# How to Calculate the PV of Minimum Lease Payments

When companies cannot afford to purchase equipment, or when they expect the equipment to become obsolete in a few years, management might choose to lease equipment. The lessor owns the equipment and rents it out_._ The lessee makes regularly scheduled payments to the lessor for the use of the equipment.

The *minimum lease payments* are the amount the lessee is expected to pay over the term of the lease. Since the value of money decreases each year due to inflation, accountants measure the present value of the minimum lease payments to determine how much the lease will cost in today's dollars.

## Lease Term and Payments

The term of the lease and the amount of each monthly payment determine the total amount that the company will pay during the lease period. For instance, suppose Generic Construction leases a bulldozer from Fictional Equipment, Inc. In the lease agreement, Generic Construction is the lessee and Fictional Equipment is the lessor.

The lease agreement specifies that Generic will pay Fictional $5,000 per month for five years to lease a bulldozer. The term of the lease is five years, so Generic will make 12 monthly payments each year for five years. The yearly payments would be $5,000 x 12, or $60,000, per year.

## Interest Rate

Lessors will often include an interest rate on their leasing agreements. The interest rate on a lease agreement is not the same as that for a standard bank loan. The interest rate in a leasing agreement is calculated on a monthly basis, rather than the annual basis of a standard bank loan. For instance, the interest rate for the bulldozer lease is listed at 6 percent per year, or 0.5 percent per month (6 percent/12 months = 0.5 percent/month).

## Residual Value

The *residual value* of a leased item is the value of the item that remains at the end of the lease. Some lease agreements allow the lessee to purchase the leased item at the residual value at the end of the lease term. In this example, the residual value of the bulldozer after five years of use is $100,000.

## P4 Present Value Formula

The formula of present value of minimum lease payments looks like this:

PV = SUM[P/(1+r)^{n}] + [RV/(1+r)^{n}]

Where PV = Present Value

P = Annual Lease Payments

r = Interest rate

n = number of years in the lease term

RV = residual value

SUM[P/(1+r)^{n}] = the total amount paid over the lease term, discounted for the interest rate.

In the above example, P = $60,000, r = 0.06, n = 5, RV = $100,000

PV = [60000/(1.06)] + [60000/(1.06)^{2}] + [60000/(1.06)^{3}] + [60000/(1.06)^{4}] + + [60000/(1.06)^{5}] + [100000/(1.06)^{5}]

= $56,603.77 + $53,399.79 + $50,377.16 + $47,525.62 + $44,835.49 + $74,725.82

= $327,467.65