Math Problem Statement

On October 1, 2022, Sandhill Manufacturing Company purchased a piece of high-tech equipment for $90,100 cash. Sandhill estimated the equipment would have a 7-year useful life and a residual value of $8,900. The company uses straight-line depreciation and has a September 30 fiscal year endo

On October 1, 2024, Sandhill paid $15,200 cash to upgrade the equipment. It is expected that the upgrade will significantly reduce the operating costs of the equipment. Sandhill also reviewed the equipment's expected useful life and estimated that, due to changing technology, the equipment's total expected useful life will be 6 years and its residual value will be $4,900.

(a)

Calculate the annual depreciation expense for the first two years of the equipment's life.

Annual depreciation expense

$

per year

Solution

To calculate the annual depreciation expense for the first two years, we will use the straight-line depreciation method.

Formula:

Depreciation Expense=Cost of EquipmentResidual ValueUseful Life\text{Depreciation Expense} = \frac{\text{Cost of Equipment} - \text{Residual Value}}{\text{Useful Life}}

Step 1: Identify the values for the initial two-year depreciation calculation.

  • Cost of Equipment = $90,100
  • Residual Value = $8,900
  • Useful Life = 7 years

Step 2: Plug in the values into the depreciation formula.

Depreciation Expense=90,1008,9007=81,2007\text{Depreciation Expense} = \frac{90,100 - 8,900}{7} = \frac{81,200}{7}

Step 3: Calculate.

Depreciation Expense=11,600per year\text{Depreciation Expense} = 11,600 \, \text{per year}

Thus, the annual depreciation expense for the first two years is $11,600 per year.

Would you like me to go over the next parts of the problem or explain more details?


Here are 5 questions that expand the information:

  1. How is straight-line depreciation different from other methods like double declining balance?
  2. What happens if the residual value is higher than the expected in future?
  3. How does the fiscal year impact depreciation calculations?
  4. How would you calculate depreciation if the equipment was sold halfway through the year?
  5. What would happen if the equipment was upgraded earlier than expected?

Tip: Always check for changes in useful life or residual value when upgrades occur to adjust depreciation correctly.

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Math Problem Analysis

Mathematical Concepts

Depreciation
Straight-line depreciation method
Asset valuation

Formulas

Depreciation Expense = (Cost of Equipment - Residual Value) / Useful Life

Theorems

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Suitable Grade Level

Grades 11-12 or College-level accounting