IRR Calculator
Internal rate of return for up to 10 cash flows, solved by bisection — plus NPV at your discount rate, the NPV profile, and a warning when multiple IRRs exist.
IRR Calculator: with the default inputs, irr per period is 18.756%.
Only the first N cash flows are used. Periods 5–9 live under More options.
Money you pay out is negative.
Your hurdle rate or cost of capital. Used for NPV, not for IRR.
Sets how the periodic IRR is annualized.
- Annualized IRR
- 18.756%(1 + periodic IRR)^periods per year − 1.
- NPV at your discount rate
- $10,682.33
- Decision at that hurdle rate
- Accept — at a 10% hurdle rate the project adds $10,682.33 of value.
- Total invested
- -$50,000
- Total received
- $78,000
- Net cash (undiscounted)
- $28,000
- Sign changes in the cash flow
- 1More than one means the IRR may not be unique.
Assumptions
- Cash flows arrive at the end of each period and periods are evenly spaced.
- The reported IRR is the lowest rate that sets NPV to zero; non-conventional flows can have several.
- NPV discounts at the effective annual rate you enter, converted to the period length.
- Reinvestment of interim cash flows at the IRR is implied — the standard IRR caveat.
| Period | Cash flow | Discount factor | Present value | Cumulative cash | Cumulative PV |
|---|---|---|---|---|---|
| 0 | -$50,000 | 1 | -$50,000.00 | -$50,000 | -$50,000 |
| 1 | $15,000 | 0.909091 | $13,636.36 | -$35,000 | -$36,364 |
| 2 | $18,000 | 0.826446 | $14,876.03 | -$17,000 | -$21,488 |
| 3 | $21,000 | 0.751315 | $15,777.61 | $4,000 | -$5,710 |
| 4 | $24,000 | 0.683013 | $16,392.32 | $28,000 | $10,682 |
Discount factors use your hurdle rate, not the IRR.
How this is worked out
The formula
IRR is the rate r that solves CF0 + CF1 ÷ (1 + r)^1 + CF2 ÷ (1 + r)^2 + … + CFn ÷ (1 + r)^n = 0 There is no closed form for n > 4, so r is found by bracketing a sign change in NPV(r) and bisecting until the equation balances. NPV = the same sum evaluated at your own discount rate instead of r. Annualized IRR = (1 + r)^(periods per year) − 1.
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- How many periods (including period 0)?
- Only the first N cash flows are used. Periods 5–9 live under More options.from 2 to 10 · whole numbers only · defaults to 5
- Period 0 — initial investment
- Money you pay out is negative.in dollars · defaults to -50000
- Period 1 cash flow
- A number.in dollars · defaults to 15000
- Period 2 cash flow
- A number.in dollars · defaults to 18000
- Period 3 cash flow
- A number.in dollars · defaults to 21000
- Period 4 cash flow
- A number.in dollars · defaults to 24000
- Period 5 cash flow(under More options)
- A number.in dollars · defaults to 0
- Period 6 cash flow(under More options)
- A number.in dollars · defaults to 0
- Period 7 cash flow(under More options)
- A number.in dollars · defaults to 0
- Period 8 cash flow(under More options)
- A number.in dollars · defaults to 0
- Period 9 cash flow(under More options)
- A number.in dollars · defaults to 0
- Discount rate for NPV
- Your hurdle rate or cost of capital. Used for NPV, not for IRR.a percentage · from 0 to 100 · defaults to 10
- One period is
- Sets how the periodic IRR is annualized.A year · A quarter · A month
What you get back
- IRR per periodmain answer
- Annualized IRR
- (1 + periodic IRR)^periods per year − 1.
- NPV at your discount rate
- Decision at that hurdle rate
- Total invested
- Total received
- Net cash (undiscounted)
- Sign changes in the cash flow
- More than one means the IRR may not be unique.
What this assumes
- Cash flows arrive at the end of each period and periods are evenly spaced.
- The reported IRR is the lowest rate that sets NPV to zero; non-conventional flows can have several.
- NPV discounts at the effective annual rate you enter, converted to the period length.
- Reinvestment of interim cash flows at the IRR is implied — the standard IRR caveat.
About this calculator
The internal rate of return is the discount rate at which a project's cash flows are exactly worth what they cost — the rate that drives net present value to zero. It is the standard way to compare investments of different sizes and shapes, because it reduces a whole timeline to one percentage.
How to use it
Set the number of periods, then enter each cash flow with period 0 as the money you put in, entered negative. Later periods are usually positive, but they don't have to be — a project that needs a second round of funding in year 3 takes a negative flow there. Set the discount rate to your hurdle rate or cost of capital; it doesn't affect the IRR, only the NPV shown alongside it.
IRR versus NPV
They usually agree and occasionally don't. Take NPV when they conflict:
- IRR assumes reinvestment at the IRR itself. A project showing 40% only actually delivers 40% if every interim cash flow can be redeployed at 40%, which is rarely true. NPV assumes reinvestment at the discount rate, which is a far more defensible assumption.
- IRR ignores scale. A 60% return on $1,000 beats 20% on $1,000,000 on the percentage, and loses badly on the dollars. NPV gets this right.
- IRR can be non-unique. Descartes' rule says a cash flow that changes sign k times can have up to k different IRRs. A mine that costs money to open and again to close has two. The calculator counts the sign changes and warns you; the figure it reports is the lowest root.
- IRR does not exist at all for cash flows that never turn positive, or that are all positive. The calculator says so rather than returning a number.
Reading the results
IRR per period is the raw answer; annualized IRR compounds it up when your periods are months or quarters — the honest way to compare a monthly project against a yearly one. NPV at your discount rate is the dollar verdict, and the NPV profile chart shows the whole relationship: where the curve crosses zero is the IRR, and how steeply it crosses tells you how sensitive the decision is to your hurdle rate.
Caveats
Cash flows are assumed to arrive at the end of each period, evenly spaced. Irregularly dated flows need XIRR, which discounts by actual days. And IRR says nothing about risk, liquidity or how long your money is tied up — a 25% IRR over four months and a 25% IRR over ten years are very different propositions.
Frequently asked questions
▸What is a good IRR?
Only compared to your cost of capital. If money costs you 8%, a 12% IRR creates value and a 6% IRR destroys it. Private equity typically targets 20%+, corporate projects 10–15%, real estate 8–12% — but the hurdle, not the headline, is what matters.
▸Why does my project have two IRRs?
Because the cash flow changes sign more than once. A polynomial with k sign changes can have up to k positive roots, and each is a rate where NPV equals zero. When this happens, IRR is meaningless as a ranking tool — use NPV at your actual discount rate.
▸What is the reinvestment assumption?
IRR implicitly assumes every interim cash flow is reinvested at the IRR itself until the end of the project. When the IRR is far above your realistic reinvestment rate, it overstates the return. MIRR fixes this by discounting outflows at your finance rate and compounding inflows at a reinvestment rate you specify.
▸How is IRR different from ROI or CAGR?
ROI is total profit over cost with no timing. CAGR is the growth rate between one starting and one ending value. IRR handles a full stream of dated cash flows, which is why it's the standard for projects and funds.
▸Can IRR be negative?
Yes — any time you get back less than you put in. The floor is −100%, which is a total loss. The calculator brackets down to −99.9999% before giving up.
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