💵 Discounted Cash Flow (DCF)

Discounted Cash Flow (DCF) valuation estimates the intrinsic value of an asset as the present value of the cash flows it is expected to generate, discounted at a rate that reflects their risk. The idea is old and foundational: John Burr Williams formalised it in The Theory of Investment Value (1938), arguing that an investment is worth the present value of the cash it returns to its owners: "a stock is worth the present value of all the dividends ever to be paid upon it". Irving Fisher's earlier work on the theory of interest (1930) provided the conceptual basis of discounting future income. Modern practitioners systematised the method in texts such as Aswath Damodaran's Investment Valuation and McKinsey's Valuation (Koller, Goedhart & Wessels).

The mechanics are always the same three steps: (1) project the future free cash flows over an explicit horizon; (2) estimate a terminal value that captures everything beyond that horizon; (3) discount both back to today at the appropriate cost of capital, then bridge from firm value to the value of the equity and, finally, to a value per share. What changes between approaches is WHICH cash flow you discount and at WHICH rate. The two must always be consistent.

FCFF (Free Cash Flow to Firm) is the cash available to all capital providers, before financing. It is computed as EBIT×(1-tax) + D&A - CapEx - ΔNet Working Capital, and is discounted at the Weighted Average Cost of Capital (WACC) to give the Enterprise Value. FCFE (Free Cash Flow to Equity) is the cash left for shareholders after debt payments (FCFF - after-tax interest + net new borrowing) and is discounted at the cost of equity (Re) to give the Equity Value directly. The two methods are equivalent when the capital structure is held constant; discounting FCFF at Re (or vice versa) is a classic error.

The cost of equity is most commonly estimated with the Capital Asset Pricing Model (Sharpe, 1964; Lintner, 1965): Re = Rf + β·ERP, where Rf is the risk-free rate, β the sensitivity to the market, and ERP the equity risk premium. Alternatives include the build-up model (adding size and company-specific risk premia, common for private firms) and multifactor models such as Fama-French (1992, 1993), which add size and value factors. Beta itself can be the raw historical estimate, the Blume-adjusted beta (0.67·raw + 0.33), or a bottom-up beta built by unlevering and relevering comparable companies' betas via the Hamada equation.

A third approach, Adjusted Present Value (APV), separates the value of the business from the value of financing. Introduced by Stewart Myers (1974), APV values the unlevered cash flows at the unlevered cost of equity (Ru) and adds the present value of the interest tax shields separately. The rate used to discount those shields is itself a modelling choice: Modigliani-Miller (1963) with fixed debt discount them at the cost of debt; the Harris-Pringle / Miles-Ezzell frameworks, which assume debt is rebalanced to firm value, discount them at Ru. APV is especially useful when leverage changes materially over time, as in leveraged buyouts.

The terminal value typically dominates a DCF, so its assumptions deserve scrutiny. The Gordon growth (perpetuity) model, TV = FCF_N·(1+g)/(r-g) from Gordon & Shapiro (1956), assumes cash flows grow forever at a constant rate g, which must be below the discount rate and no higher than the long-run nominal growth of the economy. The McKinsey key value-driver formula, TV = NOPAT_{N+1}·(1-g/RONIC)/(r-g), links growth to the return on newly invested capital (RONIC), making explicit that growth only creates value when RONIC exceeds the cost of capital. The exit-multiple approach instead applies an EV/EBITDA or EV/EBIT multiple to the final-year metric, importing a market view of terminal value. Because the terminal value can easily be 70-90% of the total, always report its weight.

From Enterprise Value to value per share runs the "bridge": subtract net financial debt (debt minus cash), minority interests, preferred stock and pension deficits, add non-consolidated associates and other items, then divide by the (diluted) share count. With FCFE this step is shorter: the value is already equity, so net debt is not subtracted again.

The Reverse DCF flips the question. Instead of asking "what is it worth?", it asks "what is the market already assuming?" by taking the market price as a constraint and solving for the operating assumptions that justify it. Popularised by writers such as Michael Mauboussin (Expectations Investing, with Alfred Rappaport), it is mathematically one equation in several unknowns, so its honest form does not "find the assumptions" but frees one lever (giving a single implied value) or two levers (giving an iso-value frontier of combinations that all reproduce the price). It is most informative when it reveals that no plausible assumption can justify the current price. Rising Gamma's DCF module implements the forward valuation, the two-way sensitivity table, and both the single-lever and two-lever reverse analyses.

Every DCF is only as good as its inputs, and those inputs are assumptions, not facts. Small changes in the discount rate or the perpetual growth rate move the value substantially, which is why sensitivity analysis and a clear log of assumptions are integral to a credible valuation, not an afterthought. A DCF is an analytical tool for understanding value drivers, not a source of investment advice.