問5
頻出度★★★
次の損益計算資料を基に算出した損益分岐点の売上高は何百万円か。 単位 百万円
| 項目 | 金額 |
|---|---|
| 売上高 | 4,000 |
| 変動製造費 | 1,400 |
| 変動販売費 | 600 |
| 固定費 | 800 |
平成24年度 春期 ITパスポート試験 問5
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 5
Incorrectア
1,200 is the current operating profit shown by this data (sales 4,000 − variable cost 2,000 − fixed cost 800 = 1,200). The question does not ask “how much profit is being made” but “at what sales amount does profit become zero”, so giving the profit figure itself as the answer is wrong. Break-even sales must always be obtained as fixed cost ÷ contribution margin ratio.
Incorrectイ
1,231 is the value you get if you treat only the variable manufacturing cost of 1,400 as the variable cost and forget to include the variable selling cost of 600. With variable cost ratio = 1,400 ÷ 4,000 = 0.35 and contribution margin ratio = 0.65, you get 800 ÷ 0.65 ≈ 1,231. However, the variable selling cost is incurred in proportion to sales, so it must be included in the variable cost regardless of whether it is a manufacturing cost or a selling cost. This is an error caused by leaving an item out of the total.
- ウ
正解 The correct answer is “ウ”, 1,600 (millions of yen). Break-even sales is the sales amount at which the contribution margin — sales minus variable cost — becomes exactly equal to the fixed cost, so that profit becomes zero. The steps are as follows. First, add up the variable costs. Variable costs are costs that rise and fall in proportion to sales, so both the variable manufacturing cost of 1,400 and the variable selling cost of 600 are variable costs, and total variable cost = 1,400 + 600 = 2,000 (millions of yen). Next, find the variable cost ratio. Variable cost ratio = variable cost ÷ sales = 2,000 ÷ 4,000 = 0.5 (50%). Then the contribution margin ratio = 1 − variable cost ratio = 1 − 0.5 = 0.5 (50%), which means that for every 1 yen of additional sales, 0.5 yen goes toward recovering the fixed cost. Finally, divide the fixed cost of 800 by this contribution margin ratio. Break-even sales = fixed cost ÷ contribution margin ratio = 800 ÷ 0.5 = 1,600 (millions of yen). Checking the result: when sales are 1,600, the variable cost is 1,600 × 0.5 = 800 and the contribution margin is 1,600 − 800 = 800, which is exactly equal to the fixed cost of 800, so profit becomes zero. This confirms that 1,600 is the break-even sales.
Incorrectエ
2,154 is the value you get if you mistakenly add the variable selling cost of 600 to the fixed cost side instead of counting it as a variable cost. Taking fixed cost = 800 + 600 = 1,400, variable cost ratio = 1,400 ÷ 4,000 = 0.35, and contribution margin ratio = 0.65, you get 1,400 ÷ 0.65 ≈ 2,154. If you sort an item incorrectly at the stage of splitting costs into fixed and variable costs, both the numerator and the denominator go wrong at the same time, which is why the result ends up this far off.
ここがポイント
- Break-even sales = fixed cost ÷ contribution margin ratio, contribution margin ratio = 1 − variable cost ratio, variable cost ratio = variable cost ÷ sales. Memorize these three formulas as a set, and always bring the problem down to the form of dividing the fixed cost by the contribution margin ratio.
- The key point is to correctly sort the costs into fixed and variable ones before calculating (fixed-variable cost separation). Both the variable manufacturing cost and the variable selling cost change in proportion to sales, so both must be added into the variable cost. Also note that what is being asked for is not the amount of profit, but the sales amount itself at which profit becomes zero.
用語