Dividend Discount Model (DDM) and Free-Cash-Flow-to-Equity Model (FCFE)

If the issuing company is assumed to be a going concern, the intrinsic value of a share is the present value of expected future dividends. If a constant required rate of return is also assumed, then the DDM expression for the intrinsic value of a share is:

V_0=\sum_{t=1}^\infin \frac{D_t}{(1+r)^t}

where

V₀ = value of a share of stock today, at t = 0
D_t = expected dividend in year t, assumed to be paid at the end of the year
r = required rate of return on the stock

At the shareholder level, cash received from a common stock investment includes any dividends received and the proceeds when shares are sold. If an investor intends to buy and hold a share for one year, the value of the share today is the present value of two cash flows—namely, the expected dividend plus the expected selling price in one year:

V_0=\frac{D_1+P_1}{(1+R)^1}=\frac{D_1}{(1+r)^1}+\frac{P_1}{(1+r)^1}

where P₁ = the expected price per share at t = 1.

To estimate the expected selling price, P₁, the analyst could estimate the price another investor with a one-year holding period would pay for the share in one year. If V₀ is based on D₁ and P₁, it follows that P₁ could be estimated from D₂ and P₂:

P_1=\frac{D_2+P_2}{1+r}

Substituting the right side of this equation for P₁, results in results in V₀ estimated as:

V_0=\frac{D_1}{1+r}+\frac{D_2+P_2}{(1+r)^2}=\frac{D_1}{1+r}+\frac{D_2}{(1+r)^2}+\frac{P_2}{(1+r)^2}

Repeating this process, we find the value for n holding periods is the present value of the expected dividends for the n periods plus the present value of the expected price in n periods:

V_0=\frac{D_1}{1+r}+\dots+\frac{D_n}{(1+r)^n}+\frac{P_n}{(1+r)^n}

Using summation notation to represent the present value of the n expected dividends, we arrive at the general expression for an n-period holding period or investment horizon:

V_0=\sum_{t=1}^n\frac{D_t}{(1+r)^t}+\frac{P_n}{(1+r)^n}

The expected value of a share at the end of the investment horizon—in effect, the expected selling price—is often referred to as the terminal stock value (or terminal value).

The calculation of FCFE starts with the calculation of cash flow from operations (CFO). CFO is simply defined as net income plus non-cash expenses minus investment in working capital. FCFE is a measure of cash flow generated in a period that is available for distribution to common shareholders.

The entire CFO is not available for distribution; the portion of the CFO needed for fixed capital investment (FCInv) during the period to maintain the value of the company as a going concern is not viewed as available for distribution to common shareholders. Net amounts borrowed (borrowings minus repayments) are considered to be available for distribution to common shareholders. Thus, FCFE can be expressed as

FCFE = CFO – FCInv + Net borrowing

The information needed to calculate historical FCFE is available from a company’s statement of cash flows and financial disclosures. Frequently, under the assumption that management is acting in the interest of maintaining the value of the company as a going concern, reported capital expenditure is taken to represent FCInv. Analysts must make projections of financials to forecast future FCFE. Valuation obtained by using FCFE involves discounting expected future FCFE by the required rate of return on equity; the expression parallels:

V_0=\sum_{t=1}^\infin \frac{FCFE_t}{(1+r)^t}

How is the required rate of return for use in present value models estimated? To estimate the required rate of return on a share, analysts frequently use the capital asset pricing model (CAPM):