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。 図1のセルB17に損益分岐点を求める計算式を入力する。セルB17に入力する計算式として, 適切なものはどれか。
※ Our check while writing this explanation could not fully confirm the published answer; scoring follows IPA's official key.
B2＊B1 means fixed cost × variable cost ratio, a multiplication with no meaning. Multiplying a fixed cost by a ratio does not give something interpretable as an amount of money, and it does not have the dimension of sales. The break-even point is obtained by dividing the fixed cost, not by multiplying it.
B2＊(1-B1) means fixed cost × contribution margin ratio. You must divide by the contribution margin ratio, not multiply by it, to obtain break-even sales. If the variable cost ratio were 0.6, the true answer would be fixed cost ÷ 0.4, a sales figure larger than the fixed cost; but this formula gives fixed cost × 0.4, a value smaller than the fixed cost, which is clearly unreasonable.
B2／B1 means fixed cost ÷ variable cost ratio, which uses the wrong divisor. What can be used to recover the fixed cost is the part of sales that remains after subtracting variable cost, that is, the portion given by the contribution margin ratio (1−variable cost ratio), not the variable cost ratio itself. This is a typical trap choice that puts B1 in the denominator instead of (1−B1).
正解 The correct answer is “エ B2／(1-B1)”. The break-even point (break-even sales) is the sales amount at which sales exactly equal total cost, so that profit becomes zero. Let sales be S, fixed cost be F, and the variable cost ratio (the share of variable cost in sales) be v. Total cost is then fixed cost + variable cost = F + v×S. At the break-even point S = F + v×S holds, so moving v×S to the left side gives S×(1−v) = F, and dividing both sides by (1−v) gives S = F ／ (1−v). In the worksheet of Figure 1, the variable cost ratio is entered in B1 and the fixed cost is entered in B2, so rewriting this formula with cell references gives B2／(1−B1); therefore choice エ is appropriate. The denominator (1−variable cost ratio) is the contribution margin ratio (the share of each unit of sales that can go toward recovering fixed cost). It helps to remember it as “dividing fixed cost by the contribution margin ratio gives break-even sales”.