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Calculation of the implicit interest rate and present value of minimum lease payments

Details of a non-cancellable lease are as follows:

(i) Fair value = €10,000

(ii) Five annual rentals payable in advance of €2,100

(iii) Lessor’s unguaranteed estimated residual value at end of five years = €1,000

The implicit interest rate in the lease is that which gives a present value of €10,000 for the five rentals plus the total estimated residual value at the end of year 5. This rate can be calculated as 6.62%, as follows:

In other words, 6.62% is the implicit interest rate that, at the inception of the lease, causes the aggregate present value of the minimum lease payments (€10,500) and the unguaranteed residual value (€1,000) to be equal to the fair value of the leased asset. Lessor’s initial direct costs have been excluded for simplicity.

This implicit interest rate is then used to calculate the present value of the minimum lease payments, i.e. €10,500 discounted at 6.62%. This can be calculated at €9,274, which is 92.74% of the asset’s fair value, indicating that the present value of the minimum lease payments is substantially all of the fair value of the leased asset and a finance lease is therefore indicated.

It would be appropriate for the lessee to record the asset at €9,274 as the present value of the minimum lease payments is lower than the fair value and this would take account of the lessor’s residual interest in the asset.