a new piece of equipment cost $18,000 with a residual value of $600 and an estimated useful life of five year. Assuming twice the straight-line rate, the book value at the end of year 2 busing the declining-balance method
7200
no. the result is 11,520
To calculate the book value of the equipment at the end of year 2 using the declining-balance method, we need to determine the depreciation rate per year.
The straight-line depreciation rate is calculated by dividing the cost of the equipment minus the residual value by the useful life.
Straight-line depreciation rate = (Cost - Residual value) / Useful life
= ($18,000 - $600) / 5
= $17,400 / 5
= $3,480 per year
Considering twice the straight-line rate for the declining-balance method, the depreciation rate will be twice the straight-line rate.
Depreciation rate per year = 2 * Straight-line depreciation rate
= 2 * $3,480
= $6,960 per year
Now, let's calculate the book value at the end of year 2.
Year 1 depreciation = Depreciation rate per year = $6,960
Year 2 depreciation = Depreciation rate per year = $6,960
Book value at the end of year 1 = Cost - Year 1 depreciation
= $18,000 - $6,960
= $11,040
Book value at the end of year 2 = Book value at the end of year 1 - Year 2 depreciation
= $11,040 - $6,960
= $4,080
Therefore, the book value at the end of year 2 using the declining-balance method is $4,080.
To calculate the book value at the end of year 2 using the declining-balance method, we need to understand how this method works.
The declining-balance method is a depreciation method where an accelerated rate is applied to the asset's book value. In this case, we are told that the rate is twice the straight-line rate.
First, we need to calculate the straight-line annual depreciation rate. It is calculated by subtracting the residual value from the cost of the equipment and then dividing it by the estimated useful life:
Straight-line annual depreciation rate = (Cost of equipment - Residual value) / Estimated useful life
= ($18,000 - $600) / 5
= $17,400 / 5
= $3,480
Now, to find the annual depreciation using the declining-balance method, we multiply the straight-line rate by the accelerated rate. In this case, the accelerated rate is twice the straight-line rate:
Accelerated rate = 2 * Straight-line rate
= 2 * $3,480
= $6,960
Now, we can calculate the depreciation for each year. Remember, with the declining-balance method, the depreciation for each year is calculated using the book value at the beginning of the year.
Year 1 depreciation = Book value at the beginning of Year 1 * Accelerated rate
= $18,000 * $6,960
= $2,072,800
Book value at the beginning of Year 1 = Cost of equipment - Accumulated depreciation
= $18,000 - $2,072,800 (since it's the first year, accumulated depreciation is zero)
= -$2,054,800
Note: In the declining-balance method, the book value at the end of each year is calculated by subtracting the accumulated depreciation for that year from the cost of the equipment.
Now, to find the book value at the end of Year 2, we need to calculate the depreciation and the book value at the beginning of Year 2.
Year 2 depreciation = Book value at the beginning of Year 2 * Accelerated rate
= -$2,054,800 * $6,960
= -$14,291,968
Book value at the beginning of Year 2 = Book value at the beginning of Year 1 - Accumulated depreciation for Year 1
= -$2,054,800 - $2,072,800
= -$4,127,600
Book value at the end of Year 2 = Book value at the beginning of Year 2 - Accumulated depreciation for Year 2
= -$4,127,600 - (-$14,291,968)
= -$4,127,600 + $14,291,968
= $10,164,368
Therefore, the book value at the end of year 2 using the declining-balance method is $10,164,368.