Costs and revenue: the building blocks
Fixed costs (FC) do not change with output in the short run: rent, salaries, insurance, loan interest.
Variable costs (VC) rise with each unit made: raw materials, packaging, power used by machines. Total variable cost = variable cost per unit × quantity.
Total cost (TC) = FC + VC. Total revenue (TR) = price × quantity sold.
Profit = TR − TC. If this is negative, it is a loss.
Contribution and the break-even point
Contribution per unit = selling price − variable cost per unit. It is the money each unit adds towards paying fixed costs (and then profit).
The break-even point is the output where TR = TC, so profit = 0:
Break-even output = Fixed costs ÷ Contribution per unit
Example: FC = $2,000, price = $5, VC = $3 per unit. Contribution = $2. Break-even = 2,000 ÷ 2 = 1,000 units. Break-even revenue = 1,000 × $5 = $5,000.
Contribution margin ratio
Contribution ÷ price gives the share of each sale that is contribution (here 2 ÷ 5 = 40%). Break-even revenue = FC ÷ this ratio = 2,000 ÷ 0.4 = $5,000.
The break-even chart
A break-even chart plots money (vertical) against output (horizontal):
- FC: a flat line.
- TC: starts at FC and slopes up by the variable cost per unit.
- TR: starts at zero and slopes up by the price.
The lines cross at the break-even point. Left of it, the gap between TC and TR is a loss; right of it, the gap is profit. A steeper TR line (higher price) or flatter TC line (lower variable cost) moves the break-even point to the left.
Margin of safety and target profit
Margin of safety = actual (or planned) sales − break-even sales. It shows how far sales can fall before the business makes a loss. As a percentage: margin of safety ÷ actual sales × 100.
Profit at a given output = (quantity × contribution) − FC.
Output for a target profit = (FC + target profit) ÷ contribution per unit.
Maximum profit, uses and limits
Break-even uses straight lines. In real markets, to sell more a firm often has to cut its price, and costs per unit can rise when a factory is very busy. Then profit does not grow forever: it is largest where the extra revenue from one more unit (marginal revenue) equals the extra cost (marginal cost), MR = MC.
Uses: testing a business idea before starting, setting prices, deciding whether to make or buy, showing a bank a plan.
Limits: assumes all output is sold, a single price, and costs that split neatly into fixed and variable; it is only as good as its forecasts.
Try it: your own stall
Plan a lemonade stall. Write your fixed costs (table hire, jug) and the cost per glass (lemons, sugar, cup). Choose a price. Work out the break-even number of glasses. Then set the same numbers on the sliders in the 3D and check that the orange dot lands at your answer.
Key formulas and definitions
- Total cost = Fixed cost + Variable cost per unit × Q
- Total revenue = Price × Q
- Contribution per unit = Price − Variable cost per unit
- Break-even output = Fixed cost ÷ Contribution per unit
- Break-even revenue = Break-even output × Price = FC ÷ (contribution ÷ price)
- Margin of safety = Actual sales − Break-even sales
- Profit = Q × Contribution − Fixed cost
- Output for target profit = (FC + Target profit) ÷ Contribution
Worked examples
1. Price $5, variable cost $3 per unit, fixed costs $2,000. Find the break-even output.
Contribution = 5 − 3 = $2. Break-even = 2,000 ÷ 2 = 1,000 units.
2. Using the same numbers, sales are 1,500 units. Find the margin of safety (units and %).
MOS = 1,500 − 1,000 = 500 units. As %: 500 ÷ 1,500 × 100 = 33.3%.
3. Find the profit at 1,500 units.
Profit = 1,500 × 2 − 2,000 = 3,000 − 2,000 = $1,000.
4. A bakery has fixed costs of ₹36,000 a month. A cake sells for ₹500 and costs ₹320 to make. How many cakes to break even? What is break-even revenue?
Contribution = 500 − 320 = ₹180. Break-even = 36,000 ÷ 180 = 200 cakes. Revenue = 200 × 500 = ₹1,00,000.
5. The bakery wants a profit of ₹18,000 a month. How many cakes must it sell?
Q = (36,000 + 18,000) ÷ 180 = 54,000 ÷ 180 = 300 cakes.
6. A firm raises its price from $5 to $6 (VC $3, FC $2,000). What happens to the break-even point?
New contribution = 6 − 3 = $3. Break-even = 2,000 ÷ 3 ≈ 666.7, so 667 units. It falls from 1,000 because each unit pays off more of the fixed cost. (Round up: you cannot sell part of a unit.)
7. Fixed costs €12,000; contribution margin ratio 30%. Find break-even revenue.
Break-even revenue = FC ÷ ratio = 12,000 ÷ 0.30 = €40,000.
Common mistakes
- Dividing fixed cost by price instead of by contribution (price − variable cost).
- Adding fixed cost again for each unit; fixed cost is counted once for the whole period.
- Rounding the break-even output down. Always round up to the next whole unit.
- Thinking break-even means "no sales"; it means sales exactly cover all costs, so profit is zero.