Discounted cash flow (DCF) valuation

Key takeaways

• Unlevered free cash flow equals NOPAT plus depreciation and amortization, less capital expenditure, less the increase in net working capital.
• Discounting unlevered free cash flow at WACC gives enterprise value; equity value follows by subtracting net debt and other claims.
• Terminal value usually makes up most of enterprise value, so the Gordon growth and exit multiple methods should be cross-checked through the implied multiple and implied growth rate.
• The mid-year convention assumes cash arrives evenly through each year and raises value relative to end-of-year discounting.
• A DCF is only as reliable as its inputs: present it with a sensitivity table of WACC against terminal growth, never as a single number.
• Free cash flow to equity, discounted at the cost of equity, values equity directly and must use consistent assumptions about borrowing.

The idea: value equals discounted future cash

A dollar received in five years is worth less than a dollar today, for two reasons: today's dollar could be invested in the meantime, and the future dollar might not arrive. Discounting reverses compounding. At a 9 percent annual rate, $100 due in one year is worth $100 / 1.09 = $91.74 today.

An unlevered DCF discounts the cash flows the operating business generates before any payment to lenders or shareholders. Those cash flows belong to all capital providers together, so they are discounted at the weighted average cost of capital (WACC), which blends the returns required by lenders and shareholders. The result is enterprise value. Subtracting net debt and other claims gives equity value.

Because no forecast can run forever, the valuation is split in two. An explicit forecast period, commonly five to ten years, projects cash flows year by year. A terminal value captures everything after that, on the assumption that the business has reached a steady state. The explicit period should be long enough for the company to reach that steady state; a fast-growing company needs a longer one.

Unlevered free cash flow from EBIT

Unlevered free cash flow, also called free cash flow to the firm (FCFF), is the cash the operations produce after paying taxes and reinvesting in the business, before any financing flows. Start from EBIT (earnings before interest and taxes), because it is operating profit before the cost of debt.

Tax EBIT as if the company had no debt: NOPAT, net operating profit after tax, equals EBIT times one minus the tax rate. This deliberately ignores the tax saving from interest. That saving is not lost; it is captured in the discount rate, where the cost of debt enters WACC after tax. Counting it in both places would double count it.

Then adjust for the gap between accounting profit and cash. Add back depreciation and amortization (D&A), which reduce EBIT but are not cash payments. Subtract capital expenditure (capex), the cash spent on fixed assets. Subtract the increase in net working capital (receivables plus inventory less payables and similar operating items), because a growing business ties up more cash in operations. A decrease in working capital releases cash and is added.

Leave out items that belong to financing (interest, debt issues and repayments, dividends) and non-operating items whose value is added separately in the bridge. Share-based compensation is a real cost; the conservative treatment keeps it as an expense in EBIT rather than adding it back.

The five-year projection

The forecast drives everything, so each line should rest on an argument: revenue growth from market growth, share gains and pricing; margins from the cost structure and operating leverage; capex and working capital from what the growth requires. Expressing D&A, capex and working capital as percentages of revenue is a common simplification that keeps the model internally consistent, provided the percentages make economic sense.

Brackley's growth fades from 8 percent to 4 percent over five years as it approaches a mature rate. Margins are held flat for clarity. Capex runs slightly above D&A throughout, which is what a growing manufacturer needs: depreciation reflects the historical cost of assets bought when the company was smaller, and growth requires net new capacity.

Terminal value by the Gordon growth method

The Gordon growth method, also called the perpetuity growth method, assumes that from the year after the forecast the free cash flow grows at a constant rate forever. The value at the end of year n of a cash flow stream that starts at FCFF(n+1) and grows at g is FCFF(n+1) / (WACC - g). The formula only works if WACC exceeds g.

The terminal growth rate should be a rate the business can sustain indefinitely. No company can outgrow the economy it sells into forever, so practitioners typically anchor g at or below long-run expected nominal growth of the relevant economy, and in practice often at or near expected long-run inflation. The rate must also be consistent with the currency of the cash flows: a forecast in a high-inflation currency supports a higher nominal g, and a correspondingly higher WACC.

Growth is not free. A business that grows needs reinvestment, so the terminal year's free cash flow must reflect the capex and working capital needed to support g, not the heavier reinvestment of the high-growth forecast years or no reinvestment at all. The textbook shortcut used below grows year 5 free cash flow by g; the pitfall at the end of this topic shows how to normalize it.

Terminal value by exit multiple, and the cross-checks

The exit multiple method assumes the business is sold at the end of the forecast at a multiple of its final-year metric, typically EV/EBITDA. It connects the DCF to market pricing and is the natural choice for a private equity investor who really does plan to sell. Its weakness is circularity: a DCF is supposed to be an intrinsic value, and an exit multiple imports today's market valuation into the terminal year.

Neither method is right by itself, so each is used to check the other. From a Gordon growth terminal value, compute the EV/EBITDA multiple it implies. From an exit multiple terminal value, solve the Gordon formula backward for the perpetual growth rate it implies. If a 9.0x exit implies growth of 6 percent forever, the multiple is too high; if a 2 percent growth assumption implies an exit multiple far below where mature peers trade, one of the inputs deserves another look.

End-of-year and mid-year discounting

Discounting year 1 cash flow by a full year assumes it all arrives on the last day of the year. In reality a business generates cash throughout the year. The mid-year convention discounts each year's cash flow by half a year less, as if it all arrived at the midpoint: exponents of 0.5, 1.5, 2.5 and so on. It raises value because the cash arrives sooner.

The terminal value needs care. The Gordon growth terminal value is the value of a stream of mid-year cash flows, so under the mid-year convention it is discounted with exponent n - 0.5 (4.5 for a five-year forecast). An exit multiple terminal value represents a sale at a point in time, the end of year n, so it keeps exponent n. Mixing these up is a common source of small but real errors.

From enterprise value to a share price, and the sensitivity table

The bridge from enterprise value to equity value is the same one used for multiples: subtract debt, preferred stock, non-controlling interest and other debt-like claims, and add cash and non-operating assets whose income is not in the free cash flow. Divide by fully diluted shares to reach a value per share.

Because terminal value dominates, the two inputs that drive it, WACC and terminal growth, deserve a sensitivity table. Each cell recomputes the whole valuation. The grid below uses the Gordon growth method and end-of-year discounting, so its center cell matches the base case. Notice the asymmetry: value rises faster as WACC falls and growth rises, because the denominator WACC - g shrinks toward zero.

Free cash flow to equity, and where DCFs go wrong

A DCF can also value equity directly. Free cash flow to equity (FCFE) is the cash left for shareholders after interest (net of its tax shield) and after net borrowing or repayment. Discounted at the cost of equity, not WACC, it gives equity value with no bridge. Banks and insurers are usually valued this way, because for them debt is raw material rather than financing, and so is a business whose capital structure will change on a set schedule.

In theory the two models give the same equity value when their assumptions are consistent. In practice they diverge whenever the leverage assumed in WACC differs from the borrowing assumed in the FCFE forecast. An FCFE model that assumes heavy borrowing inflates near-term cash flow to equity, and must raise the cost of equity to match the extra risk. A buyout model is effectively an FCFE model with a specific debt schedule, which is why it is built separately.