NPV vs IRR: How to Evaluate an Investment (Worked Example)

When deciding whether to fund a project, two metrics dominate capital budgeting: Net Present Value (NPV) and Internal Rate of Return (IRR). They are closely related but answer different questions. This guide explains both, works an example, and shows when they can disagree.

Run the numbers on any cash-flow stream with the free NPV & IRR Calculator.

What Is NPV?

NPV is the sum of all cash flows discounted to today's value at a required rate of return (the discount rate):

📐 Formula

NPV = Σ CFₜ / (1 + r)ᵗ for t = 0, 1, 2, …, n CFₜ = cash flow in period t r = discount rate (cost of capital)

The rule: accept the project if NPV ≥ 0 — it creates value.

What Is IRR?

IRR is the discount rate that makes NPV equal to zero:

📐 Formula

0 = Σ CFₜ / (1 + IRR)ᵗ

The rule: accept if IRR ≥ your required rate of return.

Worked Example

Invest $1,000 today and receive $500 per year for three years, with a required return of 10%.

Step 1: Discount each cash flow

📐 Formula

Year 0: −1000 Year 1: 500 / 1.10 = 454.55 Year 2: 500 / 1.10² = 413.22 Year 3: 500 / 1.10³ = 375.66

Step 2: Sum for NPV

📐 Formula

NPV = −1000 + 454.55 + 413.22 + 375.66 ≈ 243.43

NPV is positive, so accept the project.

Step 3: Find the IRR

The IRR is the rate where NPV = 0. For these cash flows it is about 23.4%. Since 23.4% > the 10% required return, IRR also says accept — the two agree here.

When NPV and IRR Disagree

For a single project with normal cash flows they usually agree, but conflicts arise when:

Comparing mutually exclusive projects of different sizes — IRR can favor a smaller project with a higher percentage return even though a larger project adds more absolute value. Trust NPV in this case.
Non-conventional cash flows (sign changes more than once) can produce multiple IRRs or none. NPV remains reliable.

That is why NPV is generally considered the more robust decision rule.

Payback and Profitability Index

Two supporting metrics:

Payback period — how long until cumulative cash flows recover the initial outlay.
Profitability Index (PI) = PV of future inflows ÷ initial investment; PI ≥ 1 means accept.

Try It Yourself

Enter your cash flows and discount rate into the NPV & IRR Calculator to get NPV, IRR, profitability index, and payback (both simple and discounted) with a step-by-step breakdown. To project the underlying cash flows first, use the Cash Flow Forecast; for financing costs, the Loan / EMI Calculator.

Key Takeaways

NPV discounts all cash flows to today; accept when NPV ≥ 0.
IRR is the rate that makes NPV zero; accept when IRR ≥ required return.
For −1000 then 500×3 at 10%: NPV ≈ 243, IRR ≈ 23.4%.
When they conflict (different sizes or unusual cash flows), rely on NPV.