Break Even Analysis Formula, Tables, and What a Discount Costs
A break even analysis tells you how many units you have to sell before you have made any money at all. The formula is fixed costs divided by contribution per unit, where contribution is price minus the variable cost of each unit. With $40,000 of fixed costs, a $100 price and $60 of variable cost, each sale contributes $40, so the break-even point is 1,000 units, or $100,000 of revenue. Everything below is that one division, applied to the questions it answers - including the one with the least obvious answer: what a discount does to the number.
The break even point formula
- Contribution per unit = price - variable cost
- Break-even units = fixed costs / contribution per unit
- Contribution margin ratio = contribution per unit / price
- Break-even revenue = fixed costs / contribution margin ratio
- Margin of safety = (expected units - break-even units) / expected units
Fixed costs are the ones that do not move when you sell one more unit: rent, insurance, software, salaries, the accountant. Variable costs are the ones that do: materials, packaging, shipping, payment fees, a per-job subcontractor. Get this split right first: a cost you put in the wrong bucket moves the answer more than any rounding.
A worked break even analysis
These inputs are illustrative. Swap in your own.
- Fixed costs for the year: $40,000
- Price per unit: $100
- Variable cost per unit: $60
Each unit contributes $100 - $60 = $40 toward the fixed costs. That is a contribution margin ratio of 40%: of every dollar that comes in, 40% is left to pay the fixed costs and then become profit. The same ratio sets the break-even ROAS for advertising: the return on ad spend below which each ad-driven order loses money.
- Break-even units: $40,000 / $40 = 1,000 units
- Break-even revenue: $40,000 / 40% = $100,000
The two routes land on the same place, which is a useful self-check on your own numbers.
Now suppose you expect to sell 1,250 units. That is 250 units above break-even, a margin of safety of 20%: sales can fall by 20% before the year stops making money. Profit at 1,250 units is 1,250 x $40 - $40,000 = $10,000.
The margin of safety is the number that tells you whether a slow quarter is an inconvenience or a crisis. Break-even on its own does not.
Break even analysis table: what a price change does
Here is the same business at six prices, with everything else held still. Units are rounded up, because you cannot sell a third of a unit.
| Price change | Price | Contribution per unit | Units to break even | vs today |
|---|---|---|---|---|
| +20% | $120.00 | $60.00 | 667 | -33.3% |
| +10% | $110.00 | $50.00 | 800 | -20% |
| today | $100.00 | $40.00 | 1,000 | - |
| -10% | $90.00 | $30.00 | 1,334 | +33.3% |
| -20% | $80.00 | $20.00 | 2,000 | +100% |
| -30% | $70.00 | $10.00 | 4,000 | +300% |
Read the bottom half carefully. A price cut of 10% does not need 10% more sales - it needs 33.3% more. A 20% cut needs double the volume, and a 30% cut needs four times as many units as today.
Read the top half too. The price rises and the price cuts are not mirror images. A 10% rise means you could lose 20% of your units and still break even; a 10% cut means you need 33.3% more of them.
Why a discount costs more than it looks
The discount comes off the price, but none of it comes off the variable cost. So all of it lands on the contribution, which is the smaller number.
Worked through on the 10% discount:
- The price drops from $100 to $90.00 - a cut of $10.00.
- The variable cost is still $60.
- Contribution drops from $40 to $30.00.
That $10.00 is 10% of the price, but it is 25% of the contribution. Break-even moves from 1,000 units to $40,000 / $30.00 = 1,334 units, which is 33.3% more volume just to stand still.
The intuitive check - “if it brings in more than 10% more customers, it pays for itself” - is wrong on these numbers. Suppose the discount works better than expected and lifts sales by 20%, from 1,250 to 1,500 units:
- Profit before the discount: 1,250 x $40 - $40,000 = $10,000
- Profit after: 1,500 x $30.00 - $40,000 = $5,000
Sales went up 20% and profit went down 50%. To match the old profit at the discounted price, you would need 1,667 units.
Break even analysis table: discounts at four margins
How bad a discount is depends on how much contribution you had to begin with. This table shows the extra volume each discount needs to break even, at four contribution margin ratios. Find the column closest to your own (contribution / price) and read down.
| Discount | 30% margin | 40% margin | 50% margin | 60% margin |
|---|---|---|---|---|
| 5% | +20% | +14% | +11% | +9% |
| 10% | +50% | +33% | +25% | +20% |
| 15% | +100% | +60% | +43% | +33% |
| 20% | +200% | +100% | +67% | +50% |
| 30% | impossible | +300% | +150% | +100% |
Three things stand out:
- Thin margins cannot discount. At a 30% margin, a 10% discount needs +50% more volume and a 20% discount needs +200% - three times the units. A 30% discount is impossible at any volume: it removes the whole contribution, so no number of sales covers the fixed costs.
- Fat margins have room. The same 10% discount at a 60% margin needs +20% more volume, less than half what the thin-margin business needs.
- The discount and the margin meet at “impossible”. Whenever the discount is as large as the contribution margin ratio, there is nothing left per unit.
Using it
Before you agree to a discount, a wholesale price or a volume deal, work out two numbers: your contribution per unit after the discount, and the extra volume that contribution needs. If you cannot see where the extra customers come from, the discount is a price cut you are paying for.
The same arithmetic makes the case for price rises. On these inputs a 10% rise survives losing 20% of your units, while a 10% cut needs 33.3% more of them.
How these were calculated
Every figure on this page was computed twice: once with the same code that builds the break-even kit and the free pricing check linked below, and once with a separate implementation that goes through the contribution margin ratio and break-even revenue, plus a unit-by-unit count to confirm the rounded-up unit totals. The page only builds if the two agree to the cent.
The $40,000 / $100 / $60 business is illustrative. The model assumes variable cost per unit stays the same at every volume and fixed costs stay fixed across the range shown; if either is untrue for you, recompute at the volume you actually expect. This is arithmetic, not financial, tax or legal advice.
If you want to run this on your own price and costs, the free sheet below does break-even, margin of safety and the discount calculation in a few cells:
The paid kit adds the full discount table, a margin-of-safety worksheet, and scripts for the conversations that follow - the customer asking for 10% off, the wholesale enquiry at retail-minus-40% - plus a live Excel workbook: