On January 1, 2019, Georgia Instruments sold a depreciable asset for cash of $200,000 and recognized a gain of $30,000. The asset had been purchased on January 1, 2014 with an estimated useful life of 10 years, and no salvage value. The asset was depreciated using the straight-line method.
What must have been the original cost of the asset?

Question

Quizplus · Accepted Answer

The original cost of the asset can be determined by first calculating the total depreciation over the 5 years it was used, then adding the gain on sale and the cash received from the sale. Since the asset was depreciated using the straight-line method over 10 years with no salvage value, the annual depreciation expense would be the cost of the asset divided by 10. Given that the asset was sold after 5 years, it would have been depreciated for half of its useful life. The gain of $30,000 indicates that the sale price was $30,000 more than the book value of the asset at the time of sale. The book value at the time of sale would be the original cost minus the total depreciation. Therefore, if we let $X$ be the original cost, the total depreciation over 5 years would be $\frac{X}{10} \times 5 = \frac{X}{2}$. The book value at the time of sale would then be $X - \frac{X}{2} = \frac{X}{2}$. Since the sale price ($200,000) was $30,000 more than the book value, we have $\frac{X}{2} + 30,000 = 200,000$. Solving for $X$ gives us the original cost of the asset as $340,000.

On January 1, 2019, Georgia Instruments Sold a Depreciable Asset