---
title: "IRR choose best of four, 10-year study"
subject: "Engineering Economics"
chapter: 4
key: "semester_6/engineering_economics:irr-choose-best-abcd-study-10"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/irr-choose-best-abcd-study-10
site: BCT Engineering
---

# IRR choose best of four, 10-year study

Engineering Economics · Chapter 4: Comparative Analysis of Alternatives

- Asked in: 2076 Shrawan, 6 marks
- Video: [IRR Method Board Exam Solution in NEPALI |Present , Annual and Future Worth](https://www.youtube.com/watch?v=tRDAlK2is0A) — OPengineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/irr-choose-best-abcd-study-10
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-4

## Question

Choose the best project among these alternatives using IRR, if MARR = 10% and study period is 10 years.
| Project | A | B | C | D |
|---|---|---|---|---|
| First Cost Rs. | 900 | 1500 | 2500 | 4000 |
| Annual Revenue Rs. | 150 | 276 | 400 | 925 |

## Short answer

Project C is rejected (IRR 9.61% < 10% MARR). Incremental analysis: A→B IRR 16.4% > 10%, so B beats A; B→D IRR 22.6% > 10%, so D beats B. Project D is selected.

## Answer

Assumptions: each project lasts the 10-year study period with no salvage value (none is given), so the cash flow of each is a single outlay followed by 10 equal annual revenues. IRR is the rate that makes PW = 0; for the incremental analysis the project with the larger investment is accepted only if the IRR on its extra investment is at least MARR = 10%.

#### Step 1: IRR of each project
Solve -First cost + Revenue (P/A, i, 10) = 0, i.e. (P/A, i, 10) = First cost / Revenue.

| Project | First cost | Revenue/yr | (P/A, i, 10) needed | IRR | vs MARR 10% |
|---|---|---|---|---|---|
| A | 900 | 150 | 6.000 | 10.56% | Accept |
| B | 1,500 | 276 | 5.435 | 12.96% | Accept |
| C | 2,500 | 400 | 6.250 | 9.61% | Reject |
| D | 4,000 | 925 | 4.324 | 19.10% | Accept |

(Check: at 10%, (P/A, 10%, 10) = 6.1446; a needed factor below this means IRR above 10%.)

C (IRR 9.61%) is below MARR, so it is dropped. A, B, D remain, arranged by increasing investment.

#### Step 2: incremental analysis (investment A < B < D)
| Increment | Extra investment | Extra revenue/yr | Incremental IRR | Decision |
|---|---|---|---|---|
| A → B | 600 | 126 | 16.40% | > 10%, B is better than A |
| B → D | 2,500 | 649 | 22.57% | > 10%, D is better than B |

For information, B → C would give 4.12% and C → D 32.98%.

**Answer: Choose project D** (largest investment 4,000 whose last increment still earns 22.6% > 10%; its own IRR is 19.1%).

## Check yourself

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

1. What happens to a project whose own IRR is below MARR?
   A. It is dropped
   B. It is added to the best
   C. It is chosen
   D. It is repeated
   Answer: A. C (9.61% < 10%) is rejected before incremental analysis. (Key point: Own IRR screening)

2. In incremental IRR analysis, projects are compared in order of:
   A. Alphabetical
   B. Decreasing IRR
   C. Increasing investment
   D. Increasing life
   Answer: C. They are arranged by increasing initial investment: A < B < D. (Key point: Order of increments)

3. When is the larger investment preferred?
   A. When its own IRR is highest
   B. When first cost is lowest
   C. When incremental IRR on the extra investment is at least MARR
   D. When revenue is highest
   Answer: C. The extra investment is justified only if it earns at least MARR. (Key point: Incremental rule)

4. Which project is selected?
   A. B
   B. C
   C. A
   D. D
   Answer: D. B -> D increment earns 22.57% > 10%, so D is chosen. (Key point: Final choice)

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