On January 1, 2019, Chace Instruments sold a depreciable asset for cash of $400,000 and recognized a gain of $60,000. 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?
A) $660,000
B) $800,000
C) $680,000
D) $920,000

Question

Quizplus · Accepted Answer

The original cost of the asset can be calculated by first determining the book value at the time of sale and then adding back the accumulated depreciation. The gain of $60,000 indicates that the sale price was $60,000 more than the book value. Since the asset was sold for $400,000, its book value at the time of sale was $400,000 - $60,000 = $340,000. The asset was used for 5 years (from 2014 to 2019), and it had a useful life of 10 years with no salvage value, meaning it depreciated evenly over its useful life. Therefore, the total depreciation over 5 years is the difference between the original cost and the book value at the time of sale. To find the original cost, we add the book value after 5 years to the total depreciation over those 5 years. The annual depreciation is ($400,000 - $340,000) / 5 = $12,000, but this calculation is incorrect because it mistakenly uses the sale price and book value to calculate annual depreciation, which is not how depreciation is calculated. Instead, we should recognize that the asset depreciated over its useful life, so the total depreciation over 5 years would be half of the original cost since it was halfway through its useful life. Given the book value of $340,000 at the time of sale, and knowing this represents 50% of the original cost (since half of the asset's useful life had elapsed and it was being depreciated straight-line with no salvage value), we can infer the original cost was twice the book value at sale, or $340,000 * 2 = $680,000.

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