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XYZ Ltd. purchased a piece of machinery on January 1, 2023, for $50,000. The com...

Feb 25, 2025

XYZ Ltd. purchased a piece of machinery on January 1, 2023, for

50,000. The company estimates the machine's useful life to be 5 years with a salvage value of

5,000 at the end of its life. Calculate the annual depreciation expense using the straight-line method. If the company uses the double-declining balance method, calculate the depreciation expense for the first two years.

Solution by Steps

step 1

To calculate the annual depreciation expense using the straight-line method, we use the formula:

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

step 2

Substituting the values:

\text{Annual Depreciation} = \frac{50000 - 5000}{5} = \frac{45000}{5} = 9000

step 3

For the double-declining balance method, the formula for depreciation expense in the first year is:

\text{Depreciation Expense} = \text{Book Value} \times \left(\frac{2}{\text{Useful Life}}\right)

step 4

In the first year, the book value is

50000

, so:

\text{Depreciation Expense Year 1} = 50000 \times \left(\frac{2}{5}\right) = 20000

step 5

The book value at the end of Year 1 is:

50000 - 20000 = 30000

step 6

For the second year, the depreciation expense is:

\text{Depreciation Expense Year 2} = 30000 \times \left(\frac{2}{5}\right) = 12000

Answer

Annual Depreciation:

9000

, Year 1 Depreciation:

20000

, Year 2 Depreciation:

12000

Key Concept

Depreciation methods: straight-line vs. double-declining balance

Explanation

The straight-line method spreads the cost evenly over the useful life, while the double-declining balance method accelerates depreciation, resulting in higher expenses in the earlier years.