IRR Calculator with NPV and MIRR

Year	Cash Flow	Present Value	Discount Effect
0	$-100000.00	$-100000.00	$0.00
1	$25000.00	$22727.27	$2272.73
2	$25000.00	$20661.16	$4338.84
3	$25000.00	$18782.87	$6217.13
4	$25000.00	$17075.34	$7924.66
5	$25000.00	$15523.03	$9476.97
6	$25000.00	$14111.85	$10888.15

Quick Answer: Investing $100,000 for $25,000 a year over six years gives an IRR of 12.98%. At a 10% discount rate the NPV is $8,881.52, so the project is worth doing. But the MIRR is only 10.64%, because IRR silently assumes you can reinvest every interim payment at 12.98% and you probably cannot.

Overview

The internal rate of return is the discount rate at which a project's net present value is exactly zero. It has no closed-form solution and is found numerically.

IRR is the most quoted investment metric and the most misused. Two problems recur.

First, it assumes interim cash flows are reinvested at the IRR itself. A project returning 13% does not mean the cash it throws off also earns 13% while you wait. MIRR fixes this by letting you state the rate at which money is actually reinvested, and it is almost always lower.

Second, a cash flow series that changes sign more than once can have several mathematically valid IRRs. This calculator reports when that happens rather than picking one and presenting it as the answer.

How This Is Calculated

NPV discounts every cash flow back to today:

NPV = \sum_{t=0}^{n} \frac{CF_t}{(1 + r)^t}

IRR is the rate that makes that sum zero:

\sum_{t=0}^{n} \frac{CF_t}{(1 + IRR)^t} = 0

There is no algebraic solution, so it is solved iteratively. The engine also counts sign changes in the series and flags the possibility of multiple roots.

MIRR takes all inflows forward to the final period at your reinvestment rate, takes all outflows back to today at your finance rate, and derives the single rate connecting them:

MIRR = \left(\frac{FV(\text{inflows at reinvestment rate})}{-PV(\text{outflows at finance rate})}\right)^{1/n} - 1

Worked Example

$100,000 invested, $25,000 a year for six years:

Total inflows: $150,000, an undiscounted profit of $50,000
IRR: 12.98%
NPV at a 10% discount rate: $8,881.52 -- positive, so accept
MIRR with reinvestment at 8%: 10.64%

Raising the discount rate to 13%: NPV falls to −$61.26. That it lands just below zero is not a coincidence: NPV crosses zero exactly at the IRR, which is why 13% is marginally too demanding for this project.

Cash flows growing 5% a year: IRR rises to 16.81% and NPV to $21,775.48, because more of the money arrives later but is larger.

Reinvestment at only 4%: MIRR falls to 8.79%, far below the 12.98% IRR. The gap is the entire value of the reinvestment assumption.

What This Does Not Account For

Irregular timing. This models annual cash flows at year end. Genuinely dated, uneven flows need XIRR, which the engine supports but this page does not expose.
Risk. IRR says nothing about the probability of achieving the cash flows. Two projects with identical IRRs can carry entirely different risk.
Project scale. A 40% IRR on $1,000 is worth less in absolute terms than a 12% IRR on $1 million. NPV, not IRR, ranks projects by value created.
Mutually exclusive projects. IRR and NPV can rank two projects differently. Where they disagree, NPV is the correct guide.
Tax and depreciation, which change the actual after-tax cash flows.
Inflation. Enter either all nominal figures with a nominal discount rate, or all real figures with a real one; mixing them produces a meaningless answer.
Financing structure, and the difference between project IRR and equity IRR.
Terminal or residual value, which for many real projects dominates the result.

Common Pitfalls

Treating IRR as an achievable return. It is achievable only if every interim cash flow is reinvested at the IRR. When it is not, MIRR is the honest number, and here it is 2.34 percentage points lower.
Ranking projects by IRR. IRR is a rate and ignores scale. Use NPV to decide which project creates more value.
Ignoring multiple roots. A series that changes sign more than once, typical where a project needs a large late outlay, can have several valid IRRs. This page tells you when that is possible.
Comparing IRRs of different lengths. A 15% IRR over two years and a 15% IRR over twenty are not equivalent propositions.
Mixing real and nominal figures. Cash flows in today's money discounted at a nominal rate will understate NPV substantially.
Forgetting that NPV crosses zero at the IRR. If your discount rate exceeds the IRR, the NPV must be negative. The 13% scenario above shows exactly that.

Frequently Asked Questions

What is a good IRR?

There is no universal answer. An IRR is good if it exceeds your cost of capital, which is why the NPV at your own discount rate is the more useful figure. A 12.98% IRR is attractive against an 8% cost of capital and unattractive against 15%.

Why is MIRR lower than IRR?

Because IRR assumes every interim cash flow is reinvested at the IRR itself, which is usually optimistic. MIRR uses the rate you actually expect to earn on that money. Here, reinvesting at 8% rather than 12.98% cuts the effective return to 10.64%.

Can a project have more than one IRR?

Yes, if the cash flow series changes sign more than once, which happens when a project requires further large investment partway through. The equation can then have several roots, and no single one is the answer. This calculator flags the possibility.

Should I use IRR or NPV to choose between projects?

NPV. IRR is a rate and ignores how much capital is deployed, so it can favour a small high-percentage project over one that creates far more value. Where the two disagree, follow NPV.

Why is my NPV negative when the IRR looks healthy?

Because your discount rate is above the IRR. NPV is exactly zero at the IRR and falls as the discount rate rises past it.

What discount rate should I use?

Your cost of capital, or the return available on an equivalent-risk alternative. It is a judgement about opportunity cost, not a figure that can be derived from the project itself.

Sources

Standard discounted cash flow mathematics. NPV and IRR are defined by the equations shown above and carry no jurisdictional or statutory content.
MIRR follows the conventional formulation, taking inflows forward at the reinvestment rate and outflows back at the finance rate.
The engine solves IRR numerically and counts sign changes in the series to detect the possibility of multiple roots.

IRR Calculator (Internal Rate of Return, NPV & MIRR)

Assumptions

Preset scenarios

Cash Flow vs Present Value

Cash Flows and Their Present Values