**POTENTIAL DIVIDENDS AND ACTUAL
CASH FLOWS IN EQUITY VALUATION. A
CRITICAL ANALYSIS ^{1}**

IGNACIO VÉLEZ-PAREJA*^{1}, CARLO ALBERTO MAGNI^{2}

^{1}Master of Science en Industrial Engineering, University of Missouri, Estados Unidos.
Profesor Asociado, Universidad Tecnológica de Bolívar, Colombia.
Grupo de investigación Instituto de Estudios para el Desarrollo, IDE, Colombia.
Dirigir correspondencia a: Universidad Tecnológica de Bolívar, Calle del Bouquet No 25-92, Manga,
Cartagena, Colombia
ivelez@unitecnologica.edu.co

^{2}PhD in Mathematics applied to economic problems, University of Trieste, Italia.
Associate Professor of Mathematical Methods for Economics, Actuarial and Financial Sciences, University
of Modena and Reggio Emilia, Faculty of Economics, Italia.
Grupo de investigación Instituto de Estudios para el Desarrollo, IDE, Colombia.
magni@unimo.it

* Autor para correspondencia.

Fecha de recepción: 07-05-2009 Fecha de corrección: 20-11-2009 Fecha de aceptación: 26-11-2009

**ABSTRACT**

Practitioners and most academics in valuation include changes in liquid assets (potential dividends) in the cash flows. This widespread and wrong practice is inconsistent with basic finance theory. We present economic, theoretical, and empirical arguments to support the thesis. Economic arguments underline that only flows of cash should be considered for valuation; theoretical arguments show how potential dividends lead to contradiction and to arbitrage losses. Empirical arguments, from recent studies, suggest that investors discount potential dividends with high discount rates, which means that changes in liquid assets are not value drivers. Hence, when valuing cash flows, we should consider only actual payments.

**KEYWORDS**

Cash flow to equity, potential dividends, equity value.

**JEL Classification:** M41, G12, G31

**RESUMEN**

*Dividendos potenciales y flujos
de caja reales en valoración. Un
análisis crítico.*

Profesionales y la mayoría de los académicos de valoración incluyen los cambios en activos líquidos (dividendos potenciales) en los flujos de efectivo. Esta práctica generalizada y equivocada es incompatible con la teoría básica de finanzas. Se presentan argumentos económicos, teóricos y empíricos para apoyar esta tesis. Los argumentos económicos dicen que para la valoración sólo se deben considerar flujos de caja; los teóricos muestran cómo los dividendos potenciales conducen a contradicciones y a pérdidas de arbitraje. Los argumentos empíricos sugieren que los inversionistas descuentan los dividendos potenciales con altas tasas de descuento, lo que significa que el cambio en activos líquidos destruyen valor. Por tanto, al valorar los flujos de caja, se debería considerar sólo los pagos que en realidad ocurren.

**PALABRAS CLAVE**

Flujo de caja del accionista, dividendos potenciales, valor del patrimonio.

**RESUMO**

*Potenciais dividendos e fluxo de
caixa efetivo em valoração de patrimônio.
Uma análise crítica*

Profissionais e a maioria dos académicos trabalhando no campo da valoração incluem mudanças em ativos disponíveis (potenciais dividendos) nos fluxos de caixa. Esta prática comum e incorreta é inconsistente com a teoria financeira básica. Nós apresentamos argumentos econômicos, teóricos e empíricos para apoiar essa tese. Enquanto que os argumentos econômicos afirmam que apenas os fluxos de caixa deveriam ser considerados para objetivos de valoração, os argumentos teóricos mostram como a consideração de potenciais dividendos leva a contradições/discrepâncias e perdas em arbitragem. Argumentos empíricos em estudos recentes sugerem que os investidores tendem a descontar potenciais dividendos a elevadas taxas de desconto, o que significa que as mudanças em ativos disponíveis não são acionadores de valor. Por isso, apenas pagamentos reais deveriam ser considerados ao valorar fluxos de caixa.

**PALAVRAS-CHAVE**

Fluxo de caixa para valoração, potenciais dividendos, valoração de patrimônio.

**INTRODUCTION**

In this document, we give support
to the idea that potential dividends
that are not distributed (and are
invested in liquid assets) should be
neglected in firm valuation, because
only distributed cash flows add value
to shareholders. Hence, the definition
of Cash Flow to Equity should include
only the cash flow that is actually
paid to shareholders (dividends paid
plus share repurchases minus new
equity investment). Although some
authors warn against the use of potential
dividends for valuing firms
(DeAngelo and DeAngelo, 2006, 2007;
Fernández, 2002, 2007; Tham and
Vélez-Pareja, 2004; Vélez-Pareja,
1999a, 1999b, 2004, 2005a, 2005b);
some respected authors (e.g. Benninga
and Sarig, 1997; Brealey and
Myers, 2003; Copeland,^{2} Koller and
Murrin, 1994, 2000; Damodaran,
1999, 2006a, 2006b, 2008) and many
practitioners seem to support the
idea that the Cash Flow to Equity
has to include *undistributed* potential
dividends.^{3}

To include undistributed potential
dividends in valuation is admissible
only if they are expected to be invested
at the cost of equity capital,
*k _{e}*, i.e. the net present value (NPV)
of those investments is zero from the
point of view of current shareholders.
If the latter assumption held,
then changes in liquid assets could
be indeed included in the Cash Flow
to Equity, because they would be
value-neutral (DeAngelo and DeAngelo,
2006; Magni, 2007). It should
be noted that a definition of cash flow
to equity is meant to be valid for all
possible cases, and thus should not
depend on a particular assumption
about investment in liquid assets,
otherwise the consequent definition
of firm value would depend on a
particular assumption about investment
in liquid assets. Furthermore,
this particular assumption violates
Jensen’s (1986) agency theory. DeAngelo
and DeAngelo (2006) claim that
“When MM’s assumptions are relaxed
to allow retention, payout policy
matters in exactly the same sense
that investment policy does” (p. 293)
and “irrelevance fails because some
feasible payout policies do not distribute
the full present value of FCF
to currently outstanding shares” (p.
294). The zero-NPV assumption is
not supported by the empirical data.
Literature reports that holding liquid
assets destroys value or at most does
not create a significant amount of
value. Schwetzler and Carsten (2003)
report that in Germany “persistent
excessive cash holdings lead to a

Harford (1999)^{4} finds that “cash-rich
bidder *destroys seven cents of firm
value* [italics added] for every dollar
of excess cash held” (p. 1983) and
says that “the stock market appears
to partially anticipate this behavior,
as evidenced by the *negative stock
market reaction to cash stockpiling*
[italics added]” (p. 1972). Finally,
he says that “one might expect that
stockpiling cash would be *greeted
negatively by the market *[italics
added]” (p. 1992). Opler, Pinkowitz,
Stulz and Williamson (1999) say that
*“holdings of liquid assets can make
shareholders worse off *[italics added]
in some circumstances” (p. 2) and *“In
a world of perfect capital markets*
[italics added], holdings of liquid
assets are irrelevant. If cash flow
turns out to be unexpectedly low so
that a firm has to raise funds to keep
operating and invest, it can do so at
zero cost. (…) Hence, if a firm borrows
money and invests it in liquid assets,
shareholders wealth is unchanged”
(pp. 4-5). Finally, they write that
“investing in cash can therefore have
an adverse effect on firm value. To
put it another way, *increasing firm’s
holdings of liquid assets by one dollar
may increase firm value by less
than one dollar *[italics added]” (p.
11). Faulkender and Wang (2004)
find “*that the marginal value of cash
declines with larger cash holdings*
[italics added], higher leverage, better
access to capital markets, and as
firms choose to distribute cash via
dividends rather than repurchases”
(p. 2) and they “estimate that for the
mean firm-year in the sample, *the
marginal value of cash is $0,96* [italics
added]” (p. 24).

On the other hand, Mikkelson and
Partch (2003) conclude that “persistent
large holdings of cash and
equivalents have not hindered corporate
performance” (p. 2), and that
“there is no evidence that large firms
with lower insider stock ownership,
higher inside board composition, or
a controlling founder perform differently
than other large cash firms” (p.
20). Pinkowitz, Stulz and Williamson
(2003) write: “Strikingly, while *a dollar
of cash is worth roughly a dollar
of firm value* [italics added] in the
U.S., in countries with poor institutions,
*a dollar of cash is consistently
estimated to be worth less than 65
cents *[italics added]” (p. 6).

In addition, Pinkowitz, Williamson and Stulz (2007)’s result point out that one dollar of increase in dividends creates about ten dollars in value while one dollar increase in cash creates about 29 cents of value for countries with poor shareholders rights countries. In high corruption countries one dollar increase in dividends creates more than 6,50 dollars of value and one dollar of cash and cash equivalent create 33 cents of value. In the non corrupt countries and with good protection to the shareholders one dollar of extra dividends creates near four dollars in value and one dollar in liquid assets creates about one dollar in value. On the other hand, Pinkowitz and Williamson (2002) report that, on the average, one dollar in cash is 1,25 dollars worth in value.

This article aims at reinforcing the arguments on the inconvenience of adding the change in liquid assets (undistributed potential dividends) as part of the cash flows to be used for firm valuation. The arguments used in this document to support our thesis are of three types: economic, logical, and empirical.

As for the economic reasons, they highlight that to include the change in liquid assets in the definition of Cash Flow to Equity means: (i) to confound stock with flows, (ii) to adopt the very particular assumption that the full present value of liquid assets (computed at the cost of equity) will be distributed to shareholders, (iii) to break consistency between cash flow and financial statements, (iv) to distort taxes, and (v) to refuse Jensen’s (1986) agency theory which implies that firms in real life tend to retain funds and invest them in low-return investments.

As for the logical arguments, we provide three formal proofs to show that a rational evaluator does not use undistributed potential dividends. The first proof relies on incompatibility of CAPM and the use of potential dividends for valuation. The second one shows the use of potential dividends is incompatible with the classical valuation theory (and therefore, with Modigliani and Miller’s approach). A third proof shows that investors including changes in liquid assets as value-creation factors fall prey to arbitrage losses.

As for the empirical argument, we analyze and work out some contributions in the recent literature, from which it can be inferred that investors value liquid assets much less than dividends. Also, the implicit discount rates for liquid assets are very high, which suggests that investors do not consider liquid assets as affecting a firm’s value.

The document is organized as follows:
section 1 shows that our definition
of Cash Flow to Equity as dividends
minus net capital contributions
is consistent with basic finance,
and, in particular, with Modigliani
and Miller’s approach to valuation,
whereas the definition widely used in
many applied corporate finance textbooks
and in real-life applications is
not; this section also summarizes the
different views advocated by several
authors. Section 2 furnishes several
economic reasons for supporting our
thesis. Section 3 illustrates three logical
arguments, and section 4 makes
use of findings and information collected
and analyzed by Pinkowitz *et
al. *(2007) and other scholars to find
indications of the irrelevance of liquid
assets in value creation. Section
5 proposes a (theoretically correct)
model to test the hypothesis that
changes in liquid assets do not add
value: the model proposed will be
used in future researches. Some remarks
conclude the document (main
notational conventions are collected
at the end of the document).

**1. DEFINITION(S) OF CASH
FLOW TO EQUITY**

This section proposes a definition of Cash Flow to Equity consistent with Modigliani and Miller’s (1958, 1963) and Miller and Modigliani’s (1961) approach to valuation.

According to the well known Clean Surplus Relation, change in equity book value is equal to change in capital stock plus net income (NI) minus dividends paid to shareholders (Div) as in eq. (1)

where EBV is the equity book value,
and *CS _{t+1}* is the capital stock contributed
by shareholders up to time

We use “d”,^{5} as the variation symbol,
hence, *dEBV _{t+1}* =

This is the cash flow that adds value to the equity. We define cash flow to equity (CFE) as:

As said above, our notion of CFE in eq. (3) is exactly what Miller and Modigliani (1961) use to calculate the firm value: their eq. (17) at p. 419 underscore the difference between dividends paid and net capital contributions. Using our symbols, the Miller and Modigliani’s formula is

where *E _{t}* is the equity market value at
time

Inspecting the numerator, the reader
may note that our eqs. (2) and (3)
just imply, *CFE _{t+1}* =

As a consequence, our approach is consistent with Miller and Modigliani’s approach. By contrast, a large part of practitioners and some corporate finance scholars propose a different definition. For example, Damodaran (1999, 2006a, 2006b) proposes the use of cash flow available for distribution for valuing a firm’s equity, even if it will not be paid to the equity holder. The cash available for distribution is usually called “potential dividends”; the part of it which is not actually distributed is invested in liquid assets, i.e. cash and short-term investments such as market securities, certificate of deposit, CD, etc. Damodaran’s definition of cash flow to equity, which is widely adopted in applied corporate finance textbooks and practice, may be formalized as follows:

where *Div _{pot(t+1)}* denote

with *LA _{t+1} = C_{t+1} + STI_{t+1} *(

We can express it in different terms: we divide the assets of the firm into two categories: fixed assets net of cumulated depreciation (NFA) and working capital (WC), defined as current assets (cash + short term investments + accounts receivable + inventories) minus current liabilities (accounts payable):

Then,

where *D* is the book value of the
debt. From eq. (9), *dEBV _{t+1}* =

where Investment in *dNFA _{t+1} =
NFA_{t+1} – NFA_{t} = *Fixed Assets

By contrast, a frequent definition in textbooks turns out to be:

with *WC ^{nc}* being noncash (operating)
working capital:

so that *dAR _{t+1} + dInv_{t+1} – dAP_{t+1} =
dWC^{nc}_{t + 1} *(see, for example, Damodaran,
1999, p. 128; Damodaran, 2006a, p.
79). In eq. (10) working capital is
inclusive of undistributed potential
dividends

Damodaran (2006b) acknowledges the valuation deviations derived from using potential dividends rather than actual cash flows. He appropriately observes that

- when the FCFE is greater than the
dividend and the excess cash either
earns below-market interest rates or
is invested in negative net present
value assets, the value from the FCFE
model will be greater than the value
from the dividend discount model
(p. 24).

And he admits that there is reason to believe that this is not as unusual as it would seem at the outset (p. 24).

Nevertheless, in his textbooks and documents he seems to contradict his very arguments, given that he favors the potential-dividends model over the other ones:

- Actual dividends (…) may be much
lower than the potential dividends
(that could have been paid out) (…)
When actual dividends are less than
potential dividends, using a model
that focuses only on dividends will

- (…) firms do not always pay out what
they can afford to in dividends. A more
realistic estimate of equity value may
require us to estimate the potential
dividend—the cash flow that could
have been paid out as a dividend.
(Damodaran, 2006a, p. 111)

Obviously, the fact that firms do not pay out what they have available for distribution is not a good reason for favoring potential dividends as opposed to actual cash flow. Quite the contrary, if firms do not pay out cash flows that is available, then value is affected; in principle, whatever the magnitude of potential dividends, if a firm pays out no dividend over the life of the firm, the equity’s value is zero, as Miller and Modigliani correctly recognize (1961, p. 419, footnote 12). And this is true even if the company has invested in positive NPV projects (see also DeAngelo and DeAngelo, 2006).

Benninga and Sarig (1997) share Damodaran’s view:

- Free Cash Flow (FCF) [is] a concept
that defines the amount of cash that
the firm can [italics added] distribute
to security holders (…) Cash and
marketable securities are the best
example of working capital items
that we exclude from our definition
of [change in net working capital],
as they are the firm’s stock of excess
liquidity adjustment. (p. 36)

When calculating free cash flow (and
cash flow to equity) these authors do
not subtract *dLA _{t+1}*, which entails
that they abide by eq. (11) above (they
make use of the term “net working
capital” while meaning “operating
net working capital”, exclusive of
change in liquid assets). If changes in
liquid assets are not included in the
working capital, then any increase
in liquid assets is not listed as a
reduction in the cash available (as
is correctly done in eq. (10)), even if
they are deposited in the bank or in
an investment fund. Using the funds
(a cash excess) for increasing liquid
assets reduces the cash available for
distribution; if that is not listed in the
calculation of FCF, then the increase
appears to be an amount available
for distribution even if it is not, and
hence the cash flows to investors
(FCF or CFE) are overstated, as well
as the consequent firm value.

Copeland, Koller and Murrin’s (1990, 1994, 2000) definition of free cash flow is consistent with Damodaran’s and Benninga and Sarig’s: they define it as “gross cash flow (NOPLAT plus depreciation) minus gross investment (increases in working capital plus capital expenditures)” (Copeland et al., 2000, p. 138). Like with Benninga and Sarig, they employ the expression “working capital” but refer to “operating working capital”, as they explicitly state at p. 168. As a consequence, their definition of cash flow to equity does not exclude undistributed potential dividends:

Cash flow to equity = Dividends paid + Potential Dividends +Equity repurchases – Equity Issues

(see, for example, Copeland *et al.*,
1994, p. 480, Exhibit 16.3; Copeland
*et al.*, 2000, Exhibit 21.2 at p. 430 and
Exhibit 21.10 at p. 438). Admittedly,
in the first edition of their book (Copeland
et al., 1990) they seemed to be
inclined to accept a strict definition
of cash flow to equity as cash flow
paid to shareholders: in their Exhibit
13.2 at p. 379 one finds, referred to
equity,

Free Cash Flow = Dividends to equity

and they explicitly refer to “free cash flow to shareholders, which is mathematically identical to dividends” (p. 379). Yet, from the second edition of their book a radical shift toward potential dividends is consummated, albeit with no justification.

Brealey and Myers (2003) write that
“free cash flow is the amount of cash
that a firm can pay out to investors
after paying for all investments necessary
for growth” (p. 75). Therefore,
while not being explicit, they seem to
share the above mentioned authors’
point of view. Their notion of working
capital is consistent with the
above mentioned authors, who do not
subtract the change in liquid assets:
“Working capital summarizes the
net investment in short-term assets
associated with a firm, business or
project (...) Working capital = inventory
+ accounts receivable – accounts
payable.” (p. 126)^{7}

While the practice of using potential dividends rather for valuing firms is a widespread one, there are some authors who consider it an error and correctly use only actual payments to shareholders for defining cash flow to equity. For example, Fernández (2002, p. 171) clearly states that “the forecast equity cash flow in a period must be equal to forecast dividends plus share repurchases in that period” and “the ECF in a period is the increase in cash (above the minimum cash, whose increase is included in the increase in WCR) during that period, before dividend payments, share repurchases and capital increases” (p. 172); “considering the cash in the company as an equity cash flow when the company has no plans to distribute it” (Fernández, 2007, p. 26) is a frequent error in real-life applications.

DeAngelo and DeAngelo (2007) argue
that a firm’s equity is not given by
potential dividends but by cash flow
paid to shareholders. The former
(they label them “free cash flow”)
determines the investment value, the
latter leads to the distribution value:
“Investment value is the discounted
value of the FCF* to the firm* generated
by its investment policy, which determines
the firm’s capacity to make
payouts. Distribution value is the
discounted value of the cash payouts
to currently outstanding shares, i.e.,
the cash flow paid to *stockholders*,
which determines the market value
of equity” (p. 16, italics in original).
They underline that “value is generated
for investors *only to the extent
that this capacity is transformed into
actual payouts*” (DeAngelo and DeAngelo,
2006, p. 309, italics added).

Our stance is that *nomina sunt
omina*:^{8} cash flow is a flow of cash and
therefore: (i) stock items in the balance
sheet should not be considered
flows, and (ii) changes in stock items
should be considered flow of cash only
if they are paid to (or received from)
shareholders. Hence, our definition of
CFE as dividends minus net capital
contributions (see eq. (3) above). If
management keeps cash holdings
instead of distributing it, shareholder
wealth is affected unless the unpaid
cash is invested in zero-NPV projects
and distributed to shareholders over
the life of the enterprise. But, usually
in real life, as empirical evidence suggests,
keeping cash holdings destroys
value: the NPV of those invested
funds is not zero (below zero).

**2. ECONOMIC AND FINANCIAL
ARGUMENTS**

This section summarizes economic and financial reasons for including in the cash flow only what indeed is a flow of cash.

** Cash flows and stocks.** To consider
as cash flow items that are listed in
the balance sheet is to deny the basic
concept in valuation: cash flows. And
they are just that, flows of money,
whereas items in the balance sheet
are stocks. It is a contradiction to say
that an item is at the same time a line
(or part of it) in the balance sheet and
a line in the cash flow. Furthermore,
if one considered cash flow what it is
such only potentially, then one should
consistently consider any asset in the
firm as potential dividends, because
assets may be sold and the cash may
be distributed to investors: but then
one should consider assets in the firm
as representing both stocks and flows,
which is a contradiction.

** Modigliani and Miller’s approach.**
Modigliani and Miller’s (1958, 1963)
approach to firm valuation only takes
account of cash flows paid to investors.
There are no potential dividends
in their articles. The same is true
even in Miller and Modigliani (1961)
where the irrelevance of dividends
is proved. As DeAngelo and DeAngelo
(2006) underline, in Miller and
Modigliani’s 1961 paper there are
no retained funds, and the assumption
is “to mandate 100% free cash
flow payout in every period” (p. 293).
Miller and Modigliani do not deal
with potential dividends retained
in the firms and invested in liquid
assets. There are no investments in
liquid assets in Miller and Modigliani
(1961). Miller and Modigliani’s thesis
may be extended to the case of retention
of FCF only if that investment
is made at the opportunity cost of
equity and “provided that managers
distribute the full present value
of FCF” (DeAngelo and DeAngelo,
2006, p. 303. See also Magni, 2007).
Therefore, it is true that the unpaid
dividends will be distributed at the
terminal date, so that their value is
captured in the terminal or continuing
value. But it is never sufficiently
stressed that irrelevance holds if and
only if, a perfect market exists where
cash excess not paid is invested at
the opportunity cost of equity. In
real life, excess cash is invested in
liquid assets at some available rate
that might be greater, equal or lower
than the cost of equity. This means
that the NPV of those undistributed
funds can be greater, equal or less
than zero.

** Consistency between cash flows
and financial statements. **There
should be a complete consistency
between cash flows and financial
statements. If one says that every
dollar available belongs to the equity
holders, then that fact should be
reflected in the financial statement.
That is, those funds should appear as
effectively distributed. In a valuation
where a finite planning horizon is
considered, decisions on what to do
with excess cash are reflected in the
financial model. This implies that
if management foresees to invest
in marketable securities, that decision should appear in the financial
statements. On the other hand, if
cash holdings are invested in additional
operating assets, that decision
should be included in the analysis; if
they are devoted to acquisitions or
buyouts, again, that decision should
be reflected in the cash flows with
all the financial implications it has.
After this finite planning horizon, one
makes the assumption that all available
cash is distributed to equity and
debt holders; the finite planning horizon
should cover the largest possible
period and at the end, a continuing
or terminal value should measure the
value generated for perpetuity.

* Tax distortion.* When one includes
in the CFE the excess cash invested
in liquid assets, one does distort
taxes. Instead of recording an explicit
return (usually a low return) that is
taxed and listed in the income statement,
one creates a virtual return
equivalent to the cost of equity,

** Zero-NPV assumption in real-life
applications.** One argument often
used to justify the inclusion of cash
holdings as a cash flow is that: the net
present value of those investments is
zero. We might agree on this assump
tion as a conservative approach to
avoid excessive optimism as well as
the determination (in a forecast) of
a very high return on those invested
funds. However, in constructing pro
forma financial statements (forecasting)
one should look the history of
the firm and estimate the historical
returns on those funds, and forecast
them accordingly to the historical average
return. If the forecasted return
is lower than the discount rate of the
cash flows, the effect is that there is
a destruction of value. If higher, a
creation of value occurs. The idea of
assuming without question that the
NPV of the investment in market securities
is zero implies that whatever
the analyst or the management will
do with those funds are of no concern
to investors, because their funds do
not contribute to value creation (they
are value-neutral). Then, a simple
conclusion could be drawn if one accepted
the idea that the investment
of cash excess does not affect the
firm value: whether one keeps it in
the safe box, in the bank, invested
in an investment fund or whatever
else, it will make no difference because
the NPV is zero. This should
lead many people and institutions
to refrain from offering solutions for
cash management purposes, such as
the following.

No financial discipline is more important and yet more overlooked and misunderstood than the essential principles and practices of corporate cash and liquidity management. Any business’ success – from its long-term prospects to its short-term stability – depends on smart, efficient, and creative cash management solutions for handling cash inflows and outflows. The lesson is simple: Those companies that handle cash best thrive most (Cash Management Fundamentals, 2007).

A shareholder would not accept
to be virtually paid with potential
dividends that never go to her
pocket; similarly, banks or, in general,
debt holders would not accept
that interest or principal payments
should be paid with potential interest
and principal payments. Will
practitioners and teachers accept
an invitation to tell their customers
and students to disregard the importance
of cash management? Will they
spread the idea that keeping the excess
cash in the bank account (with
no interest) would mean the same
in terms of value than investing it
wisely? Obviously not. If managers
do not or are not expected to fully
distribute the cash available, one
should not “create” cash flow where
it is not. Certainly, there should be
ways to avoid that managers waste
the excess cash in bad investments.
Jensen (1986) says it in a rather
graphical manner: “The positive
market response to debt in oil industry
takeovers (…) is consistent with
that additional debt increases efficiency
by forcing organizations with
large cash flows but few high-return
investment projects to disgorge cash
to investors. The debt helps prevent
such firms from wasting resources
on low-return projects” (pp. 10-11).
Further, he writes that “Free cash
flow is cash flow in excess of that required
to fund all projects that have
positive net present values when
discounted at the relevant cost of
capital. Conflicts of interest between
shareholders and managers over
payout policies are especially severe
when the organization generates substantial free cash flow. The problem is
how to motivate managers to disgorge
the cash rather than investing it at
below the cost of capital or wasting it
on organization inefficiencies” (p. 2)
and “Managers with substantial free
cash flow can increase dividends or
repurchase stock and thereby pay out
current cash that would otherwise
be invested in low-return projects or
wasted” (p. 3). Therefore, although
corporate financial theory may conveniently
employ the assumption of
full distribution of cash generated,
in practice this does not happen, as
Jensen underlines, so there is a need
for distinguishing between potential
cash flow available for distribution
and actual cash flow effectively paid
out to equity and debt holders.^{10} The
excess cash that managers refuse
to pay to equity holders should not
be included in the effective (actual)
distributed cash flow. The fact that
in theory firms should distribute the
available cash does not imply that
the analyst should assume that in
the future all available cash will be
distributed, if historically the firm
has not distributed it. To assume that
cash holdings are a cash flow that
creates value is counter to evidence:
“the theory is empirically refutable,
predicting that firms will distribute
the full PV of FCF, an implication
that differentiates it from Jensen’s
(1986) agency theory” (DeAngelo and
DeAngelo, 2006, p. 295).

**3. LOGICAL ARGUMENTS**

In this section we formalize three arguments that logically support the thesis according to which undistributed potential dividends do not add value to shareholders (and therefore must not be included in the definition of Cash Flow to Equity). In particular, they show that the use of potential dividends for valuation: (a) does not comply with the CAPM, (b) does not comply with the basic tenet of valuation theory, (c) does not comply with the no-arbitrage principle.

** CAPM.** The use of undistributed
potential dividends is in clear contradiction
with the Capital Asset Pricing
Model. When the CAPM is used to
estimate the cost of equity, ke, one
uses dividends paid out to calculate
the historical stock returns and historical
beta; one never uses potential
dividends.

*Suppose (i) an investor uses the
CAPM for computing the cost of equity
and (ii) uses undistributed potential
dividends for valuation. Then, the
firm lies on and above the Security
Market Line, SML*

Assume, with no loss of generality,
that *dLA _{t+1}>0*. Due to (i), the following
relation holds:

is the random rate of return and
denotes the cum-dividend equity
value at time *t+1*. This implies:

with Ft+1 being the expected value of . However, due to (ii),

Eqs. (13) and (14a) tell us that the firm lies on the SML, whereas (14b) tells us that the firm lies above the SML, given that it implies:

** The basic tenet of valuation
theory.** Section 1 has shown that our
definition of CFE is consistent with
Miller and Modigliani’s approach to
valuation. Miller and Modigliani, in
turn, strictly abide by a basic tenet
of valuation theory: value depends
on cash flow received by the investor.
This principle may be formalized
as:

(see, for example, Miller and Modigliani, 1961, eq. (2)).

*By making us of (i) undistributed
potential dividends for valuation and
(ii) the basic tenet of valuation theory,
one incurs contradictions.*

Note that one must have *dLA _{t+1} ≠ 0* (if
not, the use of undistributed potential
dividends is meaningless). If undistributed
potential dividends enters
valuation, then.

Eqs. (10)-(11) imply *dLA _{t+1} ≠ 0*. But
this contradicts the assumption

** Arbitrage: a counterexample.**
The no-arbitrage principle is a cornerstone
in financial theory (Varian,
1987) and decision theory (Smith and
Nau, 1995), and, more generally, represents
a norm of rationality in economics
(Nau and McCardle, 1991).

We now illustrate a counterexample
showing that if an investor uses undistributed
potential dividends for
valuation, then she is open to arbitrage
losses. Consider a firm whose
shares are traded in the market, and
assume, for the sake of simplicity, that
one shareholder owns all the shares.
Suppose potential dividends will be,
a perpetual 120 if state of nature 1
occurs, and a perpetual 70 if state of
nature 2 occurs, but dividends will
be, in each year, a perpetual 100 in
state of nature 1 and a perpetual 50
in state of nature 2 (equal probability
is assumed). This means that undistributed
potential dividends amount
to a constant 20 with certainty. The
probability for each state of nature
is 0,5. Suppose the required rate of
return to equity is 10%. The investors
who positively evaluate potential
dividends value the equity firm by
discounting potential dividends at
10%: *E*=0,5(120+70)/0,1=950.

Now, suppose the ownership offers such an investor all the firm’s shares at a price of 850. This means that the investor will own a firm which she values at 950. The NPV to her is positive (=100) so she accepts the bargain. Then, the ownership proposes a contract according to which the investor receives 750 and while paying the ownership a constant 100 if state of nature is 1 and a constant 50 if state of nature is 2. To the investor, such a cash flow stream is equivalent to the cash flow stream distributed by a firm which is equal to the firm just purchased but with no undistributed potential dividends. Therefore, to her the value of such a stream is equal to value of the firm just purchased less the value of the undistributed potential dividends. The undistributed potential dividends are a certain amount because she will receive them in either state of nature. Hence, the discount rate should be the risk free rate. Assuming that the risk-free rate is 4%, the value of the undistributed potential dividends is 20/0,04=500. So, the value of the cash flow stream is 950–500=450. The investor is then required to give up a value of 450 in order to get an immediate amount equal to 750. The NPV is positive to the investor (=300) so she accepts again. This strategy results in an arbitrage loss for the investor (and an arbitrage profit for the arbitrageur) (Table 1).

Hence, if one does not accept the basic tenet of valuation theory, one is open to arbitrage losses (to avoid arbitrage, one needs to value undistributed potential dividends at zero).

**4. EMPIRICAL EVIDENCE: IS THE
GLASS HALF FULL OR HALF
EMPTY?**

There is empirical evidence that dividends and not liquid assets are what increases firm value. Pinkowitz et al. (2007) have examined publicly traded firms for 35 countries and divided the sample between corrupt and non corrupt countries and between countries with good and poor protection to minority equity holders according to two Investor Protection Indices. Using our symbols, the model tested by Pinkowitz et al is described as:

where *V _{t}* is the market value of the
firm calculated at fiscal year end
as the sum of the market value of
equity and the book values of shortterm
debt and long-term debt;

They allow us to estimate the implicit
discount rate that makes an extra
dollar in each of those components
equal to the amount announced by
the authors. In Table 3a we assume
a non growing perpetuity; hence the
discount rate is 1/PV. The discount
rate the market applies to one dollar
in cash is extremely high, while the
discount rate for the dividends is
reasonable. Even if we assume that
the $1 is for ten years (length of the
study) the order of magnitude for the
cost of equity *k _{e}* in the case of cash is
the same. For dividends, it ranges
from 0,37% to 21,20%; for cash, it
ranges from 105,20% to 343,80%.

If one assumes that those coefficients are related to one period and not to a perpetuity, one obtains the results shown in Table 3b. In these cases we can see that the implicit discount rate for one period has huge differences between cash and dividends. We can say in general that the market punishes cash (compared with dividends) as seen by the discount rate, which is much greater than the discount rate for dividends.

In Table 4a some findings are shown,
assuming a perpetuity: Pinkowitz
and Williamson (2002) imply an average
discount rate of 80% (1/1,25);
according to Pinkowitz *et al. *(2003),
one dollar is worth 0,65, so that the
discount rate would be 153,85%;
according to Faulkender and Wang
(2004, p. 23) dollar is worth 0,97
(discount rate: 103,10%); according
to Harford (1999), the value of one
dollar in cash is 0,956 (discount rate:
104,60%). The discount rates shown
are very high and unusual and might
be interpreted as something undesirable
to the market. In any case, one
can only infer that dividends create
much more value than cash, not that
cash is positively evaluated (results
for a single period are shown in Table
4b).

Furthermore, Table 5 shows that dividends are between 20 and 34 times more relevant than cash in value creation in “bad” countries and about 4 times more relevant than cash in “good” countries.

As the saying goes: whether a glass is half full or half empty depends on the attitude of the person looking at it. Those who see the glass half full might say: this is a proof that cash creates value and hence should be included in the cash flows. Others (and we are in this number) see the glass half empty and say: the market is adverse to potential dividends because it discounts them with a huge rate, so trying to keep their value down to zero. Hence, they should not be included as cash flow because this is counter to evidence and overstates the value of the firm.

The findings presented in Pinkowitz
and Williamson (2002) and Pinkowitz
*et al. *(2007) just suggest that (changes
in) liquid assets should not be included
in the FCF or CFE because
they inflate the value of the firm. The
meaning of the above mentioned results
is that one dollar in liquid assets
creates less than one dollar in value
and that liquid assets or “potential”
dividends are something not desirable
by investors.

Using the aggregate data from
Pinkowitz *et al. *(2007) and without
splitting the sample between good
and bad countries, one finds that
one extra dollar of cash is valued at
zero by the market. This is an average,
and it compares with the above
mentioned findings. The data from
Pinkowitz *et al.*, represent evidence of
this fact. Data cover ten years (1988-
1998) for 35 countries with some
exceptions such as India, Philippines,
Turkey and Peru. This means that
they had near 69.000 observations.
The values in Table 6 are the mean of
the medians for each variable for each
country. Market Value to Book Value
(V/B) is the sum of market equity
value plus book value of debt divided
by book value of assets. Dividends
and liquid assets are the percent of
those items in the balance sheet on
Total assets. The liquid assets are
not calculated individually but they
are added (Pinkowitz *et al. *use the
term “Cash”).

Using the aggregated data shown
in Pinkowitz *et al. *(2007) we have
run several regressions between
V/B, Cash and Dividends. V/B is the
dependent variable and the other
two are independent variables. The
aggregated data we have used are
shown in Table 6. We depict the
scattered data for each pair of independent
and dependent variables:
in Graph 1 we can observe a trend:
the higher the dividend, the higher
the V/B. In Graph 2 the reader can
observe a slight downward trend:
the higher the cash level, the lower
the ratio V/B. Notice that the three
variables are scaled or normalized
by book value of total assets. This
means that one may compare firms
of different size and from different
countries and years.

We have analyzed eighteen regression models with the following structure:

1. Lin Lin model with the following structure:

2. Log Log model with the following structure:

3. Lin Log model with the following structure:

4. Lin Lin Log model with the following structure:

5. Log Lin Log model with the following structure:

We are aware that the model lacks
good specification because there
are other variables that have to be
included, it is based on aggregated
data and it does not represent the
true universe studied by Pinkowitz
*et al. *(2007). This exploration only
gives hints and trends.

After the regressions have been run,
significant models are only those with
the independent variable Dividends
in linear form. This means linear
(Lin Lin) and semi logarithmic (Log
Lin) models. In particular, the only
significant variable is *Dividends*. In
Table 7 we summarize the statistical
analysis. We expected to find that the
relationship between V/B and CFE
(dividends) be linear, because Miller
and Modigliani’s valuation model is
linear (see eq. (16) in section 5). And
as is suggested by Table 7, the results
in terms of statistical significance corroborate
the linearity between value
and CFE. In particular, one dollar in
dividends creates about 8 dollars in
value (see Graph 1). We are aware
that this analysis is rather restricted
because we are dealing with aggregated
data and not with the raw data
Pinkowitz *et al. *(2007) worked with.
Another restriction is related to the
interpretation of the results. Admittedly,
we do not have full information
regarding the specific model used in
each case of the report. For instance,
we do not know whether cash refers
to change in cash or level of cash, or
if it is located at a different (future)
period compared with the firm’s market
value. This is actually critical if
we are interested in defining the coefficient
of the independent variable as
the increase in value for each extra
dollar in the variable.

**5. MOVING FORWARD: A
PROPOSAL FOR FUTURE TESTS**

The previous sections have shown that change in liquid assets must not be included in the notion of CFE. However, future research should bring corroboration to the idea that the market do not positively value change in liquid assets. Armed with the theoretical toolbox we have developed in section 1, this last section proposes a model for tests, which, we expect, will add empirical evidence. The model is based on standard results of corporate financial theory and, in particular, on Modigliani and Miller (1963). We use the following equation:

where V is the value of the levered
firm, *V _{U}* is the value of the unlevered
value,

where TS is Tax Savings (or Tax Shield), CFD is the Cash Flow to Debt and CCF is the Capital Cash Flow (Ruback, 2002). From eqs. (18)-(19), and using the fact that D is the present value of CFD,

where* PV* is present value, *WACC ^{FCF}*
is the Weighted Average Cost of
Capital for the

Using eqs. (3) and (19) and the relation
*CFD _{t+1} = I_{t+1} – dD_{t+1}*, eq. (21)
becomes

where, as seen, the variation in capital
stock d*CS ^{t+1}* is obtained as difference
between new equity investment
and shares repurchases occurred
in the year. If markets positively
valued changes in liquid assets,
then the levered value of the firm, as
empirically evidenced by the market,
would not be the theoretically correct
eq. (22), but would be as in equation
23 (see end of page).

which differs from eq. (22) for the fact
that change in liquid assets *Div _{pot (t+1)}*
are included in the valuation formula.
We expect to find that in eq. (23)

For the implementation of the test, we will need to collect information which is usually publicly available:

*D* Financial debt (book value as a
proxy of market value)

*NS *# shares in the market

*Pr* Market price per share

*V *Firm value = # shares × Market
Price + debt (book value) = NS
× Pr + debt

*I *Interest payments

*CS *(cumulated) capital stock contributed
by shareholders

*Div* Dividends paid in cash

*C *Cash

*STI *Short-term investments (marketable
securities)

*B* Book value of total assets

In order to normalize the data and
avoid problems of size, currency,
time, etc., we will divide each variable
by the book value of total assets
in t, in the same way Pinkowitz *et
al. *(2007) do. As all variables will be
divided by book value of total assets,
the ratio V/B represents Tobin’s Q.
These independent variables are
the proxies for components of equation
(23). While Pinkowitz *et al. *do
not include payments of debt, we
will include them, and, tentatively,
we will not include variables that
they include, such as R&D expense.
Hence, our econometric model will be
(for each firm)

Where all variables are now meant
to be divided by book value of assets.
With this model, the value of the firm
depends on the cash flows the owners
of equity and debt expect to receive in
the future and on potential dividends
as well. Each of the elements of this
model attempts to capture investors’
expectations on future cash flows and
value. As all variables are divided by
total assets we have Tobin’s Q as the
dependent variable, while the independent
variables will be a percent
of total assets in *t*. With this model
we attempt to measure how much
value is created for a given value and
cash flows in the following period. An
alternate model is

Where a proprietary approach is followed,
and where *E _{t}* is measured as
number of shares times market price
per share (we will use data from Latin
American countries). Given that eq.
(25) requires less information, we
intend to use the latter when validating
data.

While the two models in eqs. (24)-(25)
are consistent with standard finance
theory, we do not intend to claim
that they are fully explanatory nor
to make use of them for forecasting
purposes. The models are meant to
provide information on the relevance
of the independent variables, in particular
the relevance/irrelevance of
*Div _{pot (t+1)} *to value creation. To this
end, the various betas are to be interpreted
as the discount factors for the
independent variables. In particular,
ß6 is the discount factor for change in
liquid assets, i.e. it represents the value
at time t of one dollar of

Our hypothesis may be phrased in a strong or in a soft version:

*Strong version: *We expect β_{6} to be statistically
zero (or close to zero). This
means that investors try to set down
the value of *Div _{pot (t+1)}* by discounting it
with an infinite or at least at a very
high discount rate, because they do
not consider (undistributed) potential
dividends relevant for valuation. Another
condition might be that β

*Soft version: *We expect *Div _{pot (t+1)}* to
be evaluated much less than actual
dividends. In econometric terms, we
expect Β

If our hypothesis will be corroborated (as already implied by both modern finance theory and the reported empirical findings), the practice of assuming that liquid assets are part of the cash flows will be (not only theoretically but also) empirically refuted.

**6. CONCLUSIONS**

Economics, and in particular, financial
economics provide rigorous
theoretical tools for valuing assets.
The theory is clear in stating that
the value of an asset depends on the
cash flow actually received by investors,
not on the cash flows that *could*
be received, unless undistributed
potential dividends are invested in
zero-NPV activities and their full
present value is distributed to shareholders
(DeAngelo and DeAngelo,
2006, Magni, 2007). But if, historically,
the firm has not distributed all
the available cash, there is no reason
to assume that in the future it will
be different. While some authors correctly
recognize that only cash flow
paid to shareholders should be used
for equity valuation (DeAngelo and
DeAngelo, 2007; Fernández, 2002,
2007; Shrieves and Wachowicz, 2001;
Tham and Vélez-Pareja, 2004; Vélez-
Pareja, 1999a, 1999b, 2004, 2005a,
2005b), several authors in applied
corporate finance and a large part of
practitioners include use potential
dividends for computing a firm’s equity
value (e.g. Benninga and Sarig,
1997; Copeland *et al.*, 1994, 2000;
Damodaran, 1999, 2006a, 2006b)
This document aims at showing that
the practice of adding liquid assets
to cash flows actually paid is at odds
with finance theory and seems to
be inconsistent with empirical findings.
Cash Flow to Equity should be
defined as dividends paid minus net
capital contributions, i.e. dividends
plus shares repurchases minus new
equity investment.

The issue is tackled in the document
in three ways: economic, logical, and
empirical. Economically, several
reasons are given which confirm that
only actual cash flows are relevant
in valuation; logically, three formal
proofs are provided that make use
of the CAPM, of the basic tenet in
valuation theory, and of arbitrage
theory; empirically, recent findings
in the literature are analyzed (among
which Pinkowitz et al., 2007) from
which evidence is drawn that market
values cash holdings much less than
dividends paid. An interpretation
of these findings is that the market
does not consider *potential* dividends
a value driver.

The main conclusion from this work is that practitioners and teachers should abandon the practice to not include liquid assets in the working capital when calculating cash flows. Further empirical work will be done with a model that is rigorously deducted from the theory (in particular, from Modigliani and Miller’s approach to valuation).

**FOOTNOTES**

1. Este documento fue seleccionado en la convocatoria para enviar artículos, Call for Papers, realizada en el marco del Simposio “Análisis y propuestas creativas ante los retos del nuevo entorno empresarial”, organizado en celebración a los 30 años de la Facultad de Ciencias Administrativas y Económicas de la Universidad Icesi y de los 25 años de su revista académica, Estudios Gerenciales; el 15 y 16 de octubre de 2009, en la ciudad de Cali (Colombia). El documento fue presentado en las sesiones simultáneas del área de “Finanzas”.

2. Professor Tom Copeland in a private correspondence says (August 8, 2004): “If funds are kept within the firm you still own them -- hence ‘potential dividends’ are cash flow available to shareholders, whether or not they are paid out now or in the future.”

3. The authors we analyze (Damodaran, Copeland, etc.) do not give a clear and unambiguous definition of cash flow to equity/potential dividends.

4. Quotations from this author are taken from the SSRN, version 1997.

5. Henceforth, change in a variable y is defined as: dyt+1 = yt+1 – y

6. Eqs. (9)-(10) may obviously be written as:

*CFE _{t+1} = NI_{t+1} *+ Depreciation

*CFE _{t+1} = NI_{t+1}* + Depreciation

7. It is worth noting that the definition of potential dividend is ambiguous in corporate finance textbook, because ordinary language and numerical examples are used instead of rigorous formalism, and there is no standard terminology across writers, so increasing problems of understanding.

8. This Latin sentence means “names indicate what they mean”.

9. Intuitively, people think of cash flows as net cash after adding inflows and subtracting all inflows. But inflows for capital providers are outflows for the firm.

10. Admittedly, “potential cash flow” is a linguistic contradiction, because if distribution does not occur, then the undistributed potential cash flow is not a cash flow at all, as previously seen.

11. See Table 3a and 3b in section 4 and the difference between discount rates.

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