問12
頻出度★☆☆
システム開発に関する投資プロジェクト A～D のうち，最も早く投資を回収できるものはどれか。ここで，毎年の維持管理費用として，初期投資の 10%が発生するものとする。 単位 百万円
| プロジェクト名 | 初期投資 | 利益計画 1年目 | 利益計画 2年目 | 利益計画 3年目 |
|---|---|---|---|---|
| 投資プロジェクトA | 200 | 50 | 150 | 200 |
| 投資プロジェクトB | 300 | 100 | 200 | 300 |
| 投資プロジェクトC | 500 | 200 | 400 | 400 |
| 投資プロジェクトD | 600 | 300 | 400 | 400 |
平成23年度 秋期 ITパスポート試験 問12
ストラテジ系システム企画 › システム化計画
This question's explanation and your answers so far.
解説
問 12
Incorrectア
Project A has an initial investment of 200 and a maintenance and management cost of 20 per year. At the end of Year 2 its cumulative profit is 50+150=200, which falls 40 short of the required amount 200+20×2=240, so it is not yet recovered. Recovery comes in Year 3 (cumulative profit 400 ≧ 200+60=260), later than C.
Incorrectイ
Project B has an initial investment of 300 and a maintenance and management cost of 30 per year. At the end of Year 2 its cumulative profit is 100+200=300, which does not reach the required amount 300+30×2=360. Recovery comes in Year 3 (cumulative profit 600 ≧ 300+90=390), later than C.
- ウ
正解 Whether the investment has been recovered is judged by whether the cumulative profit has reached the initial investment plus the cumulative maintenance and management cost up to that point. A maintenance and management cost equal to 10% of the initial investment is incurred every year. Project C has an initial investment of 500 million yen and a maintenance and management cost of 50 million yen per year. At the end of Year 1 the cumulative profit is 200 against a required amount of 500+50=550, so the investment is not yet recovered. At the end of Year 2 the cumulative profit is 200+400=600 and the required amount is 500+50×2=600, so with exactly 600 = 600 the investment is recovered. For A, B and D, the cumulative profit at the end of Year 2 does not reach the required amount, and recovery slips to Year 3. Therefore the project that recovers its investment the earliest (in Year 2) is C, and the correct answer is ウ.
Incorrectエ
Project D has the largest profit figures, but its initial investment of 600 and its maintenance and management cost of 60 per year are also the largest. At the end of Year 2 its cumulative profit is 300+400=700 against a required amount of 600+60×2=720, so it is 20 short and not yet recovered. Recovery comes in Year 3. A large absolute amount of profit and a fast payback are two different things, and that is the trap set here.
ここがポイント
- The payback period is judged as the length of time until the cumulative benefit (profit) reaches the cumulative investment and costs. Here, that means finding the first year that satisfies “cumulative profit ≧ initial investment + cumulative maintenance and management cost”.
- Running costs such as maintenance and management costs pile up every year, so in a payback judgement they must be multiplied by the number of years and deducted as a cumulative total. Judging only by the size of the initial investment or of a single year's profit leads to mistakes (as with D, whose profit is the largest yet whose payback is later).
用語