This question's explanation and your answers so far.
部品メーカに勤める A さんは，材料費などの変動費と人件費などの固定費を把握し，表計算ソフトを活用して，売上高と利益を検討することにした。1 か月の売上高，変動費に固定費を加えた総費用を基に，図 1 に示すような売上高の損益分析を行うためのワークシートを作成した。 変動費は売上高に連動して増減する費用であり，変動費率は変動費の売上高に占める割合である。固定費とは，売上高にかかわらず発生する一定額の費用である。損益分岐点は売上高と総費用がちょうど等しくなる売上高であり，売上高が損益分岐点以下であれば赤字になり，それ以上になれば利益が出る。 変動費率と固定費は，それぞれセル B1，B2 に入力してある。 売上高が3,000千円以上で赤字にならないようにしたい。変動費率を0.60と仮定した場合，固定費の上限は何千円か。
1,500 thousand yen comes from mistakenly using a variable cost ratio of 0.50 instead of 0.60 and computing 3,000 × (1 − 0.50) = 1,500. In fact, with fixed costs of 1,500 thousand yen, 3,000 − 1,800 − 1,500 = −300 thousand yen, a loss of 300 thousand yen, so it cannot be the upper limit.
1,300 thousand yen exceeds the contribution margin of 1,200 thousand yen: 3,000 − 1,800 − 1,300 = −100 thousand yen, a loss of 100 thousand yen. It falls outside the no-loss range, so it cannot be called the upper limit of fixed costs.
正解 The condition for avoiding a loss (profit ≧ 0) is: sales − variable costs − fixed costs ≧ 0. Since the variable cost ratio is 0.60, the variable costs at sales of 3,000 thousand yen are 3,000 × 0.60 = 1,800 thousand yen. The contribution margin, sales minus variable costs, is 3,000 − 1,800 = 1,200 thousand yen. The point where this contribution margin exactly covers the fixed costs is the break-even point, so as long as fixed costs ≦ 1,200 thousand yen there is no loss. Therefore the upper limit of fixed costs is 1,200 thousand yen, and the correct answer is ウ. You can also use the contribution margin ratio = 1 − variable cost ratio = 0.40 and get 3,000 × 0.40 = 1,200 thousand yen in one step.
With fixed costs of 1,000 thousand yen, 3,000 − 1,800 − 1,000 = 200 thousand yen, a profit, so there is indeed no loss; but since fixed costs can rise to 1,200 thousand yen and still cause no loss, this is not the maximum allowable value (the upper limit). The question asks for the maximum fixed costs that still avoid a loss.