Internal Rate of Return Calculator with Steps

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Internal Rate of Return (IRR) Calculator

Annual Cash Inflows

Resulting IRR: 0%

Step-by-Step Verification (NPV Calculation)

IRR is the rate where Net Present Value (NPV) equals zero. Below is the discounted value of each cash flow using the calculated rate:

Year Cash Flow PV Factor (1+r)^t Present Value

Total NPV: 0

function calculateIRR() { var initial = parseFloat(document.getElementById('initialInvestment').value); var y1 = parseFloat(document.getElementById('year1').value) || 0; var y2 = parseFloat(document.getElementById('year2').value) || 0; var y3 = parseFloat(document.getElementById('year3').value) || 0; var y4 = parseFloat(document.getElementById('year4').value) || 0; var y5 = parseFloat(document.getElementById('year5').value) || 0; if (isNaN(initial) || initial <= 0) { alert("Please enter a valid initial investment cost."); return; } var cashFlows = [-initial, y1, y2, y3, y4, y5]; // Iterative approach to find IRR (Newton-Raphson simplified or Bisection) var low = -1.0; var high = 10.0; var irr = 0.1; for (var i = 0; i < 100; i++) { var npv = 0; for (var t = 0; t < cashFlows.length; t++) { npv += cashFlows[t] / Math.pow(1 + irr, t); } if (Math.abs(npv) 0) { low = irr; } else { high = irr; } irr = (low + high) / 2; } displayResults(irr, cashFlows); } function displayResults(irr, cashFlows) { document.getElementById('resultArea').style.display = 'block'; document.getElementById('irrValue').innerText = (irr * 100).toFixed(2); var tableBody = document.getElementById('stepsTableBody'); tableBody.innerHTML = "; var totalNpv = 0; for (var t = 0; t < cashFlows.length; t++) { var factor = Math.pow(1 + irr, t); var pv = cashFlows[t] / factor; totalNpv += pv; var row = tableBody.insertRow(); row.innerHTML = '' + t + '' + '' + cashFlows[t].toLocaleString() + '' + '' + factor.toFixed(4) + '' + '' + pv.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + ''; } document.getElementById('finalNpv').innerText = totalNpv.toFixed(2); }

Understanding the Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) is a critical 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 (both positive and negative) from a particular project equal to zero.

The IRR Formula

While there is no simple algebraic way to isolate IRR when you have multiple years of cash flows, the logic follows this equation:

0 = CF0 + [CF1 / (1+IRR)1] + [CF2 / (1+IRR)2] + … + [CFn / (1+IRR)n]

  • CF0: Initial Investment (expressed as a negative number).
  • CF1…n: Cash inflows for each period.
  • IRR: The rate we are solving for.

Practical Example

Imagine you invest $10,000 today in a project. Over the next three years, the project returns $4,000, $4,000, and $5,000 respectively. To find the IRR, we search for a percentage rate that discounts those future payments back to exactly $10,000 in today's money.

In this example, the IRR would be approximately 13.88%. If your "Hurdle Rate" (the minimum acceptable return) is 10%, this project would be considered a good investment because the IRR exceeds the hurdle rate.

Steps to Calculate IRR Manually

  1. Identify Cash Flows: List your initial outlay (negative) and all expected future inflows (positive).
  2. Set NPV to Zero: Set up the equation where the sum of discounted cash flows equals zero.
  3. Trial and Error: Since you cannot solve for IRR directly, pick a rate (e.g., 10%) and calculate the NPV. If the NPV is positive, your rate is too low. If it's negative, your rate is too high.
  4. Interpolate: Narrow down the range until you find the rate where NPV is as close to zero as possible.

Why Use IRR?

The primary advantage of IRR is that it provides a single percentage figure that summarizes the efficiency and quality of an investment. It allows managers to compare projects of different sizes and durations on a level playing field. However, it should always be used alongside NPV, as IRR can sometimes provide misleading results for projects with non-conventional cash flows (e.g., alternating between positive and negative cash flows).

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