IRR Calculator - calculatorpeak.com

About the IRR Calculator

The internal rate of return is the discount rate at which a project's NPV is zero — the return the cash flows themselves imply, without assuming any cost of capital.

That independence is what makes it attractive. "This project returns 11.62%" is a statement about the project; "this project has an NPV of £4,018" is a statement about the project and whatever rate you picked.

IRR is genuinely useful. It also has three failure modes that are rarely mentioned, and this calculator reports each of them when it applies.

How to Use the IRR Calculator

Enter the cost up front as a positive number, then the cash flow for each period. Negative flows are allowed and are exactly where the interesting behaviour appears.

The reinvestment rate is what returned cash can realistically earn. It is used for the modified IRR.

Step-by-Step Example

£50,000 up front, then £15,000, £18,000, £20,000 and £12,000.

  The rate at which those discount to exactly zero:  11.62%

£65,000 back on £50,000 out, over four periods. The cash flows change sign once, so this rate is unique — there is no ambiguity about which answer to take.

Note that 11.62% is also exactly the crossover rate the NPV calculator reports for the same figures. They are the same number by definition.

Failure One: The Reinvestment Assumption

IRR quietly assumes that every pound the project returns is immediately reinvested at the IRR itself.

For a project returning 11.62%, that means assuming each £15,000 and £18,000 that comes back can go straight into something else earning 11.62%. For an unusually good project, that is precisely the thing you cannot do — if opportunities like it were freely available, it would not be unusually good.

The modified IRR fixes this by reinvesting at a rate you specify:

  IRR:                         11.62%
  MIRR, reinvesting at 6%:      9.27%
                               ──────
  Difference:                   2.34 points

MIRR is the more honest figure, and it is almost always lower. The gap widens the better the project looks and the longer it runs — which is to say, it is largest exactly where IRR is most likely to be quoted at you.

A neat way to see the assumption: set the reinvestment rate to the IRR, and MIRR returns the IRR exactly. IRR is simply MIRR with the reinvestment rate silently set to itself.

Failure Two: There Can Be More Than One IRR

Whenever the cash flows change sign more than once, the NPV equation has more than one root — and every one of them is a rate at which NPV is zero.

Take £1,000 out, £6,000 in, £11,000 out, £6,000 in:

  NPV = 0 at  0%
  NPV = 0 at  100%
  NPV = 0 at  200%

All three are correct. None of them is "the" IRR. A calculator that returns a single figure here is not solving the problem; it is hiding it, and which one you get depends on where its search happened to start.

This is not an exotic construction. Any project with a large cost at the end has it:

Decommissioning a plant or a site.
A restoration or make-good obligation on a lease.
A final tax charge.
A mid-life refit.

When it happens, use NPV at your actual cost of capital. NPV always gives one answer. Alternatively use MIRR, which is unique by construction — it collapses the series to a single outflow and a single inflow before taking a root, so there is only ever one.

Failure Three: IRR Is Blind to Scale

IRR is a rate, so it has no idea how much money is involved.

  Project A:  60% IRR on 1,000
  Project B:  12% IRR on 1,000,000

IRR ranks A higher. B is worth vastly more. If you can only do one, the rate is the wrong basis entirely.

This matters whenever IRR is used to rank rather than to screen. As a screen — "does this clear our hurdle?" — it is fine. As a ranking between projects of different sizes, it is actively misleading, and NPV is the figure that knows about size.

A Negative IRR Is a Real Answer

If £50,000 returns £2,000 in total, the IRR is about −84.82%. That is not an error and the calculator reports it rather than refusing.

There is one case where no IRR exists: when the flows are so large relative to the outlay that the NPV stays positive at every rate the calculator will consider. That is a different situation from never paying back, and it gets a different message — reporting "the flows never recover the outlay" to someone whose £1 returned £1,000,000 would be exactly backwards.

Understanding Your Result

Internal rate of return is the rate, or a count of them if there is more than one.

The cash flows restates what was entered, including the total returned.

Modified IRR is the same project without the reinvestment fiction.

Is this rate unique? counts the sign changes and says whether the answer is ambiguous.

Worth knowing gives the caution that applies: scale-blindness on an ordinary project, or how to proceed when there are several rates.

When Should You Use This Calculator?

Screening a project against a hurdle rate. IRR's best use.

Assessing a fund or deal that quotes an IRR. Ask what reinvestment it assumes, then compare against the MIRR.

Checking for multiple rates. Especially on anything with end-of-life costs.

Alongside NPV, never instead of it. They answer different questions, and NPV answers the one that decides.

Common Mistakes

Taking IRR at face value on a high-return project. The reinvestment assumption flatters it most exactly there.

Ranking projects by IRR. It ignores size.

Accepting a single IRR without checking sign changes. If the flows change sign twice, the single figure is arbitrary.

Comparing IRRs over different lengths. A 30% IRR over one year and a 30% IRR over ten are not the same opportunity.

Using IRR when cash flows are uncertain. It gives a precise-looking number regardless of how rough the inputs were.

Forgetting the terminal value. An asset worth something at the end belongs in the final flow, and leaving it out understates the rate badly.

Every figure here is an estimate for planning, not financial advice.