問28
頻出度★☆☆
導入を検討している機械について採算性の評価を行う。評価には予想される費用と, 期待される利益を対比する方法を用いる。採算評価の期間は10年間であり, 導入によって, 毎年110万円の利益を得られる。また, 保守費用として毎年取得費用の1%が発生する。この機械の取得費用が何万円未満であれば, 採算がとれるか。
平成22年度 春期 ITパスポート試験 問28
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 28
- ア
正解 The correct answer is “ア 1,000”. This question is a cost-effectiveness analysis (cost-benefit analysis): you compare the total cost and the total benefit over the 10 years. Let the acquisition cost be X ten-thousand yen. The cost consists of (1) the acquisition cost of X ten-thousand yen (paid once at the beginning) and (2) the maintenance cost (1% of X per year = 0.01X ten-thousand yen, which over 10 years is 0.01X × 10 = 0.1X ten-thousand yen), so the total cost is X + 0.1X = 1.1X ten-thousand yen. The benefit, on the other hand, is 110 ten-thousand yen per year × 10 years = 1,100 ten-thousand yen. The condition for being profitable (the benefit exceeding the cost) is 1.1X < 1,100, and dividing both sides by 1.1 gives X < 1,000. In other words, it is profitable if the acquisition cost is less than 1,000 ten-thousand yen. Note that when X is exactly 1,000 ten-thousand yen, the cost is 1,000 + 100 of maintenance = 1,100 ten-thousand yen, the same amount as the benefit of 1,100 ten-thousand yen; the benefit does not exceed the cost, which is why the question says “less than 1,000 ten-thousand yen”.
Incorrectイ
1,100 ten-thousand yen is exactly the total benefit over the 10 years (110 ten-thousand yen × 10 years) itself; it is the value you get if you leave the maintenance cost out of the calculation and only consider “acquisition cost < total benefit”. In fact, if X = 1,100 ten-thousand yen, the maintenance cost is 1,100 × 1% × 10 years = 110 ten-thousand yen, so the total cost becomes 1,210 ten-thousand yen, which exceeds the benefit of 1,100 ten-thousand yen and therefore is not profitable. The maintenance cost incurred every year (the running cost) must also be added on the cost side.
Incorrectウ
1,111 ten-thousand yen corresponds to 1,100 ÷ 0.99 ≒ 1,111; it is the value you get when, instead of adding the maintenance cost (one year of it = 1% of the acquisition cost) to the cost, you subtract it from the acquisition cost. Note that adding only one year of maintenance cost gives 1,100 ÷ 1.01 ≒ 1,089 ten-thousand yen, which is also wrong. The maintenance cost occurs every year, so over the 10 years 10% of the acquisition cost must be added on the cost side. In fact, if X = 1,111 ten-thousand yen, the maintenance cost is 1,111 × 1% × 10 years ≒ 111 ten-thousand yen and the total cost is about 1,222 ten-thousand yen, which exceeds the benefit of 1,100 ten-thousand yen and therefore is not profitable.
Incorrectエ
1,222 ten-thousand yen corresponds to 1,100 ÷ 0.9 ≒ 1,222; it is the value you get when the sign is mistaken, that is, when the maintenance cost is subtracted from the acquisition cost (or added to the benefit side) instead of being “added” to the cost. Maintenance cost is an expenditure, so it must be added on the cost side. If X = 1,222 ten-thousand yen, the total cost is 1,222 + 122.2 = about 1,344 ten-thousand yen, far exceeding the benefit of 1,100 ten-thousand yen, and therefore it is not profitable.
ここがポイント
- In a cost-effectiveness analysis, you compare the “total cost” and the “total effect (benefit)” for the whole evaluation period, lining them up over the same period. The key point is that the cost must include not only the initial acquisition cost (the initial cost) but also running costs that occur every year, such as the maintenance cost, counted for the entire period; in this question, 10 years of maintenance cost = 1% of the acquisition cost × 10 years = 10% of the acquisition cost.
- The condition for being profitable is “total benefit > total cost”. Letting the acquisition cost be X, set up the inequality 1.1X < 110 × 10 and solve it to get X < 1,000. Also note that at equality (1.1X = 1,100) there is neither loss nor gain, that is, the break-even point, so the answer is “less than 1,000 ten-thousand yen”.
用語