A lease agreement allows individuals or companies to use land, buildings or equipment, without the need to purchase them outright. The owner of the property, known as the lessor, allows the user, also called the lessee, to use the asset in exchange for lease payments. A capital lease allows the lessee the opportunity to purchase the asset after the lease term expires. The lessee can calculate the value of a capital lease to determine how much they may expect to pay to buy the item at the end of the lease term.
A lease agreement resembles a standard asset loan, in that the lessor allows the lessee to pay for the use of the asset over time. While a standard loan agreement will include the loan's annual interest rate, a lease agreement will contain a lease factor rate. The lease factor is the interest rate divided by 24. For instance, Generic Construction wants to lease a bulldozer from Fictional Equipment Co. The lease agreement mentions the lease factor of 0.0025. The lease factor translates to an annual interest rate of 6 percent. (0.0025x24=0.06)
Capital lease agreements also will include a residual value. The residual value is the price that the lessee can pay to buy the asset at the end of the lease. Since the asset will have depreciated from age and use during the lease term, the residual value often is less than the market value for a new asset. For instance, the bulldozer lease agreement for Generic Construction includes a residual value of $50,000 at the end of the five-year lease term. The company can then choose to buy the used bulldozer for $50,000 when the lease expires.
Present Value of Lease Payments
Since the lessee pays the lessor for the use of the item over time, the interest rate will cause the value of each payment to fall over time. The lessor must determine the present value of the lease payments with this interest rate in mind. The formula for present value looks like this:
P = PMT [(1 - (1 / (1 + r)n)) / r] + RV[(1 / (1 + r)n]
Where P = Present value of lease payments,
PMT = monthly lease payment amount,
r = interest rate,
n = number of payments,
and RV = residual value.
For instance, the lease agreement for Generic Construction calls for 60 monthly payments of $2,000 at an annual interest rate of 6 percent. The monthly interest rate would be 0.06/12, or 0.005.
P = 2000[(1 - (1 / (1 + 0.005)60)) /0.005] + 50000/[(1 + 0.005)60]
= 2000[(1 - (1 / (1.005)60)) /0.005] + 50000/[(1.005)60]
= 2000[(1 - (1 / (1.35))) /0.005] + 50000/[1.35]
= 2000[(1 - (0.74)) /0.005] + 50000/(1.35)
= 2000[0.26/0.005] + 50000/(1.35)
= 2000[51.72] + 37,037
= 104,000 + 37,037 = $141,037
Uses for Lease Value
The lease value calculation can show managers if the company would save money by leasing an asset versus purchasing it outright. In this example, Fictional Equipment may offer to allow Generic Construction two options. Generic can lease the bulldozer at $2,000 a month for 60 months at 6 percent interest, or purchase the bulldozer for $150,000 in cash today. The present value calculation shows that Generic would save nearly $9,000 by taking the lease.