Journal of Service Science and Management, 2011, 4, 79-85
doi:10.4236/jssm.2011.41011 Published Online March 2011 (
Copyright © 2011 SciRes. JSSM
Agency Cost under the Restriction of Free
Cash Flow
Junhong Chu
Department of Finance Zhuhai Campus, Jinan University, Zhuhai, China.
Received November 12th, 2010; revised December 22nd, 2010, accepted December 24th, 2010.
Agency cost theory is an important branch of capital structural theory. Free cash flow has significant impact on agency
cost. The combination of research on these two fields would help to build and extend the theoretical system. Based on
agency cost theory, the present study firstly categorized the characteristics of free cash flow as well as the statistical
methodologies. Furthermore, the existence of investing free cash flow in agency cost was proved by a model. Then free
cash flow was introduced into agency cost theory as restriction, the analysis shows that it will change agency cost, in
turn, will have an impact on the relationship between agency cost and capital structure, finally, will influence the opti-
mal capital structure point to maintain the equilibrium. Concretely, with the increasing free cash flow, correspondingly,
debt proportion will decrease.
Keywords: Capital Structure, Free Cash Flow, Agency Cost, Non-Pecuniary Benefit
1. Introduction
Agency cost theory, financial contract theory, signaling
model and new pecking order theory are the main
branches of new capital structure theory. Financial con-
tract theory focuses on restricting stockholders’ behavior
by contract and solving the conflict between stockholders
and creditors. Signaling model and new pecking order
theory center on solving the conflict between investors
and managers. These two types of conflict are the main
conflict in business organizations. Agency cost theory
considers how equilibrium is reached in both types of
conflict and how capital structure is formed, which is
more theory is more comprehensive than the previous
two to some degree.
In the famous paper “Theory of the Firm: Managerial
Behavior, Agency Costs and Ownership Structure” in
1976, Jensen argues that the ownership of outsiders will
generates agency costs [1,2]. However, Jensen’s model is
too perfect to be actualized. In his model, there is an im-
portant precondition: the manager-owner can use up all
value of the firm as non-pecuniary benefits [3]. While in
fact, the value of firm contains many compositions which
can’t be abused, so it might be better to introduce a new
variable to modify the original model. Free cash flow
could be one.
2. Literature Review
Jensen acknowledged the important role of free cash
flow himself. He considered that the free cash flow can
represent agency costs to a great degree, so in stock
market the announcement of free cash flow might lead to
explicit price fluctuation. However, he didn’t introduce it
into his classical model to provide a reasonable explana-
Figure 1 is the original model in Jensen’s paper. The
y-axis V represents the value of firm, and the x-axis F
represents consumed, and Uj (j = 1, 2, 3) represents
owner’s indifference curves between wealth and non-
pecuniary benefits. When the manager-owner has 100
percents of the equity, the slope of VF is 1, the value of
the firm will be V* where indifference curve U2 is tan-
gent to VF, and the level of non-pecuniary benefits con-
sumed is F*.
Supposing the owner sells a fraction of the firm, 1 α,
and holds α for himself, the slope of constraint line will
change to –α. As a result, the deal will bargain on the
price of V’, as shown in the Figure 1, where the line with
slope –α tangent the indifference curve on the location of
the constraint line. Now the value of the firm is F’, which
This paper is sponsored by the Incubating Program for Outstanding and
Creative Talented Youths in Guangdong Colleges and Universities
(No.: WYM08050).
Agency Cost under the Restriction of Free Cash Flow
Figure 1. The original model of Jensen.
is lower then F*. As Jensen stated, selling to outsiders
brings about the drop of value, which is a kind of agency
costs. Jensen called it the agency cost associated with
outside equity.
In this model, a very important condition is that the
manager can choose the level of non-pecuniary benefits
“free”, which means every point on the VF is accessible.
But in reality, can this condition be fulfilled?
Similar with outside stock ownership, enterprise debt
consequentially leads to internal managers’ acts of
agency to funds of outside creditors, which generates
agency cost too. Jensen discussed the agency cost of debt
in a simple case. Besides agency cost in Jensen’s paper,
Myers analyzed agency cost of debt from the other per-
spective. Although they used different analysis methods
and models, they drew similar conclusion that agency
cost of debt exists and increases with the amount of debt
As mentioned above, outside stock ownership and debt
will bring agency cost to enterprises. Thus, the amount of
outside stock ownership and debt will determine the
agency cost paid by the enterprise and in turn determine
the value of enterprise when the scale of enterprise re-
mains the same.
Adopting this argument, Jensen and Meckling pre-
sented the theoretical framework that agency cost deter-
mines capital structure.
Assuming other conditions as constant value, the value
of enterprise is Vm when agency cost is 0 which is an
ideal state. Since agency cost is the only antecedent of
the value of enterprise, then the maximum of enterprise
value will be the point of the lowest agency cost E*, on
which value of enterprise is Vm A
T(E*). The point
represents the optimal capital structure under the condi-
tion of enterprise scale and financing scale. This maxi-
mum point of enterprise value is achieved by adjusting
capital structure, which supports the proposition pre-
sented by Jensen and Meckling that capital structure de-
termines enterprise value.
3. Propositions Development
The value of firm contains several kinds of components,
such as real estate, equipment, brand and cash. In these
components, only cash can be used by the manager freely.
In fact, not all cash could be “freely” used. The part that
can be used freely is described as free cash flow. This is
the essence of free cash flow. According to this essence,
there are several different explicit definitions of free cash
Jensen defined that free cash flow is cash flow in ex-
cess of that required to fund all projects that have posi-
tive net present values when discounted at the relevant
cost of capital. His definition is difficult to be executed in
accounting, because there is no way to judge whether a
project has net present value when the project is just set-
tled. Rubin used the similar definition with Jensen. Their
definition can be expressed as below [4]:
INC = operating income before depreciation,
INCF = financial income,
TAX = total income tax,
INTEXP = gross interest expense on short- and
long-term debt,
INVEST = expense on invest activity
Standard & Poor Index accounts the free cash flow as
pretax profit minus capital expenditure. Many investors
use the method of pretax profit plus depreciation and
minus capital expenditure, or the cash flow generated by
operating activity minus the capital expenditure which is
necessary to guarantee the normal operating activity.
In research field, the method brought forward by Lehn
is widely adopted [5]. He accounts free cash flow as the
following expression:
PREDIV = total amount of preferred dividend re-
quirement on cumulative preferred stock and dividends
paid on noncumulative preferred stock
COMDIV = total dollar amount of dividend declared
on common stock
This method is adopted in several research works, such
as Lang’s [6], Howe’s [7], Doukas’ [8], and Ferdinand’s
studies [9]. Except these methods, there are several other
widely adopted methods, which would not be enumer-
ated here.
The relationship between FCF1 and FCF2 can be dis-
Copyright © 2011 SciRes. JSSM
Agency Cost under the Restriction of Free Cash Flow 81
played in Figure 2.
As shown in Figure 2, there are four components: INC
the first component, the second, the third, and the fourth
in turn. The first, the third, and the fourth component
make up FCF1, and the first component and the second
component make up FCF2. As the mutual component,
the first component represents the part that can be used
freely by the manager in any condition, which can be
called the “core” of free cash flow.
The third, the fourth and the second component repre-
sents discrepant request on free cash flow in different
conditions. When the manager has enough autonomy on
investment decision-making, the cash of invest is the
main source of his non-pecuniary benefits, so the cash of
investment should be involved in the expression. But
when the owner has not enough authority on investment
decision-making, the cash of invest is not “free” for the
director. T dividend should be paid to the stockholder
every year. But if the payment is not obligatory for the
firm, then the manager can abuse the cash to get non-
pecuniary benefits, so the third component will be in-
volved in. These different conditions lead to different
expressions such as FCF1 and FCF2. Considering the
condition that both the cash of investment and the cash of
dividend are “free” for manager, we can get the expres-
sion of free cash flow in this loosest condition:
If both the cash of investment and the cash of dividend
are not “free” for manager, then the expression will
change into FCF4 as shown below:
The expression of FCF3 generalizes the total scope
where free cash flow may exist, so we think this expres-
sion possesses the universality, and can be applied in
different field. In this paper, the free cash flow means the
cash accounted as FCF3, if there is no special comment.
Based on the analysis of essence of free cash flow, we
know that not all of the firm’s value but only the free
Figure 2. The relationship between FCF1 and FCF2.
cash flow can be used “freely” by the manager, just as
the hypothesis brought forward in the first section.
Assuming T is the free cash flow held by the firm, ac-
cording to Jensen’s model, when the fraction of out-
side-ownership is 1 α, the non-pecuniary benefits of
equilibrium point is F*, and the value of firm is V*. The
non-pecuniary benefits are transferred from the value of
firm, so if the transferable value is restricted, then F*
might be unreachable.
If T > F*, the volume of free cash flow can meet the
demand of manager, and the equilibrium will still stay at
point of B. When T = F*, the volume of free cash flow
will be used up, regardless of the demand of manager.
But if T > F*, even all free cash flow used up, the de-
mand of manager hasn’t been fulfilled, and the constraint
of free cash flow is restrict, the manager can’t change it,
so the non-pecuniary benefits is just the same as the
volume of free cash flow, but lower than F*. The relation
of free cash flow and F* can be shown in Figure 3.
As shown in Figure 3, the x-axis is the volume of free
cash flow, and CB3H3 represents the shape of relation
between free cash flow and the non-pecuniary benefits
when the inside ownership is α. B3 is the turning point,
where T equals to the equilibrium demand of non-pecu-
niary benefits. Before the point of B3, the shape of line is
upwards, with a slope of 1, while behind the point of B3,
the line is horizontal.
When enterprise scale, inside stock ownership value
and capital structure remains the same, if free cash flow
is higher than non-pecuniary benefits required by equi-
librium, free cash flow will overplus.
Theoretically, agent’s non-pecuniary benefits is ful-
filled. However, because the surplus of free cash flow
will lead to waste, it is inevitable to seek for new invest-
ment opportunities which generate more agency cost
Considering the agency cost derived from the invest-
ment of free cash flow surplus, under the constraint of
free cash flow and inside ownership, agency cost will
increase from H to H' as shown in the Figure 4 below.
(On the point N, free cash flow equals to agency cost of
Figure 3. The relationship between free cash flow and F*.
Copyright © 2011 SciRes. JSSM
Agency Cost under the Restriction of Free Cash Flow
Figure 4. The relationship between agency cost and inside
stock ownership under the proportion of stock ownership,
which satisfies agent’s motivation to occupy. When the
proportion of stock ownership is higher than that of point
N, agency cost of stock ownership on equilibrium point
will decrease, and then the surplus of free cash flow will
be used in new investment which generates agency cost
of investment. When the proportion of stock ownership is
lower than that of point N, free cash flow is not enough
to afford agency cost of stock ownership and deficiency
Moreover, corresponding to a certain level of free cash
flow and enterprise scale, the larger the proportion of
inside ownership is, the non-pecuniary benefit on the
equilibrium point will be lower and the surplus of free
cash flow will be higher. Furthermore, agency cost of
investment will be higher due to its positive relationship
with free cash flow. To sum up, the curve GN will rise to
As for the situation that the proportion of inside stock
ownership is less thanα3’, non-pecuniary benefit will not
be enough for the level of equilibrium point even free
cash flow is totally used for non-pecuniary benefits. If
free cash flow is restricted and remains constant, in the
other words, managers cannot acquire their non-pecuni-
ary benefit by increasing free cash flow or any other
ways, besides existing free cash flow, non-pecuniary
benefits will remain constant with the level of free cash
However, in reality free cash flow is not restricted rig-
idly in reality. Although managers would prefer cash free
flow when it is available, managers’ motivation to ac-
quire non-pecuniary benefits still exist when free cash
flow cannot meet managers’ demand on non-pecuniary
benefits. As a result, managers will try their best to ex-
pand individual benefits.
Comparing to free cash flow, other ways to expand in-
dividual benefits are easier to be monitored by owners
and cost more, so the non-pecuniary benefit will be lower
than that of the equilibrium point ultimately, though the
non-pecuniary benefit increases and is higher than free
cash flow. Moreover, when the decrease of inside stock
ownership, the gap between non-pecuniary benefit and
free cash flow on the equilibrium point will be enlarged
and managers’ motivation to acquire their non-pecuniary
benefit will be enhanced. Hence, non-pecuniary benefit
increases, enterprise value decreases and agency cost
increases. As shown in Figure 4, NK is the change of
agency cost curve on the left of point N. NK is lower than
the former agency cost curve NJ and higher than free
cash flow and will increase with the decrease of inside
stock ownership. Considering the continuity of measures
taken by managers as the ownership ratio changes, curve
GNK will be smooth.
The curve of agency cost will change with different
free cash flow correspondingly. When free cash flow
increases, the amount of funds that managers could use
to transform to non-pecuniary benefit will increase. New
equilibrium point will be reached under lower proportion
of inside stock ownership, crossing GNK at higher point.
When the curve of agency costs is changed, the con-
clusion of Jensen’s model should be modified. As shown
in Figure 5, AT(K) is the original curve of total agency
costs, which is the sum of agency costs associated with
outside equity Aso(K) and agency costs associated with
debt AB(K). Assuming the AB(K) is an invariable, when
Aso(K) changed to Aso(K)’, the curve of total agency
costs will change to AT(K)’. The original equilibrium
point is K*, where the total agency costs are minimum.
According to the minimum condition, the differential
coefficient of K* should be zero.
dd dd
Figure 5. The relationship between agency cost and the
proposition of debt.
Copyright © 2011 SciRes. JSSM
Agency Cost under the Restriction of Free Cash Flow 83
 
0Ts B
 
0Ts B
the expression can be written as
 
dd dd
 K
 
dd dd
According as the character of agency cost, we know that
the differential coefficient of both
K and
is negative and increases by degrees, and
is smaller than
, so we can get the expres-
sion below:
 
dd dd
 ;
At the point of K*,
0, it implies the
point isn’t the minimum point. With the decrease of
KK decreases too, but
KK in-
increases, there must be a point where
 
, and it’s the point of
It means, with the constraint of free cash flow, the
equilibrium point will move to K*’, where the fraction of
outside debt is less than K*. This implies that when the
constraint of free cash flow is considered, the firm will
choose to borrow less money but sell more equity out
than that in ideal condition to obtain optimal utility.
When the volume of free cash flow is changing, the
location of equilibrium point will keep moving conse-
quently as shown in Figure 6. The direction of moving
depends on the slope of total agency costs curve. With
the same fraction of outside debt, the slope of AT(K) with
higher free cash flow is larger than that with lower free
cash flow (the absolute value is less, but the slope is
negative), so the equilibrium point will move towards the
left direction, staying at a lower fraction of debt. This
relationship can be described in Figure 7.
It should be pointed out that, considering agency cost,
the true value of enterprise equals the original value of
enterprises subtracting agency cost. According to the
rules concluded above, it seems that enterprise value will
be maximized when free cash flow is zero. By this token,
enterprise should try its best to compress free cash flow
to increase enterprise value. However, in fact, even en-
terprise’s scale keep constant, too little free cash flow
will affect the normal operation which decreases enter-
prise value. Therefore, analysis on the convenient earn-
ings of free cash flow might be needed under extreme
Chu’s study on 2007 focused on free cash flow and
capital structure empirically. In this study, he argued that
the relationship between free cash flow and capital
structure could be explained as a reciprocal relationship
Figure 6. The location of equilibrium point.
Figure 7. The relationship between free cash flow and the
optimal of debt.
rather than a casual relationship between an independent
variable and a dependent variable. When there is incre-
mental free cash flow, the requirement of managers’
non-pecuniary benefits will emerge. As a result, manag-
ers would increase their non-pecuniary benefits, which
shifts agency cost curve up and makes the lowest agency
cost point move. Finally, capital structure will be stabi-
lized at the point of lower debt portion and higher inter-
nal stock ownership. However, capital structure will not
just change passively following the change of free cash
flow. Other factors besides free cash flow will lead to the
change of capital structure too. The mechanism involved
is not just to fit free cash flow. These could be regarded
as active change of capital structure. Corporate agency
cost curve will move accordingly with the change of
capital structure. For example, carrying out internal stock
ownership plan leads to higher proportion of internal
stock ownership, which will decrease of agency cost of
stock ownership. The motivation that managers expand
their own non-pecuniary benefits by occupying company
Copyright © 2011 SciRes. JSSM
Agency Cost under the Restriction of Free Cash Flow
property declines too. Managers might adopt some meas-
ures to adapt the motivation change, such as free cash
Because of the reciprocal relationship between free
cash flow and capital structure, liner regression through
simple equation will be not appropriate to describe the
correlative relationship precisely.
The simultaneous equations between free cash flow
and other variables are proposed as below:
FCF = F1 (DebtPort, Dividend, InEquity, InstOwn,
AssetSal, ProftMar, OseaSale, Issuance, Ca shBu y, Cash-
Sell, StkBuy, StkSell)
DebtPort = F2 (FCF, InEquity, Issuance, Dividend,
DebtIss, CashBuy , CashS e ll, StkBuy, TobinsQ)
FCF = free cash flow
DebtPort = debt proportion
Dividend = stock dividend
InEquity = inside equity
InstOwn = the equity owned by institution
AssetSal = the ratio of sales to asset
ProftMar = profit margin
OseaSale = overseas sales
Issuance = the issuance of equity
Cashbuy = the Acquisition in cash
Cashsell = the assets sale in cash
StkBuy = the acquisition in the form of stock
StkSell = the sale in the form of stock
DebtIssu = the issuance of debt
Tobins’Q = the Q defined by Tobin
The empirical study adopted 2SLS method to analyze
the data from 1990 to 2004 in North American stock
market. Filtering out disqualified and abnormal cases, the
sample size is 42491. 16382 cases involved in merge and
acquisitions were included too.
As shown in the analysis result, the regression coeffi-
cient of debt portion on free cash flow is 2.02500 (t =
14.234, p < 0.0001), which means debt portion is sig-
nificantly negatively related to free cash flow. [10] The
result supports the proposition in the theoretical deduc-
tion: corresponding to the increase of free cash flow, debt
portion will be decreased to fit free cash flow, which
makes agency cost on level as low as possible. Because
the incremental free cash flow will increase agency cost
and debt portion will decrease to fit the change of agency
4. Conclusions
In classic capital structure theories, default assumption is
managers make decision freely on the level of
non-pecuniary benefit which could be as high as full en-
terprise value. However, considering the characteristics
of free cash flow, this assumption is not supported in
reality. Under the restriction of rigidity, the maximum
non-pecuniary benefit managers acquired will be the
amount of free cash flow, which is just a limit part of
enterprise full value.
With this restriction, when free cash flow is more than
or equal to non-pecuniary benefit on the equilibrium
point, the original equilibrium point will be reached. But
when free cash flow is less than non-pecuniary benefit on
the equilibrium point, the original point will not be
reached and a new equilibrium point will come out ac-
cording to the amount free cash flow. On the new point,
market value of enterprise will be higher than that of the
original point and agency cost will decrease. Considering
the occupation and the possible abuse of rest free cash
flow when free cash flow is insufficient, we can find that
under the restriction of free cash flow, the curve of
agency cost of ownership will intersect the original one
with changing slope and smooth curve.
The point of intersection of the agency cost curve and
the original one is different corresponding to different
amount of free cash flow. Non-pecuniary benefit on the
point of intersection is the amount of free cash flow. The
curves of ownership agency cost under different free
cash flow mutually disjoint. With the increasing free cash
flow, the curve of ownership agency cost rises continu-
ously, and the slope decreases. As a result, gross agency
cost curve deviates and the minimum of gross agency
cost moves left continuously. Therefore, when free cash
flow increases, gross agency cost will increase and en-
terprise value will decrease. Correspondingly, the opti-
mal point of capital structure moves left and the propor-
tion of debt decreases. That is, free cash flow is nega-
tively related to the proportion of debt.
This law is consistent with the correlation of free cash
flow and agency cost shown in reality. This study ex-
tends the classic agency cost theory and involves free
cash flow in theoretical framework systematically. Fur-
ther analysis and empirical studies about the relationship
might be needed.
[1] S. C. Myers, “The Capital Structure Puzzle,” Journal of
Finance, Vol. 39, No. 1, 1984, pp. 575-592.
[2] S. C. Myers and N. S. Majluf, “Corporate Financing and
Investment Decisions When Firms Have Information That
Investors Do Not Have,” Journal of Financial Economics,
Vol. 13, No. 2, 1984, pp. 187-221.
[3] M. P. Narayanan, “Debt Versus Equity under Aysmmet-
ric Information,” Journal of Financial and Quantitative
Analysis, Vol. 23, 1988, pp. 39-52.
Copyright © 2011 SciRes. JSSM
Agency Cost under the Restriction of Free Cash Flow
Copyright © 2011 SciRes. JSSM
[4] P. H. Rubin, “Managing Business Transactions,” The
Free Press, New York, 1990.
[5] K. Lehn and A. Poulsen, “Free Cash Flow and Stock-
holder Gains in Going Private Transactions,” Journal of
Finance, Vol. 44, No. 3, 1989, pp. 771-787.
[6] L. H. P. Lang, R. M. Stulz and R. A. Walkling, “A Test
of the Free Cash Flow Hypothesis, the Case of Bidder
Returns,” Journal of Financial Economics, Vol. 29, No. 2,
1991, pp. 315-335. doi:10.1016/0304-405X(91)90005-5
[7] K. M. Howe, J. He and G. W. Kao, “One-Time Cash
Flow Announcements and Free Cash Flow Theory: Share
Repurchases and Special Dividends,” Journal of Finance,
Vol. 47, No. 5, 1992, pp. 1963-1975.
[8] J. Doukas, “Overinvestment, Tobin’s Q and Gains from
Foreign Acquisitions,” Journal of Banking and Finance,
Vol. 19, No. 7, 1995, pp. 1285-1303.
[9] A. G. Ferdinand, “Free Cash Flow, Debt-Monitoring and
Managers’ LIFO/FIFO Policy Choice,” Journal of Cor-
porate Finance, Vol. 7, 2001, pp. 475-492.
[10] J. Chu, “The Empirically Study on the Relationship be-
tween Free Cash Flow and Agency Cost,” The Sociologist,
No. 5, 2007, pp. 159-161.