Free IRR Calculator – Internal Rate of Return

The Internal Rate of Return (IRR) is the discount rate that makes the net present value of all cash flows from a project equal to zero, effectively the annualized expected return on an investment, computed iteratively using the Newton-Raphson method.

Investment Details

Initial Investment

Amount invested at Year 0 (entered as positive, treated as outflow)

Discount Rate (for NPV)

Used to calculate Net Present Value alongside IRR

Cash Flow Period

Cash Flows by Year

IRR Analysis

0.00%

Internal Rate of Return

The discount rate that makes NPV equal to zero

NPV at Discount Rate

Payback Period

– yrs

Total Return

Cash Flow Timeline

Detailed Breakdown

What is IRR?

Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of all cash flows equal to zero. It represents the annualized effective compounded return rate of an investment.

NPV = -C0 + C1/(1+r) + C2/(1+r)^2 + … + Cn/(1+r)^n = 0

IRR = the value of r that satisfies the equation above

A higher IRR indicates a more profitable investment. If the IRR exceeds your required rate of return (discount rate), the investment is generally considered worthwhile.

IRR vs NPV

IRR: Gives you a percentage return. Great for comparing investments of different sizes.
NPV: Gives you a dollar value of wealth created. Better for choosing between mutually exclusive projects.
Decision Rule: If IRR > discount rate, or NPV > 0, the investment adds value.
Conflict: IRR and NPV can sometimes disagree on project ranking, especially with non-conventional cash flows.

Limitations of IRR

Multiple IRRs: Cash flows that change sign more than once can produce multiple IRRs.
Reinvestment assumption: IRR assumes interim cash flows are reinvested at the IRR rate itself, which may be unrealistic.
Scale blind: A 50% IRR on $1,000 is less valuable than a 20% IRR on $1,000,000.
No solution: Some cash flow patterns have no real IRR solution.

Frequently Asked Questions

What is the IRR formula?

IRR is the value of r that satisfies: 0 = −C0 + C1/(1+r) + C2/(1+r)² + … + Cn/(1+r)^n. Because this equation has no closed-form solution, the calculator uses Newton-Raphson iteration — starting from an initial guess and refining r until NPV is within tolerance of zero. The result is the annualized rate of return if all projected cash flows are realized.

What is the difference between IRR and NPV?

NPV calculates the present value of cash flows at a given discount rate you supply, expressing the answer in dollars. IRR finds the single rate at which NPV equals exactly zero. You compare IRR to your required hurdle rate: if IRR exceeds your cost of capital, the investment adds value; if not, it destroys value.

Can IRR be calculated for monthly cash flows?

Yes — the calculator supports both annual and monthly cash flow modes. When monthly is selected, the computed rate is a monthly IRR; the calculator then annualizes it as (1 + monthly IRR)^12 − 1 to give an annual figure for easier comparison. Make sure all cash flows you enter correspond to the same frequency.

What is payback period and how does it differ from IRR?

Payback period is the number of periods required to recover the initial investment in nominal (undiscounted) cash flows. IRR accounts for the time value of money; payback period does not. A project can have a short payback period but a low IRR if later-year cash flows are small. The calculator shows both metrics.

Can an investment have multiple IRRs?

Yes — if the cash flow stream changes sign more than once (for example, negative, then positive, then negative again), there can be multiple mathematical solutions. The Newton-Raphson method returns one of them based on the starting guess. The calculator is best suited to conventional investments with a single upfront outflow followed by inflows.

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