- 2068 Jestha · 8 marks
ERR from separate inflow and outflow rows
Short answer
Using ε=8%, PW of net outflows = Rs 954,810; FW of net inflows = Rs 773,971. ERR = –4.11%, which is below MARR 10%, so the project is rejected.
Evaluate ERR. MARR = 10%, ε = 8%.
| EOY | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Cash inflow | – | +40,000 | +150,00 [?] | +120,000 | +800,000 | +200,000 |
| Cash outflow | -480,000 | -80,000 | -50,000 | 500,000 | -200,000 | -400,000 |
Assumptions for unclear entries
- The year-2 inflow "+150,00" is read as +1,50,000.
- The year-3 outflow "500,000" has no sign printed; it is placed in the outflow row, so it is taken as −5,00,000.
- Year-4 inflow is taken as printed, +8,00,000.
Net cash flow (inflow + outflow)
| EOY | Inflow | Outflow | Net CF |
|---|---|---|---|
| 0 | 0 | −4,80,000 | −4,80,000 |
| 1 | 40,000 | −80,000 | −40,000 |
| 2 | 1,50,000 | −50,000 | +1,00,000 |
| 3 | 1,20,000 | −5,00,000 | −3,80,000 |
| 4 | 8,00,000 | −2,00,000 | +6,00,000 |
| 5 | 2,00,000 | −4,00,000 | −2,00,000 |
Net: -4.8L -0.4L +1.0L -3.8L +6.0L -2.0L
yr : 0 1 2 3 4 5
The net flow changes sign four times, so IRR may be multiple; ERR is suitable. ε = 8% is the external reinvestment rate and MARR = 10% is the decision rate.
Step 1: PW of net outflows at ε = 8%
PW = 4,80,000 + 40,000 (P/F, 8%, 1) + 3,80,000 (P/F, 8%, 3) + 2,00,000 (P/F, 8%, 5) = 4,80,000 + 37,037 + 301,656 + 136,117 = Rs 954,810
Step 2: FW of net inflows at ε = 8% (year 5)
FW = 1,00,000 (F/P, 8%, 3) + 6,00,000 (F/P, 8%, 1) = 1,00,000 × 1.2597 + 6,00,000 × 1.08 = 125,971 + 648,000 = Rs 773,971
Step 3: ERR
(1 + ERR)^5 = 773,971 / 954,810 = 0.8106
ERR = (0.8106)^(1/5) − 1 = -4.11%
Answer: ERR ≈ -4.1% < MARR 10%, so the project is rejected (total net outflows exceed total net inflows).
Note: if the year-3 outflow were instead a +5,00,000 inflow, net CF at year 3 would be +6,20,000, giving ERR = 18.0% > 10%, and the project would be accepted.
✓ Answer checked by Claude Opus 5.5 (high effort)
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