An asset used in a four-year project falls in the five-year MACRS class for tax purposes. The asset has an acquisition cost of $6,050,000 and will be sold for $1,250,000 at the end of the project. If the tax rate is 35 percent, what is the aftertax salvage value of the asset? Refer to Table 10.7. (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567.)
The Correct Answer and Explanation is :
To calculate the after-tax salvage value of the asset, we need to follow these steps:
- Determine the depreciation schedule using the MACRS (Modified Accelerated Cost Recovery System) for the asset. The asset falls into the five-year MACRS class for tax purposes. According to the IRS MACRS depreciation schedule, the depreciation percentages for the first five years are as follows (assuming the asset is placed in service during the first year of the project):
| Year | MACRS Depreciation Percentage (5-year class) |
|---|---|
| 1 | 20% |
| 2 | 32% |
| 3 | 19.2% |
| 4 | 11.52% |
| 5 | 11.52% |
| 6 | 5.76% |
- Calculate the depreciation for each year. The total depreciation is based on the acquisition cost of $6,050,000, using the percentages from the MACRS table.
- Year 1: $6,050,000 × 20% = $1,210,000
- Year 2: $6,050,000 × 32% = $1,936,000
- Year 3: $6,050,000 × 19.2% = $1,161,600
- Year 4: $6,050,000 × 11.52% = $698,160
By the end of Year 4, the asset has been depreciated by a total of:
$1,210,000 + $1,936,000 + $1,161,600 + $698,160 = $5,005,760
- Determine the book value at the time of sale (end of Year 4):
Book value = Acquisition cost – Accumulated depreciation
Book value = $6,050,000 – $5,005,760 = $1,044,240
- Calculate the tax impact of the sale. The asset is sold for $1,250,000, and the book value is $1,044,240. The difference between the sale price and the book value is the capital gain:
Capital gain = Sale price – Book value
Capital gain = $1,250,000 – $1,044,240 = $205,760
The capital gain is subject to tax at a rate of 35%. The tax on the gain is:
Tax = $205,760 × 35% = $71,016
- Calculate the after-tax salvage value:
After-tax salvage value = Sale price – Tax on gain
After-tax salvage value = $1,250,000 – $71,016 = $1,178,984
Final Answer:
The after-tax salvage value of the asset is $1,178,984.