Valuing Stocks: Dividends, Payouts, and Free Cash Flow

What is a share worth?

A company can report collapsing earnings and still trade at a high multiple of those earnings, because a share price reflects expected future cash flows, not last quarter’s results. So the question “what is a share worth?” reduces to: what cash will reach shareholders, and what is it worth today?

We build three progressively more general answers:

1. Dividend-discount model (DDM). Value the share from the dividends it will pay.
2. Total-payout model. Add the cash returned through share repurchases, which for many firms dwarfs dividends.
3. Discounted free cash flow (DCF). Value the entire firm from the cash its operations generate, then back out equity. This is the same machinery as project NPV from the previous lesson, applied to the whole company.

The dividend-discount model

Hold a share for one year. You collect dividend $Div_1$ and sell at price $P_1$. Discounting that one-year payoff at the cost of equity $r_E$ (the return investors require on equally risky equity):

$$P_0 = \frac{Div_1 + P_1}{1 + r_E}.$$

The date-1 buyer faces the same one-period trade, so $P_1$ depends on $Div_2$ and $P_2$, and so on. Rolling the substitution forward, the sale price drops out and a share is worth the present value of all future dividends:

$$P_0 = \sum_{t=1}^{\infty} \frac{Div_t}{(1 + r_E)^t}.$$

The Gordon growth special case

If dividends grow at a constant rate $g$ forever (with $g < r_E$), the sum collapses to the perpetuity-with-growth formula:

$$P_0 = \frac{Div_1}{r_E - g}.$$

This fits mature, stable payers (utilities, consumer staples) whose payout policy is set and whose growth is predictable.

Growth is not free: it has to be funded

Where does $g$ come from? A firm splits each dollar of earnings between paying it out and reinvesting it. Let $b$ be the retention rate (the fraction reinvested) and let those reinvestments earn a return on new investment. Then:

$$g = b \times (\text{return on new investment}), \qquad Div_1 = EPS_1 \times (1 - b).$$

Retaining more raises $g$ but lowers the current dividend. Whether that trade is worth it depends entirely on the return earned. The benchmark is a firm that pays out everything: $P = EPS_1 / r_E$. Reinvestment beats that benchmark only when the return on new investment is above $r_E$. If it is below $r_E$, the firm is plowing money into projects that earn less than shareholders require, and growth destroys value.

Move the sliders. Watch the price relative to the no-growth benchmark as you change the return on new investment:

Next-year EPS₁: $5.00Retention b: 40%Return on new investment: 12.0%Cost of equity r_E: 10.0%

Growth g = b × ROI

4.80%

Dividend Div₁

$3.00

Price P₀

$57.69

vs no-growth benchmark

+$7.69

Price vs retention (benchmark = pay out everything, $50.00)

When the return on new investment exceeds r_E, the curve rises above the benchmark: retaining and reinvesting creates value. When it is below r_E, the curve falls and the same growth destroys value. Equal to r_E, the line is flat, so growth is value-neutral.

Baseline: EPS_1 = \5$,$r_E = 10%$, return on new investment$= 12%$. Because 12$r_E$, retaining earnings adds value; drag the return below 10% and watch the same growth start to destroy it.

The headline: growth at the wrong return is value-destroying. A firm can grow earnings every year and still shrink the value of a share.

Multi-stage DDM

Constant growth forever is a poor fit for firms growing faster than $r_E$ for a while (the Gordon formula would return a negative or infinite price). Split the firm’s life into an explicit forecast and a terminal value:

$$P_0 = \sum_{t=1}^{T} \frac{Div_t}{(1+r_E)^t} + \frac{1}{(1+r_E)^T}\cdot\frac{Div_{T+1}}{r_E - g_{L}}.$$

The first term is the PV of forecasted dividends through year $T$. The second is the PV of a Gordon terminal value at a sustainable long-run rate $g_L$, discounted back to today.

Worked example. Div_1 = \2$, growing 12forever, with$r_E = 10%. Years 1 to 5 dividends are 2.00, 2.24, 2.51, 2.81, 3.15, with PV about \9.46. The year-6 dividend is $3.15 \times 1.03 = 3.24$, so the terminal value at the end of year 5 is 3.24 / (0.10 - 0.03) = \46.32$, worth$46.32 / 1.10^5 \approx $28.76 today. Share value: about \38.22.

A one-percentage-point change in the long-run rate can move the price 20% or more. Forecasts that hinge on a single growth assumption are fragile, which motivates models that lean less on dividend forecasts.

The total-payout model

Many firms return far more cash through share repurchases than through dividends. A pure DDM, which counts only dividends per share, misses that cash entirely.

The fix: discount total payouts (dividends plus repurchases) to get the value of total equity, then divide by shares outstanding. Growth here applies to total payouts, not to per-share dividends.

Discounted free cash flow: valuing the whole enterprise

What if a firm pays no dividends and does no buybacks, plowing all cash back in? Value the enterprise directly from its free cash flows, the same FCF you built for a project last lesson, now for the whole company:

$$V_0 = \sum_{t=1}^{T} \frac{FCF_t}{(1+\text{WACC})^t} + \frac{1}{(1+\text{WACC})^T}\cdot\frac{FCF_{T+1}}{\text{WACC} - g_{FCF}}.$$

Two things differ from the DDM. First, free cash flow belongs to all investors, debt and equity, so discount it at the WACC, not at $r_E$. Second, this yields enterprise value. Back out equity:

$$\text{Equity value} = V_0 - \text{Net debt}, \qquad P_0 = \frac{\text{Equity value}}{\text{shares outstanding}}.$$

As with any terminal-value model, the terminal piece often accounts for the majority of enterprise value, so small changes in $g_{FCF}$ swing the answer. Treat the long-run growth assumption with care and sanity-check the result against the market.

Multiples as a cross-check

A discounted cash flow estimate rests on many assumptions. A quick cross-check is to compare the firm to similar firms using a multiple such as P/E or EV/EBITDA. Multiples are fast and market-based but assume the comparables are fairly priced and truly comparable. We treat them in depth in the Multiples and Comparables lesson.

Why the estimate keeps changing

If your careful valuation differs sharply from the market price, the honest first question is who has better information. In a competitive market, prices already embed widely available information, so a model built from public data rarely uncovers a bargain on its own. The limits of that idea, and what moves prices, are the subject of the Factor Models and Market Efficiency lesson.

Deferred to capital structure

Two refinements wait until Unit 5, once leverage is on the table: the full derivation of the WACC, and Adjusted Present Value, which values the unlevered firm and adds the tax shield separately. Both are alternative routes to the same equity value.