- 2069 Poush
Both BCR with FW, gradient revenue
Short answer
Conventional B/C = 1.05; modified B/C = 1.07. Both exceed 1, so the project is marginally acceptable at 15% MARR.
Determine both types of B/C ratio by using FW formulation.
| Initial investment (Rs.) | 2,50,000 |
|---|---|
| Annual revenue (Rs.) | 50,000 at the end of first year and increasing by Rs. 30,000 for each year |
| Annual O&M cost (Rs.) | 30,000 |
| Salvage value (Rs.) | 50,000 |
| Useful life (year) | 5 |
| MARR | 15% |
Revenue is a gradient series: 50,000, 80,000, 1,10,000, 1,40,000, 1,70,000 (base 50,000, G = 30,000). O&M = 30,000 per year, salvage 50,000 at year 5, MARR = 15%.
revenue: 50k 80k 110k 140k 170k O&M: 30k each year
year : 1 2 3 4 5 yr 5: +50k salvage; yr 0: -2,50,000
Factors at 15%, 5 years: (F/A) = 6.7424, (F/P) = 2.0114, (A/G) = 1.7228
- Equivalent uniform revenue = 50,000 + 30,000 (A/G, 15%, 5) = 50,000 + 30,000 × 1.7228 = 101,684
- FW(B) = 101,684 × 6.7424 = Rs 685,595
- FW(O&M) = 30,000 × 6.7424 = Rs 202,271
- FW(I) = 2,50,000 × 2.0114 = Rs 502,839
- S = Rs 50,000
Conventional B/C = FW(B) / [FW(I) + FW(O&M) − S] = 685,595 / (502,839 + 202,271 − 50,000) = 685,595 / 655,111 = 1.047
Modified B/C = [FW(B) − FW(O&M)] / [FW(I) − S] = (685,595 − 202,271) / (502,839 − 50,000) = 483,324 / 452,839 = 1.067
Answer: conventional B/C = 1.05, modified B/C = 1.07. Both are slightly greater than 1, so the project is marginally acceptable at MARR = 15%.
✓ Answer checked by Claude Opus 5.5 (high effort)
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