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Business Strategy and Accounting Basics

A business has fixed costs of ¥27 million and a variable cost ratio of 40%, and has no costs other than variable and fixed costs. Which is the sales needed to achieve an operating profit margin (operating profit ÷ sales) of 15%?

  1. A¥45 million
  2. B¥60 million
  3. C¥108 million
Show answer and explanation

Answer: B. ¥60 million

If sales are S (in ¥ million), operating profit is S − 0.4S − 27 = 0.6S − 27, and this must equal 0.15S, so 0.45S = 27 and S = ¥60 million. In other words, of the contribution margin ratio of 0.6, 0.15 is kept as profit and the remaining 0.45 covers the fixed costs. As a check, at sales of ¥60 million operating profit is 36 − 27 = ¥9 million, and 9 ÷ 60 = 15%.

  • A. This is break-even sales (27 ÷ 0.6), at which operating profit is zero.
  • B. Correct. It is fixed costs ÷ (contribution margin ratio − target margin) = 27 ÷ 0.45.
  • C. This divides by 0.25, the variable cost ratio of 0.4 minus the margin of 0.15. The margin should be subtracted from the contribution margin ratio (0.6), not from the variable cost ratio.
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