Calculate depreciation expense for years 2022 to 2027 for the machine using the straight-line and double diminishing-balance methods.

Steps to Solve

1. Calculate the Annual Depreciation using Straight-Line Method

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

[ \text{Annual Depreciation Expense} = \frac{\text{Cost} - \text{Residual Value}}{\text{Useful Life}} ]

Given:

• Cost = $180,000
• Residual Value = $18,000
• Useful Life = 5 years

Calculate:

[ \text{Annual Depreciation Expense} = \frac{180,000 - 18,000}{5} = \frac{162,000}{5} = 32,400 ]

2. Record Depreciation Expense for Each Year (Straight-Line)

Since the straight-line method allocates a constant depreciation expense each year, fill in the table with the calculated annual depreciation for all years from 2022 to 2027.

3. Calculate Annual Depreciation using Double Diminishing-Balance Method

For the double declining balance method, calculate the rate and apply it to the remaining balance each year:

[ \text{Depreciation Rate} = \frac{1}{\text{Useful Life}} \times 2 = \frac{1}{5} \times 2 = 40% ]

Apply this rate to the remaining book value each year.

4. Record Depreciation Expense for Each Year (Double Diminishing-Balance)

• Year 2022: [ \text{Depreciation } = 180,000 \times 0.40 = 72,000 ] Remaining Book Value = $180,000 - $72,000 = $108,000

• Year 2023: [ \text{Depreciation } = 108,000 \times 0.40 = 43,200 ] Remaining Book Value = $108,000 - $43,200 = $64,800

• Year 2024: [ \text{Depreciation } = 64,800 \times 0.40 = 25,920 ] Remaining Book Value = $64,800 - $25,920 = $38,880

• Year 2025: [ \text{Depreciation } = 38,880 \times 0.40 = 15,552 ] Remaining Book Value = $38,880 - $15,552 = $23,328

• Year 2026: [ \text{Depreciation } = 23,328 \times 0.40 = 9,331.20 ] Remaining Book Value = $23,328 - $9,331.20 = $13,996.80

• Year 2027: [ \text{Depreciation } = 13,996.80 \times 0.40 = 5,598.72 ] Remaining Book Value = $13,996.80 - $5,598.72 = $8,398.08 (or residual value if it reaches)