問22
頻出度★☆☆
新規システムの開発に当たって, 初期投資額は 2,400 万円, 稼働後の効果額は 100 万円/月, システム運用費は 20 万円/月, 年間のシステム保守費は初期投資額の 15%のとき, 投資額を回収するための回収期間は何年か。ここで, 金利コストなどは考慮しないものとする。
平成23年度 特別試験 ITパスポート試験 問22
ストラテジ系システム戦略 › システム活用促進・評価
This question's explanation and your answers so far.
解説
問 22
Incorrectア
2 years is the value you get by looking only at the benefit of 1 million yen per month and subtracting no costs at all. Taking 1 million × 12 = 12 million yen per year gives 24 million ÷ 12 million = 2 years. However, once the system goes live there are continuing outlays of 2.4 million yen per year in operating cost and 3.6 million yen per year in maintenance cost, and the amount that can actually go toward recovering the investment is reduced by that much. The payback period must be found by dividing by the net benefit (benefit − running costs), not by the benefit, so this choice is wrong.
Incorrectイ
2.5 years is the value you get if you subtract only the operating cost and forget to include the maintenance cost. Taking (1 million − 200 thousand) × 12 = 9.6 million yen per year gives 24 million ÷ 9.6 million = 2.5 years. But the question clearly states that the annual system maintenance cost is 15% of the initial investment, and that maintenance cost of 24 million × 0.15 = 3.6 million yen per year is also a running cost incurred every year. Both the operating cost and the maintenance cost have to be subtracted, so this choice is wrong.
Incorrectウ
2.9 years is the value you get if you subtract only the maintenance cost and forget to include the operating cost. Subtracting just the 3.6 million yen of maintenance from the annual benefit of 12 million yen leaves 8.4 million yen per year, and 24 million ÷ 8.4 million is about 2.86 years, that is roughly 2.9 years. Unlike choice イ, the mistake here is overlooking the system operating cost of 200 thousand yen per month (2.4 million yen per year); only one of the two running costs is deducted, so the payback period is estimated as shorter than it really is.
- エ
正解 The correct answer is エ (4 years). The payback period is found by dividing the initial investment by the annual net benefit (the benefit minus running costs such as operating and maintenance costs). First, put the conditions of the question on a yearly basis. The benefit is 1 million yen per month, so per year it is 1 million × 12 = 12 million yen. Next, there are two kinds of running cost: the system operating cost is 200 thousand yen per month, which is 200 thousand × 12 = 2.4 million yen per year, and the system maintenance cost is given on a yearly basis as 15% of the initial investment, which is 24 million × 0.15 = 3.6 million yen per year. Therefore the net benefit that can actually go toward recovering the investment is 12 million − 2.4 million − 3.6 million = 6 million yen per year. All that is left is to divide the initial investment of 24 million yen by this net benefit: payback period = 24 million ÷ 6 million = 4 years. Working in monthly amounts gives the same result. The maintenance cost of 3.6 million yen per year comes to 300 thousand yen per month, so the net benefit is 1 million − 200 thousand − 300 thousand = 500 thousand yen per month, and 24 million ÷ 500 thousand = 48 months = 4 years. There are two key points here. First, divide by the net benefit, that is the benefit minus both the operating cost and the maintenance cost, not by the benefit itself. Second, line up the time units before calculating, because the benefit and the operating cost are given per month while the maintenance cost is given per year. Also, since the question says that interest costs and the like are not taken into account, there is no discounting to present value (DCF); a simple division is enough.
ここがポイント
- The formula for the payback period — payback period = initial investment ÷ annual net benefit. The net benefit is the amount left after subtracting all the running costs incurred every year once the system is live, as in benefit − operating cost − maintenance cost; you must not divide by the benefit itself. When interest costs are not taken into account, there is no discounting to present value, just a simple division.
- Lining up units and finding the maintenance cost — when the benefit and the operating cost are given per month while the maintenance cost is given as a yearly percentage such as 15% of the initial investment, convert everything to either a yearly or a monthly basis before calculating. In this question the maintenance cost is 24 million yen × 15% = 3.6 million yen per year (= 300 thousand yen per month), which is a basic calculation step in cost-effectiveness analysis.
用語