Calculating Initial Liability and ROU
Overview
Under ASC 842, IFRS 16, and GASB 87, the initial liability and right-of-use (ROU) asset for a lease are both equal to the present value of the rents, with adjustments:
Right-of-use asset: Starts with the present value of the rents at the appropriate discount rate, which is the incremental borrowing rate (not limited by the fair value), unless the implicit rate can be calculated (which should reflect the lessor's initial direct costs as well as unguaranteed residual, if known). To this is added any lessee's initial direct costs, then lease incentives are subtracted.
Initial liability: Equal to the present value of the rents.
This article briefly describes the calculations that EZLease uses to determine the initial liability and ROU asset, whether the lease has a single rent step or multiple steps.
PV Formula
Sometimes, customers or auditors want to validate EZLease’s calculations. In Excel, the function for present value is =PV(rate, nper, pmt, fv, type), which has the following parameters:
Rate: entered as a decimal per payment period, so a 6% annual rate for a lease paid monthly would be .005
Nper: Number of periods the payment is made
Pmt: Payment amount per period
FV: Future value; this is described more below
Type: 0 for payments in arrears, 1 for payments in advance. Almost all leases are payments in advance.
Single Rent Step
For a lease with a single rent step, the calculation is simple:
Say we have a 3 year lease, $100 rent paid monthly, incremental borrowing rate 6%. The present value is: =PV(.06 / 12, 3 * 12, 100, 0, 1), which is 3,303.54.
If the lease has a guaranteed residual or reasonably certain purchase option, the residual or option price is added as the FV. So if there is a $500 buyout option at the end of the lease which is considered reasonably certain to be exercised, the formula becomes =PV(.06 / 12, 3 * 12, 100, 500, 1), which is 3,721.36.
Multiple Rent Steps
If a lease has multiple rent steps, the calculation gets more complicated, because the result of one step has to be fed into the previous step. The present value of step 2 is the future value for step 1, etc. So to take our 3-year lease, let’s say the rent is $100/month for the first year, $110/month for the second year, $120/month for the third year, with a $500 reasonably certain purchase option. We calculate in reverse order:
Third year: =PV(.06 / 12, 12, 120, 500, 1): 1,872.20
Second year: =PV(.06 / 12, 12, 110, -1872.20, 1): 3,047.90
First year: =PV(.06 / 12, 12, 100, -3047.90, 1): 4,038.54
Note: The result of the PV function is a negative number, so if you are going to feed the result directly into the next formula, be sure to put a negative in front of the result when using it as the FV parameter (such as =PV(.06 / 12, 12, 110, -A3, 1) ).
The initial liability is equal to the present value of the rents. The ROU asset is the liability, minus any lease incentives and deferred rent liabilities, plus any initial direct costs.