問34
頻出度★★★
商品の販売数が700個のときの営業利益は表のとおりである。拡販のために販売単価を20%値下げしたところ, 販売数が20%増加した。このときの営業利益は何円か。 ここで, 商品1個当たりの変動費は変わらないものとする。 単位 円
| 項目 | 金額 | |
|---|---|---|
| 売上高 | 700,000 | |
| 費用 | 変動費 | 140,000 |
| 固定費 | 300,000 | |
| 営業利益 | 260,000 |
平成31年度 春期 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
200,000 yen is close to the correct answer of 204,000 yen but is not equal to it. The correct calculation is Sales 672,000 − Variable cost 168,000 − Fixed cost 300,000 = 204,000 yen; there is no calculation path that yields 200,000 yen (it is a trap value that easily appears when a digit or the per-unit variable cost is miscalculated along the way).
- イ
正解 Operating profit is found by ‘Sales − Variable cost − Fixed cost’. First derive the unit price and the variable cost per unit from the original table. Unit price = Sales 700,000 ÷ 700 units = 1,000 yen; variable cost per unit = Variable cost 140,000 ÷ 700 units = 200 yen. After the price cut the unit price drops by 20% to 1,000 × 0.8 = 800 yen, and the sales volume rises by 20% to 700 × 1.2 = 840 units. The variable cost per unit stays at 200 yen, so the figures become: Sales = 800 × 840 = 672,000 yen; Variable cost = 200 × 840 = 168,000 yen; Fixed cost stays at 300,000 yen regardless of quantity. Therefore operating profit = 672,000 − 168,000 − 300,000 = 204,000 yen, so ‘イ’ is correct.
Incorrectウ
260,000 yen is exactly the original operating profit before the price cut. It reflects the mistaken belief that a 20% price cut and a 20% volume increase offset each other and leave profit unchanged. In reality 0.8 × 1.2 = 0.96, so sales actually decrease (700,000 → 672,000 yen), and variable cost rises as the quantity grows (140,000 → 168,000 yen), so profit must end up lower than the original.
Incorrectエ
320,000 yen is larger than the original profit of 260,000 yen, presupposing that profit increased. However, even though the unit price is cut by 20%, the sales volume rises by only 20%, so sales shrink to 0.96 times, and on top of that the variable cost increases; therefore operating profit can never exceed the original.
ここがポイント
- Operating profit = Sales − Variable cost − Fixed cost. Grasp the nature of the costs: variable cost is fixed per unit and proportional to quantity, while fixed cost stays constant regardless of quantity.
- When the unit price is −20% and the quantity is +20%, sales become 0.8 × 1.2 = 0.96 times (i.e., they decrease). The key point is not to jump to the conclusion that the two cancel out to zero.
用語