Return to the application

What does one more sale cover?

This four-input lesson compares assumed sales and entered costs. It cannot find the best price without a justified demand model.

Predict before calculating

  1. Keep price $20, variable cost $12 and fixed cost $500. Predict the result for 100, 62 and 63 sold units.
  2. Save the 100-unit default as your reference. Change price to $22, keeping 100 assumed units; then change quantity to 70. Which assumption changes the conclusion?
  3. Load the ten-cent-contribution case. Predict the minimum non-loss quantity with fixed costs $100 and then $100.01.
Reveal the worked answers

Contribution is $20 − $12 = $8 per unit. $8 × 100 − $500 = $300. At 62 units, $496 − $500 = −$4; at 63, $504 − $500 = $4. The theoretical threshold is 62.5, while whole-unit cost coverage requires 63. The default's assumed sales cushion is 100 − 63 = 37 units.

At $22 and 100 units the result is $500. At the same price and 70 units it is $200, below the original $300. Neither volume is predicted: a lower break-even quantity alone does not make a price preferable.

$19.90 − $19.80 = $0.10. $100 ÷ $0.10 = 1000 units. $100.01 ÷ $0.10 = 1000.1, requiring 1001 whole units. Integer cents avoid floating-point rounding at the boundary.

Explain the edge cases

Try price zero, unit cost above price, fixed cost zero, quantity zero, and price $0.01/cost zero/fixed $1,000,000. Predict whether more sales can help.

Check the boundary explanations

Zero quantity leaves a loss equal to positive fixed costs. Nonpositive contribution cannot cover positive fixed costs. With zero fixed cost, zero units is a minimum non-loss quantity, but negative contribution makes every positive quantity a loss; zero contribution makes every quantity exactly cover entered costs. Positive contribution makes every added unit improve the result. With one-cent contribution and $1,000,000 fixed costs the threshold is 100,000,000 units, beyond the supported scenario quantity limit; the app must say so.

Keep your reasoning

Copy the scenario record before leaving the tab. It includes the four inputs, USD/period units, formula, answer and limits. The reference table is temporary and reload restores the synthetic default.

Extension: price with demand response

Specify a demand-versus-price assumption with a source or an explicit hypothetical range. Define the decision objective, feasible prices, uncertainty and an independent validation plan. Recompute volume at every candidate price; do not label a price “best” by holding sales constant without justification. Demand response is outside this shipped deterministic model.