---
title: "Sensitivity chart of PW to interest and investment"
subject: "Engineering Economics"
chapter: 6
key: "semester_6/engineering_economics:sensitivity-chart-interest-investment"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/sensitivity-chart-interest-investment
site: BCT Engineering
---

# Sensitivity chart of PW to interest and investment

Engineering Economics · Chapter 6: Risk Analysis

- Asked in: 2072 Asoj, 8 marks
- Video: [Project Risk | Break-Even Analysis |Sensitivity Analysis |Scenario Analysis](https://www.youtube.com/watch?v=wEVHCLBFPT8) — 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-chart-interest-investment
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-6

## Question

Draw sensitivity chart using PW formulation of the following cash information. It is desired to evaluate the sensitivity of PW to ±30% changes on (i) interest (ii) investment.
[Figure: cash flow diagram, outflow 10000 at year 0; inflows 4000, 4500, 5000, 5500, 6000 at the ends of years 1, 2, 3, 4, 5]

## Short answer

Base PW = Rs 8,594 (i=10%). Over ±30%, investment is more sensitive: 10% investment change alters PW by Rs 1,000 vs ~Rs 500 for interest. PW remains positive; zero at ~86% investment increase or 37.4% IRR.

## Answer

**Assumption:** the interest rate (MARR) is not printed; take **i = 10%**. Cash flows: −10,000 at year 0 and 4,000, 4,500, 5,000, 5,500, 6,000 at years 1 to 5. The receipts form an arithmetic gradient series, so PW can be found term by term (or as 4,000(P/A) + 500(P/G)).

PW = −I + 4,000/(1+i) + 4,500/(1+i)² + 5,000/(1+i)³ + 5,500/(1+i)⁴ + 6,000/(1+i)⁵

#### Base case (i = 10%, I = 10,000)
```text
PW₀ = −10,000 + 4,000(0.9091) + 4,500(0.8264) + 5,000(0.7513) + 5,500(0.6830) + 6,000(0.6209)
    = −10,000 + 3,636 + 3,719 + 3,757 + 3,757 + 3,725 = 8,594
```
#### Results (one factor changed at a time)
| Change | Interest i | PW (varying i) | Investment | PW (varying I) |
|---|---|---|---|---|
| -30% | 7.0% | 10,224 | 7,000 | 11,594 |
| -20% | 8.0% | 9,657 | 8,000 | 10,594 |
| -10% | 9.0% | 9,114 | 9,000 | 9,594 |
| +0% | 10.0% | 8,594 | 10,000 | 8,594 |
| +10% | 11.0% | 8,096 | 11,000 | 7,594 |
| +20% | 12.0% | 7,618 | 12,000 | 6,594 |
| +30% | 13.0% | 7,159 | 13,000 | 5,594 |

#### Sensitivity chart
```text
    11.6 |   V
         |          V
    10.1 |   I
         |          I      *
     8.7 |                        *
         |                               I      I
     7.2 |                               V             I
         |                                      V
     5.8 |                                             V
         |
     4.3 |
         |
     2.9 |
         |
     1.4 |
         |
     0.0 |-------------------------------------------------
         +-------------------------------------------------
            -30    -20    -10     0     10     20     30   
          % change   (y: PW in Rs '000; I = interest, V = investment)
```
#### Interpretation
- A 10% change in investment alters PW by exactly Rs 1,000 (slope 100 per 1%). A 10% change in interest (1 percentage point) alters PW by only about Rs 460 to 570.
- PW is zero when investment rises by about 86% (to Rs 18,594) or when the interest rate reaches the project IRR of 37.4% (a rise of 274%).

**Answer:** The project is acceptable throughout ±30% (PW > 0 everywhere). PW is **more sensitive to the investment than to the interest rate**.

## Check yourself

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

1. How is PW found for inflows 4000, 4500, ..., 6000 over 5 years?
   A. Multiply 6000 by 5
   B. Discount each inflow term by term (or 4000(P/A) + 500(P/G)) and subtract the investment
   C. Average the inflows and subtract 10,000
   D. Use (P/F) only for the last year
   Answer: B. The inflows form a gradient series, so PW is the discounted sum less the initial outlay. (Key point: PW of gradient cash flow)

2. What is the base PW at i = 10% and investment 10,000?
   A. Rs 8,594
   B. Rs 10,000
   C. Rs 25,000
   D. Rs 5,594
   Answer: A. -10,000 + 3,636 + 3,719 + 3,757 + 3,757 + 3,725 = 8,594. (Key point: Base case PW)

3. A 10% change in investment changes PW by Rs 1,000. A 10% change in interest changes PW by:
   A. Rs 1,000
   B. More than Rs 1,000
   C. Zero
   D. Only about Rs 480 to 560
   Answer: D. PW is more sensitive to the investment than to interest, so the investment line is steeper. (Key point: Which factor is more sensitive)

## 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 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×
- [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
- [Find A from cash flow with 25000, 5A, 10000](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Afind-a-25000-5a-10000) — Engineering Economics, chapter 2
- [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
- [U/B diagram, BCR with PW, discounted payback](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aub-diagram-bcr-pw-dpp) — Engineering Economics, chapter 3

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