---
title: "IRR evaluation, MARR 20%"
subject: "Engineering Economics"
chapter: 3
key: "semester_6/engineering_economics:irr-60000-cash-flow-20"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/irr-60000-cash-flow-20
site: BCT Engineering
---

# IRR evaluation, MARR 20%

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

- Asked in: 2069 Poush
- Video: [How to calculate the internal rate of return (IRR)](https://www.youtube.com/watch?v=a2kGbQkeYrM) — Corporate finance with Medson Nyirenda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/irr-60000-cash-flow-20
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-3

## Question

Use IRR method to evaluate the following project when MARR is 20%.
| End of year | Cash flow |
|---|---|
| 0 | -60,000 |
| 1 | 20,000 |
| 2 | 40,000 |
| 3 | 50,000 |
| 4 | 50,000 |
| 5 | 70,000 |

## Short answer

Solve PW=0 by trial: between 50% and 55%, IRR ≈ 54.5%, far above MARR of 20%, so the project is highly acceptable.

## Answer

```text
 Year : 0        1       2       3       4       5
 CF   : -60,000  20,000  40,000  50,000  50,000  70,000
```
The cash flow has one sign change, so a single IRR exists. IRR is the i at which PW(i) = 0.

#### Trial and error
| i | PW(i) |
|---|---|
| 20% | +65,624 |
| 40% | +18,946 |
| 60% | -5,363 |
| 50% | +5,021 |
| 55% | -534 |

PW changes sign between 50% and 55%. Interpolating:

IRR = 50 + 5 × 5021 / (5021 − (-534)) = **54.5%** (exact root 54.49%)

#### Decision
IRR = 54.5% > MARR = 20%. (At MARR 20%, PW = +Rs 65,624 > 0 confirms this.)

**Answer: IRR ≈ 54.5%, which is much higher than 20%, so the project is acceptable.**

## Check yourself

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

1. Why does this cash flow have a single IRR?
   A. Because MARR is 20%
   B. Only one sign change
   C. Because life is 5 years
   D. All flows are equal
   Answer: B. One sign change allows only one positive root. (Key point: Single IRR)

2. Between which rates does PW change sign?
   A. 50% (+5,021) and 55% (-534)
   B. 20% and 40%
   C. 40% and 50%
   D. 55% and 60%
   Answer: A. Sign change brackets the IRR. (Key point: Bracketing)

3. What is the IRR?
   A. About 50%
   B. About 20%
   C. About 54.5%
   D. About 65%
   Answer: C. 50 + 5 x 5021/(5021+534) = 54.5%. (Key point: IRR)

4. What is the decision?
   A. Reject, since IRR is too high
   B. Accept only if PW < 0
   C. Cannot decide
   D. Accept, since IRR 54.5% exceeds 20%
   Answer: D. IRR > MARR, and PW at 20% = +65,624 agrees. (Key point: Decision)

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