ITPEC FE Morning October 2019 Question 78
When a company sells a product at 17 dollars per unit, and the fixed costs and the variable costs are as shown in the tables below (in dollars), how many units does the company have to sell to earn a profit of 42,000 dollars?
Fixed costs:
Variable costs per unit:
Explanation
18,200 units — each unit contributes its price minus its variable cost, and the contributions must cover the fixed costs plus the target profit.
- •Fixed costs: 130,000 + 10,000 = 140,000 dollars
- •Variable cost per unit: 4 + 3 = 7 dollars
- •Contribution per unit: 17 − 7 = 10 dollars
- •Units needed: (140,000 + 42,000) ÷ 10 = 18,200
Check: profit at a quantity N is 10N − 140,000, so 10 × 18,200 − 140,000 = 42,000 dollars, and the break-even point is 14,000 units.
Answer (d)
Why not others:
- •(a) 10,200 — below break-even: 102,000 − 140,000 is a loss of 38,000 dollars
- •(b) 14,200 — only 200 units past break-even, a profit of 2,000 dollars
- •(c) 16,200 — a profit of 22,000 dollars, 20,000 short of the target
Key rule: Required quantity = (fixed costs + target profit) ÷ (price − variable cost per unit); with a profit of zero it gives the break-even quantity.
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