How can two businesses with the same sales have different break-even points?

Define cost behavior over a stated range

The U.S. Small Business Administration presents a single-product break-even calculation using fixed cost divided by price less variable cost per unit. OpenStax’s managerial-accounting material explains the related cost-volume-profit framework. These are planning models rather than proof that future demand will appear.

Stipulate two fictional businesses selling one identical teaching unit at 50. Over the modeled range, A has variable cost 30 per unit and fixed operating costs 1,000 per period. B has variable cost 20 and fixed operating costs 2,000. Assume every produced unit sells, price and costs stay constant, and there are no inventory changes, interest or taxes.

Compute the two break-even points

A contributes 50−30=20 per unit, so its zero-profit volume is 1,000/20=50 units. B contributes 30 per unit, so its zero-profit volume is 2,000/30=66.666667 units. If units cannot be divided, B needs 67 units to avoid a loss; at 67 its modeled profit is 10.

At 50 units, A’s sales 2,500 less variable costs 1,500 and fixed costs 1,000 leaves zero. B’s sales 2,500 less variable costs 1,000 and fixed costs 2,000 leaves a 500 loss. The higher contribution per unit does not by itself establish the lower break-even point.

Find where the profit ordering changes

Write profit as 20 q−1,000 for A and 30 q−2,000 for B. Equating the expressions gives q=100. At 100 units, both have sales 5,000 and operating profit 1,000. Their expense mixes differ even though those two headline numbers match.

At 80 units, A’s profit is 600 and B’s is 400. At 120, A’s is 1,400 and B’s is 1,600. The ordering reverses because each extra unit adds 30 to B’s contribution but only 20 to A’s, provided the assumed capacity and cost behavior still hold.

Measure sensitivity around one positive-profit base

From 100 to 120 units, volume rises 20%. A’s profit rises 40%, from 1,000 to 1,400; B’s rises 60%, from 1,000 to 1,600. Around the 100-unit base, contribution divided by operating profit is 2 for A and 3 for B. Those ratios describe the modeled operating leverage at that base.

This proportional comparison becomes unstable when base profit is zero or near zero. It is not a constant risk score for every volume. A 20% volume decline to 80 produces a 40% profit decline for A and a 60% decline for B under this same linear model.

Separate operating profit from cash funding

Fixed expense can include noncash depreciation, while cash may be needed for equipment, receivables, interest, tax or debt repayment outside this simplified profit equation. Conversely, a cash payment may settle a prior-period obligation. A zero operating-profit calculation is therefore not a complete liquidity plan.

Real costs can step up when capacity expands, and selling price, returns or product mix can change with volume. Define the relevant range and test those assumptions before extending a straight line. The worksheet supplies a cost bridge, not a recommendation to choose either operating model.

Method, sources, and limits

All unit prices, costs and volumes are invented teaching inputs, recomputed during drafting on 27 October 2026. No business’s demand or profitability was measured. The analysis excludes financing and tax advice; AI-assisted drafting is not qualified human accounting or business review.