IRR is not calculated on already-discounted cash flows. Instead, IRR is itself the discount rate that makes a set of future cash flows equal in value to the initial investment. In other words, you feed raw, undiscounted cash flows into the IRR formula, and it tells you what discount rate would bring the net present value (NPV) of those cash flows to exactly zero.
This is a common point of confusion because IRR and discounted cash flow (DCF) analysis are closely related. Both NPV and IRR are types of discounted cash flow analysis. But the key distinction is that with NPV, you choose a discount rate and apply it to calculate a dollar value. With IRR, the discount rate is the unknown you’re solving for.
How IRR Actually Works
The IRR formula takes your raw projected cash flows, including the initial investment (a negative number) and all expected future returns (positive numbers), and finds the single rate that makes the whole series net out to zero. Written out, it looks like this:
0 = Cash Flow at Year 0 + (Cash Flow at Year 1 ÷ (1 + IRR)) + (Cash Flow at Year 2 ÷ (1 + IRR)²) + … and so on for every period.
The “(1 + IRR)” in each term is doing the discounting. So the calculation does involve discounting, but the discounting happens inside the formula as part of the solving process. You don’t pre-discount the cash flows before plugging them in. If you did, you’d be double-discounting, which would give you a meaningless result.
Why IRR Can’t Be Solved Directly
Unlike simpler financial formulas, you can’t rearrange the IRR equation to isolate the answer on one side. Because the unknown rate appears in every term and is raised to a different power each time, the formula has no clean algebraic solution. Instead, IRR is calculated iteratively through trial and error: software tests one discount rate, checks whether NPV comes out above or below zero, adjusts, and tries again until it converges on the rate that hits zero.
This is why IRR is almost always computed by a spreadsheet function (like Excel’s =IRR()) or financial calculator rather than by hand. The tool is running dozens of iterations behind the scenes to home in on the answer.
IRR vs. NPV: Same Family, Different Questions
Both IRR and NPV belong to the discounted cash flow family of analysis. Both take estimated future payments from a project and discount them back to present value. The difference is what each one tells you.
NPV asks: “Given a specific discount rate I’ve chosen (say, 8%), how much value does this project create in today’s dollars?” The answer is a dollar amount. IRR asks: “What rate of return does this project actually deliver?” The answer is a percentage. You then compare that percentage to your required rate of return (sometimes called a hurdle rate). If the IRR exceeds the hurdle rate, the project creates value. If it falls short, it doesn’t.
For straightforward projects with a single upfront investment followed by a series of positive returns, IRR and NPV will always agree on whether a project is worth pursuing. The two methods only diverge when you’re ranking multiple projects against each other or dealing with unusual cash flow patterns.
When IRR Gets Unreliable
IRR works cleanly when cash flows follow a conventional pattern: one negative outflow at the start, then positive inflows for the remaining years. But some projects have non-conventional cash flows, where the sign flips more than once. For example, a project might require an initial investment (negative), generate returns for several years (positive), then need a large decommissioning cost at the end (negative again).
When cash flows change sign more than once, the math can produce multiple IRR values, or no valid IRR at all. A rule from algebra called Descartes’ Rule of Signs tells us the maximum number of possible IRRs equals the number of sign changes. So a cash flow sequence of negative, positive, positive, positive, negative has two sign changes and could yield two different IRRs. Neither one is more “correct” than the other, which makes the result impossible to interpret meaningfully.
In these situations, NPV is the more reliable tool because it always produces a single, clear answer for any given discount rate.
The Practical Takeaway
If you’re building an IRR calculation, always use your projected cash flows in their raw, undiscounted form. The initial investment goes in as a negative number at time zero, and each future period’s expected cash flow goes in at face value. The IRR function handles all the discounting internally as it searches for the rate that zeroes out the NPV. Pre-discounting those cash flows before running the calculation is one of the most common spreadsheet errors in financial modeling, and it will significantly understate the project’s actual rate of return.