A truck costs $35,000 with a residual value of $2,000. Its service life is five years. Using the declining-balance method at twice the straight-line rate, the book value at the end of 2 years is?
The declining-balance method is a method to calculate the depreciation of an item. For this problem, we are prompted to use this method at twice the straight-line rate.
We are presented with the following variables:1. Truck Cost = $35,0002. Residual Value = $2,0003. Service Life = 5 years.
We will be using the following formula:Year 1: (Truck Cost) ÷ (Service Life in years) = xx * 2 = Depreciation for Year 1
As the residual value is the value of the item after the service life, we will not be using this variable.$55,000 ÷ 5 = $7,000$7,000 * 2 = $14,000
$14,000.00 is the depreciation for Year 1.$35,000 - $14,000 = $21,000. At the end of the first year, the book value of the truck is $21,000.
For Year 2, we will apply the same formula to the book value of the truck by the end of Year 1.$21,000 ÷ 5 = ( $4,200 * 2) = $8,400 $21,000 - $8,400 = $12,600. At the end of the second year the book value is $12,600.
The correct answer is $12,600.
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To calculate the book value at the end of 2 years using the declining-balance method at twice the straight-line rate, we need to determine the annual depreciation rate.
The straight-line depreciation rate is calculated by dividing the difference between the initial cost and the residual value by the service life:
Straight-line depreciation rate = (Initial cost - Residual value) / Service life
Straight-line depreciation rate = ($35,000 - $2,000) / 5 years
Straight-line depreciation rate = $33,000 / 5 years
Straight-line depreciation rate = $6,600 per year
Twice the straight-line rate would be $6,600 x 2 = $13,200 per year.
To find the book value at the end of 2 years, we subtract the accumulated depreciation from the initial cost.
Accumulated depreciation after 2 years = Depreciation rate x Number of years = $13,200 x 2 = $26,400
Book value at the end of 2 years = Initial cost - Accumulated depreciation after 2 years = $35,000 - $26,400 = $8,600
Therefore, the book value at the end of 2 years using the declining-balance method at twice the straight-line rate is $8,600.
To find the book value of the truck at the end of 2 years using the declining-balance method at twice the straight-line rate, we need to follow these steps:
Step 1: Calculate the straight-line depreciation rate.
The straight-line depreciation rate is determined by dividing the cost of the truck by its service life. In this case, the truck costs $35,000 and has a service life of 5 years.
Straight-line depreciation rate = Cost / Service life
= $35,000 / 5
= $7,000
Step 2: Calculate the double-declining-balance rate.
The double-declining-balance rate is twice the straight-line depreciation rate.
Double-declining-balance rate = 2 * Straight-line depreciation rate
= 2 * $7,000
= $14,000
Step 3: Calculate the depreciation expense for the first year.
To calculate the depreciation expense for the first year using the double-declining-balance method, multiply the double-declining-balance rate by the truck's book value at the beginning of the year.
Depreciation expense for the first year = Double-declining-balance rate * Book value at the beginning of the year
At the beginning of year one, the book value is the cost of the truck, which is $35,000.
Depreciation expense for the first year = $14,000 * $35,000
= $490,000
Step 4: Calculate the book value at the end of the first year.
To calculate the book value at the end of the first year, subtract the depreciation expense for the year from the cost of the truck.
Book value at the end of the first year = Cost - Depreciation expense for the first year
= $35,000 - $14,000
= $21,000
Step 5: Calculate the depreciation expense for the second year.
To calculate the depreciation expense for the second year, multiply the double-declining-balance rate by the book value at the beginning of the year.
Depreciation expense for the second year = Double-declining-balance rate * Book value at the beginning of the year
At the beginning of year two, the book value is $21,000.
Depreciation expense for the second year = $14,000 * $21,000
= $294,000
Step 6: Calculate the book value at the end of the second year.
To calculate the book value at the end of the second year, subtract the depreciation expense for the second year from the book value at the beginning of the year.
Book value at the end of the second year = Book value at the beginning of the year - Depreciation expense for the second year
= $21,000 - $294,000
= -$273,000
The book value at the end of the second year is -$273,000. However, it is not realistic to have a negative book value, so we assume it is zero.
Therefore, the book value at the end of 2 years using the declining-balance method at twice the straight-line rate is $0.