問14
頻出度★★★
売価が 20 万円の新商品を売り出して，8,000 万円を売り上げた。固定費は 4,000 万円であり，利益は 2,000 万円のマイナスであった。利益をマイナスにしないためには，あと何個以上売る必要があるか。
平成21年度 春期 ITパスポート試験 問14
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 14
Incorrectア
100 is the loss of 20 million yen divided by the unit price of 200,000 yen (20 million ÷ 200,000 = 100). It comes from the mistake of ignoring the variable cost and assuming that the whole selling price becomes profit. In reality, each unit sold increases the profit only by the contribution margin of 50,000 yen, so selling 100 more units improves the profit by only 50,000 × 100 = 5 million yen, leaving a profit of −20 million + 5 million = −15 million yen, which is still negative.
Incorrectイ
200 is the value obtained by dividing the fixed cost of 40 million yen by the unit price of 200,000 yen (40 million ÷ 200,000 = 200), the kind of value that appears when the unit price is used as the divisor instead of the contribution margin. Even if 200 more units are sold, the profit improves by only 50,000 × 200 = 10 million yen, leaving a profit of −20 million + 10 million = −10 million yen, so the loss is still not eliminated.
- ウ
正解 The correct answer is ウ (400 units). First, organize the current situation numerically. The product sells for 200,000 yen each and generated 80 million yen in sales, so the number of units sold is 80 million ÷ 200,000 = 400 units. Next, work backward to find the variable cost. From profit = sales − variable cost − fixed cost, we get −20 million = 80 million − variable cost − 40 million, so the variable cost is 60 million yen. The variable cost per unit is 60 million ÷ 400 = 150,000 yen, so the contribution margin per unit (unit price − variable cost per unit) is 200,000 − 150,000 = 50,000 yen. This is the key to the solution: the fixed cost of 40 million yen does not increase when more units are sold, so every additional unit improves the profit by the full contribution margin of 50,000 yen. The number of additional units needed to wipe out the current loss of 20 million yen is 20 million ÷ 50,000 = 400 units. Therefore, if 400 or more additional units are sold, the profit is no longer negative. As a check, when 800 units are sold in total, sales are 160 million yen, the variable cost is 120 million yen, and the fixed cost is 40 million yen, so the profit is exactly 0, confirming that the break-even point is reached.
Incorrectエ
800 is the sales volume at the break-even point itself (fixed cost of 40 million yen ÷ contribution margin of 50,000 yen = 800 units), not the number of additional units required. Since 400 units have already been sold, 800 − 400 = 400 additional units are enough. The question asks not for the total sales volume but for the additional amount, that is “how many more units”, so answering without subtracting the units already sold gives 800.
ここがポイント
- Contribution margin = unit price − variable cost per unit. The fixed cost does not change even when the sales volume increases, so every additional unit sold raises the profit by one contribution margin. Therefore, “how many more units are needed to wipe out the loss” is found as loss amount ÷ contribution margin per unit.
- Break-even sales volume = fixed cost ÷ contribution margin per unit expresses the total sales volume. When a question asks for the number of additional units to sell, the units already sold must be subtracted from it (in this question, 800 − 400 = 400 units).
- Even when the variable cost is not given directly, it can be calculated backward by substituting the known sales, fixed cost, and profit into the relation profit = sales − variable cost − fixed cost.
用語