Calcul Irr

Internal Rate of Return (IRR) Calculator

function calculateIRR() { var initialInvestment = parseFloat(document.getElementById('initialInvestment').value); if (isNaN(initialInvestment) || initialInvestment >= 0) { document.getElementById('irrResult').innerHTML = "Please enter a valid negative initial investment."; return; } var cashFlows = [initialInvestment]; for (var i = 1; i <= 5; i++) { // Assuming 5 cash flow periods var cf = parseFloat(document.getElementById('cashFlow' + i).value); if (isNaN(cf)) { document.getElementById('irrResult').innerHTML = "Please enter valid numbers for all cash flows."; return; } cashFlows.push(cf); } // IRR calculation logic (Newton-Raphson method) var irr = 0.1; // Initial guess (10%) var precision = 0.000001; // Desired precision var maxIterations = 1000; var foundIRR = false; // Function to calculate NPV for a given rate function calculateNPV(rate, cfs) { var npv = 0; for (var j = 0; j < cfs.length; j++) { npv += cfs[j] / Math.pow(1 + rate, j); } return npv; } // Iterative search for IRR for (var iter = 0; iter < maxIterations; iter++) { var npv = calculateNPV(irr, cashFlows); if (Math.abs(npv) < precision) { foundIRR = true; break; } // Calculate derivative of NPV with respect to rate // dNPV/dr = sum(-j * CFj / (1+r)^(j+1)) var derivative = 0; for (var k = 0; k 0 ? 0.001 : -0.001); } else { irr = irr – npv / derivative; } // Prevent rate from going too low (e.g., below -100%) or excessively high if (irr 100) { // Cap at 10000% to prevent extreme values irr = 100; } } if (foundIRR) { document.getElementById('irrResult').innerHTML = "Calculated IRR: " + (irr * 100).toFixed(2) + "%"; } else { document.getElementById('irrResult').innerHTML = "Could not find a converging IRR. Please check your cash flows or try different values."; } }

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 or investment equal to zero. In simpler terms, it's the expected annual rate of return that an investment is projected to generate.

How IRR Works

When evaluating an investment, businesses often look at the cash flows it will generate over its lifetime. These cash flows include an initial outlay (the investment itself, typically a negative cash flow) and subsequent inflows (profits, savings, etc.). The IRR calculation attempts to find the rate at which these future cash inflows, when discounted back to the present, exactly offset the initial investment.

The formula for NPV, which IRR aims to set to zero, is:

NPV = CF₀ + CF₁/(1+r)¹ + CF₂/(1+r)² + … + CF_n/(1+r)ⁿ = 0

Where:

• CF₀ = Initial Investment (Cash Flow at Year 0)
• CF₁, CF₂, …, CF_n = Cash Flows in Year 1, Year 2, …, Year n
• r = Internal Rate of Return (the rate we are solving for)
• n = Number of periods

Since 'r' cannot be solved directly in most cases, iterative numerical methods are used to approximate its value.

Interpreting the IRR

A higher IRR generally indicates a more desirable investment. Companies often compare the calculated IRR to their required rate of return, also known as the "hurdle rate."

• If IRR > Hurdle Rate: The project is generally considered acceptable, as it is expected to generate a return higher than the minimum required.
• If IRR < Hurdle Rate: The project is typically rejected, as it does not meet the company's minimum return expectations.
• If IRR = Hurdle Rate: The project is marginally acceptable.

IRR is particularly useful for comparing different investment opportunities, helping decision-makers prioritize projects that offer the highest potential returns.

Limitations of IRR

While a powerful tool, IRR has some limitations:

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

How to Use This IRR Calculator

Our IRR calculator simplifies the process of finding the Internal Rate of Return for your investment projects. Follow these steps:

1. Initial Investment (Year 0): Enter the initial cost of the investment. This should typically be a negative number, representing a cash outflow.
2. Cash Flow Year 1 to Year 5: Input the expected net cash flows for each subsequent year. These can be positive (inflows) or negative (additional outflows).
3. Calculate IRR: Click the "Calculate IRR" button.

The calculator will then display the Internal Rate of Return as a percentage. Use this value to assess the profitability of your investment against your hurdle rate or other investment opportunities.

Examples:

Example 1: Standard Investment

• Initial Investment: -100,000
• Cash Flow Year 1: 30,000
• Cash Flow Year 2: 40,000
• Cash Flow Year 3: 50,000
• Cash Flow Year 4: 20,000
• Cash Flow Year 5: 10,000
• Calculated IRR: Approximately 18.92%

Example 2: Longer Payback Period

• Initial Investment: -50,000
• Cash Flow Year 1: 15,000
• Cash Flow Year 2: 15,000
• Cash Flow Year 3: 15,000
• Cash Flow Year 4: 15,000
• Cash Flow Year 5: 15,000
• Calculated IRR: Approximately 15.24%