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。 先月の売上高は10,000千円あり，1,650千円の利益があった。利益を向上させるために，今月から原材料を変更し，変動費率を0.05下げる予定である。しかし人件費が150千円増えて，固定費が増加した。今月の売上高が先月と同じ10,000千円のとき，利益は先月に比べて幾ら増減するか。
“Decreases by 200 thousand yen” is what you get if you mishandle the 500 thousand yen profit gain from the lower variable cost ratio, or if you reverse the sign of the change. In fact the 500 thousand yen gain from the lower variable cost ratio is larger than the 150 thousand yen rise in labor costs, so profit increases rather than decreases.
Profit would “stay the same” only if the gain from the lower variable cost ratio exactly matched the rise in fixed cost. Here the gain is 500 thousand yen while the fixed cost rises by only 150 thousand yen, so they do not balance. Profit moves by the difference of 350 thousand yen.
“Increases by 200 thousand yen” appears when the 150 thousand yen is subtracted twice (500 − 150 − 150 = 200 thousand yen). The variable cost ratio is applied to sales, so its effect is 10,000 thousand yen × 0.05 = 500 thousand yen, and subtracting 150 thousand yen just once gives +350 thousand yen.
正解 Profit can be written as: Profit = Sales − Variable cost − Fixed cost = Sales × (1 − Variable cost ratio) − Fixed cost. This month the sales are the same as last month, 10,000 thousand yen, so only two things change: the variable cost ratio and the fixed cost. First, when the variable cost ratio drops by 0.05, the variable cost falls by 10,000 thousand yen × 0.05 = 500 thousand yen, so profit rises by 500 thousand yen. On the other hand, labor costs rise by 150 thousand yen, so the fixed cost increases by 150 thousand yen and profit falls by that 150 thousand yen. The change in profit is therefore +500 thousand yen − 150 thousand yen = +350 thousand yen, so “Increases by 350 thousand yen” is correct. Incidentally, profit goes from 1,650 thousand yen last month to 2,000 thousand yen this month, but since the question asks for the amount of change, you can get the answer from the differences alone, without working out last month's actual variable cost ratio or fixed cost.