Unlike dividends, FCFF and FCFE are not readily available data. Analysts need to compute these quantities from available financial information, which requires a clear understanding of free cash flows and the ability to interpret and use the information correctly. Forecasting future free cash flows is also a rich and demanding exercise. The analyst’s understanding of a company’s financial statements, its operations, its financing, and its industry can pay real “dividends” as he addresses that task. Many analysts consider free cash flow models to be more useful than DDMs in practice. Free cash flows provide an economically sound basis for valuation.

Analysts like to use free cash flow as the return (either FCFF or FCFE) whenever one or more of the following conditions is present:

Common equity can be valued directly by using FCFE or indirectly by first using an FCFF model to estimate the value of the firm and then subtracting the value of non-common-stock capital (usually debt) from FCFF to arrive at an estimate of the value of equity. The purpose of this chapter is to develop the background required to use the FCFF or FCFE approaches to value a company’s equity.

Section 2 defines the concepts of free cash flow to the firm and free cash flow to equity and then presents the two valuation models based on discounting of FCFF and FCFE. We also explore the constant-growth models for valuing FCFF and FCFE, which are special cases of the general models, in this section. After reviewing the FCFF and FCFE valuation process in Section 2, we turn in Section 3 to the vital task of calculating and forecasting FCFF and FCFE. Section 4 explains multistage free cash flow valuation models and presents some of the issues associated with their application. Analysts usually value operating assets and nonoperating assets separately and then combine them to find the total value of the firm, an approach described in Section 5.

Free cash flow to equity is the cash flow available to the company’s holders of common equity after all operating expenses, interest, and principal payments have been paid and necessary investments in working and fixed capital have been made. FCFE is the cash flow from operations minus capital expenditures minus payments to (and plus receipts from) debt holders.

The way in which free cash flow is related to a company’s net income, cash flow from operations, and measures such as EBITDA (earnings before interest, taxes, depreciation, and amortization) is important: The analyst must understand the relationship between a company’s reported accounting data and free cash flow in order to forecast free cash flow and its expected growth. Although a company reports cash flow from operations (CFO) on the statement of cash flows, CFO is not free cash flow. Net income and CFO data can be used, however, in determining a company’s free cash flow.

The advantage of FCFF and FCFE over other cash flow concepts is that they can be used directly in a DCF framework to value the firm or to value equity. Other cash flow- or earnings-related measures, such as CFO, net income, EBIT, and EBITDA, do not have this property because they either double-count or omit cash flows in some way. For example, EBIT and EBITDA are before-tax measures, and the cash flows available to investors (in the firm or in the equity of the firm) must be after tax. From the stockholders’ perspective, EBITDA and similar measures do not account for differing capital structures (the after-tax interest expenses or preferred dividends) or for the funds that bondholders supply to finance investments in operating assets. Moreover, these measures do not account for the reinvestment of cash flows that the company makes in capital assets and working capital to maintain or maximize the long-run value of the firm.

Using free cash flow in valuation is more challenging than using dividends because in forecasting free cash flow, the analyst must integrate the cash flows from the company’s operations with those from its investing and financing activities. Because FCFF is the after-tax cash flow going to all suppliers of capital to the firm, the value of the firm is estimated by discounting FCFF at the weighted average cost of capital (WACC). An estimate of the value of equity is then found by subtracting the value of debt from the estimated value of the firm. The value of equity can also be estimated directly by discounting FCFE at the required rate of return for equity (because FCFE is the cash flow going to common stockholders, the required rate of return on equity is the appropriate risk -adjusted rate for discounting FCFE).

The two free cash flow approaches, indirect and direct, for valuing equity should theoretically yield the same estimates if all inputs reflect identical assumptions. An analyst may prefer to use one approach rather than the other, however, because of the characteristics of the company being valued. For example, if the company’s capital structure is relatively stable, using FCFE to value equity is more direct and simpler than using FCFF. The FCFF model is often chosen, however, in two other cases:

In the following, we present the general form of the FCFF valuation model and the FCFE valuation model.

Because FCFF is the cash flow available to all suppliers of capital, using WACC to discount FCFF gives the total value of all of the firm’s capital. The value of equity is the value of the firm minus the market value of its debt:

The cost of capital is the required rate of return that investors should demand for a cash flow stream like that generated by the company being analyzed. WACC depends on the riskiness of these cash flows. The calculation and interpretation of WACC were discussed in Chapter 2—that is, WACC is the weighted average of the after (corporate) tax required rates of return for debt and equity, where the weights are the proportions of the firm’s total market value from each source, debt and equity. As an alternative, analysts may use the weights of debt and equity in the firm’s target capital structure when those weights are known and differ from market value weights. The formula for WACC is MV(Debt) and MV(Equity) are the current market values of debt and equity, not their book or accounting values, and the ratios of MV(Debt) and MV(Equity) to the total market value of debt plus equity define the weights in the WACC formula. The quantities r_d (1 - Tax rate) and r are, respectively, the after-tax cost of debt and the after-tax cost of equity (in the case of equity, one could just write “cost of equity” because net income, the income belonging to equity, is after tax). In Equation 4-3, the tax rate is in principle the marginal corporate income tax rate.

Because FCFE is the cash flow remaining for equity holders after all other claims have been satisfied, discounting FCFE by r (the required rate of return on equity) gives the value of the firm’s equity. Dividing the total value of equity by the number of outstanding shares gives the value per share.

The value of equity if FCFE is growing at a constant rate is

In this section, we presented the basic ideas underlying free cash flow valuation and the simplest implementation, single-stage free cash flow models. The next section examines the precise definition of free cash flow and introduces the issues involved in forecasting free cash flow.

For most of this section, we assume that the company has two sources of capital, debt and common stock. Once the concepts of FCFF and FCFE are understood for a company financed by using only debt and common stock, it is easy to incorporate preferred stock for the relatively small number of companies that actually use it (in Section 3.8 we incorporate preferred stock as a third source of capital).

Consider each component of FCFF. The starting point in Equation 4-7 is net income available to common shareholders—the bottom line in an income statement. It represents income after depreciation, amortization, interest expense, income taxes, and the payment of dividends to preferred shareholders (but not payment of dividends to common shareholders).

Net noncash charges represent an adjustment for noncash decreases and increases in net income. This adjustment is the first of several that analysts generally perform on a net basis. If noncash decreases in net income exceed the increases, as is usually the case, the adjustment is positive. If noncash increases exceed noncash decreases, the adjustment is negative. The most common noncash charge is depreciation expense. When a company purchases fixed capital, such as equipment, the balance sheet reflects a cash outflow at the time of the purchase. In subsequent periods, the company records depreciation expense as the asset is used. The depreciation expense reduces net income but is not a cash outflow. Depreciation expense is thus one (the most common) noncash charge that must be added back in computing FCFF. In the case of intangible assets, there is a similar noncash charge, amortization expense, which must be added back. Other noncash charges vary from company to company and are discussed in Section 3.3.

After-tax interest expense must be added back to net income to arrive at FCFF. This step is required because interest expense net of the related tax savings was deducted in arriving at net income and because interest is a cash flow available to one of the company’s capital providers (i.e., the company’s creditors). In the United States and many other countries, interest is tax deductible (reduces taxes) for the company (borrower) and taxable for the recipient (lender). As we explain later, when we discount FCFF, we use an after-tax cost of capital. For consistency, we thus compute FCFF by using the after-tax interest paid.⁸⁹

Similar to after-tax interest expense, if a company has preferred stock, dividends on that preferred stock are deducted in arriving at net income available to common shareholders. Because preferred stock dividends are also a cash flow available to one of the company’s capital providers, this item is added back to arrive at FCFF. Further discussion of the effects of preferred stock is in Section 3.8.

Investments in fixed capital represent the outflows of cash to purchase fixed capital necessary to support the company’s current and future operations. These investments are capital expenditures for long-term assets, such as the property, plant, and equipment (PP&E) necessary to support the company’s operations. Necessary capital expenditures may also include intangible assets, such as trademarks. In the case of cash acquisition of another company instead of a direct acquisition of PP&E, the cash purchase amount can also be treated as a capital expenditure that reduces the company’s free cash flow (note that this treatment is conservative because it reduces FCFF). In the case of large acquisitions (and all noncash acquisitions), analysts must take care in evaluating the impact on future free cash flow. If a company receives cash in disposing of any of its fixed capital, the analyst must deduct this cash in calculating investment in fixed capital. For example, suppose we had a sale of equipment for $100,000. This cash inflow would reduce the company’s cash outflows for investments in fixed capital.

The company’s cash flow statement is an excellent source of information on capital expenditures as well as on sales of fixed capital. Analysts should be aware that some companies acquire fixed capital without using cash—for example, through an exchange for stock or debt. Such acquisitions do not appear in a company’s cash flow statement but, if material, must be disclosed in the footnotes. Although noncash exchanges do not affect historical FCFF, if the capital expenditures are necessary and may be made in cash in the future, the analyst should use this information in forecasting future FCFF.

The final point to cover is the important adjustment for net increases in working capital. This adjustment represents the net investment in current assets (such as accounts receivable) less current liabilities (such as accounts payable). Analysts can find this information by examining either the company’s balance sheet or its cash flow statement.

Although working capital is often defined as current assets minus current liabilities, working capital for cash flow and valuation purposes is defined to exclude cash and short-term debt (which includes notes payable and the current portion of long-term debt). When finding the net increase in working capital for the purpose of calculating free cash flow, we define working capital to exclude cash and cash equivalents as well as notes payable and the current portion of long-term debt. Cash and cash equivalents are excluded because a change in cash is what we are trying to explain. Notes payable and the current portion of long-term debt are excluded because they are liabilities with explicit interest costs that make them financing items rather than operating items.

Example 4-2 shows all of the adjustments to net income required to find FCFF.

In a statement of cash flows, cash flows are separated into three components: cash flow from operating activities (or cash flow from operations), cash flow from investing activities, and cash flow from financing activities. Cash flow from operations is the net amount of cash provided by the company’s operating activities. The operating section of the cash flow statement shows such cash flows as cash received from customers and cash paid to suppliers. Cash flow from investing activities includes the company’s investments in (or sales of) long-term assets—for example, PP&E and long-term investments in other companies. Cash flow from financing activities relates to the company’s activities in raising or repaying capital. International Financial Reporting Standards (IFRS) allow the company to classify interest paid as either an operating or financing activity. Furthermore, IFRS allow dividends paid to be classified as either an operating or financing activity. Interestingly, under U.S. generally accepted accounting principles (GAAP), interest expense paid to providers of debt capital must be classified as part of cash flow from operations (as is interest income) but payment of dividends to providers of equity capital is classified as a financing activity.

Exhibit 4-4 summarizes IFRS and U.S. GAAP treatment of interest and dividends.

To estimate FCFF by starting with CFO, we must recognize the treatment of interest paid. If the after-tax interest expense was taken out of net income and out of CFO, as with U.S. GAAP, then after-tax interest expense must be added back to get FCFF. In the case of U.S. GAAP, FCFF can be estimated as follows:

To reiterate, the after-tax interest expense is added back because it was previously taken out of net income. The investment in working capital does not appear in Equation 4-8 because CFO already includes investment in working capital. Example 4-3 illustrates the use of CFO to calculate FCFF. In this example, the calculation of CFO begins with calculating net income, an approach known as the indirect method.⁹⁰

Noncash restructuring charges may also cause an increase in net income in some circumstances—for example, when a company reverses part or all of a previous accrual. Gains and losses (e.g., of operating assets) are another noncash item that may increase or decrease net noncash charges. If a company sells a piece of equipment with a book value of €60,000 for €100,000, it reports the €40,000 gain as part of net income. The €40,000 gain is not a cash flow, however, and must be subtracted in arriving at FCFF. Note that the €100,000 is a cash flow and is part of the company’s net investment in fixed capital. A loss reduces net income and thus must be added back in arriving at FCFF. Aside from depreciation, gains and losses are the most commonly seen noncash charges that require an adjustment to net income. Analysts should examine the company’s cash flow statement to identify items particular to a company and to determine what adjustments the analyst might need to make for the accounting numbers to be useful for forecasting purposes.

Exhibit 4-8 summarizes the common noncash charges that affect net income and indicates for each item whether to add it to or subtract it from net income in arriving at FCFF.

The item “Deferred taxes” requires special attention because deferred taxes result from differences in the timing of reporting income and expenses in the company’s financial statements and the company’s tax return. The income tax expense deducted in arriving at net income for financial reporting purposes is not the same as the amount of cash taxes paid. Over time, these differences between book income and taxable income should offset each other and have no impact on aggregate cash flows. Generally, if the analyst’s purpose is forecasting and, therefore, identifying the persistent components of FCFF, then the analyst should not add back deferred tax changes that are expected to reverse in the near future. In some circumstances, however, a company may be able to consistently defer taxes until a much later date. If a company is growing and has the ability to indefinitely defer its tax liability, adding back deferred taxes to net income is warranted. Nevertheless, an acquirer must be aware that these taxes may be payable at some time in the future.

Companies often record expenses (e.g., restructuring charges) for financial reporting purposes that are not deductible for tax purposes. In this case, current tax payments are higher than taxes reported in the income statement, resulting in a deferred tax asset and a subtraction from net income to arrive at cash flow in the cash flow statement. If the deferred tax asset is expected to reverse in the near future (e.g., through tax depreciation deductions), to avoid underestimating future cash flows, the analyst should not subtract the deferred tax asset in a cash flow forecast. If the company is expected to have these charges on a continual basis, however, a subtraction that will lower the forecast of future cash flows is warranted.

Employee share-based compensation (stock options) provides another challenge to the forecaster. Under IFRS and U.S. GAAP, companies must record in the income statement an expense for options provided to employees. The granting of options themselves does not result in a cash outflow and is thus a noncash charge; however, the granting of options has long-term cash flow implications. When the employee exercises the option, the company receives some cash related to the exercise price of the option at the strike price. This cash flow is considered a financing cash flow. Also, in some cases, a company receives a tax benefit from issuing options, which could increase operating cash flow but not net income. Both IFRS and U.S. GAAP require that a portion of the tax effect be recorded as a financing cash flow rather than an operating cash flow in the cash flow statement. Analysts should review the cash flow statement and footnotes to determine the impact of options on operating cash flows. If these cash flows are not expected to persist in the future, analysts should not include them in their forecasts of cash flows. Analysts should also consider the impact of stock options on the number of shares outstanding. When computing equity value, analysts may want to use the number of shares expected to be outstanding (based on the exercise of employee stock options) rather than the number currently outstanding.

Example 4-5 illustrates that when forecasting cash flows for valuation purposes, analysts should consider the sustainability of historical working capital effects on free cash flow.

As Equation 4-9 shows, FCFE is found by starting from FCFF, subtracting after-tax interest expenses, and adding net new borrowing. The analyst can also find FCFF from FCFE by making the opposite adjustments—by adding after-tax interest expenses and subtracting net borrowing: FCFF = FCFE + Int(1 - Tax rate) - Net borrowing.

Exhibit 4-10 uses the values for FCFF for Cane Distribution calculated in Example 4-3 to show the calculation of FCFE when starting with FCFF. To calculate FCFE in this manner, we subtract after-tax interest expense from FCFF and then add net borrowing (equal to new debt borrowing minus debt repayment).

To reiterate, FCFE is the cash flow available to common stockholders—the cash flow remaining after all operating expenses (including taxes) have been paid, capital investments have been made, and other transactions with other suppliers of capital have been carried out. The company’s other capital suppliers include creditors, such as bondholders, and preferred stockholders. The cash flows (net of taxes) that arise from transactions with creditors and preferred stockholders are deducted from FCFF to arrive at FCFE.

FCFE is the amount that the company can afford to pay out as dividends. In actuality, for various reasons companies often pay out substantially more or substantially less than FCFE, so FCFE often differs from dividends paid. One reason for this difference is that the dividend decision is a discretionary decision of the board of directors. Most corporations manage their dividends; they prefer to raise them gradually over time, partly because they do not want to have to cut dividends. Many companies raise dividends slowly even when their earnings are increasing rapidly, and companies often maintain their current dividends even when their profitability has declined. Consequently, earnings are much more volatile than dividends.

In Equations 4-7 and 4-8, we show the calculation of FCFF starting with, respectively, net income and cash flow from operations. As Equation 4-9 shows, FCFE = FCFF - Int(1 - Tax rate) + Net borrowing. By subtracting after-tax interest expense and adding net borrowing to Equations 4-7 and 4-8, we have equations to calculate FCFE starting with, respectively, net income and CFO:

To show the relationship between EBIT and FCFF, we start with Equation 4-7 and assume that the only noncash charge (NCC) is depreciation (Dep):

The relationship between FCFF and EBITDA can also be easily shown. Net income can be expressed as

Many adjustments for noncash charges that are required to calculate FCFF when starting from net income are not required when starting from EBIT or EBITDA. In the calculation of net income, many noncash charges are made after computing EBIT or EBITDA, so they do not need to be added back when calculating FCFF based on EBIT or EBITDA. Another important consideration is that some noncash charges, such as depreciation, are tax deductible. A noncash charge that affects taxes must be accounted for.

In summary, in calculating FCFF from EBIT or EBITDA, whether an adjustment for a noncash charge is needed depends on where in the income statement the charge has been deducted; furthermore, the form of any needed adjustment depends on whether the noncash charge is a tax-deductible expense.

We can also calculate FCFE (instead of FCFF) from EBIT or EBITDA. An easy way to obtain FCFE based on EBIT or EBITDA is to use Equation 4-12 (the expression for FCFF in terms of EBIT) or Equation 4-13 (the expression for FCFF in terms of EBITDA), respectively, and then subtract Int(1 - Tax rate) and add net borrowing, because FCFE is related to FCFF as follows (see Equation 4-9):

Example 4-7 uses the Pitts Corporation financial statements to find FCFF and FCFE from EBIT and EBITDA.

In general, a firm has the following alternative uses of positive FCFF: (1) Retain the cash and thus increase the firm’s balances of cash and marketable securities; (2) use the cash for payments to providers of debt capital (i.e., interest payments and principal payments in excess of new borrowings); and (3) use the cash for payments to providers of equity capital (i.e., dividend payments and/or share repurchases in excess of new share issuances). Similarly, a firm has the following general alternatives for covering negative free cash flows: draw down cash balances, borrow additional cash, or issue equity.

The effects on the company’s capital structure of its transactions with capital providers should be noted. For a simple example, assume that free cash flows are zero and that the company makes no change to its cash balances. Obtaining cash via net new borrowings and using the cash for dividends or net share repurchases will increase the company’s leverage, whereas obtaining cash from net new share issuances and using that cash to make principal payments in excess of new borrowings will reduce leverage.

We calculate uses of FCFF as follows:

Increases (or minus decreases) in cash balances

Plus: Net payments to providers of debt capital, calculated as:

Plus: Payments to providers of equity capital, calculated as:

Free cash flows to equity reflect free cash flows to the firm net of the cash used for payments to providers of debt capital. Accordingly, we can calculate FCFE as follows:

Plus: Increases (or minus decreases) in cash balances

Plus: Payments to providers of equity capital, calculated as:

To illustrate the equivalence of sources and uses of FCFF and FCFE for the Pitts Corporation, whose financial statements are given in Exhibit 4-11 in Example 4-6, note the following for 2007:

In summary, an analysis of the uses of free cash flows shows that Pitts Corporation was using free cash flows to manage its capital structure by increasing debt. The additional debt was not needed to cover capital expenditures; the statement of cash flows showed that the company’s operating cash flows of $495 were more than adequate to cover its capital expenditures of $400. Instead, the additional debt was used, in part, to make dividend payments to the company’s shareholders.

One method for forecasting free cash flow involves applying some constant growth rate to a current level of free cash flow (possibly adjusted). The simplest basis for specifying the future growth rate is to assume that a historical growth rate will also apply to the future. This approach is appropriate if a company’s free cash flow has tended to grow at a constant rate and if historical relationships between free cash flow and fundamental factors are expected to continue. Example 4-8 asks that the reader apply this approach to the Pitts Corporation based on 2007 FCFF of $155 million as calculated in Examples 4-6 and 4-7.

A more complex approach is to forecast the components of free cash flow. This approach is able to capture the complex relationships among the components. One popular method⁹² is to forecast the individual components of free cash flow: EBIT(1 - Tax rate), net noncash charges, investment in fixed capital, and investment in working capital. EBIT can be forecasted directly or by forecasting sales and the company’s EBIT margin based on an analysis of historical data and the current and expected economic environment. Similarly, analysts can base forecasts of capital needs on historical relationships between increases in sales and investments in fixed and working capital.

In this discussion, we illustrate a simple sales-based forecasting method for FCFF and FCFE based on the following major assumption:

In addition, for FCFE forecasting, we assume that the capital structure represented by the debt ratio (DR)—debt as a percentage of debt plus equity—is constant. Under that assumption, DR indicates the percentage of the investment in fixed capital in excess of depreciation (also called net new investment in fixed capital) and in working capital that will be financed by debt. This method involves a simplification because it considers depreciation as the only noncash charge, so the method does not work well when that approximation is not a good assumption.

If depreciation reflects the annual cost for maintaining the existing capital stock, the difference between fixed capital investment and depreciation—incremental FCInv—should be related to the capital expenditures required for growth. In this case, the following inputs are needed:

In the case of FCFF forecasting, FCFF is calculated by forecasting EBIT(1 - Tax rate) and subtracting incremental fixed capital expenditures and incremental working capital expenditures (see Rappaport 1997). To estimate FCInv and WCInv, we multiply their past proportion to sales increases by the forecasted sales increases. Incremental fixed capital expenditures as a proportion of sales increases are computed as follows:

When depreciation is the only significant net noncash charge, this method yields the same results as the previous equations for estimating FCFF or FCFE. Rather than adding back all depreciation and subtracting all capital expenditures when starting with EBIT(1 - Tax rate), this approach simply subtracts the net capital expenditures in excess of depreciation.

Although the recognition may not be obvious, this approach recognizes that capital expenditures have two components: those expenditures necessary to maintain existing capacity (fixed capital replacement) and those incremental expenditures necessary for growth. In forecasting, the expenditures to maintain capacity are likely to be related to the current level of sales, and the expenditures for growth are likely to be related to the forecast of sales growth.

When forecasting FCFE, analysts often make an assumption that the financing of the company involves a target debt ratio. In this case, they assume that a specified percentage of the sum of (1) net new investment in fixed capital (new fixed capital minus depreciation expense) and (2) increase in working capital is financed based on a target DR. This assumption leads to a simplification of FCFE calculations. If we assume that depreciation is the only noncash charge, Equation 4-10, which is FCFE = NI + NCC - FCInv - WCInv + Net borrowing, becomes

Equation 4-15 says that FCFE equals NI minus the amount of fixed capital expenditure (net of depreciation) and working capital investment that is financed by equity. Again for Equation 4-15, we have assumed that the only noncash charge is depreciation.

Examples 4-9 and 4-10 illustrate this sales-based method for forecasting free cash flow to the firm.

This model can be used to forecast multiple periods and is flexible enough to allow varying sales growth rates, EBIT margins, tax rates, and rates of incremental capital increases.

The model need not begin with sales; it could start with net income, cash flow from operations, or EBITDA.

A similar model can be designed for FCFE, as shown in Example 4-11. In the case of FCFE, the analyst should begin with net income and must also forecast any net new borrowing or net preferred stock issue.

When the company being analyzed has significant noncash charges other than depreciation expense, the approach we have just illustrated will result in a less accurate estimate of FCFE than one obtained by forecasting all the individual components of FCFE. In some cases, the analyst will have specific forecasts of planned components, such as capital expenditures. In other cases, the analyst will study historical relationships, such as previous capital expenditures and sales levels, to develop a forecast.

For instance, in many corporate financial statements, the changes in balance sheet items (the increase in an asset or the decrease in a liability) differ from the changes reported in the statement of cash flows. Similarly, depreciation in the statement of cash flows may differ from depreciation expense in the income statement. How do such problems arise?

Factors that can cause discrepancies between changes in balance sheet accounts and the changes reported in the statement of cash flows include acquisitions or divestitures and the presence of nondomestic subsidiaries. For example, an increase in an inventory account may result from purchases from suppliers (which is an operating activity) or from an acquisition or merger with another company that has inventory on its balance sheet (which is an investing activity). Discrepancies may also occur from currency translations of the earnings of nondomestic subsidiaries.

Because the CFO figure from the statement of cash flows may be contaminated by cash flows arising from financing and/or investing activities, when analysts use CFO in a valuation context, ideally they should remove such contaminations. The resulting analyst-adjusted CFO is then the starting point for free cash flow calculations.

We have defined FCFF and FCFE and presented alternative (equivalent) ways to calculate both of them. So the reader should have a good idea of what is included in FCFF or FCFE but may wonder why some cash flows are not included. Specifically, what impact do dividends, share repurchases, share issuance, or changes in leverage have on FCFF and FCFE? The simple answer is: not much. Recall the formulas for FCFF and FCFE: and

Notice that dividends and share repurchases and issuance are absent from the formulas. The reason is that FCFF and FCFE are the cash flows available to investors or to stockholders; dividends and share repurchases are uses of these cash flows. So the simple answer is that transactions between the company and its shareholders (through cash dividends, share repurchases, and share issuances) do not affect free cash flow. Leverage changes, such as the use of more debt financing, have some impact because they increase the interest tax shield (reduce corporate taxes because of the tax deductibility of interest) and reduce the cash flow available to equity. In the long run, the investing and financing decisions made today will affect future cash flows.

If all the inputs were known and mutually consistent, a DDM and an FCFE model would result in identical valuations for a stock. One possibility would be that FCFE equals cash dividends each year. Then both cash flow streams would be discounted at the required return for equity and would have the same present value.

Generally, however, FCFE and dividends will differ, but the same economic forces that lead to low (high) dividends lead to low (high) FCFE. For example, a rapidly growing company with superior investment opportunities will retain a high proportion of earnings and pay low dividends. This same company will have high investments in fixed capital and working capital and have a low FCFE (which is clear from the expression FCFE = NI + NCC - FCInv - WCInv + Net borrowing). Conversely, a mature company that is investing relatively little might have high dividends and high FCFE. In spite of this tendency, however, FCFE and dividends will usually differ.

FCFF and FCFE, as defined in this book, are measures of cash flow designed for valuation of the firm or its equity. Other definitions of free cash flow frequently appear in textbooks, articles, and vendor-supplied databases of financial information on public companies. In many cases, these other definitions of free cash flow are not designed for valuation purposes and thus should not be used for valuation. Using numbers supplied by others without knowing exactly how they are defined increases the likelihood of making errors in valuation. As consumers and producers of research, analysts should understand (if consumers) or make clear (if producers) the definition of free cash flow being used.

Because using free cash flow analysis requires considerable care and understanding, some practitioners erroneously use earnings components such as NI, EBIT, EBITDA, or CFO in a discounted cash flow valuation. Such mistakes may lead the practitioner to systematically overstate or understate the value of a stock. Shortcuts can be costly.

A common shortcut is to use EBITDA as a proxy for the cash flow to the firm. Equation 4-13 clearly shows the differences between EBITDA and FCFF:

Depreciation charges as a percentage of EBITDA differ substantially for different companies and industries, as does the depreciation tax shield (the depreciation charge times the tax rate). Although FCFF captures this difference, EBITDA does not. EBITDA also does not account for the investments a company makes in fixed capital or working capital. Hence, EBITDA is a poor measure of the cash flow available to the company’s investors. Using EBITDA (instead of free cash flow) in a DCF model has another important aspect as well: EBITDA is a before-tax measure, so the discount rate applied to EBITDA would be a before-tax rate. The WACC used to discount FCFF is an after-tax cost of capital.

EBITDA is a poor proxy for free cash flow to the firm because it does not account for the depreciation tax shield and the investment in fixed capital and working capital, but it is an even poorer proxy for free cash flow to equity. From a stockholder’s perspective, additional defects of EBITDA include its failure to account for the after-tax interest costs or cash flows from new borrowing or debt repayments. Example 4-12 shows the mistakes sometimes made in discussions of cash flows.

For example, in Equation 4-7, which calculates FCFF starting with net income available to common shareholders, preferred dividends paid would be added to the cash flows to obtain FCFF. In Equation 4-10, which calculates FCFE starting with net income available to common shareholders, if preferred dividends were already subtracted when arriving at net income, no further adjustment for preferred dividends would be required. Issuing (redeeming) preferred stock increases (decreases) the cash flow available to common stockholders, however, so this term would have to be added in. The existence of preferred stock in the capital structure has many of the same effects as the existence of debt, except that unlike interest payments on debt, preferred stock dividends paid are not tax deductible.

Example 4-13 shows how to calculate WACC, FCFE, and FCFF when the company has preferred stock.

Paying cash dividends on common stock does not affect FCFF or FCFE, which are the amounts of cash available to all investors or to common stockholders. It is simply a use of the available cash. Share repurchases of common stock also do not affect FCFF or FCFE. Share repurchases are, in many respects, a substitute for cash dividends. Similarly, issuing shares of common stock does not affect FCFF or FCFE.

Changing leverage, however (changing the amount of debt financing in the company’s capital structure), does have some effects on FCFE particularly. An increase in leverage will not affect FCFF (although it might affect the calculations used to arrive at FCFF). An increase in leverage affects FCFE in two ways. In the year the debt is issued, it increases the FCFE by the amount of debt issued. After the debt is issued, FCFE is then reduced by the after-tax interest expense.

In Section 3, we have discussed the concepts of FCFF and FCFE and their estimation. The next section presents additional valuation models that use forecasts of FCFF or FCFE to value the firm or its equity. These free cash flow models are similar in structure to dividend discount models, although the analyst must face the reality that estimating free cash flows is more time-consuming than estimating dividends.

In Section 2.3, we presented the single-stage free cash flow model, which has a constant growth rate. In the following, we use the single-stage model to address selected valuation issues; we then present multistage free cash flow models.

Several securities firms have adapted the single-stage FCFE model to address some of the challenges of international valuation. They choose to analyze companies by using real cash flows and real discount rates instead of nominal values. To estimate real discount rates, they use a modification of the build-up method mentioned in Chapter 2. Starting with a country return, which is a real required rate of return for stocks from a particular country, they then make adjustments to the country return for the stock’s industry, size, and leverage:

The adjustments in the model should have sound economic justification. They should reflect factors expected to affect the relative risk and return associated with an investment.

The securities firms making these adjustments predict the growth rate of FCFE also in real terms. The firms supply their analysts with estimates of the real economic growth rate for each country, and each analyst chooses a real growth rate for the stock being analyzed that is benchmarked against the real country growth rate. This approach is particularly useful for countries with high or variable inflation rates.

The value of the stock is found with an equation essentially like Equation 4-6 except that all variables in the equation are stated in real terms:

Whenever real discount rates and real growth rates can be estimated more reliably than nominal discount rates and nominal growth rates, this method is worth using. Example 4-14 shows how this procedure can be applied.

The base-year values for the FCFF or FCFE growth models are also critical. Given the same required rates of return and growth rates, the value of the firm or the value of equity will increase or decrease proportionately with the initial value of FCFF or FCFE used.

To examine how sensitive the final valuation is to changes in each of a valuation model’s input variables, analysts can perform a sensitivity analysis. Some input variables have a much larger impact on stock valuation than others. Example 4-15 shows the sensitivity of the valuation of Petroleo Brasileiro to four input variables.

In two-stage free cash flow models, the growth rate in the second stage is a long-run sustainable growth rate. For a declining industry, the second-stage growth rate could be slightly below the GDP growth rate. For an industry that is expected to grow in the future faster than the overall economy, the second-stage growth rate could be slightly greater than the GDP growth rate.

The two most popular versions of the two-stage FCFF and FCFE models are distinguished by the pattern of the growth rates in stage 1. In one version, the growth rate is constant in stage 1 before dropping to the long-run sustainable rate in stage 2. In the other version, the growth rate declines in stage 1 to reach the sustainable rate at the beginning of stage 2. This second type of model is like the H-model for discounted dividend valuation, in which dividend growth rates decline in stage 1 and are constant in stage 2.

Unlike multistage DDMs, in which the growth rates are consistently dividend growth rates, in free cash flow models, the growth rate may refer to different variables (which variables should be stated or should be clear from the context). The growth rate could be the growth rate for FCFF or FCFE, the growth rate for income (either net income or operating income), or the growth rate for sales. If the growth rate is for net income, the changes in FCFF or FCFE also depend on investments in operating assets and the financing of these investments. When the growth rate in income declines, such as between stage 1 and stage 2, investments in operating assets probably decline at the same time. If the growth rate is for sales, changes in net profit margins as well as investments in operating assets and financing policies will determine FCFF and FCFE.

A general expression for the two-stage FCFF valuation model is

The general expression for the two-stage FCFE valuation model is

In Equation 4-17, the terminal value of the stock at t = n, TV_n, is found by using the constant-growth FCFE model. In this case, TV_n = FCFE_n+1/(r - g). (Of course, the analyst might choose to estimate terminal value another way, such as using a price-to earnings ratio (P/E) multiplied by the company’s forecasted EPS.) The terminal value estimation is critical for a simple reason: The present value of the terminal value is often a substantial portion of the total value of the stock. For example, in Equation 4-17, when the analyst is calculating the total present value of the first n cash flows (FCFE) and the present value of the terminal value, the present value of the terminal value is often substantial. In the examples that follow, the terminal value usually represents a substantial part of total estimated value. The same is true in practice.

In this section, we present two examples of the two-stage model with declining growth rates in stage 1. In the first example, the growth rate of EPS declines during stage 1. As a company’s profitability declines and the company is no longer generating high returns, the company will usually reduce its net new investment in operating assets. The debt financing accompanying the new investments will also decline. Many highly profitable, growing companies have negative or low free cash flows. Later, when growth in profits slows, investments will tend to slow and the company will experience positive cash flows. Of course, the negative cash flows incurred in the high-growth stage help determine the cash flows that occur in future years.

Example 4-17 models FCFE per share as a function of EPS that declines constantly during stage 1. Because of declining earnings growth rates, the company in the example also reduces its new investments over time. The value of the company depends on these free cash flows, which are substantial after the high-growth (and high-profitability) period has largely elapsed.

The FCFE in Example 4-17 was based on forecasts of future EPS. Analysts often model a company by forecasting future sales and then estimating the profits, investments, and financing associated with those sales levels. For large companies, analysts may estimate the sales, profitability, investments, and financing for each division or large subsidiary. Then they aggregate the free cash flows for all of the divisions or subsidiaries to get the free cash flow for the company as a whole.

Example 4 -18 is a two-stage FCFE model with declining sales growth rates in stage 1, with profits, investments, and financing keyed to sales. In stage 1, the growth rate of sales and the profit margin on sales both decline as the company matures and faces more competition and slower growth.

A second common model is a three-stage model with constant growth rates in stages 1 and 3 and a declining growth rate in stage 2. Again, the growth rates could be applied to sales or to FCFF or FCFE. Although future FCFF and FCFE are unlikely to follow the assumptions of either of these three-stage growth models, analysts often find such models to be useful approximations.

Example 4-19 is a three-stage FCFF valuation model with declining growth rates in stage 2. The model directly forecasts FCFF instead of deriving FCFF from a more complicated model that estimates cash flow from operations and investments in fixed and working capital.

The next section discusses an important technical issue, the treatment of nonoperating assets in valuation.