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IRR Calculator

The Internal Rate of Return (IRR) is a fundamental capital budgeting metric that calculates the annualized discount rate at which the Net Present Valu

Finance
$ Outflow
Initial capital invested at inception (enter as a negative number)
$ Inflow
Net cash flow at the end of period 1
$ Inflow
Net cash flow at the end of period 2
$ Inflow
Net cash flow at the end of period 3
$ Inflow
Net cash flow at the end of period 4 (0 if concluded)
$ Inflow
Net cash flow at the end of period 5 (0 if concluded)
Formula & Methodology
0 = C₀ + [C₁ ÷ (1 + IRR)¹] + [C₂ ÷ (1 + IRR)²] + ... + [C_n ÷ (1 + IRR)^n]

Because polynomials of degree five or higher possess no general algebraic closed-form solution (Abel-Ruffini theorem), IRR must be solved numerically through iterative approximations (such as the Secant or Newton-Raphson methods) that converge on the discount rate where discounted inflows balance initial outlays.

Internal Rate of Return (IRR)

+23.38% per period

Overview

The Internal Rate of Return (IRR) is a fundamental capital budgeting metric that calculates the annualized discount rate at which the Net Present Value (NPV) of all future cash flows from an investment equals exactly zero. It reflects the inherent profitability and compound yield of irregular multi-period capital projects.

Educational & Financial Decision Disclaimer: This calculator computes IRR using numerical root-finding algorithms under end-of-period timing assumptions. It is not financial or investment advice. The IRR rule assumes interim cash flows are reinvested at the IRR itself; evaluate projects alongside Net Present Value (NPV).

Worked Examples

Acceptance Standard: -$1,000 Outlay Followed by 3 Annual Inflows of $500

Year 0 = -$1,000, Year 1 = $500, Year 2 = $500, Year 3 = $500.

  1. Setup equation: 0 = -1,000 + [500 ÷ (1+r)] + [500 ÷ (1+r)²] + [500 ÷ (1+r)³].
  2. Test r = 20%: NPV = -1,000 + 416.67 + 347.22 + 289.35 = +$53.24.
  3. Test r = 25%: NPV = -1,000 + 400.00 + 320.00 + 256.00 = -$24.00.
  4. Interpolate root numerically: r ≈ 23.375% → 23.38%.
  5. Verify: 500/1.23375 + 500/(1.23375)² + 500/(1.23375)³ = 405.27 + 328.48 + 266.25 = $1,000.00.
Final Answer: 23.38% IRR

Even Payback Example: -$10,000 Outlay with $4,000/yr for 3 Years

Year 0 = -$10,000, Year 1 = $4,000, Year 2 = $4,000, Year 3 = $4,000.

  1. Total cash returned: $12,000 ($2,000 profit).
  2. Numerical convergence: r = 9.70%.
  3. Discounted value: $4,000/1.097 + $4,000/1.097² + $4,000/1.097³ = $10,000.
Final Answer: 9.70% IRR

All-Positive Outflow Error Detection

Demonstrates solver error prevention when all cash flows are positive (e.g. +$1000, +$500, +$500).

  1. All flows are positive; no negative outflow exists.
  2. No rate can make positive numbers sum to zero.
  3. Calculator gracefully intercepts condition and reports clear educational error.
Final Answer: Error: Must contain negative outflow and positive inflow

How to Use This Calculator

  1. Enter the initial investment capital as a negative number in Year 0 (e.g. -1000).
  2. Enter positive net cash flows received at the end of each subsequent period (Years 1 to 5).
  3. Leave unused future periods set to 0.
  4. View the calculated Internal Rate of Return along with iteration details and cash flow breakdowns.

Frequently Asked Questions

What is the main limitation of the Internal Rate of Return (IRR)?
The primary theoretical flaw of IRR is the reinvestment rate assumption: it implicitly assumes all interim cash flows can be reinvested at the project’s own IRR rate, which is often unrealistically high for highly profitable ventures. Modified IRR (MIRR) corrects this by assuming reinvestment at the cost of capital.
Why does an investment need both negative and positive cash flows to compute IRR?
By definition, IRR is the discount rate that makes Net Present Value equal zero. If all numbers are positive, the discounted sum is always positive; if all are negative, the sum is always negative. A rate can only balance NPV to zero when capital invested (negative) offsets returns received (positive).
What causes the "Multiple IRR" problem?
According to Descartes’ Rule of Signs, a polynomial has as many real roots as there are sign changes in its coefficients. If a project has multiple cash flow reversals (e.g. negative outlay, positive profits, then a large negative cleanup cost), multiple mathematical rates can yield NPV = 0.
How do companies use IRR to make capital investment decisions?
Corporations compare a project’s IRR against their required hurdle rate (Weighted Average Cost of Capital, or WACC). If the IRR exceeds the hurdle rate, the project is considered economically viable and accepted.
What timing convention is used for these cash flows?
This calculator applies the standard end-of-period cash flow convention (ordinary cash flows), where cash inflows are assumed to be realized at the conclusion of each full annual period.

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Reviewed & Authored by: OnlineConvers Quantitative Finance Editorial Team · Last Updated: 2026-10-07
Solves for Internal Rate of Return using bounded numerical root-finding algorithms (Secant and Bisection methods). Evaluates the polynomial NPV(r) = Σ [C_t / (1 + r)^t] with a convergence tolerance of 1e-7 and a hard ceiling of 100 iterations to guarantee bounded, non-hanging execution. Detects sign-change frequency and flags multiple-IRR conditions.
Citations: Capital Budgeting and the Internal Rate of Return (Journal of Finance (Lorie & Savage)) · Principles of Corporate Finance (Brealey, Myers, and Allen (McGraw-Hill))