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:

Depreciation Expense per Year=Cost of AssetResidual ValueUseful Life (in years)\text{Depreciation Expense per Year} = \frac{\text{Cost of Asset} - \text{Residual Value}}{\text{Useful Life (in years)}}

Where:

  • Cost of Asset = $138,700
  • Residual Value = $14,500
  • Useful Life = 4 years

So,

Depreciation Expense per Year=138,70014,5004=124,2004=31,050\text{Depreciation Expense per Year} = \frac{138,700 - 14,500}{4} = \frac{124,200}{4} = 31,050

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:

Depreciation for 2023=31,050×812=31,050×0.6667=20,700\text{Depreciation for 2023} = 31,050 \times \frac{8}{12} = 31,050 \times 0.6667 = 20,700

Step 3: Prepare the Depreciation Schedule

Now, we can prepare the depreciation schedule for the four-year life of the equipment:

YearDepreciation ExpenseAccumulated DepreciationBook Value at Year-End
202320,70020,700118,000
202431,05051,75086,950
202531,05082,80055,900
202631,050113,85024,850
202710,350 (Remaining)124,20014,500 (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:

  1. How is the straight-line method different from the units-of-production method?
  2. What would the depreciation schedule look like if the equipment was purchased in January 2023?
  3. How does the residual value impact the depreciation expense?
  4. How would the depreciation schedule change if the useful life was extended to 5 years?
  5. 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