EQ 3 – Free Cash Flow Valuation

Every discounted cash flow model rests on the same idea: the intrinsic value of a security is the present value of the cash it is expected to throw off. A dividend discount model applies that idea to the cash a company actually hands to shareholders. Free cash flow valuation applies it to the cash a company is able to hand over without damaging itself. That single change of definition is the whole reason this reading exists.

Two measures carry the argument. Free cash flow to the firm (FCFF) is the cash left for every provider of capital once operating expenses and taxes have been paid and once the investments in working capital and fixed capital that the business needs have been made. Put crudely, FCFF is operating cash flow less capital expenditure, and its claimants are common shareholders, bondholders and sometimes preferred shareholders. Free cash flow to equity (FCFE) goes one step further: it is the cash left for common shareholders alone, after operating expenses, interest, principal payments and the same necessary investments. FCFE is operating cash flow less capital expenditure less net payments to debtholders.

Neither figure is reported. Dividends are printed in the financial statements; free cash flow has to be constructed by the analyst from the income statement, the balance sheet and the statement of cash flows. That construction work is most of what follows.

When analysts reach for free cash flow

A survey of professional practice (Pinto, Robinson and Stowe 2019) reports that, among analysts valuing individual equities, 92.8% apply market multiples and 78.8% apply a discounted cash flow approach. Within that discounted cash flow group, the residual income model is used by 20.5%, the dividend discount model by 35.1% and a discounted free cash flow model by 86.9%. Where free cash flow models are chosen, the FCFF variety appears about twice as often as the FCFE variety. Free cash flow analysis is close to universal, and most analysts run more than one method side by side.

Four conditions in particular push an analyst away from dividends and towards free cash flow:

• The company pays no dividend at all, so a dividend discount model would have to invent the date of initiation, the opening level and the growth path from there.
• The company pays a dividend, but the amount differs materially from what the company could afford to pay.
• Free cash flow lines up with profitability over a forecast horizon the analyst is willing to defend.
• The investor takes a control perspective. Control brings discretion over the uses of free cash flow: dividends can be reset near the company capacity to pay, or the cash can be redirected to service acquisition debt.

That last point is the ownership perspective implicit in FCFE. A minority shareholder receives whatever the board declares. An owner who controls the company receives, in economic substance, the whole of FCFE, because the owner decides what to do with it. Valuing FCFE is therefore valuing the company from the point of view of someone who can direct the cash, which is exactly the right lens for a takeover analysis.

Why the obvious shortcuts fail

Analysts sometimes reach for cash flow from operations (CFO), net income, EBIT or EBITDA as if any of them could be discounted directly. None of them can. Each either double counts a cash flow or leaves one out. EBIT and EBITDA are pre-tax figures, whereas the cash available to investors is after tax. From an equity holder point of view, EBITDA ignores differences in capital structure, so it ignores after-tax interest and preferred dividends, and it ignores the funds bondholders supply to finance operating assets. None of these measures subtracts the reinvestment in fixed and working capital that the business must make to protect its long-run value. FCFF and FCFE are constructed precisely so that they can be dropped into a discounted cash flow framework without any of these defects.

The two routes to equity value

Because FCFF belongs to all suppliers of capital, it must be discounted at the weighted average cost of capital, which is the blended after-tax required return of those suppliers. The result is the value of the whole firm.

Two details in Equation 3 are examined regularly. The weights are market values of debt and equity, although analysts may substitute the weights of a target capital structure when those are known and differ from current market weights. And the tax rate is in principle the marginal corporate income tax rate, because the deduction applies at the margin.

The second route bypasses the firm entirely. FCFE is the cash flow to common shareholders, so the risk-adjusted rate that belongs with it is the required return on equity, r.

Choosing between the routes

In theory the two approaches agree. In practice the characteristics of the company decide which is easier to defend. Where the capital structure is stable, valuing FCFE is the shorter and more direct path. The FCFF model is usually chosen in two situations:

• A levered company with negative FCFE. Discounting a stream of negative numbers is unhelpful. Discount FCFF instead to obtain the value of operating assets, add excess cash and marketable securities and any other material non-operating assets, then subtract the market value of debt.
• A levered company whose capital structure is changing. Historical FCFF growth tends to reflect fundamentals more cleanly than FCFE growth, which swings with net borrowing. Looking forward, the required return on equity is more sensitive to leverage changes than WACC is, so holding the discount rate constant is harder to justify on the equity route.

Where the capital structure is expected to change substantially, a specialised approach such as adjusted present value (APV) can be used. Under APV, firm value is the sum of two pieces: the value of the company assuming it uses no debt, found by discounting FCFF at the unlevered cost of equity, plus the net present value of the effects of debt, such as the tax benefit of interest and the costs of financial distress.

The Gordon growth model assumes dividends grow forever at a constant rate. Assume the same of free cash flow and the infinite sums of Equations 1 and 4 collapse into two one-line expressions. These are the single-stage, or stable-growth, free cash flow models.

One warning is worth carrying into the exam room: the growth rate of FCFF and the growth rate of FCFE do not have to be equal, and frequently are not. FCFE growth absorbs changes in net borrowing that FCFF growth never sees. A question that hands you two different growth rates for the same company is not testing your arithmetic; it is testing whether you know that the two rates are separate inputs.

The most common starting point is net income available to common shareholders, usually the bottom line of the income statement. That figure is already net of depreciation, amortisation, interest, income taxes and preferred dividends, but not of common dividends. Four adjustments turn it into FCFF.

Take the four adjustments one at a time.

Net noncash charges

A noncash charge is an expense that reduced reported income without moving any cash. Depreciation is the archetype, and amortisation of intangibles is its counterpart. Both are added back. Where noncash decreases in net income exceed noncash increases, which is the usual case, the total adjustment is positive; where noncash increases dominate, it is negative. Other items in this category are treated in the next section.

After-tax interest expense

Interest, net of the tax it saved, was deducted on the way to net income. But interest is cash going to one of the company capital providers, and FCFF is defined as the cash available to all of them, so it must be added back. The reason the add-back is made after tax is consistency: FCFF is discounted at an after-tax WACC. It is legitimate to work instead with a pre-tax WACC and add back the full interest paid, but the definitions of FCFF and WACC must then match each other. Mixing the two conventions is a silent and expensive error.

Preferred dividends are handled the same way. If they were deducted in arriving at net income available to common shareholders, they must be added back for FCFF, because preferred shareholders are capital providers too.

Investment in fixed capital

This is the cash spent on the long-lived assets that support current and future operations: property, plant and equipment, and where necessary intangible assets such as trademarks. A cash acquisition of another company may be treated as a capital expenditure, which is conservative because it reduces FCFF. If the company received cash from disposing of fixed capital, that inflow reduces the outflow figure. The statement of cash flows is the natural source for both purchases and disposals. One trap: assets acquired without cash, for instance in exchange for stock or debt, never appear in the statement of cash flows and must be found in the footnotes. Such acquisitions do not change historical FCFF, but if the spending is necessary and will eventually be made in cash, the forecast must reflect it.

Investment in working capital

The final adjustment is the net increase in current assets less current liabilities. For valuation purposes the definition is narrower than the textbook one. Cash and cash equivalents are excluded, because the change in cash is the quantity being explained. Notes payable and the current portion of long-term debt are also excluded, because they carry explicit interest and are therefore financing items rather than operating items. Working capital for free cash flow is operating current assets minus operating current liabilities, and nothing else.

The statement of cash flows has already done part of the work. Cash flow from operations incorporates the add-back of noncash expenses and the change in operating working capital, so starting there removes two of the four adjustments in Equation 7.

Neither depreciation nor the working capital change appears here, because CFO already contains both. Only two items remain: after-tax interest, which was taken out of net income and therefore out of CFO, and capital expenditure, which the operating section never touched. Under US GAAP interest paid must sit in operating cash flow. Under IFRS a company may place it in either operating or financing, although research by Gordon, Henry, Jorgensen and Linthicum (2017) reports that most IFRS-reporting European firms put interest paid in the operating section. Check the classification before applying Equation 8, because if interest paid was reported as a financing outflow it was never subtracted from CFO and must not be added back.

Whichever entry point an analyst chooses, some items refuse to behave. This section deals with the two families of them: cash flow statement classification choices that differ between reporting frameworks, and noncash adjustments whose treatment depends on judgement rather than on a rule.

Where interest and dividends are allowed to sit

IFRS permits interest paid to be reported as operating or financing, and permits dividends paid to be reported as operating or financing. US GAAP is stricter: interest paid to debt providers belongs in operating cash flow, alongside interest income and dividend income, while dividends paid to equity providers are a financing item.

The add-back of after-tax interest in Equation 8 is only correct if interest paid was deducted inside CFO in the first place.

Noncash items and the direction of the adjustment

The operating section of the statement of cash flows lists the adjustments that bridge net income to operating cash flow. The same list, with the same signs, bridges net income to FCFF.

Any item that was expensed in arriving at net income without a matching cash outflow in the period has to be reversed. Gains and losses are removed for two separate reasons. First, the underlying transaction is usually not an operating activity: selling a fixed asset is an investing activity, so its effect must leave the operating section. Second, the reported gain or loss is not the same number as the cash involved. Consider equipment with a book value of €60,000 sold for €100,000. The €40,000 gain flows into net income, so it is subtracted in deriving operating cash flow, while the full €100,000 shows up as an investing inflow. Reverse the price and the logic reverses with it: the same equipment sold for €40,000 produces a €20,000 loss, and that loss is added back.

Deferred taxes

Deferred taxes arise because income and expenses are recognised on different timetables for financial reporting and for tax. The tax expense on the income statement is therefore not the cash paid. Over a long enough period the differences reverse and net to nothing. The forecasting implication follows directly: if the analyst is trying to isolate the persistent part of FCFF, deferred tax changes that are expected to reverse soon should not be added back. If instead the company is growing and can defer the liability indefinitely, the add-back is justified, though an acquirer should remember the liability may one day come due.

The mirror image also occurs. A company may expense restructuring charges that are not tax deductible, or recognise revenue for tax before it recognises it for reporting. Taxable income then exceeds reported income, cash taxes exceed reported tax expense, and a deferred tax asset appears. That amount is subtracted in deriving operating cash flow. If the deferred tax asset is expected to reverse shortly, the analyst should leave the subtraction out of a forecast to avoid understating future cash flow. If the charges are expected to recur indefinitely, the subtraction belongs in the forecast.

Share-based compensation

Both IFRS and US GAAP require an expense in the income statement for options granted to employees. Granting and expensing options move no cash, so the expense is a noncash charge. The longer-term cash consequences are real, though. When an employee exercises, the company receives the strike price, and that receipt is classified as a financing cash flow. A company may also obtain a tax benefit from issuing options, which can raise operating cash flow without raising net income, and both frameworks require part of the tax effect to be shown as financing rather than operating. Read the statement of cash flows and the footnotes together, exclude any of these flows that are not expected to persist, and remember the separate effect on the share count: when computing value per share, the shares expected to be outstanding after option exercise may be the more appropriate denominator.

Sustainability of the historical baseline

Any forecast built on history inherits history distortions. Before extrapolating a historical FCFF or FCFE figure, satisfy yourself that the base year is free of non-recurring items. Working capital swings deserve particular suspicion, because a favourable swing in one year can look like operating strength when it is simply a balance that cannot fall any further.

FCFE is FCFF minus the cash that belongs to debtholders plus the cash that debtholders supply. Two adjustments, no more.

The relationship runs in both directions. Given FCFE, add back after-tax interest and subtract net borrowing to recover FCFF. Substituting Equation 9 into Equations 7 and 8 gives the two direct routes to FCFE:

Applying Equation 9 to the Cane Distribution figures shows the mechanics on numbers already derived.

FCFE exceeds FCFF in all three years because Cane borrowed steadily and repaid nothing.

FCFE is the dividend the company could pay

FCFE is what remains after operating expenses and taxes, after the required investment, and after every transaction with the other suppliers of capital. It is therefore the amount the company could afford to distribute. Actual dividends are usually a different number, and often a very different one. Boards manage dividends: they raise them gradually, they resist cutting them, they hold them flat when earnings fall and they hold them back when earnings surge. The consequence is that earnings are far more volatile than dividends, and neither series tracks FCFE closely.

Net income and CFO are the usual entry points, but the income statement offers two more. Both derivations begin from Equation 7 with depreciation assumed to be the only noncash charge.

Start with FCFF = NI + Dep + Int(1 − Tax rate) − FCInv − WCInv, and write net income in terms of EBIT: NI = (EBIT − Int)(1 − Tax rate) = EBIT(1 − Tax rate) − Int(1 − Tax rate). Substituting, the two interest terms cancel:

Do the same from EBITDA. Here NI = (EBITDA − Dep − Int)(1 − Tax rate), which expands to EBITDA(1 − Tax rate) − Dep(1 − Tax rate) − Int(1 − Tax rate). Substituting into Equation 7 leaves only the tax portion of depreciation:

The contrast between Equations 12 and 13 is the point worth memorising. From EBIT you add back all of depreciation, because EBIT is already net of it and the deduction has already sheltered tax. From EBITDA you add back only the tax shield, Dep × Tax rate, because taxing EBITDA directly would have overtaxed the company by the amount the depreciation deduction saved.

More generally, many of the noncash add-backs required when starting from net income are unnecessary from EBIT or EBITDA, simply because those charges were deducted further down the income statement. Whether an adjustment is needed depends on where in the income statement the charge sits, and the form of the adjustment depends on whether the charge is tax deductible. To move on to FCFE from either equation, apply Equation 9: subtract after-tax interest and add net borrowing.

Everything so far has computed free cash flow from the income and cash flow statements, which is the sources view: where did the cash come from. There is a second view. Follow the money out instead of in, and you get the uses view. It serves two purposes: it is an arithmetic check on the sources calculation, and it exposes what management is actually doing with capital structure and cash.

A company with positive FCFF has three places to put it. It can retain the cash, raising balances of cash and marketable securities. It can pay debt providers, through interest and through principal repayment beyond new borrowing. Or it can pay equity providers, through dividends and through share repurchases beyond new share issuance. When free cash flow is negative, the same three channels run in reverse: draw down cash, borrow, or issue equity.

Notice what these transactions do to leverage. Suppose free cash flow is zero and cash balances are unchanged. Raising cash by net new borrowing and spending it on dividends or net buybacks increases leverage. Raising cash by issuing shares and spending it on principal repayments beyond new borrowing reduces leverage. The uses statement makes that shift visible in a way the sources statement does not.

Where new borrowing exceeds repayment, the excess enters as a negative item. Where share issuance exceeds repurchases, that excess is negative too. Uses must equal sources in both columns.

Pitts Corporation reconciled

Take the 2020 figures from Example 5. Cash and equivalents rose by $10 million (200 − 190). After-tax interest was $60 million, being $100 million × (1 − 0.40). Net borrowing was $75 million, from $50 million of notes payable plus $25 million of long-term debt. Cash dividends were $160 million. Share repurchases and share issuance were both zero.

Both totals match the sources figures computed earlier, $155 million and $170 million. The interpretation is more interesting than the arithmetic. Operating cash flow of $495 million comfortably covered capital expenditure of $400 million, so the extra debt was not needed for investment. It went, in part, to pay the dividend. Pitts was managing its capital structure by adding leverage and passing the proceeds to shareholders, and only the uses view makes that visible at a glance.

Computing free cash flow from history is mechanical. Forecasting it is not. There are two broad approaches, and the choice between them depends on whether the future is expected to resemble the past.

Approach one: grow the historical figure

The simplest method applies a constant growth rate to a current level of free cash flow, adjusted first to strip out non-recurring components. It is defensible when free cash flow has in fact grown steadily and when the historical relationships between free cash flow and the underlying drivers are expected to hold.

Approach two: forecast the components from sales

The richer method forecasts the pieces separately: EBIT(1 − Tax rate), noncash charges, fixed capital investment and working capital investment. EBIT can be projected directly, or projected as a margin on forecast sales. Investment needs can be tied to the historical relationship between sales increases and capital spending. The sales-based version rests on one large assumption:

Fixed capital investment in excess of depreciation, and investment in working capital, both bear a constant relationship to the forecast increase in sales.

For forecasting FCFE, one more assumption is added: the debt ratio (DR), meaning debt as a percentage of debt plus equity, is constant. That fixed proportion then tells you how much of the incremental investment is funded with debt. The method treats depreciation as the only noncash charge, so it works poorly where that approximation is weak.

If depreciation approximates the annual cost of maintaining the existing capital stock, then fixed capital investment in excess of depreciation is the spending needed for growth. This is the economic content of the method: capital expenditure has a maintenance component, which tracks the level of sales, and a growth component, which tracks the increase in sales. The inputs required are forecasts of sales growth, of the after-tax operating margin for FCFF or the net profit margin for FCFE, of the relationship of incremental fixed capital investment to sales increases, of the relationship of working capital investment to sales increases, and an estimate of DR.

Rather than adding all depreciation back and subtracting all capital expenditure, this approach nets the two and subtracts only the excess. Where depreciation really is the only significant noncash charge, it reproduces the earlier equations exactly.

The target debt ratio shortcut for FCFE

Assume depreciation is the only noncash charge and Equation 10 simplifies to:

Assume further that a constant share DR of the incremental investment is debt financed. Then net borrowing no longer needs a separate forecast: Net borrowing = DR(FCInv − Dep) + DR(WCInv). Substituting that into Equation 14 and collecting terms gives the workhorse expression:

Read Equation 15 in words and it becomes obvious. Shareholders keep net income, less the part of the growth investment that shareholders themselves have to fund. The debt-funded part costs them nothing today.

When the statements do not articulate

In many published accounts, the change in a balance sheet item does not equal the corresponding change shown in the statement of cash flows. Statements in which the balance sheet movements in working capital accounts differ from the working capital amounts in the cash flow statement are described as lacking articulation, and it is not a rare condition. Research points to several causes (see, among others, Huefner, Ketz and Largay 1989; Wilkins and Loudder 2000; Hribar and Collins 2002; Shi and Zhang 2011; Casey, Gao, Kirschenheiter, Li and Pandit 2016). Two stand out: acquisitions or divestitures, including related discontinued operations, and the presence of nondomestic subsidiaries. An inventory balance can rise because the company bought goods from suppliers, which is operating, or because it absorbed the inventory of an acquired business, which is investing. Currency translation of foreign earnings introduces further gaps.

Where a company has been active in acquisitions or disposals, the reported CFO figure may be contaminated by investing and financing flows, and using it unadjusted as the base of a free cash flow forecast will mislead. The remedy is more detail: adjust the CFO starting point, or forecast the individual components and pay close attention to how forecast sales connect to specific working capital items.

Why analysts often prefer FCFE to a dividend discount model

Neither model has a theoretical edge. The preference arises in application. Many companies pay no dividend or a token one, which forces a dividend discount model to guess the initiation date, the opening level and the growth path. Dividends are set by the board, so they may signal long-run profitability imperfectly, with some companies paying far less than free cash flow and others far more. And when a company is being analysed as a takeover target, the relevant measure is the cash that can be distributed without impairing value, not the cash the current board chooses to distribute, because the new owner will decide that question afresh.

Given identical and mutually consistent inputs, a dividend discount model and an FCFE model return the same value. One special case makes this transparent: if FCFE equals the cash dividend every year, the two streams are identical and both are discounted at the required return on equity. In practice the two differ, but they are driven by the same forces. A fast-growing company with attractive projects retains earnings and pays small dividends, and that same company invests heavily in fixed and working capital, which depresses FCFE. A mature company that invests little tends to have both high dividends and high FCFE.

What dividends, buybacks, issuance and leverage do to free cash flow

Look again at the two definitions:

FCFF = NI + NCC + Int(1 − Tax rate) − FCInv − WCInv, and FCFE = NI + NCC − FCInv − WCInv + Net borrowing.

Dividends, share repurchases and share issuance are absent from both. That is not an oversight. Free cash flow is the cash available to investors; dividends and buybacks are what is done with it afterwards. Transactions between a company and its own shareholders therefore leave free cash flow untouched.

Leverage is the exception, and only partially. An increase in leverage does not change FCFF, though it may change the intermediate figures used to reach it. It changes FCFE twice over. In the year the debt is issued, FCFE rises by the amount borrowed, because net borrowing is a direct addition. In every subsequent year, FCFE is lower by the after-tax interest on that debt. Leverage also raises the interest tax shield, which reduces corporate taxes. The investing and financing decisions taken today shape the free cash flows of many later years.

The cost of using an earnings number instead

Because free cash flow analysis is laborious, some practitioners substitute net income, EBIT, EBITDA or CFO in a discounted cash flow model. Each substitution introduces a systematic bias, in one direction or the other, and the error is not small. Definitions of free cash flow published in textbooks, articles and commercial databases are frequently built for purposes other than valuation, so using a supplied number without knowing its definition invites mistakes. Anyone consuming research should establish which definition is in use; anyone producing it should state the definition plainly.

The most popular shortcut is EBITDA as a stand-in for FCFF. Equation 13 shows exactly what is being thrown away: FCFF = EBITDA(1 − Tax rate) + Dep(Tax rate) − FCInv − WCInv. Depreciation as a proportion of EBITDA varies enormously across companies and industries, and so does the depreciation tax shield. FCFF captures that variation; EBITDA does not. EBITDA also ignores investment in fixed and working capital altogether. And there is a discount rate problem on top: EBITDA is pre-tax, so a consistent model would have to discount it at a pre-tax rate, whereas the WACC used with FCFF is an after-tax cost of capital. EBITDA is a poor proxy for FCFF and a worse one for FCFE, since from a shareholder point of view it also ignores after-tax interest and the cash flows from new borrowing and repayment.

Everything so far assumed two sources of capital, debt and common equity. Preferred stock is a third, and although relatively few companies use it, the adjustments are worth knowing because they follow a clean logic.

Preferred stock behaves like debt in most respects, with one significant difference: preferred dividends are not tax deductible, whereas interest generally is. That difference shows up in the WACC, where the preferred component enters at its full required return with no (1 − Tax rate) factor.

In Equation 7, which starts from net income available to common shareholders, preferred dividends paid have already been deducted and must be added back to reach FCFF, exactly as after-tax interest is. In Equation 10, which starts from the same net income figure to reach FCFE, no add-back is required, because preferred dividends are genuinely not available to common shareholders. Issuing preferred stock increases the cash available to common shareholders and redeeming it decreases that cash, so net preferred issuance joins net borrowing in the FCFE calculation.

Two extensions of the single-stage model deserve separate treatment. The first replaces nominal quantities with real ones. The second stops treating the output as a single number.

Working in real terms

Valuing inflation-adjusted cash flows with an inflation-adjusted discount rate has obvious appeal where inflation is high or unstable. Analysts apply the technique to domestic stocks too, but it earns its keep on international ones. Cross-border valuation raises two problems: economic conditions such as interest rates, inflation and growth differ between countries, and accounting standards differ as well. A team covering many countries faces a third problem, which is keeping assumptions consistent across all of them.

Several securities firms have adapted the single-stage FCFE model to cope. They work in real cash flows and real discount rates. The real required return is built up from a country return, which is a real required rate of return for equities in that country, adjusted for the industry, the size and the leverage of the specific company:

Each adjustment needs an economic justification, and should reflect a factor genuinely expected to change the risk and return of the investment.

The growth side is handled the same way. The firm supplies each analyst with an estimate of the real economic growth rate of the country, and the analyst picks a real growth rate for the company benchmarked against it. The valuation equation is Equation 6 with every variable expressed in real terms:

Sensitivity analysis

Growth in free cash flow ultimately depends on future profitability, and profitability depends on sales growth and net profit margins. Those two in turn reflect where the company sits in its own growth cycle and how attractive the economics of its industry are. A business earning high returns in an expanding market can compound profits for years, but competition eventually squeezes the margin, and the scope for winning more market or more share eventually narrows. Neither the rate of growth nor its duration is easy to forecast.

The base-year figure matters just as much. Hold the required return and growth rate fixed, and firm value or equity value moves in exact proportion to the starting FCFF or FCFE. A base year distorted by a one-off working capital swing propagates straight through to the valuation.

Sensitivity analysis is the disciplined response. Vary one input at a time between a low and a high estimate, holding the others at base case, and record the resulting value. The output is not a better point estimate; it is a map of which assumptions the answer actually depends on.

A single growth rate held forever is rarely credible. Multistage models split the future into a near horizon that is forecast explicitly and a distant horizon that is capitalised. Free cash flow versions are more demanding than their dividend equivalents, because reaching FCFF or FCFE requires assumptions about sales, profitability, investment, financing costs and new financing all at once.

In the second stage the growth rate is a long-run sustainable rate. For a declining industry it might sit slightly below the growth rate of GDP; for an industry expected to outgrow the wider economy it might sit slightly above.

A further warning about vocabulary. In multistage dividend models, the growth rate always refers to dividends. In free cash flow models the growth rate may refer to FCFF, to FCFE, to net income, to operating income or to sales, and which one is meant must be stated or must be clear from the context. If the growth rate is a net income growth rate, FCFF and FCFE also depend on the investment in operating assets and on how that investment is financed. If it is a sales growth rate, then changes in net profit margin, in investment and in financing policy all feed through as well. When income growth steps down between stages, investment in operating assets usually steps down at the same time.

Terminal value

In Equation 17 the terminal value at time n is found from the constant-growth FCFE model, TV_n = FCFE_n+1 ÷ (r − g). That is not the only way. An analyst may instead apply a price multiple, for instance a chosen P/E multiplied by forecast EPS at the horizon, or a multiple of EBITDA. The choice matters more than it looks, because the present value of the terminal value is usually a large share of the total, both in the examples that follow and in practice.

Growth rates rarely fall off a cliff the way the previous model assumes. A small company outgrows the share of the market that made rapid growth possible. A highly profitable company attracts competitors who erode its margins. The second family of two-stage models therefore lets growth decline through Stage 1 and settle at a sustainable rate in Stage 2. This is the free cash flow analogue of the H-model in dividend valuation.

The pattern has an important consequence for cash flow. As profitability falls and the company stops earning high returns, it usually cuts back net new investment in operating assets, and the debt financing that accompanied that investment falls with it. Many highly profitable growth companies show negative or barely positive free cash flow precisely because they are investing so heavily. When growth in profits slows, investment slows and free cash flow turns positive. The negative cash flows of the high-growth years are what create the positive ones later.

The previous example built FCFE from forecast EPS. Analysts more often start from sales and derive profits, investment and financing from the sales path, sometimes division by division for a large company, aggregating the divisional free cash flows at the end. The next example does exactly that, with both the sales growth rate and the profit margin declining as the company matures.

Three-stage models extend the two-stage framework in the obvious way. One common version assumes a constant growth rate in each of the three stages, applied to sales, profits and investment in fixed and working capital, with external financing tied either to the level of sales or to the change in sales. A simpler variant applies the growth rate directly to FCFF or FCFE. A second common version keeps constant growth in Stages 1 and 3 and lets growth decline through Stage 2, which is the transition period.

No real company follows either script exactly. Analysts use these models because they are useful approximations to cash flow streams that in reality wander from year to year, not because the pattern is literally believed.

Environmental, social and governance factors can move a valuation materially. Some of them are quantitative and enter the model directly: a projected environmental fine is simply a cash outflow, and a delay to a project start date simply moves the revenue. Others are qualitative and resist measurement. One workable treatment for those is to add a risk premium to the cost of equity, sized by the judgement of the analyst. There is no formula for the size of such an adjustment, which is precisely why it must be disclosed and defended rather than buried.

Turning a value estimate into a verdict

The last step in any free cash flow valuation is a comparison, not a calculation. Compute the intrinsic value per share, set it against the market price, and label the stock. Where intrinsic value exceeds price the stock is undervalued; where it falls below price the stock is overvalued; where the two are close enough to lie inside the uncertainty of the model, the honest conclusion is fairly valued. The ACMC case ends at $97 against $110, a shortfall of about 12%, which is well outside rounding error and supports a sell.

Two disciplines protect this final step. First, the sensitivity analysis of the previous section tells you how wide the plausible range around $97 really is; if the range straddles $110, the correct label is fairly valued rather than overvalued. Second, the terminal value share of total value tells you how much of the verdict rests on assumptions about a period no one can see. A verdict that flips when the perpetual growth rate moves by 50 basis points is a weak verdict, and should be described as such.

Free cash flow valuation values the assets that generate operating cash flows, or that are needed to generate them. It says nothing about the rest of the balance sheet. Where a company holds significant non-operating assets, such as cash in excess of operating needs, excess marketable securities or land held for investment, those assets must be valued separately and added on.

The rule generalises. If an asset was left out of the set used to project future cash flows, its estimated value belongs in the total. Companies frequently hold substantial noncurrent investments in stocks and bonds that are financial investments rather than operating subsidiaries. Those should be carried at current market value, and any holding reported at book value under accounting convention should be revalued to market before it is added.

The mirror image of this rule is a common examination trap. If excess cash has already been included in the cash flow projection, adding it again double counts. The discipline is to decide once, explicitly, which assets are inside the projection and which are outside, and then to be consistent.

Pulling the reading together

Five ideas carry most of the weight. First, free cash flow is what a company can distribute, which is why it is the right measure for an investor with control and often a better measure than dividends even for one without. Second, FCFF and FCFE can be reached from net income, from CFO, from EBIT or from EBITDA, and every route must give the same number; if two routes disagree, a definition has slipped. Third, FCFF is discounted at WACC and needs a debt deduction, while FCFE is discounted at the required return on equity and does not. Fourth, transactions with shareholders leave free cash flow untouched, while changes in leverage move FCFE up in the year of issuance and down thereafter. Fifth, in every multistage model, the terminal value dominates, so the sustainable growth rate and the normalisation of the final explicit year deserve more attention than the early years that are easier to forecast.