain volume.
- Everything sold is paid for. It ignores discounts, returns and the timing of cash.
- One period. Fixed costs must be for the same period as the units. Monthly fixed costs give monthly units.