Question

Federated Fabrications leased a tooling machine on January 1, 2018, for a three-year period ending December 31, 2020. The lease agreement specified annual payments of $36,000 beginning with the first payment at the beginning of the lease, and each December 31 through 2019. The company had the option to purchase the machine on December 30, 2020, for $45,000 when its fair value was expected to be $60,000, a sufficient difference that exercise seems reasonably certain. The Machine's estimated useful life was six years with no salvage value. Federated was aware that the lessor's implicit rate of return was 12%.

Question: When calculating the right-of-use asset/lease liability for Federated, why do we use the present value of annuity due and not the present value of ordinary annuity (since the payments are made at the end of the year)?

Answer 1

Solution:

When lease payment are made at the beginning of year then we use present value of annuity due while calculating right to use assets. Further when lease payments are made at the end of year then we use present value of ordinary annuity while calculating right to use asset.

When we make payment at beginning of year then first payment will have present value equal to the payment amount. further when we make payment at the end of year then first payment present value differs from payment amount as payment is made at one year later. Therfore present value factor will provide different values under both situations.

In view of above when payment are made at beginning of year, we use present value of annity due when calculating the right of use asset.