2.3 Capital Budgeting Cash Flows
Key Takeaways
- Build NPV from incremental cash flows only: ignore sunk costs; include opportunity costs, side effects, and cannibalization.
- After-tax salvage = salvage − t × (salvage − book). At a 25% tax rate, $45,000 salvage and $30,000 book produce $41,250 of after-tax salvage.
- Depreciation tax shield = t × Depreciation. $70,000 of depreciation at 25% tax is a $17,500 annual shield.
- Net working capital invested at t = 0 is a cash outflow and is recovered as an inflow at exit; NWC is not depreciated.
- Do not deduct interest in project cash flows when discounting at WACC — the after-tax cost of debt is already in the discount rate.
Which Cash Flows Belong in the NPV
Section 2.2 told you to accept when NPV is positive. That answer is only as good as the cash-flow vector you discount. CFI's corporate-finance treatment, and the unlevered free cash flow you will later build in DCF courses, both insist on incremental cash flows: the difference between the firm's cash flows with the project and without it. Accounting profit, allocated overhead, and "we already spent it" are not that difference.
Ignore Sunk Costs
A sunk cost is a cash outflow that has already been spent and will not be recovered whether you accept or reject. Last year's $18,000 feasibility study, a non-refundable deposit already wired, or R&D charged in a prior period does not enter Year 0 of the NPV. Managers like to "earn back" sunk costs. Capital budgeting does not. Including the $18,000 makes a good project look worse and a bad project look even worse, but it never changes the incremental decision correctly.
Include Opportunity Costs
An opportunity cost is the cash the firm forgoes by using an asset in this project instead of the next-best alternative. If the project occupies a building you could sell today for $80,000 with a book value of $50,000 and a 25% tax rate, the time-0 opportunity cost is the after-tax sale you skip:
After-tax sale = 80,000 − 0.25 × (80,000 − 50,000) = 80,000 − 7,500 = $72,500
Put −$72,500 at t = 0. Using "book value of $50,000" as the cost understates the sacrifice. Using the pre-tax $80,000 overstates it by the tax you would have paid on the $30,000 gain.
Side Effects and Cannibalization
Side effects are incremental cash flows the project causes elsewhere in the firm. Cannibalization is the common negative side effect: a new SKU steals sales from an existing SKU. If the new product takes $20,000 per year of pre-tax contribution margin from the old product, the after-tax drag at a 25% tax rate is 20,000 × (1 − 0.25) = $15,000 per year. Subtract that from project operating cash flow. Positive side effects (a new product that lifts complementary spare-parts sales) are added the same way. Allocated headquarters overhead that does not change in cash is not a side effect; extra cash overhead that does change is.
Net Working Capital
Net working capital (NWC) for project analysis is the incremental operating current assets minus incremental operating current liabilities the project requires — typically inventory + receivables − payables, not excess cash and not short-term debt. Launching a product usually invests NWC at t = 0 (or as sales ramp). That investment is a cash outflow. At the end of the project you recover NWC as inventory is sold and receivables are collected — a cash inflow. NWC is not depreciated and is not tax-deductible when invested; recovery is not taxable if you recover the same book dollars you put in. Forgetting recovery is a classic way to bias NPV down; forgetting the initial investment biases it up.
After-Tax Salvage and Book Value
When you sell a depreciable asset, the cash is not the headline salvage price. Tax applies to the gap versus book value:
After-tax salvage = salvage − t × (salvage − book)
If salvage > book, you pay tax on the gain. If salvage < book, t × (book − salvage) is a tax saving (a larger after-tax cash inflow than the salvage price). If salvage = book, there is no tax on the sale.
Worked numbers you will reuse below: salvage $45,000, book $30,000, t = 25%.
After-tax salvage = 45,000 − 0.25 × (45,000 − 30,000) = 45,000 − 3,750 = $41,250
Depreciation Tax Shield
Depreciation is not a cash outflow, but it reduces taxable income. The cash benefit is the depreciation tax shield:
Shield = t × Depreciation
Two equivalent operating-cash-flow identities, used throughout CFI unlevered-cash-flow work:
OCF = NOPAT + Depreciation
OCF = (Sales − cash operating costs) × (1 − t) + t × Depreciation
The second form makes the shield explicit. At t = 25% and depreciation = $70,000, the shield is $17,500 per year. Tax depreciation may follow a schedule that differs from book (for example, accelerated tax depreciation). The shield always uses tax depreciation, because that is what the tax authority allows. Straight-line to a salvage-linked book value is the clean exam setup; the identity does not change if the amounts do.
Do Not Put Interest in Project Cash Flows When You Discount at WACC
WACC already includes the after-tax cost of debt, Rd × (1 − t), weighted by the target debt share. If you also subtract interest in the project's operating cash flows, you double-count financing: once in the cash flows, once in the discount rate. Project cash flows for a WACC-based NPV are unlevered — they are the cash the assets generate before interest, after tax as if the firm had no debt on this project. That is the same logic as unlevered free cash flow in a DCF: NOPAT + D&A − capex − ΔNWC, with no interest subtracted.
Interest belongs in the cash flows only if you switch methods (for example, a levered-equity residual cash flow discounted at the cost of equity). FMVA core capital budgeting and DCF valuation discount unlevered cash at WACC. Leave interest out.
Worked Three-Year Project: Capex, NWC, Operations, Salvage
A manufacturer is evaluating a machine. Put every principle above on one timeline, then compute NPV at WACC. Year-end cash flows; do not apply mid-year unless the case says cash is earned evenly.
Given
| Item | Amount |
|---|---|
| Machine capex at t = 0 | $240,000 |
| Incremental NWC at t = 0, recovered at t = 3 | $30,000 |
| Economic and tax life | 3 years |
| Straight-line to ending book value | $30,000 |
| Expected salvage at t = 3 | $45,000 |
| Annual incremental sales | $180,000 |
| Annual cash operating costs | $95,000 |
| Tax rate t | 25% |
| WACC | 10% |
| Feasibility study spent last year | $18,000 (sunk — ignore) |
Step 1 — Depreciation and the Tax Shield
Annual depreciation = (cost − ending book) / life = (240,000 − 30,000) / 3 = $70,000
Depreciation tax shield = 0.25 × 70,000 = $17,500 per year
Step 2 — Annual Operating Cash Flow
EBIT = 180,000 − 95,000 − 70,000 = $15,000
Tax = 15,000 × 0.25 = $3,750
NOPAT = $11,250
OCF = NOPAT + depreciation = 11,250 + 70,000 = $81,250
Cross-check with the shield identity:
OCF = (180,000 − 95,000) × (1 − 0.25) + 70,000 × 0.25 = 85,000 × 0.75 + 17,500 = 63,750 + 17,500 = $81,250
There is no interest line. If someone built EBT = EBIT − interest, they have already broken the WACC method.
Step 3 — After-Tax Salvage and NWC Recovery at t = 3
After-tax salvage = 45,000 − 0.25 × (45,000 − 30,000) = $41,250
NWC recovery = +$30,000 (untaxed, same dollars that went out at t = 0)
Terminal non-operating cash = 41,250 + 30,000 = $71,250
Step 4 — Timeline
| Year | Capex | NWC | OCF | After-tax salvage | Project CF |
|---|---|---|---|---|---|
| 0 | −240,000 | −30,000 | — | — | −$270,000 |
| 1 | — | — | 81,250 | — | $81,250 |
| 2 | — | — | 81,250 | — | $81,250 |
| 3 | — | +30,000 | 81,250 | +41,250 | $152,500 |
The $18,000 study never appears. If the floor space had an after-tax opportunity cost, that amount would have been added to the t = 0 outflow. If the machine stole $20,000 of pre-tax margin from an old product, OCF would be $15,000 lower each year.
Step 5 — NPV at 10%
NPV = −270,000 + 81,250/1.10 + 81,250/1.21 + 152,500/1.331
= −270,000 + 73,863.64 + 67,148.76 + 114,575.51
= −$14,412
Reject. Accounting income was positive ($11,250 of NOPAT per year) and undiscounted inflows 81,250 + 81,250 + 152,500 = $315,000 exceed the $270,000 outlay, but at a 10% cost of capital the project destroys about $14,400 of value. That is the entire point of combining Section 2.1, 2.2, and 2.3: sign of profit ≠ sign of NPV.
Payback is 2 + (270,000 − 162,500) / 152,500 = 2.70 years, which might look "fine" against a three-year life. Discounted payback never arrives, because the present value of all inflows is only $255,588. Payback would have given the wrong primary decision.
Sensitivity Check (Same Costs, Higher Sales)
If incremental sales were $200,000 instead of $180,000, holding cash costs, depreciation, tax, NWC, and salvage fixed:
OCF = (200,000 − 95,000) × 0.75 + 17,500 = 78,750 + 17,500 = $96,250
Year-3 project CF = 96,250 + 41,250 + 30,000 = $167,500
NPV = −270,000 + 96,250/1.10 + 96,250/1.21 + 167,500/1.331 = +$22,891
The same machine accepts at $200,000 of sales. NPV lives in the cash-flow assumptions, which is why CFI drills scenario and sensitivity analysis after the three-statement and DCF cores. For this chapter, lock the method: incremental, after-tax, unlevered, NWC on and off the books, salvage taxed versus book, discount at WACC, then read the sign of NPV.
Exam Checklist for Project Cash Flows
- Start from cash with the project minus cash without it.
- Drop sunk costs. Add opportunity costs at after-tax resale value.
- Subtract after-tax cannibalization; add after-tax complements.
- Capex at t = 0 (and any mid-life capex) is an outflow; do not depreciate capex in the cash-flow row — depreciate it only to compute the tax shield.
- ΔNWC: outflow when the balance rises, inflow when it falls or is recovered.
- OCF = (Sales − cash costs)(1 − t) + t × (tax depreciation).
- After-tax salvage = salvage − t × (salvage − book).
- No interest in the cash flows when r is WACC.
- Then apply NPV from Section 2.2, with Excel NPV(rate, CF1:CFn) + CF0.
A machine will be sold for $45,000. Book value is $30,000. The tax rate is 25%. What is the after-tax salvage cash flow?
When you discount project cash flows at WACC, how should interest expense be treated?
A firm spent $18,000 last year on a feasibility study. The project needs $30,000 of net working capital at t = 0, recovered at t = 3. Which Year 0 treatment is correct?