---
title: "Sensitivity of PW, most sensitive parameter"
subject: "Engineering Economics"
chapter: 6
key: "semester_6/engineering_economics:sensitivity-125000-pw-15"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-125000-pw-15
site: BCT Engineering
---

# Sensitivity of PW, most sensitive parameter

Engineering Economics · Chapter 6: Risk Analysis

- Asked in: 2076 Shrawan, 6+2+2 marks
- 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-125000-pw-15
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-6

## Question

A project costs Rs 125,000 with annual revenue of Rs 65,000 and annual cost of Rs 35,000. Salvage value will be 8% of the initial investment. Perform sensitivity analysis using PW formulation over a range of ±15% in (i) initial investment (ii) annual revenue (iii) useful life. Draw the sensitivity diagram and indicate which parameter is most sensitive.

## Short answer

Base PW = Rs 63,192 (N=10, MARR=10%, salvage=Rs 10,000). Over ±15%, annual revenue is most sensitive (PW swing Rs 119,819), then initial investment (Rs 37,500), then useful life (Rs 32,078). PW stays positive; revenue would need ~16% fall to reach zero.

## Answer

**Assumptions (not given in the question):** useful life N = 10 years, MARR = 10%, salvage value S = 8% × 125,000 = 10,000 (kept at this base value when the investment is varied). Net annual revenue = 65,000 − 35,000 = 30,000.

PW = −I + (R − C)(P/A,10%,N) + S(P/F,10%,N)

#### Base case
```text
PW₀ = −125,000 + 30,000(P/A,10%,10) + 10,000(P/F,10%,10)
    = −125,000 + 30,000(6.1446) + 10,000(0.3855)
    = 63,192
```
One parameter is changed at a time; the others stay at base values. For useful life the factors are computed by formula for the (fractional) life, e.g. at +15%, N = 11.5.

#### Results of ±15% change
| Change | PW: Initial investment | PW: Annual revenue | PW: Useful life |
|---|---|---|---|
| -15% | 81,942 | 3,283 | 46,009 |
| -10% | 75,692 | 23,253 | 52,012 |
| -5% | 69,442 | 43,223 | 57,735 |
| +0% | 63,192 | 63,192 | 63,192 |
| +5% | 56,942 | 83,162 | 68,396 |
| +10% | 50,692 | 103,132 | 73,357 |
| +15% | 44,442 | 123,102 | 78,087 |

#### Sensitivity diagram
```text
   123.1 |                                             A
         |
   107.7 |
         |                                      A
    92.3 |
         |   I                           A
    76.9 |          I                           U      U
         |                 I             U
    61.6 |                 U      *
         |          U                    I      I
    46.2 |   U             A                           I
         |
    30.8 |
         |          A
    15.4 |
         |
     0.0 |---A---------------------------------------------
         +-------------------------------------------------
            -15    -10    -5      0      5     10     15   
          % change   (y: PW in Rs '000; I = Initial investment, A = Annual revenue, U = Useful life)
```
#### Interpretation
- **Annual revenue:** PW changes from 3,283 to 123,102 over the range (swing 119,819). PW becomes zero at about -15.8% change (beyond the range tested).
- **Initial investment:** PW changes from 44,442 to 81,942 over the range (swing 37,500). PW becomes zero at about +50.6% change (beyond the range tested).
- **Useful life:** PW changes from 46,009 to 78,087 over the range (swing 32,078). PW becomes zero at about -47.0% change (beyond the range tested).

Steepest line (largest swing): **Annual revenue**. A 15% fall in annual revenue (= Rs 9,750 a year) cuts PW by about Rs 59,910, about 3.2 times the effect of a 15% rise in investment (Rs 18,750).

**Answer: The most sensitive parameter is annual revenue**, then initial investment, then useful life. The project remains acceptable (PW > 0) in all cases; only a fall of about 16% in revenue would make PW zero.

## Check yourself

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

1. Which PW formula is used, with salvage S = 8% of 125,000 = 10,000?
   A. PW = -I + (R - C)(P/A,10%,N) + S(P/F,10%,N)
   B. PW = -I + R x N
   C. PW = -I + (R + C)(P/A,10%,N)
   D. PW = -I(1 + S)
   Answer: A. Net annual revenue R - C = 30,000 is discounted by (P/A) and the salvage by (P/F). (Key point: PW formula and assumptions)

2. What is the base PW (N = 10, i = 10%)?
   A. Rs 30,000
   B. Rs 125,000
   C. Rs 10,000
   D. Rs 63,192
   Answer: D. -125,000 + 30,000(6.1446) + 10,000(0.3855) = 63,192. (Key point: Base case PW)

3. Which parameter is most sensitive and why?
   A. Useful life, because it has the smallest swing
   B. Initial investment, because it is largest
   C. Annual revenue, because it has the steepest line (swing about 119,819 over +/-15%)
   D. All equally sensitive
   Answer: C. A 15% fall in annual revenue cuts PW by about Rs 59,910, far more than the other parameters. (Key point: Most sensitive parameter)

4. How far must annual revenue fall for PW to become zero?
   A. About 50.6%
   B. About 15.8%
   C. About 47%
   D. It never becomes zero
   Answer: B. PW is zero at about -15.8% revenue, just beyond the tested range; investment needs +50.6% and life -47%. (Key point: Acceptability range)

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