問9
頻出度★★★
販売価格1,000円の商品の利益計画において，10,000個売った場合は1,000千円，12,000個販売した場合は1,800千円の利益が見込めるとき，この商品の1個当たりの変動費は何円か。
平成29年度 秋期 ITパスポート試験 問9
ストラテジ系企業活動 › 会計・財務
This question's explanation and your answers so far.
解説
問 9
Incorrectア
400 yen is the value of the 'marginal profit per unit (= selling price − variable cost)', not the variable cost itself. Since the question asks for the variable cost, you must go one step further from here: selling price 1,000 yen − marginal profit 400 yen = 600 yen. This is the mistake of giving the marginal profit as the answer.
- イ
正解 It can be expressed as: Profit = (selling price − variable cost per unit) × number of units sold − fixed cost. The selling price, variable cost, and fixed cost are all constant regardless of the number of units sold, so when you take the difference between the two profit plans, the fixed cost cancels out and only the marginal profit (= selling price − variable cost) remains. When the selling price is 1,000 yen, selling 10,000 units gives a profit of 1,000 thousand yen and selling 12,000 units gives a profit of 1,800 thousand yen, so when the quantity rises by 12,000 − 10,000 = 2,000 units, the profit rises by 1,800 − 1,000 = 800 thousand yen (800,000 yen). This increase equals 'marginal profit per unit × increase in units', so the marginal profit per unit = 800,000 ÷ 2,000 = 400 yen. Therefore the variable cost = selling price − marginal profit = 1,000 − 400 = 600 yen, and the correct answer is イ. Check: fixed cost = 400 × 10,000 − 1,000,000 = 3,000,000 yen, and for 12,000 units as well, 400 × 12,000 − 3,000,000 = 1,800,000 yen, which matches.
Incorrectウ
850 yen is the value obtained when the marginal profit is mistakenly calculated as 150 yen (1,000 − 850). Correctly, the marginal profit is the increase in profit of 800 thousand yen ÷ the increase of 2,000 units = 400 yen, which does not match 150 yen.
Incorrectエ
900 yen is the value when the marginal profit is mistaken for 100 yen (1,000 − 900). It gets the difference calculation between the two plans wrong and is inconsistent with the actual marginal profit of 400 yen (and is too large as a variable cost).
ここがポイント
- Marginal profit (contribution margin) = selling price − variable cost per unit. When you take the difference between the two sales plans, the fixed cost cancels out, and the marginal profit per unit can be found from 'increase in profit ÷ increase in units'.
- Variable cost = selling price − marginal profit. In profit planning and break-even point analysis, fixed costs and variable costs are considered separately (the idea behind direct costing).
用語