CHAPTER 14 : FREE CASH FLOW TO EQUITY DISCOUNT MODELS

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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.

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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:

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Free Cash Flow to Equity
=
Net Income
- (Capital Expenditures - Depreciation)(1 - δ)
- (∆ Working Capital)(1-δ)
Note that the net debt payment item is eliminated, because debt repayments are
financed with new debt issues to keep the debt ratio fixed. It is particularly useful to
assume that a specified proportion of net capital expenditures and working capital needs
will be financed with debt if the target or optimal debt ratio of the firm is used to forecast
the free cash flow to equity that will be available in future periods. Alternatively, in
examining past periods, we can use the firm’s average debt ratio over the period to arrive
at approximate free cash flows to equity.
What about preferred dividends?
In both the long and short formulations of free cashflows to equity described in
the section above, we have assumed that there are no preferred dividends paid. Since the
equity that we value is only common equity, you would need to modify the formulae
slightly for the existence of preferred stock and dividends. In particular, you would
subtract out the preferred dividends to arrive at the free cashflow to equity:

Free Cash Flow to Equity (FCFE)
=
Net Income - (Capital Expenditures -
Depreciation) - (Change in Non-cash Working Capital) – (Preferred Dividends + New
Preferred Stock Issued) + (New Debt Issued - Debt Repayments)

In the short form, you would obtain the following:
Free Cash Flow to Equity
=
Net Income - Preferred Dividend - (Capital
Expenditures - Depreciation)(1 - δ) - (∆ Working Capital)(1-δ)
The non-equity financial ratio (δ) would then have to include the expected financing from
new preferred stock issues.
Illustration 14.1: Estimating Free Cash Flows to Equity – The Home Depot and Boeing
In this illustration, we estimate the free cash flows to equity for the Home Depot,
the home improvement retail giant, and Boeing. We begin by estimating the free cash flow

1 The mix has to be fixed in book value terms. It can be varying in market value terms.

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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
Capital
Change in
Net Debt
FCFE
n
Spending
Non-cash
Issued
Working
Capital
1
$111.95
$21.12
$190.24
$6.20
$181.88
$118.51
2
$163.43
$34.36
$398.11
$10.41
$228.43
$17.70
3
$249.15
$52.28
$431.66
$47.14
-$1.94
($179.31)
4
$362.86
$69.54
$432.51
$93.08
$802.87
$709.68
5
$457.40
$89.84
$864.16
$153.19
-$2.01
($472.12)
6
$604.50
$129.61
$1,100.65
$205.29
$97.83
($474.00)
7
$731.52
$181.21
$1,278.10
$247.38
$497.18
($115.57)
8
$937.74
$232.34
$1,194.42
$124.25
$470.24
$321.65
9
$1,160.00
$283.00
$1,481.00
$391.00
-$25.00
($454.00)
10
$1,615.00
$373.00
$2,059.00
$131.00
$238.00
$36.00
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-
Change in Non-Cash WC
FCFE
DR)
(1-DR)
1
$111.95
$124.24
$4.55
($16.84)
2
$163.43
$267.21
$7.65
($111.43)

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3
$249.15
$278.69
$34.63
($64.17)
4
$362.86
$266.64
$68.38
$27.85
5
$457.40
$568.81
$112.53
($223.95)
6
$604.50
$713.32
$150.81
($259.63)
7
$731.52
$805.77
$181.72
($255.98)
8
$937.74
$706.74
$91.27
$139.72
9
$1,160.00
$880.05
$287.23
($7.28)
10
$1,615.00
$1,238.53
$96.23
$280.24
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
14.3
Table 14.3: Approximate FCFE on Boeing from 1989 to 1998
Year
Net Income Net Capital Expenditures (1- Change in Non-Cash WC
FCFE
DR)
(1-DR)
1
$973.00
$423.80
$333.27
$215.93
2
$1,385.00
$523.55
$113.59
$747.86
3
$1,567.00
$590.44
($55.35)
$1,031.92
4
$552.00
$691.34
($555.26)
$415.92
5
$1,244.00
$209.88
$268.12
$766.00
6
$856.00
($200.08)
$6.34
$1,049.74
7
$393.00
($232.95)
($340.77)
$966.72
8
$1,818.00
($155.68)
($21.91)
$1,995.59
9
($178.00)
$516.63
($650.98)
($43.65)
10
$1,120.00
$754.77
$107.25
$257.98
Average
$973.00
$312.17
($79.57)
$740.40

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∂ = Average debt ratio during the period = 42.34%
During the period, Boeing financed a high proportion of its reinvestment needs with debt,
and its market debt ratio increased from about 1% to approximately 20%. The average
free cash flow to equity during the period was $740.40 million. Note that the 1997 and
1998 capital expenditures include the amount spent by Boeing to acquire McDonnell
Douglas.
Comparing Dividends to Free Cash Flows to Equity
The conventional measure of dividend policy –– the dividend payout ratio ––
gives us the value of dividends as a proportion of earnings. In contrast, our approach
measures the total cash returned to stockholders as a proportion of the free cash flow to
equity.
Dividends
Dividend Payout Ratio = Earnings
Dividends +
Repurchase
Equity
s
Cash to Stockholders to FCFE Ratio =
FCFE
The ratio of cash to FCFE to the stockholders shows how much of the cash available to
be paid out to stockholders is actually returned to them in the form of dividends and
stock buybacks. If this ratio, over time, is equal or close to 1, the firm is paying out all
that it can to its stockholders. If it is significantly less than 1, the firm is paying out less
than it can afford to and is using the difference to increase its cash balance or to invest in
marketable securities. If it is significantly over 1, the firm is paying out more than it can
afford and is either drawing on an existing cash balance or issuing new securities (stocks or
bonds).
We can observe the tendency of firms to pay out less to stockholders than they
have available in free cash flows to equity by examining cash returned to stockholders
paid as a percentage of free cash flow to equity. In 1998, for instance, the average
dividend to free cash flow to equity ratio across all firms on the NYSE was 51.55%.
Figure 14.1 shows the distribution of cash returned as a percent of FCFE across all firms.

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Figure 14.1: Dividends/FCFE: US firms in 2000
350
300
250
200
150
Number of Firms
100
50
0
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
> 100%
Dividends/FCFE
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.

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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:

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Figure 14.2: Dividend Changes : 1989-1998
60.00%
50.00%
40.00%
30.00%
% of all firms 20.00%
10.00%
0.00%
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
Year
Increasing dividends
Decreasing dividends
Not changing dividends
Source: Compustat
The number of firms increasing dividends outnumbers that decreasing dividends, seven to
one. The number of firms, however, that do not change dividends outnumbers firms that
do, about four to one. Dividends are also less variable than either FCFE or earnings, but
this reduced volatility is a result of keeping dividends significantly below the FCFE.
2. Future Investment Needs
A firm might hold back on paying its entire FCFE as dividends, if it expects
substantial increases in capital expenditure needs in the future. Since issuing securities is
expensive (from a flotation cost standpoint), it may choose to keep the excess cash to
finance these future needs. Thus, to the degree that a firm may be unsure about its future
financing needs, it may choose to retain some cash to take on unexpected investments or
meet unanticipated needs.
3. Tax Factors
If dividends are taxed at a higher tax rate than capital gains, a firm may choose to
retain the excess cash and pay out much less in dividends than it has available. This is
likely to be accentuated if the stockholders in the firm are in high tax brackets, as is the
case with many family-controlled firms. If on the other hand, investors in the firm like

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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.
1. 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.

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