問9
頻出度★★★
製品 A の生産及び販売に必要な固定費は年間3,000万円である。製品 A の単価が2万円，生産及び販売に掛かる1個当たりの変動費が5,000円であるとき，製品 A の損益分岐点における販売個数は何個か。
平成25年度 春期 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
1,500 comes from the calculation fixed cost 30 million yen ÷ unit price 20,000 yen = 1,500, the mistake of dividing the fixed cost by the unit price itself without subtracting the 5,000 yen variable cost. In reality, 5,000 yen goes out as variable cost for every unit sold, so only 15,000 yen is available to cover the fixed cost. At 1,500 units, sales revenue is 30 million yen while the cost is variable cost 7.5 million yen + fixed cost 30 million yen = 37.5 million yen, giving a loss of 7.5 million yen.
- イ
正解 The break-even point is the point where sales revenue and total cost are equal, so that profit is exactly zero. If the number of units sold is x, then sales revenue = 20,000x yen, and total cost = fixed cost 30,000,000 yen + variable cost 5,000x yen. Setting the two equal gives 20,000x = 30,000,000 + 5,000x, that is, 15,000x = 30,000,000, so x = 2,000 units. Looking at the same thing in terms of contribution margin, each unit sold provides unit price 20,000 yen − variable cost 5,000 yen = 15,000 yen that can go toward covering the fixed cost. The number of units needed to cover the 30,000,000 yen of fixed cost at 15,000 yen per unit is 30,000,000 ÷ 15,000 = 2,000 units, so the correct answer is イ, 2,000 units.
Incorrectウ
4,000 is the break-even sales revenue expressed in units of 10,000 yen, not the number of units sold. The variable cost ratio is 5,000 ÷ 20,000 = 0.25, so break-even sales revenue = 30 million yen ÷ (1 − 0.25) = 40 million yen. Dividing that 40 million yen by the unit price of 20,000 yen gives 2,000 units, which matches the correct answer. This choice confuses the units of sales revenue with the number of units.
Incorrectエ
6,000 comes from the calculation fixed cost 30 million yen ÷ variable cost 5,000 yen = 6,000, the mistake of dividing by the variable cost instead of by the unit price or the contribution margin. If 6,000 units are sold, sales revenue is 120 million yen and total cost is 30 million yen + 30 million yen = 60 million yen, giving a profit of as much as 60 million yen, far beyond the break-even point.
ここがポイント
- Break-even sales volume = fixed cost ÷ (unit selling price − variable cost per unit). The denominator, “unit price − variable cost”, is the contribution margin per unit, and it is the source of funds that covers the fixed cost.
- The break-even point is sometimes asked about as a number of units and sometimes as sales revenue, so do not confuse the units. Break-even sales revenue = fixed cost ÷ (1 − variable cost ratio), where variable cost ratio = variable cost per unit ÷ unit price. Also, always make the money units (10,000 yen and yen) consistent before calculating.
用語