- 2069 Bhadra · 4+4+4 marks
IRR by AW, both BCR by FW, and ERR
Short answer
IRR by AW formulation is 21.58%. Using FW at 20%, conventional B/C = 1.03, modified B/C = 1.04. ERR = 20.88%. All exceed MARR, so accept.
Equipment costs 2,50,000 and has salvage value of 50,000 at the end of its expected life of 5 years. Annual expenses will be 40,000. It will produce a revenue of 120,000 per year. MARR = 20% = ε. i) Evaluate IRR using AW formulation. ii) Evaluate both types of B/C ratio with FW formulation. iii) Find ERR.
Net annual inflow = 1,20,000 − 40,000 = Rs 80,000. I = 2,50,000, S = 50,000, N = 5, MARR = ε = 20%.
yr 0: -2,50,000 yr 1..5: +80,000 (net) yr 5: +50,000
i) IRR using AW
AW(i) = −2,50,000 (A/P, i, 5) + 50,000 (A/F, i, 5) + 80,000 = 0
| i | (A/P, i, 5) | (A/F, i, 5) | AW(i) |
|---|---|---|---|
| 20% | 0.33438 | 0.13438 | +3,124 |
| 25% | 0.37185 | 0.12185 | -6,869 |
| 22% | 0.34921 | 0.12921 | -841 |
| 21% | 0.34177 | 0.13177 | +1,147 |
Interpolating between 21% and 22%: IRR = 21 + 1147/(1147 − (-841)) = 21.58% > 20%. Accept.
ii) B/C ratios with FW (i = 20%)
(F/A, 20%, 5) = 7.4416; (F/P, 20%, 5) = 2.4883
- FW(B) = 1,20,000 × 7.4416 = Rs 892,992
- FW(O&M) = 40,000 × 7.4416 = Rs 297,664
- FW(I) = 2,50,000 × 2.4883 = Rs 622,080
Conventional B/C = 892,992 / (622,080 + 297,664 − 50,000) = 1.027
Modified B/C = (892,992 − 297,664) / (622,080 − 50,000) = 1.041
Both are greater than 1, so accept.
iii) ERR (ε = 20%)
- PW of outflows at ε = 2,50,000 (only at year 0)
- FW of inflows at year 5 = 80,000 (F/A, 20%, 5) + 50,000 = 80,000 × 7.4416 + 50,000 = Rs 645,328
- (1 + ERR)^5 = 645,328 / 2,50,000 = 2.5813
- ERR = (2.5813)^(1/5) − 1 = 20.88%
ERR = 20.88% > MARR = 20%, so accept.
Answer: IRR ≈ 21.58%; conventional B/C = 1.03, modified B/C = 1.04; ERR ≈ 20.88%. All give the same decision: accept.
✓ Answer checked by Claude Opus 5.5 (high effort)
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