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Why do we subtract out the first payment? Isn’t that what the point of using the PV of annuity due is? I thought it incorporated that into its present value.
On December 31, 2005, Neal, Inc. leased machinery with a fair value of $105,000 from Frey Rentals Co. The agreement is a 6-year noncancelable lease requiring annual payments of $20,000 beginning December 31, 2005.
The lease is appropriately accounted for by Neal as a capital lease.
Neal’s incremental borrowing rate is 11%. Neal knows the interest rate implicit in the lease payments is 10%.
The present value of an annuity due of $1 for 6 years at 10% is 4.7908.
The present value of an annuity due of $1 for 6 years at 11% is 4.6959.
In its December 31, 2005 balance sheet, Neal should report a lease liability of
A. $75,816.
B. $85,000.
C. $93,918.
D. $95,816.
Correct!
The $75,816 lease liability at December 31, 2005 is the initial liability at inception less the first payment, which is completely a principal payment. The first payment occurs at inception and therefore could have no interest component. The initial liability at inception is the present value of an annuity due of six periods.
Ending 2005 lease liability = liability at inception – $20,000 first payment
= $20,000(4.7908) – $20,000
= $75,816
The lessee must use the lower of its incremental borrowing rate (11%) and the rate implicit in the lease (10%), hence the use of the 4.7908 present value factor.
What is the difference in this question?
Tag Question
Koby Co. entered into a capital lease with a vendor for equipment on January 2 for 7 years. The equipment has no guaranteed residual value. The lease required Koby to pay $500,000 annually on January 2, beginning with the current year. The present value of an annuity due for 7 years was 5.35 at the inception of the lease.
What amount should Koby capitalize as leased equipment?
A. $500,000
B. $825,000
C. $2,675,000
D. $3,500,000
Correct!
The amount to be capitalized is the present value of the lease payments. This amount is $2,675,000 ($500,000 x 5.35) and should be equal to the market value of the equipment if the useful life is also 7 years.
Although $3,500,000 (7 x $500,000) will be paid by Koby over the lease term, the difference between that amount and $2,675,000 represents interest to be recognized over the term. The $2,675,000 amount is the current sacrifice required to obtain the use of the equipment and should be close to the purchase price if the equipment is available by purchase.
If Koby invested that amount at the interest rate implied in the lease, the investment would be sufficient to cover all seven payments.
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