Free Cash Flow to the Firm (FCFF): Cash available to shareholders and bondholders after taxes, capital investment, and WC investment.

Free Cash Flow to Equity (FCFE): Cash available to stockholders after payments to and inflows from bondholders. It is the cash flow from operations net of capital expenditures and debt payments (including both interest and repayment of principal).

Free cash flow models belong to the group of discounted cash flow valuation models. They are quite similar to another DCF model - the dividend discount model. The main difference is the definition of cash flows. It is also very important to use the correct rate for discounting free cash flows in the two models. The discounting rate is the average cost of capital supplied by the parties that have claims on the cash flow. Consequently, we use WACC for discounting FCFF and cost of equity for discounting FCFE.

Present value of FCFF

Firm value = FCFF discounted at the WACC.

Firm value = Σ [FCFF_t / (1 + WACC)_t)]
Σ: t = 1 to infinite.

Equity value = firm value - debt value.

Equity value = Firm value - MV_d
MV_d: the market value of debt.

Dividing the total value of equity by the number of outstanding shares gives the value per share.

WACC can be either based on the current market weights of equity and debt or target weights. In case of market weights-based WACC, the formula is

WACC = MV_d / [MV_d + MV_e] x r_d (1 - T) + MV_e / [MV_d + MV_e] x r_e

Where

• MV_d is the market value of debt.
• MV_e is the market value of equity.
• r_d is the pre-tax cost of debt.
• r_e is the cost of equity.
• T is the tax rate.

The cost of debt can be obtained directly from the market as the yield to maturity on the company's debt or comparable companies' debt. To calculate the cost of equity we can use methods such as CAPM, APT or cost of debt plus risk premium.

If FCFF is growing at a constant rate g, the value of the firm is:

Firm value = FCFF₁/(WACC - g) = FCFF₀(1 + g) / (WACC - g)

Present value of FCFE

Equity value = FCFE discounted at the required return on equity (r).

These cash flows belong to the stockholders only. Therefore, the present value of FCFE stream gives us the intrinsic value of a company:

Equity value = Σ[FCFE_t / (1 + r_e)^t]
Σ: t = 1 to infinite.

Similarly, if FCFE is growing at a constant rate g, the value of the equity is:

Equity value = FCFE₁/(r - g) = FCFE₀(1 + g) / (r - g)

Strengths and limitations of the FCFE model.

Advantages:

• Wide applicability for different dividend and financing policies.
  Free cash flow always reflects the capital that can potentially be paid out to shareholders, notwithstanding the dividend policy. This model is preferable to DDM models, when actual dividends differ significantly from FCFE.

• In contrast to dividends, a record of free cash flows is observable for any company.

• Since FCF model is based on the capital exceeding operational needs, it is useful for valuation of control ownership that allows investors to redeploy this capital.

Disadvantages:

• If FCF < 0 due to capital demands.
  Many companies have negative free cash flow for years due to large capital demands. Since prediction of free cash flow far in the future would be imprecise, FCF model cannot be used for growth companies.

The implicit ownership perspective

• FCF models are useful for control perspective. Acquirer can change the firm's dividend policy.
  FCFE represents cash flow that can be redeployed outside the company without affecting the company's capital investments. A controlling equity interest can affect such a redeployment. If an investor can take control of a company, dividends can be changed substantially, possibly coming closer to the company's capacity to pay dividends. Consequently, historical dividend patterns may not necessarily be a good basis for valuation of control ownership interest in a company. Since free cash flow to equity is a measure of potential dividend payments, it is a more relevant indicator for valuation of company control.

• Dividend discount models are useful for minority shareholder perspective with no control over dividend policy.