---
title: "Sensitivity on investment, revenue and life; interpret"
subject: "Engineering Economics"
chapter: 6
key: "semester_6/engineering_economics:sensitivity-30-initial-100000-useful-10"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-30-initial-100000-useful-10
site: BCT Engineering
---

# Sensitivity on investment, revenue and life; interpret

Engineering Economics · Chapter 6: Risk Analysis

- Asked in: 2068 Jestha, 10 marks
- Video: [Sensitivity analysis](https://www.youtube.com/watch?v=o6-HCOG1Cp4) — The Finance Storyteller
- 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-initial-100000-useful-10
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-6

## Question

Perform sensitivity analysis over a range of ±30% in (i) initial investment (ii) annual net revenue (iii) useful life.
| Initial investment = Rs 100,000 | Salvage value = Rs 10,000 |
|---|---|
| Annual benefits = Rs 25,000 | Annual expenses = Rs 3,000 |
| Useful life = 10 years | MARR = 10% |
Draw sensitivity diagram and interpret the result.

## Short answer

Base PW = Rs 39,036. Most sensitive to net annual revenue (PW zero at -28.9% change), then initial investment (PW zero at +39%), least to useful life (PW zero at -41.3%). Project accepted except when revenue falls ~29% or more.

## Answer

Net annual revenue = benefits − expenses = 25,000 − 3,000 = 22,000. PW = −I + R(P/A,10%,N) + S(P/F,10%,N), S = 10,000, MARR = 10%.

#### Base case
```text
PW₀ = −1,00,000 + 22,000(P/A,10%,10) + 10,000(P/F,10%,10)
    = −1,00,000 + 22,000(6.1446) + 10,000(0.3855)
    = −1,00,000 + 135,180 + 3,855 = 39,036
```
#### PW for ±30% change (other factors at base values)
| Change | PW: Initial investment | PW: Net annual revenue | PW: Useful life |
|---|---|---|---|
| -30% | 69,036 | -1,518 | 12,237 |
| -20% | 59,036 | 12,000 | 22,033 |
| -10% | 49,036 | 25,518 | 30,940 |
| +0% | 39,036 | 39,036 | 39,036 |
| +10% | 29,036 | 52,554 | 46,396 |
| +20% | 19,036 | 66,072 | 53,088 |
| +30% | 9,036 | 79,590 | 59,170 |

#### Sensitivity diagram
```text
    79.6 |                                             N
         |
    69.5 |   I
         |                                      N
    59.3 |          I                                  U
         |                               N      U
    49.2 |                 I
         |                               U
    39.0 |                        *
         |
    28.9 |                 U             I
         |          U      N
    18.8 |                                      I
         |   U      N
     8.6 |                                             I
         |
    -1.5 |---N---------------------------------------------
         +-------------------------------------------------
            -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 -1,518 to 79,590 over the range (swing 81,108). PW becomes zero at about -28.9% change (inside the range tested).
- **Initial investment:** PW changes from 9,036 to 69,036 over the range (swing 60,000). PW becomes zero at about +39.0% change (beyond the range tested).
- **Useful life:** PW changes from 12,237 to 59,170 over the range (swing 46,934). PW becomes zero at about -41.3% change (beyond the range tested).

- The project has a healthy margin: PW = Rs 39,036 at the base case.
- Net annual revenue has the steepest line. PW falls to zero if revenue is 29% lower (about Rs 15,647 a year), so a fall of 30% in revenue alone would make the project unacceptable.
- Investment must rise by about 39% before PW is zero, and life must fall by about 41% (to 5.9 years).

**Answer:** Base PW = Rs 39,036. The result is **most sensitive to net annual revenue**, then to initial investment, and least to useful life. The project is accepted in every case except when revenue falls by about 29% or more.

## Check yourself

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

1. What net annual revenue is used and what is the base PW?
   A. 25,000; PW 39,036
   B. 22,000; PW 39,036
   C. 22,000; PW 100,000
   D. 3,000; PW 3,855
   Answer: B. Benefits 25,000 minus expenses 3,000 = 22,000; PW = -100,000 + 22,000(6.1446) + 10,000(0.3855) = 39,036. (Key point: Net annual revenue)

2. Which parameter is most sensitive?
   A. Initial investment
   B. Useful life
   C. Salvage value
   D. Net annual revenue
   Answer: D. Net annual revenue has the steepest line (swing 81,108) versus 60,000 for investment and 46,934 for life. (Key point: Most sensitive parameter)

3. When does the project become unacceptable within the +/-30% range?
   A. When revenue falls by about 29% or more
   B. When life rises 30%
   C. When investment falls 30%
   D. Never within any change
   Answer: A. PW reaches zero at about -28.9% revenue; investment and life would need much larger changes (+39% and -41%). (Key point: Acceptability)

## Related in Engineering Economics

- [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
- [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
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- [Sensitivity in 10% steps; interpret](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-30-step-10-20000) — 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 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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