How to Find Crossover Rate on Financial Calculator

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Crossover Rate Calculator

Project A

Project B

What is the Crossover Rate?

The crossover rate is the specific cost of capital (discount rate) at which the Net Present Value (NPV) of two competing projects is identical. In capital budgeting, this is the "indifference point" where a financial manager would be equally satisfied choosing either Project A or Project B.

How to Find Crossover Rate on a Financial Calculator

While most financial calculators (like the TI BAII Plus or HP 12C) don't have a dedicated "Crossover" button, you can find it using the Incremental Cash Flow Method:

  1. Subtract the Cash Flows: Take the cash flows of Project B and subtract them from Project A (or vice versa) for every time period (Year 0 through Year N).
  2. Enter into Cash Flow Register: Enter these differences as a new series of cash flows into your calculator's CF list.
  3. Compute IRR: Press the IRR button. The resulting Internal Rate of Return of the incremental cash flows is your Crossover Rate.
Realistic Example:
Project A: -$10,000 upfront, $6,000 Year 1, $6,000 Year 2.
Project B: -$10,000 upfront, $2,000 Year 1, $11,000 Year 2.
Incremental CFs: $0, +$4,000, -$5,000.
Crossover Rate: Finding the IRR of (0, 4000, -5000) yields approximately 25%.

Why the Crossover Rate Matters

If your company's actual cost of capital is lower than the crossover rate, you should generally choose the project with the steeper NPV profile (usually the one with higher total cash flows but received later). If the cost of capital is higher than the crossover rate, you should choose the project that pays back faster.

function calculateCrossover() { var resDiv = document.getElementById("crossover-result"); // Collect Cash Flows var cfa = [ -Math.abs(parseFloat(document.getElementById("a0").value)), parseFloat(document.getElementById("a1").value), parseFloat(document.getElementById("a2").value), parseFloat(document.getElementById("a3").value), parseFloat(document.getElementById("a4").value) ]; var cfb = [ -Math.abs(parseFloat(document.getElementById("b0").value)), parseFloat(document.getElementById("b1").value), parseFloat(document.getElementById("b2").value), parseFloat(document.getElementById("b3").value), parseFloat(document.getElementById("b4").value) ]; // Check for NaN for(var i=0; i<5; i++) { if(isNaN(cfa[i]) || isNaN(cfb[i])) { resDiv.innerHTML = "Please enter valid numeric values for all fields."; resDiv.className = "result-error"; resDiv.style.display = "block"; return; } } // Calculate Incremental Cash Flows (A – B) var deltaCF = []; var hasPositive = false; var hasNegative = false; for(var j=0; j 0) hasPositive = true; if(deltaCF[j] < 0) hasNegative = true; } // Solve for IRR of deltaCF var crossoverRate = solveIRR(deltaCF); if (crossoverRate === null || isNaN(crossoverRate)) { resDiv.innerHTML = "No clear crossover rate found. Ensure the projects have different cash flow timings."; resDiv.className = "result-error"; } else { resDiv.innerHTML = "The Crossover Rate is: " + (crossoverRate * 100).toFixed(2) + "%"; resDiv.className = "result-success"; } resDiv.style.display = "block"; } function solveIRR(cashFlows) { var precision = 0.0000001; var maxIterations = 1000; var guess = 0.1; // 10% initial guess for (var i = 0; i < maxIterations; i++) { var npv = 0; var dNpv = 0; for (var t = 0; t 0) { dNpv -= (t * cashFlows[t]) / Math.pow(1 + guess, t + 1); } } var nextGuess = guess – (npv / dNpv); if (Math.abs(nextGuess – guess) < precision) { return nextGuess; } guess = nextGuess; } return null; // Could not converge }

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