---
title: "Hydropower project recommendation to government"
subject: "Engineering Economics"
chapter: 3
key: "semester_6/engineering_economics:hydropower-multipurpose-bcr-60yr"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/hydropower-multipurpose-bcr-60yr
site: BCT Engineering
---

# Hydropower project recommendation to government

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

- Asked in: 2067 Mangsir, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/hydropower-multipurpose-bcr-60yr
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-3

## Question

A preliminary estimate of a multipurpose hydropower project produced the following data:
| Initial Investment | Annual Power sales | Annual irrigation benefit | Annual recreational benefit | Annual operation and maintenance | Life of the project | Salvage value |
|---|---|---|---|---|---|---|
| Rs. 50 crore | Rs. 8 crore | Rs. 1 crore | Rs. 2 crore | Rs. 1.5 crore | 60 yrs | Rs. 40 crore |
Give your suggestion to the government about the implementation of the project. Take MARR = 8%.

## Short answer

Conventional B/C ≈ 2.00, modified B/C ≈ 2.37, and NPW ≈ Rs 68 crore. The project is economically justified and should be implemented, as benefits far exceed costs.

## Answer

Government (public) projects are judged by the benefit–cost ratio on a social basis, taking all benefits (power, irrigation, recreation). Amounts are in Rs crore, MARR = 8%, N = 60 years.

```text
 yr 0: -50        yr 1..60: benefits +11, O&M -1.5        yr 60: +40
```
- Annual benefit B = 8 + 1 + 2 = Rs 11 crore
- (P/A, 8%, 60) = 12.3766; (P/F, 8%, 60) = 0.00988
- PW(B) = 11 × 12.3766 = Rs 136.14 crore
- PW(O&M) = 1.5 × 12.3766 = Rs 18.56 crore
- PW(S) = 40 × 0.00988 = Rs 0.395 crore (very small, because it comes after 60 years)

**Conventional B/C** = 136.14 / (50 + 18.56 − 0.40) = 136.14 / 68.17 = **2.00**

**Modified B/C** = (136.14 − 18.56) / (50 − 0.40) = 117.58 / 49.60 = **2.37**

Net present worth = 136.14 − 18.56 − 50 + 0.40 = Rs 68.0 crore (positive).

**Suggestion: B/C is about 2.0 (> 1) and NPW is about Rs 68 crore, so the project is economically justified and should be implemented.** Power sales alone (Rs 8 crore a year) would justify the project (B/C ≈ 1.45), and the irrigation and recreation benefits (Rs 3 crore) add further value. The project stays acceptable unless the total benefits fall by about half: at about Rs 5.5 crore a year, B/C ≈ 1.0 (break-even). Before final approval, the government should also check environmental and resettlement costs, construction delay, and the sensitivity to the MARR and to hydrological risk, which are not in the data.

## Check yourself

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

1. What annual benefit is used?
   A. Rs 8 crore
   B. Rs 9.5 crore
   C. 8 + 1 + 2 = Rs 11 crore
   D. Rs 12.5 crore
   Answer: C. All benefits to society count, not only power sales. (Key point: Total benefit)

2. Why is PW of the 40 crore salvage tiny?
   A. Salvage is ignored
   B. It arrives after 60 years, (P/F, 8%, 60) = 0.00988
   C. Salvage is divided by 60
   D. MARR is zero
   Answer: B. PW(S) = 0.395 crore. (Key point: Salvage)

3. What is the conventional B/C?
   A. About 2.0
   B. About 0.5
   C. About 1.0
   D. About 2.37
   Answer: A. 136.14 / (50 + 18.56 - 0.40). (Key point: B/C)

4. What should the government do?
   A. Reject
   B. Implement without checks
   C. Reject because power sales are only 8 crore
   D. Implement; B/C > 1 and NPW about Rs 68 crore, subject to checks of environment and resettlement
   Answer: D. Benefits comfortably exceed costs, though uncounted risks should be checked. (Key point: Recommendation)

## Related in Engineering Economics

- [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
- [Sensitivity to investment, revenue and life](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-30-investment-revenue-life-500000) — Engineering Economics, chapter 6
- [Sensitivity on investment, revenue and life; interpret](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-30-initial-100000-useful-10) — 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 with varying benefit and O&M; unrecovered balance](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Airr-500000-unrecovered-balance) — Engineering Economics, chapter 3
- [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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- [Define project; irrigation project estimate](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aproject-irrigation-estimate) — Estimating and Costing, chapter 5, asked 4×
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