To solve this depreciation problem, we need to calculate the depreciation expense under the double-declining balance (DDB) method for 2022 and 2023. Let’s break it down step by step:

1. Determine the Double-Declining Rate

• Straight-line depreciation rate for a 5-year life is: $\text{Straight-line rate} = \frac{1}{5} = 20\%$
• Double the straight-line rate: $\text{DDB Rate} = 20\% \times 2 = 40\%$

2. Depreciation for 2022

• The asset was purchased on October 1, 2022, so it is in use for only 3 months in 2022 (October, November, December).
• Depreciation is calculated on the book value, which is initially the cost of the machine: $\text{Depreciation} = \text{Book Value} \times \text{DDB Rate} \times \frac{\text{Months Used}}{12}$ Substituting values: $\text{Depreciation (2022)} = 118,000 \times 40\% \times \frac{3}{12} = 118,000 \times 0.4 \times 0.25 = 11,800$

3. Book Value at End of 2022

• New book value after 2022 depreciation: $\text{Book Value (2023)} = 118,000 - 11,800 = 106,200$

4. Depreciation for 2023

• Now we compute depreciation for the full year (12 months) using the updated book value: $\text{Depreciation (2023)} = \text{Book Value (2023)} \times \text{DDB Rate}$ Substituting values: $\text{Depreciation (2023)} = 106,200 \times 40\% = 42,480$

Final Depreciation Expenses:

• 2022 Depreciation: $11,800
• 2023 Depreciation: $42,480

Let me know if you want further clarification or more details!

Related Questions:

1. How does the double-declining balance method differ from the straight-line method?
2. How is depreciation affected if the salvage value changes?
3. What happens if the useful life is extended or shortened?
4. How can you ensure compliance with accounting standards for depreciation?
5. Why is salvage value excluded from the DDB calculation?

Tip: Always ensure to prorate depreciation when an asset is used for less than a full year!