Enter the cash flows for your project over time. The first value should be your initial investment (negative), followed by expected cash inflows (positive) or outflows (negative) for subsequent periods.
Internal Rate of Return (IRR)
— %
Understanding the Internal Rate of Return (IRR)
The Internal Rate of Return (IRR) is a crucial metric in capital budgeting and financial project analysis. It represents the discount rate at which the Net Present Value (NPV) of all cash flows (both positive and negative) from a particular project or investment equals zero. In simpler terms, it's the effective rate of return that an investment is expected to yield over its lifespan.
How is IRR Calculated?
The IRR is found by solving the following equation for 'r' (the IRR):
NPV is the Net Present Value (which we set to 0 for IRR).
CF_t is the cash flow during period 't'.
r is the Internal Rate of Return (the unknown we are solving for).
t is the time period (starting from 0 for the initial investment).
n is the total number of periods.
Because this equation often cannot be solved algebraically for 'r' when there are multiple cash flows, it's typically solved using iterative methods, trial-and-error, or built-in functions in financial software like Excel (=IRR()). This calculator employs a numerical method to approximate the IRR.
Interpreting the IRR
The calculated IRR is then compared to the company's hurdle rate or cost of capital.
IRR > Hurdle Rate: The project is generally considered financially attractive and should be accepted. It's expected to generate returns higher than the minimum acceptable rate.
IRR < Hurdle Rate: The project is likely not financially viable and should be rejected. It's not expected to generate returns sufficient to cover the cost of capital.
IRR = Hurdle Rate: The project is expected to generate returns exactly equal to the cost of capital, making it a borderline decision.
Use Cases for IRR
Project Evaluation: Deciding whether to invest in new equipment, facilities, or R&D projects.
Investment Appraisal: Comparing the potential returns of different investment opportunities.
Financial Planning: Assessing the long-term profitability of business ventures.
How to Use This Calculator
In the "Cash Flows" field, enter a comma-separated list of all expected cash flows for your project.
The first value must be your initial investment, entered as a negative number (e.g., -10000 for a $10,000 initial outlay).
Subsequent values represent the cash inflows (positive numbers, e.g., 3000) or outflows (negative numbers) for each period (year, quarter, etc.) thereafter.
Click "Calculate IRR". The result will be displayed as a percentage.
Note: This calculator uses a numerical approximation. For complex or highly sensitive cash flow series, always cross-reference with dedicated financial software like Excel's =IRR() function.
function calculateIRR() {
var cashFlowInput = document.getElementById("cashFlowValues").value;
var resultDiv = document.getElementById("irrResult");
if (!cashFlowInput) {
resultDiv.innerText = "Error";
return;
}
var cashFlows = cashFlowInput.split(',').map(function(item) {
return parseFloat(item.trim());
});
// Validate cash flows
for (var i = 0; i < cashFlows.length; i++) {
if (isNaN(cashFlows[i])) {
resultDiv.innerText = "Invalid Input";
return;
}
}
// Basic check for at least one negative and one positive cash flow for a meaningful IRR
var hasNegative = cashFlows.some(function(cf) { return cf 0; });
if (!hasNegative || !hasPositive) {
// This condition might be too strict for some edge cases, but generally IRR requires this.
// Excel's IRR handles cases with only positive or only negative cash flows by returning an error.
// We'll return an error for simplicity as a meaningful IRR cannot be determined without opposing signs.
resultDiv.innerText = "Invalid Cash Flows";
return;
}
// Numerical method to find IRR (Newton-Raphson or similar iterative approach)
// This is a simplified implementation for demonstration.
// A robust implementation would involve more sophisticated root-finding algorithms.
var guess = 0.1; // Initial guess for IRR
var tolerance = 0.0001; // Desired precision
var maxIterations = 1000; // Prevent infinite loops
var irr = guess;
for (var iter = 0; iter < maxIterations; iter++) {
var npv = 0;
var derivative = 0;
for (var t = 0; t < cashFlows.length; t++) {
npv += cashFlows[t] / Math.pow(1 + irr, t);
derivative += -t * cashFlows[t] / Math.pow(1 + irr, t + 1);
}
var newIrr = irr – npv / derivative;
if (Math.abs(newIrr – irr) < tolerance) {
irr = newIrr;
break;
}
irr = newIrr;
// Handle cases where derivative is close to zero or IRR becomes invalid
if (isNaN(irr) || !isFinite(irr) || derivative === 0) {
resultDiv.innerText = "Calculation Error";
return;
}
}
// Check if loop finished without converging
if (iter === maxIterations) {
resultDiv.innerText = "No Convergence";
return;
}
// Format result to percentage
resultDiv.innerText = (irr * 100).toFixed(2) + " %";
}