Break-Even Sensitivity and Impossible Results

Break-even sensitivity asks which operating assumptions most change the volume needed to cover costs. It is more useful than calculating one threshold and treating it as permanent. Change one input at a time to understand its effect, then test combinations that could realistically occur together. Keep the reporting period and the definition of a unit constant.

Recalculate each assumption from the formula

Assume hypothetical monthly fixed costs of $9,000, a $50 selling price, and $32 variable cost per unit. Contribution is $18, so break-even is 500 units. Reducing price to $47 lowers contribution to $15 and raises break-even to 600 units. Raising variable cost to $35 has the same effect when price stays $50.

The combined case requires 750 units, not 700. Adding the separate 100-unit effects would be incorrect because both changes affect the denominator. Recalculate the full formula for each combination instead of adding threshold changes from isolated cases.

Test whether the threshold can be delivered

If capacity is limited to 650 units, the combined scenario cannot break even within available capacity. At 650 units, operating profit is 650 × $12 − $9,000 = −$1,200. The mathematical 750-unit threshold still exists, but it is operationally unavailable under the stated capacity. Show both results rather than presenting the threshold alone.

For a fractional threshold, round units upward only when units are indivisible. At $9,000 fixed costs and $17 contribution, the threshold is approximately 529.4118 units, so 530 whole units are required. Selling 529 units leaves a $7 loss; 530 units produces $10 of modeled profit. Retain full precision until that final unit decision.

Handle nonpositive contribution explicitly

With positive fixed costs and zero contribution, no sales volume covers those fixed costs. With negative contribution, additional sales increase the loss. A negative or zero denominator should therefore produce an explanation, not an arbitrary zero-unit answer.

If both fixed costs and contribution are zero, every volume produces zero modeled profit; there is no unique threshold. If fixed costs are zero and contribution is negative, zero sales is the only nonloss point, while positive sales lose money. These edge cases matter because the formula alone cannot describe them correctly. Break-even remains a simplified operating model and does not establish customer demand or cash availability.

Method references: OpenStax: Break-Even Sensitivity Analysis. Accessed October 22, 2026. All dollar figures are hypothetical worked examples.