Answer :
To determine the book value of a \[tex]$4000 computer after 2 years using the MACRS (Modified Accelerated Cost Recovery System) rates provided, follow these steps:
1. Identify the initial cost:
\[
\text{Initial cost} = \$[/tex]4000
\]
2. Year 1 Depreciation:
[tex]\[ \text{Year 1 MACRS rate} = 20.0\% = 0.20 \][/tex]
[tex]\[ \text{Depreciation for Year 1} = \text{Initial cost} \times \text{Year 1 MACRS rate} \][/tex]
[tex]\[ \text{Depreciation for Year 1} = 4000 \times 0.20 \][/tex]
[tex]\[ \text{Depreciation for Year 1} = 800 \][/tex]
3. Book Value after Year 1:
[tex]\[ \text{Book Value after Year 1} = \text{Initial cost} - \text{Depreciation for Year 1} \][/tex]
[tex]\[ \text{Book Value after Year 1} = 4000 - 800 \][/tex]
[tex]\[ \text{Book Value after Year 1} = 3200 \][/tex]
4. Year 2 Depreciation:
[tex]\[ \text{Year 2 MACRS rate} = 32.0\% = 0.32 \][/tex]
[tex]\[ \text{Depreciation for Year 2} = \text{Initial cost} \times \text{Year 2 MACRS rate} \][/tex]
[tex]\[ \text{Depreciation for Year 2} = 4000 \times 0.32 \][/tex]
[tex]\[ \text{Depreciation for Year 2} = 1280 \][/tex]
5. Book Value after Year 2:
[tex]\[ \text{Book Value after Year 2} = \text{Book Value after Year 1} - \text{Depreciation for Year 2} \][/tex]
[tex]\[ \text{Book Value after Year 2} = 3200 - 1280 \][/tex]
[tex]\[ \text{Book Value after Year 2} = 1920 \][/tex]
Therefore, the book value of a \[tex]$4000 computer after 2 years is \$[/tex]1920.00 when rounded to the nearest cent.
\]
2. Year 1 Depreciation:
[tex]\[ \text{Year 1 MACRS rate} = 20.0\% = 0.20 \][/tex]
[tex]\[ \text{Depreciation for Year 1} = \text{Initial cost} \times \text{Year 1 MACRS rate} \][/tex]
[tex]\[ \text{Depreciation for Year 1} = 4000 \times 0.20 \][/tex]
[tex]\[ \text{Depreciation for Year 1} = 800 \][/tex]
3. Book Value after Year 1:
[tex]\[ \text{Book Value after Year 1} = \text{Initial cost} - \text{Depreciation for Year 1} \][/tex]
[tex]\[ \text{Book Value after Year 1} = 4000 - 800 \][/tex]
[tex]\[ \text{Book Value after Year 1} = 3200 \][/tex]
4. Year 2 Depreciation:
[tex]\[ \text{Year 2 MACRS rate} = 32.0\% = 0.32 \][/tex]
[tex]\[ \text{Depreciation for Year 2} = \text{Initial cost} \times \text{Year 2 MACRS rate} \][/tex]
[tex]\[ \text{Depreciation for Year 2} = 4000 \times 0.32 \][/tex]
[tex]\[ \text{Depreciation for Year 2} = 1280 \][/tex]
5. Book Value after Year 2:
[tex]\[ \text{Book Value after Year 2} = \text{Book Value after Year 1} - \text{Depreciation for Year 2} \][/tex]
[tex]\[ \text{Book Value after Year 2} = 3200 - 1280 \][/tex]
[tex]\[ \text{Book Value after Year 2} = 1920 \][/tex]
Therefore, the book value of a \[tex]$4000 computer after 2 years is \$[/tex]1920.00 when rounded to the nearest cent.
