---
title: "Sensitivity to investment, revenue and life"
subject: "Engineering Economics"
chapter: 6
key: "semester_6/engineering_economics:sensitivity-30-investment-revenue-life-500000"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-30-investment-revenue-life-500000
site: BCT Engineering
---

# Sensitivity to investment, revenue and life

Engineering Economics · Chapter 6: Risk Analysis

- Asked in: 2069 Poush
- Video: [Sensitivity Analysis |Economics |Board Exam Solution in NEPALI](https://www.youtube.com/watch?v=Zo-O4TCa8TA) — OPengineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-30-investment-revenue-life-500000
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-6

## Question

Perform sensitivity analysis of the following project over a range of ±30% in (i) initial investment (ii) net annual revenue (iii) useful life (year). Draw also sensitivity diagram.
| Initial investment (Rs.) | 5,00,000 |
|---|---|
| Net annual revenue (Rs.) | 1,20,000 |
| Salvage value (Rs.) | 80,000 |
| Useful life (year) | 6 |
| MARR | 10% |

## Short answer

Base PW = Rs 67,789. Most sensitive to net annual revenue (PW zero at -13% change), then initial investment (PW zero at +13.6%), least to useful life (PW zero at -17.8%). Project acceptable at base but unacceptable if investment rises >14% or revenue falls >13%.

## Answer

PW = −I + A(P/A,10%,N) + S(P/F,10%,N). One parameter is varied at a time, the others held at base values (fractional lives use the same formula).

#### Base case
```text
PW₀ = −5,00,000 + 1,20,000(P/A,10%,6) + 80,000(P/F,10%,6)
    = −5,00,000 + 1,20,000(4.3553) + 80,000(0.5645)
    = −5,00,000 + 522,631 + 45,158 = 67,789
```
#### PW for ±30% change
| Change | PW: Initial investment | PW: Net annual revenue | PW: Useful life |
|---|---|---|---|
| -30% | 217,789 | -89,000 | -50,531 |
| -20% | 167,789 | -36,737 | -8,815 |
| -10% | 117,789 | 15,526 | 30,582 |
| +0% | 67,789 | 67,789 | 67,789 |
| +10% | 17,789 | 120,052 | 102,929 |
| +20% | -32,211 | 172,315 | 136,115 |
| +30% | -82,211 | 224,579 | 167,457 |

#### Sensitivity diagram
```text
   224.6 |   I                                         N
         |
   185.4 |
         |          I                           N      U
   146.2 |
         |                 I             N      U
   107.0 |                               U
         |
    67.8 |                        *
         |
    28.6 |                 U
     9.0 |-----------------N-------------I-----------------
   -10.6 |          U
         |          N                           I
   -49.8 |   U
         |
   -89.0 |   N                                         I
         +-------------------------------------------------
            -30    -20    -10     0     10     20     30   
          % change   (y: PW in Rs '000; I = Initial investment, N = Net annual revenue, U = Useful life)
```
#### Interpretation
- **Net annual revenue:** PW changes from -89,000 to 224,579 over the range (swing 313,579). PW becomes zero at about -13.0% change (inside the range tested).
- **Initial investment:** PW changes from -82,211 to 217,789 over the range (swing 300,000). PW becomes zero at about +13.6% change (inside the range tested).
- **Useful life:** PW changes from -50,531 to 167,457 over the range (swing 217,988). PW becomes zero at about -17.8% change (inside the range tested).

**Answer:** The project is acceptable at the base values (PW = Rs 67,789) and over most of the range. It becomes unacceptable (PW < 0) if the investment rises by more than about 14% or the net annual revenue falls by more than about 13%. PW is **most sensitive to net annual revenue** and then to the initial investment; useful life is the least sensitive, but a life shorter by more than about 18% also gives PW < 0.

## Check yourself

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

1. What is the base PW (I = 5,00,000, A = 1,20,000, S = 80,000, N = 6, 10%)?
   A. Rs 67,789
   B. Rs 522,631
   C. Rs 45,158
   D. Rs 580,000
   Answer: A. -500,000 + 120,000(4.3553) + 80,000(0.5645) = 67,789. (Key point: Base case PW)

2. Which parameter gives the largest swing in PW over +/-30%?
   A. Initial investment
   B. Salvage value
   C. Net annual revenue
   D. Useful life
   Answer: C. Net annual revenue swing is 313,579, the largest; useful life is the least sensitive. (Key point: Most sensitive parameter)

3. By roughly how much can the investment rise before PW becomes zero?
   A. About 30%
   B. About 13.6%
   C. About 50%
   D. About 5%
   Answer: B. PW becomes zero at about +13.6% change in investment, inside the tested range. (Key point: Break-even change in investment)

4. Which statement fits the result?
   A. Project is unacceptable at the base values
   B. Revenue can fall 30% without effect
   C. It becomes unacceptable if investment rises more than about 14% or revenue falls more than about 13%
   D. Life changes never matter
   Answer: C. Base PW is positive but the margin is small, so those changes make PW negative. (Key point: Conclusion)

## Related in Engineering Economics

- [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
- [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
- [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
- [Sensitivity of PW, most sensitive parameter](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-125000-pw-15) — Engineering Economics, chapter 6
- [Sensitivity of PW to investment and MARR](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-investment-marr-10-50) — Engineering Economics, chapter 6, asked 2×

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