IPA FE Subject A sample Question 59
A question IPA Japan published in 基本情報技術者試験 科目A サンプル問題 問59, translated into English. ITPEC is based on the same exams.
When sales are 100 million yen, variable costs are 60 million yen and fixed costs are 30 million yen. Assuming that the variable cost ratio and the fixed costs do not change, what are the sales, in millions of yen, required to achieve a target profit of 18 million yen?
Explanation
120 million yen — the marginal profit from sales must cover the fixed costs plus the target profit.
- •Variable cost ratio: 60 ÷ 100 = 0.6, so each yen of sales leaves a marginal profit of 1 − 0.6 = 0.4
- •Required marginal profit: fixed costs + target profit = 30 + 18 = 48 million yen
- •Required sales: 48 ÷ 0.4 = 120 million yen
Check: at 120, variable costs are 120 × 0.6 = 72, and profit is 120 − 72 − 30 = 18.
Answer (b)
Why not others:
- •(a) 108 — adds the target profit to the current total cost, 60 + 30 + 18, as if variable costs stayed at 60; at sales of 108 they are 64.8 and profit is only 13.2
- •(c) 156 — gives a profit of 156 × 0.4 − 30 = 32.4, well above the target
- •(d) 180 — gives a profit of 180 × 0.4 − 30 = 42, more than twice the target
Key rule: Sales for a target profit = (fixed costs + target profit) ÷ (1 − variable cost ratio); with a target profit of 0 this is the break-even point.
Corporate Activities · AI-written, may contain errors
This question comes from the past questions IPA Japan publishes, translated into English by ITPEC Practice. ITPEC Practice is an independent study tool and is not affiliated with IPA or ITPEC. See the original paper (PDF) or Report an issue.