7.3  Assessing Intrinsic Value

 The intrinsic value of a firm in the free cash flow to equity model is defined as:

V₀ = (fcfe₁ + V₁)/(1 + k_e)                                                                                                            

Here, V₀ is the value of the stock, fcfe₁ is next period’s free cash flow to equity,   V₁ is the value in one period and k_e is the discount rate, which a model like CAPM equates to the stock’s cost of equity capital.  The equation says that the value must equal the present value of next period’s free cash flow to equity plus next period’s value, discounted by the cost of equity capital.

We can similarly write V₁ in terms of fcf₂ and V₂:

V₁ = (fcfe₂ + V₂)/(1 + k_e)                                                                               

And similarly for V₂, V₃¸and so on.

If we substitute for V₁ in equation 1), we get

V₀ = fcfe₁/(1+k_e) + (fcfe₂+V₂)/(1+k_e)²

By substituting for V₂, and then for V₃, and so on, we get the fundamental relationship that value of a stock equals the present value of future free cash flow to equity discounted at the stock’s cost of equity capital.  This is the definition of the intrinsic value of a stock:

Intrinsic value =V₀ = fcfe₁/(1+k_e) + fcfe₂/(1+k_e)² + fcfe₃/(1+k_e)³ + ….      

Analogous to the dividend model, the key to implementing this model to value a firm is to estimate free cash flow to equity and project it into the future.  The future values are usually determined by assuming that current free cash flows grow at some estimated growth rate.   

FCFE models come in a variety of flavors, mainly because there are several different ways to calculate the free cash flow.  For example, you can start with the income statement or the cash flow statement.  We implement one-stage and two-stage versions of the model in Valuation Tutor. 

We focus now on the three main inputs required for the FCFE models: economic dividends, growth behavior of economic dividends, and the discount rate or cost of equity capital.