Investment appraisal Updated November 2026

IRR (internal rate of return)

The internal rate of return is the discount rate at which the NPV of a project's cash flows is exactly zero. Accept the project if the IRR exceeds the required return. There is no closed formula except in simple cases; it is found by iteration, which Excel's IRR function does for you.

Syntax

0 = CF_0 + CF_1 / (1 + IRR) + ... + CF_n / (1 + IRR)^n

Part	What it is
`CF_t`	Cash flows, starting with the negative investment at t = 0
`IRR`	The rate solved for

Examples

Invest 1,000, receive 500 a year for 3 years
Solve -1,000 + 500 x (1 - (1 + i)^-3) / i = 0

Result: IRR = 23.38%

Excel: =IRR({-1000, 500, 500, 500})

Invest 10,000, receive 3,000, 4,000, 5,000

Result: IRR = 8.90% (NPV at 8% was +176.29, so IRR is just above 8%)

Excel: =IRR(A1:A4) with the four cash flows in A1:A4

Single cash flow: invest 1,000, receive 1,331 after 3 years
IRR = (1,331 / 1,000)^(1/3) - 1

Result: IRR = 10.00%

Common mistakes

Entering all positive cash flows: IRR needs at least one negative and one positive value, otherwise Excel returns #NUM!.
Trusting IRR when cash flows change sign more than once (for example a clean-up cost at the end); there can be multiple IRRs or none, so use NPV.
Ranking mutually exclusive projects by IRR: a small project can have a higher IRR but a lower NPV than a large one.

Practice IRR (internal rate of return)

These drills check your answer on live data, free, no account needed.

Internal rate of returnAn investment costs $25,000 today and returns $17,500, $15,500 and $14,000 at the end of years 1 to 3. What is its internal rate of return?
Return needed to reach a goalYou have $2,000 today and want $3,000 in 5 years, with no further deposits. What annual return, compounded annually, gets you there exactly?

Questions

What is a good IRR?

One above the cost of capital or hurdle rate for the project's risk. For a company with a 9% WACC, a 12% IRR is attractive; for a venture investor, 25% or more is typical.

IRR vs CAGR: what is the difference?

CAGR is the IRR of a single investment with a single ending value. IRR generalizes it to many cash flows in and out at different times.

NPV (net present value)Net present value is the sum of discounted cash flows minus the initial investment. Examples at 10% and 8%, the accept rule, Excel NPV and the sign mistake.
CAGRCAGR = (ending value / beginning value)^(1/years) - 1. Examples for investments and revenue growth, Excel RRI, and why CAGR differs from the average return.
Payback periodPayback period is the time it takes cumulative cash inflows to equal the initial investment. Formula for even and uneven cash flows, examples, interpolation.
Profitability indexThe profitability index is the present value of future cash flows divided by the initial investment, or 1 + NPV / investment. Examples and the accept rule.