--- title: "ERR to select between projects A and B" subject: "Engineering Economics" chapter: 4 key: "semester_6/engineering_economics:err-project-a-b-18-12" source: https://www.bctengineer.com/q/semester_6/engineering_economics/err-project-a-b-18-12 site: BCT Engineering --- # ERR to select between projects A and B Engineering Economics · Chapter 4: Comparative Analysis of Alternatives - Asked in: 2066 Magh, 8 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-project-a-b-18-12 - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-4 ## Question Select the best project using ERR method. MARR = 18%, E = 12%. | Year | 0 | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---|---| | Project A | -40,000 | -38,000 | +35,000 | +35,000 | +35,000 | +35,000 | | Project B | -60,000 | +25,000 | +40,000 | -50,000 | +50,000 | +75,000 | ## Short answer Compound receipts at reinvestment rate 12%, discount expenditures at the same rate. ERR(A) = 17.74% (< 18%), ERR(B) = 18.84% (>= 18%). Project B is acceptable; A is not. Select B. ## Answer ERR: receipts are compounded to the end of year 5 at ε = 12%, expenditures are discounted to year 0 at ε, and the ERR i' is found from PW(E)(1 + i')^5 = FW(R). A project is acceptable if ERR ≥ MARR = 18%. #### Project A FW(R) = 35,000[(1.12)³ + (1.12)² + (1.12)¹ + 1] = 35,000(F/A, 12%, 4) = 35,000(4.7793) = 167,276 PW(E) = 40,000 + 38,000(P/F, 12%, 1) = 40,000 + 38,000(0.8929) = 73,929 (1 + i')^5 = 2.2627 → **ERR(A) = 17.74%** < 18%, so A is not acceptable. #### Project B Receipts: year 1 = 25,000, year 2 = 40,000, year 4 = 50,000, year 5 = 75,000. Expenditures: year 0 = 60,000, year 3 = 50,000. FW(R) = 25,000(1.12)⁴ + 40,000(1.12)³ + 50,000(1.12)¹ + 75,000 = 39,338 + 56,197 + 56,000 + 75,000 = 226,535 PW(E) = 60,000 + 50,000(P/F, 12%, 3) = 60,000 + 50,000(0.7118) = 95,589 (1 + i')^5 = 2.3699 → **ERR(B) = 18.84%** > 18%, so B is acceptable. #### Incremental check (B - A) Increment flows: [-20000, 63000, 5000, -85000, 15000, 40000] ERR(B - A) = 15.15% < 18%. This is the return on the extra investment in B. Since A itself fails the MARR test, it is not a valid defender; the comparison to apply is B against the "do nothing" option, which B passes. | Project | ERR | Acceptable at MARR 18%? | |---|---|---| | A | 17.74% | No | | B | 18.84% | Yes | **Answer: Select Project B** (ERR 18.84% ≥ 18%). Project A (ERR 17.74%) falls just below the MARR. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In the ERR method, how are receipts and expenditures treated before ERR is found? A. Receipts are discounted to year 0 and expenditures compounded to year 5 at MARR B. Receipts are compounded to the end of year 5 and expenditures discounted to year 0, both at the reinvestment rate E C. Both are compounded to year 5 at MARR D. Both are discounted to year 0 at the ERR itself Answer: B. ERR uses the external reinvestment rate E: FW of receipts at the end of the life and PW of expenditures at year 0, then PW(E)(1+i')^n = FW(R). (Key point: ERR compounding and discounting) 2. Project A has ERR = 17.74% with MARR = 18%. What is the conclusion? A. Accept A because ERR is close to MARR B. Accept A because ERR is above E = 12% C. Reject A because ERR is below MARR D. Cannot decide without IRR Answer: C. A project is acceptable only if ERR >= MARR; 17.74% < 18%, so A is not acceptable. (Key point: Acceptance rule) 3. In Project B, which flows are classified as expenditures when computing ERR? A. Year 0 (60,000) and year 3 (50,000) B. Only year 0 (60,000) C. Years 1 and 2 only D. Year 3 (50,000) and year 5 (75,000) Answer: A. Negative flows (year 0 and year 3) are expenditures discounted to year 0; the positive flows in years 1, 2, 4, 5 are receipts compounded to year 5. (Key point: Project B cash flows) 4. Why is Project B selected? A. It has the larger initial investment B. Its incremental ERR over A is above 18% C. Its ERR of 18.84% is at least the MARR of 18%, while A fails D. It has the lower FW of receipts Answer: C. B passes the MARR test (18.84% >= 18%) and A does not; the B-A increment (15.15%) is not needed since A is not a valid defender. 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