Enter the cash flows for two mutually exclusive projects to find the discount rate where their NPVs are equal.
Period
Project A Flow
Project B Flow
Note: Use negative values for outflows (investments).
The calculated Crossover Rate is: 0.00%
function calculateCrossover() {
var flowsA = [
parseFloat(document.getElementById('flowA0').value) || 0,
parseFloat(document.getElementById('flowA1').value) || 0,
parseFloat(document.getElementById('flowA2').value) || 0,
parseFloat(document.getElementById('flowA3').value) || 0,
parseFloat(document.getElementById('flowA4').value) || 0,
parseFloat(document.getElementById('flowA5').value) || 0
];
var flowsB = [
parseFloat(document.getElementById('flowB0').value) || 0,
parseFloat(document.getElementById('flowB1').value) || 0,
parseFloat(document.getElementById('flowB2').value) || 0,
parseFloat(document.getElementById('flowB3').value) || 0,
parseFloat(document.getElementById('flowB4').value) || 0,
parseFloat(document.getElementById('flowB5').value) || 0
];
var diffFlows = [];
for (var i = 0; i < flowsA.length; i++) {
diffFlows.push(flowsA[i] – flowsB[i]);
}
var irr = findIRR(diffFlows);
var resultArea = document.getElementById('crossover-result-area');
var display = document.getElementById('crossover-rate-display');
var desc = document.getElementById('res-desc');
resultArea.style.display = 'block';
if (irr === null) {
display.innerHTML = "No Crossover";
display.style.color = "#e74c3c";
desc.innerHTML = "Based on these cash flows, there is no single discount rate where the NPVs cross within a realistic range (0% to 100%). Check your inputs.";
} else {
var irrPercent = (irr * 100).toFixed(2);
display.innerHTML = irrPercent + "%";
display.style.color = "#27ae60";
desc.innerHTML = "At a cost of capital of " + irrPercent + "%, both projects will have the exact same Net Present Value (NPV). If your actual cost of capital is lower than this rate, the project with the steeper NPV curve (usually the one with higher total cash flows further in the future) is generally preferred.";
}
}
function findIRR(cashFlows) {
var guest = 0.1;
var maxIterations = 1000;
var precision = 0.000001;
for (var i = 0; i < maxIterations; i++) {
var npv = 0;
var dNpv = 0;
for (var t = 0; t < cashFlows.length; t++) {
npv += cashFlows[t] / Math.pow(1 + guest, t);
dNpv -= t * cashFlows[t] / Math.pow(1 + guest, t + 1);
}
var nextGuest = guest – (npv / dNpv);
if (Math.abs(nextGuest – guest) -1 && nextGuest < 10) return nextGuest;
return null;
}
guest = nextGuest;
}
return null;
}
Understanding and Calculating the Crossover Rate
In capital budgeting, when financial managers evaluate two mutually exclusive projects, they often encounter a conflict between the Net Present Value (NPV) and the Internal Rate of Return (IRR). The Crossover Rate is the specific discount rate at which the NPVs of two different projects are equal.
Why the Crossover Rate Matters
The crossover rate is critical because it identifies the "turning point" for decision-making. If the company's cost of capital is less than the crossover rate, one project will be superior. If the cost of capital exceeds the crossover rate, the other project becomes the better choice. It visually represents the point where the NPV profiles of two projects intersect on a graph.
How to Calculate Crossover Rate (Step-by-Step)
While a financial calculator like the TI-BAII Plus or HP 12C doesn't have a single "Crossover" button, you can calculate it easily using the IRR function:
Calculate the Differences: Subtract the cash flows of Project B from Project A for every single period (Year 0, Year 1, Year 2, etc.).
Input Into Cash Flow Register: Treat these differences as the cash flows for a new, hypothetical "Project Delta."
Solve for IRR: Use the [IRR] button on your financial calculator. The resulting IRR of the differences is the Crossover Rate.
Practical Example
Imagine two projects with the following cash flows:
Project A: Year 0: -$1,000 | Year 1: $450 | Year 2: $450 | Year 3: $450
Project B: Year 0: -$1,000 | Year 1: $200 | Year 2: $200 | Year 3: $1,000
To find the crossover rate:
Year 0 Difference: -1000 – (-1000) = 0
Year 1 Difference: 450 – 200 = 250
Year 2 Difference: 450 – 200 = 250
Year 3 Difference: 450 – 1000 = -550
Input these differences (0, 250, 250, -550) into your financial calculator's cash flow worksheet and hit IRR. The resulting percentage is the rate where both projects offer the same value.
Interpreting the Results
If the Cost of Capital < Crossover Rate, the project with the higher total cash flows (often the one with flows weighted toward the later years) usually has a higher NPV.
If the Cost of Capital > Crossover Rate, the project that returns cash faster (weighted toward earlier years) will typically have a higher NPV because those early dollars are less affected by a high discount rate.