- 2065 Kartik · 12 marks
ERR to recommend best of A, B, C
Short answer
Individual ERR: A28.3%, B26.4%, C28.5% all >20%. Incremental ERR: B over A =14.32% (reject), C over A =27.10% (accept). Recommend project C.
Recommend the best using ERR method, E = 20%. (End of year cash flows in Rs. '000.)
| ERR | Project | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|---|
| 28.3% | A | -640 | 262 | 290 | 302 | 310 | 310 | 260 |
| 26.4% | B | -680 | -40 | 392 | 380 | 380 | 380 | 380 |
| 28.5% | C | -755 | 205 | 406 | 400 | 390 | 390 | 324 |
ERR method. Compound all positive cash flows to year 6 at the reinvestment rate ε = 20% and discount all negative cash flows to year 0 at ε. ERR is the rate i' that satisfies PW(outflows)(1 + i')⁶ = FW(inflows). The MARR is not stated; assume MARR = ε = 20%. (Figures in Rs '000.)
Step 1: ERR of each project
A: FW = 262(1.2)⁵ + 290(1.2)⁴ + 302(1.2)³ + 310(1.2)² + 310(1.2) + 260 = 2853.5
PW(out) = 640
ERR = (2853.5/640)^(1/6) − 1 = 28.29%
B: FW = 392(1.2)⁴ + 380(1.2)³ + 380(1.2)² + 380(1.2) + 380 = 2852.7
PW(out) = 680 + 40/1.2 = 713.3
ERR = (2852.7/713.3)^(1/6) − 1 = 25.99%
C: FW = 205(1.2)⁵ + 406(1.2)⁴ + 400(1.2)³ + 390(1.2)² + 390(1.2) + 324 = 3396.8
PW(out) = 755
ERR = (3396.8/755)^(1/6) − 1 = 28.49%
(The values printed with the question are 28.3%, 26.4% and 28.5%; recomputation gives B slightly lower, which does not change the ranking.) All three exceed 20%, so all are acceptable. ERR of the individual projects cannot be used to rank mutually exclusive projects of different size, so use incremental analysis, starting with the cheapest project A.
Step 2: Incremental ERR
Year 0 1 2 3 4 5 6
B − A −40 −302 102 78 70 70 120
C − A −115 −57 116 98 80 80 64
- B − A: FW of inflows at year 6 = 651.1; PW of outflows = 40 + 302/1.2 = 291.7; ERR = 14.32% < 20%. The extra investment in B is not justified, so A stays the defender.
- C − A: FW = 685.1; PW of outflows = 115 + 57/1.2 = 162.5; ERR = 27.10% > 20%. The extra investment in C is justified, so C replaces A.
| Comparison | Incremental ERR | Decision |
|---|---|---|
| B vs A | 14.32% | Keep A |
| C vs A | 27.10% | Choose C |
Answer: Recommend project C. Its extra investment of Rs 1,15,000 over A earns 27.10%, above the required 20%, and C also has the highest individual ERR (28.49%).
✓ Answer checked by Claude Opus 5.5 (high effort)
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