--- title: "ERR to recommend best of A, B, C" subject: "Engineering Economics" chapter: 4 key: "semester_6/engineering_economics:err-recommend-best-abc-e20" source: https://www.bctengineer.com/q/semester_6/engineering_economics/err-recommend-best-abc-e20 site: BCT Engineering --- # ERR to recommend best of A, B, C Engineering Economics · Chapter 4: Comparative Analysis of Alternatives - Asked in: 2065 Kartik, 12 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/err-recommend-best-abc-e20 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-4 ## Question 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 | ## 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. ## Answer **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 ```text 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 ```text 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%). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What equation defines ERR for these projects (E = 20%)? A. PW(inflows)(1+i')^6 = FW(outflows) B. PW(outflows)(1+i')^6 = FW(inflows at year 6) C. FW(outflows) = PW(inflows) D. Sum of flows = 0 at i' Answer: B. Negatives are discounted to year 0 and positives compounded to year 6 at E, then PW(out)(1+i')^6 = FW(in). (Key point: ERR equation) 2. Why is incremental ERR used even though all three ERRs exceed 20%? A. Because ERR is invalid B. Because MARR is unknown C. Because individual ERRs cannot reliably rank mutually exclusive projects of different size D. Because B has negative flows Answer: C. Different investment sizes require checking whether each extra investment earns at least MARR. (Key point: Why incremental analysis) 3. The incremental ERR of B over A is 14.32%. What follows? A. B replaces A B. A stays as defender because the extra investment in B is below 20% C. C is rejected D. A is rejected Answer: B. 14.32% < 20%, so the additional investment in B is not justified. (Key point: B vs A) 4. Which project is recommended and why? A. A, the cheapest B. B, the most inflows C. A, highest incremental ERR D. C, because its extra investment over A earns 27.10% > 20% Answer: D. C vs A increment earns 27.10%, above the required 20%, so C replaces A. 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