Calculating Salvage Value. Consider an asset that costs $640,000 and is depreciated straight-line to zero over its eight-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 $175,000. If the relevant tax rate is 35%, what is the after tax cash flow from the sale of this asset?
The Correct Answer and Explanation is :
To calculate the after-tax cash flow from the sale of an asset, we need to follow these steps:
Step 1: Determine the depreciation per year
The asset is depreciated using the straight-line method over eight years. The cost of the asset is $640,000, and the asset is fully depreciated to zero over eight years. The annual depreciation expense can be calculated as:
[
\text{Depreciation per year} = \frac{\text{Cost of asset}}{\text{Depreciation period}} = \frac{640,000}{8} = 80,000
]
Step 2: Determine the book value at the time of sale
The asset is being used in a five-year project, so after five years, the book value of the asset is:
[
\text{Book value at year 5} = \text{Cost of asset} – (\text{Annual depreciation} \times \text{Years of use}) = 640,000 – (80,000 \times 5) = 640,000 – 400,000 = 240,000
]
Step 3: Calculate the taxable gain or loss on sale
The asset is sold for $175,000 at the end of the project. The taxable gain or loss is the difference between the sale price and the book value at the time of sale:
[
\text{Taxable gain/loss} = \text{Sale price} – \text{Book value at year 5} = 175,000 – 240,000 = -65,000
]
Since the result is negative, it represents a loss of $65,000 on the sale.
Step 4: Determine the tax effect
A loss on the sale of an asset reduces taxable income, meaning it generates a tax savings. The tax savings can be calculated by multiplying the loss by the tax rate:
[
\text{Tax savings} = \text{Loss} \times \text{Tax rate} = -65,000 \times 0.35 = -22,750
]
Step 5: Calculate the after-tax cash flow
The after-tax cash flow from the sale of the asset is the sale price of the asset plus the tax savings:
[
\text{After-tax cash flow} = \text{Sale price} + \text{Tax savings} = 175,000 + 22,750 = 197,750
]
Conclusion:
The after-tax cash flow from the sale of the asset is $197,750.
Explanation:
The after-tax cash flow takes into account the fact that the asset was sold for less than its book value, resulting in a loss. The tax benefit of this loss reduces the overall tax liability, increasing the cash flow. The formula used includes the sale price of the asset and the tax savings generated by the loss on the sale. This process is critical for determining the actual benefit the company will receive from the sale after considering taxes.
