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 4-5,000 units; 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 method, we need to follow these steps:<br /><br />1. Determine the straight-line depreciation rate.<br />2. Double the straight-line rate to get the double-declining rate.<br />3. Apply the double-declining rate to the book value of the asset at the beginning of the year.<br /><br />### Step 1: Calculate the Straight-Line Depreciation Rate<br />The straight-line depreciation rate is calculated as:<br />\[ \text{Straight-Line Rate} = \frac{1}{\text{Useful Life}} \]<br /><br />Given that the useful life is 8 years:<br />\[ \text{Straight-Line Rate} = \frac{1}{8} = 0.125 \text{ or } 12.5\% \]<br /><br />### Step 2: Calculate the Double-Declining Rate<br />The double-declining rate is twice the straight-line rate:<br />\[ \text{Double-Declining Rate} = 2 \times 0.125 = 0.25 \text{ or } 25\% \]<br /><br />### Step 3: Apply the Double-Declining Rate to the Book Value<br />The initial book value of the equipment is \( \$180,000 \).<br /><br />Depreciation expense for the first year:<br />\[ \text{Depreciation Expense} = \text{Book Value} \times \text{Double-Declining Rate} \]<br />\[ \text{Depreciation Expense} = \$180,000 \times 0.25 = \$45,000 \]<br /><br />Therefore, the depreciation expense for the first year using the double-declining-balance method is \( \$45,000 \).<br /><br />The correct answer is:<br />\[ \$45,000 \]