- 2076 Shrawan · 6 marks
ERR with MARR 12% and reinvestment 14%
Short answer
Outflows are discounted to present worth at 14% and inflows compounded to future worth at the same rate; the rate equating them is the ERR. ERR ≈ 16.19%, exceeding the MARR of 12%, so the project is acceptable.
Calculate the ERR of the following cash flow. MARR = 12%, reinvestment rate = 14%.
| EOY | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Cash flow | -90,000 | 25,000 | 40,000 | -30,000 | 50,000 | 75,000 |
The ERR method moves all net outflows to time 0 and all net inflows to the end of the project at the external reinvestment rate ε. ERR is the rate that equates the two. Accept if ERR ≥ MARR. Here ε = 14% and MARR = 12% (used only for the decision).
EOY : 0 1 2 3 4 5
CF : -90,000 +25,000 +40,000 -30,000 +50,000 +75,000
Step 1: PW of outflows at ε = 14% (years 0 and 3)
PW = 90,000 + 30,000 (P/F, 14%, 3) = 90,000 + 30,000 × 0.67497 = Rs 110,249.15
Step 2: FW of inflows at ε = 14% (at year 5)
FW = 25,000 (F/P, 14%, 4) + 40,000 (F/P, 14%, 3) + 50,000 (F/P, 14%, 1) + 75,000
- 25,000 × 1.68896 = 42,224.00
- 40,000 × 1.48154 = 59,261.76
- 50,000 × 1.14 = 57,000.00
- 75,000
- Total = Rs 233,485.76
Step 3: ERR
(1 + ERR)^5 = 233,485.76 / 110,249.15 = 2.1178
ERR = (2.1178)^(1/5) − 1 = 16.19%
Answer: ERR ≈ 16.19% > MARR 12%, so the project is acceptable. (The cash flow changes sign three times, so IRR may be unreliable; ERR avoids this problem.)
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- ERR with MARR = ε = 10% · Engineering Economics, chapter 3
- AW sensitivity to investment and net annual cash flow · Engineering Economics, chapter 6
- ERR from separate inflow and outflow rows · Engineering Economics, chapter 3
- After-tax cash flow, DDB with switchover · Engineering Economics, chapter 7
- ERR to select between projects A and B · Engineering Economics, chapter 4
- After-tax cash flow, sinking fund depreciation · Engineering Economics, chapter 7
- Porosity at 50%, 75%, 90% hydration · Concrete Technology and Masonry Structure, chapter 4
- Brayton cycle pressure ratio 12: mass flow for 90 MW · Fundamental of Thermodynamics & Heat Transfer, chapter 6
- Drawing hall 40 × 25 × 6 m, 90 lm/m² LED · Industrial Power Distribution and Illumination, chapter 7 · asked 2×
- EVA; 60 days, 25% work, Rs 12,00,000 · Project Engineering, chapter 4