問6
頻出度★★★
単価 200 円の商品を 5 万個販売したところ, 300 万円の利益を得た。固定費が 300 万円のとき, 商品 1 個当たりの変動費は何円か。
平成23年度 秋期 ITパスポート試験 問6
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 6
Incorrectア
60 yen is the value obtained by dividing the fixed cost of 3,000,000 yen by the sales volume of 50,000 units (the amount of fixed cost borne per unit); it is not the variable cost per unit. If the variable cost were 60 yen, the total variable cost would be 3,000,000 yen and the profit would be 10,000,000 − 3,000,000 − 3,000,000 = 4,000,000 yen, exceeding the stated 3,000,000 yen by 1,000,000 yen, so it is wrong.
- イ
正解 Sales revenue is 200 yen per unit × 50,000 units sold = 10,000,000 yen. The profit formula is “Profit = Sales revenue − Total variable cost − Fixed cost”, so substituting the numbers gives 3,000,000 yen = 10,000,000 yen − Total variable cost − 3,000,000 yen, and the total variable cost works out to 10,000,000 yen − 3,000,000 yen − 3,000,000 yen = 4,000,000 yen. Variable cost is a cost that arises in proportion to the sales volume, so the variable cost per unit of the product is 4,000,000 yen ÷ 50,000 units = 80 yen. Checking the result: the profit contribution per unit (the contribution margin) is 200 − 80 = 120 yen, which for 50,000 units is 6,000,000 yen; subtracting the fixed cost of 3,000,000 yen from that leaves a profit of 3,000,000 yen, matching the stated conditions. Therefore the correct answer is “イ”.
Incorrectウ
If it were 100 yen, the total variable cost would be 100 yen × 50,000 units = 5,000,000 yen, and the profit would come to only 10,000,000 − 5,000,000 − 3,000,000 = 2,000,000 yen, which is 1,000,000 yen short of the stated 3,000,000 yen. A rough guess such as “half of the 200 yen unit price” does not satisfy the conditions, so you must always verify with the formula.
Incorrectエ
140 yen is the value you get if you forget to subtract the fixed cost of 3,000,000 yen and instead calculate 3,000,000 yen = 10,000,000 yen − total variable cost. In reality the total variable cost of 7,000,000 yen plus the fixed cost of 3,000,000 yen equals 10,000,000 yen, so the costs exactly equal the sales revenue and the profit becomes 0 yen (the break-even point); therefore it is wrong.
ここがポイント
- Profit = Sales revenue − (Total variable cost + Fixed cost). Here Sales revenue = unit price × sales volume and Total variable cost = variable cost per unit × sales volume; be able to rearrange this formula so that an unknown variable cost per unit can be worked out backwards.
- Distinguish the two: variable cost is a cost that rises and falls in proportion to the sales volume, while fixed cost is a cost incurred at a constant amount regardless of the sales volume. The point at which the contribution margin per unit (unit price − variable cost per unit) × sales volume = fixed cost is the break-even point.
用語