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To solve this problem, let's go through the double-declining-balance (DDB) depreciation method. 

### Given Data:
1. **Cost of Machine:** $86,800
2. **Salvage Value:** $6,000
3. **Useful Life:** 20 years

### Steps to Calculate Second-Year Depreciation:

1. **Determine the Depreciable Base:**
   - Depreciable Base = Cost - Salvage Value = $86,800 - $6,000 = $80,800

2. **Calculate the Double-Declining Rate:**
   - Straight-line depreciation rate = 1 / Useful Life = 1 / 20 = 5%
   - Double-declining rate = 2 * Straight-line rate = 2 * 5% = 10%

3. **Calculate First-Year Depreciation Expense:**
   - First-year depreciation = Depreciable Base * Double-declining rate
   - First-year depreciation = $80,800 * 10% = $8,080
   - Accumulated depreciation after Year 1 = $8,080

4. **Calculate the Second-Year Depreciation Expense:**
   - Beginning Book Value for Year 2 = Cost - Accumulated Depreciation after Year 1
   - Beginning Book Value for Year 2 = $86,800 - $8,080 = $78,720
   - Second-year depreciation = Beginning Book Value for Year 2 * Double-declining rate
   - Second-year depreciation = $78,720 * 10% = $7,872

### Answer:
The **second-year depreciation** expense using the double-declining balance method is **$7,872**.

Would you like more details on any of these steps or have any questions?

### Related Questions
1. How would the calculation differ if we used the straight-line depreciation method?
2. What would be the third-year depreciation using the double-declining balance method?
3. How is the book value affected after each year of depreciation?
4. How does changing the salvage value affect the annual depreciation expense?
5. What is the difference between units of production and time-based depreciation methods?

### Tip
Remember, with the double-declining method, the depreciation expense decreases each year as the book value declines.

Determine the machine’s second-year depreciation using the double-declining-balance method.

Learn how to calculate the second-year depreciation for Ramirez Company's machine using the double-declining-balance method. This solution walks through key accounting concepts like the depreciable base, double-declining rate, and annual depreciation expense calculations. Useful for college-level accounting students.

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