問9
頻出度★★★
ある製品を生産，販売するのに，固定費が100万円，製品1個当たりの変動費が7万円である。この製品を単価10万円で販売するとき，利益を170万円以上確保するためには，少なくとも何個を販売する必要があるか。
平成28年度 秋期 ITパスポート試験 問9
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 9
- ア
正解 Think in terms of profit = sales − (fixed cost + variable cost). Let the number of units sold be x; then sales = 10x and variable cost = 7x (both in units of 10,000 yen), so profit = 10x − (100 + 7x) = 3x − 100 (in units of 10,000 yen). Here the marginal profit per unit is unit price 100,000 yen − variable cost per unit 70,000 yen = 30,000 yen. The condition for profit to be 1,700,000 yen or more is 3x − 100 ≥ 170, that is 3x ≥ 270, x ≥ 90. Therefore at least 90 units are needed. Alternatively, the required number of units sold = (fixed cost + target profit) ÷ marginal profit per unit = (100 + 170) ÷ 3 = 270 ÷ 3 = 90, which gives the same result. Therefore the correct answer is ア.
Incorrectイ
270 is fixed cost 100 + target profit 170 = 2,700,000 yen, that is, the “total amount (money) of marginal profit that must be recovered”, not the number of units sold. This error forgets the step of dividing this amount by the marginal profit per unit of 30,000 yen, mistaking the figure expressed in units of 10,000 yen directly for a number of units.
Incorrectウ
The minimum number of units satisfying the correct condition 3x − 100 ≥ 170 is 90, and 630 greatly exceeds it. It is an excessively large value resulting from setting up the equation or doing the division incorrectly (such as dividing by the wrong denominator or performing an extra multiplication), and it is not the “minimum number of units sold” that the question asks for.
Incorrectエ
900 is 2,700,000 yen divided not by the marginal profit per unit of 30,000 yen but by the marginal profit ratio of 0.3 (= 30,000 yen ÷ unit price 100,000 yen), that is 270 ÷ 0.3 = 900. It is the error of confusing the “marginal profit per unit (an amount of money)” with the “marginal profit ratio” when finding the number of units.
ここがポイント
- The number of units sold needed to achieve the target profit = (fixed cost + target profit) ÷ marginal profit per unit. Marginal profit = unit price − variable cost per unit (in this question, 10 − 7 = 30,000 yen).
- “At least how many units” asks for the minimum number of units that satisfies profit ≥ target profit, so solve the inequality 3x − 100 ≥ 170 to obtain x ≥ 90.
用語