Question

Silverman Company purchased machinery for $162,000 on January 1, 2020. It is estimated that the machinery will have a useful life of 20 years, salvage value of $15,000, production of 84,000 units, and working hours of 42,000. During 2020, the company uses the machinery for 14,300 hours, and the machinery produces 20,000 units. Compute depreciation under the straight-line, units-of-output, working hours, sum-of-the-years’-digits, and double-declining-balance methods.

Answer 1

To calculate depreciation under various methods, we will first establish relevant information:

- **Cost of Machinery**: $162,000
- **Useful Life**: 20 years
- **Salvage Value**: $15,000
- **Total Production**: 84,000 units
- **Total Working Hours**: 42,000 hours
- **Hours used in 2020**: 14,300 hours
- **Units produced in 2020**: 20,000 units

### 1. Straight-Line Method:
The straight-line method of depreciation is calculated as follows:

\[
\text{Depreciation Expense} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Useful Life}}
\]

\[
\text{Depreciation Expense} = \frac{162,000 - 15,000}{20} = \frac{147,000}{20} = 7,350
\]

### 2. Units-of-Output Method:
This method is based on the number of units produced:

\[
\text{Depreciation Expense per Unit} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Total Production}}
\]
\[
\text{Depreciation Expense per Unit} = \frac{162,000 - 15,000}{84,000} = \frac{147,000}{84,000} = 1.75 \text{ per unit}
\]

Now calculate the depreciation for the units produced in 2020:

\[
\text{Depreciation Expense for 2020} = \text{Depreciation Expense per Unit} \times \text{Units Produced in 2020}
\]
\[
\text{Depreciation Expense for 2020} = 1.75 \times 20,000 = 35,000
\]

### 3. Working Hours Method:
This method calculates based on hours used:

\[
\text{Depreciation Expense per Hour} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Total Working Hours}}
\]
\[
\text{Depreciation Expense per Hour} = \frac{162,000 - 15,000}{42,000} = \frac{147,000}{42,000} = 3.50 \text{ per hour}
\]

Now calculate the depreciation for hours used in 2020:

\[
\text{Depreciation Expense for 2020} = \text{Depreciation Expense per Hour} \times \text{Hours Used in 2020}
\]
\[
\text{Depreciation Expense for 2020} = 3.50 \times 14,300 = 50,050
\]

### 4. Sum-of-the-Years'-Digits Method:
The Sum-of-the-Years'-Digits method involves a fraction based on years of service:

\[
\text{Sum of the Years} = \text{n} + \ldots + 1 = \frac{n(n + 1)}{2}
\]
In this case \( n = 20\):

\[
\text{Sum of the Years} = \frac{20(20 + 1)}{2} = \frac{20 \times 21}{2} = 210
\]

For the first year's depreciation (2020), the fraction for the 1st year is 20:

\[
\text{Depreciation Expense for 2020} = \frac{20}{210} \times (162,000 - 15,000) = \frac{20}{210} \times 147,000
\]
\[
= \frac{20 \times 147,000}{210} = \frac{2,940,000}{210} = 14,000
\]

### 5. Double-Declining-Balance Method:
In this method, we first determine the straight-line depreciation rate and then double it:

\[
\text{Straight-Line Rate} = \frac{1}{\text{Useful Life}} = \frac{1}{20} = 0.05 \text{ or } 5\%
\]
\[
\text{Double Declining Rate} = 2 \times 5\% = 10\%
\]

In the first year:

\[
\text{Depreciation Expense for 2020} = \text{Double Declining Rate} \times \text{Cost}
\]
\[
= 10\% \times 162,000 = 0.10 \times 162,000 = 16,200
\]

### Summary of Depreciation Expenses for 2020
- **Straight-Line**: $7,350
- **Units-of-Output**: $35,000
- **Working Hours**: $50,050
- **Sum-of-the-Years'-Digits**: $14,000
- **Double-Declining-Balance**: $16,200

Each method provides a different perspective on the depreciation of the asset for the year 2020.