Download INDIVIDUAL REFLECTIVE REPORT [edited] and more Study Guides, Projects, Research Project Management in PDF only on Docsity!
CHAPTER 14
FREE CASH FLOW TO EQUITY DISCOUNT MODELS
The dividend discount model is based upon the premise that the only cashflows received by stockholders is dividends. Even if we use the modified version of the model and treat stock buybacks as dividends, we may misvalue firms that consistently return less or more than they can afford to their stockholders. This chapter uses a more expansive definition of cashflows to equity as the cashflows left over after meeting all financial obligations, including debt payments, and after covering capital expenditure and working capital needs. It discusses the reasons for differences between dividends and free cash flows to equity, and presents the discounted free cashflow to equity model for valuation.
Measuring what firms can return to their stockholders Given what firms are returning to their stockholders in the form of dividends or stock buybacks, how do we decide whether they are returning too much or too little? We measure how much cash is available to be paid out to stockholders after meeting reinvestment needs and compare this amount to the amount actually returned to stockholders.
Free Cash Flows to Equity To estimate how much cash a firm can afford to return to its stockholders, we begin with the net income –– the accounting measure of the stockholders’ earnings during the period –– and convert it to a cash flow by subtracting out a firm’s reinvestment needs. First, any capital expenditures, defined broadly to include acquisitions, are subtracted from the net income, since they represent cash outflows. Depreciation and amortization, on the other hand, are added back in because they are non-cash charges. The difference between capital expenditures and depreciation is referred to as net capital expenditures and is usually a function of the growth characteristics of the firm. High-growth firms tend to have high net capital expenditures relative to earnings, whereas low-growth firms may have low, and sometimes even negative, net capital expenditures.
Second, increases in working capital drain a firm’s cash flows, while decreases in working capital increase the cash flows available to equity investors. Firms that are growing fast, in industries with high working capital requirements (retailing, for instance), typically have large increases in working capital. Since we are interested in the cash flow effects, we consider only changes in non-cash working capital in this analysis. Finally, equity investors also have to consider the effect of changes in the levels of debt on their cash flows. Repaying the principal on existing debt represents a cash outflow; but the debt repayment may be fully or partially financed by the issue of new debt, which is a cash inflow. Again, netting the repayment of old debt against the new debt issues provides a measure of the cash flow effects of changes in debt. Allowing for the cash flow effects of net capital expenditures, changes in working capital and net changes in debt on equity investors, we can define the cash flows left over after these changes as the free cash flow to equity (FCFE). Free Cash Flow to Equity (FCFE) = Net Income
- (Capital Expenditures - Depreciation)
- (Change in Non-cash Working Capital)
- (New Debt Issued - Debt Repayments) This is the cash flow available to be paid out as dividends or stock buybacks. This calculation can be simplified if we assume that the net capital expenditures
and working capital changes are financed using a fixed mix1 of debt and equity. If δ is the proportion of the net capital expenditures and working capital changes that is raised from debt financing, the effect on cash flows to equity of these items can be represented as follows: Equity Cash Flows associated with Capital Expenditure Needs = – (Capital Expenditures
- Depreciation)(1 - δ) Equity Cash Flows associated with Working Capital Needs = - (∆ Working Capital)(1-δ) Accordingly, the cash flow available for equity investors after meeting capital expenditure and working capital needs, assuming the book value of debt and equity mixture is constant, is:
to equity for the Home Depot each year from 1989 to 1998 in Table 14.1, using the full calculation described in the last section. Table 14.1: Estimates of Free Cashflow to Equity for The Home Depot: 1989 – 1998 Year Net Income Depreciatio n
Capital Spending
Change in Non-cash Working Capital
Net Debt Issued
FCFE
Average $639.36 $146.63 $942.99 $140.89 $248.75 ($49.15) As Table 14.1 indicates, the Home Depot had negative free cash flows to equity in 5 of the 10 years, largely as a consequence of significant capital expenditures. The average net debt issued during the period was $248.75 million and the average net capital expenditure and working capital needs amounted to $937.25 million ($ 942.99-146.63+140.89) resulting in a debt ratio of 26.54%. Using the approximate formulation for the constant debt and equity financing mixture for FCFE, Table 14.2 yields the following results for FCFE for the same period. Table 14.2: Approximate FCFE Using Average Debt Ratio Year Net Income Net Capital Expenditures (1- DR)
Change in Non-Cash WC (1-DR)
FCFE
Average $639.36 $585.00 $103.50 ($49.15)
∂ = Average debt ratio during the period = 26.54%
Note that the approximate formulation yields the same average FCFE for the period. Since new debt issues are averaged out over the 10 years in the approach, it also smoothes out the annual FCFE, since actual debt issues are much more unevenly spread over time. A similar estimation of FCFE was done for Boeing from 1989 to 1998 in Table
Table 14.3: Approximate FCFE on Boeing from 1989 to 1998 Year Net Income Net Capital Expenditures (1- DR)
Change in Non-Cash WC (1-DR)
FCFE
Average $973.00 $312.17 ($79.57) $740.
Source: Compustat database 1998 A percentage less than 100% means that the firm is paying out less in dividends than it has available in free cash flows and that it is generating surplus cash. For those firms that did not make net debt payments (debt payments in excess of new debt issues) during the period, this cash surplus appears as an increase in the cash balance. A percentage greater than 100% indicates that the firm is paying out more in dividends than it has available in cash flow. These firms have to finance these dividend payments either out of existing cash balances or by making new stock and debt issues. The implications for valuation are simple. If we use the dividend discount model and do not allow for the build-up of cash that occurs when firms pay out less than they can afford, we will under estimate the value of equity in firms. The rest of this chapter is designed to correct for this limitation.
dividends.xls : This spreadsheet allows you to estimate the free cash flow to equity and the cash returned to stockholders for a period of up to 10 years.
Figure 14.1: Dividends/FCFE: US firms in 2000
0
50
100
150
200
250
300
350
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% > 100% Dividends/FCFE
Number of Firms
divfcfe.xls : There is a dataset on the web that summarizes dividends, cash returned to stockholders and free cash flows to equity, by sector, in the United States.
Why Firms may pay out less than is available Many firms pay out less to stockholders, in the form of dividends and stock buybacks, than they have available in free cash flows to equity. The reasons vary from firm to firm and we list some below.
1. Desire for Stability Firms are generally reluctant to change dividends; and dividends are considered 'sticky' because the variability in dividends is significantly lower than the variability in earnings or cashflows. The unwillingness to change dividends is accentuated when firms have to reduce dividends and, empirically, increases in dividends outnumber cuts in dividends by at least a five-to-one margin in most periods. As a consequence of this reluctance to cut dividends, firms will often refuse to increase dividends even when earnings and FCFE go up, because they are uncertain about their capacity to maintain these higher dividends. This leads to a lag between earnings increases and dividend increases. Similarly, firms frequently keep dividends unchanged in the face of declining earnings and FCFE. Figure 14.2 reports the number of dividend changes (increases, decreases, no changes) between 1989 and 1998:
dividends or tax laws favor dividends, the firm may pay more out in dividends than it has available in FCFE, often borrowing or issuing new stock to do so.
4. Signaling Prerogatives Firms often use dividends as signals of future prospects, with increases in dividends being viewed as positive signals and decreases as negative signals. The empirical evidence is consistent with this signaling story, since stock prices generally go up on dividend increases, and down on dividend decreases. The use of dividends as signals may lead to differences between dividends and FCFE. 5. Managerial Self-interest The managers of a firm may gain by retaining cash rather than paying it out as a dividend. The desire for empire building may make increasing the size of the firm an objective on its own. Or, management may feel the need to build up a cash cushion to tide over periods when earnings may dip; in such periods, the cash cushion may reduce or obscure the earnings drop and may allow managers to remain in control.
FCFE Valuation Models The free cash flow to equity model does not represent a radical departure from the traditional dividend discount model. In fact, one way to describe a free cash flow to equity model is that it represents a model where we discount potential dividends rather than actual dividends. Consequently, the three versions of the FCFE valuation model presented in this section are simple variants on the dividend discount model, with one significant change - free cashflows to equity replace dividends in the models.
Underlying Principle When we replace the dividends with FCFE to value equity, we are doing more than substituting one cash flow for another. We are implicitly assuming that the FCFE will be paid out to stockholders. There are two consequences.
- There will be no future cash build-up in the firm, since the cash that is available after debt payments and reinvestment needs is paid out to stockholders each period.
- The expected growth in FCFE will include growth in income from operating assets and not growth in income from increases in marketable securities. This follows directly from the last point. How does discounting free cashflows to equity compare with the modified dividend discount model, where stock buybacks are added back to dividends and discounted? You can consider stock buybacks to be the return of excess cash accumulated largely as a consequence of not paying out their FCFE as dividends. Thus, FCFE represent a smoothed out measure of what companies can return to their stockholders over time in the form of dividends and stock buybacks.
Estimating Growth in FCFE Free cash flows to equity, like dividends, are cash flows to equity investors and you could use the same approach that you used to estimate the fundamental growth rate in dividends per share. Expected Growth rate = Retention Ratio * Return on Equity The use of the retention ratio in this equation implies that whatever is not paid out as dividends is reinvested back into the firm. There is a strong argument to be made, though, that this is not consistent with the assumption that free cash flows to equity are paid out to stockholders which underlies FCFE models. It is far more consistent to replace the retention ratio with the equity reinvestment rate, which measures the percent of net income that is invested back into the firm. Equity Reinvestment Rate =
Net Income 1 −NetCapEx+Changein WorkingCapital-NetDebtIssues
The return on equity may also have to be modified to reflect the fact that the conventional measure of the return includes interest income from cash and marketable securities in the numerator and the book value of equity also includes the value of the cash and marketable securities. In the FCFE model, there is no excess cash left in the firm and the return on equity should measure the return on non-cash investments. You could construct a modified version of the return on equity that measures the non-cash aspects.
significantly different from one.) To estimate the reinvestment for a stable growth firm, you can use one of two approaches.
- You can use the typical reinvestment rates for firms in the industry to which the firm belongs. A simple way to do this is to use the average capital expenditure to depreciation ratio for the industry (or better still, just stable firms in the industry) to estimate a normalized capital expenditure for the firm.
- Alternatively, you can use the relationship between growth and fundamentals developed in Chapter 12 to estimate the required reinvestment. The expected growth in net income can be written as: Expected growth rate in net income = Equity Reinvestment Rate * Return on equity This allows us to estimate the equity reinvestment rate: Equity reinvestment rate = ExpectedReturnongrowthEquityrate
To illustrate, a firm with a stable growth rate of 4% and a return on equity of 12% would need to reinvest about a third of its net income back into net capital expenditures and working capital needs. Put another way, the free cash flows to equity should be two thirds of net income.
Best suited for firms This model, like the Gordon growth model, is best suited for firms growing at a rate comparable to or lower than the nominal growth in the economy. It is, however, the better model to use for stable firms that pay out dividends that are unsustainably high (because they exceed FCFE by a significant amount) or are significantly lower than the FCFE. Note, though, that if the firm is stable and pays outs its FCFE as dividend, the value obtained from this model will be the same as the one obtained from the Gordon growth model.
Illustration 14.2: FCFE Stable Growth Model: Singapore Airlines Rationale for using Model
- Singapore Airlines is a large firm in a mature industry. Given the competition for air passengers and the limited potential for growth, it seems reasonable to assume stable
growth for the future. Singapore Air’s revenues have grown about 3% a year for the last 5 years.
- Singapore Airlines has maintained a low book debt ratio historically and its management seems inclined to keep leverage low. Background Information In the financial year ended March 2001, Singapore Airlines reported net income of S$1,164 million on revenues of S$7,816 million, representing a non-cash return on equity of 10% for the year. The capital expenditures during the year amounted to S$2, million, but the average capital expenditures between 1997 and 2000 were S$1, million. The depreciation in 2000 was S$1,205 million. The firm has no working capital requirements. The book value debt to capital ratio at the end of 2000 was 5.44%. Estimation We begin by estimating a normalized free cash flow to equity for the current year. We will assume that earnings will grow 5% over the next year. To estimate net capital expenditures, we will use the average capital expenditures between 1997 and 2000 (to smooth out the year-to-year jumps) and the depreciation from the most recent year. Finally, we will assume that the 5.44% of future reinvestment needs will come from debt,
reflecting the firm’s current book debt ratio. Net Income this year = $1,164 m Net Cap Ex (1- Debt Ratio) = (1520-1205)(1-.0544) = $ 298 m Change in Working Capital (1- Debt Ratio) = 303 (1-.0544) = $ 287 m Normalized FCFE for current year = $ 580 m As a check, we also computed the equity reinvestment rate that Singapore Airlines would need to maintain to earn a growth of 5%, based upon its return on equity of 10%:
Equity reinvestment rate = (^) ROEg^ = 105 %%=50%
With this reinvestment rate, the free cash flows to equity would have been half the net income. The reinvestment we used in the calculation above is very close to this value:
(^2) In making estimates for the future, you can go with either book or market debt ratios, depending upon what you think about firm financing policy.
Leverage, FCFE and Equity Value Embedded in the FCFE computation seems to be the makings of a free lunch. Increasing the debt ratio increases free cash flow to equity because more of a firm’s reinvestment needs will come from borrowing and less is needed from equity investors. The released cash can be paid out as additional dividends or used for stock buybacks. In the case for Singapore Airlines, for instance, the free cash flow to equity is shown as a function of the debt to capital ratio in Figure 14.3:
If the free cash flow to equity increases as the leverage increases, does it follow that the value of equity will also increase with leverage? Not necessarily. The discount rate used is the cost of equity, which is estimated based upon a beta or betas. As leverage increases, the beta will also increase, pushing up the cost of equity. In fact, in the levered beta equation that we introduced in Chapter 8, the levered beta is: Levered beta = Unlevered beta (1 + (1- tax rate) (Debt/Equity)) This, in turn, will have a negative effect on equity value. The net effect on value will then depend upon which effect – the increase in cash flows or the increase in betas –
Figure 14.3: FCFE and Leverage- Singapore Airlines
$0.
$200.
$400.
$600.
$800.
$1,000.
$1,200.
0% 10% 20% 30% (^) Debt to Capital Ratio40% 50% 60% 70% 80% 90%
FCFE
dominates. Figure 14.4 graphs out the value of Singapore as a function of the debt to capital ratio
The value of equity is maximized at a debt ratio of 30%, but beyond that level, debt’s costs outweigh its benefits.
Figure 14.4: Singapore Air- Leverage and Value of Equity
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% Debt Ratio
Beta
$0.
$2,000.
$4,000.
$6,000.
$8,000.
$10,000.
$12,000.
$14,000.
Value of Equity
Value of Equity Beta
II. The Two-stage FCFE Model The two stage FCFE model is designed to value a firm which is expected to grow much faster than a stable firm in the initial period and at a stable rate after that.
The Model The value of any stock is the present value of the FCFE per year for the extraordinary growth period plus the present value of the terminal price at the end of the period.
Value
t n n
P
e e
t 1 k 1 k
FCFE
PVofFCFE PVofterminalprice
where, FCFEt = Free Cashflow to Equity in year t Pn = Price at the end of the extraordinary growth period ke = Cost of equity in high growth (hg) and stable growth (st) periods The terminal price is generally calculated using the infinite growth rate model,
Pn r − gn = FCFEn+^1
where, gn = Growth rate after the terminal year forever.
Calculating the terminal price The same caveats that apply to the growth rate for the stable growth rate model, described in the previous section, apply here as well. In addition, the assumptions made to derive the free cashflow to equity after the terminal year have to be consistent with the assumption of stability. For instance, while capital spending may be much greater than depreciation in the initial high growth phase, the difference should narrow as the firm enters its stable growth phase. We can use the two approaches described for the stable growth model – industry average capital expenditure requirements or the fundamental growth equation (equity reinvestment rate = g/ROE) to make this estimate.
The beta and debt ratio may also need to be adjusted in stable growth to reflect the fact that stable growth firms tend to have average risk (betas closer to one) and use more debt than high growth firms.
Illustration 14.3: Capital Expenditure, Depreciation and Growth Rates Assume you have a firm that is expected to have earnings growth of 20% for the next five years and 5% thereafter. The current earnings per share is $2.50. Current capital spending is $2.00 and current depreciation is $1.00. We assume that capital spending and depreciation grow at the same rate as earnings and there are no working capital requirements or debt.
Earnings in year 5 = 2.50 * (1.20)5 = $ 6. Capital spending in year 5 = 2.00 * (1.20)5 = $ 4. Depreciation in year 5 = 1.00 * (1.20)5 = $ 2. Free cashflow to equity in year 5 = $6.22 + 2.49 - 4.98 = $3. If we use the infinite growth rate model, but fail to adjust the imbalance between capital expenditures and depreciation, the free cashflow to equity in the terminal year is -- Free cashflow to equity in year 6 = 3.73* 1.05 = $ 3. This free cashflow to equity can then be used to compute the value per share at the end of year 5, but it will understate the true value. There are two ways in which you can adjust for this:
- Adjust capital expenditures in year 6 to reflect industry average capital expenditure needs: Assume, for instance, that capital expenditures are 150% of depreciation for the industry in which the firm operates. You could compute the capital expenditures in year 6 as follows: Depreciation in year 6 = 2.49 (1.05) = $2. Capital expenditures in year 6 = Depreciation in year 6* Industry average capital expenditures as percent of depreciation = $2.61 *1.50 = $3. FCFE in year 6 = $6.53 + $2.61 - $3.92 = $5.
- Estimate the equity reinvestment rate in year 6, based upon expected growth and the firm’s return on equity. For instance, if we assume that this firm’s return on
