Capital Budgeting: Incremental Free Cash Flows

The cash flow we need

NPV uses free cash flow (FCF) — the cash a project actually generates that can be paid to debt or equity holders. Starting from operating projections:

$$\text{FCF} = \text{NOPAT} + \text{D\&A} - \Delta\text{WC} - \text{CapEx}.$$

Where:

• NOPAT = EBIT × (1 − tax rate). Operating profit, after taxes, before any financing costs. (Net income would also subtract interest expense; FCF deliberately excludes interest because the cost of debt is captured in the discount rate, not the cash flows.)
• D&A added back because it’s a non-cash deduction.
• ΔWC subtracted because growing receivables and inventory tie up cash even though they don’t show up in net income that year.
• CapEx subtracted in the year the cash leaves the firm.

In practice this is a two-step forecast. First project the project’s incremental earnings (revenue, costs, depreciation, taxes). Then convert those earnings to free cash flow with the adjustments above. Earnings are an accounting story; free cash flow is the cash the project actually throws off, and only the cash drives NPV.

Play with it

Year-1 revenue: $1000Revenue growth: 5.0%Gross margin: 30%Tax rate: 25%Working capital / sales: 10.0%Initial CapEx: $800Discount rate: 10.0%Horizon: 8 yrs

NPV = $512

FCF by year (additions above zero, subtractions below)

Cumulative NPV

Try this: hold revenue and margin constant, then double initial CapEx. Watch how the cumulative NPV curve sinks below zero before the project’s operating cash flows can recover. Capital intensity matters as much as profitability for NPV.

What to include — and what not to

The principles for what counts as an incremental cash flow:

1. Include opportunity costs. If the project uses a building you already own, the cash flow to include is what you’d otherwise have earned by renting or selling it. Not zero just because no money changes hands.

2. Include cannibalization (or growth) effects. Apple launching an iPhone replaces some iPod sales. The right incremental revenue counts only what’s new, net of erosion of existing products. If the new product also boosts Mac sales (the “halo” effect), include that too.

3. Exclude sunk costs. You spent $2M on market research before deciding whether to launch. That $2M is gone whether you launch or not. Do not include it in NPV. The decision is forward-looking; sunk costs are backward-looking.

4. Exclude financing cash flows. Interest, principal, and dividends are not in FCF. They belong in the discount rate. Including them double-counts the cost of capital.

5. Allocate overhead carefully. A new product line is often charged a share of corporate overhead (HR, the head office, existing IT). Include only the overhead that actually rises because of the project. Costs the firm would incur anyway are not incremental, even when the accountants assign a slice of them to the project.

Working capital — the hidden cost of growth

Growing firms tie up cash in working capital even when they’re profitable. Each new dollar of revenue typically requires an extra $0.10-$0.20 of working capital (accounts receivable + inventory − accounts payable). For a fast-growing project:

• ΔAR rises with sales (booked revenue not yet collected).
• ΔInventory rises with sales (cash spent on product not yet sold).
• ΔAP rises with COGS (cash owed to suppliers but not yet paid).
• ΔWC = ΔAR + ΔInventory − ΔAP.

When ΔWC > 0, it subtracts from FCF. This is why a profitable growing company can still need outside financing — the income statement says everything is fine, the cash flow statement says you need money.

Reverse direction: when a project winds down, working capital is released (collected receivables, sold inventory). Don’t forget this at the project’s terminal year — it’s real cash.

Terminal value

Most projects don’t have a natural end. Two common ways to capture value beyond the forecast horizon:

Gordon growth (perpetuity). Assume year $T+1$ cash flow grows forever at rate $g$, with discount rate $r$:

$$TV_T = \frac{FCF_{T+1}}{r - g}.$$

The total PV is then the explicit forecast plus $TV_T / (1+r)^T$. Be conservative with $g$: long-run terminal growth shouldn’t exceed the long-run growth of the broader economy (call it 2-3% in real terms).

Exit multiple. Assume the project (or business) sells in year $T$ for some multiple of its EBITDA or EBIT. Used heavily in private-equity and M&A valuations:

$$TV_T = \text{Exit multiple} \times \text{EBITDA}_T.$$

Both methods are sensitive to assumptions. Sensitivity-test them both (next lesson).

A worked summary

Suppose a 5-year project with year-1 revenue $1,000, growing 5% annually, gross margin 30%, tax rate 25%, working capital at 10% of sales, initial CapEx $800 with 5-year straight-line depreciation, no maintenance CapEx. Discount rate 10%. Terminal value via Gordon with $g = 2\%$.

The interactive viz above calculates all this in real time. Slide the inputs and watch NPV move. The lesson here is that NPV is not one number — it’s a function of every input you put in. The next lesson is about how to be honest about that uncertainty.