A new piece of equipment costs $18,000 with a residual value of $600 and estimated useful life of 5 years. Assuming twice the straight line rate, the book value at the end of year 2 using the declining balance method would be?

To find the book value of the equipment at the end of year 2 using the **double-declining balance method** (DDB), we follow these steps:

1. **Identify key values:**
   - **Initial cost:** $18,000
   - **Residual value:** $600
   - **Useful life:** 5 years

2. **Calculate the straight-line depreciation rate:**
   The straight-line rate is calculated as:
   \[
   \text{Straight-line rate} = \frac{1}{\text{Useful life}} = \frac{1}{5} = 0.20 \text{ or } 20\%
   \]

3. **Double the straight-line rate:**
   Under the double-declining balance method, the rate is doubled:
   \[
   \text{Double-declining rate} = 2 \times 0.20 = 0.40 \text{ or } 40\%
   \]

4. **Apply depreciation for each year until the end of year 2:**

   - **Year 1:**
     \[
     \text{Depreciation expense} = 40\% \times 18,000 = 7,200
     \]
     \[
     \text{Book value at the end of Year 1} = 18,000 - 7,200 = 10,800
     \]

   - **Year 2:**
     \[
     \text{Depreciation expense} = 40\% \times 10,800 = 4,320
     \]
     \[
     \text{Book value at the end of Year 2} = 10,800 - 4,320 = 6,480
     \]

Therefore, the book value of the equipment at the end of year 2 is **$6,480**.

Would you like a further breakdown of these steps, or do you have any questions?

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1. How does the double-declining balance method differ from straight-line depreciation?
2. Why does the declining balance method ignore the residual value in annual calculations?
3. How would the depreciation schedule look for the remaining years in this problem?
4. What would be the effect of a higher initial cost on book value under this method?
5. How is the declining balance method useful in financial decision-making?

**Tip:** In the double-declining balance method, you stop depreciating once the book value reaches the residual value.

Learn how to find the book value of a $18,000 equipment with a $600 residual value after 2 years using the double-declining balance method. This step-by-step guide covers key concepts like depreciation rate calculation and book value updates. Ideal for high school students learning advanced financial math.

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