For one fictional school market day, fixed costs are CAD 120, selling price is CAD 5 per item and variable cost is CAD 3 per item. How many items must be sold to break even? Assume every item made is sold and costs/prices stay constant.
Break-even is 60 items for the market day.
- Find contribution per item
Each sale brings in CAD 5 and uses CAD 3 of variable cost. The remaining CAD 2 contributes toward fixed costs before profit.
\(c=p-v=5-3=2\text{ CAD/item}\)
- Cover the fixed costs
Divide fixed costs for the day by contribution per item. CAD divided by CAD/item gives items.
\(Q^*=\frac{F}{p-v}=\frac{120}{5-3}=60\text{ items}\)
- Check revenue against total cost
At 60 items, revenue is CAD 300. Total cost is CAD 120 + CAD 180 = CAD 300, so profit is zero.
\(\pi=5(60)-[120+3(60)]=0\)
At 59 items profit would be CAD −2; at 61 it would be CAD 2. The threshold is therefore 60 whole items.