Answer:
Under the double-declining-balance method, the annual depreciation expense is calculated as a percentage of the book value of the asset at the beginning of the year, and the percentage is double the straight-line rate.
The straight-line rate is calculated as 1 / useful life, which in this case is 1/5 = 0.20 or 20%. Double that rate gives us the double-declining-balance rate of 2 x 20% = 40%.
So, for the first year, the depreciation expense would be:
Depreciation expense = Book value at beginning of year x Double-declining-balance rate
Depreciation expense = $93,000 x 40%
Depreciation expense = $37,200
The book value at the end of the first year would be:
Book value = Cost - Accumulated depreciation
Book value = $93,000 - $37,200
Book value = $55,800
For the second year, the depreciation expense would be:
Depreciation expense = Book value at beginning of year x Double-declining-balance rate
Depreciation expense = $55,800 x 40%
Depreciation expense = $22,320
The book value at the end of the second year would be:
Book value = Cost - Accumulated depreciation
Book value = $93,000 - $37,200 - $22,320
Book value = $33,480
The book value on December 31, 2024, would be the same as the book value at the end of the second year, which is $33,480.
Therefore, the depreciation for 2024 would be $37,200 and the book value on December 31, 2024, would be $33,480.