Dividends, FCFE, FCFF or residual income: which cash flow, which discount rate

Which measures can a present value model use?

Four, plus one that analysts often reach for: dividends, free cash flow to equity (FCFE), free cash flow to the firm (FCFF) and residual income, and earnings before interest, taxes, depreciation, and amortization (EBITDA). These are the present value metrics . The first three are cash flows taken from the cash flow statement; residual income is an income measure (net income less a charge for the cost of equity), not a cash flow; EBITDA is a rough operating cash flow before tax and investment.

• Dividends are cash paid to every shareholder.
• FCFE is cash available to shareholders, paid out or not (lesson 1).
• FCFF is cash available to lenders and shareholders, used to value the whole firm.
• Residual income is profit above what shareholders require on the book value of their equity.

Present value measuresmatch the discount rate to the owner

• Dividends Memorize paid to all shareholders; never negative
• FCFE Memorize available to shareholders; can be negative
• FCFF Memorize available to lenders and shareholders; values the firm
• Residual income Memorize profit above the equity charge; not a cash flow
• EBITDA Know the idea before tax and investment; a pre-tax rate

The rule that ties them together is matching the discount rate to the claim : the rate must fit whoever owns the cash flow in the numerator. Shareholders’ cash flows take the required return on equity, $r_e$. A cash flow shared with lenders takes a blend of the two claims, the weighted average cost of capital (WACC), which lesson 5 computes.

What is free cash flow to the firm?

Free cash flow to the firm (FCFF) is the cash flow available to all capital providers, lenders as well as shareholders, after operating expenses, taxes and investment. It is broader than FCFE and is used to value the whole firm.

$$\text{FCFF} = \text{Cash flow from operations} + \text{Interest expense} \times (1 - \text{Tax rate}) - \text{Capital expenditures}$$

Interest is added back because it is a payment to lenders, who are among the owners of FCFF. Only the after-tax interest expense is added back, because interest saves tax.

$$\text{FCFF} = \text{FCFE} + \text{Interest expense} \times (1 - \text{Tax rate}) - \Delta\text{Debt}$$

Here $\Delta$Debt is net debt issuance: debt issued minus debt repaid. This is the FCFF and FCFE relationship .

Does the borrowing plan matter? For the same firm, FCFE is 310 − 140 + net debt issuance, and FCFF follows from the FCFE formula:

Net debt issuance	FCFE	FCFF
repays 20	150	150 + 45 + 20 = 215
borrows 30	200	200 + 45 − 30 = 215
borrows 80	250	250 + 45 − 80 = 215

FCFF does not move with borrowing; FCFE does. FCFF is above FCFE while debt is unchanged or falling, but borrowing more than the after-tax interest (here 80 is more than 45) puts FCFE above FCFF for now; the extra interest lowers later cash flows. For an all-equity firm, FCFF equals FCFE.

FCFF is the better measure when the capital structure is changing (more debt, buybacks, irregular dividends), so that FCFE would swing with financing choices, or when the investor is a controlling investor who sets both investment and debt policy. Corrin Hotels has bought rival chains with borrowed money, started and then cut a dividend, and launched a large buyback. FCFF, which ignores how the cash is split between lenders and shareholders, gives a steadier base for valuation.

Lesson 5 discounts FCFF at the weighted average cost of capital and subtracts the market value of debt to reach the value of equity.

Go deeper Why FCFF hardly moves when borrowing changes

FCFF is measured before any payment to lenders or shareholders, so how the firm splits it between them does not change it. Borrowing more raises FCFE today, but the interest on the new debt lowers future FCFE and is added back in FCFF. That is why FCFF estimates stay stable while FCFE estimates swing with debt assumptions.

Why is EBITDA not a free cash flow?

Earnings before interest, taxes, depreciation, and amortization (EBITDA) is revenue minus operating expenses before payments to lenders, non-cash charges and taxes. It ignores taxes, capital expenditures and working capital investment, so it overstates the cash a business throws off.

$$\text{EBITDA} = \frac{\text{Net income}}{1 - \text{Tax rate}} + \text{Interest} + \text{Depreciation}$$

$$\text{FCFF} = \text{EBITDA}(1 - \text{Tax rate}) + \text{Depreciation} \times \text{Tax rate} - \Delta\text{Gross long-term assets} - \Delta\text{Working capital}$$

Analysts still use EBITDA because it works for a company with a net loss but positive operating income, shows cash generation before discretionary spending, and allows comparisons across firms with different leverage, tax rates and investment.

Its dangers are real. EBITDA and adjusted EBITDA (EBITDA plus one-time expenses, or minus non-operating or one-time income) are not earnings measures under US generally accepted accounting principles (US GAAP) or International Financial Reporting Standards (IFRS), and nobody agrees on what may be adjusted, so a company can flatter its results. Pelham Meals, a fast-growing meal-kit delivery start-up, reports a net loss every year but publishes an “adjusted EBITDA” that adds back customer discounts, share-based pay and the cost of launching in new cities. On its own measure it looks profitable; on cash, it is not. Research has found that firms that lead with EBITDA tend to be smaller, more indebted, more asset-heavy and less profitable.

EBITDA is a before-tax measure, so any rate applied to it must also be before tax, a pre-tax discount rate for EBITDA , unlike the after-tax WACC used for FCFF. Depreciation as a share of EBITDA also varies widely by industry.

Exam tip Capital spending moves FCFF one for one and leaves EBITDA untouched. If a question changes capital expenditures, EBITDA is the answer that does not move.

What is residual income?

Residual income is the profit a company earns above the opportunity cost of its shareholders’ capital, also called economic profit . A company with positive net income adds value for shareholders only if its return on equity beats $r_e$.

$$RI_t = EPS_t - r_e \times \left(\frac{BVE}{\text{Share}}\right)_{t-1}$$

Here EPS is earnings per share and BVE is the book value of equity. The book value per share is the value at the start of the period, so the charge is for the capital shareholders had invested during the year. This is residual income per share .

A residual income model starts from today’s book value and adds the value of future residual income; the formula is in Learning Module 5. It relies on clean surplus accounting : book value changes only through earnings and transactions with shareholders (dividends, buybacks, share issues). Items booked straight to equity, such as currency translation gains, must be adjusted for. In theory its value should be close to an FCFE value. Like FCFE and FCFF it does not need the company to pay anything out, and unlike them it can be used when free cash flow is currently negative.

How do the measures compare?

Measure	Whose cash	Strengths	Watch out	Discount at
Dividends	shareholders, paid to all of them	easiest to observe; one clear payout	zero or positive only; misses buybacks and retained cash	$r_e$
FCFE	shareholders, paid out or not	broader than dividends; includes buybacks, issues and cash kept	not all of it reaches every shareholder; moves with debt; can be negative	$r_e$
FCFF	lenders and shareholders (and preferred holders)	the most complete cash measure; does not change with borrowing; suits a controlling investor	values the firm: subtract debt for equity	WACC
EBITDA	before interest, tax and investment	usable with a net loss; compares firms with different leverage, tax and investment	not standardized; adjustments vary; ignores investment	a pre-tax rate
Residual income	shareholders, above the equity charge	economic profit; works with negative free cash flow	not a cash flow; needs reliable book values	$r_e$

What are the five steps of a present value valuation?

Memorize

The five-step valuation process is the same whichever measure you choose.

1. Select the cash flow measure.
2. Forecast it over a horizon (constant growth, multistage growth or a detailed forecast of the financial statements).
3. Choose a required return that matches who owns the cash flow.
4. Set a terminal value.
5. Reach a point estimate of intrinsic value ($IV_t$), or a range from different assumptions, and compare it with the share price and other estimates.

Intrinsic value, IV_t

• 1 Select the measure Memorize dividends, FCFE, FCFF, EBITDA or residual income
• 2 Forecast it Memorize constant, multistage or detailed
• 3 Set the rate Memorize r_e or WACC, matched to the owner
• 4 Set the terminal value Memorize constant growth, multiples or book value
• 5 Estimate and compare Memorize a point or a range against the price

A note on each step. In step 2, the forecast method matters: a cyclical company’s cash flow can rise and fall with the business cycle, which constant growth ignores (Learning Module 8 builds detailed forecasts). In step 3, use $r_e$ for dividends, FCFE and residual income, WACC for FCFF and a pre-tax rate for EBITDA (lesson 5). In step 4, this module uses constant growth, and Learning Module 7 uses multiples (residual income models can also end with book value). In step 5, compare the range with the recent trading range.