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Using the MACRS rates from the table, what is the book value of a [tex]$4,000 computer after 2 years?

\[
\begin{tabular}{|c|r|}
\hline
Year & MACRS Rate \\
\hline
1 & 20.0\% \\
\hline
2 & 32.0\% \\
\hline
3 & 19.2\% \\
\hline
4 & 11.52\% \\
\hline
5 & 11.52\% \\
\hline
6 & 5.76\% \\
\hline
\end{tabular}
\]

Book Value = $[/tex][?]$

Round to the nearest cent.


Sagot :

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.