Archie Co. purchased a framing machine for $45,000 on January 1, 2018. The machine is expected to have a four-year life, with a residual value of $5,000 at the end of four years. Using the sum-of-the-years-digits method, depreciation for 2018 and book value at December 31, 2018, would be:. A) $18,000 and $27.000.
B) $16,000 and $29,000.
C) $16,000 and $24,000
D) $18,000 and $22,000

Option B is the correct answer.

Explanation:

Depreciation is the systematic allocation of the cost of the asset over its estimated useful life. The sum of the years digit method of depreciation is an accelerated method to calculate the depreciation expense on an asset. This means that a higher depreciation expense is charged in the initial years of the asset's life and a lower depreciation expense is charged in the later years.

The formula for the depreciation expense per year under the sum of the digits method is attached.

Depreciable cost = Cost - residual value

Depreciable cost = 45000 - 5000

Depreciable cost = $40000

Sum of the years' digit = 1+2+3+4 = 10

Depreciation expense (2018) = 4 / 10 * 40000

Depreciation expense (2018) = $16000

Book value of the asset = Cost - Accumulated depreciation

Book value of the asset = 45000 - 16000

Book value of the asset = $29000

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