Final answer:
The depreciation expense for the first year using the straight-line method is $6,525, using the double-declining-balance method is $14,500, and using the activity-based method is $4,333.33.
Step-by-step explanation:
Depreciation expense for the first year can be calculated using different depreciation methods:
1. Straight-Line Method:
The annual depreciation expense is calculated by subtracting the residual value from the initial cost and dividing the result by the service life.
Depreciation expense = (Initial cost - Residual value) / Service life
Depreciation expense = ($29,000 - $2,900) / 4 = $6,525
2. Double-Declining-Balance Method:
The annual depreciation expense is calculated by multiplying the book value at the beginning of the year by twice the straight-line depreciation rate.
Depreciation expense = Book value at beginning of year * (2 / Service life)
Book value at beginning of year = Initial cost - Accumulated depreciation
Depreciation expense = ($29,000 - $0) * (2 / 4) = $14,500
3. Activity-Based Method:
The annual depreciation expense is calculated by multiplying the depreciation rate per hour by the number of hours of machine usage in the first year.
Depreciation expense = Depreciation rate per hour * Number of hours of machine usage in the first year
Depreciation expense = ($29,000 - $2,900) / 18,000 * 3,000 = $4,333.33
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