On January 1, a machine with a useful life of five years and a residual value of $29900 was purchased for $91000. What is the depreciation expense for year 2 under the double-declining- balance method of depreciation? O $29200 O $36400 O $21840 O $17680

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### Depreciation Calculation Exercise

**Question:**
On January 1, a machine with a useful life of five years and a residual value of $29,900 was purchased for $91,000. What is the depreciation expense for year 2 under the double-declining-balance method of depreciation?

**Options:**
- $29,200
- $36,400
- $21,840
- $17,680

**Explanation:**
The double-declining-balance (DDB) method is an accelerated depreciation method. It doubles the regular depreciation rate, applies it to the diminishing book value, and ignores the residual value until the book value of the asset drops to the residual value.

Here’s how you can calculate the depreciation expense step-by-step:

1. **Determine the straight-line depreciation rate:**
   \[
   \text{Straight-line depreciation rate} = \frac{1}{\text{Useful life}} = \frac{1}{5} = 20\%
   \]

2. **Double the straight-line rate to get the double-declining rate:**
   \[
   \text{Double-declining rate} = 2 \times 20\% = 40\%
   \]

3. **Calculate Year 1 depreciation:**
   \[
   \text{Year 1 Depreciation Expense} = \text{Initial Book Value} \times \text{Double-declining rate} = \$91,000 \times 40\% = \$36,400
   \]
   \[
   \text{Book Value at the end of Year 1} = \$91,000 - \$36,400 = \$54,600
   \]

4. **Calculate Year 2 depreciation:**
   \[
   \text{Year 2 Depreciation Expense} = \text{Book Value at the end of Year 1} \times \text{Double-declining rate} = \$54,600 \times 40\% = \$21,840
   \]

So, the correct answer is **$21,840**.
Transcribed Image Text:### Depreciation Calculation Exercise **Question:** On January 1, a machine with a useful life of five years and a residual value of $29,900 was purchased for $91,000. What is the depreciation expense for year 2 under the double-declining-balance method of depreciation? **Options:** - $29,200 - $36,400 - $21,840 - $17,680 **Explanation:** The double-declining-balance (DDB) method is an accelerated depreciation method. It doubles the regular depreciation rate, applies it to the diminishing book value, and ignores the residual value until the book value of the asset drops to the residual value. Here’s how you can calculate the depreciation expense step-by-step: 1. **Determine the straight-line depreciation rate:** \[ \text{Straight-line depreciation rate} = \frac{1}{\text{Useful life}} = \frac{1}{5} = 20\% \] 2. **Double the straight-line rate to get the double-declining rate:** \[ \text{Double-declining rate} = 2 \times 20\% = 40\% \] 3. **Calculate Year 1 depreciation:** \[ \text{Year 1 Depreciation Expense} = \text{Initial Book Value} \times \text{Double-declining rate} = \$91,000 \times 40\% = \$36,400 \] \[ \text{Book Value at the end of Year 1} = \$91,000 - \$36,400 = \$54,600 \] 4. **Calculate Year 2 depreciation:** \[ \text{Year 2 Depreciation Expense} = \text{Book Value at the end of Year 1} \times \text{Double-declining rate} = \$54,600 \times 40\% = \$21,840 \] So, the correct answer is **$21,840**.
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