Fields Company purchased equipment on January 1 for 180,000 This system has a useful life of 8 years and a salvage value of 20,000 The company estimates that the equipment will produce 40,000 units over its 8-year useful life Actual units produced are: Year 1 - 4,000 units; Year 2-6,000 units; Year 3 - 8 ,000 units; Year 4-5,000units Year 5 - 4,000 units Year 6 - 5,000 units; Year 7 - 7,000 units; . Year 8 - 3 ,000 units. What would be the depreciation expense for the first year of its useful life using the double-declining-balance method? 20,000 16,000 24,000 33,750 45,000

To calculate the depreciation expense for the first year using the double-declining-balance (DDB) method, we need to follow these steps:<br /><br />1. **Determine the straight-line depreciation rate**: <br /> The straight-line depreciation rate is calculated as \( \frac{1}{\text{useful life}} \). <br /> For this equipment, the useful life is 8 years, so the straight-line rate is \( \frac{1}{8} = 0.125 \) or 12.5%.<br /><br />2. **Double the straight-line rate**: <br /> The DDB method requires doubling the straight-line rate. <br /> So, the DDB rate is \( 0.125 \times 2 = 0.25 \) or 25%.<br /><br />3. **Calculate the first year's depreciation expense**: <br /> The initial book value of the equipment is its purchase price, which is \$180,000. <br /> The first year's depreciation expense is calculated by multiplying the book value by the DDB rate: <br /> \[<br /> \text{Depreciation Expense} = \text{Book Value} \times \text{DDB Rate} = \$180,000 \times 0.25 = \$45,000<br /> \]<br /><br />Therefore, the depreciation expense for the first year using the double-declining-balance method is \(\$45,000\).