This question's explanation and your answers so far.
問92
頻出度★★★
電化製品を製造している G 社では，新たに開発した製品 H の発売を予定しており，その製造方法及び販売計画について検討を行っている。
製品 H の製造方法として案 A と案 B の二つの案が検討されていて，それぞれの案の固定費と変動費は表1のようになると見込んでいる。
表1 案Aと案Bの固定費と変動費の見込額
※ Our check while writing this explanation could not fully confirm the published answer; scoring follows IPA's official key.
×Incorrectア
20% is the value you get if you treat the sales matching a gross profit of 20,000,000 yen as 100,000,000 yen (1,000 units). Under Plan B, gross profit is exactly 20,000,000 yen at 800 units, that is at sales of 80,000,000 yen; if you make 1,000 units, gross profit becomes 50,000 × 1,000 − 20,000,000 = 30,000,000 yen (a margin of 30%). Sales of 100,000,000 yen and a gross profit of 20,000,000 yen cannot hold at the same time, and this also does not match the condition of the minimum number of units.
○イ
正解The cost assumptions for Plan B are given in Table 1, which is shared by this group of questions: a fixed cost of 20,000,000 yen per month and a variable cost of 50,000 yen per unit. In the [Monthly Profit Plan], the selling price is 100,000 yen per unit. Let N be the number of units manufactured and sold. Then sales = 100,000N yen, manufacturing cost (cost of sales) = 20,000,000 + 50,000N yen, and gross profit = 100,000N − (20,000,000 + 50,000N) = 50,000N − 20,000,000 yen. To satisfy a monthly gross profit of 20,000,000 yen, we need 50,000N − 20,000,000 ≧ 20,000,000, that is N ≧ 800, so the minimum number of units is 800. At that point sales are 100,000 yen × 800 units = 80,000,000 yen and gross profit is 20,000,000 yen, so the gross profit margin = 20,000,000 ÷ 80,000,000 × 100 = 25%. The correct answer is イ.
×Incorrectウ
33% is the result of 20,000,000 yen ÷ 60,000,000 yen, that is the number you get when you divide gross profit by the manufacturing cost (at 800 units, 20,000,000 + 50,000 × 800 = 60,000,000 yen) instead of by sales. The denominator of the gross profit margin is sales (80,000,000 yen), not cost, so this is wrong.
×Incorrectエ
50% is the value you get if you leave the fixed cost of 20,000,000 yen per month out of the calculation and use only the per-unit profit of 100,000 − 50,000 = 50,000 yen, solving 50,000N = 20,000,000 to get 400 units (a profit of 20,000,000 yen against sales of 40,000,000 yen). This is the contribution margin ratio, which subtracts only the variable cost; at 400 units the actual gross profit is 50,000 × 400 − 20,000,000 = 0 yen, which does not satisfy the plan. It is the mistake of forgetting to recover the fixed cost.
ここがポイント
Gross profit = sales − cost of sales, and gross profit margin = gross profit ÷ sales × 100. The denominator is always sales, not the cost and not the profit amount itself.
Set up the linear expression manufacturing cost = fixed cost + variable cost per unit × number of units manufactured, then work backward from the required profit amount to the required number of units. If you forget to subtract the fixed cost, you underestimate the number of units and end up calculating too high a margin.