問27
頻出度★★★
ある商品の前期, 当期2期分の売上高と総費用は表のとおりである。この商品の1期間の固定費は何千円か。ここで, 総費用は固定費と変動費の合計であり, 固定費, 及び売上高に対する変動費の割合は, 前期, 当期ともに変わらないものとする。 単位 千円
| 前期 | 当期 | |
|---|---|---|
| 売上高 | 10,000 | 11,000 |
| 総費用 | 9,000 | 9,600 |
平成30年度 春期 ITパスポート試験 問27
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 27
Incorrectア
If the fixed cost is taken as 2,400, the variable cost ratio is (9,000 − 2,400) ÷ 10,000 = 0.66 for the previous period and (9,600 − 2,400) ÷ 11,000 ≈ 0.655 for the current period, so they do not match. This contradicts the condition that the variable cost ratio is constant, so it is wrong.
- イ
正解 Total cost can be expressed as “fixed cost + variable cost”, and variable cost equals “sales × variable cost ratio”. Since the fixed cost and the variable cost ratio stay unchanged in both the previous and current periods, two equations hold: for the previous period, 9,000 = fixed cost + variable cost ratio × 10,000, and for the current period, 9,600 = fixed cost + variable cost ratio × 11,000. Subtracting one equation from the other, the increase in total cost of 600 is the increase in variable cost caused by the increase in sales of 1,000, so the variable cost ratio = 600 ÷ 1,000 = 0.6. Substituting this into the previous-period equation gives fixed cost = 9,000 − 0.6 × 10,000 = 9,000 − 6,000 = 3,000 (thousand yen), so the correct answer is イ, “3,000”. Checking with the current period, 9,600 − 0.6 × 11,000 = 3,000, which matches.
Incorrectウ
If the fixed cost is taken as 3,600, the variable cost ratio is (9,000 − 3,600) ÷ 10,000 = 0.54 for the previous period and (9,600 − 3,600) ÷ 11,000 ≈ 0.545 for the current period, so they do not match. The variable cost ratio would not stay constant, so it is wrong.
Incorrectエ
If the fixed cost is taken as 4,000, the variable cost ratio is (9,000 − 4,000) ÷ 10,000 = 0.5 for the previous period and (9,600 − 4,000) ÷ 11,000 ≈ 0.509 for the current period, so they do not match. The two equations cannot be satisfied simultaneously, so it is wrong.
ここがポイント
- Total cost = fixed cost + variable cost ratio × sales. If the fixed cost and the variable cost ratio are constant, you can set up simultaneous equations using the data from two periods and solve for both.
- The variable cost ratio can be found as “increase in total cost ÷ increase in sales” (since the fixed cost is constant, the entire increase is variable cost). Here it is 600 ÷ 1,000 = 0.6.
用語