Contribution pays the fixed bill
Fenwick Prints sells framed posters for $50. The frame, paper and ink cost $30 a print. Rent and the studio's one employee cost $4,000 a month whether it sells one print or a thousand. The owner wants one number: how many prints pay the bills.
Contribution is what a sale leaves after its own variable costs. Unit contribution = price − variable cost = 50 − 30 = $20. Which costs count as variable is a stated definition, not a law of nature; say which ones you used. Contribution pays the fixed costs first, and only the remainder is profit.
Break-even is fixed costs divided by unit contribution. 4,000 ÷ 20 = 200 prints a month, provided contribution is positive. At 250 prints, profit = 250 × 20 − 4,000 = $1,000. If break-even lands on a fraction, round up: 205.5 prints means 206, because 205 still loses money.
- Total contribution ($20 a print)
- Fixed costs
This is a Scorecard (income statement) question with a stock-or-flow twist. Fixed costs are a flow per period, so break-even is a volume per period. Two hundred prints means 200 a month, every month, not 200 and done.
When variable cost exceeds price, volume makes the loss bigger. At $60 of variable cost, each print loses $10 before rent, so 250 prints lose 250 × 10 + 4,000 = $6,500 and 500 prints lose $9,000. There is no volume that breaks even, because the fixed cost never gets covered. Only price, cost, mix or the model itself can fix negative contribution.
Fixed means fixed within a range and a period. A second employee, a bigger studio or a new press is a step, and each step moves the line. A straight line drawn past the studio's capacity is a drawing, not a plan.
Margin of safety is how far sales can fall before break-even. At 250 prints against a break-even of 200, it is 50 prints, or 50 ÷ 250 = 20%. Operating leverage is how sharply profit reacts when fixed costs are large. Sell 275 prints instead of 250, a 10% rise, and profit goes from $1,000 to 275 × 20 − 4,000 = $1,500, a 50% rise. That is arithmetic near break-even, not evidence that demand is volatile.
Fenwick's fixed costs rise to $9,000 a month. It lifts the price to $80 and variable cost is now $50. Break-even?