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Answer :
Final answer:
The lathe's book value after 3 years of depreciation depends on the depreciation method used. If we use the straight-line method, the book value would be $71,000. If we use the sum-of-years-digits method, the book value would be $87,250. To calculate the gain/loss if the lathe is sold for $60,000 at the start of year 4, we need to compare the selling price with the book value after 3 years of depreciation.
Explanation:
To calculate the lathe's book value after 3 years of depreciation, we need to use each of the given depreciation methods:
- Straight Line Method: The straight-line method evenly distributes the depreciation expense over the useful life of the asset. Since the lathe has a useful life of 10 years, the annual depreciation expense is ($95,000 - $15,000) / 10 = $8,000. After 3 years, the accumulated depreciation is $8,000 * 3 = $24,000. The book value after 3 years is $95,000 - $24,000 = $71,000.
- SOYD Method: The sum-of-years-digits method allocates more depreciation in the early years and less in the later years. The sum of the digits for a 10-year useful life is 1 + 2 + 3 + ... + 10 = 55. In year 1, the depreciation expense is ($95,000 - $15,000) * (10/55) = $14,545. After 3 years, the accumulated depreciation is $14,545 * (1/10 + 1/9 + 1/8) = $14,545 * 0.533 = $7,750. The book value after 3 years is $95,000 - $7,750 = $87,250.
- 10-year MACRS Method: The 10-year MACRS method assigns a specific percentage of the asset's value to each year. The depreciation percentages for the 10-year MACRS method are provided by the tax regulations. After 3 years, the accumulated depreciation using the MACRS method can be calculated based on the assigned percentages for each year.
- 150% Declining Balance Method: The 150% declining balance method allows for accelerated depreciation, with a higher depreciation expense in the early years. The depreciation rate for the 150% declining balance method is 1.5 times the straight-line rate. After 3 years, the accumulated depreciation using the 150% declining balance method can be calculated based on the depreciation rate.
To calculate the gain/loss if the lathe is sold for $60,000 at the start of year 4, we need to compare the selling price with the book value after 3 years of depreciation. If the selling price is higher than the book value, there is a gain. If the selling price is lower than the book value, there is a loss.
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