CFA Level I: Equity Valuation - Free Cash Flow Models

While accounting earnings can be manipulated, cash is a fact. Free cash flow models cut through accrual accounting to value a company based on the actual cash it generates and can distribute to its providers of capital. For analysts and investors, mastering these models is essential for building intrinsic valuations that are resilient to accounting distortions, providing a direct line of sight to a firm’s fundamental ability to create value.

Understanding the Core Cash Flows: FCFF and FCFE

All free cash flow models start with a precise definition of cash flow. Free cash flow to the firm (FCFF) is the cash available to all of the firm’s investors—both debt and equity holders—after the company has paid all operating expenses and made the necessary investments in working capital and fixed capital to maintain and grow the business. It is a pre-debt, after-tax cash flow.

FCFF can be calculated starting from net income, operating income, or EBITDA. A common and robust formula starting from earnings before interest and taxes (EBIT) is: $$FCFF=EBIT\times (1-TaxRate)+Depreciation-CapitalExpenditures-IncreaseinWorkingCapital$$ This formula adds back the non-cash charge of depreciation, then subtracts the cash outflows for reinvesting in the business (capex) and funding its growth (working capital).

In contrast, Free cash flow to equity (FCFE) is the cash available to the company’s common equity holders only, after all expenses, reinvestment, and debt financing flows (interest and principal payments). It can be derived directly from FCFF: $$FCFE=FCFF-Interest\times (1-TaxRate)+NetBorrowing$$ Here, you subtract the after-tax cost of debt financing paid to lenders and add the cash inflow from new borrowing (or subtract net debt repayment). FCFE represents the theoretical dividend-paying capacity of the firm.

Valuation Models: From Single-Stage to Multi-Stage

Once the appropriate stream of cash flows is projected, it must be discounted to present value. For FCFF, the correct discount rate is the weighted average cost of capital (WACC), which reflects the required returns of all capital providers. The value of the firm (enterprise value) is calculated as: $$ValueoftheFirm=\sum _{t=1}^n\frac{FCF{F}_t}{(1+WACC{)}^t}+\frac{TerminalValu{e}_n}{(1+WACC{)}^n}$$

For FCFE, the correct discount rate is the required rate of return on equity (r), often estimated using models like the CAPM. The value of equity is: $$ValueofEquity=\sum _{t=1}^n\frac{FCF{E}_t}{(1+r{)}^t}+\frac{TerminalValu{e}_n}{(1+r{)}^n}$$

The simplest implementation is the single-stage (Gordon growth) model, which assumes cash flows grow at a constant perpetual rate g. The formulas simplify to: $$ValueofFirm=\frac{FCF{F}_1}{WACC-g}$$ $$ValueofEquity=\frac{FCF{E}_1}{r-g}$$ This model is only suitable for mature, stable companies in a steady state.

Most companies, however, go through phases of growth, making multi-stage models necessary. A two-stage model, for example, might project a high-growth phase for a specific number of years, followed by a perpetual stable-growth phase. The valuation is the sum of the present value of the cash flows during the initial stage and the present value of the terminal value representing the subsequent perpetual stage.

Estimating Terminal Value and the Critical Growth Rate

Terminal value often constitutes a large percentage of total estimated value, making its calculation critical. The most common method is the Gordon growth model applied to terminal cash flow. The key assumption is the perpetual growth rate g. This rate must be realistic and cannot exceed the long-term growth rate of the economy (often proxied by nominal GDP growth). For a firm in perpetuity, it is also imprudent to assume a growth rate higher than the WACC or required return on equity, as the denominator would become negative or imply infinite value.

A prudent check is to examine the reinvestment implied by the terminal growth rate. The relationship is given by: $$g=ROIC\times ReinvestmentRate$$ Where ROIC is the return on invested capital. For the terminal period, analysts must ensure the assumed growth rate aligns with a plausible, sustainable ROIC and reinvestment rate for a mature company.

The Relationship Between FCFF and FCFE Valuation

While both approaches can be used to estimate the value of equity, they must reconcile. The FCFF approach values the entire enterprise. To find equity value, you subtract the market value of debt (and add cash if not already in working capital): $$ValueofEquity(fromFCFF)=ValueofFirm-MarketValueofDebt$$

The FCFE approach values equity directly. In a consistent forecast, both approaches should yield similar equity values, providing a useful sanity check for your model. The choice between them often depends on capital structure. If a company has a stable capital structure or is leveraged, FCFE can be more straightforward. If the firm’s capital structure is complex or changing significantly (e.g., high leverage or undergoing recapitalization), the FCFF approach is preferred because it is not impacted by the noise of debt repayments and issuances, allowing you to focus on core operating performance.

Common Pitfalls

1. Mismatching Cash Flows and Discount Rates: This is the cardinal sin. Discounting FCFF at the cost of equity or FCFE at the WACC will produce a fundamentally flawed and meaningless valuation. Always remember: FCFF → WACC; FCFE → Required Return on Equity.
2. Using Unrealistic Perpetual Growth Rates: Setting the terminal growth rate (g) too high is a classic error that inflates value. The perpetual growth rate must be less than the nominal growth rate of the economy and, for a mature company, likely less than the historical GDP growth rate. It is a mature, stable growth rate.
3. Incorrectly Handling Interest in FCFE: A common calculation mistake is using pre-tax interest when deriving FCFE from FCFF or net income. Remember, interest expense provides a tax shield, so you must use Interest × (1 - Tax Rate). Similarly, ensure net borrowing is included—forgetting it will misstate the cash available to equity holders.
4. Ignoring the Balance Sheet in Terminal Value: The terminal value formula $TV=\frac{FC{F}_1}{r-g}$ assumes the company is in a steady state. This implies stable margins and a consistent capital structure. Projecting terminal cash flows with margins or reinvestment rates that are incompatible with a mature, stable company is a subtle but significant mistake.

Summary

• Free cash flow models value a company based on its fundamental cash generation, with FCFF representing cash to all investors and FCFE representing cash available to equity holders only.
• The choice of discount rate is critical and must match the cash flow: FCFF is discounted at the WACC, while FCFE is discounted at the required return on equity.
• Multi-stage models are necessary for most companies, combining explicit forecast periods with a terminal value calculated using a perpetual growth model, where the growth rate (g) must be sustainable and less than the discount rate.
• The two approaches are linked; equity value from FCFF equals the value of the firm minus debt, and this should reconcile with the equity value derived directly from FCFE in a consistent model.
• Avoid fatal errors by never mismatching cash flows and discount rates, using plausible long-term growth assumptions, and correctly accounting for the tax shield on interest and net borrowing in FCFE calculations.