A machine costing $212,600 with a four-year life and an estimated $17,000 salvage value is installed in Luther Company’s factory on January 1. The factory manager estimates the machine will produce 489,000 units of product during its life. It actually produces the following units: 123,000 in Year 1, 122,400 in Year 2, 119,700 in Year 3, 133,900 in Year 4. The total number of units produced by the end of Year 4 exceeds the original estimate—this difference was not predicted. Note: The machine cannot be depreciated below its estimated salvage value.

Required:
Compute depreciation for each year (and total depreciation of all years combined) for the machine under each depreciation method.

Note: Round your per unit depreciation to 2 decimal places. Round your answers to the nearest whole dollar.



To compute the depreciation of the machine, we will use two common methods of depreciation: **straight-line depreciation** and **units-of-production depreciation**.

### 1. **Straight-Line Depreciation Method**

The formula for straight-line depreciation is:

\[
\text{Annual Depreciation Expense} = \frac{\text{Cost of Asset} - \text{Salvage Value}}{\text{Useful Life (in years)}}
\]

#### Step-by-step:
- **Cost of Asset (Initial cost)** = $212,600
- **Salvage Value** = $17,000
- **Useful Life** = 4 years

\[
\text{Annual Depreciation Expense} = \frac{212,600 - 17,000}{4} = \frac{195,600}{4} = 48,900
\]

Thus, the depreciation for each year under the straight-line method is **$48,900**. This will be the same for all four years, and the **total depreciation** over the four years will be:

\[
48,900 \times 4 = 195,600
\]

---

### 2. **Units-of-Production Depreciation Method**

For the units-of-production method, depreciation is based on the actual units produced each year. The formula is:

\[
\text{Depreciation Expense} = \left(\frac{\text{Cost of Asset} - \text{Salvage Value}}{\text{Total Estimated Units of Production}}\right) \times \text{Units Produced in the Year}
\]

#### Step-by-step:
- **Cost of Asset (Initial cost)** = $212,600
- **Salvage Value** = $17,000
- **Total Estimated Units of Production** = 489,000
- **Units Produced Each Year**: 123,000 in Year 1, 122,400 in Year 2, 119,700 in Year 3, 133,900 in Year 4.

1. **Depreciation per Unit:**

\[
\text{Depreciation per Unit} = \frac{212,600 - 17,000}{489,000} = \frac{195,600}{489,000} \approx 0.3992 \text{ per unit (rounded to 4 decimal places)}
\]

2. **Yearly Depreciation Calculation:**
   - **Year 1**: 
     \[
     0.3992 \times 123,000 \approx 49,009
     \]
   - **Year 2**: 
     \[
     0.3992 \times 122,400 \approx 48,811
     \]
   - **Year 3**: 
     \[
     0.3992 \times 119,700 \approx 47,817
     \]
   - **Year 4**: 
     \[
     0.3992 \times 133,900 \approx 53,463
     \]

3. **Total Depreciation** over 4 years under units-of-production method:

\[
49,009 + 48,811 + 47,817 + 53,463 = 199,100
\]

### Summary of Depreciation:
| **Method**                 | **Year 1** | **Year 2** | **Year 3** | **Year 4** | **Total**  |
|----------------------------|------------|------------|------------|------------|------------|
| **Straight-Line**           | $48,900    | $48,900    | $48,900    | $48,900    | $195,600   |
| **Units-of-Production**     | $49,009    | $48,811    | $47,817    | $53,463    | $199,100   |

**Note**: Under both methods, the machine cannot be depreciated below its salvage value of $17,000.

Would you like further details or clarifications? Here are some related questions to consider:

1. What happens if the machine produces fewer units than estimated?
2. How does salvage value affect depreciation methods?
3. What are the tax implications of using different depreciation methods?
4. How does the useful life of an asset impact depreciation calculations?
5. What if the machine had no salvage value? How would that affect depreciation?

**Tip**: Depreciation methods are crucial for both tax reporting and financial planning, as they affect net income and asset values over time.

A machine costing $212,600 with a four-year life and an estimated $17,000 salvage value is installed in Luther Company’s factory on January 1. The factory manager estimates the machine will produce 489,000 units of product during its life. It actually produces the following units: 123,000 in Year 1, 122,400 in Year 2, 119,700 in Year 3, 133,900 in Year 4. The total number of units produced by the end of Year 4 exceeds the original estimate—this difference was not predicted. Note: The machine cannot be depreciated below its estimated salvage value. Required: Compute depreciation for each year (and total depreciation of all years combined) for the machine under each depreciation method.

Learn how to calculate depreciation for a machine costing $212,600 with a $17,000 salvage value using both straight-line and units-of-production methods. This detailed breakdown includes step-by-step calculations based on yearly production, helping students understand key depreciation concepts in asset management.

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