From Accounting Forecasts to Project Cash Flows
Accounting forecasts are usually expressed as revenues, expenses, depreciation, taxes, and net income. A project cash-flow forecast must instead show the cash generated or used at each date. The conversion is not simply a matter of copying net income: depreciation reduces accounting income but is not a cash payment, capital expenditures are cash outflows that may not appear as current-period expenses, and changes in net working capital tie up or release cash.
The central task is to keep three things distinct: operating cash flow, investment in long-term assets, and investment in net working capital. Taxes must be based on the project’s taxable income under the stated tax assumptions. This framework is aligned with the SOA VEE Accounting and Finance syllabus.
For the standard EBIT-based conversion below, assume no interest expense is included in the project forecast, the tax rate is constant, taxable income is positive, tax losses do not restrict the tax benefit, and book depreciation equals tax depreciation. Under these assumptions, let \(R_t\) be revenue, \(C_t\) cash operating costs, \(D_t\) depreciation, and \(T\) the tax rate. Then \(EBIT_t=R_t-C_t-D_t\), and cash taxes are \(T\,EBIT_t\).
Here \(NI_t\) is net income from the project’s operations under the stated assumptions, and \(CapEx_t\) is cash spent on long-term project assets during the period. The initial project outlay is recorded at time 0 when incurred; it is not a current-period operating expense. If the initial date also requires working capital, that investment is a separate time-0 cash outflow.
Why Depreciation Is Added Back
The add-back is needed because depreciation is subtracted to calculate accounting EBIT, but it is not a cash payment in the period. Its tax effect remains important: when depreciation reduces taxable income, it reduces cash taxes. The result is that the project receives a depreciation tax shield, equal under the standard assumptions to \(TD_t\).
Project revenue less cash operating costs is \(R_t-C_t\).
Subtract depreciation: \(EBIT_t=R_t-C_t-D_t\). Cash taxes are \(T(R_t-C_t-D_t)\) under the stated assumptions.
\(OCF_t=(R_t-C_t)-T(R_t-C_t-D_t)\).
\((R_t-C_t)-T(R_t-C_t-D_t)=(R_t-C_t)(1-T)+TD_t\). Thus depreciation affects cash flow through its tax shield, not as a cash receipt.
This derivation also explains why adding back depreciation to net income does not mean depreciation is irrelevant. It removes a noncash expense from the cash-flow calculation while retaining the cash-tax reduction that the deduction creates.
Worked Example: One-Year Forecast With a Working-Capital Increase
A hypothetical project forecasts revenue of $520,000, cash operating costs of $342,000, and depreciation of $28,000 for the year. The tax rate is 25%; book and tax depreciation are equal; taxable income is positive; and there are no interest costs or tax-loss limitations. Capital expenditures during the year are $46,000. Net working capital rises from $24,000 to $31,000. Find net income, operating cash flow, and project free cash flow. The method is to calculate taxes from EBIT, add back noncash depreciation, then deduct capital expenditures and the working-capital increase. This avoids treating depreciation as a cash cost or reversing the sign of the NWC change.
1. Calculate EBIT.
2. Calculate cash taxes and net income. Taxes are \(0.25(150{,}000)=\$37{,}500\). Therefore, net income is \(\$150{,}000-\$37{,}500=\$112{,}500\).
3. Convert net income to operating cash flow. Depreciation is noncash, so add it back: \(OCF=\$112{,}500+\$28{,}000=\$140{,}500\).
4. Find the change in net working capital. \(\Delta NWC=\$31{,}000-\$24{,}000=\$7{,}000\), an increase and therefore a cash use.
5. Calculate project free cash flow. \(FCF=\$140{,}500-\$46{,}000-\$7{,}000=\$87{,}500\).
Check. Cash before taxes is \(\$520{,}000-\$342{,}000=\$178{,}000\). Subtracting cash taxes of \(\$37{,}500\) gives the same operating cash flow, \(\$140{,}500\). After the two cash uses, free cash flow is \(\$87{,}500\).
Separate Operating Cash Flow From Investment
The operating calculation answers how much cash the project’s operations generate after taxes. It does not include purchases of long-term assets or changes in working capital. Those adjustments are made afterward, with signs tied to the direction of cash movement:
| Item | Cash-flow treatment | Reason |
|---|---|---|
| Capital expenditure | Subtract \(CapEx_t\) | Cash is spent to acquire or improve a long-term project asset. |
| Increase in NWC | Subtract \(\Delta NWC_t\) | More cash is tied up in the project’s current operating investment. |
| Decrease in NWC | Subtract a negative \(\Delta NWC_t\), adding cash | Previously tied-up cash is released. |
| Depreciation | Add back after net income, or use the EBIT-based OCF formula | It reduces accounting income but is not a period cash payment. |
Working capital is measured as a balance, while the project cash flow uses its change during the period. A balance of $20,000 is not automatically a $20,000 cash outflow every year. If the balance rises from $20,000 to $23,000, the period’s investment is $3,000. If it falls from $23,000 to $20,000, the project releases $3,000. Initial funding is captured at time 0, and any later recovery is captured as a decrease in the balance.
Worked Example: Building Cash Flows Across Three Years
A hypothetical three-year project has a 25% tax rate, no interest expense or tax-loss limitation, positive taxable income in every year, and equal book and tax depreciation. Its forecasts are shown below. Find the time-0 cash flow and each year’s free cash flow. At time 0, the project spends $90,000 on equipment and invests $10,000 in NWC.
| Year | Revenue | Cash costs | Depreciation | Capital expenditures | Ending NWC |
|---|---|---|---|---|---|
| 1 | $260,000 | $180,000 | $20,000 | $8,000 | $14,000 |
| 2 | $300,000 | $190,000 | $20,000 | $16,000 | $19,000 |
| 3 | $320,000 | $200,000 | $20,000 | $0 | $0 |
The method is to compute annual operating cash flow first, then apply the year-specific capital expenditure and change in NWC. This avoids subtracting the entire NWC balance in each year instead of just its change.
Time 0. The equipment purchase and initial NWC investment are both cash outflows: \(-\$90{,}000-\$10{,}000=-\$100{,}000\).
Year 1. \(EBIT_1=\$260{,}000-\$180{,}000-\$20{,}000=\$60{,}000\). Taxes are \(0.25(\$60{,}000)=\$15{,}000\), and net income is \(\$45{,}000\). Operating cash flow is \(\$45{,}000+\$20{,}000=\$65{,}000\). The NWC change is \(\$14{,}000-\$10{,}000=\$4{,}000\). Thus \(FCF_1=\$65{,}000-\$8{,}000-\$4{,}000=\$53{,}000\).
Year 2. \(EBIT_2=\$300{,}000-\$190{,}000-\$20{,}000=\$90{,}000\). Taxes are \(\$22{,}500\), net income is \(\$67{,}500\), and operating cash flow is \(\$67{,}500+\$20{,}000=\$87{,}500\). The NWC change is \(\$19{,}000-\$14{,}000=\$5{,}000\). Thus \(FCF_2=\$87{,}500-\$16{,}000-\$5{,}000=\$66{,}500\).
Year 3. \(EBIT_3=\$320{,}000-\$200{,}000-\$20{,}000=\$100{,}000\). Taxes are \(\$25{,}000\), net income is \(\$75{,}000\), and operating cash flow is \(\$75{,}000+\$20{,}000=\$95{,}000\). NWC falls from $19,000 to $0, so \(\Delta NWC_3=\$0-\$19{,}000=-\$19{,}000\). Therefore \(FCF_3=\$95{,}000-\$0-(-\$19{,}000)=\$114{,}000\).
Check. The Year 3 NWC decrease adds $19,000 to operating cash flow, giving $114,000. The time-0 cash flow includes both initial investments, not just the equipment purchase.
When Book and Tax Depreciation Differ
An accounting forecast may use one depreciation amount for reporting income and another for calculating taxable income. In that case, do not automatically calculate cash taxes by applying the tax rate to book EBIT. Use tax depreciation to determine the project’s taxable income and cash taxes. If the accounting net income supplied is based on book depreciation and a book tax expense at the stated rate, the reconciliation is:
This reconciliation presumes positive taxable income, no tax-loss limitations, and that the stated book tax expense is calculated at the same rate on book EBIT. Actual financial statements may distinguish current and deferred tax expense; a project cash-flow estimate needs the cash-tax amount, not an unexamined reported tax-expense figure.
Worked Example: Reconciling Different Book and Tax Depreciation
A hypothetical project forecasts revenue of $400,000 and cash operating costs of $250,000. Book depreciation is $30,000, but tax depreciation is $40,000. The tax rate is 25%, taxable income is positive, and there are no interest costs or tax-loss limitations. Capital expenditures are $35,000, and NWC falls from $18,000 to $12,000. Assume the accounting net income forecast uses book depreciation and a 25% tax expense on book EBIT. Find project free cash flow. The method is to use tax depreciation for cash taxes and reconcile from book net income. This avoids taxing book EBIT when the tax deduction is based on a different depreciation amount.
1. Calculate book EBIT, book tax expense, and net income. Book EBIT is \(\$400{,}000-\$250{,}000-\$30{,}000=\$120{,}000\). The stated book tax expense is \(0.25(\$120{,}000)=\$30{,}000\), so book net income is \(\$120{,}000-\$30{,}000=\$90{,}000\).
2. Calculate cash taxes using tax depreciation. Taxable operating income is \(\$400{,}000-\$250{,}000-\$40{,}000=\$110{,}000\). Cash taxes are \(0.25(\$110{,}000)=\$27{,}500\).
3. Calculate operating cash flow. Cash before taxes is \(\$400{,}000-\$250{,}000=\$150{,}000\), so operating cash flow is \(\$150{,}000-\$27{,}500=\$122{,}500\). As a reconciliation, add book depreciation and the additional tax shield from the $10,000 excess of tax over book depreciation: \(\$90{,}000+\$30{,}000+0.25(\$40{,}000-\$30{,}000)=\$122{,}500\).
4. Adjust for investments. \(\Delta NWC=\$12{,}000-\$18{,}000=-\$6{,}000\), a cash release. Therefore \(FCF=\$122{,}500-\$35{,}000-(-\$6{,}000)=\$93{,}500\).
Check. The direct cash calculation and the reconciliation both give operating cash flow of $122,500. Adding the $6,000 working-capital release and subtracting $35,000 of capital expenditures gives free cash flow of $93,500.
Common Exam Traps and Applicability
- Leaving depreciation as a cash cost. It reduces taxable income, but it is not a cash payment. Add it back when starting from net income, or use the EBIT-based formula that already accounts for its tax effect.
- Using the NWC balance instead of its change. The period cash adjustment is \(-\Delta NWC_t\), not \(-NWC_t\). A fall in NWC creates a positive cash-flow adjustment.
- Subtracting capital expenditures twice. Capital expenditures are cash investment outflows. They are not deducted again as operating expenses merely because depreciation is also included in the income forecast.
- Applying the tax rate to the wrong income measure. Under the standard EBIT method, cash taxes use taxable operating income. If tax depreciation differs from book depreciation, adjust the tax calculation accordingly.
- Applying the simple tax formula when its assumptions fail. If taxable income is negative or tax losses cannot be used immediately, cash taxes and tax benefits may differ from \(T\,EBIT\). If interest is included, distinguish operating project cash flow from financing cash flows rather than silently including interest in operating costs.
A reliable check is to compute operating cash flow in two ways when the assumptions permit: from net income plus depreciation, and from cash revenue less cash operating costs less cash taxes. Then independently verify each capital expenditure and each change in NWC against its dates and direction.
Check Your Understanding
Use the stated assumptions in each problem. Answers are shown at the end of each question.
- A project has annual revenue of $180,000, cash costs of $120,000, and depreciation of $10,000. The tax rate is 20%; book and tax depreciation are equal; taxable income is positive; and there are no interest costs or tax-loss limits. Capital expenditures are $15,000, and NWC rises from $12,000 to $17,000. Find project free cash flow. (Answer: $30,000)
- A hypothetical project forecasts revenue of $500,000, cash operating costs of $330,000, and depreciation of $40,000. The tax rate is 30%, book and tax depreciation are equal, and taxable income is positive with no interest costs or tax-loss limits. Capital expenditures are $25,000, and NWC declines from $20,000 to $14,000. Find operating cash flow and project free cash flow. (Answer: operating cash flow $131,000; free cash flow $112,000)
- A three-year project has a 25% tax rate, positive taxable income, no interest costs or tax-loss limits, and equal book and tax depreciation. At time 0 it spends $60,000 on equipment and invests $5,000 in NWC. Annual data are: Year 1 revenue $240,000, cash costs $160,000, depreciation $20,000, capital expenditures $10,000, ending NWC $9,000; Year 2 revenue $280,000, cash costs $180,000, depreciation $20,000, capital expenditures $12,000, ending NWC $11,000; Year 3 revenue $300,000, cash costs $190,000, depreciation $20,000, no capital expenditures, ending NWC $0. Find the time-0 cash flow and each annual free cash flow. (Answer: time 0 \(-\$65,000\); Year 1 $51,000; Year 2 $66,000; Year 3 $98,500)
- A project has revenue of $220,000, cash costs of $140,000, book depreciation of $12,000, and tax depreciation of $20,000. The tax rate is 25%; taxable income is positive; and there are no interest costs or tax-loss limits. Assume book tax expense is 25% of book EBIT. Capital expenditures are $18,000, and NWC falls from $10,000 to $7,000. Find project free cash flow. (Answer: $50,000)
- At time 0, a project spends $70,000 on equipment and invests $6,000 in NWC. It has a 20% tax rate, positive taxable income, no interest costs or tax-loss limits, and equal book and tax depreciation. In Year 1, revenue is $150,000, cash costs are $100,000, depreciation is $10,000, capital expenditures are $4,000, and ending NWC is $9,000. In Year 2, revenue is $180,000, cash costs are $115,000, depreciation is $10,000, capital expenditures are zero, and all NWC is recovered. Find the time-0 cash flow and annual free cash flows. (Answer: time 0 \(-\$76,000\); Year 1 $35,000; Year 2 $63,000)