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Sagot :
Let's work through the depreciation computations for both machines step by step.
### Machine #1
- Purchase Price: \[tex]$137,600 - Salvage Value: \$[/tex]9,600
- Useful Life: 5 years
- Depreciation Method: Straight-line
- Purchase Date: July 1, 2018
- Date Sold: July 1, 2022
Step 1: Calculate the annual depreciation using the straight-line method.
The straight-line method formula is:
[tex]\[ \text{Annual Depreciation} = \frac{\text{Purchase Price} - \text{Salvage Value}}{\text{Useful Life}} \][/tex]
Substitute the given values:
[tex]\[ \text{Annual Depreciation} = \frac{137,600 - 9,600}{5} = \frac{128,000}{5} = 25,600 \][/tex]
Step 2: Determine the number of years the machine has been used until the date of disposal.
Purchase date to sale date span 4 full years (2018 - 2022), but we need to determine the depreciation up to the sale date (July 1, 2022).
Step 3: Calculate the accumulated depreciation.
For a machine sold halfway through the final year, we will compute the depreciation for each full year and then half of the year 2022.
[tex]\[ \text{Accumulated Depreciation}: \][/tex]
[tex]\[ \text{For 2018 - 2019 (1 year)} = 25,600 \][/tex]
[tex]\[ \text{For 2019 - 2020 (1 year)} = 25,600 \][/tex]
[tex]\[ \text{For 2020 - 2021 (1 year)} = 25,600 \][/tex]
[tex]\[ \text{For 2021 - 2022 (1 year)} = 25,600 \][/tex]
[tex]\[ \text{Total Full Years Depreciation} = 4 \times 25,600 = 102,400 \][/tex]
So, the accumulated depreciation to the disposal date is \[tex]$102,400. ### Machine #2 - Purchase Price: \$[/tex]152,000
- Salvage Value: \[tex]$8,000 - Useful Life: 5 years - Depreciation Method: Double-declining-balance (DDB) - Purchase Date: January 1, 2021 - Date Sold: December 31, 2022 Step 1: Calculate the first year's depreciation using the double-declining-balance method (DDB). The DDB method formula is: \[ \text{Depreciation for Year} = \left(\frac{2}{\text{Useful Life}}\right) \times \text{Book Value at Beginning of Year} \] For the first year: \[ \text{Annual Depreciation (2021)} = \left(\frac{2}{5}\right) \times 152,000 = 0.4 \times 152,000 = 60,800 \] Book value at end of 2021: \[ \text{Book Value (end 2021)} = 152,000 - 60,800 = 91,200 \] Step 2: Calculate the second year's depreciation. For the second year: \[ \text{Annual Depreciation (2022)} = \left(\frac{2}{5}\right) \times 91,200 = 0.4 \times 91,200 = 36,480 \] Step 3: Calculate the accumulated depreciation to the disposal date. Accumulated depreciation is the sum of the annual depreciations: \[ \text{Accumulated Depreciation} = 60,800 (\text{2021}) + 36,480 (\text{2022}) = 97,280 \] ### Summary of Computations - Machine #1: - Annual Depreciation: \$[/tex]25,600
- Accumulated Depreciation (2018 - 2022): \[tex]$102,400 - Machine #2: - Year 2021 Depreciation: \$[/tex]60,800
- Year 2022 Depreciation: \[tex]$36,480 - Accumulated Depreciation (2021 - 2022): \$[/tex]97,280
### Machine #1
- Purchase Price: \[tex]$137,600 - Salvage Value: \$[/tex]9,600
- Useful Life: 5 years
- Depreciation Method: Straight-line
- Purchase Date: July 1, 2018
- Date Sold: July 1, 2022
Step 1: Calculate the annual depreciation using the straight-line method.
The straight-line method formula is:
[tex]\[ \text{Annual Depreciation} = \frac{\text{Purchase Price} - \text{Salvage Value}}{\text{Useful Life}} \][/tex]
Substitute the given values:
[tex]\[ \text{Annual Depreciation} = \frac{137,600 - 9,600}{5} = \frac{128,000}{5} = 25,600 \][/tex]
Step 2: Determine the number of years the machine has been used until the date of disposal.
Purchase date to sale date span 4 full years (2018 - 2022), but we need to determine the depreciation up to the sale date (July 1, 2022).
Step 3: Calculate the accumulated depreciation.
For a machine sold halfway through the final year, we will compute the depreciation for each full year and then half of the year 2022.
[tex]\[ \text{Accumulated Depreciation}: \][/tex]
[tex]\[ \text{For 2018 - 2019 (1 year)} = 25,600 \][/tex]
[tex]\[ \text{For 2019 - 2020 (1 year)} = 25,600 \][/tex]
[tex]\[ \text{For 2020 - 2021 (1 year)} = 25,600 \][/tex]
[tex]\[ \text{For 2021 - 2022 (1 year)} = 25,600 \][/tex]
[tex]\[ \text{Total Full Years Depreciation} = 4 \times 25,600 = 102,400 \][/tex]
So, the accumulated depreciation to the disposal date is \[tex]$102,400. ### Machine #2 - Purchase Price: \$[/tex]152,000
- Salvage Value: \[tex]$8,000 - Useful Life: 5 years - Depreciation Method: Double-declining-balance (DDB) - Purchase Date: January 1, 2021 - Date Sold: December 31, 2022 Step 1: Calculate the first year's depreciation using the double-declining-balance method (DDB). The DDB method formula is: \[ \text{Depreciation for Year} = \left(\frac{2}{\text{Useful Life}}\right) \times \text{Book Value at Beginning of Year} \] For the first year: \[ \text{Annual Depreciation (2021)} = \left(\frac{2}{5}\right) \times 152,000 = 0.4 \times 152,000 = 60,800 \] Book value at end of 2021: \[ \text{Book Value (end 2021)} = 152,000 - 60,800 = 91,200 \] Step 2: Calculate the second year's depreciation. For the second year: \[ \text{Annual Depreciation (2022)} = \left(\frac{2}{5}\right) \times 91,200 = 0.4 \times 91,200 = 36,480 \] Step 3: Calculate the accumulated depreciation to the disposal date. Accumulated depreciation is the sum of the annual depreciations: \[ \text{Accumulated Depreciation} = 60,800 (\text{2021}) + 36,480 (\text{2022}) = 97,280 \] ### Summary of Computations - Machine #1: - Annual Depreciation: \$[/tex]25,600
- Accumulated Depreciation (2018 - 2022): \[tex]$102,400 - Machine #2: - Year 2021 Depreciation: \$[/tex]60,800
- Year 2022 Depreciation: \[tex]$36,480 - Accumulated Depreciation (2021 - 2022): \$[/tex]97,280
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