Math Problem Statement
A new piece of equipment costs $18,000 with a residual value of $600 and estimated useful life of 5 years. Assuming twice the straight line rate, the book value at the end of year 2 using the declining balance method would be?
Solution
To find the book value of the equipment at the end of year 2 using the double-declining balance method (DDB), we follow these steps:
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Identify key values:
- Initial cost: $18,000
- Residual value: $600
- Useful life: 5 years
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Calculate the straight-line depreciation rate: The straight-line rate is calculated as:
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Double the straight-line rate: Under the double-declining balance method, the rate is doubled:
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Apply depreciation for each year until the end of year 2:
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Year 1:
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Year 2:
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Therefore, the book value of the equipment at the end of year 2 is $6,480.
Would you like a further breakdown of these steps, or do you have any questions?
- How does the double-declining balance method differ from straight-line depreciation?
- Why does the declining balance method ignore the residual value in annual calculations?
- How would the depreciation schedule look for the remaining years in this problem?
- What would be the effect of a higher initial cost on book value under this method?
- How is the declining balance method useful in financial decision-making?
Tip: In the double-declining balance method, you stop depreciating once the book value reaches the residual value.
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Math Problem Analysis
Mathematical Concepts
Depreciation
Double-Declining Balance Method
Book Value Calculation
Formulas
Straight-line rate = 1 / Useful life
Double-declining rate = 2 * Straight-line rate
Depreciation expense (Year N) = Double-declining rate * Book value at start of Year N
Book value (Year N) = Book value at start of Year N - Depreciation expense (Year N)
Theorems
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Suitable Grade Level
Grades 10-12
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