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Define inflation; NPW or IRR in constant dollars

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.

Define inflation. Calculate the net present worth or IRR if MARR = 13% and inflation rate is 10%.

Year01234
Constant Dollar-50001000200020002500

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%.

YearConstant $Factor (1.10)^nActual $
0-5,0001.0000-5,000
11,0001.10001,100
22,0001.21002,420
32,0001.33102,662
42,5001.46413,660

Net present worth

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.

✓ Answer checked by Claude Opus 5.5 (high effort)

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