Enter an investment's cash flows period by period to find the internal rate of return, and the net present value at a discount rate you choose
Enter the money you put in as a negative number in period 0, then the cash you get back (or pay in) each period after, including any sale proceeds in the last period. The calculator finds the internal rate of return — the yearly rate at which the cash flows' net present value is zero — and the net present value (NPV) at a discount rate you choose. Periods are years unless you enter monthly flows, in which case the IRR is per month.
NPV = CF₀ + CF₁ ÷ (1 + r) + CF₂ ÷ (1 + r)² + … + CFₙ ÷ (1 + r)ⁿ. IRR is the rate r that makes NPV = 0. There's no closed-form answer, so the calculator narrows it down by bisection, as a spreadsheet's IRR function does by iteration. For $10,000 invested and $3,000, $4,200, $6,800 back over three years, IRR is 16.34% and NPV at 8% is $1,776.66.
| Discount rate | NPV |
|---|---|
| 0% | $4,000 |
| 5% | $2,540.76 |
| 8% | $1,776.66 |
| 10% | $1,307.29 |
| 15% | $255.61 |
| 20% | $-648.15 |
A positive NPV at your discount rate means the cash flows return more than that rate; the IRR is where NPV crosses zero (between 15% and 20% in the table). A single lump sum that grows to $16,105 after five years has an IRR of 10.00%, the same as its compound annual growth rate. For cash flows that change sign more than once (for example a big repair partway through), there can be more than one IRR; the calculator flags that case.
The discount rate is the return you require or could earn elsewhere. A common benchmark for a low-risk alternative is the Treasury yield for a similar term, published in the Federal Reserve's H.15 release. Riskier projects usually call for a higher rate. IRR assumes the cash you receive along the way could be reinvested at the IRR itself, which can flatter high IRRs.
Cash flows here are what you enter — before or after tax. Gains on a sale are capital gains (IRS Topic 409), and rental income is taxed yearly (IRS Topic 414). Future cash flows are estimates; try a low and a high case.
The internal rate of return is the yearly rate at which the present value of everything an investment pays back equals what you put in — the rate where NPV is zero.
Find the rate r where CF₀ + CF₁/(1+r) + … + CFₙ/(1+r)ⁿ = 0, by trial and error or bisection. For −$10,000 then $3,000, $4,200 and $6,800, r ≈ 16.34%.
NPV is a dollar amount at a chosen discount rate; IRR is the rate at which NPV is zero. In the example, NPV at 8% is $1,776.66 and IRR is 16.34%.
Yes, when the cash flows switch between negative and positive more than once. In that case NPV at a stated discount rate is the more reliable measure.
For a single investment and a single payout, IRR equals the compound annual growth rate. With cash flows in between, IRR weights each flow by when it happens, which a simple average return doesn't.
Tax rules, limits and pay data change. Check the current figures with the primary source before acting on them.