Determine the internal rate of return for lease accounting (ASC 842 & IFRS 16)
End of Period (Arrears)
Beginning of Period (Advance)
Calculated Implicit Rate
0.00%
What is the Implicit Rate in a Lease?
The implicit rate is the interest rate that causes the aggregate present value of (a) the lease payments and (b) the amount that a lessor expects to derive from the underlying asset at the end of the lease term (residual value) to equal the sum of the fair value of the underlying asset and any initial direct costs incurred by the lessor.
In accordance with ASC 842 and IFRS 16, the lessee is required to use the rate implicit in the lease if it is readily determinable. If it is not, the lessee uses its incremental borrowing rate (IBR).
Key Components of the Calculation
Fair Value: The price that would be received to sell the asset in an orderly transaction between market participants.
Initial Direct Costs: Incremental costs of a lease that would not have been incurred if the lease had not been obtained.
Lease Payments: The fixed and variable payments made during the term.
Residual Value: The estimated value of the asset at the end of the lease, including both guaranteed and unguaranteed portions.
Practical Example
Imagine a company leases a machine with a Fair Value of $100,000. The lease term is 60 months with monthly payments of $1,800 paid at the beginning of each month. The lessor estimates the machine will be worth $15,000 at the end of the term. There are no initial direct costs.
By inputting these values into the calculator, the tool iterates to find the specific discount rate where the Present Value of those payments and the $15,000 residual value equals exactly $100,000.
Why the Implicit Rate Matters
Finding the correct implicit rate is crucial for determining the Right-of-Use (ROU) Asset and the Lease Liability on the balance sheet. A lower implicit rate generally results in a higher lease liability and ROU asset, which impacts the timing of expense recognition and various financial ratios (like Debt-to-Equity).
function calculateImplicitRate() {
var fairValue = parseFloat(document.getElementById('fairValue').value);
var directCosts = parseFloat(document.getElementById('directCosts').value) || 0;
var pmt = parseFloat(document.getElementById('leasePayment').value);
var nper = parseInt(document.getElementById('leaseTerm').value);
var rv = parseFloat(document.getElementById('residualValue').value) || 0;
var type = parseInt(document.getElementById('paymentTiming').value);
if (isNaN(fairValue) || isNaN(pmt) || isNaN(nper) || nper <= 0) {
alert("Please enter valid positive numbers for Fair Value, Payments, and Lease Term.");
return;
}
var targetValue = fairValue + directCosts;
// We need to find 'r' such that:
// targetValue = PV(pmt, nper, r, type) + PV(rv, nper, r)
var low = 0;
var high = 1.0; // Starting with max 100% per period
var r = 0.05; // Initial guess
var iterations = 100;
var tolerance = 0.0000001;
// Binary search for the IRR (Rate)
for (var i = 0; i targetValue) {
low = mid;
} else {
high = mid;
}
if (Math.abs(pv – targetValue) < tolerance) {
r = mid;
break;
}
r = mid;
}
var resultBox = document.getElementById('resultBox');
var rateOutput = document.getElementById('rateOutput');
var periodNote = document.getElementById('periodNote');
var periodicRatePercent = r * 100;
var annualRatePercent = periodicRatePercent * 12;
rateOutput.innerHTML = annualRatePercent.toFixed(4) + "% Annualized";
periodNote.innerHTML = "Periodic (per payment) rate: " + periodicRatePercent.toFixed(4) + "%";
resultBox.style.display = 'block';
}