Calculate depreciation expense for years 2022 to 2027 for the machine using the straight-line method. Please round to 2 decimals. If no depreciation is required in a year please no... Calculate depreciation expense for years 2022 to 2027 for the machine using the straight-line method. Please round to 2 decimals. If no depreciation is required in a year please note a zero (0). Then calculate depreciation expense for years 2022 to 2027 using the double diminishing-balance method and finally using the units-of-production method. Read more

Steps to Solve

1. Calculate Straight-Line Depreciation

First, determine the annual depreciation expense using the straight-line method. The formula is:

$$ \text{Annual Depreciation} = \frac{\text{Cost} - \text{Residual Value}}{\text{Useful Life}} $$

For this problem:

• Cost = $580,000
• Residual Value = $158,000
• Useful Life = 5 years

So,

$$ \text{Annual Depreciation} = \frac{580,000 - 158,000}{5} = \frac{422,000}{5} = 84,400 $$

Each year from 2022 to 2027 will have a depreciation expense of $84,400.

2. Calculate Double Diminishing Balance Depreciation

For the double diminishing balance method, the depreciation rate is twice the straight-line rate. First, find the straight-line rate:

$$ \text{Straight-Line Rate} = \frac{1}{\text{Useful Life}} = \frac{1}{5} = 0.20 $$

Thus, the double declining rate is:

$$ \text{Double Declining Rate} = 0.20 \times 2 = 0.40 $$

Calculate depreciation for each year:

• Year 2022:

  • Depreciation = $580,000 \times 0.40 = $232,000
  • Book Value = $580,000 - $232,000 = $348,000

• Year 2023:

  • Depreciation = $348,000 \times 0.40 = $139,200
  • Book Value = $348,000 - $139,200 = $208,800

• Year 2024:

  • Depreciation = $208,800 \times 0.40 = $83,520
  • Book Value = $208,800 - $83,520 = $125,280

• Year 2025:

  • Depreciation = $125,280 \times 0.40 = $50,112
  • Book Value = $125,280 - $50,112 = $75,168

• Year 2026:

  • Depreciation = $75,168 \times 0.40 = $30,067.20
  • Book Value = $75,168 - $30,067.20 = $45,100.80

• Year 2027:

  • Depreciation = $45,100.80 \times 0.40 = $18,040.32

Round to two decimals for final totals.

3. Calculate Units-of-Production Depreciation

Using the units-of-production method, calculate the depreciation based on actual usage. The total depreciation per hour can be calculated as:

$$ \text{Depreciation per Hour} = \frac{\text{Cost} - \text{Residual Value}}{\text{Total Useful Hours}} $$

Total hours = 75,000 hours over 5 years, resulting in:

$$ \text{Depreciation per Hour} = \frac{580,000 - 158,000}{75,000} = \frac{422,000}{75,000} \approx 5.62667 $$

Using the hours for each respective year from the problem statement, multiply the depreciation per hour by the hours used.

For 2022 to 2027, the calculations will be:

• 2022: $5.62667 \times 2205 \approx 12,417.68
• 2023: $5.62667 \times 2340 \approx 13,188.13
• 2024: $5.62667 \times 3375 \approx 18,383.46
• 2025: $5.62667 \times 3750 \approx 21,600.47
• 2026: $5.62667 \times 4200 \approx 23,603.65
• 2027: $5.62667 \times 2800 \approx 15,761.67

4. Summarizing the Depreciation Expenses

Organize the calculated depreciation expenses by method and year into a table format for clarity.