Enter as a positive number. Logic treats it as negative.
Internal Rate of Return
0.00%
How to Calculate IRR Rate: A Comprehensive Guide
The Internal Rate of Return (IRR) is one of the most widely used metrics in financial analysis, capital budgeting, and real estate investing. It represents the annualized effective compounded return rate that makes the Net Present Value (NPV) of all cash flows (both positive and negative) from a particular investment equal to zero.
Unlike simple yield calculations, IRR accounts for the time value of money. This means it recognizes that a dollar received today is worth more than a dollar received five years from now.
The Mathematical Formula for IRR
To calculate IRR, you are essentially solving for the discount rate ($r$) in the following equation where NPV equals zero:
CF₀: Initial Investment (usually a negative number representing cost).
CF₁, CF₂, etc.: Cash flows in subsequent periods.
n: The total number of periods.
r: The Internal Rate of Return (IRR).
Because the "r" is in the denominator with an exponent, there is no simple algebraic formula to solve for IRR directly. Instead, it requires an iterative numerical method (like the Newton-Raphson method or trial-and-error interpolation), which is exactly what the calculator above performs.
Step-by-Step Calculation Example
Let's look at a practical example of a small business investment to understand how the numbers work.
Period
Action
Cash Flow Value
Year 0
Initial Equipment Purchase
-$10,000
Year 1
Net Profit
$2,000
Year 2
Net Profit
$3,000
Year 3
Net Profit + Salvage Value
$8,000
If you were to sum these numbers simply (-10,000 + 2,000 + 3,000 + 8,000), you would see a total profit of $3,000. However, because the money comes in over three years, the IRR will calculate the specific annual growth rate. In this scenario, the IRR is approximately 13.4%.
Why is IRR Important?
1. Benchmarking Projects
Companies often have a "hurdle rate" or a Required Rate of Return (RRR). If a project's calculated IRR exceeds this hurdle rate, the project is typically considered viable. For example, if a company's cost of capital is 8% and a project has an IRR of 15%, it adds value.
2. Comparing Unequal Investments
IRR allows you to compare two different projects with different cash flow patterns. Project A might return a lump sum in 10 years, while Project B returns smaller amounts annually. IRR normalizes these streams into a single percentage for easy comparison.
Limitations of IRR
While powerful, the IRR metric is not flawless:
Reinvestment Assumption: IRR assumes that all future cash flows are reinvested at the same rate as the IRR itself, which may be unrealistic for projects with exceptionally high returns.
Multiple IRRs: If cash flows alternate between positive and negative multiple times (e.g., a major repair cost in Year 3), the formula may produce multiple valid mathematical solutions.
How to Interpret Your Result
When using the calculator above:
Positive High Percentage: Indicates a potentially profitable investment.
Percentage < Risk-Free Rate: If the IRR is lower than what you could earn in a safe government bond, the risk of the project is likely not worth the reward.
Negative Percentage: The project loses money relative to the time value of money; the total undiscounted cash flows might even be less than the initial investment.
function calculateInternalRate() {
// 1. Get DOM elements
var initialInput = document.getElementById('initialInvest');
var cf1Input = document.getElementById('cf1');
var cf2Input = document.getElementById('cf2');
var cf3Input = document.getElementById('cf3');
var cf4Input = document.getElementById('cf4');
var cf5Input = document.getElementById('cf5');
var resultBox = document.getElementById('irrResult');
var resultValue = document.getElementById('irrValue');
var resultMessage = document.getElementById('irrMessage');
// 2. Parse Inputs
// Note: We treat initial investment as negative for the calculation
var initial = parseFloat(initialInput.value);
if (isNaN(initial) || initial initial investment
var totalInflows = cashFlows.reduce(function(a, b) { return a + b; }, 0) + initial; // Add initial back to cancel the negative
if (totalInflows <= initial) {
// If total money back is less than investment, IRR is negative.
// We still run the loop, but guess needs to start lower or handle carefully.
guess = -0.1;
}
var found = false;
for (var i = 0; i < maxIterations; i++) {
var npv = 0;
var d_npv = 0; // Derivative of NPV
for (var t = 0; t < cashFlows.length; t++) {
var denom = Math.pow(1 + guess, t);
npv += cashFlows[t] / denom;
// Derivative: -t * CF / (1+r)^(t+1)
d_npv += -t * cashFlows[t] / Math.pow(1 + guess, t + 1);
}
var newGuess = guess – (npv / d_npv);
if (Math.abs(newGuess – guess) 0) {
resultMessage.innerHTML = "This investment yields a positive return.";
resultValue.style.color = "#27ae60";
} else {
resultMessage.innerHTML = "This investment yields a negative return.";
resultValue.style.color = "#c0392b";
}
} else {
resultValue.innerHTML = "Error";
resultValue.style.color = "#c0392b";
resultMessage.innerHTML = "Calculation did not converge. Ensure you have entered at least one positive cash flow significantly large enough to cover the investment over time.";
}
}