This question's explanation and your answers so far.
ASP利用方式と自社開発の自社センター利用方式（以下“自社方式”という）の採算性を比較する。次の条件のとき，ASP利用方式の期待利益（効果額－費用）が自社方式よりも大きくなるのは，自社方式の初期投資額が何万円を超えたときか。ここで，比較期間は5年とする。 〔条件〕 ・両方式とも，システム利用による効果額は500万円/年とする。 ・ASP利用方式の場合，初期費用は0円，利用料は300万円/年とする。 ・自社方式の場合，初期投資額は定額法で減価償却計算を行い，5年後の残存簿価は0円とする。また，運用費は100万円/年とする。 ・金利やその他の費用は考慮しないものとする。
When the initial investment is 500 ten-thousand yen, the in-house method's 5-year profit is 2,000－500＝1,500 ten-thousand yen, which is greater than the ASP's 1,000 ten-thousand yen, so the in-house method is still more advantageous. For the ASP to overtake it, the initial investment must be larger; 500 ten-thousand yen does not yet reach the break-even point (1,000 ten-thousand yen).
正解 For both methods the benefit amount is 500 ten-thousand yen/year and is exactly equal, and the 5-year totals (2,500 ten-thousand yen) cancel out, so the statement can be restated as: a larger expected profit means a smaller total cost. Comparing the 5-year total cost, the ASP usage method is initial cost 0 yen ＋ usage fee 300 ten-thousand yen/year × 5 years ＝ 1,500 ten-thousand yen; the in-house method is initial investment X (with straight-line depreciation the residual book value after 5 years is 0, so the 5-year total cost is the whole of X) ＋ operating cost 100 ten-thousand yen/year × 5 years ＝ X＋500 ten-thousand yen. The condition for the ASP usage method's expected profit to exceed the in-house method is that the ASP cost is less than the in-house cost, that is 1,500＜X＋500, which simplifies to X＞1,000. Therefore, when the in-house method's initial investment exceeds 1,000 ten-thousand yen, the ASP usage method becomes more advantageous, and the correct answer is イ.
When the initial investment is 1,500 ten-thousand yen, the in-house method's profit is 2,000－1,500＝500 ten-thousand yen, which is indeed below the ASP's 1,000 ten-thousand yen, but the boundary at which the ASP begins to overtake (the break-even point) is 1,000 ten-thousand yen, not 1,500 ten-thousand yen. 1,500 overshoots the break-even point and is too large to be the boundary amount that the question asks the investment must exceed.
When the initial investment is 2,000 ten-thousand yen, the in-house method's profit is 2,000－2,000＝0 ten-thousand yen and the ASP overtakes it by a wide margin, but this too is a value far larger than the break-even point (1,000 ten-thousand yen). The question asks for the boundary amount of how many ten-thousand yen the investment must exceed for the ASP to begin overtaking, so 2,000 ten-thousand yen is too large.