---
title: "Both types of B/C ratio using PW"
subject: "Engineering Economics"
chapter: 3
key: "semester_6/engineering_economics:bcr-pw-initial-25-lakh"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/bcr-pw-initial-25-lakh
site: BCT Engineering
---

# Both types of B/C ratio using PW

Engineering Economics · Chapter 3: Basic Methodologies of Engineering Economic Analysis

- Asked in: 2066 Magh, 6 marks
- Video: [Benefit cost ratio | Present Worth calculation |Engineering Economics |Board Exam Solution in NEPALI](https://www.youtube.com/watch?v=Nl1CN7e--7U) — OPengineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/bcr-pw-initial-25-lakh
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-3

## Question

Evaluate both types of B/C ratio using PW.
Initial cost = Rs. 25 lakh
Salvage value = Rs. 5 lakh
Useful life = 10 years
Annual benefits = Rs. 10 lakh
Annual O & M = Rs. 5 lakh
MARR = 8%

## Short answer

Conventional B/C = 1.19, Modified B/C = 1.48. Both exceed 1, so project is acceptable. Calculated using present worth of benefits (Rs 67.101 lakh), costs (Rs 56.234 lakh), and salvage at 8% over 10 years.

## Answer

Amounts in Rs lakh. I = 25, S = 5, N = 10, annual benefit = 10, O&M = 5, MARR = 8%.

```text
 yr 0: -25      yr 1..10: +10 benefit, -5 O&M      yr 10: +5
```
Factors: (P/A, 8%, 10) = 6.7101; (P/F, 8%, 10) = 0.4632

- PW(B) = 10 × 6.7101 = 67.101
- PW(O&M) = 5 × 6.7101 = 33.550
- PW(S) = 5 × 0.4632 = 2.316

**Conventional B/C** = PW(B) / [I + PW(O&M) − PW(S)] = 67.101 / (25 + 33.550 − 2.316) = 67.101 / 56.234 = **1.193**

**Modified B/C** = [PW(B) − PW(O&M)] / [I − PW(S)] = (67.101 − 33.550) / (25 − 2.316) = 33.550 / 22.684 = **1.479**

**Answer: conventional B/C = 1.19, modified B/C = 1.48. Both are greater than 1, so the project is acceptable.**

## Check yourself

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

1. In the conventional B/C ratio using PW, what goes in the denominator?
   A. Initial cost + PW(O&M) + PW(salvage)
   B. Initial cost + PW(O&M) - PW(salvage)
   C. PW of O&M only
   D. Initial cost - PW(salvage)
   Answer: B. Conventional B/C treats O&M and investment as costs in the denominator, with salvage value reducing the cost. (Key point: Conventional B/C formula)

2. How does the modified B/C ratio treat O&M cost?
   A. It is added to the denominator
   B. It is ignored
   C. It is multiplied by the salvage value
   D. It is subtracted from benefits in the numerator
   Answer: D. Modified B/C = [PW(B) - PW(O&M)] / [I - PW(S)], so O&M reduces the numerator. (Key point: Modified B/C formula)

3. For the Rs 25 lakh project, which pair of ratios is correct?
   A. Conventional 1.19, modified 1.48
   B. Conventional 1.48, modified 1.19
   C. Conventional 0.84, modified 1.48
   D. Both 1.19
   Answer: A. Conventional = 67.101/56.234 = 1.19; modified = 33.550/22.684 = 1.48. (Key point: Result values)

4. Both ratios are greater than 1. What is the conclusion?
   A. Project is only break-even
   B. Cannot decide without IRR
   C. Reject, as ratio must be below 1
   D. Project is acceptable
   Answer: D. A B/C ratio above 1 means benefits exceed costs, so the project is acceptable. (Key point: Decision rule)

## Related in Engineering Economics

- [Sensitivity on initial cost and life; interpret](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-30-initial-cost-life-25) — Engineering Economics, chapter 6
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- [Both types of BCR, gradient income and cost](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Abcr-both-growing-12years) — Engineering Economics, chapter 3
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