- 2072 Asoj · 6 marks
Both types of BCR, gradient income and cost
Short answer
Compute PW of benefits (growing at 5%) = Rs 154,014, PW of O&M (Rs 500 gradient) = Rs 31,559, salvage PW = Rs 6,417. Conventional B/C = 1.23, modified B/C = 1.31 (both >1, acceptable).
Calculate both types of BCR of a project with the following details. MARR = 12%.
| Initial Investment | Annual Income | Annual Cost | Useful Life | Salvage Value |
|---|---|---|---|---|
| Rs. 100000 | Rs. 20000 at the end of first year and increase by 5% per year | Rs. 3000 at the end of first year and increase by Rs. 500 per year | 12 years | 25000 |
Assumption: PW formulation is used. Definitions:
- Conventional B/C = PW(B) / [I + PW(O&M) − PW(S)]
- Modified B/C = [PW(B) − PW(O&M)] / [I − PW(S)]
Benefit : 20,000 grows 5%/yr -> 20,000, 21,000, 22,050 ...
Cost : 3,000 + 500/yr -> 3,000, 3,500, 4,000 ...
Year 12 : salvage 25,000; Year 0: investment 1,00,000
Factors at i = 12%, n = 12: (P/A) = 6.1944, (P/G) = 25.9523, (P/F) = 0.2567
PW of benefits (geometric, g = 5%)
PW(B) = 20,000 × [1 − (1.05/1.12)^12] / (0.12 − 0.05) = 20,000 × 7.7007 = Rs 154,014
PW of O&M cost (gradient)
PW(M) = 3,000 (P/A, 12%, 12) + 500 (P/G, 12%, 12) = 3,000 × 6.1944 + 500 × 25.9523 = 18,583 + 12,976 = Rs 31,559
PW of salvage
PW(S) = 25,000 × 0.2567 = Rs 6,417
Conventional B/C = 154,014 / (1,00,000 + 31,559 − 6,417) = 154,014 / 125,142 = 1.231
Modified B/C = (154,014 − 31,559) / (1,00,000 − 6,417) = 122,455 / 93,583 = 1.309
Answer: conventional B/C = 1.23, modified B/C = 1.31. Both are greater than 1, so the project is acceptable at MARR = 12%.
✓ Answer checked by Claude Opus 5.5 (high effort)
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