Archie Co. purchased a framing machine for $45,000 on January 1, 2021. 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 2021 and book value at December 31, 2021, would be:

depreciation for 2021 is $ 18,000

book value at December 31, 2021 is $ 27,000

Explanation:

Sum of Digits Method is a depreciation method that provides for higher depreciation to be charged early in the life of an asset with a lower depreciation in later years.

Sum of digits for the  framing machine is calculated as follows :

Year                                           Sum of Digits

1                                                          4

2                                                         3

3                                                         2

4                                                          1

Total                                                   10

Depreciation for 2021 is calculated as :

= 4/10× $ 45,000

= 18,000

Book value at December 31, 2021 is calculated as :

=Cost - Accumulated Depreciation

=$45,000 - $ 18,000

=$ 27,000

$16,000.

Book value : $29,000

Explanation:

Sum of the digit depreciation method is a depreciation based on the assumption that the production capacity of an asset decreases with age.On this note , a higher depreciation is charged to the early years and the latter years carry lower charges

Workings

Useful life : 4 years

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

Depreciable cost = (original cost -salvage value)

Depreciation for the first year = $(45000-5000 )*4/10 = $16,000

Book value at the year ending = $45000-$16,000 =$29,000

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