GATE 2023 CH – Question 63
A design engineer needs to purchase a membrane module (M) for a plant. Details about the two available options, M1 and M2, are given in the table below. The overall plant has an expected life of 7 years. If the interest rate is 8% per annum, compounded annually, the difference in the net present value (NPV) of these two options, in lakhs of rupees, is ______ (rounded off to one decimal place).
| M1 | M2 | |
|---|---|---|
| Purchase cost (in lakhs of rupees) | 10 | 5 |
| Expected life (years) | 5 | 3 |
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Show answer and explanation
Correct answer: 4.68 to 4.72
Explanation
Over the plant life of 7 years, each module is replaced when its life ends. M1 is bought at year 0 and at year 5, so its present cost is $10 + \frac{10}{1.08^5} = 10 + 6.806 = 16.806$ lakhs. M2 is bought at years 0, 3 and 6: $5 + \frac{5}{1.08^3} + \frac{5}{1.08^6} = 5 + 3.969 + 3.151 = 12.120$ lakhs. The difference is $16.806 - 12.120 = 4.7$ lakhs.