---
title: "IRR selection among A, B, C, D"
subject: "Engineering Economics"
chapter: 4
key: "semester_6/engineering_economics:irr-abcd-mutually-exclusive-combination"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/irr-abcd-mutually-exclusive-combination
site: BCT Engineering
---

# IRR selection among A, B, C, D

Engineering Economics · Chapter 4: Comparative Analysis of Alternatives

- Asked in: 2070 Bhadra, 8+4 marks
- Video: [Incremental IRR - Engineering Economics Lightboard](https://www.youtube.com/watch?v=g1hI58w_FtI) — Engineering Economics Guy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/irr-abcd-mutually-exclusive-combination
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-4

## Question

Use IRR method to select best project. MARR = 12%.
|  | A | B | C | D |
|---|---|---|---|---|
| Initial Investment | 1100 | 1500 | 2750 | 2000 |
| Annual Income | 500 | 700 | 1200 | 950 |
| Useful Life | 4 | 4 | 4 | 4 |
| Salvage Value | 250 | 500 | 800 | 1000 |
| MARR | 15% | 15% | 15% | 15% |
Select the best combination if A, B and C are mutually exclusive.

## Short answer

Part 1: All four mutually exclusive. Incremental IRRs: A→B 45.1%, B→D 50.0%, D→C 3.1% (<12%). Select D. Part 2: A,B,C mutually exclusive, D independent. Best of A,B,C is C; add D. Select C+D combination.

## Answer

Assumptions: MARR = 12% as stated in the question (the table repeats MARR = 15%; the decisions below are the same at 15%, see the note at the end). Cash flows over 4 years are: -Initial investment at year 0, annual income each year, and salvage value added in year 4. The IRR of an increment is compared with MARR.

#### Part 1: IRR of each project and incremental analysis (all four mutually exclusive)
| Project | Investment | Income/yr | Salvage | IRR | Result |
|---|---|---|---|---|---|
| A | 1,100 | 500 | 250 | 33.57% | accept |
| B | 1,500 | 700 | 500 | 36.87% | accept |
| C | 2,750 | 1200 | 800 | 32.58% | accept |
| D | 2,000 | 950 | 1000 | 40.51% | accept |

All IRRs are above 12%. Rank by investment: A (1,100) < B (1,500) < D (2,000) < C (2,750). Incremental cash flows are in years 0, 1-3, 4.

| Increment | Cash flows | Incremental IRR | Decision |
|---|---|---|---|
| A → B | [-400, 200, 200, 200, 450] | 45.1% | > 12%, keep B |
| B → D | [-500, 250, 250, 250, 750] | 50.0% | > 12%, keep D |
| D → C | [-750, 250, 250, 250, 50] | 3.1% | < 12%, reject C, keep D |

**Best single project: D.**

#### Part 2: A, B, C mutually exclusive; D independent
Among A, B, C only one can be taken. D can be added to whichever is chosen, and D itself is acceptable (IRR 40.5% > 12%).

Best of A, B, C by incremental IRR:
- A → B: 45.1% > 12%, B beats A
- B → C: 27.2% > 12%, C beats B

So C is the best of the three. Because D is independent and acceptable, it is added to the best of the exclusive group.

**Answer: Part 1: select D. Part 2: select the combination C + D** (total investment 4,750). Note: at MARR = 15% the same choices hold because all incremental IRRs used are above 15% (the D → C increment is only 3.1%, still rejected).

## Check yourself

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

1. How is salvage included?
   A. Added in year 4
   B. Subtracted at year 0
   C. Ignored
   D. Added each year
   Answer: A. Salvage is a year-4 inflow along with the annual income. (Key point: Cash flows)

2. With all four mutually exclusive, which is selected?
   A. D
   B. A
   C. C
   D. B
   Answer: A. B -> D earns 50% and D -> C only 3.1% < 12%, so D is best. (Key point: Part 1 result)

3. In Part 2, A, B, C are mutually exclusive and D independent. What is chosen?
   A. C + D
   B. D only
   C. A + D
   D. B + D
   Answer: A. C beats B (27.2% > 12%), and D is independent and acceptable. (Key point: Part 2 structure)

## Related in Engineering Economics

- [Incremental IRR to select best of A to D](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aincremental-irr-abcd-salvage-25) — Engineering Economics, chapter 4
- [IRR to select best of A, B, C (15 years)](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Airr-select-abc-15yr) — Engineering Economics, chapter 4
- [PW sensitivity to investment, income, life by ±25%](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-pw-400000-60000-25) — Engineering Economics, chapter 6
- [Repeatability assumption, select best of three projects](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Arepeatability-abc-14) — Engineering Economics, chapter 4, asked 2×
- [Best project for 4-year and 8-year service periods](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aselect-best-project-fw-4yr-irr) — Engineering Economics, chapter 4
- [IRR by trial and error; investment decision](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Airr-trial-error-25000) — Engineering Economics, chapter 3

## Related in other subjects

- [Feasibility using two methods, MARR 15%](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Afeasibility-two-methods-marr-15) — Project Engineering, chapter 6
- [RoR best installed capacity (USD 1200 million)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aror-best-capacity-usd-1200) — Hydropower Engineering, chapter 3
- [Bulb life of two companies: grouped data](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Abulbs-two-companies-grouped-data) — Probability and Statistics, chapter 6, asked 2×
- [Best installed capacity at 12% interest](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Abest-installed-capacity-12pct) — Hydro Power, chapter 3