To solve this depreciation problem using the double-declining-balance (DDB) method, let's follow these steps:

Problem Analysis

1. Cost of Asset (Initial Value): $30,000
2. Useful Life: 6 years
3. Residual Value: $6,000 (although DDB does not consider this directly in each year's calculation, the asset value shouldn't go below this residual value).
4. Depreciation Method: Double-declining-balance method.

Step-by-Step Solution

The double-declining-balance method calculates depreciation at twice the rate of the straight-line method.

Step 1: Calculate the Straight-Line Depreciation Rate

$\text{Straight-Line Depreciation Rate} = \frac{1}{\text{Useful Life}} = \frac{1}{6} = 16.67\%$

Step 2: Double the Straight-Line Rate for the Double-Declining Rate

$\text{Double-Declining Rate} = 2 \times 16.67\% = 33.33\%$

Step 3: Calculate the First Year Depreciation Expense

The DDB method applies the depreciation rate to the book value at the beginning of each year.

For the first year: $\text{Depreciation Expense} = \text{Double-Declining Rate} \times \text{Beginning Book Value}$ $= 33.33\% \times 30,000 = 0.3333 \times 30,000 = 10,000$

Answer

The first-year depreciation expense is $10,000, which corresponds to option (b).

Would you like further details on any step? Here are some related questions for further exploration:

1. How does the residual value impact later years of depreciation in the double-declining method?
2. How would the depreciation expense change if we used the straight-line method instead?
3. What would the depreciation expense be in the second year using the double-declining-balance method?
4. Why is the double-declining-balance method considered an accelerated depreciation method?
5. How does the double-declining-balance method affect a company's financial statements differently than the straight-line method?

Tip: The double-declining-balance method results in higher depreciation in the earlier years of an asset’s life, making it useful for assets that lose value quickly or become obsolete fast.