The GATE Grind

GATE 2024 CH – Question 49

Plant Design and Economics · Depreciation, rate of return, payback period and discounted cash flow · 2 marks · Multiple choice

For purchasing a batch reactor, three alternatives P, Q and R have emerged, as summarized in the table. For a compound interest rate of 10% per annum, choose the correct option that arranges the alternatives, in order, from the least expensive to the most expensive.

PQR
Installed Cost (lakh rupees)152535
Equipment Life (years)357
Maintenance Cost (lakh rupees per year)432
  1. P, Q, R
  2. R, P, Q
  3. R, Q, P
  4. Q, R, P

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) R, Q, P

Explanation

Compare the equivalent annual costs, using the capital recovery factor $\frac{i(1 + i)^n}{(1 + i)^n - 1}$ at 10%. P: $15 \times 0.4021 + 4 = 10.03$. Q: $25 \times 0.2638 + 3 = 9.60$. R: $35 \times 0.2054 + 2 = 9.19$ lakhs per year. So the order from the least to the most expensive is R, Q, P.