- 2066 Magh · 8 marks
ERR to select between projects A and B
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.
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 |
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- ERR method to select best of three projects · Engineering Economics, chapter 4
- ERR with MARR 12% and reinvestment 14% · Engineering Economics, chapter 3
- Best of three mutually exclusive projects, 10-year study · Engineering Economics, chapter 4
- ERR to select best proposal A or B · Engineering Economics, chapter 4
- Repeatability assumption, select best of three projects · Engineering Economics, chapter 4 · asked 2×
- Best project for 4-year and 8-year service periods · Engineering Economics, chapter 4
- EVA; 60 days, 25% work, Rs 12,00,000 · Project Engineering, chapter 4
- Best financing option; EBIT Rs 350,000 · Project Engineering, chapter 6
- EVA; 60 days, 25% work, 50% budget spent · Project Engineering, chapter 4
- Gumbel flood at given risk, 50-year project life · Engineering Hydrology, chapter 6