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.)
Depreciable
Amount
x
Depr.
Rate
Year
2023
2024
Depr.
Expense
Accum. [ Year
Depr.
Expense
Accum. Depr.
Carrying
Amount
Solution
To prepare a depreciation schedule for the life of the asset under the straight-line method, we need to follow these steps:
Step 1: Determine Depreciable Amount
- Cost of the equipment: $138,700
- Residual value: $14,500
- Depreciable amount:
Step 2: Calculate the Straight-Line Depreciation Rate
- Useful life: 4 years (as given)
The depreciation rate per year is calculated as:
However, since the equipment was purchased on April 22, 2023, the depreciation for 2023 will be prorated based on the months used.
- From April 22, 2023 to December 31, 2023, the equipment is used for 8 months. The partial depreciation for 2023 will be:
Step 3: Prepare the Depreciation Schedule
Year | Depreciation Expense | Accumulated Depreciation | Carrying Amount |
---|---|---|---|
2023 | 20,700 | 20,700 | |
2024 | 31,050 | 20,700 + 31,050 = 51,750 | |
2025 | 31,050 | 51,750 + 31,050 = 82,800 | |
2026 | 31,050 | 82,800 + 31,050 = 113,850 | |
2027 | 10,350 (final year) | 113,850 + 10,350 = 124,200 | (Residual Value) |
Summary:
- Depreciable amount: $124,200
- Annual depreciation rate: $31,050 (except prorated for 2023 and 2027)
- The carrying amount at the end of the asset's life will be the residual value of $14,500.
Would you like further details on any part of this calculation?
Here are 5 questions to deepen understanding:
- How is depreciation prorated when an asset is purchased mid-year?
- What are the differences between straight-line and usage-based depreciation?
- How would salvage value affect depreciation in other methods?
- Why does the accumulated depreciation increase each year?
- What happens to depreciation after the asset reaches its residual value?
Tip: Always check the purchase date of an asset to accurately calculate the depreciation for the first and last years!
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Math Problem Analysis
Mathematical Concepts
Depreciation
Straight-Line Depreciation
Asset Valuation
Formulas
Depreciable Amount = Cost of Asset - Residual Value
Annual Depreciation = Depreciable Amount / Useful Life
Prorated Depreciation = Annual Depreciation × (Months Used / 12)
Theorems
-
Suitable Grade Level
Grades 11-12 / College
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