ITPEC FE Subject A October 2024 Question 59
When the selling price of a product is $50 and the fixed costs for production and sales are $100,000, which of the following is the number of units to be sold to achieve the desired profit of $50,000? Here, the variable cost ratio is 60%.
Explanation
7,500 units — the contribution margin must cover the fixed costs plus the target profit.
- •Variable cost per unit: 50 × 0.6 = 30 dollars
- •Contribution margin per unit: 50 − 30 = 20 dollars
- •Required units: (100000 + 50000) ÷ 20 = 7500
Check: 7,500 units bring sales of $375,000, variable costs of $225,000 and fixed costs of $100,000, leaving a profit of $50,000.
Answer (b)
Why not others:
- •(a) 5,000 — is the break-even quantity, 100000 ÷ 20, with zero profit; the same number comes from dividing by the $30 variable cost instead of the $20 margin
- •(c) 10,000 — gives a profit of 10000 × 20 − 100000 = 100000, double the target
- •(d) 12,500 — gives a profit of 12500 × 20 − 100000 = 150000, three times the target
Key rule: Required units = (fixed costs + target profit) ÷ (price × (1 − variable cost ratio)); the break-even quantity is the same formula with the target profit set to zero.
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