Haystack, Inc. manufactures machinery used in the mining industry. On January 2, 2015 it leased equipment with a cost of $320,000 to Silver Point Co. The 5-year lease calls for a 10% down payment and equal annual payments at the end of each year. The equipment has an expected useful life of 5 years. Silver Point's incremental borrowing rate is 10%, and it depreciates similar equipment using the double-declining balance method. The selling price of the equipment is $520,000, and the rate implicit in the lease is 8%, which is known to Silver Point Co. What is the amount of interest expense recorded by Silver Point Co. for the year ended December 31, 2015?
A) $46,800
B) $37,440
C) $41,600
D) $52,000

Question

Haystack, Inc. manufactures machinery used in the mining industry. On January 2, 2015 it leased equipment with a cost of $320,000 to Silver Point Co. The 5-year lease calls for a 10% down payment and equal annual payments at the end of each year. The equipment has an expected useful life of 5 years. Silver Point's incremental borrowing rate is 10%, and it depreciates similar equipment using the double-declining balance method. The selling price of the equipment is $520,000, and the rate implicit in the lease is 8%, which is known to Silver Point Co. What is the amount of interest expense recorded by Silver Point Co. for the year ended December 31, 2015? 
A) $46,800 
B) $37,440 
C) $41,600 
D) $52,000

Quizplus · Accepted Answer

The annual lease payment can be calculated using the present value of an annuity formula:
PV of annuity = (annual payment) x [(1 - (1 / (1 + r)^n)) /r]
where r is the interest rate implicit in the lease (8%), n is the number of years (5) and PV of annuity is the present value of the lease payments discounted at the implicit rate.
Solving for annual payment, we get:
320,000 = (annual payment) x [(1 - (1 / (1 + 0.08)^5)) /0.08]
Annual payment = $80,368.91
The interest expense for the first year can be calculated as the interest on the lease liability at the beginning of the year. The lease liability at the beginning of the year is calculated as:
Lease liability = present value of minimum lease payments not yet paid
Year 1 lease payment = $80,368.91
Present value of remaining lease payments discounted at 8%:
PV of lease payments = 80,368.91 x [(1 - (1 / (1 + 0.08)^4)) / 0.08] = $295,527.38
Lease liability at beginning of year 1 = $295,527.38 - ($80,368.91 x 1) = $215,158.47
Interest expense for year 1 = lease liability at beginning of year 1 x incremental borrowing rate
Interest expense = $215,158.47 x 0.10 = $21,515.85
Therefore, the amount of interest expense recorded by Silver Point Co. for the year ended December 31, 2015 is $21,515.85.
However, be careful to note that the question is asking for interest expense only, not total lease expense. The total lease expense for year 1 would be the sum of the interest expense and the lease amortization expense, which is calculated as the difference between the lease payment and the interest expense. The total lease expense for year 1 is $80,368.91.