Tax on Asset Disposal and After-Tax Salvage

Why Disposal Taxes Change Salvage Proceeds

An asset sold at the end of a project produces cash, but the sale price is not necessarily the project’s cash flow after tax. For tax purposes, the sale is compared with the asset’s remaining tax book value. A sale above that value creates a taxable gain under the basic model; a sale below it creates a deductible loss. The tax or tax saving changes the cash the project retains.

This calculation is a specific terminal cash-flow component. It does not replace the project’s operating cash flows or other terminal cash-flow items. Keep the disposal calculation focused on the asset’s sale proceeds and the tax effect of the difference between those proceeds and tax book value.

Definition: Let $S$ be the asset’s sale price, $B$ its tax book value immediately before disposal, and $\tau$ the applicable tax rate. The disposal gain or loss is $S-B$. Under the basic model, after-tax salvage proceeds are $$ S_{\text{AT}}=S-\tau(S-B)=S(1-\tau)+\tau B. $$ A positive $S-B$ is a taxable gain. A negative $S-B$ is a deductible loss, whose tax benefit increases net proceeds if that benefit can be used.

Tax Book Value and the Disposal Tax

Tax book value is the asset’s tax cost basis less accumulated tax depreciation through the date of sale. It is not the sale price, and it need not equal the asset’s accounting book value if accounting and tax depreciation differ. Use the tax book value specified in a problem or calculate it from the tax basis and tax depreciation.

The formula uses these assumptions: the tax rate is constant and applies to the full gain or loss; the tax payment or saving occurs at the disposal date; a loss produces a usable tax benefit; and there are no transaction costs or special disposal rules. The model treats $S$ as the sale proceeds before the disposal tax. If a problem specifies selling costs, special tax treatment, or that a loss benefit cannot be used, adjust the calculation to those conditions rather than applying the formula without modification. Tax treatment varies by jurisdiction; the formula here is a standard project-analysis model, not tax advice.

\text{Disposal tax}=\tau(S-B), \qquad \text{After-tax salvage}=S-\text{disposal tax}.

The disposal tax is signed. If $S>B$, it is positive and reduces proceeds. If $S<B$, it is negative: subtracting that negative amount adds a tax saving to proceeds. If $S=B$, there is no gain or loss in this model, so after-tax salvage equals the sale price.

Why the After-Tax Salvage Formula Holds

The derivation follows directly from measuring the taxable difference. The asset generates sale cash of $S$, while the tax on disposal is $\tau$ times the gain $S-B$. Net the tax payment against the sale cash:

Find the taxable difference.
The gain or loss is sale price minus tax book value: $S-B$.

Calculate the signed tax effect.
At rate $\tau$, the tax payment is $\tau(S-B)$. A negative result represents a tax saving under the stated assumptions.

Net tax against the sale cash.
Subtract the signed tax payment from $S$, giving $S-\tau(S-B)$.

Rearrange if useful.
Expanding gives $S-\tau S+\tau B=S(1-\tau)+\tau B$. The tax applies to the gain or loss, not automatically to the entire sale price.

This rearrangement also shows how tax book value affects the result: for a fixed sale price and tax rate, a higher tax book value means a smaller taxable gain—or a larger deductible loss—and therefore higher after-tax salvage under this model.

Worked Disposal Calculations

Worked Example: Sale Above Tax Book Value

A hypothetical project disposes of equipment for $96,000. Its original tax basis was $180,000. Tax depreciation claimed was $24,000, $36,000, $30,000, and $18,000 over four years. The applicable tax rate is 25%. Assume the disposal tax is settled immediately and any tax due is fully payable. Calculate the after-tax salvage proceeds.

Method. Find tax book value, calculate the taxable gain, and subtract the tax on that gain from the sale price. This avoids treating the entire sale price as taxable.

First total accumulated tax depreciation:

$$ 24{,}000+36{,}000+30{,}000+18{,}000=108{,}000. $$

Tax book value is the original tax basis less accumulated tax depreciation:

$$ B=180{,}000-108{,}000=72{,}000. $$

The disposal gain is:

$$ S-B=96{,}000-72{,}000=24{,}000. $$

Tax on the gain is $0.25(24{,}000)=\$6{,}000$. Therefore:

S_{\text{AT}}=96{,}000-6{,}000=\$90{,}000.

Check. The equivalent formula gives $0.75(96{,}000)+0.25(72{,}000)=72{,}000+18{,}000=\$90{,}000$. The result is below the sale price by exactly the $6,000 tax on the $24,000 gain.

Worked Example: Sale Below Tax Book Value

A hypothetical production machine had a tax basis of $125,000. Accumulated tax depreciation at disposal is $75,000. The machine sells for $38,000, and the applicable tax rate is 30%. Assume a disposal loss produces an immediately usable tax benefit. Calculate the after-tax salvage proceeds.

Method. Calculate tax book value first, then apply the tax rate to the signed loss. The key condition is that the loss benefit is usable; without it, this calculation would not be justified.

Tax book value is:

$$ B=125{,}000-75{,}000=50{,}000. $$

The signed disposal difference is:

$$ S-B=38{,}000-50{,}000=-12{,}000. $$

The negative $12,000 difference is a loss. The signed tax amount is $0.30(-12{,}000)=-\$3{,}600$, representing a tax saving rather than a tax payment. Thus:

S_{\text{AT}}=38{,}000-(-3{,}600)=\$41{,}600.

Check. Using the rearranged formula, $0.70(38{,}000)+0.30(50{,}000)=26{,}600+15{,}000=\$41{,}600$. Net proceeds exceed the sale price because the assumed tax saving is $3,600.

Worked Example: Finding the Sale Price for a Target After-Tax Amount

A hypothetical asset has a tax book value of $40,000 when a project ends. The project requires after-tax salvage proceeds of at least $68,000. The applicable tax rate is 25%, and any tax on a gain is payable immediately. What sale price produces exactly $68,000 of after-tax salvage?

Method. Use the rearranged formula with the sale price as the unknown. This matters because the target is after tax, not the amount the buyer must pay.

Substitute $B=40{,}000$, $\tau=0.25$, and $S_{\text{AT}}=68{,}000$:

$$ 68{,}000=0.75S+0.25(40{,}000) =0.75S+10{,}000. $$

Subtract $10,000 from each side and divide by $0.75$:

58{,}000=0.75S, \qquad S=\frac{58{,}000}{0.75}=\$77{,}333.33

Round the sale price to the nearest cent. To check, the gain is $\$77{,}333.33-\$40{,}000=\$37{,}333.33$. Tax is $0.25(\$37{,}333.33)=\$9{,}333.33$, rounded to the nearest cent. Net proceeds are $\$77{,}333.33-\$9{,}333.33=\$68{,}000.00$.

Common Mistakes and Exam Traps

A frequent error is to multiply the full sale price by $1-\tau$, as though the full price were taxable. In the first worked example, that incorrect calculation is $96{,}000(1-0.25)=\$72{,}000$. It incorrectly taxes $96,000 rather than the $24,000 gain. The correct disposal tax is $0.25(96{,}000-72{,}000)=\$6{,}000$, so after-tax salvage is $90,000.

A second trap is to treat a sale below tax book value as if it generated a tax payment. With $S-B<0$, the signed tax is negative. Under the usable-loss assumption, subtracting the negative tax adds the tax benefit to sale proceeds. Writing the signed difference before calculating the tax helps preserve this direction.

Using the wrong book value. The relevant amount is tax book value, not necessarily accounting book value or current market value.
Ignoring tax depreciation already claimed. Accumulated tax depreciation reduces tax book value; do not subtract it twice.
Forgetting the loss-benefit condition. A deductible loss does not automatically create an immediate cash saving if the benefit cannot be used under the problem’s tax assumptions.
Mixing up sale price and after-tax salvage. The sale price is the cash received before the disposal tax; after-tax salvage is what remains after the tax effect.

Key takeaway: Calculate $B$, then $S-B$, then the signed tax $\tau(S-B)$. After-tax salvage is $S-\tau(S-B)$. A gain reduces proceeds; a usable loss tax benefit increases them.

Check Your Understanding

For each hypothetical disposal, use the stated basic-model assumptions and check whether the disposal difference is a gain or a loss before applying tax.

An asset has a tax basis of $150,000 and accumulated tax depreciation of $90,000. It sells for $75,000 at a 28% tax rate. What are its tax book value and after-tax salvage proceeds? (Answer: Tax book value $60,000; after-tax salvage $70,800.)
A hypothetical machine has a tax basis of $84,000 and accumulated tax depreciation of $60,000. It sells for $18,000. At a 30% tax rate, assume the loss benefit is immediately usable. What are after-tax salvage proceeds? (Answer: $19,800.)
An asset’s tax basis is $240,000 and accumulated tax depreciation is $180,000. If it sells for $45,000 at a 20% tax rate and a loss benefit is usable, calculate its after-tax salvage. (Answer: $48,000.)
An asset has a tax book value of $32,000. At a 20% tax rate, what sale price produces after-tax salvage of $52,000? (Answer: $57,000.)
A hypothetical asset has tax book value $30,000 and sells for $40,000. The tax rate is 25%. A candidate calculates after-tax salvage as $0.75(40{,}000)=\$30{,}000$. Identify the error and give the correct proceeds. (Answer: The calculation taxes the entire sale price instead of only the $10,000 gain; tax is $2,500 and after-tax salvage is $37,500.)

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