IRR Calculator

How the calculator finds the IRR

There is no algebraic formula for IRR once there are more than a couple of cash flows, so it is found numerically. This calculator scans NPV across rates from −99% to 1,000% on a fine grid (0.1-point steps up to 100%, 1-point steps above), and wherever NPV changes sign it halves that interval 200 times until the rate is pinned down far beyond two decimals.

Cash flows are entered as a comma-separated list for years 1, 2, 3 and so on (up to 50). The initial investment is entered as a positive number and treated as an outflow at time zero. A later year can be negative, for example a major repair, by typing a minus sign. The calculator reports an error if there is no positive inflow at all, or if NPV never changes sign anywhere between −99% and 1,000%, which means the flows have no IRR in that range. If it finds more than one IRR, it shows the smallest and tells you how many there are (see below).

NPV profile: what the IRR actually is

Plot NPV against the discount rate and IRR is the point where the curve crosses zero. For the example flows:

For a conventional project (one outflow, then inflows), NPV falls as the rate rises. So a hurdle rate below the IRR always gives a positive NPV and one above it a negative NPV, and the IRR and NPV rules give the same accept-or-reject answer.

IRR vs NPV: where they disagree

The size problem in one example: Project A costs $1,000 and returns $1,500 after one year (IRR 50%). Project B costs $100,000 and returns $120,000 (IRR 20%). At a 10% cost of capital, A's NPV is $363.64 and B's is $9,090.91. If you can only do one, B creates far more value despite the lower IRR. The 1992 edition of OMB Circular A-94 makes the same point in policy terms: IRR "does not generally provide an acceptable decision criterion", but is useful when budgets are constrained or the right discount rate is uncertain.

Multiple IRRs and no IRR

NPV is a polynomial in 1/(1+r), and by Descartes' rule of signs it can have as many positive roots as the cash flows have sign changes. A normal project has one sign change (out, then in) and one IRR. A project with a large outflow at the end, such as a mine reclamation or a lease-end payment, can have two.

Example: invest $100, receive $230 after one year, pay $132 after two. NPV is zero at both 10% and 20%: at 10%, −100 + 209.09 − 109.09 = 0, and at 20%, −100 + 191.67 − 91.67 = 0. Neither rate is "the" return. The calculator finds both, shows the smaller one (10%) and reports that there are 2 solutions, so you know the single figure is not the whole story. For flows like these, decide with NPV at your required rate, or use the modified IRR.

Matching Excel and Google Sheets

Put the flows in one column with the investment as a negative number first: −25000, 6000, 7000, 8000, 9000, 4000. Then =IRR(A1:A6) returns 11.38%. Microsoft's documentation for IRR notes that:

• the values must contain at least one positive and one negative number;
• the optional guess defaults to 10%;
• Excel iterates from the guess until the result is accurate to within 0.00001 percent, and returns #NUM! if it has not converged after 20 tries.

Because Excel starts from a guess, it can land on a different root than you expect when there are multiple IRRs; trying a different guess shows whether another root exists. Use XIRR when cash flows fall on irregular dates and MIRR when you want to set the reinvestment rate yourself. If your flows are monthly, the result is a monthly rate: annualize it as (1 + r)¹² − 1.

The reinvestment question and MIRR

IRR is often said to assume that interim cash flows are reinvested at the IRR itself. Whether that is an assumption of the measure or of how people interpret it is debated in the finance literature, and Kierulff's review in the *American Journal of Business Education* lists reinvestment among IRR's practical problems, alongside multiple IRRs and choices between unequal investments. The practical fix is the modified IRR: compound the inflows forward at a realistic reinvestment rate, then solve

MIRR = (future value of inflows ÷ present value of outflows)^(1/n) − 1

For the example, reinvesting at 8% gives a future value of $40,032.12 in year 5, and MIRR = (40,032.12 ÷ 25,000)^(1/5) − 1 = 9.87%, lower than the 11.38% IRR because the interim cash is assumed to earn 8%, not 11.38%. Iowa State University's capital budgeting guide lists MIRR alongside NPV and IRR among the standard methods, and notes that companies often look at several of them together.