On April 22, 2023, Sandhill Enterprises purchased equipment for $138,700. The company expects to use the equipment for 11,500 working hours during its four-year life and that it will have a residual value of $14,500. Sandhill has a December 31 year end and prorates depreciation to the nearest month. The actual machine usage was: 1,500 hours in 2023; 3,000 hours in 2024; 3,600 hours in

2025; 2,600 hours in 2026; and 1,000 hours in 2027. Prepare a depreciation schedule for the life of the asset under the double diminishing-balance method. (Round partial-period depreciation rate to 4 decimal palces, e.g. 15.2563% and other answers to 0 decimal places, e.g. 5,276.)

To prepare a depreciation schedule using the **double diminishing-balance (DDB)** method, we need to follow a systematic process. Here’s the approach we'll use:

### Key Information:
- **Cost of equipment:** $138,700
- **Residual value (salvage value):** $14,500
- **Useful life:** 4 years (prorated depreciation by month)
- **Depreciation method:** Double diminishing-balance (DDB)

### Steps to Calculate Depreciation:

1. **Depreciation Rate**:
   - Under DDB, the depreciation rate is calculated as:
     \[
     \text{DDB rate} = \frac{2}{\text{useful life in years}} = \frac{2}{4} = 0.5 \text{ or } 50\%
     \]
   
2. **Prorate for 2023**:
   - Since the equipment was purchased on **April 22, 2023**, only part of the year will be used for depreciation in 2023.
   - The fraction of the year used for depreciation in 2023 will be from **April 22 to December 31**, which is **8.5 months** (rounded to 8 months).
   - Therefore, depreciation for 2023 should be prorated based on 8/12 of a year.

3. **Depreciation Calculation**:
   - For each year, we calculate depreciation by multiplying the book value at the beginning of the year by the depreciation rate. The residual value is considered at the end of the asset's life to ensure the book value doesn’t drop below the salvage value.

Let's proceed with the calculations.

### Year 2023:
- **Starting book value:** $138,700
- **Depreciation for 2023**:
  \[
  \text{Depreciation} = \text{Starting book value} \times \text{DDB rate} \times \frac{8}{12}
  \]

I will now calculate the depreciation for 2023 and subsequent years.Here is the **depreciation schedule** using the **double diminishing-balance (DDB) method** for the equipment over its four-year life:

| Year  | Beginning Book Value | Depreciation | Ending Book Value |
|-------|----------------------|--------------|-------------------|
| 2023  | $138,700             | $46,233      | $92,467           |
| 2024  | $92,467              | $46,233      | $46,233           |
| 2025  | $46,233              | $23,117      | $23,117           |
| 2026  | $23,117              | $8,617       | $14,500           |

### Explanation:
- **2023**: The depreciation is prorated for 8 months, which amounts to $46,233.
- **2024**: Full year's depreciation of $46,233 is calculated at 50% of the book value.
- **2025**: Depreciation is reduced to $23,117 as the book value decreases.
- **2026**: Depreciation ensures that the book value reaches the residual value of $14,500 by the end of the year.

Let me know if you would like further clarifications or details!

### 5 Related Questions:
1. How does the straight-line depreciation method differ from the DDB method?
2. What happens if the actual residual value at the end of the asset’s life differs from the estimated value?
3. How would the schedule change if the equipment had a longer useful life, say 6 years?
4. Can we apply the same method to intangible assets like patents?
5. What is the impact of different depreciation methods on tax reporting?

### Tip:
DDB depreciation accelerates the write-off in the early years of an asset’s life, which can be useful for assets that lose value quickly.

On April 22, 2023, Sandhill Enterprises purchased equipment for $138,700. The company expects to use the equipment for 11,500 working hours during its four-year life and that it will have a residual value of $14,500. Sandhill has a December 31 year end and prorates depreciation to the nearest month. The actual machine usage was: 1,500 hours in 2023; 3,000 hours in 2024; 3,600 hours in 2025; 2,600 hours in 2026; and 1,000 hours in 2027. Prepare a depreciation schedule for the life of the asset under the double diminishing-balance method. (Round partial-period depreciation rate to 4 decimal places, e.g. 15.2563% and other answers to 0 decimal places, e.g. 5,276.)

Learn how to calculate a depreciation schedule for equipment purchased at $138,700 over four years using the double diminishing-balance method. This example includes prorated depreciation for 2023, residual value of $14,500, and detailed calculations for each year.

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