Introduction
A project’s cash flows are not the same as its accounting income. Depreciation reduces taxable income but is not itself a cash payment, while the sale of equipment can generate a tax payment or tax benefit that depends on the asset’s tax book value. Net working capital can also tie up cash during a project and release it when the project ends.
A complete project schedule keeps these effects distinct until the relevant year, then combines them into one cash flow for each date. This tutorial focuses on building that schedule when equipment is sold for a price that may differ from its tax book value. The examples use hypothetical projects and assume project cash flows are measured before financing.
Build the Schedule in Separate Pieces
For a project with no interest expense in its operating forecast, define EBITDA as earnings before interest, taxes, depreciation, and amortization. In the examples, there is no amortization, so taxable operating income is EBITDA less depreciation. Assume that taxable income is taxed at rate \(T\), that depreciation is deductible in the year incurred, and that any tax effect from a disposal is usable immediately. Under these assumptions, operating cash flow is:
Capital spending is a cash outflow when paid. An increase in net working capital (NWC) is also a cash outflow because cash is tied up in inventory, receivables, or other operating assets net of operating liabilities. A decrease in NWC is a cash inflow. If the project’s NWC is fully recovered at termination, its remaining balance is a terminal inflow.
The tax book value used for disposal tax is the asset’s tax cost less accumulated tax depreciation through the disposal date. For a sale price \(S\) and tax book value \(B\), the taxable gain is \(S-B\). A positive amount creates tax; a negative amount creates a tax benefit if the loss is deductible and usable.
Why the After-Tax Salvage Formula Works
The sale itself provides cash \(S\). Its tax effect is determined by the gain or loss relative to book value. With a constant tax rate \(T\) and an immediately usable tax effect, the incremental tax on disposal is \(T(S-B)\). This expression is negative when the sale creates a deductible loss, so it represents a tax benefit in that case.
Subtract the tax effect from the sale cash to obtain the amount retained after tax:
This is a direct consequence of taxing the difference between proceeds and tax book value, rather than taxing the entire sale price. The expression applies under the stated tax assumptions. If a loss cannot be deducted or its tax benefit cannot be used immediately, the assumed immediate benefit must not be included in that period’s cash flow.
Worked Example: A Sale Above Tax Book Value
A hypothetical project buys equipment for $120,000 and depreciates it straight-line by $30,000 per year. It operates for three years, then sells the equipment for $45,000. The tax rate is 25%. EBITDA is $70,000 in year 1, $80,000 in year 2, and $90,000 in year 3. The project requires $12,000 of NWC at the outset, with no later change before the full balance is recovered at the end of year 3. Construct the project cash-flow schedule. Assume the disposal tax is paid immediately.
Method. Calculate operating cash flow year by year, calculate tax book value and after-tax salvage at the sale date, and then place capital spending and NWC changes in their actual periods. This avoids treating the equipment’s sale price as if it were already after tax.
Initial outlay. At time 0, the project pays $120,000 for equipment and invests $12,000 in NWC. Therefore, the initial cash flow is \(-\$120{,}000-\$12{,}000=-\$132{,}000\).
Year 1 operating cash flow. Taxable operating income is \(\$70{,}000-\$30{,}000=\$40{,}000\). Tax is \(0.25(\$40{,}000)=\$10{,}000\). Operating cash flow is \(\$40{,}000-\$10{,}000+\$30{,}000=\$60{,}000\). Equivalently, \(\$40{,}000(0.75)+\$30{,}000=\$60{,}000\).
Year 2 operating cash flow. Taxable operating income is \(\$80{,}000-\$30{,}000=\$50{,}000\), and tax is \(0.25(\$50{,}000)=\$12{,}500\). Operating cash flow is \(\$50{,}000-\$12{,}500+\$30{,}000=\$67{,}500\).
Year 3 operating cash flow. Taxable operating income is \(\$90{,}000-\$30{,}000=\$60{,}000\), and tax is \(0.25(\$60{,}000)=\$15{,}000\). Operating cash flow is \(\$60{,}000-\$15{,}000+\$30{,}000=\$75{,}000\).
Terminal items. After three years, accumulated depreciation is \(3(\$30{,}000)=\$90{,}000\), so tax book value is \(\$120{,}000-\$90{,}000=\$30{,}000\). The sale creates a gain of \(\$45{,}000-\$30{,}000=\$15{,}000\), with tax of \(0.25(\$15{,}000)=\$3{,}750\). After-tax salvage is \(\$45{,}000-\$3{,}750=\$41{,}250\). The $12,000 NWC balance is recovered in year 3.
Schedule and check. The year-3 cash flow is \(\$75{,}000+\$41{,}250+\$12{,}000=\$128{,}250\). Thus the schedule is time 0: \(-\$132{,}000\); year 1: \(\$60{,}000\); year 2: \(\$67{,}500\); year 3: \(\$128{,}250\). The year-3 total includes operating cash flow, after-tax salvage, and the full NWC recovery exactly once.
Depreciation and Disposal Tax Effects
Depreciation affects a project’s cash flow through taxes, not because depreciation is a cash payment. In the operating cash-flow formula, depreciation lowers taxable income and then is added back as a noncash expense. This produces a tax shield of \(T\) times depreciation when the deduction can be used against taxable income.
At disposal, the gain or loss is measured against tax book value at that date, not original cost and not the amount of depreciation remaining in some accounting forecast. The same sale price can therefore produce different tax effects for assets with different depreciation histories. The tax-book-value calculation should be shown explicitly before calculating after-tax salvage.
Worked Example: A Deductible Loss on Disposal
A hypothetical project purchases equipment for $100,000 and depreciates it by $20,000 per year. It sells the equipment at the end of year 3 for $31,000. The tax rate is 30%. EBITDA is $55,000 in year 1, $65,000 in year 2, and $75,000 in year 3. The project invests $8,000 in NWC at time 0, adds $2,000 of NWC at the end of year 1, and recovers the full $10,000 at the end of year 3. Assume the disposal loss is deductible and the resulting tax benefit is usable immediately. Find each project cash flow.
Method. Treat operating taxes, changes in NWC, and disposal tax as separate entries. In particular, an NWC increase is a cash outflow in the year it occurs; it is not an operating expense.
Operating cash flows. Annual depreciation is $20,000. In year 1, taxable operating income is \(\$55{,}000-\$20{,}000=\$35{,}000\); tax is \(0.30(\$35{,}000)=\$10{,}500\); and operating cash flow is \(\$35{,}000-\$10{,}500+\$20{,}000=\$44{,}500\). In year 2, taxable income is \(\$65{,}000-\$20{,}000=\$45{,}000\); tax is $13,500; and operating cash flow is \(\$45{,}000-\$13{,}500+\$20{,}000=\$51{,}500\). In year 3, taxable income is \(\$75{,}000-\$20{,}000=\$55{,}000\); tax is $16,500; and operating cash flow is \(\$55{,}000-\$16{,}500+\$20{,}000=\$58{,}500\).
Disposal. Accumulated depreciation after three years is \(3(\$20{,}000)=\$60{,}000\), so tax book value is \(\$100{,}000-\$60{,}000=\$40{,}000\). The sale is below book value by \(\$40{,}000-\$31{,}000=\$9{,}000\). The deductible loss creates a tax benefit of \(0.30(\$9{,}000)=\$2{,}700\). After-tax salvage is therefore \(\$31{,}000+\$2{,}700=\$33{,}700\).
Cash-flow schedule. At time 0, equipment and initial NWC require \(\$100{,}000+\$8{,}000=\$108{,}000\), so cash flow is \(-\$108{,}000\). In year 1, operating cash flow of $44,500 is reduced by the $2,000 NWC increase, giving $42,500. In year 2, there is no additional NWC change, so cash flow is $51,500. In year 3, add operating cash flow of $58,500, after-tax salvage of $33,700, and recovery of $10,000 NWC: total year-3 cash flow is \(\$58{,}500+\$33{,}700+\$10{,}000=\$102{,}200\).
Check. The year-1 NWC increase takes total NWC from $8,000 to $10,000; the terminal recovery returns that entire $10,000. The disposal loss increases, rather than decreases, sale proceeds after tax because the assumed tax benefit is immediately usable.
Putting All Terminal Components Together
A terminal-year cash flow may contain several different items. The operating cash flow for the final year is still calculated from that year’s operations. Then add after-tax salvage and any NWC released at project end. If capital spending or another working-capital change occurs in that same year, include it as a separate cash flow as well.
The terminal year is not automatically a single “salvage” amount. It is a collection of cash flows that happen at the end of the project. Keeping the components visible makes it easier to check both the tax calculation and the timing of working capital.
Worked Example: Sale at Tax Book Value and Full NWC Recovery
A hypothetical project buys equipment for $96,000 and depreciates it by $24,000 per year. The equipment is sold at the end of year 3 for $24,000. The tax rate is 28%. EBITDA is $60,000, $72,000, and $84,000 in years 1, 2, and 3, respectively. The project initially requires $10,000 of NWC, then requires an additional $4,000 at the end of year 1. The entire NWC balance is recovered at the end of year 3. Assume tax deductions and any disposal tax effect are immediately usable. Construct the schedule.
Initial outlay. Time-0 cash flow is equipment spending of $96,000 plus initial NWC of $10,000, or \(-\$106{,}000\).
Year 1. Taxable operating income is \(\$60{,}000-\$24{,}000=\$36{,}000\). Tax is \(0.28(\$36{,}000)=\$10{,}080\), so operating cash flow is \(\$36{,}000-\$10{,}080+\$24{,}000=\$49{,}920\). The additional $4,000 NWC investment makes year-1 project cash flow \(\$49{,}920-\$4{,}000=\$45{,}920\).
Year 2. Taxable operating income is \(\$72{,}000-\$24{,}000=\$48{,}000\). Tax is \(0.28(\$48{,}000)=\$13{,}440\), and operating cash flow is \(\$48{,}000-\$13{,}440+\$24{,}000=\$58{,}560\). There is no NWC change in year 2.
Year 3 and disposal. Taxable operating income is \(\$84{,}000-\$24{,}000=\$60{,}000\). Tax is \(0.28(\$60{,}000)=\$16{,}800\), and operating cash flow is \(\$60{,}000-\$16{,}800+\$24{,}000=\$67{,}200\). After three years, tax book value is \(\$96{,}000-3(\$24{,}000)=\$24{,}000\). Since the sale price is also $24,000, there is no taxable gain or deductible loss, and after-tax salvage is $24,000. NWC accumulated to \(\$10{,}000+\$4{,}000=\$14{,}000\), all of which is recovered. Year-3 cash flow is \(\$67{,}200+\$24{,}000+\$14{,}000=\$105{,}200\).
Check. The complete schedule is time 0: \(-\$106{,}000\); year 1: \(\$45{,}920\); year 2: \(\$58{,}560\); year 3: \(\$105{,}200\). Selling at book value creates no disposal tax effect, but the $24,000 sale proceeds remain a cash inflow.
Common Mistakes and Limits of the Calculation
A frequent error is to calculate the disposal gain or loss using the asset’s original cost instead of its tax book value at the sale date. Another is to call the sale price “after-tax salvage” without checking whether the asset has a gain or loss. These errors can materially change the terminal-year cash flow.
For example, using the second worked example, the incorrect calculation might treat the $31,000 sale price as the after-tax salvage and report terminal cash flow of \(\$58{,}500+\$31{,}000+\$10{,}000=\$99{,}500\). This omits the $2,700 tax benefit from the deductible $9,000 loss. Under the stated assumptions, the correction is to use after-tax salvage of \(\$31{,}000+\$2{,}700=\$33{,}700\), giving terminal cash flow of $102,200.
The immediate tax treatment is an assumption, not a universal guarantee. A loss may not create an immediately usable tax benefit if the project or firm cannot use the deduction in that period. In that case, the cash-flow schedule should reflect when the benefit can actually be realized, rather than adding it automatically at disposal. A schedule should also avoid counting the NWC recovery twice: it is the release of the balance built up through prior investments, not a second operating cash inflow.
Check Your Understanding
For each hypothetical project, assume the stated disposal tax effect is immediately usable. Give the requested cash flow in dollars.
- Equipment costs $60,000 and is depreciated by $15,000 per year. At the end of year 2 it sells for $24,000. The tax rate is 25%, year-2 EBITDA is $40,000, and $5,000 of NWC is recovered at termination. What is total year-2 cash flow? (Answer: $64,250)
- Equipment costs $200,000 and is depreciated by $40,000 per year. It sells at the end of year 3 for $95,000. The tax rate is 30%, year-3 EBITDA is $110,000, and $14,000 of NWC is recovered. What is total year-3 cash flow? (Answer: $193,500)
- Equipment costs $75,000 and is depreciated by $15,000 per year. At the end of year 3 it sells for $18,000. The tax rate is 20%, year-3 EBITDA is $70,000, and the project recovers $8,000 of NWC. What is total year-3 cash flow? (Answer: $87,400)
- An asset with original cost $140,000 has accumulated tax depreciation of $105,000 when it is sold for $50,000. At a 24% tax rate, what are its tax book value and after-tax salvage? (Answer: tax book value $35,000; after-tax salvage $46,400)
- Equipment costs $180,000 and is depreciated by $30,000 per year for four years. It sells at the end of year 4 for $48,000. The tax rate is 30%, year-4 EBITDA is $100,000, and $17,000 of NWC is recovered. What is total year-4 cash flow? (Answer: $147,600)