---
title: "Define inflation; NPW or IRR in constant dollars"
subject: "Engineering Economics"
chapter: 8
key: "semester_6/engineering_economics:inflation-define-npw-irr"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/inflation-define-npw-irr
site: BCT Engineering
---

# Define inflation; NPW or IRR in constant dollars

Engineering Economics · Chapter 8: Inflation and Its Impact on Project Cashflows

- Asked in: 2076 Shrawan, 1+3 marks
- Video: [Lesson 5 video 3: Escalated and constant dollar rate of return analysis](https://www.youtube.com/watch?v=Fw9D1qV3dms) — Farid Tayari
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/inflation-define-npw-irr
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-8

## Question

Define inflation. Calculate the net present worth or IRR if MARR = 13% and inflation rate is 10%.
| Year | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Constant Dollar | -5000 | 1000 | 2000 | 2000 | 2500 |

## Short answer

Inflation is the general increase in prices eroding purchasing power. Convert constant-dollar cash flows to actual dollars by (1.10)^n. Discounting at 13% yields NPW = Rs 1,958 and actual-dollar IRR ≈ 27.7%, so project is acceptable.

## Answer

**Inflation** is the general rise in prices over time, so the purchasing power of money falls: the same amount buys fewer goods and services in future years.

#### Interpretation of the data
The cash flows are given in constant dollars and MARR = 13% is the market (combined) rate, so the cash flows must be converted to actual dollars before discounting at 13%: actual = constant × (1.10)^n, f = 10%.

| Year | Constant \$ | Factor (1.10)^n | Actual \$ |
|---|---|---|---|
| 0 | -5,000 | 1.0000 | -5,000 |
| 1 | 1,000 | 1.1000 | 1,100 |
| 2 | 2,000 | 1.2100 | 2,420 |
| 3 | 2,000 | 1.3310 | 2,662 |
| 4 | 2,500 | 1.4641 | 3,660 |

#### Net present worth
```text
NPW = −5,000 + 1,100/1.13 + 2,420/1.13² + 2,662/1.13³ + 3,660.25/1.13⁴
    = −5,000 + 973.5 + 1,895.2 + 1,844.9 + 2,244.9
    = 1,958
```
**Check using constant dollars:** i' = (0.13 − 0.10)/1.10 = 2.727%. NPW = −5,000 + 1,000/1.02727 + 2,000/1.02727² + 2,000/1.02727³ + 2,500/1.02727⁴ = 1,958 (the same).

#### IRR
Solving PW = 0 on the actual-dollar flows gives IRR = 27.7% (market). In constant dollars this is (1.277 / 1.10) − 1 = 16.1%.

**Answer:** NPW = **Rs 1,958** > 0 and IRR = 27.7% (actual dollars; 16.1% in real terms) > 13%, so the project is acceptable.

## Check yourself

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

1. What does inflation mean?
   A. A general rise in prices that lowers the purchasing power of money
   B. A rise in the price of one commodity only
   C. A fall in interest rates
   D. An increase in the value of money
   Answer: A. Inflation is the general rise in prices, so money buys less over time. (Key point: Inflation)

2. The cash flows are in constant dollars and MARR = 13% is a market rate. What must be done?
   A. Discount the constant dollars directly at 13%
   B. Convert to actual dollars with (1.10)^n, then discount at 13%
   C. Discount actual dollars at 10%
   D. Subtract 10% from each cash flow
   Answer: B. Market rate applies to actual dollars, so constant flows are first inflated at f = 10%. (Key point: Consistency of rates)

3. What inflation-free rate gives the same NPW using constant dollars?
   A. 3.00%
   B. 2.73%
   C. 23%
   D. 1.30%
   Answer: B. i' = (0.13 - 0.10)/1.10 = 2.727%. (Key point: Equivalent real rate)

4. What is the NPW and conclusion?
   A. Rs 1,958; acceptable
   B. Rs 1,958; reject
   C. Rs -1,958; reject
   D. Rs 500; acceptable
   Answer: A. Both methods give NPW = Rs 1,958 > 0, so the project is acceptable (IRR 27.7% actual > 13%). (Key point: NPW result)

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