Irr Calculation

Internal Rate of Return (IRR) Calculator

Enter the initial cash outflow as a positive number.
Enter cash inflows/outflows for each period, separated by commas. Negative values for outflows.
Calculated IRR: –

Understanding the Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) is a financial metric used in capital budgeting to estimate the profitability of potential investments. It is the discount rate that makes the Net Present Value (NPV) of all cash flows from a particular project equal to zero. In simpler terms, it's the expected annual rate of growth that an investment is projected to generate.

How IRR Works

When evaluating an investment, you typically have an initial outlay (a negative cash flow) followed by a series of cash inflows (and sometimes outflows) over several periods. The IRR calculation attempts to find the rate at which these future cash flows, when discounted back to the present, exactly offset the initial investment.

A higher IRR generally indicates a more desirable investment. Companies often use IRR to compare different projects and select those with the highest IRR, provided it exceeds a predetermined minimum acceptable rate of return (often called the hurdle rate or cost of capital).

Interpreting the IRR Result

  • IRR > Hurdle Rate: If the calculated IRR is greater than the company's required rate of return, the project is generally considered acceptable.
  • IRR < Hurdle Rate: If the IRR is less than the hurdle rate, the project is typically rejected as it does not meet the minimum profitability requirements.
  • Comparing Projects: When choosing between mutually exclusive projects, the one with the highest IRR is usually preferred, assuming other factors are equal.

Limitations of IRR

While a powerful tool, IRR has some limitations:

  • Multiple IRRs: For projects with unconventional cash flow patterns (e.g., alternating between positive and negative cash flows multiple times), there can be more than one IRR, making interpretation difficult.
  • Reinvestment Rate Assumption: IRR assumes that all intermediate cash flows are reinvested at the IRR itself. This might not be a realistic assumption, especially for projects with very high IRRs.
  • Scale of Projects: IRR does not consider the absolute size of the investment. A small project with a high IRR might be less valuable than a large project with a slightly lower IRR but much higher total profit.

How This Calculator Works

This calculator uses an iterative numerical method (specifically, a bisection method) to find the discount rate that equates the present value of future cash flows to the initial investment. You provide the initial investment as a positive number (the calculator treats it as an outflow) and then a comma-separated list of subsequent cash flows for each period. The result is the IRR expressed as a percentage.

Example: If you invest $100,000 today and expect to receive $20,000 in year 1, $30,000 in year 2, $40,000 in year 3, and $50,000 in year 4, the calculator will determine the IRR for this series of cash flows.

function calculateIRR() { var initialInvestment = parseFloat(document.getElementById('initialInvestment').value); var cashFlowsInput = document.getElementById('cashFlowsInput').value; var resultDiv = document.getElementById('irrResult'); if (isNaN(initialInvestment) || initialInvestment <= 0) { resultDiv.innerHTML = "Please enter a valid initial investment (a positive number)."; return; } var cashFlows = cashFlowsInput.split(',').map(function(item) { return parseFloat(item.trim()); }); // Filter out any non-numeric or empty string entries from cash flows cashFlows = cashFlows.filter(function(item) { return !isNaN(item); }); if (cashFlows.length === 0) { resultDiv.innerHTML = "Please enter at least one subsequent cash flow."; return; } // Combine initial investment (as negative) with subsequent cash flows var allCashFlows = [-initialInvestment].concat(cashFlows); // Function to calculate Net Present Value (NPV) for a given rate function calculateNPV(rate, flows) { var npv = 0; for (var i = 0; i < flows.length; i++) { // Handle case where (1 + rate) is zero or negative, which would make Math.pow invalid if ((1 + rate) 0) { // Only relevant for future cash flows return NaN; // Indicate an invalid rate for NPV calculation } npv += flows[i] / Math.pow(1 + rate, i); } return npv; } var lowRate = -0.9999; // Slightly above -100% var highRate = 10.0; // Up to 1000% var precision = 0.000001; // Desired precision for IRR (0.0001%) var maxIterations = 1000; var irrFound = false; var irrValue = NaN; // Check for trivial cases or impossible scenarios var sumCashFlows = allCashFlows.reduce(function(a, b) { return a + b; }, 0); if (sumCashFlows 0) { // If the sum of all cash flows (including initial investment) is negative or zero, // and there's an initial investment, it's unlikely to have a positive IRR. // More specifically, if all subsequent cash flows are negative or zero, no positive IRR. var allSubsequentNegativeOrZero = true; for(var i = 1; i 0) { allSubsequentNegativeOrZero = false; break; } } if (allSubsequentNegativeOrZero) { resultDiv.innerHTML = "All subsequent cash flows are negative or zero. No positive IRR possible."; return; } } // Bisection method to find the IRR for (var i = 0; i < maxIterations; i++) { var midRate = (lowRate + highRate) / 2; // Ensure midRate is valid for (1 + rate) if (midRate <= -1) { lowRate = midRate; // Try higher rates continue; } var npvMid = calculateNPV(midRate, allCashFlows); if (isNaN(npvMid)) { // If NPV calculation failed for this rate lowRate = midRate; // Try higher rates continue; } if (Math.abs(npvMid) < precision) { irrValue = midRate; irrFound = true; break; } var npvLow = calculateNPV(lowRate, allCashFlows); if (isNaN(npvLow)) { // If NPV calculation failed for lowRate lowRate = midRate; // Adjust lowRate to midRate and continue continue; } // If NPV at lowRate and midRate have different signs, the root is between low and mid if (npvLow * npvMid < 0) { highRate = midRate; } else { // Otherwise, the root is between mid and high lowRate = midRate; } // If the interval becomes too small without finding a precise root if (Math.abs(highRate – lowRate) < precision && !irrFound) { // Use the midRate as the best approximation if its NPV is closest to zero var npvHigh = calculateNPV(highRate, allCashFlows); if (Math.abs(npvMid) < Math.abs(npvLow) && Math.abs(npvMid) < Math.abs(npvHigh)) { irrValue = midRate; irrFound = true; } break; } } if (irrFound) { resultDiv.innerHTML = "Calculated IRR: " + (irrValue * 100).toFixed(2) + "%"; } else { // If not found by bisection, check if any of the boundary/mid points are very close var finalNPV_low = calculateNPV(lowRate, allCashFlows); var finalNPV_high = calculateNPV(highRate, allCashFlows); var finalNPV_mid = calculateNPV((lowRate + highRate) / 2, allCashFlows); if (Math.abs(finalNPV_low) < precision) { irrValue = lowRate; irrFound = true; } else if (Math.abs(finalNPV_high) < precision) { irrValue = highRate; irrFound = true; } else if (Math.abs(finalNPV_mid) < precision) { irrValue = (lowRate + highRate) / 2; irrFound = true; } if (irrFound) { resultDiv.innerHTML = "Calculated IRR: " + (irrValue * 100).toFixed(2) + "%"; } else { resultDiv.innerHTML = "Could not find a valid IRR within the search range. This might indicate no real IRR, multiple IRRs, or an unusual cash flow pattern."; } } }

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