A light truck is purchased on January 1 at a cost of $27,000. It is expected to serve for eight years and have a salvage value of $3,000. Calculate the depreciation expense for the first and third years of the truck's life using the following methods. If required, round your answers to two decimal places.
Depreciation Expense
Year 1 Year 3
1. Straight-line $ $
2. Double-declining-balance $ $
3. Sum-of-the-years'-digits $ $
To calculate the depreciation expense using different methods, we need to understand the formulas for each depreciation method.
1. Straight-line depreciation:
The formula for straight-line depreciation is:
Depreciation Expense = (Cost - Salvage Value) / Useful Life
2. Double-declining-balance depreciation:
The formula for double-declining-balance depreciation is:
Depreciation Expense = Book Value * Depreciation Rate
The Depreciation Rate is calculated as:
Depreciation Rate = 2 / Useful Life
Book Value is calculated as:
Book Value = Cost - Accumulated Depreciation
3. Sum-of-the-years'-digits depreciation:
The formula for sum-of-the-years'-digits depreciation is:
Depreciation Expense = ((Cost - Salvage Value) / Sum of Years) * Remaining Useful Life
Sum of Years is calculated as:
Sum of Years = n * (n + 1) / 2
Where n is the useful life in years.
Let's calculate the depreciation expense for the first and third years using each method:
1. Straight-line depreciation:
Given:
Cost = $27,000
Salvage Value = $3,000
Useful Life = 8 years
Depreciation Expense (Year 1) = (27,000 - 3,000) / 8
Depreciation Expense (Year 3) = (27,000 - 3,000) / 8
2. Double-declining-balance depreciation:
Given:
Cost = $27,000
Salvage Value = $3,000
Useful Life = 8 years
Depreciation Rate = 2 / 8
Depreciation Expense (Year 1) = Book Value * Depreciation Rate
Book Value (Year 1) = Cost - Accumulated Depreciation (Year 0)
Depreciation Expense (Year 3) = Book Value * Depreciation Rate
Book Value (Year 3) = Cost - Accumulated Depreciation (Year 2)
3. Sum-of-the-years'-digits depreciation:
Given:
Cost = $27,000
Salvage Value = $3,000
Useful Life = 8 years
Sum of Years = 8 * (8 + 1) / 2
Depreciation Expense (Year 1) = ((27,000 - 3,000) / Sum of Years) * Remaining Useful Life
Remaining Useful Life (Year 1) = 8 - 1
Depreciation Expense (Year 3) = ((27,000 - 3,000) / Sum of Years) * Remaining Useful Life
Remaining Useful Life (Year 3) = 8 - 3
By using these formulas, you can calculate the depreciation expense for the first and third years of the truck's life using different methods.