問13
頻出度★★★
ある製品の今月の売上高と費用は表のとおりであった。販売単価を1,000円から800円に変更するとき，赤字にならないためには少なくとも毎月何個を販売する必要があるか。ここで，固定費及び製品1個当たりの変動費は変化しないものとする。
| 項目 | 金額 |
|---|---|
| 売上高 | 2,000,000円 |
| 販売単価 | 1,000円 |
| 販売個数 | 2,000個 |
| 固定費 | 600,000円 |
| 1個当たりの変動費 | 700円 |
令和5年度 ITパスポート試験 問13
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 13
Incorrectア
At 2,400 units, the total contribution margin is only 100 × 2,400 = 240,000 yen, which falls 360,000 yen short of the fixed cost of 600,000 yen, resulting in a deficit. This value comes from dividing the fixed cost by an incorrect contribution margin, and it does not satisfy the break-even condition 100 × x ≧ 600,000.
Incorrectイ
2,500 units is the value obtained by dividing the original sales revenue of 2,000,000 yen by the new unit price of 800 yen (2,000,000 ÷ 800), ignoring costs entirely. In reality the contribution margin is 100 × 2,500 = 250,000 yen, which does not reach the fixed cost of 600,000 yen, producing a deficit of 350,000 yen.
Incorrectウ
4,800 is the break-even “sales revenue” of 4,800,000 yen (= 600,000 ÷ 0.125) mistaken for a number of units, or the result of dividing by the old unit price of 1,000 yen. The question asks for the number of units sold, and at 4,800 units the contribution margin of 100 × 4,800 = 480,000 yen does not reach the fixed cost of 600,000 yen, resulting in a deficit of 120,000 yen.
- エ
正解 The new unit selling price is 800 yen and the variable cost per unit is 700 yen, so the contribution margin (marginal profit) earned per unit sold is 800 − 700 = 100 yen. To avoid a deficit (profit of 0 or more), the total contribution margin only needs to reach the fixed cost of 600,000 yen or more. Letting the number of units sold be x, we have 100 × x ≧ 600,000, that is x ≧ 6,000. Therefore at least 6,000 units must be sold per month, so エ is correct.
ここがポイント
- Break-even sales volume = fixed cost ÷ (unit selling price − variable cost per unit). The condition for avoiding a deficit is “contribution margin per unit (marginal profit) × number of units ≧ fixed cost”.
- Note that changing the unit price changes the contribution margin per unit (here from 300 yen to 100 yen). Even when the fixed cost and variable cost stay the same, the required sales volume increases greatly.
用語