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. Sometimes, customers or auditors want to validate EZLease’s calculations. The following is a brief description of the calculations EZLease uses to determine the initial liability and asset.

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.

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.

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 that 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.