Break-even analysis
Contribution and break-even
- Contribution is how much each sale adds towards the fixed costs:
$$\text{contribution per unit} = \text{selling price} - \text{variable cost per unit}$$
- Break-even is where total revenue = total costs, so profit is zero:
$$\text{break-even point} = \frac{\text{fixed costs}}{\text{contribution per unit}}$$
Practice
A product sells for 20 with a variable cost of 12 per unit. What is the contribution per unit (in dollars)?
Contribution = selling price − variable cost = 20 − 12 = 8.
Practice
Fixed costs are 4,000 and contribution is 8 per unit. What is the break-even point (in units)?
Break-even = fixed costs ÷ contribution per unit = 4,000 ÷ 8 = 500 units.
Margin of safety & limits
$$\text{margin of safety} = \text{actual output} - \text{break-even output}$$
- A large margin means sales can fall a lot before a loss.
- Limitations: it assumes price and costs stay the same, and that everything made is sold.
Practice
Actual output is 700 units and the break-even output is 500. What is the margin of safety (in units)?
Margin of safety = actual − break-even = 700 − 500 = 200 units.
You've got it
Key idea
- contribution = price − variable cost per unit
- break-even = fixed costs ÷ contribution per unit (profit = 0 there)
- margin of safety = actual − break-even output; the model assumes constant price/costs and all sold