Math Problem Statement
On April 22, 2023, Sandhill Enterprises purchased equipment for $138,700. The company expects to use the equipment for 11,500 working hours during its four-year life and that it will have a residual value of $14,500. Sandhill has a December 31 year end and prorates depreciation to the nearest month. The actual machine usage was: 1,500 hours in 2023; 3,000 hours in 2024; 3,600 hours in
2025; 2,600 hours in 2026; and 1,000 hours in 2027.
(a1)
Prepare a depreciation schedule for the life of the asset under the straight-line method. (Round partial-period depreciation rate to 4 decimal palces, e.g. 15.2563% and other answers to 0 decimal places, e.g. 5,276.)
Solution
To prepare a depreciation schedule using the straight-line method, we'll follow these steps:
Step 1: Calculate Straight-Line Depreciation
The straight-line depreciation formula is:
Where:
- Cost of Asset = $138,700
- Residual Value = $14,500
- Useful Life = 4 years
So,
Step 2: Prorate Depreciation for 2023 (Partial Year)
Since the equipment was purchased on April 22, 2023, the depreciation for 2023 is prorated. From April 22 to December 31 is 8 months. Therefore, the prorated depreciation for 2023 is calculated as:
Step 3: Prepare the Depreciation Schedule
Now, we can prepare the depreciation schedule for the four-year life of the equipment:
Year | Depreciation Expense | Accumulated Depreciation | Book Value at Year-End |
---|---|---|---|
2023 | 20,700 | 20,700 | 118,000 |
2024 | 31,050 | 51,750 | 86,950 |
2025 | 31,050 | 82,800 | 55,900 |
2026 | 31,050 | 113,850 | 24,850 |
2027 | 10,350 (Remaining) | 124,200 | 14,500 (Residual Value) |
Explanation:
- 2023 Depreciation: $20,700 is calculated based on 8/12 of the annual depreciation.
- 2024-2026 Depreciation: Full-year depreciation of $31,050 for each year.
- 2027 Depreciation: Since we stop depreciating when the book value reaches the residual value of $14,500, only $10,350 is needed to reach the residual value.
Would you like further clarifications on any steps or additional details?
Related Questions:
- How is the straight-line method different from the units-of-production method?
- What would the depreciation schedule look like if the equipment was purchased in January 2023?
- How does the residual value impact the depreciation expense?
- How would the depreciation schedule change if the useful life was extended to 5 years?
- What are the advantages of using the straight-line method over other methods?
Tip:
When calculating depreciation, always consider whether the asset is used for a full year or part of the year. Prorating for partial periods is a key step in accurate financial reporting.
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Math Problem Analysis
Mathematical Concepts
Depreciation
Straight-Line Method
Prorated Depreciation
Formulas
Depreciation Expense per Year = (Cost of Asset - Residual Value) / Useful Life
Prorated Depreciation = Annual Depreciation * (Months of Usage / 12)
Theorems
Straight-Line Depreciation
Suitable Grade Level
College-Level Accounting or Finance
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