Billy's Plumbing Supplies is considering the purchase of an asset that costs $450 000 and is depreciated straight-line to zero over its six-year tax life. The asset is to be used in a four-year project; at the end of the project, the asset can be sold for $120 000. If the relevant tax rate is 30%, what is the after-tax cash flow from the sale of this asset?

Question

BlackTom AI · Accepted Answer

The problem describes purchasing an asset for 450,000, depreciating it straight-line to zero over 6 years, using it for 4 years, and then selling it for 120,000. The tax rate is 30%. We need the after-tax cash flow from the sale of the asset.

First, compute annual depreciation: 450,000 / 6 = 75,000 per year.
Over 4 years, accumulated depreciation = 4 × 75,000 = 300,000.
Book value at sale = cost − accumulated depreciation = 450,000 − 300,000 = 150,000.
Sale price = 120,000. Tax treatment depends on the gain or loss on the sale relative to book value.
Taxable gain (or loss) on sale = sale price − book value = 120,000 − 150,000 = −30,000, i.e., a loss of 30,000.
A loss on sale generates a tax shield: tax saving = 30,000 × 0.30 = 9,000.
Because this is a loss, the after-tax cash inflow from the sale equals the sale price plus the tax shield: 120,000 + 9,000 = 129,000.

Now evaluate each option:
- Option "$165,000": This would imply either no depreciation effects or an incorrect tax treatment of the sale, ignoring the book value and the tax shield from the loss.
- Option "$111,000": This might result from applying tax on the entire sale price without accounting for the offsetting book value or miscomputing the tax impact of the loss.
- Option "$150,000": This could reflect the book value itself without adding the after-tax cash from the sale proceeds; it ignores the sale price and the tax shield.
- Option "$129,000": This matches the correct logic: the cash received from sale (120,000) plus the tax shield from the 30,000 loss on sale (0.30 × 30,000 = 9,000) gives 129,000.
- Option "$45,000": This appears to misplace either the depreciation tax shield or a portion of the sale proceeds, leading to an incorrect, much smaller figure.

In summary, the key idea is: compute book value at sale, compare to sale price to determine gain or loss, apply the tax effect of that gain or loss, and add the after-tax cash proceeds from the sale. The only option that aligns with 120,000 of cash from sale plus a 9,000 tax shield from the 30,000 loss is 129,000.

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