Question

Zebra Company as lessor enters into a lease agreement with United Company, on July 1, 2022, to give the right of use of its equipment to United. The following data are relevant to the lease agreement: 1. The term of the noncancelable lease is 4 years. Annual payments are due on July 1 of each year. There is an guaranteed residual value of $500,000 at the end of the least term. United Company estimates the residual value of the equipment at the end of the lease to be $200,000. 2. The fair value of the equipment on July 1, 2022 is $3,500,000 and cost to Zebra Company is 2,500,000. The equipment has an economic life of 5 years with no salvage value. 3. United depreciates similar machinery it owns on the sum-of-the-years’-digits basis. 4. The lessee pays all executory costs. 5. Zebra used an implicit rate of 8% in computing the lease payments. The implicit rate is unknown to United and United’s incremental borrowing rate is 10% per year. (Present value factor for 4 periods at 8%, 3.57710; at 10%, 3.48685, present value of 1 in 4 year time at 8%, 0.735; at 10%, 0.683).

(a) Compute the annual lease payment required by Zebra on July 1 each year.

Answer 1

The annual lease payment required by Zebra is approximately $875,823.93, calculated by subtracting the present value of the guaranteed residual value from the equipment's fair value and dividing the result by the present value annuity factor for 4 periods at 8%.

Step-by-step explanation:

To compute the annual lease payment required by Zebra on July 1 each year, we need to consider the present value of the annual payments plus the present value of the guaranteed residual value because the lessor, Zebra Company, would want to recover the fair value of the equipment through the lease payments and the residual value.

The fair value of the equipment is $3,500,000. The present value of the guaranteed residual value, which is $500,000 paid at the end of the 4-year term, discounted at the implicit rate of 8%, is calculated as follows:

($500,000) × (Present value of 1 in 4 year time at 8%) = $500,000 × 0.735 = $367,500

Now, subtracting the present value of the guaranteed residual value from the fair value of the equipment gives us:

$3,500,000 - $367,500 = $3,132,500

This amount is what the annual lease payments should cover. Using the present value annuity factor for 4 periods at 8%, the annual lease payment can be calculated by dividing the adjusted fair value by the present value factor of an annuity.

Annual Lease Payment = $3,132,500 / 3.57710 = $875,823.93 (rounded to the nearest cent)

Therefore, the annual lease payment that Zebra will require from United on July 1 each year is approximately $875,823.93.