- 2072 Asoj · 6 marks
Modified BCR with co-termination, AW
Short answer
Co-terminated at 5 years, salvage 10% first cost, MARR 15%. Modified B/C: A=1.323, B=1.083. Incremental B/C (B over A) = 0.764 < 1. Select Project A.
Co-terminating both projects at 5 years and select the best project by modified BCR (using AW formulation). Take MARR = 15%. Salvage value of each project = 10% of first cost.
| PROJECT | First Cost | Annual Benefits | Annual O & M Costs | Useful Life |
|---|---|---|---|---|
| A | Rs. 4,00,000 | Rs. 175,000 | Rs. 25,000 | 6 years |
| B | Rs. 7,00,000 | Rs. 250,000 | Rs. 35,000 | 8 years |
Co-termination: both projects are used for the same study period of 5 years (the shorter of the two lives is 6, and the study period is stated as 5). The projects are truncated at year 5 and the asset is assumed sold then for its salvage value, taken as 10% of first cost (assumption: this is the market value at year 5 for both).
Modified B/C (AW formulation) = (AW of benefits - AW of O&M) / CR, where CR = I(A/P, 15%, 5) - S(A/F, 15%, 5) is the capital recovery cost. (A/P, 15%, 5) = 0.2983, (A/F, 15%, 5) = 0.1483
Project A (I = 400,000, S = 40,000)
CR = 400,000(0.2983) - 40,000(0.1483) = 119,326 - 5,933 = 113,394 Modified B/C = (175,000 - 25,000) / 113,394 = 1.323
Project B (I = 700,000, S = 70,000)
CR = 700,000(0.2983) - 70,000(0.1483) = 208,821 - 10,382 = 198,439 Modified B/C = (250,000 - 35,000) / 198,439 = 1.083
Incremental analysis (B over A)
Extra net benefit = 215,000 - 150,000 = 65,000 per year Extra CR = 198,439 - 113,394 = 85,045 Incremental B/C = 65,000 / 85,045 = 0.764 < 1
Both are above 1, so each is acceptable alone, but the extra investment in B does not pay for itself.
| Project | CR (Rs./yr) | Modified B/C | AW (net) |
|---|---|---|---|
| A | 113,394 | 1.323 | 36,606 |
| B | 198,439 | 1.083 | 16,561 |
Answer: Select Project A (higher modified B/C and incremental B/C of B over A is only 0.76).
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- IRR to select best of A, B, C (15 years) · Engineering Economics, chapter 4
- IRR by AW, both BCR by FW, and ERR · Engineering Economics, chapter 3
- Both types of BCR, gradient income and cost · Engineering Economics, chapter 3
- Repeatability assumption, select best of three projects · Engineering Economics, chapter 4 · asked 2×
- Both types of BCR (FW) for Machine A · Engineering Economics, chapter 3
- Best of three mutually exclusive projects, 10-year study · Engineering Economics, chapter 4
- Feasibility using two methods, MARR 15% · Project Engineering, chapter 6
- RoR best installed capacity (NRs, 45 years) · Hydropower Engineering, chapter 3