Using the MACRS rates from the following table, what is the book value of a $4,500 computer after 4 years?
| Year | MACRS Rate |
|------|------------|
| 1 | 20.0 % |
| 2 | 32.0 % |
| 3 | 19.2 % |
| 4 | 11.52 % |
| 5 | 11.52 % |
| 6 | 5.76 % |
Book Value = $ [?]
Round to the nearest cent.
Answer (2)
Calculate the depreciation for each year: Year 1: 4500 × 0.20 = $900 , Year 2: 4500 × 0.32 = $1440 , Year 3: 4500 × 0.192 = $864 , Year 4: 4500 × 0.1152 = $518.40 .
Calculate the accumulated depreciation: 900 + 1440 + 864 + 518.40 = $3722.40 .
Subtract the accumulated depreciation from the initial cost to find the book value: 4500 − 3722.40 = $777.60 .
The book value of the computer after 4 years is $777.60 .
Explanation
Understanding the Problem We are given the initial cost of a computer as $4 , 500 and the MACRS depreciation rates for the first 6 years. We need to find the book value of the computer after 4 years. The book value is the initial cost minus the accumulated depreciation.
Calculating Annual Depreciation First, we calculate the depreciation for each of the first 4 years by multiplying the initial cost by the corresponding MACRS rate.
Year 1 Depreciation Year 1 depreciation: 4500 × 0.20 = $900
Year 2 Depreciation Year 2 depreciation: 4500 × 0.32 = $1440
Year 3 Depreciation Year 3 depreciation: 4500 × 0.192 = $864
Year 4 Depreciation Year 4 depreciation: 4500 × 0.1152 = $518.40
Calculating Accumulated Depreciation Next, we calculate the accumulated depreciation by summing the depreciation from years 1 through 4.
Total Depreciation Accumulated depreciation = 900 + 1440 + 864 + 518.40 = $3722.40
Calculating Book Value Finally, we calculate the book value after 4 years by subtracting the accumulated depreciation from the initial cost.
Final Book Value Book Value = 4500 − 3722.40 = $777.60
Examples
Understanding depreciation is crucial in business for tax purposes and asset valuation. For example, a company might use MACRS depreciation to write off the cost of equipment over its useful life, reducing its taxable income. Knowing the book value of an asset helps in making informed decisions about when to replace it. This is similar to how a car's value decreases over time, affecting its resale price and insurance costs. Businesses use depreciation schedules to plan for future investments and manage their financial health.
The book value of a $4,500 computer after 4 years, calculated using MACRS rates, is $777.60. This was determined by calculating the annual depreciation for each of the first 4 years and then subtracting the total accumulated depreciation from the initial cost. The accumulated depreciation amounted to $3,722.40, leaving a book value of $777.60.
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