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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)**.

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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.

How much depreciation should be recorded for the first year for a delivery truck with a cost of $30,000, an expected life of six years, and an estimated residual value of $6,000? Assume the double-declining-balance method is used.

Learn how to calculate the first-year depreciation for a $30,000 delivery truck using the double-declining-balance method. This problem considers an asset life of six years and a residual value of $6,000. Ideal for accounting and finance students.

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