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:

Annual Depreciation=650,0009=72,222.22\text{Annual Depreciation} = \frac{650,000}{9} = 72,222.22

After 5 years, the accumulated depreciation is:

Accumulated Depreciation=72,222.22×5=361,111.11\text{Accumulated Depreciation} = 72,222.22 \times 5 = 361,111.11

Therefore, the book value of the asset after 5 years is:

Book Value=650,000361,111.11=288,888.89\text{Book Value} = 650,000 - 361,111.11 = 288,888.89

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:

Loss=131,000288,888.89=157,888.89\text{Loss} = 131,000 - 288,888.89 = -157,888.89

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:

Tax Savings=157,888.89×0.23=36,314.44\text{Tax Savings} = 157,888.89 \times 0.23 = 36,314.44

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:

After-Tax Cash Flow=131,000+36,314.44=167,314.44\text{After-Tax Cash Flow} = 131,000 + 36,314.44 = 167,314.44

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:

  1. How would the after-tax cash flow change if the tax rate was higher?
  2. What happens if the asset was sold for a profit instead of a loss?
  3. How would the depreciation method affect the after-tax cash flow?
  4. Can we use MACRS depreciation for this calculation? How would it affect the results?
  5. 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)