# How to calculate the PV of minimum lease payments

Under generally accepted accounting principles, or GAAP, if you are leasing something, then you recognise the lease in your accounting books at the start of the lease. But that is not the case if the start of the lease and the time that you sign the lease are not the same.

In this instance, you would want to recognise the present value, or PV, of the minimum lease payments by using the interest rate as a discount rate. With a little math, you can quickly calculate the PV of minimum lease payments.

Confirm the lease term. To calculate the PV of minimum lease payments, you will need to know the term of the lease or the expected useful life of the item you are leasing. The term will be listed in the lease agreement that you have signed. You will want to know the term in years.

Add up your yearly lease payments. You may make lease payments yearly, monthly, quarterly or semiannually. Confirm your payment schedule and amount in your lease agreement. Then calculate what your yearly lease payment is for the lease.

Find the interest rate. Check your lease agreement to confirm what your borrowing interest rate is for the term of the lease. You will want to convert the interest rate to a number you can use by moving the decimal point two spaces to the left. For example, if your interest rate is 7.5 per cent, then you will convert it to 0.075 for the PV calculation.

Confirm the residual value. If you are leasing equipment for a business, then the company you are leasing from will typically guarantee a specific residual value for the equipment. This amount will be listed in your lease agreement. If you are looking for the PV of minimum lease payments for something like a consumer vehicle lease, then you will not have a residual value. If you do not have a residual value, that is OK because you can still calculate the PV of the minimum lease payments.

Solve for the PV of the minimum lease payments. The equation you will use is L / (1 + r to the nth power) where "L" is the yearly lease payment amount, "r" is the interest rate and "n" is the number of years. For example, if your annual lease payments are £13,000 for 3 years at an interest rate of 8 per cent and you have a guaranteed residual value of £3,250, your equation would look like this: [ 20,000 / (1.08) ] + [20,000 / (1.08)(1.08) ] + [ 20,000 / (1.08)(1.08)(1.08) ] + [ 5,000 / (1.08)(1.08)(1.08)] = PV of minimum lease payments. To break that down, it would look like 18,518.52 + 17,146.78 + 15,876.64 + 3,969.16 = 55,511.10. So, the PV of the minimum lease payments is £36,082.2 in this example.