- 2066 Magh · 6 marks
Both types of B/C ratio using PW
Short answer
Conventional B/C = 1.19, Modified B/C = 1.48. Both exceed 1, so project is acceptable. Calculated using present worth of benefits (Rs 67.101 lakh), costs (Rs 56.234 lakh), and salvage at 8% over 10 years.
Evaluate both types of B/C ratio using PW. Initial cost = Rs. 25 lakh Salvage value = Rs. 5 lakh Useful life = 10 years Annual benefits = Rs. 10 lakh Annual O & M = Rs. 5 lakh MARR = 8%
Amounts in Rs lakh. I = 25, S = 5, N = 10, annual benefit = 10, O&M = 5, MARR = 8%.
yr 0: -25 yr 1..10: +10 benefit, -5 O&M yr 10: +5
Factors: (P/A, 8%, 10) = 6.7101; (P/F, 8%, 10) = 0.4632
- PW(B) = 10 × 6.7101 = 67.101
- PW(O&M) = 5 × 6.7101 = 33.550
- PW(S) = 5 × 0.4632 = 2.316
Conventional B/C = PW(B) / [I + PW(O&M) − PW(S)] = 67.101 / (25 + 33.550 − 2.316) = 67.101 / 56.234 = 1.193
Modified B/C = [PW(B) − PW(O&M)] / [I − PW(S)] = (67.101 − 33.550) / (25 − 2.316) = 33.550 / 22.684 = 1.479
Answer: conventional B/C = 1.19, modified B/C = 1.48. Both are greater than 1, so the project is acceptable.
✓ Answer checked by Claude Opus 5.5 (high effort)
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