---
title: "Best combination with independent and contingent projects"
subject: "Engineering Economics"
chapter: 4
key: "semester_6/engineering_economics:combination-a-independent-b-contingent-c"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/combination-a-independent-b-contingent-c
site: BCT Engineering
---

# Best combination with independent and contingent projects

Engineering Economics · Chapter 4: Comparative Analysis of Alternatives

- Asked in: 2066 Magh, 10 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/combination-a-independent-b-contingent-c
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-4

## Question

Select the best combination of the projects where A is independent and B is contingent on C.
| Project | A | B | C |
|---|---|---|---|
| Initial Investment | 40,000 | 70,000 | 50,000 |
| Annual Revenues | 15,000 | 20,000 | 20000 |
| Annual cost | 2,500 | 3,500 | 0 |
| Useful life (Yrs.) | 8 | 8 | 8 |
The investment is limited to Rs. 120,000. MARR = 10%.

## Short answer

Find PW of each project (A: 26,687, B: 18,026, C: 56,699). Feasible combinations within Rs. 120,000 budget and contingency B only with C. A+C yields highest PW of Rs. 83,385 at investment Rs. 90,000.

## Answer

A is independent; B is contingent on C (B can be taken only if C is taken). Budget = Rs. 120,000, MARR = 10%, life 8 years. Net annual benefit = revenue - annual cost.

(P/A, 10%, 8) = 5.3349

#### PW of each project
| Project | Investment | Net benefit/yr | PW = -I + NB(P/A,10%,8) |
|---|---|---|---|
| A | 40,000 | 12,500 | -40,000 + 12,500(5.3349) = 26,687 |
| B | 70,000 | 16,500 | -70,000 + 16,500(5.3349) = 18,026 |
| C | 50,000 | 20,000 | -50,000 + 20,000(5.3349) = 56,699 |

#### Feasible combinations
Because B needs C, the combinations "B alone", "A + B" are infeasible. Remaining combinations (1 = taken):

| Combination | A | B | C |
|---|---|---|---|
| Do nothing | 0 | 0 | 0 |
| A | 1 | 0 | 0 |
| C | 0 | 0 | 1 |
| A + C | 1 | 0 | 1 |
| B + C | 0 | 1 | 1 |
| A + B + C | 1 | 1 | 1 |

#### Budget test and PW
| Combination | Investment (Rs.) | PW (Rs.) |
|---|---|---|
| Do nothing | 0 | 0 |
| A | 40,000 | 26,687 |
| C | 50,000 | 56,699 |
| A + C | 90,000 | 83,385 |
| B + C | 120,000 | 74,725 |
| A + B + C | 160,000 | exceeds budget |

**Answer: Select A + C** (investment Rs. 90,000), which has the highest PW of Rs. 83,385. The combination B + C uses the whole budget but gives only Rs. 74,725; A + B + C costs Rs. 160,000 and violates the limit. Each of A, B, C is individually profitable, so the budget and the contingency decide the result.

## Check yourself

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

1. B is contingent on C. Which statement is correct?
   A. B can be taken only if C is taken
   B. C can be taken only if B is taken
   C. B and C cannot be taken together
   D. B must always be taken with A
   Answer: A. A contingent project depends on a prerequisite; B requires C, so B alone and A+B are infeasible. (Key point: Contingent projects)

2. Why is A+B+C rejected?
   A. Its PW is negative
   B. B is not contingent on C
   C. A is independent so it cannot be combined
   D. Its investment of Rs. 160,000 exceeds the Rs. 120,000 budget
   Answer: D. 40,000 + 70,000 + 50,000 = 160,000 > 120,000, so it is infeasible regardless of PW. (Key point: Budget constraint)

3. Among feasible combinations, which is chosen and why?
   A. B + C, because it uses the full budget
   B. A + C, because it has the highest PW (Rs. 83,385) within budget
   C. C alone, because it has the highest individual PW
   D. A alone, because it is the cheapest
   Answer: B. Choose the budget-feasible combination with maximum PW: A+C = 26,687 + 56,699 = 83,385, above B+C at 74,725. (Key point: Selecting best combination)

## Related in Engineering Economics

- [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×
- [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
- [Best of three mutually exclusive projects, 10-year study](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Amutually-exclusive-abc-study-10-years) — Engineering Economics, chapter 4
- [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
- [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
- [Mutually exclusive, independent and contingent projects](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Amutually-exclusive-independent-contingent) — Engineering Economics, chapter 4, asked 4×

## Related in other subjects

- [EPS and book value; 500 shares, EBIT 40,000, tax 40%](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeps-bv-500-shares-300-pref) — Project Engineering, chapter 6
- [Gumbel flood at given risk, 50-year project life](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Agumbel-risk-63-58-4200) — Engineering Hydrology, chapter 6
- [Best financing option; EBIT Rs 350,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Abest-option-two-options-ebit-350000) — Project Engineering, chapter 6
- [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