The debt level just ensures that the shareholders prefer the expected residual in the low state to the reduction in rents inby
Alan V. S. Douglas JEL classification codes: G3, D82. Keywords: Capital structure, Optimal Compensation, Manager-Owner and Shareholder- Bondholder Incentive Conflicts, Information Asymmetries, Corporate Efficiency Corresponding author: Alan V. S. Douglas Finance Centre 289 Hagey Hall, University of Waterloo Waterloo, Ont., Canada N2L 3G1 Office: (519) 888-4567
e-mail: adouglas@uwaterloo.ca
Abstract
This paper models the influence of capital structure on managerial incentives in the presence of explicit compensation contracts. Capital structure can mitigate a managerial incentive to substitute into riskier first period investments that increase his second period information advantage. In particular, if such asset substitution makes second period debt risky, the shareholders offer a compensation contract that focuses excessively on the manager’s information rents (as they accrue only in high states). The optimal capital structure therefore balances shareholder-bondholder and manager-owner incentive conflicts. An interesting feature of this balance is that the shareholder-bondholder conflict dominates when the firm performs poorly, and manager-owner conflict dominates when the firm is doing well. In addition, the shareholder-bondholder conflict can be effectively controlled via short-term debt obligations and the manager-owner conflict can be effectively controlled via short-term dividend payments. Optimal capital structure and debt maturity are therefore related to both contracting costs and dividend policy, in a manner that is consistent with existing evidence and suggests some interesting directions for future investigations.
2
The literature studying corporate incentive conflicts provides invaluable insight into the
determinants of corporate capital structure. In their seminal studies, Fama and Miller (1972) and
Jensen and Meckling (1976) illustrate that the shareholders have an incentive to expropriate
bondholder wealth by substituting into riskier investments, and Myers (1977) illustrates that the
shareholders have an incentive to under-invest when part of the return accrues to bondholders.
Other studies distinguish between managers and shareholders, and examine the effects of capital
structure on managerial incentives. For example, Jensen (1986) and Zwiebel (1996) argue that
debt can focus managers on value maximization rather than personal objectives, and Stulz (1990)
illustrates that debt can force the disbursement of cash flows to deter over-investment.
A potential criticism of this literature is that it does not explain why managerial decisions
are influenced by capital structure rather than explicit managerial compensation contracts.
Indeed, studies that focus on the explicit design of managerial incentive contracts have questioned
the insights above. For example, Dybvig and Zender (1991) illustrate that if the owners can
implement a long-term compensation contract at the outset, managerial decisions are in fact
independent of capital structure (effectively resurrecting the Modigliani-Miller irrelevancy
results). In response, Persons (1994) illustrates that such a long-term contract is dynamically
inconsistent: the shareholders can profitably renegotiate the contract when the opportunity to
expropriate bondholder wealth arises. While the implication is that capital structure is indeed
relevant, Persons stops short of illustrating the capital structure that is optimal in the presence of
dynamically consistent compensation contracts.
In this paper, we formally investigate the interaction between capital structure and
dynamically consistent compensation contracts, and illustrate the value-maximizing (optimal)
capital structure. The interaction between capital structure and compensation stems from
managerial discretion over an initial investment choice that affects his subsequent (second period)
information advantages. These second period information advantages include both hidden
actions and hidden knowledge regarding the success of the investments in place. The value-
maximizing second period compensation contract trades off managerial rents in the high state
with inefficient actions in the low state, such that the resulting level of rents increases with the
manager’s information advantage. The manager can therefore increase his rents by choosing first
period investments that generate greater second period information advantages. Such
3
investments, however, increase risk (produce a mean preserving spread in project outcomes) and
reduce firm value (i.e. reduce the cash flow available for the firm’s owners). The manager’s
incentive to choose such investments therefore represents an adverse asset substitution incentive
in the first period.
Long-term debt can deter this asset substitution because the second period incentive contract
that maximizes shareholder wealth also depends on the amount of debt outstanding. In particular,
risky debt distorts the shareholders incentive to choose an incentive contract that efficiently trades
off managerial rents in the high state with inefficient actions in the low state – i.e. if the debt level
is risky, the bondholders bear the cost of inefficient actions in the low state, inducing the
shareholders to choose a compensation contract that minimizes the manager’s rents (debt
overhang leads to ‘under-investment’ in the low state, similar to Myers (1977)). This implies that
a long-term debt level that becomes risky with asset substitution, but not otherwise, can induce
efficient investment in the first period. Moreover, with efficient first period investment, the long-
term does not become risky and the shareholders optimally choose the value-maximizing second
period compensation contract.
The interaction between long-term debt and compensation also creates a role for short-term
debt and dividend payments. This role arises because the incentives associated with long-term
debt also depend on the firm’s short-term performance (represented by the realization of first
period cash flows): particularly low cash flow realizations can make the second period debt
payment risky even without asset substitution (causing under-investment), while particularly high
cash flow realizations can ensure the second period payment despite asset substitution. To
control for the effects of first period cash flows, the firm optimally issues short-term debt. Short-
term debt can deter asset substitution by forcing the manager to disburse excess cash when the
realization is particularly high, and can deter under-investment by providing the debt holders with
additional power when the realization is particularly low (so that the firm defaults).
In addition, when default costs are substantial, the firm can substitute (performance-
contingent) dividends for short-term debt, in order to deter asset substitution following high cash
flows but avoid default costs. Since the manager is reluctant to disburse a self-disciplining
dividend, however, the optimal combination of short-term debt and dividends reflects the relative
cost of inducing such a dividend, which is positively related to the cost of managerial
replacement. The resulting capital structure therefore combines short and long term debt
4
payments in a manner that reflects the firm’s ability to control managerial investment incentives
via dividend policy.
Dewatripont and Tirole (1994) also present a theoretical analysis in which capital structure
combines with an explicit managerial compensation contract to induce an efficient first period
action (effort choice) by the manager. In their model, however, the manager’s effort choice
depends on a non-contractible second period asset substitution choice made by the controlling
investor – specifically, the controlling party, shareholders or bondholders, can stop existing
investments, which reduces risk (Berkovitch, Israel and Speigel (2000) provide a similar analysis,
except that stopping the current investments (framed as replacement) leads to an increase rather
than a decrease in risk). The second period asset substitution choice affects effort because the
optimal compensation scheme provides higher compensation for higher outcomes, so that the
incentive to provide effort reflects the probability of high outcomes. In the end, therefore, the
firm’s debt level affects asset substitution because default transfers decision rights, and the
shareholders and bondholders have different asset substitution preferences.
Our analysis differs from Dewatripont and Tirole (and Berkovitch, Israel and Speigel
(2000)) in a number of ways. First, building on the work of Dybvig and Zender (1991) and
Persons (1994), we focus on the implications of capital structure when shareholders and
bondholders have conflicting incentives with respect to the actions induced by managerial
incentive contracts (in Dewatripont and Tirole, and Berkovitch, Israel and Speigel, both
shareholders and bondholders prefer a compensation contract that induces high managerial
effort). Additionally, long-term debt in our analysis can support efficient first period behavior
without sacrificing ex-post efficiency.1 Most importantly, however, we focus on the case where
the manager’s first period action is designed to affect the subsequent contracting environment.
Dow and Raposo (2002) also examine a manager’s incentive to pursue initial strategies that affect
subsequent compensation contracts. While Dow and Raposo focus on the links between the
firm’s environment (the scope for opportunistic strategies) and the features of optimal
compensation schemes (e.g. ex-ante versus ex-post contracting), our analysis focuses on the links
between incentives and optimal capital structure.2
Finally, our analysis has a number of interesting empirical implications. In particular,
capital structure and dividend policy are jointly determined, with optimal debt and dividend
payments decreasing in equilibrium contracting costs. These implications are consistent with the
5
findings of Titman and Wessels (1988), Jensen, Solberg and Zorn (1992), Barclay Smith and
Watts (1995), Rajan and Zingales (1995), and Fama and French (2002). In addition, the maturity
structure is consistent with the original finding of Barclay and Smith (1995) that debt maturity
(measured by the proportion of debt with a maturity of at least three years) decreases with
contracting costs (measured by market to book), and can reconcile this finding with the mixed
relationship between maturity and contracting costs found by Stohs and Mauer (1996), since
optimal maturity also depends on contracting costs that are avoided in our model. Specifically,
our analysis predicts that the potential for asset substitution is reflected in the firm’s debt to
dividend ratio, such that negative relationship between maturity and contracting costs is stronger
for firms with a higher debt to dividend ratio. Additionally, since the cost of inducing dividends
is positively related to the cost of managerial replacement, our model predicts that both dividends
and debt maturity are negatively related to managerial entrenchment.
Our analysis also implies that the corporate agency conflict of greatest concern is related
to the firm’s performance. Specifically, the shareholder-bondholder conflict (i.e. the under-
investment incentive) is the major concern when performance is low, whereas the manager-owner
conflict (i.e. manager’s asset substitution incentive) is the major concern when performance is
high. Although it is intuitive that managers are less inclined to pursue self-serving projects in bad
times, and shareholders are less inclined to induce managerial actions that expropriate bondholder
wealth in good times, to the best of our knowledge, this prediction has yet to be directly tested.
The analysis is organized as follows. Section I presents the basic model. The
dynamically consistent second period compensation contracts are characterized in section I.1, and
the asset substitution and under-investment problems are presented in sections I.2 and I.3
respectively. Section II illustrates the role of short-term debt and dividend payments, and
presents the optimal capital structure. Section III discusses empirical implications and
extensions, and section IV concludes.
I. Model.
This section develops an agency model in which non-contractible decisions significantly
affect corporate value. We begin with a general outline of the time line and the sequence of
events, as given in figure 1:
Figure 1: Time Line and Sequence of Events.
t = 0 t = 1 t = 2
At t =
second period
of investment
second period
substitution c
information a
Capital structure (short and long- term debt levels, F1 and F2) chosen
2nd period compensation contract designed
Investment success (εi) learned by manager, Managerial action (a) chosen
Final value distributed
Manager’s asset substitution choice (y)
Cash flow c1 realized, Debt and dividend payments, F1 and d1, made (if possible)
6
0, the firm chooses its capital structure, defined as the combination of first and
debt payments F1 and F2. During the first period, cash flow c C1 0∈ ( , ) is realized
bt and dividends payments F1 and d1 are made (if c1 < F1, the firm defaults as
e manager makes a non-contractible asset substitution choice. Similar to Jensen
(1976) and Gorton and Kahn (2000), the asset substitution choice determines the
n) in second period outcomes, denoted by ε ≡ εH – εL. Specifically, the manager
the existing dispersion, in which case ε = x, or add a mean preserving spread y,
x + y (where x ≡ xH – xLand y ≡ yH – yL). In contrast to standard asset
.
sure dynamic consistency, the manager’s second period compensation contract is
= 1.3 In particular, compensation is designed to maximize t = 1 shareholder wealth,
manager’s second period information advantages. These information advantages
anager’s hidden second period action, represented by a, and her hidden knowledge
success, represented by ε. As above, there are two equally likely realizations of the
uncertainty term, ε ε ε∈ { , }L H with ε εH L> ≥ 0 . Since the manager’s asset
hoice determines ε ≡ εH – εL as above, it influences the manager’s second period
dvantage.
7
The total cash flow (value) available at the end of the second period (t = 2) is given by
v c F d a= − − + +1 1 1 ε . This value is divided between the shareholders, debt holders and the
manager according to the contracts outstanding. The investors receive total value less the
payment to the manager specified in the compensation contract. Of this, the debt holders receive
up to the face value F2 in the debt contract, and shareholders receive the residual. The investors
care only about expected returns, while the manager has utility given by
u w a w A a( , ) ( )= −
where w is monetary compensation, and A(a) is the manager’s disutility of her action a (e.g.
effort or foregone perquisites). The action is defined on the set a a a∈ [ , ], and to simplify, the
disutility function is given by4
A a ka a
if if .
Finally, the manager's reservation utility, denoted u, is normalized to zero, as is the manager’s
outside wealth.
The remainder of this section analyses the decisions made after the capital structure is
chosen at t = 0. Section I.1 presents the t = 1 compensation design problem when the outstanding
debt level is risk free. Section I.2 illustrates the manager’s asset substitution incentive associated
with this compensation scheme, and section I.3 illustrates the effects of risky debt on the
shareholders’ compensation design problem (i.e. the shareholders’ under-investment incentive).
Section II presents the capital structure and dividend policy that maximize the initial (t = 0) value
of the firm.
I.1 Second Period incentive contracts
To simplify, we begin with the t = 1 compensation design problem in the case without
first period debt or dividends (F1 = d1 = 0) and where the second period debt level F2 ≥ 0 is risk-
free. Three factors in our model determine whether F2 is risk-free at t = 1: the level of F2, the
realization of c1 and the choice of ε. The analysis here represents any combination of these
factors such that F2 is risk-free, so that there are no shareholder-bondholder agency conflicts and
the incentive contract addresses only manager-owner agency conflicts. We present the case of
risky debt (due to a higher F2, lower c1, or higher ε) in section I.3, and introduce first period debt
and dividends in section II.
8
Risk Free Debt
At t = 1, both the assets in place, ε ∈ { , }x y x + , and the existing cash flow,
c C1 0∈ ( , ) , are observed by the shareholders (though neither variable is contractible, as noted
above). The dynamically consistent compensation contract therefore focuses on the manager’s
second period information advantages, which include the realization of ε and the choice of a as
above.
Specifically, the shareholders observe only the combined outcome ε + a (or equivalently,
total value v c a= + +1 ε ), knowing that each realization εi was equally likely. Thus, they design
the incentive contract to maximize their t = 1 expected payoff
. ( ) . ( )5 51 1 2c a w c a w FH H H L L L+ + − + + + − −ε ε ,
where ai denotes the incentive compatible action for each realization of εi. The incentive contract
must satisfy the manager's reservation utility constraint for each possibility (w A a ui i− ≥( ) ) to
ensure the manager’s participation both when there is good news and when there is bad news. It
must also satisfy the manager's incentive compatibility constraints for each possibility, given by
w A a w A aL L H H− ≥ − +( ) ( )ε and w A a w A aH H L L− ≥ − −( ) ( )ε .
These incentive compatibility constraints ensure that the manager in fact chooses the intended
levels of ai, given his ability to claim that either value of εi was realized.5
Some important features of the optimal contract follow immediately from the constraints.
In particular, the incentive compatibility constraint for the high state enables the manager to
obtain rents, as seen by substituting w u A aL L= + ( ) into the constraint, yielding
w A a u A a A aH H L L− ≥ + − −( ) ( ) ( )ε .
Thus, the simultaneous information advantages provide the manager with an information rent
equal to A a A aL L( ) ( )− − ε in the high state and the reservation utility constraint for i = H does
not bind. Additionally, the two incentive compatibility constraints cannot simultaneously bind, as
seen by rewriting them as
w w A a A aH L H L− ≤ + −( ) ( )ε and w w A a A aH L H L− ≥ − −( ) ( ) .ε
Since A > 0 and A > 0, A a A a A a A aH L H L( ) ( ) ( ) ( )+ − > − − ε ε and only one constraint can
bind. To induce the manager's actions with the lowest payments necessary, it is the constraint for
9
the high state that binds (otherwise the shareholders would pay the manager more than necessary
when i = H).
Thus, the optimal contract maximizes the shareholders' expected return subject to the
incentive compatibility constraint for the high state and the reservation utility constraint for the
low state, so that the Lagrangian is
max . ( ) . ( )
RU L L L
L c a w c a w F
w A a u w A a w A a
5 51 1 2ε ε
θ θ ε
The first order conditions for wL and wH yield θ RU L = 1 and θ IC
H =.5, and the first order condition
for aH yields
∂ ∂ = − ′ = ⇒ ′ =L a A a A aH H H/ . ( ( )) ( ) ,5 1 0 1
illustrating that the optimal contract induces the first best action if i = H, aH = aFB. However, it
induces a lower level of the action in the bad state, as seen from the first order condition for aL
∂ ∂ = − ′ + ′ − =L a A a A aL L L/ . ( ) . ( )5 5 0ε ,
so that
1 1− ′ = ′ − ′ − ⇒ ′ <A a A a A a x A aL L L L( ) ( ) ( ) ( ) (1)
The optimal contract sets aL < aFB since this reduces the information rent A a A aL L( ) ( )− − ε
required to satisfy the incentive compatibility constraint for the high state, as above. The
information rent decreases when aL is reduced because A = k > 0.
The manager’s second period information advantage therefore leads to contracting costs
that consist of two components: (i) the inefficiency cost of a aL FB< , denoted
α( ) ( ( )) ( ( )),a a A a a A aL FB FB L L≡ − − −
and (ii) the manager’s information rent if i = H, denoted
ρ ε ε( , ) ( ) ( ).a A a A aL L L ≡ − −
The optimal contract is designed to minimize the expected contracting costs, denoted
κ ε α ρ ε( , ) . ( ) . ( , ),a a aL L L ≡ +5 5
as seen by writing the expression for the optimal value of aL in (1) as
10
. ( ) .5 0 (1')
The optimal value of aL in (1) characterizes the value-maximizing second period
compensation contract in our analysis and is denoted aL* (i.e. aL* characterizes the contract that
maximizes the cash flow available for investors, given the unavoidable managerial information
advantages). This is the dynamically consistent value of aL when F2 is risk free (as above), so
that maximizing shareholder wealth is equivalent to maximizing firm value. Such low debt
levels, however, leave the manager with an asset substitution incentive in the first period, as seen
next.
I.2 The Asset Substitution Choice
As discussed above, asset substitution is modeled as a mean preserving spread in project
outcomes such that ε increases from x to x +y. In contrast to standard analyses, however,
the decision to unilaterally add risk reflects a positive association between risk and the manager’s
information advantages, which arises in our model because the manager asymmetrically observes
ε. Asset substitution therefore alters the value-maximizing compensation contract characterized
by (1).
In particular, asset substitution increases the cost of contracting with an asymmetrically
informed manager, and therefore lowers firm value, as stated formally in lemma 1.
Lemma 1: A mean preserving spread in investment outcomes (asset substitution) increases the
level of contracting costs under the value-maximizing second period compensation contract to
K x y K x( ) ( ) + > , thereby reducing firm value.
Lemma 1 can be seen by totally differentiating the contracting costs K aL( ) ( ( ), )* ε κ ε ε≡ ,
while recognizing that daL*/dε = -1 (from differentiation of (1) with A′(a) = ka). This
adjustment in aL* reflects that, ceteris paribus, the increased information asymmetry increases the
marginal benefit of reducing the manager’s rents but not the marginal inefficiency cost of aL <
aFB, so that aL* is optimally decreased as in (1′). The increase in expected contracting costs K(ε)
is therefore6
L
ε κ ε
ε κ ε
ε κ ε
11
Despite the adverse effect on firm value, the manager may pursue asset substitution to
increase the information rents she receives under the value-maximizing second period
compensation contract, ρ ε ε( , ) ( ) ( ))* * *a A a A aL L L ≡ − − . The effect of ε on the manager’s
information rents is given by
d d A a da d
A a A a A a kL L
L L Lρ ε ε ε
ε ε ε/ ( ) ( )( ( ) ( )) ( )) .* *
* *
= ′ − + ′ − ′ − = ′ − −
The first term represents the direct effect of ε, which increases the manager’s rents, and the
second term represents the effect of the offsetting adjustment in aL* to maintain the optimality
condition (1) (i.e. daL*/dε = -1).
In contrast to firm value (which is monotonically decreasing in ε), the manager’s rents
are concave in ε (i.e. d2ρ/dε2 = -3k), reaching a maximum at ε = 1/(3k). To maintain focus,
we restrict attention to the case where the direct effect of the additional information asymmetry
dominates, so that asset substitution increases the manager’s rents (a sufficient condition is that
x + y ≤ 1/(3k)).
Thus, when F2 is risk-less and the incentive contract is designed to maximize t = 1
shareholder wealth (i.e. characterized by (1)), the manager pursues asset substitution, as stated in
lemma 2.
Lemma 2: When the debt level F2 remains risk-less, the manager pursues the riskier
investment in the first period, increasing ε from x to x + y.
Lemma 2 illustrates that the manager will pursue a sub-optimal investment strategy if the firm has
low (risk-less) levels of debt.
Higher debt levels, however, alter this investment incentive, because risky debt
introduces the familiar agency conflicts between shareholders and bondholders. This alters the
shareholders’ compensation design problem, and therefore the manager’s first period investment
incentives, as seen next.
I.3 Risky debt and Under-investment in aL
We now illustrate the case where the debt level F2 is risky in the analysis above. Risky
debt levels leave no residual in the low state, so that the shareholders are primarily concerned
with value in the high state and the standard shareholder-bondholder agency conflicts arise
(Myers (1977), Jensen and Meckling (1976)).
Since the manager in our model makes the operating decisions, the effects of shareholder-
bondholder conflicts manifest through the effects on managerial incentives. In particular, the
opportunity to expropriate bondholder wealth distorts the shareholders’ contract design problem
at t = 1, since the incentive contract that maximizes shareholder wealth now induces highly
inefficient actions when low value is realized (aL = 0) to increase the return when high value is
realized. This expropriation incentive is similar to the under-investment incentive in Myers
(1977) where shareholders forego profitable projects because part of the return would accrue to
debt holders. Here, the shareholders forego a profitable ex-post "investment" of wL since the
benefit, an increase in aL, accrues to the bondholders.
The effect of risky debt on the incentive contract designed by shareholders is presented in
lemma 3.
Lemma 3: When the second period debt payment F2 is risky, the dynamically consistent
compensation contract offered by the shareholders induces a highly inefficient level of aL, i.e.
aL = 0. This reduces firm value despite reducing managerial rents to zero.
The formal explanation (proof) of lemma 3 follows from the change in the shareholders’
objective in the contract design problem, which becomes
max . ( )
i i L c a w F
w A a u w A a w A a
5 1 2ε
θ θ ε
The first order conditions for wi and aH now yield θ RU L =.5 and θ IC
H =.5, ′ =A a H( ) ,1 and
∂ ∂ = − ′ − ′ − =L a A a A aL L L/ . ( ( ) ( ))5 0ε
⇒ =a L 0. (2)
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The shareholders now prefer to reduce aL because this decreases ρ(aL,ε) as above (they are
unconcerned with the corresponding increase in α(aL) since their payoffs are insensitive to
inefficiency costs when i = L). As illustrated above, however, firm value (i.e. the value of equity
plus debt) is maximized at aL* (i.e. κ(aL*,ε) < κ(0,ε) as in (1′)). Thus, setting aL = 0
expropriates bondholder wealth but reduces firm value.
Although the creditors bear the t = 1 cost of the under-investment in aL, they anticipate
the possibility at t = 0, so that the original owners ultimately bear any residual loss (Jensen and
Meckling (1976)). The owners therefore issue t = 0 debt only to the extent that there are
offsetting benefits. In our model, these offsetting benefits stem from the interaction between the
first period asset substitution incentive and the second period under-investment incentive, as seen
next.
managerial compensation contracts in our model. In particular, lemma 2 illustrates that the
dynamically consistent compensation contract will induce the manager to pursue asset
substitution if the second period debt payment F2 remains risk-less. Lemma 3 illustrates,
however, that the manager has an incentive to avoid asset substitution if the riskier investment
makes F2 risky, since the dynamically consistent compensation scheme then leaves the manager
with no rents. These results imply that the manager’s first period investment choice depends on
whether asset substitution makes the second period debt payment risky.
As discussed above, there are three factors that determine whether F2 is risky at t = 1: the
level of F2 chosen at t = 0, the first period realization of c1 and the first period asset substitution
choice ε. In this section, we develop the manager’s asset substitution choice as a function of c1,
given the (potentially risky) value of F2.7 To do so, we first determine the realizations of c1 for
which F2 becomes risky if the manager pursues asset substitution, but not otherwise. For these
realizations, the manager refrains from asset substitution to deter the shareholders from the under-
investment compensation scheme in lemma 3. Indeed, when the manager refrains from asset
substitution following these realizations, it is dynamically consistent for the shareholders to
choose the value-maximizing contract (induce aL*), so that the second period debt level produces
efficient corporate decisions at no additional cost.
14
To show this formally, we identify the value of c1 that just deters the shareholders’ under-
investment incentive. For lower realizations of c1, the second period debt payment is risky and
the shareholders prefer under-investment (aL = 0), as in lemma 3. This reduces managerial rents
to zero in the high state, so that w A aH FB= ( ) and expected shareholder wealth is
. [ ( ) ] . [ ]5 5 01 2c a A a FH FB FB+ + − − +ε .
With higher values of c1, however, the shareholders receive a residual in the low state if they
induce aL* rather than aL = 0, and expected shareholder wealth is
. [ ( ) ( , ) ] . [ ( ) ].* * *5 51 2 1 2c a A a a F c a A a FH FB FB L L L L+ + − − − + + + − −ε ρ ε ε
The value of c1 at which the shareholders are indifferent between the value-maximizing (aL = aL*)
and under-investment (aL = 0) solutions is found by equating (3) and (4). This level of cash flow,
denoted !c , is given by
!( ) ( ) ( )c F a A a KL FB FB ε ε ε= − − + +2 2 (3)
where again K a aL L( ) . ( ( )) . ( ( ), ) ε α ε ρ ε ε= +5 5 as above. For c c1 < ! , shareholder wealth is
maximized by offering the under-investment contract (inducing aL = 0), and for c c1 ≥ ! ,
shareholder wealth is maximized by offering the value-maximizing contract inducing (aL = aL*).
As seen from (3), the range of first period cash flows that produce the value-maximizing
contract depends on the manager’s asset substitution choice, ε. A mean preserving spread in ε
from x to x + y increases !c for two reasons. First, because y is mean preserving, yL < 0 and
yH > 0, so that εL decreases from xL to xL + yL. Second, adding y increases the contracting costs
from K(x) to K(x+y) as in lemma 1. The effect of asset substitution on the range of cash
flows that produce the value-maximizing contract is therefore given by
φ ≡ + − = + − − >!( ) !( ) ( ( ) ( ))c x y c x K x y K x yL 2 0 . (4)
Equation (4) implies that, upon observing !( ) !( )c x c c x y ≤ ≤ +1 , the manager will
refrain from asset substitution; otherwise the dynamically consistent compensation contract will
expropriate bondholder wealth to reduce the manager’s rents. When the manager refrains from
asset substitution, the shareholders offer the value-maximizing second period contract and
therefore positive managerial rents of ρ( ( ), )*a x xL >0 . This result is stated formally as
proposition 1:
15
Proposition 1: When the first period cash flow realization satisfies !( ) !( )c x c c x y ≤ ≤ +1 , the
second period debt level F2 deters asset substitution in the first period and produces the value
maximizing incentive contract in the second period. For lower realizations, c c x1 < !( ) , the
shareholders pursue under-investment, aL=0, and for higher realizations, c c x y1 > +!( ) , the
manager pursues asset substitution, y.
Proposition 1 illustrates that, for a particular range of first period cash flows, the long-
term debt payment F2 can simultaneously control the asset substitution and under-investment
incentives, thereby increasing firm value. The optimal capital structure exploits this benefit of
long-term debt, while accounting for the incentive problems associated with any other
realizations of c1, as seen next.
II. Optimal Capital Structure
In this section, we present the optimal capital structure in our analysis. To do so, we first
illustrate the optimal second period debt payment in the absence of first period debt or dividend
payments as above. We subsequently extend the analysis to illustrate how first period debt and
dividend payments can reduce the cost of any incentive problems that remain.
Proposition 1 illustrates that a long-term debt payment can induce value-maximizing
decisions at no additional cost over a range of first period cash flows given by
!( ) !( )c x c c x y ≤ ≤ +1 . The optimal F2 (and more generally the optimal t = 0 capital structure)
therefore depends on the set of possible values of c1, as given by the support c C1 0∈ ( , ) with
uniform density function g(c1) = g.
The long-term debt payment F2 cannot produce value-maximizing incentives for all first
period realizations when C > φ, where φ ≡ + −!( ) !( )c x y c x as in (4), and we focus on this case
for the remainder of the analysis. In this case, if the firm sets F2 sufficiently low to avoid under-
investment for all c1, i.e. such that !( )c x = 0 , the manager will invest opportunistically when the
highest realizations obtain. Alternatively, if the firm sets F2 sufficiently high to avoid asset
16
substitution for all c1, i.e. !( )c x y C + = , the shareholders will pursue under-investment when
the lowest realizations obtain.
The optimal choice of F2 therefore depends on the relative cost of asset substitution and
under-investment. The cost of asset substitution is given by
AS ≡ κ(aL*(x+y),x+y) – κ(aL*(x),x) ≡ K(x+y) – K(x),
and the cost of under-investment is given by
UI ≡ κ(0,x) – κ(aL*(x),x).
Since κ(0,x) = κ(0,x+y) > κ(aL*(x+y),x+y), asset substitution is less costly in our
model. Thus, a capital structure that includes only a second period debt payment optimally sets a
low debt level to deter under-investment, allowing high managerial rents for the highest
realizations of c1. This result is presented formally in proposition 2.
Proposition 2. When C > φφφφ, a capital structure that includes only a second period debt payment
F2 allows either under-investment for the lowest realizations of c1, or asset substitution for the
highest realizations. In the absence of first period debt or dividend payments, the latter is
optimal since asset substitution is less costly than under-investment.
Proposition 2 implies that the long-term debt payment in fact increases firm value. With no debt,
the manager pursues asset substitution for all c1 as in lemma 2. The debt level in proposition 2,
however, prevents asset substitution for 0 1≤ ≤c φ, thereby reducing expected contracting costs
by g·φ·AS.
Since C > φ, however, significant costs (equal to g·(C-φ)·AS) remain. These costs can be
reduced, however, by incorporating a short-term debt and dividend payments to help control sub-
optimal investment incentives, as seen next.
Short-term debt
Introducing a short-term debt payment, F1, has two effects on the analysis above. First,
when the payment is made, less cash flow is available for the second period debt payment F2.
This implies that, ceteris paribus, the under-investment incentive arises for more values of c1,
whereas the asset substitution incentive arises for fewer values. Specifically, the under-
17
investment incentive now arises for c c x F1 1< +!( ) , whereas the asset substitution incentive arises
for c c x y F1 1> + +!( ) .
Second, short-term debt creates the possibility of default at t = 1, which occurs when c1 <
F1. Default can be costly due to the opportunity cost of each party’s time, reputation damage, and
legal costs. Default, however, is also beneficial in our model, as it can facilitate a renegotiation to
deter sub-optimal investment. For example, default may reduce the free-rider and hold-out
problems associated with disperse claimants, and take advantage of the strong bondholder
incentive to deter under-investment (e.g., the legal right to seize collateral would produce a
financial restructuring in which the bondholders receive an equity payment in return for reducing
F2 to deter under-investment).8
To maintain focus, we do not formally model the process of default, and restrict attention
to the case where default produces the value-maximizing managerial incentive contract at a cost γ
that is less than the cost of sub-optimal investment (i.e. γ < AS < UI). Specifically, we assume
that if c1 < F1, the shareholders and bondholders renegotiate the second period debt level to Fr 2 ,
such that
F x a A a K x c F x y a A a K x yr L FB FB r L L FB FB 2 1 22 2− − + + ≤ ≤ − − − + + +( ) ( ) ( ) ( ) ,
which deters both asset substitution and under-investment as in proposition 1.9
Since the cost of default (including debt contract restructuring) is less than that of sub-
optimal investment, a short-term debt payment can be designed to increase firm value. To do so,
the first period debt level F1 is designed such that it causes default if (and only if) the under-
investment incentive exists, as shown in lemma 4.
Lemma 4: The optimal combination of short and long-term debt is designed to place the firm
in default (force renegotiation) whenever the under-investment incentive arises. In the
absence of dividend payments, default is optimal for the lowest realizations of c1, as it is less
costly than asset substitution.
Lemma 4 implies that the first period payment F1 can be designed to effectively reduce
the cost of the under-investment incentive to γ, and therefore increase value when default is less
costly than asset substitution, i.e. when γ < AS. The relevant comparison is between γ and AS
18
because asset substitution is less costly than under-investment (i.e. AS < UI as above), so that the
firm optimally avoids under-investment even without short-term debt (i.e. when F1 = 0) as in
proposition 2. That is, in proposition 2 the firm sets F2 such that !( )c x = 0 , allowing asset
substitution for the highest cash flow realizations, φ < c1 < C. Adding the short-term debt
payment increases the probability of default but reduces the probability of asset substitution, and
since γ < AS, the optimal F1 reduces the probability of asset substitution to zero. In particular, the
optimal combination of F1 and F2 causes default for the lowest cash flow realizations and
produces efficient incentives for the highest realizations. This is accomplished by augmenting the
same F2 with a first period debt payment equal to F1 = C - φ. The firm then defaults when the
under-investment incentive arises, i.e. when 0 < c1 < C - φ, and the combination of F1 and F2
deters asset substitution for the remaining realizations, C - φ ≤ c1 < C. This reduces the expected
cost of the incentive problems from AS·g·(C-φ) in proposition 2 to γ·g·(C-φ), where again g·(C-φ)
is the ex-ante probability of realizing a value of c1 for which an incentive problem remains in
proposition 1.
The solution with debt only in lemma 4, however, leaves significant costs when default
costs are substantial (e.g. when firm is doing well so that the costs of managerial time and
reputation are higher). In this case, it is possible to reduce costs further by integrating capital
structure with dividend policy, as seen next.
Dividends
The introduction of first period dividends, D1, also has two effects on the analysis above.
First, similar to F1, the disbursement of a dividend further reduces the cash flow available to make
the second period debt payment, such that the under-investment incentive arises for
c c x F D1 1 1< + +!( ) and the asset substitution incentive arises for c c x F D1 1 1> + + +!( ) φ .
The second effect differs from that of debt payments, however, reflecting the
discretionary nature of dividend payments (F1 and F2 are, by definition, fixed payments). In
particular, a dividend need not be paid when it creates the under-investment incentive, so that the
increase in the set of realizations causing under-investment can be avoided. And since default
costs are optimally incurred only to deter under-investment (lemma 4), this discretion can relax
the trade-off between asset substitution and default described above. Specifically, a dividend
payment equal to D c c x F1 1 1= − − −!( ) φ that is paid only when c c x F1 1> + +!( ) φ deters asset
19
additional default costs).10
The discretionary nature of dividends, however, can impose costs of its own.
Specifically, it can be costly to induce the manager to disburse a dividend that restricts his
investment choice (and therefore reduces his utility). The cost of inducing such a dividend
depends on the dynamically consistent penalty for choosing a sub-optimal dividend, which in turn
depends on the cost of managerial replacement.11 In this section, we focus on the case where
replacement costs are substantial and the manager can choose a low dividend without being
replaced (lower replacement costs are discussed in the extensions). This implies that the manager
will pay a dividend that deters asset substitution only if he is compensated for his lost rents.
Specifically, the dividend is incentive compatible only if the manager is offered additional
compensation equal to the foregone rents of .5ρ, where
ρ ≡ ρ (aL*(x+y),x+y) – ρ (aL*(x),x) > 0
denotes the reduction in the manager’s rents in the high state (which occurs with probability .5).
It is optimal for the shareholders to offer the additional compensation of .5ρ because it
is less than the cost of asset substitution, and as usual the residual accrues to the shareholders.
That is, the cost of asset substitution includes both the increase in rents and the increase in
inefficiency costs, α(aL*(x+y)) – α(aL*(x)) >0, so that dividends reduce the cost of controlling
the asset substitution incentive, as seen in lemma 5.
Lemma 5: It is optimal for the shareholders to induce a dividend payment to deter asset
substitution whenever the incentive arises.
Lemma 5 implies that the shareholders can employ dividends to effectively reduce the cost of the
asset substitution incentive to .5ρ. Again, by recognizing this possibility at t = 0, the initial
owners can design a capital structure that further increases firm value. Indeed, the optimal capital
structure reflects the firm’s ability to employ first period debt that effectively reduces the cost of
the under-investment incentive to γ, and dividends that effectively reduce the cost of the asset
substitution problem to .5ρ, as follows.
20
The optimal combination of debt and dividend payments
The optimal t = 0 capital structure specifies the combination of first and second period
debt payments that, together with the dynamically consistent dividend payments at t = 1,
minimizes the cost of the corporate incentive problems.
As seen above, without dividends it is optimal is optimal for F1 to cause default for the
lowest realizations and F2 to produce efficient incentives for higher realizations (lemma 4).
Lemma 5 implies that default costs of γ can be avoided by reducing F1 and offering additional
compensation of ρ/2 if the manager disburses a dividend when the asset substitution incentive
arises (i.e. disburses D c c x F1 1 1≥ − − −!( ) φ when c c x F1 1> + +!( ) φ ).
The optimal combination of first period payments therefore depends on the cost of
default relative to the cost of inducing the dividend: dividends are preferable when γ > .5ρ and
debt is preferable when γ < .5ρ. Since default costs are likely to be higher when the firm is
doing well (especially reputation costs, the cost of managerial time, and hold-up costs), we allow
for the possibility that γ is a function of c1, and present the results for the simplest case where
γ(c1) = λ·c1 ≥ 0.12 The optimal combination of debt and dividend payments is therefore given by
proposition 3.
Proposition 3: The optimal capital structure includes both short and long-term debt payments
and is jointly determined with dividend policy. The optimal second period debt level is
F x a A a K xL FB FB 2 2= + − −( ) ( ) .
The optimal first period debt payment depends on the cost of default relative to the cost of
inducing dividends. Specifically,
a. When γ(C-φφφφ) ≤≤≤≤ .5ρ, it is optimal to set F1 = C-φφφφ and D1 = 0,
b. When .5ρ < γ(C-φφφφ), it is optimal to set F1 = .5ρ/λ and D1 = c1-F1-φφφφ for F1+φφφφ < c1 < C.
The optimal capital structure in proposition 3 reflects the firm’s ability to use first period
debt and dividend payments to control the incentive problems that remain in proposition 2. In
each case, the debt payments (F1 and F2) alone produce efficient incentives for F1 ≤ c1 < F1 + φ,
the first period debt payment produces efficient incentives via renegotiation for 0 < c1 < F1, and
the optimal dividend produces efficient incentives for F1 + φ ≤ c1 < C.
21
The optimal mix of first period debt and dividend payments is determined by their
relative costs. In particular, when default costs are relatively low as in part a, dividends are sub-
optimal and the incentive problems are optimally controlled with debt payments alone. In the
special case where default costs are zero (i.e. λ = 0), the incentive problems that remain in
proposition 2 are also controlled without cost. When default costs increase with firm
performance as in part b, dividends are substituted for F1 at the point where γ(F1) ≡ λF1 = .5ρ,
since at this point the cost of controlling the under-investment incentive begins to exceed the cost
of controlling the asset substitution incentive.
Proposition 3 therefore illustrates how the optimal capital structure in our model is
related to the firm’s dividend policy. It also illustrates the determinants of the firm’s optimal
short and long-term debt levels, and provides new insight into the literature on optimal maturity
structure (i.e. the optimal percentage of total leverage that is comprised of long term debt). For
example, in their pioneering study, Barclay and Smith (1995) argue that maturity structure
reflects the cost of controlling the adverse incentives of debt overhang as in Myers (1977). In
developing their empirical hypotheses, Barclay and Smith point out that, since short-term debt
avoids the debt overhang incentives, its use must be limited by unspecified costs, such as (i)
flotation costs, (ii) the opportunity cost of the management time (required to roll over short term
debt), and (iii) reinvestment risk and potential costs of illiquidity. Our analysis, however, predicts
an optimal combination of short and long-term debt even in the absence of such costs. In our
analysis, substituting short-term for long-term debt is sub-optimal because it removes the credible
threat required to control the asset substitution incentive – i.e., short term debt is limited because
debt overhang can help motivate managers. Further, short-term debt is limited by the
substitutability of dividends as in part b of proposition 3.
The empirical implications of our analysis, as well as some interesting extensions, are
presented next.
III. Extensions and Empirical Implications
In this section, we relate our analysis to the empirical literature on capital structure, and
discuss extensions regarding replacement costs, contractible variables and security design.
Proposition 3 has a number of implications that are consistent with the empirical
literature. First, part b of proposition 3 shows that short-term debt and dividend payments can
serve as substitutes to control the effects of interim cash flow realizations, such that capital
structure and dividend policy are jointly determined. This is consistent with the empirical
findings of Jensen, Solberg and Zorn (1992), Barclay Smith and Watts (1995), and Fama and
French (2002).
Second, contracting costs are a major determinant of optimal debt and dividend
payments. The optimal long term payment, F x a A a K xL FB FB 2 2= + − −( ) ( ) , decreases in the
equilibrium level of contracting costs, K(x). This is because, ceteris paribus, higher contracting
costs reduce the second period debt levels that avoid under-investment. The optimal first period
payments also depend on contracting costs. When both D1 and F1 are optimal (part b of
proposition 3), F1 decreases with equilibrium contracting costs, as determined by the manager’s
information advantage x in section I. This is because the relative cost of inducing dividends
(.5ρ) decreases with x, reflecting that the manager’s information rents ρ are concave in x as
in section I.2. In contrast, for the zero dividend firms in part a of proposition 3, the short term
debt level F1 = C - φ increases because the range of cash flows for which F2 alone can provide
efficient incentives, i.e. φ, decreases with x. In this latter case, however, the decrease in F2
dominates, so that total leverage (F1 + F2) again decreases. In each case, therefore, our analysis
predicts a negative relationship between leverage and contracting costs that is consistent with the
empirical literature (Titman and Wessels (1988), Barclay, Smith and Watts (1995), Rajan and
Zingales (1995)). This is proven formally in proposition 4:
Proposition 4: Optimal leverage (F1 + F2) is negatively related to contracting costs, as
determined by x.
Third, the maturity structure implied by proposition 3 is consistent with the empirical
literature. Barclay and Smith (1995) find that debt maturity (defined as the proportion of debt
23
with a maturity of at least three years) decreases with contracting costs (defined as the ‘market to
book’ ratio). In contrast, Stohs and Mauer (1996) find only weak evidence of this relationship.
Our model predicts that the proportion of total payments comprised of long-term debt, i.e. F2/(D1
+ F1 + F2), decreases with contracting costs, since F2 decreases and F1 + D1 increases with x.
Specifically, in the case without dividends, F1 = C - φ increases because φ decreases with x as
above. In this case, therefore debt maturity, F2/(F1 + F2) decreases with contracting costs as in
Barclay and Smith. With dividends, as in part b proposition 3, F1 + D1 = c1 - φ increases, but F1 =
.5ρ decreases with x (as above), which implies that the effect on debt maturity is ambiguous,
as in Stohs and Mauer. That is, since both F1 and F2 decrease with contracting costs, the effect on
debt maturity is determined by the relative percentage changes, and is in general ambiguous. Our
model suggests, however, how this ambiguity might be resolved. In particular, it implies that the
(absolute) percentage change in F1 is relatively high when there is little potential for asset
substitution (i.e. when y is small), since then dividends are less costly so that F1 is low but still
sensitive to costs. This suggests that a negative relationship between maturity and contracting
costs is more likely in firms with greater potential for asset substitution. These results are
presented in proposition 5.
Proposition 5: The optimal maturity structure of the firm’s capital structure depends on
contracting costs as follows:
a. For zero dividend firms (part a of proposition 3), debt maturity F2/(F1 + F2) is decreasing
in equilibrium contracting costs, as determined by x.
b. For firms combining first period debt and dividends (part b of proposition 3), the maturity
structure of the total payments, i.e. F2/(D1 + F1 + F2), is decreasing in equilibrium
contracting costs. The effect of x on debt maturity F2/(F1 + F2) is ambiguous, but
decreases with the potential for asset substitution, as determined by y.
Proposition 5 illustrates that our model can reconcile the findings of Barclay and Smith
(1995) with the ambiguous results of Stohs and Mauer (1996). In addition, propositions 4 and 5
are consistent with the findings of Stohs and Mauer (1996) and Barclay, Marx and Smith (2001)
that leverage and maturity are jointly determined, and support the latter authors’ conjecture that
the inconsistency between their leverage and maturity regressions reflects omitted dividend or
compensation variables, and the difficulty of obtaining proxies for the relevant exogenous
variables.
24
Indeed, our analysis suggests that it is useful to develop proxies that distinguish between
contracting costs that are incurred in equilibrium and contracting costs that are avoided (more
precisely, between x and y). While it is particularly difficult to develop a proxy for potential
asset substitution (possibilities include asset maturity and regulation variables), our model
predicts that this potential is reflected in the relative size of the debt and dividend payments, F1
and D1. Specifically, firms with a greater potential cost of asset substitution (a greater y)
optimally have a higher ratio of debt to dividends, F1/D1, as seen in proposition 6.
Proposition 6: Ceteris paribus, the optimal ratio of debt to dividend payments F1/D1 increases
with the potential cost of asset substitution, as determined by y.
Intuitively, as the potential for asset substitution increases, the flexibility associated with
dividends becomes more costly, so that the harder debt payment becomes more attractive.
Together, the results in propositions 5 and 6 imply that the inverse relationship between debt
maturity F2/(F1 + F2) and contracting costs x should be strongest for firms with a high debt to
dividend ratio, F1/D1. To the best of our knowledge, such an interaction between dividends and
debt maturity has yet to be tested.
An immediate extension of our analysis can further relate the debt-dividend mix to the
cost of managerial replacement, denoted R. As discussed in section II, the cost of inducing
dividends is based on substantial replacement costs (in particular, R > .5ρ). If R < .5ρ, the
shareholders can credibly threaten to replace a manager who refuses to pay a dividend that deters
asset substitution, such that it becomes costless to induce dividends. In this case, the firm
optimally combines long-term debt with relatively high dividends (as in part c of proposition 3),
and controls both asset substitution and under-investment without cost. This implies that both
dividend levels and debt maturity are negatively related to managerial entrenchment.
Further extensions include contractible proxies for the realization of first period cash flow
c1, and an analysis of the more general problem of optimal security design. If c1 were directly
contractible in our model, the firm could again design its capital structure to control the incentive
problems at no additional cost (i.e., so that total costs are K(x) for all c1). In particular, the firm
could issue a long-term cash flow contingent bond – i.e. a security that specifies F2(c1), so that
F c a A a K x c F c a A a K x yL FB FB L FB FB 2 1 1 2 12 2( ) ( ) ( ) ( ) ( ) ( )− − + + ≤ ≤ − − + + +ε ε
25
as in (3). This face value deters asset substitution and induces the value maximizing
compensation contract for all realizations of c1, as in proposition 1. This security would be
optimal, as the maximum value that can be achieved in our model is that associated with the
relatively low contracting costs K(x).
In reality, however, it is prohibitively costly to contract on the firm’s actual cash flows,
so that contractible proxies for c1, such as accounting reports, are employed (the credibility of
which can be enhanced, at additional cost, through external audits). The effect of including such
proxies would then depend on their reliability. For example, if accounting income can serve as
perfect, costless proxy for c1, an ‘accounting income’ contingent long-term bond would be an
optimal security as above (since c1 would effectively become contractible). Alternatively, if
accounting reports are imperfect but still informative, accounting covenants could be employed to
reduce the cost of controlling the incentive problems that arise in proposition 2, since first period
accounting covenants can provide bondholders with the power to deter expropriation similar to
first period debt payments, but without increasing the risk of the second period payment. This
benefit could then be balanced against the cost of unnecessary violations (defaults) resulting from
accounting imperfections. Finally, if accounting values are completely unreliable (so that c1 is
effectively non-contractible as above), the standard debt and equity securities derived above are
in fact optimal. In this case, only the actual cash payments made by the firm are contractible, so
that the optimal securities specify first period cash disbursements that cannot be met when
renegotiation is optimal. This is indeed a feature of the optimal debt contract derived above
(lemma 4).
Finally, in all of the cases considered above, our analysis implies that the importance of
the different agency conflicts within the firm is contingent on firm performance (represented by
the realization of c1). Specifically, when performance is low, the shareholders’ incentive to
expropriate bondholder wealth (via under-investment) is the major concern, whereas when
performance is high, the manager’s incentive to pursue asset substitution (self-serving projects) is
the major concern. Although this prediction is intuitively appealing, in that managers seem less
likely to pursue pet projects when the firm is short of cash flows (as in the free cash flow theory
of Jensen (1986)), and shareholders are less likely to expropriate bondholder wealth when the
firm is doing well, to the best of our knowledge, this prediction has yet to be directly tested.
26
bondholder or manager-owner conflicts, paying relatively little attention to the interactions
between these conflicts (Allen and Winton (1995)). Our paper presents a theory of capital
structure based on these interactions; specifically the interaction between a managerial incentive
to increase future compensation via information advantages, and a shareholder incentive to design
future compensation that expropriates wealth from longer-term debt holders.
The interactions in our analysis are derived endogenously from the primitive objectives
of managers, shareholders, and bondholders, as is the finding that bondholder wealth
expropriation is the greatest concern when the firm is performing poorly whereas managerial
opportunism is the greatest concern when the firm is doing well. This finding has further
implications for short-term financial policy, since wealth expropriation can be effectively
controlled via short-term debt obligations and managerial opportunism can be effectively
controlled via short-term dividend payments. Capital structure and debt maturity are therefore
related to both contracting costs and dividend policy (which in turn is related to managerial
entrenchment), in a manner that is consistent with existing evidence and suggests some
interesting directions for future investigations.
Our analysis also suggests directions for future theoretical work. In particular, our
analysis focuses on the case where compensation is designed in the presence of outstanding debt,
which provides a credible threat to punish managerial opportunism. Future work could
incorporate additional opportunities to adjust the long-term debt level (e.g. in the absence of
default). For example, our analysis assumes that the board maintains sufficient discipline to deter
opportunistic adjustments by the manager. Allowing for managerial influence over both debt and
compensation contracts may help to reconcile our analysis with other theories of managerial
opportunism. If the manager obtains moderate influence in our analysis, the primitive objectives
and information structure still produce the asset substitution problem and the interaction between
capital structure and compensation design, so that the optimal debt and compensation contracts
reflect the manager’s influence but produce similar results to above. In the more extreme case,
however, where the manager effectively controls the board (including the compensation
committee), the debt and compensation contracts would effectively be designed to maximize
managerial rents subject to the possibility of external discipline (e.g. a hostile takeover). In this
27
case, our results would be similar to studies that focus on the ability of debt to discipline
managers while neglecting the ability of compensation to influence managerial decisions, such as
Jensen (1986) and Zweibel (1996).
28
Appendix
Proof of Proposition 2: Define c c xx ≡ !( ) and c c x yy ≡ +!( ) . When C > cy – cx ≡ φ, there
exist c1 less than cx or greater than cy. From proposition 1, the former leads to under-investment
at additional cost of UI ≡ κ(0,x) – κ(aL*(x),x), and the latter leads to asset substitution at
additional cost AS ≡ κ(aL*(x+y),x+y) – κ(aL*(x),x). The expected cost of the additional
incentive problems when C > φ is therefore
EC F UI g c dc g c dc AS g c dc c
c
c
c
Cx
x
y
y( ) ( ) ( ) ( )2 0 0= ⋅ + ⋅ + ⋅z z z .
Since ∂ ∂ = ∂ ∂ =c F c Fx y/ /2 2 1 as in (3), ∂ ∂ = −EC F UIg c ASg cx y/ ( ) ( )2 . Since κ(0,x) =
κ(0,x+y),
UI – AS = κ(0,x+y) – κ(aL*(x+y),x+y) > 0.
Thus, the expected cost increases in F2 for g(cx) > 0, and F2 is optimally reduced until g(cx) = 0, or
c F x a A a K xx L FB FB= − − + + =2 2 0( ) ( ) and F x a A a K xL FB FB 2 2= + − −( ) ( ) .
Proof of lemma 4: By definition, the firm defaults when c1 < F1 forcing renegotiation at
additional cost γ. Defining c c xx ≡ !( ) as in the proof of proposition 2, for any F1 ≤ c1 < cx + F1,
the shareholders induce under-investment, at additional cost UI. For cx + F1 ≤ c1 < cx + F1 + φ,
the combination of F1 and F2 produces efficient incentives. For any cx + F1 +φ ≤ c1 < C, the
managers pursues asset substitution, at additional cost AS. Thus, the expected cost of the
incentive problems becomes:
EC F F g c dc UI g c dc g c dc AS g c dc F
F
Cx
x
x
x( , ) ( ) ( ) ( ) ( )1 2 0 1 1 1 1 1 1 1 1 1
1
1
1
1
+
+ +
φ .
Since ∂ ∂ = + − + + >EC F UIg c F ASg c Fx x/ ( ) ( )2 1 1 0φ for cx > 0, F2 is again reduced until cx = 0,
avoiding UI. This implies ∂ ∂ = + − + + <EC F g c F ASg c Fx x/ ( ) ( )1 1 1 0γ φ for cx + F1 + φ < C, so
that F1 is optimally increased until F1 = C – cx - φ = C - φ, avoiding AS.
Proof of lemma 5: For any c c x F c x y F1 1 1> + + = + +!( ) !( ) φ , the manager pursues asset
substitution if no dividend is paid, increasing his expected rents by ρ/2 > 0 as in lemma 2. A
dividend satisfying D c c x F1 1 1≥ − − −!( ) φ implies !( ) !( ) !( )c x c F D c x c x y ≤ − − ≤ + = +1 1 1 φ
and therefore deters asset substitution as in proposition 2, but is incentive compatible only with
29
additional compensation equal to ρ/2 if the (contractible) dividend is paid. It is optimal to offer
this compensation since AS = .5(ρ + α) > .5ρ, where α ≡ α(aL*(x+y)) – α(aL*(x)) > 0
since aL*(x+y) < aL*(x).
Proof of Proposition 3: Lemma 4 implies that the optimal F2 is such that cx = 0 so that
F x a A a K xL FB FB 2 2= + − −( ) ( ) and the additional cost is γ(c1) for c1 < F1. Similarly, lemma 5
implies that the additional cost is .5ρ for c1 > F1 + φ. Thus, the cost minimization problem
reduces to EC F c g c dc g c dc g c dc
F
F
F
F
1
1
1
+ γ ρφ
φ .
The first order condition is ∂ ∂ = − +EC F F g F g F/ ( ) ( ) . ( )1 1 1 15γ ρ φ . Thus,
a. .5ρ ≥ γ(C-φ) ⇒ ∂ ∂ <EC F/ 1 0 for F1 + φ < C, which implies that F1 is optimally
increased until g(F1+φ) = 0 ⇒ F1 = C - φ.
b. .5ρ < γ(C-φ) ⇒ ∂ ∂ =EC F/ 1 0 at 0< F1 < C - φ, which implies that F1 is optimally
increased until γ(F1) = λF1 = .5ρ ⇒ F1 = .5ρ/λ.
Proof of proposition 4: F x a A a K xL FB FB
2 2= + − −( ) ( ) , where K x a x xL( ) ( ( ), )* ≡κ as in
section I. A mean preserving increase in x reduces xL (i.e., dxL/dx = – dxH/dx < 0) and
increases K(x) as in lemma 1, so that
dF d x dx d x dK x d x dx d x A a x xL L 2 2 0/ / ( ) / / ( ( ) ))* = − = − ′ − < .
In part a of proposition 3, F1 = C - φ, where φ = + − −2 2K x y K x y L( ) ( ) , so that
F F C x y a A a K x yL L FB FB 1 2 2+ = + + + − − +( ) ( )
and d F F d x dx d x A a x y x yL( ) / / ( ( ) ))*
1 2 0+ = − ′ + − − < .



y k x y y y k x y
L L
2 2
2
so that dF d x k y1 3 2 0/ / = − <λ . Thus, both F1 and F2 are decreasing in x, and thus K(x).
30
Proof of proposition 5: In part a of proposition 3, F1 = C - φ, so that
dF d x d d x A a x y x y A a x x k k x y k k x k y
1
[ ( / ( )) ( / )] .
* *
= − = − ′ + − − − ′ − = − − + − − = >
φ
Since F2 is decreasing and F1 is increasing in x, debt maturity is decreasing. In part b, D1 + F1 =
c1 - φ increases with x analogously. However, F1 = .5ρ/λ decreases with x as in proposition
4, so that the change in debt maturity F2/(F1 + F2) depends on the relative percentage changes.
The percentage change in F2 is independent of y, and the (absolute) percentage change in F1
decreases with y, since
1
1
.
Thus, when y is high, the percentage change in F2 is relatively high, so that the effect of x on
debt maturity decreases.
Proof of proposition 6: F1 = (.5ρ + μ)/λ increases in y since dF d y d d y1 5/ . ( / ) / = ρ λ and
d d y k x y k y ρ / ( ( / )) /= − − + >1 3 2 3 2 0 (from ρ > 0). The sum D1 + F1 = c1 - φ
decreases in y since d d y dK x y d y dy d yLφ / ( ) / / = + − >2 0 as above. Thus, D1
decreases and F1 increases with y.
31
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Notes: 1 In Dewatripont and Tirole (1994), ex-post efficiency can be achieved through renegotiation (so that the asset substitution choice is independent of capital structure). Renegotiation does not affect the manager’s effort choice because he has no bargaining power and an informed judge (implicitly) controls the compensation contract during the renegotiation. For example, renegotiation to allow the riskier distribution (i.e. continuation rather than stopping) requires new compensation that provides the prior level of expected compensation, despite the manager’s preference for his original contract (which would provide higher expected compensation). Without the judge, the owners could force any new contract on the manager (even in the absence of renegotiation), so that the dynamically consistent compensation level would be zero and no effort would be induced. In contrast, the role of compensation in Berkovitch, Israel and Speigel (1998) requires the manager to possess substantial ex-post bargaining power; if not, the dynamically consistent compensation level is again zero. 2 A number of other papers link capital structure to explicit compensation contracts, but are less related to the analysis here. Notably, in John and John (1993), compensation serves as an ex-ante commitment that nullifies the shareholders’ incentive to expropriate bondholder wealth (similar to Dybvig and Zender (1991) and therefore subject to renegotiation concern in Persons (1994)). In Chang (1993), managerial incentives are linked to capital structure because only financial variables (debt and dividend payments) are contractible. In Holmstrom and Tirole (1993), external equity affects the incentives to monitor managerial performance, and in Douglas (2002), capital structure serves to offset managerial influence over the incentive setting process. 3 The managerial incentive contract is optimally designed at t = 1 in our model, because it is contingent on first period cash flow c1 and the investments in place at the beginning of the second period (represented by ε), both of which are non-contractible yet observed at t = 1. The assumption that c1 is non-contractible reflects excessive costs of verifying internal cash flows (similar to Townsend (1979), Gale and Hellwig (1985), Chang (1993), Fluck (1998), Gorton and Kahn (2000) and Myers (2000)). This assumption is further justified in that c1 essentially proxies for first period performance in our model, and it is straightforward to incorporate, for example, an observable but non-contractible persistence in t = 1 cash flows (and therefore t = 1 performance). The inclusion of contractible accounting variables is discussed in section III. Because c1 and ε are observable but non-contractible, value cannot be increased by implementing a t = 0 contract and awaiting renegotiation at t = 1, as this only increases the potential for managerial opportunism. For models where a t = 0 contract can be optimal, see Aghion, Dewatripont and Tirole (1994) and Dow and Raposo (2002). 4We specify A(a) = 0 for a < 0 to avoid adding corner constraints (we also assume a ≤ −ε and a k≥ 1 / to ensure that the values of a in the analysis below exist). This simplifies the exposition without affecting the results. 5 Of course, the incentive compatible values of a associated with each value of ε must also be preferred to any other a, which in our setting would be immediately detectable and therefore result in the minimum compensation payment of zero – i.e., technically, the compensation contract specifies
w v w v c a w v c a
L L L
H H H( ) {= = + + = + +
ε ε
6 The result that asset substitution is endogenously sub-optimal further contrasts our model from standard analyses, where an exogenous cost is often required to make a mean preserving spread inefficient (e.g. Gorton and Kahn (2000)). 7 The optimal value of F2 is contingent on the relationship between first period cash flows and asset substitution, and is determined recursively in section II.
34
8 For a discussion of free-rider and hold-out problems, see Hart (1995), chapters 5 and 6. It can be useful to provide bondholder power in the presence of these problems, since under-investment decreases bondholder wealth by more than firm value (due to the offsetting increase in shareholder value). Indeed, by requiring default to avoid under-investment, our analysis implicitly assumes that legal contracts are needed to make renegotiation less costly than sub-optimal investment. Such an assumption is implicit in most articles studying shareholder-bondholder conflicts, as addressed in the seminal articles of Jensen and Meckling (1976) and Myers (1977). Without this assumption, sub-optimal investment incentives would never be acted upon, as instead there would be a renegotiation to split the surplus (as in the Coase theorem). In our model, this failure of the Coase theorem is beneficial, as otherwise capital structure is again irrelevant and managerial asset substitution cannot be controlled. 9 The surplus from this renegotiation would be split according to the specific rights (e.g. collateral) specified in the initial debt contract and the bargaining power of each party during default procedures. 10 In fact, any D c c x F1 1 1≥ − − −!( ) φ deters asset substitution, and we focus on the minimum dividend required for brevity. Note that the shareholders cannot induce a dividend that expropriates bondholder wealth, since even if D1 = c1 – F1, we have c F D c x1 1 1 0− − = = !( ) so that efficient incentives are again produced as in proposition 2. 11 In practice, the board must approve the manager’s dividend choice, so that a sub-optimal choice may lead to a stalemate. The resolution of this stalemate, however, would again depend on the threat of dismissal, and therefore the cost of replacement. 12 Our results are qualitatively unchanged if γ(c1) = μ + λ·c1 ≥ 0, which allows the further possibility that .5ρ < γ(0), so that it is optimal to set F1 = 0 and D1 = C - φ in proposition 3. The relative cost of dividends could also reflect replacement costs, which affect the cost of inducing dividends, as discussed in the extensions.
II. Optimal Capital Structure
Lemma 5: It is optimal for the shareholders to induce a dividend payment to deter asset substitution whenever the incentive arises.
III. Extensions and Empirical Implications
Appendix