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# What is the present value of a lease?

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US GAAP and IFRS accounting for leases and lease pricing are based on the fair value of the leased assets and the expected cash flowsThe current value of one or a series of discounted cash flows due and payable at a specific future date or dates is present value (PV).  The present value of cash inflow less the present value of cash outflows is net present value (NPV).  Leased assets and related liabilities are recognized by the lessee at lease inception at the lower of the leased asset’s fair value and the NPV of the minimum lease payments.

Net Present Value = PV(Cash Inflows) - PV(Cash Outflows)

The lessee’s incremental borrowing rate is the rate of interest that the lessee would have to pay on a similar lease or, if this is not determinable, would incur to borrow the funds required to purchase the asset over the same term and with similar security.  Under US GAAP, the lessee’s incremental borrowing rate is used to calculate the NPV of the MLPs, unless a lower implicit rate can be determined – because the lessee will not know the lessor’s implicit rate, the lessee generally uses the incremental rate.  Under IFRS, if practical to determine, the implicit interest rate is used to discount the MLPs; otherwise, the lessee’s incremental borrowing rate is used.

Present Value of a Lease
PV of Lease = (MLP + URV)/(1 + r)n
Where:
MLP = Minimum lease payments
URV = Unguaranteed residual value
r = Incremental/implicit interest rate
n = Lease term
 PVLease MLP1 + MLP2 + MLP3 ...+ URVn (1+r)1 (1+r)2 (1+r)3 (1+r)n

Discounting is the process of computing present value.  The interest rate at which expected future cash flows are discounted in the process of computing present value is the discount rate.  The discount rate at lease inception that causes the gross investment in the lease (MLPs + URV) to equal the net investment in the lease (PV(MLPs + URV)) is the lease’s implicit interest rate.