 # Minimum Lease Payment

The minimum amount a lessee can pay over the term or lifetime of the lease

## What is a Minimum Lease Payment?

The minimum lease payment is the minimum amount a lessee can pay over the term or lifetime of the lease. The present value of minimum lease payments determines the value of the lease, which is then recorded in the accounting books of a company. Minimum lease payments are also very important in determining the classification of the lease – whether it should be an operating lease or a capital lease. It is important because an operating lease is treated as an expense and would not be included in the assets of a company, whereas a capital lease would be included in the assets of a company. Minimum lease payments are integral for the accounting practices of a company and a key part of corporate accounting.

### Minimum Lease Payments and Accounting Standard Setting Boards

The method for calculating minimum lease payments varies with different accounting standard setting boards, along with the classification of a lease being a capital lease or operating lease. Furthermore, classification standards of operating leases and capital leases are frequently revised. It is recommended that you visit the appropriate accounting standard board’s website to stay up-to-date on current regulations.

### How to Calculate a Minimum Lease Payment?

One method of calculating the present value of minimum lease payments is below: Where:

• PV – Present Value of minimum lease payment
• Paymentn – The lease payment for period n
• r – The corresponding interest rate
• Residual Amount – Estimated value of asset once the lease is over
• N – The total amount of periods in the lease contract

Conclusively, the present value of the minimum lease payment is simply the sum of all of the lease payments that are to be made in the future, in today’s dollar terms, added to the value of the estimated value of the leased asset once the lease is over.

The reason the payments and residual amount is divided by 1 plus the interest rate adjusted for time, is to bring the terms into today’s dollars. To adjust for the timing of the payments and residual amount, you must power the term (1+r) to the value of the period in which the payment and/or the residual amount occurs.

### Numerical Example

A numerical example of a minimum lease payment is very useful to understand the workings of the equation above.

The following is an example:

• Three-year lease
• Annual payments of \$100
• Annual interest rate of 5%
• Residual amount of \$50

PV of Payment 1: \$100 / (1 + 5%) = \$95.24

PV of Payment 2: \$100 / [(1 + 5%) ^ 2] = \$90.70

PV of Payment 3: \$100 / [(1+5%) ^ 3] = \$86.38

Sum of PV’s: \$95.24 + \$90.70 + \$86.38 = \$272.32

PV of Residual Amount: \$50 / [(1 + 5%) ^ 3] = \$43.19

PV of Minimum Lease Payment: \$43.19 + \$272.32 = \$315.51

In the example above, we first take the present value of all of the annual lease payments individually. Then, we add them. Finally, we take the present value of the residual amount and add that to the sum of the present value of the annual lease payments.

It is important to notice the periodicity of the annual lease payments and the terms in which the interest rate is stated in. In such a case, the interest rate is stated in an APR (annual percentage rate) format.

The lease payments are also annual. Thus, no adjustments to the interest rate are needed. However, if the given interest rate was semi-annual or the lease payments were semi-annual, you would need to adjust the interest rate. A general rule of thumb is to match the periodicity of the interest rate to that of the periodicity of the lease payments.

### Minimum Lease Payment Using Annuities

Calculating the present value of minimum lease payments can also be achieved using an annuity formula. It holds because the periodicity of the lease payments is typically evenly spaced out. Below is an example of using an annuity to solve the above problem.

PV of Annuity of Annual Lease Payments: \$100 * [1– (1+ 5%) ^ (-3)] / 5% = \$272.32

PV of Residual Amount: \$50 / [(1 + 5%) ^ 3] = \$43.19

PV of Minimum Lease Payment: \$43.19 + \$272.32 = \$315.51