Math Problem Statement

What is the expected after-tax cash flow from selling a piece of equipment if Gray Cave Technology purchases the equipment today for $335,000, the tax rate is 20 percent, the equipment would be sold in 14 years for $36,000, and the equipment would be depreciated to $104,000 over 11 years using straight-line depreciation?

Input instructions: Round your answer to the nearest dollar.

Solution

To find the expected after-tax cash flow from selling the equipment, we need to calculate the cash flow after accounting for taxes on any gain or loss from the sale. Here's how we can approach it:

  1. Calculate Annual Depreciation:
    Since the equipment is depreciated over 11 years from its initial cost of $335,000 to a book value of $104,000: Annual Depreciation=Initial CostBook ValueDepreciation Period\text{Annual Depreciation} = \frac{\text{Initial Cost} - \text{Book Value}}{\text{Depreciation Period}} =335,000104,00011=231,00011=21,000= \frac{335,000 - 104,000}{11} = \frac{231,000}{11} = 21,000

  2. Determine the Book Value at the Time of Sale (after 14 years):
    The equipment is depreciated for 11 years, reaching a book value of $104,000. Since the equipment is held for 14 years, and depreciation stops after 11 years, the book value remains $104,000 at the time of sale.

  3. Calculate the Gain or Loss on Sale:
    The equipment will be sold for $36,000, while the book value at the time of sale is $104,000. The loss on sale is: Loss on Sale=Book ValueSale Price\text{Loss on Sale} = \text{Book Value} - \text{Sale Price} =104,00036,000=68,000= 104,000 - 36,000 = 68,000

  4. Determine the Tax Impact on the Sale:
    Since this is a loss, it will provide a tax shield. The tax savings from the loss is: Tax Savings=Loss on Sale×Tax Rate\text{Tax Savings} = \text{Loss on Sale} \times \text{Tax Rate} =68,000×0.20=13,600= 68,000 \times 0.20 = 13,600

  5. Calculate the After-Tax Cash Flow from the Sale:
    The after-tax cash flow is the sale price plus the tax savings from the loss: After-Tax Cash Flow=Sale Price+Tax Savings\text{After-Tax Cash Flow} = \text{Sale Price} + \text{Tax Savings} =36,000+13,600=49,600= 36,000 + 13,600 = 49,600

Answer: The expected after-tax cash flow from selling the equipment is $49,600.

Would you like further details or have any questions?

Here are five related questions:

  1. How would the calculation change if the tax rate was different?
  2. What if the equipment was depreciated over its entire life instead of 11 years?
  3. How does depreciation affect the book value of assets in accounting?
  4. What other factors might influence the after-tax cash flow in a sale like this?
  5. Why is the tax shield from a loss on sale beneficial to a company?

Tip: Understanding depreciation schedules can help optimize tax savings in asset management decisions.

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Math Problem Analysis

Mathematical Concepts

Depreciation
Book Value
After-Tax Cash Flow
Tax Shield

Formulas

Annual Depreciation = (Initial Cost - Book Value) / Depreciation Period
Loss on Sale = Book Value - Sale Price
Tax Savings = Loss on Sale * Tax Rate
After-Tax Cash Flow = Sale Price + Tax Savings

Theorems

Basic Tax Shield Principle

Suitable Grade Level

College/University level (Finance or Accounting course)