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

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

A bond’s cash flows are fixed by contract and end at maturity. A share’s distributions are set by management, are uncertain and have no end date. So a generalized discounted cash flow model forecasts the cash flow available to investors and discounts it at their required return. If the company is a going concern, intrinsic value is the present value of the cash flows expected for its shareholders, plus an expected price at the end of the period that can be forecast.

$$IV_t = \sum_{i=1}^{n} \frac{E(CF_{t+i})}{(1 + \text{Required rate of return})^{i}} + \frac{E(P_{t+n})}{(1 + \text{Required rate of return})^{n}}$$

Here $IV_t$ is the intrinsic value today, $E(CF_{t+i})$ is the expected cash flow in period $i$ and $E(P_{t+n})$ is the terminal value : the expected price at the end of the forecast horizon , which stands in for every cash flow after it. The horizon $n$ is how far the analyst can forecast with confidence; it has nothing to do with how long any investor plans to hold the share.

The discount rate is the required return on equity (cost of equity) , $r_e$, the return shareholders demand for the risk they bear. This module takes $r_e$ as given; Learning Module 12 shows how analysts estimate it.

The cash flow can be dividends, free cash flow to equity (FCFE), free cash flow to the firm (FCFF) or, in a related form, residual income. This lesson covers the first two and lesson 2 the others.

When are dividends the right cash flow?

Know the idea

Cash dividends are the narrowest measure: the part of net income that is neither reinvested nor used for share repurchases. A dividend discount model (DDM) assumes the shareholder’s only access to the firm’s value is the cash dividend, so it values the share from the non-controlling shareholder perspective : someone with no say over dividend policy.

It fits best when earnings are positive and stable and a large, consistent share is paid out, with little change in the number of shares, because then dividends can be forecast with confidence. Dividends are paid to every shareholder in proportion, and their history is easy to observe. Two settings where dividends track earnings closely are real estate investment trusts (REITs), which must pay out almost all their taxable income to avoid corporate tax, and regulated utilities, whose regulated prices cap growth so that most of the shareholders’ return comes as dividends.

What a DDM leaves out is share repurchases, new share issues, cash the company keeps and changes in borrowing. For a firm that pays little, prefers buybacks or is changing its debt, dividends understate what is available to shareholders. Dividends can never be negative.

Lindvik Water, a regulated water utility, has paid out about 85% of its earnings for a decade with the same number of shares. Its dividends are close to everything shareholders can expect, so a DDM fits. Arden Software pays a token dividend and spends three times as much on buybacks; a DDM would miss most of what it returns.

If dividends grow at a constant rate, the model becomes the constant growth model of lesson 3.

What is free cash flow to equity?

Free cash flow to equity (FCFE) is the cash left for shareholders after operating expenses, interest and taxes are paid and after all the investment in working capital and long-term assets the business needs to continue and grow. It includes dividends and everything else available to shareholders, whether paid out or not.

$$\text{FCFE} = \text{Cash flow from operations} - \text{Capital expenditures} + \text{Net debt issuance}$$

Cash flow from operations is net income plus depreciation minus the change in working capital . Net debt issuance (written $\Delta$Debt) is additional borrowing minus debt repayment. Depreciation is added back because it is an expense that uses no cash; capital expenditures here mean the change in gross long-term assets.

FCFEcash available to shareholders

• Cash flow from operations Memorize net income + depreciation − Δworking capital
• minus Capital expenditures Memorize the change in gross long-term assets
• plus Net debt issuance Memorize additional borrowing − debt repayment

What else does FCFE equal?

FCFE must go somewhere: it is paid out as dividends or buybacks, or kept as cash, and money raised by issuing shares reduces it. Working from the other side gives the same number.

$$\text{FCFE} = \Delta\text{Cash} + \text{Dividends} + \text{Stock repurchases} - \text{Stock issuance}$$

This is also written FCFE = $\Delta$cash + dividends − $\Delta$equity, where $\Delta$equity is share issuance minus repurchases.

So FCFE equals dividends only when a company pays out everything available and neither buys back shares, issues shares nor builds up cash.

How does a target debt ratio simplify FCFE?

Use it

Forecasting borrowing year by year is hard, so analysts often assume the firm finances growth at a target debt ratio , DR = total debt ÷ (total debt + total equity). The equity holders then fund only $(1 - DR)$ of the net investment , the cash put into long-term assets and working capital beyond depreciation. Lenders fund the rest.

$$\begin{aligned} \text{FCFE} &= \text{Net income} - (1 - DR) \times \text{Net investment} \\ \text{Net investment} &= (\Delta\text{Gross long-term assets} - \text{Depreciation}) + \Delta\text{Working capital} \\ \Delta\text{Debt} &= DR \times \text{Net investment} \end{aligned}$$

Depreciation is assumed to be the only non-cash charge.

When is FCFE positive or negative?

Positive and negative FCFE depend on how the company funds and uses cash. Assuming positive cash flow from operations:

Feature	Points to positive FCFE	Points to negative FCFE
Capital expenditures	modest, or funded with debt	large and funded with equity, relative to cash flow from operations
Debt	growing	being paid down heavily
Cash	building up	being run down heavily
Payouts	dividends or buybacks	none
Share issuance	little or none	large

FCFE suits the controlling investor perspective : an investor who can change those policies, and firms whose dividends bear little relation to earnings or that pay none. It is less useful for firms with large future capital needs (FCFE may stay negative) or big changes in capital structure (FCFE swings); lesson 2’s FCFF handles those.

Cash flow to shareholdersdiscounted at r_e

• Dividend discount model (DDM) Memorize dividends actually paid; never negative
  • Best for stable, high, consistent payout; REITs, regulated utilities
  • Point of view non-controlling shareholder
  • Weak for ignores buybacks, share issues, retained cash and debt changes
• FCFE model Memorize cash available, paid out or not; can be negative
  • Best for irregular or no dividends; buybacks matter
  • Point of view controlling investor
  • Weak for large capital needs; big capital structure changes

$$IV_t = \sum_{i=1}^{n} \frac{\text{FCFE}_{t+i}}{(1 + r_e)^{i}} + \frac{E(P_{t+n})}{(1 + r_e)^{n}}$$

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

Which model fits which company?

	Dividend discount model	FCFE model
Cash flow	dividends paid	cash available to shareholders, paid out or not
Formula	$IV_t = \sum D_{t+i}/(1+r_e)^i + E(P_{t+n})/(1+r_e)^n$	same with FCFE in place of dividends
Point of view	non-controlling shareholder	controlling investor
Best for	stable, high, consistent payers; REITs; regulated utilities	irregular or no dividends; buybacks or share issues matter
Weak for	firms that pay little or buy back shares	big capital needs; big capital structure changes
Can it be negative?	no	yes

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 what is left for shareholders after lenders are paid. Free cash flow to the firm (FCFF) is the cash available to lenders and shareholders together: it adds back after-tax interest and ignores net borrowing. Lesson 2 builds FCFF and lesson 5 discounts it at the weighted average cost of capital (WACC) and subtracts the market value of debt. The rule: equity cash flow, equity discount rate.

Go deeper Why the terminal value is usually most of the value

With a short horizon 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 expected price at the horizon supplies 94% of the value. This is the same pattern you will meet in the two-stage model in lesson 4, where the terminal value dominates.