A capital lease was recorded for piece of equipment. There was a buy-out option, but the price of the buy-out was not specified in the lease. The final lease payment is now being made and the lessor has determined the buy-out price to be $10,000. How is the $10,000 cash payment recorded, since the loan is fully amortized with no final buy-out payment remaining, and the asset is fully depreciated. Is this recorded as another fixed asset and depreciated even though the original capital asset is fully depreciated?

By the sounds of it, the asset has been depreciated over the lease term rather than its useful life, so still has useful life remaining - after all, who's going to pay $10k at the end of a lease term for something that is no use to them?

In which case, you would record a new asset at $10k and depreciate it over the remainder of its useful life.