問34
頻出度★★★
ある商品を5,000個販売したところ，売上げが6,000万円，利益が400万円となった。商品1個当たりの変動費が7,000円であるとき，利益を1,000万円以上にするためには，少なくともあと何個販売すればよいか。
令和7年度 ITパスポート試験 問34
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 34
Incorrectア
“500” is too small as an additional quantity. Even if 500 more units are sold, the added profit is only the contribution margin of 5,000 yen/unit × 500 units = 2.5 million yen, making the profit 4 million yen + 2.5 million yen = 6.5 million yen, which falls short of the 10 million yen target. To increase profit by 6 million yen, an additional 6 million yen ÷ 5,000 yen/unit = 1,200 units is required, so 500 units is not enough.
- イ
正解 First, find the selling price per unit: sales of 60 million yen ÷ 5,000 units = 12,000 yen/unit. Against this, the variable cost is 7,000 yen/unit, so the contribution margin (marginal profit) left for each unit sold is 12,000 yen − 7,000 yen = 5,000 yen/unit. Next, work backward from the initial data to find the fixed cost: the total contribution margin is 5,000 yen × 5,000 units = 25 million yen, and what remains after subtracting the fixed cost is the profit of 4 million yen, so the fixed cost = 25 million yen − 4 million yen = 21 million yen. Now, let N be the total sales volume needed to make the profit 10 million yen or more: “5,000 yen × N − 21 million yen ≧ 10 million yen”, that is 5,000 yen × N ≧ 31 million yen ⇒ N ≧ 6,200 units. The question asks how many more units must be sold in addition to the initial 5,000 units, so 6,200 units − 5,000 units = 1,200 units. Therefore the correct answer is イ. The key idea: only the contribution margin beyond the fixed cost becomes profit, and once you pass the break-even point, each additional unit sold builds up 5,000 yen of profit.
Incorrectウ
“6,200” is the total sales volume needed to make the profit 10 million yen or more, not the number of additional units to sell. The question (stem) asks how many more units must be sold relative to the initial 5,000, so the answer is the total of 6,200 minus the 5,000 already sold, namely 1,200 units. This is the mistake of confusing total sales volume with additional sales volume.
Incorrectエ
“7,500” is too large. If 7,500 more units are sold, the added profit is 5,000 yen/unit × 7,500 units = 37.5 million yen, making the profit 4 million yen + 37.5 million yen = 41.5 million yen, far exceeding the target. Since the question asks for the at least (minimum) additional sales volume required, the answer is the 1,200 units that brings the profit to exactly 10 million yen; 7,500 units is not the minimum.
ここがポイント
- Contribution margin (marginal profit) = selling price per unit − variable cost per unit. The selling price per unit is sales ÷ quantity, and the fixed cost can be worked backward from the single initial data point as “total contribution margin − profit”. Find the required sales volume using the idea that each unit sold increases profit by this contribution margin.
- Do not mistake whether the question asks for total sales volume or additional sales volume. This question's stem asks how many more units must be sold, so subtract the 5,000 units already sold from the computed total of 6,200 units to get the answer of 1,200 units.
用語