To determine the book value of a \[tex]$4,000 computer after 2 years using the MACRS (Modified Accelerated Cost Recovery System) rates, follow these steps:
1. Identify the MACRS rates for the first two years:
- Year 1: \(20.0\% \)
- Year 2: \(32.0\% \)
2. Calculate the depreciation for each of the first two years:
- Depreciation for Year 1:
- Given the cost of the computer is \$[/tex]4,000 and the MACRS rate for Year 1 is [tex]\(20.0\%\)[/tex],
[tex]\[
\text{Depreciation\_Year\_1} = \text{Cost} \times \text{Rate\_Year\_1} = 4000 \times 0.20 = 800
\][/tex]
- Depreciation for Year 2:
- Given the cost of the computer is \[tex]$4,000 and the MACRS rate for Year 2 is \(32.0\%\),
\[
\text{Depreciation\_Year\_2} = \text{Cost} \times \text{Rate\_Year\_2} = 4000 \times 0.32 = 1280
\]
3. Sum the depreciations for the first two years:
\[
\text{Total Depreciation for 2 years} = \text{Depreciation\_Year\_1} + \text{Depreciation\_Year\_2} = 800 + 1280 = 2080
\]
4. Calculate the book value after 2 years:
- Subtract the total depreciation from the initial cost:
\[
\text{Book Value after 2 years} = \text{Cost} - \text{Total Depreciation for 2 years} = 4000 - 2080 = 1920
\]
Thus, the book value of the \$[/tex]4,000 computer after 2 years is \$1,920.
