Math Problem Statement
Consider an asset that costs $650,000 and is depreciated straight-line to zero over its nine-year tax life. The asset is to be used in a five-year project; at the end of the project, the asset can be sold for $131,000. If the relevant tax rate is 23 percent, what is the aftertax cash flow from the sale of this asset?
Solution
To calculate the after-tax cash flow from the sale of the asset, we need to follow these steps:
1. Determine the Book Value of the Asset After 5 Years
Since the asset is being depreciated straight-line over its 9-year tax life, the annual depreciation is:
After 5 years, the accumulated depreciation is:
Therefore, the book value of the asset after 5 years is:
2. Calculate the Gain or Loss on the Sale
The asset is sold for $131,000, and the book value after 5 years is $288,888.89, so the loss on the sale is:
3. Calculate the Tax Impact
Since the sale results in a loss, this loss will reduce the taxable income. The tax savings from this loss are:
4. Determine the After-Tax Cash Flow
The after-tax cash flow from the sale is the sale price plus the tax savings from the loss:
Final Answer:
The after-tax cash flow from the sale of the asset is $167,314.44.
Do you need any further clarification or more details on the calculation?
Here are 5 related questions:
- How would the after-tax cash flow change if the tax rate was higher?
- What happens if the asset was sold for a profit instead of a loss?
- How would the depreciation method affect the after-tax cash flow?
- Can we use MACRS depreciation for this calculation? How would it affect the results?
- What if the project lasted for more than 5 years; how would that change the book value?
Tip: When selling assets in a project, it's important to account for tax impacts of any gains or losses to accurately measure after-tax cash flow.
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Math Problem Analysis
Mathematical Concepts
Depreciation
Tax Impact
After-Tax Cash Flow
Formulas
Annual Depreciation = Asset Cost / Tax Life
Accumulated Depreciation = Annual Depreciation × Number of Years
Book Value = Asset Cost - Accumulated Depreciation
Loss on Sale = Sale Price - Book Value
Tax Savings = Loss on Sale × Tax Rate
After-Tax Cash Flow = Sale Price + Tax Savings
Theorems
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Suitable Grade Level
College Level (Finance or Accounting)
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