Question

Universal Leasing leases electronic equipment to a variety of businesses. The company's primary service is providing alternate financing by acquiring equipment and leasing it to customers under long-term direct financing leases. Universal earns interest under these arrangements at a 10% annual rate.

The company leased an electronic typesetting machine it purchased for $30,900 to a local publisher, Desktop Inc., on December 31, 2015. The lease contract specified annual payments of $8,000 beginning January 1, 2016, the inception of the lease, and each December 31 through 2017 (three-year lease term). The publisher had the option to purchase the machine on December 30, 2018, the end of the lease term, for $12,000 when it was expected to have a residual value of $16,000.

Show how Universal calculated the $8,000 annual lease payments for this direct financing lease.

Answer 1

Universal Leasing calculated the $8,000 annual lease payments by setting up and solving an equation that balances the present value of the lease payments and the present value of the residual value against the initial cost of the equipment. A 10% annual interest rate and a three-year lease term were factored in, along with the $16,000 residual value. Financial calculators or software are typically used to determine this payment accurately.

Step-by-step explanation:

The calculation of the annual lease payments for this direct financing lease involves considering the initial cost of the equipment, the interest rate, the lease term, and the residual value.

To calculate the $8,000 annual lease payments, Universal Leasing would have followed an approach similar to calculating the payments of an annuity, taking into account the 10% annual interest rate, the amount financed ($30,900), and the three-year term.

The residual value of $16,000 that Desktop Inc. has the option to pay at the end of the lease term also influences the calculation since it reduces the depreciable base that Universal Leasing needs to recover over the lease period.

Using a present value formula for annuities, the calculation accounts for the fact that the lease payments are an annuity in arrears (payments made at the end of each period).

The calculation would equate the present value of the lease payments plus the present value of the residual value to the cost of the equipment.

The $8,000 figure is derived from setting this equation to balance and solving for the annual lease payments.

Though a financial calculator or specialized software is typically used for these calculations in practice, conceptually,

the lease payment reflects the need to repay the initial cost of the equipment plus interest over the lease term while considering that a portion of the equipment value is implicitly paid at the end of the lease term through the 'purchase option' at a price less than the expected residual value.