Dividend discount and free-cash-flow-to-equity models

Why value a share as the present value of its cash flows?

An investment is worth what you expect to get from it, adjusted for when and how surely you get it. For a share that means cash. If the company is a going concern, the intrinsic value of a share is the present value of the cash flows it is expected to deliver to shareholders. The discount rate is the required rate of return on equity , which carries both the time value of money and the risk.

The simplest dividend discount model (DDM) says the cash flow is the dividend.

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

Here $D_t$ is the dividend expected at the end of year $t$ and $r$ is the required return. The sum runs forever because a company has no planned end date.

What if the investor sells after a few years?

Real investors do not hold forever. Over a holding period of $n$ years they receive $n$ dividends and then sell. The expected sale price is called the terminal stock value .

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

This does not contradict the infinite-horizon formula. The sale price $P_n$ is what the next buyer will pay, and that buyer is paying for the dividends after year $n$. Replace $P_n$ with the present value at year $n$ of those later dividends and you are back to the infinite sum. So the intrinsic value is the same whatever the investor’s own holding period. A one-year investor depends directly on the first dividend and indirectly on all later ones.

The one-year version is the building block for many exam questions.

$$V_0 = \frac{D_1 + P_1}{1 + r}$$

Where does the required return come from?

There is no single correct required return. Analysts most often use the capital asset pricing model: a risk-free rate plus the stock’s beta times the market risk premium. They can also add a judgment-based risk premium to a government bond yield, or add a premium to the yield on the company’s own bonds. Different analysts feed CAPM different inputs and so reach different answers. Many firms set required returns by policy. Portfolio Management develops CAPM.

$$r = R_f + \beta \times \text{market risk premium}$$

For example, a risk-free rate of 3%, a beta of 1.2 and a market risk premium of 5.5% give 3 + 1.2 × 5.5 = 9.6%.

What is the free-cash-flow-to-equity model?

Dividends are a choice. Many analysts prefer to value the cash a company could pay out, its dividend-paying capacity. Free-cash-flow-to-equity models discount free cash flow to equity (FCFE) in place of dividends. They are also the usual fallback for a company that pays no dividend, where forecasting the timing and size of the first dividend is mostly guesswork.

Start with cash flow from operations (CFO), which is net income plus non-cash expenses minus investment in working capital. Not all of it is available to shareholders. The company must spend on fixed capital to stay a going concern. Money borrowed, net of repayments, adds to what is available.

$$FCFE = CFO - FCInv + \text{net borrowing}$$

FCFEcash available to common shareholders

• Cash flow from operations (CFO) Memorize net income + non-cash charges − investment in working capital
• minus Fixed capital investment (FCInv) Memorize reported capital expenditure is the usual proxy
• plus Net borrowing Memorize new borrowing minus repayments, not gross borrowing

Historical FCFE comes from the statement of cash flows. Reported capital expenditure is usually taken as the fixed capital investment. Forecast FCFE needs projected financial statements.

The valuation mirrors the DDM, with FCFE per share in place of the dividend.

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

Discount at the required return on equity, not at the weighted average cost of capital. FCFE is a cash flow to equity holders only, after debt flows, so it takes the equity rate.

Which model fits which company?

Present value (discounted cash flow) modelsdiscount cash flows to shareholders at the required return on equity

• Dividend discount model (DDM) Memorize cash flow is the dividend actually paid
  • Best for stable payers; minority holders who only receive dividends
  • Weak for non-payers; payouts that do not track capacity
• Free-cash-flow-to-equity model (FCFE) Memorize cash flow is dividend-paying capacity
  • Best for non-payers; control perspective
  • Weak for FCFE can be negative and volatile; needs full forecasts

	Dividend discount model	FCFE model
Cash flow	dividends actually paid	cash available to shareholders after reinvestment and debt flows
Formula	$V_0 = \sum D_t / (1+r)^t$	$V_0 = \sum FCFE_t / (1+r)^t$
Best for	dividend payers with a stable payout tied to profits; minority shareholders, who can only count on dividends	non-payers, or firms whose dividends do not reflect capacity; the view of an owner who controls the payout
Weakness	hard to use for non-payers; needs dividend forecasts	FCFE can be negative and volatile; needs full forecasts of the financial statements

As a family, present value models are grounded in theory and force you to state assumptions. Their weakness is sensitivity: small changes in the required return or growth move the value a lot, and long forecasts are needed.

Exam tip A company that pays no dividend is not a company worth nothing. It points you to FCFE, not away from present value models.

Go deeper FCFE and FCFF in one paragraph

FCFE is the cash left for shareholders after the company has paid its lenders, discounted at the cost of equity. Free cash flow to the firm (FCFF) is the cash available to all capital providers before debt flows, discounted at the weighted average cost of capital. Level II builds FCFF models. At Level I, the rule is: equity cash flow, equity discount rate.

Go deeper Why the sale price is usually most of the value

With a short holding period and a growing company, the dividends in the next few years are small relative to the price a buyer will pay for the rest of the stream. In the two-year example the sale price supplies 94% of the value. This is the same pattern you will meet in the two-stage model later in this module, where the terminal value dominates.