問1
頻出度★★★
商品の販売数が500個のときの営業利益は表のとおりである。販売単価を10%値下げしたとき，損益分岐点の売上高は何円か。ここで，商品1個当たりの変動費及び販売数は，販売単価の値下げの前後で変わらないものとする。 単位 円
| 売上高 | 900,000 |
| 費用 | |
| 変動費 | 324,000 |
| 固定費 | 300,000 |
| 営業利益 | 276,000 |
平成26年度 秋期 ITパスポート試験 問1
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 1
Incorrectア
468,750 yen is the value calculated with the contribution margin ratio before the price cut. Before the price cut, the variable cost ratio = 324,000 ÷ 900,000 = 0.36 and the contribution margin ratio = 0.64, so 300,000 ÷ 0.64 = 468,750 yen. This does not reflect the effect of the price reduction, so it is not the break-even point sales for the case the question asks about, namely when the unit selling price is reduced by 10%.
Incorrectイ
486,000 yen is the amount of the contribution margin, obtained by multiplying the sales after the price cut, 900,000 × 0.9 = 810,000 yen, by the contribution margin ratio of 0.6; it is not the break-even point sales. This confuses the formula for the contribution margin with the break-even point, which must be obtained by dividing the fixed cost by the contribution margin ratio.
- ウ
正解 The correct answer is ウ, 500,000. Break-even point sales is the sales amount at which the contribution margin (sales − variable cost) is exactly equal to the fixed cost, and it is obtained as fixed cost ÷ contribution margin ratio. First, break the amounts in the table down to a per-unit basis. Sales are 900,000 yen for a sales volume of 500 units, so the unit selling price is 900,000 ÷ 500 = 1,800 yen; the variable cost is 324,000 yen, so the variable cost per unit is 324,000 ÷ 500 = 648 yen. If only the unit selling price is now reduced by 10%, the price becomes 1,800 × 0.9 = 1,620 yen, while the variable cost per unit stays at 648 yen according to the given condition. Therefore the variable cost ratio after the reduction is 648 ÷ 1,620 = 0.4, and the contribution margin ratio is 1 − 0.4 = 0.6 (the contribution margin per unit is 1,620 − 648 = 972 yen). The fixed cost of 300,000 yen is incurred regardless of sales, so the break-even point sales = 300,000 ÷ 0.6 = 500,000 yen. It is worth remembering this relationship: when a price cut lowers the unit price, the variable cost ratio rises (0.36 → 0.4) and the contribution margin ratio falls (0.64 → 0.6), so the break-even point sales become higher than before the price cut.
Incorrectエ
576,000 yen is the contribution margin before the price cut itself, 900,000 − 324,000 = 576,000 yen, that is, merely the sales in the table minus the variable cost. It does not carry out the break-even point calculation of dividing the fixed cost of 300,000 yen by the contribution margin ratio, and it does not reflect the price reduction either.
ここがポイント
- Break-even point sales = fixed cost ÷ contribution margin ratio, and contribution margin ratio = 1 − variable cost ratio = (sales − variable cost) ÷ sales. The fixed cost stays constant regardless of sales, while the variable cost increases or decreases in proportion to sales.
- Even when the unit selling price is reduced, the variable cost per unit does not change, so the variable cost ratio rises and the contribution margin ratio falls. As a result, the break-even point sales become higher than before the price cut. For questions that involve a change in unit price, it is best to first divide the totals by the sales volume to break them down into the price and variable cost per unit, and then do the calculation.
用語