## Step-by Solution ### 1. **Identify the Method** The Double-Declining Balance (DDB) method is an accelerated depreciation method. Formula for annual depreciation expense: \[ \text{Depreciation Expense} = \text{Book Value at Beginning of Year} \times \left(\frac{2}{\text{Useful Life}}\right) \] ### 2. **List the Given Data** - **Cost of asset:** $50,000 - **Useful life:** 5 years - **Salvage value:** $5,000 ### 3. **Calculate the DDB Rate** \[ \text{DDB Rate} = 2 \times \left(\frac{1}{\text{Useful Life}}\right) = 2 \times \left(\frac{1}{5}\right) = .4 \text{ or } 40\% \] ### 4. **Calculate Depreciation for Year 1** \[ \text{Depreciation Expense (Year 1)} = \text{Book Value at Beginning of Year 1} \times \text{DDB Rate} \] \[ = \$50,000 \times .4 = \$20,000 \] ### 5. **Final Answer** \[ \boxed{\$20,000} \] **The depreciation expense for the first year is $20,000.** --- **Note**: For the DDB method, the salvage value is not subtracted in the depreciation calculation each year, but the asset should not be depreciated below the salvage value over its useful life.