---
title: "Rank projects by payback, PW, IRR, B/C"
subject: "Project Engineering"
chapter: 6
key: "semester_7/project_engineering:rank-projects-payback-pw-irr-bc"
source: https://www.bctengineer.com/q/semester_7/project_engineering/rank-projects-payback-pw-irr-bc
site: BCT Engineering
---

# Rank projects by payback, PW, IRR, B/C

Project Engineering · Chapter 6: Introduction to Project Financing

- Asked in: 2066 Bhadra (old course), 8 marks
- Video: [Pay Back Period Method, Capital Budgeting techniques, Business Finance bcom, payback period method,](https://www.youtube.com/watch?v=IKfJXYgOQTs) — DWIVEDI GUIDANCE
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/project_engineering/rank-projects-payback-pw-irr-bc
- Whole chapter: https://www.bctengineer.com/md/semester_7/project_engineering/chapter-6

## Question

Rank by using payback method, present worth, IRR and B/C ratio method.

| Item | Initial Investment | Annual Cash Flow | Life in years |
|---|---|---|---|
| 1 | Rs 60000 | 12000 | 15 |
| 2 | Rs 88000 | 22000 | 22 |
| 3 | Rs 2150 | 1500 | 3 |
| 4 | Rs 20500 | 4500 | 10 |

## Short answer

Assuming MARR 10%, payback ranking (years): Item3 (1.43) > Item2 (4.00) > Item4 (4.56) > Item1 (5.00). Present worth (Rs): Item2 (104,974) > Item1 (31,273) > Item4 (7,151) > Item3 (1,580). IRR: Item3 (48.4%) > Item2 (24.8%) > Item1 (18.4%) > Item4 (17.6%). B/C ratio: Item2 (2.193) > Item3 (1.735) > Item1 (1.521) > Item4 (1.349). Item2 gives the largest absolute gain.

## Answer

MARR is not given, so **10% per year is assumed** for present worth and B/C. Annual cash flows are treated as end-of-year benefits with no salvage value.

#### Formulas

$$
\begin{aligned}
\text{Payback} &= \frac{I}{A}\\
PW &= -I + A\,\frac{(1+i)^n - 1}{i(1+i)^n}\\
IRR:\ & PW(i) = 0\\
B/C &= \frac{A\,(P/A, i, n)}{I}
\end{aligned}
$$

#### Calculation

| Item | Payback (years) | PW at 10% (Rs) | IRR | B/C at 10% |
|---|---|---|---|---|
| 1 | 5.00 | 31,273 | 18.42% | 1.521 |
| 2 | 4.00 | 104,974 | 24.81% | 2.193 |
| 3 | 1.43 | 1,580 | 48.43% | 1.735 |
| 4 | 4.56 | 7,151 | 17.62% | 1.349 |

Example for item 1: $(P/A,10\%,15) = 7.6061$, so $PW = -60{,}000 + 12{,}000 \times 7.6061 = 31,273$ and $B/C = 1.521$. IRR is found by trial so that $PW = 0$.

#### Ranking (best first)

| Method | Ranking |
|---|---|
| Payback (shorter is better) | Item 3 > Item 2 > Item 4 > Item 1 |
| Present worth (larger is better) | Item 2 > Item 1 > Item 4 > Item 3 |
| IRR (larger is better) | Item 3 > Item 2 > Item 1 > Item 4 |
| B/C ratio (larger is better) | Item 2 > Item 3 > Item 1 > Item 4 |

**Answer:** Item 3 is best by payback and IRR and Item 2 is best by present worth and B/C. All four items have PW > 0, IRR > 10% and B/C > 1. Item 2 gives the largest absolute gain; Item 3 is very small in size (Rs 2,150), so present worth is preferred for the final decision (select Item 2 if only one can be taken).

## Check yourself

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

1. Payback best item is Item 3 because:
   A. It has the largest PW
   B. It has the shortest payback (1.43 years)
   C. It has the longest life
   D. It has the highest investment
   Answer: B. Payback = I/A = 2150/1500 = 1.43 years, the shortest. (Key point: Payback ranking)

2. The best item by present worth is:
   A. Item 1
   B. Item 3
   C. Item 2
   D. Item 4
   Answer: C. Item 2 has PW 104,974, the largest. (Key point: PW ranking)

3. The best item by IRR is:
   A. Item 2
   B. Item 1
   C. Item 4
   D. Item 3 (48.43%)
   Answer: D. Item 3 has IRR 48.43%, highest. (Key point: IRR ranking)

4. Why is present worth preferred for the final decision?
   A. Item 3 is very small in size, while Item 2 gives the largest absolute gain
   B. Payback ignores nothing
   C. IRR is always wrong
   D. B/C is not computed
   Answer: A. IRR and payback favour small Item 3, but PW shows Item 2 adds most wealth. (Key point: Final choice)

## Related in Project Engineering

- [Sources of finance; ARR, payback, IRR, PI decision](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aproject-finance-sources-investment-decision-c75) — Project Engineering, chapter 6
- [Conventional vs project financing; ARR, NPV, PI, payback](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aconventional-vs-project-financing-numerical) — Project Engineering, chapter 6
- [Capital structure; cash flowability, leverage ratio](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acapital-structure-cashflowability-leverage) — 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
- [EPS; total capital Rs 15,00,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeps-capital-1500000-pref-loan-a74) — Project Engineering, chapter 6
- [Capital budgeting; ARR numerical, Rs 100000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acapital-budgeting-arr-numerical-c72) — Project Engineering, chapter 6

## Related in other subjects

- [AW sensitivity to investment and net annual cash flow](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-aw-500000-75000) — Engineering Economics, chapter 6
- [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
- [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
- [U/B diagram, BCR with PW, discounted payback](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aub-diagram-bcr-pw-dpp) — Engineering Economics, chapter 3