---
title: "Best of three mutually exclusive projects, 10-year study"
subject: "Engineering Economics"
chapter: 4
key: "semester_6/engineering_economics:mutually-exclusive-abc-study-10-years"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/mutually-exclusive-abc-study-10-years
site: BCT Engineering
---

# Best of three mutually exclusive projects, 10-year study

Engineering Economics · Chapter 4: Comparative Analysis of Alternatives

- Asked in: 2067 Mangsir, 8 marks
- Video: [Combination of projects | Engineering economics numerical | 2017 PU](https://www.youtube.com/watch?v=Qk6na2Thgls) — Sudip Dhakal
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/mutually-exclusive-abc-study-10-years
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-4

## Question

Recommend which one is best out of the following three mutually exclusive projects. Study period is 10 years. MARR = 12%.
| Project | A | B | C |
|---|---|---|---|
| Initial Investment | 5,00,000 | 6,00,000 | 7,00,000 |
| Annual Revenues | 1,50,000 | 1,50,000 | 1,70,000 |
| Annual cost | 25,000 | 25,000 | 25,000 |
| Salvage value | 1,00,000 | 1,00,000 | 70,000 |
| Useful life | 4 | 6 | 8 |

## Short answer

Compute net annual benefits (A: Rs. 125,000, B: Rs. 125,000, C: Rs. 145,000). At 12% MARR, PW over respective lives: A -56,780, B -35,411, C 48,580. Only C has positive PW, so select Project C.

## Answer

Net annual benefit = revenue - cost: A = 150,000 - 25,000 = 125,000; B = 125,000; C = 170,000 - 25,000 = 145,000.

#### Assumption for the study period (10 years)
Each project is bought once and used for its own life (4, 6, 8 years). At the end of the life it is sold at its salvage value and the money is invested elsewhere at the MARR (12%) up to year 10. Money earning exactly MARR has zero net present worth, so the extra years add nothing to PW and the projects can be compared by PW over their own lives. (Under the repeatability assumption with AW instead, the ranking is the same: AW(A) = -18,694, AW(B) = -8,613, AW(C) = +9,779 per year, so C is still best.)

#### PW calculations at 12%
| Project | N | (P/A,12%,N) | (P/F,12%,N) |
|---|---|---|---|
| A | 4 | 3.0373 | 0.6355 |
| B | 6 | 4.1114 | 0.5066 |
| C | 8 | 4.9676 | 0.4039 |

PW(A) = -500,000 + 125,000(3.0373) + 100,000(0.6355) = -500,000 + 379,669 + 63,552 = **-56,780**
PW(B) = -600,000 + 125,000(4.1114) + 100,000(0.5066) = -600,000 + 513,926 + 50,663 = **-35,411**
PW(C) = -700,000 + 145,000(4.9676) + 70,000(0.4039) = -700,000 + 720,308 + 28,272 = **48,580**

| Project | PW (Rs.) | Decision |
|---|---|---|
| A | -56,780 | reject (PW < 0) |
| B | -35,411 | reject (PW < 0) |
| C | 48,580 | accept |

**Answer: Select Project C**, the only project with positive PW (Rs. 48,580).

## Check yourself

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

1. Why are PWs compared over own lives?
   A. Study period equals lives
   B. Salvage ignored
   C. Projects repeat
   D. Money reinvested at MARR has zero PW
   Answer: D. Extra years at MARR add nothing to PW. (Key point: Study period assumption)

2. Net annual benefit of C?
   A. 25,000
   B. 170,000
   C. 145,000
   D. 125,000
   Answer: C. 170,000 - 25,000. (Key point: Net annual benefit)

3. Which PWs?
   A. A -56,780; B -35,411; C +48,580
   B. All positive
   C. A +56,780
   D. C negative
   Answer: A. Only C is positive. (Key point: PW results)

4. Which is selected?
   A. A
   B. None
   C. C, the only positive PW
   D. B
   Answer: C. A and B are rejected for negative PW. (Key point: Decision)

## Related in Engineering Economics

- [Best of P and Q for 5-year study period](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Abest-project-pq-study-5yr) — Engineering Economics, chapter 4
- [Repeatability, two mutually exclusive options](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Arepeatability-option-1-2) — Engineering Economics, chapter 4
- [IRR choose best of four, 10-year study](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Airr-choose-best-abcd-study-10) — Engineering Economics, chapter 4
- [P vs Q: 10-year study and capitalized worth](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Apq-study-10-years-capitalized-worth) — Engineering Economics, chapter 4
- [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
- [Best combination with independent and contingent projects](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Acombination-a-independent-b-contingent-c) — Engineering Economics, chapter 4

## Related in other subjects

- [Asphalt Institute design: 5.11×10⁴ ESAL/year, 12 years](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Aasphalt-institute-design-5-11e4-esal) — Transportation Engineering II, chapter 2
- [EVA; BCWS 9,50,000, BCWP 8,00,000, ACWP 10,00,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeva-bcws-bcwp-actual-s73) — Project Engineering, chapter 4
- [24-hr maximum rainfall for 50-year return period](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Agumbel-24hr-max-50yr-semilog) — Engineering Hydrology, chapter 6
- [EPS and book value; ABC project Rs 6,00,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeps-bv-abc-project-600000-b79) — Project Engineering, chapter 6