Final answer:
To record the giveaway of an asset at the end of its useful life, remove the asset and its accumulated depreciation from the books while recording any loss if the asset's book value differs from the value received.
Step-by-step explanation:
When an asset with an original cost of $75,000, a residual value of $7,500, and a useful life of 5 years is given away without any consideration at the end of year five, the entry to record this transaction would involve removing the asset and the associated accumulated depreciation from the books. Assuming straight-line depreciation, the annual depreciation would be ($75,000 - $7,500) / 5 years = $13,500 per year. By the end of the fifth year, the accumulation depreciation would be $13,500 x 5 years = $67,500. The book value of the asset at the time it is given away is the original cost minus the accumulated depreciation, which would be $75,000 - $67,500 = $7,500. This is equal to the residual value, so when the asset is given away, the company would remove the asset from its books by debiting accumulated depreciation for $67,500, debiting a loss on disposal or write-down (if applicable) for the difference between the book value and the value received (in this case, zero since it was given away), and crediting the asset account for $75,000.