---
title: "ERR from separate inflow and outflow rows"
subject: "Engineering Economics"
chapter: 3
key: "semester_6/engineering_economics:err-cash-inflow-outflow-480000"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/err-cash-inflow-outflow-480000
site: BCT Engineering
---

# ERR from separate inflow and outflow rows

Engineering Economics · Chapter 3: Basic Methodologies of Engineering Economic Analysis

- Asked in: 2068 Jestha, 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-cash-inflow-outflow-480000
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-3

## Question

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 |

## 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.

## Answer

#### 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 |

```text
 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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the first step with inflow and outflow rows?
   A. Use only the inflow row
   B. Add them per year to get net CF
   C. Use only the outflow row
   D. Average them
   Answer: B. Net flow = inflow + outflow each year. (Key point: Netting)

2. Which years' net flows are discounted to year 0?
   A. Years 2 and 4
   B. Only year 0
   C. Years 0, 1, 3 and 5
   D. All years
   Answer: C. These have negative net CF: -480k, -40k, -380k, -200k. (Key point: Outflows)

3. What is epsilon used for versus MARR?
   A. MARR moves flows
   B. Epsilon moves flows; MARR is for the decision
   C. Both are the decision
   D. Epsilon is the decision
   Answer: B. Epsilon = 8% reinvests; MARR = 10% is the threshold. (Key point: Rates)

4. ERR = -4.1%. Conclusion?
   A. Accept
   B. Accept since IRR may exceed
   C. Cannot compute
   D. Reject, as ERR is below MARR
   Answer: D. Total net outflows exceed net inflows. (Key point: Result)

## Related in Engineering Economics

- [ERR with MARR = ε = 10%](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aerr-six-year-cash-flow) — Engineering Economics, chapter 3
- [ERR with MARR 12% and reinvestment 14%](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aerr-reinvestment-14) — Engineering Economics, chapter 3
- [ERR method to select best of three projects](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aerr-select-best-abc) — Engineering Economics, chapter 4
- [IRR by AW, both BCR by FW, and ERR](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Airr-aw-bcr-fw-err-250000) — Engineering Economics, chapter 3
- [IRR evaluation, MARR 20%](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Airr-60000-cash-flow-20) — Engineering Economics, chapter 3
- [Define IRR; find IRR and ERR of project](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Airr-err-define-project-15) — Engineering Economics, chapter 3, asked 2×

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