ITPEC IP April 2019 Question 68

1,600 million yen — divide the fixed cost by the marginal profit ratio.

• •Variable cost: 1400 + 600 = 2000, since manufacturing and selling costs both vary with sales
• •Variable cost ratio: 2000 ÷ 4000 = 0.5
• •Marginal profit ratio: 1 − 0.5 = 0.5
• •Break-even sales: 800 ÷ 0.5 = 1600 million yen

Check: at sales of 1,600 the variable cost is 800 and the fixed cost 800, so the profit is zero.

Answer (c)

Why not others:

• •(a) 1,200 — the current operating profit, 4000 − 2000 − 800, not a break-even sales amount
• •(b) 1,231 — leaves out the variable selling cost: 800 ÷ (1 − 1400 ÷ 4000) = 800 ÷ 0.65
• •(d) 2,154 — treats the variable selling cost as fixed: (800 + 600) ÷ 0.65

Key rule: Break-even sales = fixed cost ÷ (1 − variable cost ÷ sales); every cost that moves with sales, selling as well as manufacturing, belongs in the variable cost.

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