The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
Contingent Debt and Performance Pricing
in an Optimal Capital Structure Model with
Financial Distress and Reorganization
WP 18-17
Borys Grochulski
Federal Reserve Bank of Richmond
Russell Wong
Federal Reserve Bank of Richmond
Contingent debt and performance pricing in an optimal capital
structure model with …nancial distress and reorganization
Borys Grochulskiy
Russell Wongz
September 30, 2018
Abstract
Building on the trade-o¤ between agency costs and monitoring costs, we develop a dynamic
theory of optimal capital structure with …nancial distress and reorganization. Costly monitoring eliminates the agency friction and thus the risk of ine¢ cient liquidation. Our key
assumption is that monitoring cannot be applied instantaneously. Rather, transitions between agency and monitoring are subject to search frictions. In the optimal contract, the
…rm seeks a monitoring opportunity whenever it is …nancially distressed, i.e., when the risk
of liquidation is high. If a monitoring opportunity arrives in time, the manager is dismissed,
the capital structure is reorganized as in Chapter 11 bankruptcy, and the search for a new
manager begins. In agency, an optimal capital structure consists of equity, long-term debt,
contingent long-term debt, and a credit line with performance pricing. In …nancial distress,
coupon payments to contingent debt are suspended but the interest rate on the credit line is
stepped-up, which gives the …rm simultaneously debt relief and a steep incentive to improve
its …nancial position. An episode of distress can end with …nancial recovery, transition to
bankruptcy reorganization, or liquidation.
Keywords: capital structure, contingent debt, performance pricing, monitoring costs,
agency costs, dynamic incentives, liquidation, …nancial restructuring, bankruptcy reorganization, search frictions, CEO compensation, CEO replacement
JEL codes: G32, G33, D86, D82, M52, C61
The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank
of Richmond or the Federal Reserve System.
y
Federal Reserve Bank of Richmond, borys.grochulski@rich.frb.org.
z
Federal Reserve Bank of Richmond, russell.wong@rich.frb.org.
1
1
Introduction
In …nancial distress, a …rm is much more likely to seek to reorganize its capital structure
and continue to operate rather than to stop its operations and liquidate.1 Modern theories
of optimal capital structure of the …rm, built around resolving dynamic agency problems,
however, allow only for …nancial recovery or liquidation and do not consider the possibility of
exiting …nancial distress by …nancial reorganization. In this paper, our objective is to take a
step toward bridging this gap.
We build a dynamic model in which an optimal capital structure, in the spirit of Jensen (1986),
is determined by the trade-o¤ between agency costs and monitoring costs. To model agency
costs, we follow DeMarzo and Sannikov (2006), DeMarzo and Fishman (2007), and Biais et al.
(2007) in solving an optimal contracting problem between the …rm owners and a manager
who can divert funds to private use. To provide incentives, an optimal contract must credibly
threaten (ex-post ine¢ cient) liquidation. We model monitoring as an alternative to agency
that eliminates the risk of liquidation but entails direct costs.
Our key assumption is that monitoring cannot be applied instantaneously. Rather, transitions
between agency and monitoring are subject to search frictions. That is, agency and monitoring are states. Under an optimal contract, in the agency state, the …rm seeks a monitoring
opportunity whenever it is …nancially distressed, i.e., when the risk of liquidation is high. If
a transition to monitoring arrives in time, the …rm’s cash ‡ows become publicly observable,
and the manager is dismissed. If such a transition does not arrive in time, the …rm is forced
to liquidate, as in the standard model. The monitoring costs incurred in the monitoring state
are su¢ ciently high for the …rm to seek to hire a new manager and transition to the agency
state again.
In agency, an optimal capital structure consists of equity, long-term debt, contingent long-term
debt, and a credit line with performance pricing. Financial distress is de…ned by a leverage
trigger, i.e., when the balance on the credit line exceeds a threshold. When the balance remains
above the distress threshold, the interest rate on the credit line is elevated but coupon payments
on contingent debt are suspended. The …rm issues enough contingent debt ex ante that these
two interest rate adjustments imply a net relief in terms of the debt servicing costs to the …rm
in distress. This relief moderates the risk of liquidation and helps cover any expenses related
to preparation for transition to the monitoring state. An episode of distress can end with
…nancial recovery, a transition to monitoring, or in liquidation that takes place if the …rm is
unable to transition to monitoring before it exhausts its total credit limit.
1
See, e.g., Bris et al. (2006), Jacobs Jr et al. (2012), and Corbae and D’Erasmo (2017).
2
In the monitoring state, as in Chapter 11 bankruptcy, the …rm reorganizes its capital structure
while paying the costs of monitoring its cash ‡ow and searching for an opportunity to emerge
from bankruptcy with a new capital structure and a new manager. Upon transitioning to
agency again, new debt is issued and new equity is allocated to the owners and the new
manager.
This optimal capital structure and the conditions under which the …rm searches for an opportunity to replace management and reorganize, i.e., our de…nition of …nancial distress, are
determined endogenously by the trade-o¤ between agency and monitoring costs.
Our theory provides a new explanation of the role of performance pricing and contingent debt
in the …rm’s capital structure, which we view as the main contribution of this paper. The
optimality of performance pricing and the suspension of contingent debt coupon payments in
…nancial distress is a consequence of the jump that the manager’s continuation value experiences under the optimal contract upon a transition to monitoring. Although we allow for a
severance payment to the manager, the optimal contract calls for zero severance, as this way the
manager’s loss of value at the transition to monitoring is maximized. Prior to the transition,
this loss is compensated with higher expected growth (drift) of the manager’s continuation
value, which helps reduce the risk of liquidation. When leverage is high, i.e., the draw on
the credit line is above the distress threshold, the …rm searches for a transition to bankruptcy
reorganization and the manager faces a positive probability of being instantaneously dismissed
with no severance. When leverage is low, i.e., the credit balance is below the distress threshold,
the …rm is …nancially sound, does not search for bankruptcy, and the manager faces no risk of
being dismissed. This di¤erence between distress and …nancially sound conditions gives a role
for performance pricing and contingent debt in our model.
Contingent debt that we obtain as a part of an optimal capital structure shares features with
contingent convertible (CoCo) bonds, which have recently been introduced into bank capital
structures in Asia and Europe, and have received a lot of attention from regulators an academics.2 The main similarity is the idea of providing a “going concern” capital relief to a …rm
in …nancial distress. In our model, the contingent debt contract mandates a (noncumulative)
suspension of coupon payments, based on an accounting trigger, similar to many CoCo bonds
used in practice. Conversion to equity or a write-down at default, although feasible, are not
essential features of the optimal capital structure in our model.3
We compute security values and comparative statics. The option to seek monitoring and
2
See, e.g., Flannery (2005, 2014), Hanson et al. (2011), Chen et al. (2017).
In non-bank capital structures, the function of contingent capital is often assumed by preferred equity. In
our model, di¤erences between contingent debt and preferred equity are relatively minor. We discuss them in
the Appendix.
3
3
reorganization makes the …rm’s securities less risky. While the total debt capacity of the …rm
is increased, the optimal size of the credit line is shorter, allowing the …rm to pay dividends
sooner and making the risk of liquidation lower. Valuation of the …rm’s securities depends on
their seniority structure in reorganization or liquidation. For example, if contingent debt is
junior to uncontingent long-term debt, the latter form of debt becomes much less risky. Using
an example, we show that the optimal contract may actually call for very little uncontingent
debt to be issued, thus making it completely riskless.
Relation to the literature This paper is primarily related to the literature on agency-based
theory of optimal capital structure and managerial compensation: DeMarzo and Sannikov
(2006), DeMarzo and Fishman (2007), Biais et al. (2007), among others. We extend the model
by allowing for agent dismissal and monitoring of the cash ‡ow with …nancial restructuring,
subject to search frictions.
Piskorski and Wester…eld (2016) study the impact of monitoring on the optimal contract in the
dynamic agency setting, but their monitoring technology is di¤erent. In their model, monitoring can generate an imperfect signal of the manager’s resource diversion or shirking. Although
such signals remain o¤-equilibrium, monitoring complements performance-based compensation in providing incentives to the manager. In our model, in contrast, monitoring directly
substitutes the manager, who is dismissed when the …rm transitions to the monitoring state,
which does occur in equilibrium. The dismissal of the manager is an important element of our
theory of …nancial restructuring, as in reorganization the manager’s equity position in the …rm
is wiped out.
Tchistyi (2016) shows that a credit line with performance pricing is a part of an optimal
capital structure in an agency-based model with correlated cash ‡ows, where the agent has
a stronger incentive to divert resources when the cash ‡ow is high. Our analysis provides
an alternative explanation of performance pricing based on the risk of a discrete jump in the
agent’s continuation value at dismissal.
In a structural model in the tradition of Leland (1994), where debt is valued for its tax advantages, Manso et al. (2010) study performance-sensitive debt and show that contingent debt
instruments can be useful as a screening device allowing high-growth …rms to signal their type
in a separating equilibrium. In the same tradition, Antill and Grenadier (2018) study the
choice of leverage and the pricing of debt allowing the …rm to use a bankruptcy reorganization
as an alternative to straight liquidation. Our paper complements these studies, as we obtain
contingent debt and bankruptcy reorganization as a part of an optimal contract trading o¤
agency and monitoring costs.
This paper is also related to the large literature on optimal contracts with information frictions
4
and costly monitoring, which goes back to Townsend (1979) and Gale and Hellwig (1985) in
static settings and includes dynamic analyses of Monnet and Quintin (2005), Wang (2005),
Antinol… and Carli (2015), Chen et al. (2017), and Varas et al. (2017), among others. The
innovation of our model is to add a search friction in the spirit of Mortensen and Pissarides
(1994) and Du¢ e et al. (2005).
Organization Section 2 describes the contracting environment. Sections 3 and 4 characterize
the …rm value and the optimal contract. Section 5 discusses a capital structure implementation.
Section 6 computes security values and derives comparative statics. Section 7 concludes.
2
Model
The contracting problem builds on DeMarzo and Sannikov (2006), hereafter DS, and extends
it to two states: an agency state and a monitoring state. The …rm can switch between the two
states subject to search frictions. The agency state is similar to DS except for an additional
choice variable, which represents the decision to search for a transition to the monitoring
state. In the agency state, an agent/manager/CEO is hired to run the …rm, as in DS. In
the monitoring state, the …rm is run by an expert, and the cash ‡ow is public information,
i.e., there are no agency frictions, but the …rm is subject to additional monitoring costs. Any
negative cash ‡ows are covered by external …nancing, which must be secured during the process
of searching for a transition to monitoring.
Cumulative cash ‡ow up to date t, Yt , follows
dYt = dt + dZt ;
where Zt is a standard Brownian motion on ( ; F; P ), and
> 0 and
> 0 are constant.
In the monitored state, an expert runs the …rm and absorbs the risk of the cash ‡ow. The
owners compensate the expert and pay the costs of searching for a new manager to reenter
the agency state.4 Net of this compensation, the owners receive the ‡ow of
B , which can
be negative. The ‡ow cost B 0 covers the expert costs. In the monitoring state, the cash
‡ow is public information, i.e., it cannot be diverted to private use. The ‡ow cost B also
covers the cost of searching for an opportunity to exit the monitoring state, back to the agency
state, which arrives with intensity > 0. When this opportunity arrives, the owners hire the
manager and release the expert, thus avoiding paying the ‡ow cost B .
4
We will make assumptions on the parameter values of the model su¢ cient for staying in the monitoring
state permanently to be ine¢ cient. I.e., the …rm wants to exit the monitoring state as soon as possible.
5
In the agency state, the agent/manager runs the …rm subject to the standard agency friction.
The cash ‡ow is privately observed by the agent. The agent can divert the cash ‡ow to private
use. Of each unit diverted, the agent retains 0 <
1 and 1
is wasted.5
In the agency state, the …rm can also take a costly action of searching for an opportunity to
transition to monitoring. In monitoring, the …rm must have …nancing available to cover any
negative cash ‡ows. Our key assumption is that such …nancing cannot be obtained instantaneously, but rather only after a search period of random duration. The cost of searching for
a transition to monitoring is
0. Conditional on searching, such transitions arrive with
intensity > 0. Upon transition, the operations are taken over by the expert, the manager is
forced out, possibly with severance St 0, and the …rm enters the monitoring stage.6
The …rm discounts at the marker rate r > 0 and the agent at > r. The liquidation value of
the …rm is 0 L < r . The manager’s outside value, available at dismissal, is R 0.
A contract with a manager consists of ( ; I; Y^ ; s; S), where is the manager’s dismissal date,
It is the nondecreasing process of cumulative payments to the manager, Y^t is the process of
recommended reporting, st 2 f0; 1g is the indicator of searching for an expert to replace the
agent, and St is severance. Because recommending Y^t = Yt at all t is without loss of generality,
we will denote a contract simply by ( ; I; s; S).
Dismissal of the agent can be due to liquidation or transition to monitoring. Let L be
liquidation date and M be the date of switching into the monitoring state. We have =
minf M ; L g.
The agent chooses a reporting process dY^t dYt to maximize
Z
R+1
E
e t dIt + (dYt dY^t ) + 1 = L e
=
M
e
r
(R + St ) :
0
The contract is incentive compatible (IC) if the strategy of reporting dY^t = dYt at all t attains
a maximum in the above objective.
Under an IC contract, the agency-state payo¤s to the agent and the …rm are
Z
E
e t dIt + 1 = L e
R + 1 = M e r (R + St ) :
0
and
E
Z
e
rt
((
st )dt
dIt ) + 1
=
L
e
r
L+1
=
M
e
r
M
(M
St ) ;
0
5
For brevity of exposition, we assume that all diverted cash ‡ow is consumed by the agent on the spot. DS
show that this assumption is inessential. Hidden savings can be allowed as long as the rate of return in the
hidden account is not too large.
6
We assume that the project can be run either by the manager or by the monitoring expert but not both.
Thus, …ring of the manager is a necessary condition for a transition to monitoring.
6
where M is the value of the …rm upon entering the monitoring state.
Next, we study the optimal contract.
3
Firm value in the monitoring stage
We begin by solving for the value the …rm obtains in the monitoring state. In this state, there
is no need to provide incentives to the expert, as there is no agency friction. Let ^ be the time
of arrival of an exit from monitoring (reversion to agency with a new manager). The payo¤ to
the …rm in the monitoring state is
Z
M =E
^
e
rt
(
B )dt
r^
+e
b0 ;
0
where b0 is the value of starting with a new agent, which we can compute as
rM =
r
(
r+
B)
+
r+
rb0 ;
or
(r + )M =
B
+ b0 :
(1)
To ensure that monitoring forever is not e¢ cient, we assume the monitoring costs to be high
enough for the …rm to generate expected losses while in monitoring, i.e., we assume B
,
which implies M < b0 . Under this assumption, the value of the …rm in the monitoring state
comes exclusively from the expectation of a transition to the agency state and the ‡ow payo¤
losses are covered by external …nancing. Next, we proceed to characterize the optimal contract
in the agency state and the value it gives to the …rm.
4
Optimal contract in the agency stage
We follow the standard approach of using the agent’s continuation value as the state variable
in the …rm’s problem of designing an optimal contract for the agent in the agency state.
Let st 2 f0; 1g be the indicator of searching for a transition out of the agency state. The
agent’s continuation value follows
dWt = Wt dt
dIt +
^
t (dYt
dt) + st
t (dNt
dt);
where t is the sensitivity to the reported cash ‡ow, t is the sensitivity to the switch in the
state to the monitoring state, and Nt is a Poisson process with arrival rate > 0.
7
The contract is IC if t
at all t in the agency state. Given the concavity of the …rm’s value
function, b(W ), we will have t = all t in the agency state (with or without search). With
this sensitivity, we have Y^t = Yt at all t.
Denote t = Wt0 Wt , where Wt0 is the post-arrival value to the agent if the arrival comes
when the agent’s continuation value is Wt . As long as a transition to the monitoring state or
liquidation do not occur, we have
dWt =
Wt dt
dIt + (dYt
= (( + st )Wt
st Wt0 )dt
dt) + st (Wt0
dIt +
Wt )(0
dt)
dZt ;
where Wt0 = R + St . At dismissal, the agent’s continuation value is delivered by the outside
value R and a lump-sum payment St , as there is no reason to delay payments to the agent
beyond the point of dismissal.
The HJB equation for the …rm’s value b is
rb(W ) = max
s;S
4.1
s + (( + s)W
s (R + S))b0 (W ) +
1
2
2 2 00
b (W ) + s (M
S
b(W )):
Optimal severance payment
Lemma 1 S = 0:
Proof The optimal S maximizes s Sb0 (W ) s S = ( b0 (W ) 1)s S, which is decreasing
in S because b is strictly concave and b0 (W 1 ) = 1, which means b0 (W ) > 1 at all W < W 1 .
The optimal severance payment to the agent is zero in this model. The smaller the agent’s postdismissal value, the larger the loss of value to the agent upon …nding a monitoring opportunity.
This loss of value increases the drift in Wt in the agency state, which is valuable to the …rm
everywhere in the search region, as it reduces the risk of liquidation.
With this simpli…cation, in the interior of [R; W 1 ], the agent’s continuation value process Wt
has constant volatility
and drift Wt + st (Wt R), which, as we see, has two components.
The Wt component is compensation for the zero payment ‡ow to the agent at all W < W 1 .
The (Wt R) component, which is only e¤ective when the …rm searches for monitoring, is
compensation for the risk of losing Wt R in case the …rm …nds a monitoring opportunity.
With St = 0, the HJB can be written as
rb(W ) = max
s2f0;1g
s + (( + s )W
s R)b0 (W ) +
8
1
2
2 2 00
b (W ) + s (M
b(W )):
(2)
4.2
The region of search for monitoring
First, we derive a condition for monitoring to be used in equilibrium.
Denote by O(W ) the value of searching at W , i.e., the di¤erence between searching and not
searching in the HJB equation (2):
O(W )
R)b0 (W ) + (M
+ (W
b(W )):
(3)
Let bL denote the value function of a …rm that is permanently denied the option to search for
monitoring. This value function is derived in DS. Denote by bL;0 its unique peak value. Suppose
now this …rm is about to liquidate at W = R, and at this point it unexpectedly gains the option
to search for monitoring. If this …rm chooses to ignore this option, then so will the …rm that
is always able to search; meaning the parameters , and B , are such that monitoring is
just too costly relative to the liquidation value L. Conversely, if this …rm chooses to search,
then monitoring is useful, i.e., it will be used in equilibrium at least in a small neighborhood
of R. The condition for this …rm’s preference to search is O(R) =
+ (M
L) > 0,
B
where M = r+ + r+ bL;0 . Thus, the necessary and su¢ cient condition for the monitoring
technology to be used in equilibrium is
<
B
r+
+
r+
bL;0
L:
(4)
We will maintain this condition throughout.
Second, we partially characterize the region of the state space in which the …rm searches for
monitoring under the optimal contract.
~ ] with W
~ < W0
Lemma 2 The region of search is an interval (R; W
arg max b(W ).
Proof Di¤erentiating (3), we have O0 (W ) = b0 (W ) + (W R)b00 (W )
b0 (W ) = (W
R)b00 (W ) < 0 by strict concavity of b. Therefore, O(W ) > 0 implies O(W 0 ) > 0 for all W 0 W ,
i.e., the search region is an interval connected to R. By (4), this interval is nonempty. It
~ < W0 . Indeed, with M < b0 = b(W0 ) and with b0 (W0 ) = 0, we have
remains to show that W
O(W0 ) =
+ (M b(W0 )) < 0.
4.3
Veri…cation
The veri…cation argument showing that the solution of the HJB equation that satis…es the
boundary conditions given in DS is in fact the …rm’s value function is standard.
9
Theorem 1 The unique solution b of the HJB equation that satis…es b0 (W 1 ) = 1 at a point
W 1 such that rb(W 1 ) + W 1 = and b(R) = L with M given in (1) is the true value function
for the …rm under the optimal contract.
Proof Follows DS with minor changes related to the jump to the value M .
4.4
Computation
The agency HJB equation depends on the value of the monitoring stage, M , which in turn
depends on b0 . Yet, thanks to Lemma 2, we can solve the HJB in a single pass going backward
from the agent payment boundary.
We can write the …rm’s value function in the agency stage as b(W ) = maxfbN S (W ); bS (W )g,
where bN S is the value of not searching for transition to monitoring and bS is the value of
searching.
The HJB equation for the function bN S is the same as in DS:
1 2 2 00
bN S (W ):
(5)
2
~
~ is not
From Lemma 2 we have that b(W ) = bN S (W ) for all W
W
W 1 . Although the W
~ < W0 . Thus, starting from W 1 we can solve the HJB (5)
known exactly, we know that W
backwards until the solution reaches its peak. At this point, we have found W0 and b0 , and,
hence, M . To the left of the peak, we can continue solving the HJB equation (2) allowing for
both search and no search, as now, with M known, the value of searching for monitoring is
known.
rbN S (W ) =
+ W b0N S (W ) +
This computational procedure can be simpli…ed further. At the upper boundary of the search
~ , we have O(W
~)=
~ R)b0 (W
~ ) + (M b(W
~ )) = 0 and we also know that
interval, W
+ (W
~ ) = bN S (W
~ ), and b0 (W
~ ) = b0 (W
~ ). Therefore, in order to pin down W
~ , we can continue
b(W
NS
to solve (5) to the left of the peak of bN S until the stopping condition
= (W
R)b0N S (W ) + (M
bN S (W ))
is met. To the left of this point, searching for a monitoring opportunity maximizes the …rm’s
value. This value function, which we denoted by bS (W ), solves the HJB equation
rbS (W ) =
+ (( + )W
R)b0S (W ) +
1
2
2 2 00
bS (W )
+ (M
bS (W ));
~ given by bS (W
~ ) = bN S (W
~ ), b0 (W
~ ) = b0 (W
~ ). After
with the boundary conditions at W
S
NS
reaching R, we update the initial agent payment threshold W 1 depending on whether bS (R)
is larger or smaller than L.
10
50
45
40
35
30
25
20
0
2
4
6
8
10
12
Figure 1: Value function b(W ) in the agency state and the value M in the monitoring state. R > 0.
Figure 1 presents a computed solution. The …rm’s value function b consists of the no-search
segment bN S , in black, and a search segment bS , in blue. In addition, the value function of the
…rm that, as in DS, can only use liquidation, bL , is depicted in red.
5
Capital structure implementation
In the agency state, we consider a capital structure similar to DS, but with two new features.
First, the credit line (short-term debt) has a performance pricing feature. Second, payments
to long-term debt have a component contingent on the …rm’s …nancial position, i.e., leverage.
This component can be implemented with a contingent bond.
Let x be the ‡ow of payment to long-term debt (regular and contingent together), and let i
be the interest rate on the line of credit. Let the credit limit on the credit line be C L , and
let C~ L < C L be a …nancial distress threshold, i.e., the trigger of performance pricing. Let Bt
denote the balance on the credit line outstanding at t. As in DS, let the agent hold fraction
of the …rm’s equity.
11
The agent’s problem under capital structure (x; i; ) is to choose a reporting process Y^t and the
dividend process Divt to maximize their expected payo¤, where the balance process follows
dY^t :
dBt = i(Bt )Bt dt + x(Bt )dt + dDivt
Proposition 1 Let C L =
optimal contract. Suppose
W1 R
i(Bt ) =
and
x(Bt ) =
~
W1 W
and C~ L =
(
(
~ and W 1 are determined in the
, where W
if Bt < C~ L ;
if Bt C~ L ;
+
(7)
if Bt < C~ L ;
R) if Bt C~ L :
W1
(W 1
W1
(6)
(8)
Then the dividend process
It
Divt =
;
the balance process
Bt =
W1
Wt
;
(9)
and the reporting process Y^t = Yt solve the agent’s optimization problem under the capital
structure (x; i; ).
Proof First, we check that if the agent follows the proposed policy, then (9) holds, where the
process (Wt ; t 0) is determined by the optimal contract.
For Bt = 0, we have Wt = W 1 .
For all 0
Bt < C~ L , from (7) and (8), we have i =
dBt =
Bt dt
Bt + W 1 dt
=
dDivt + dY^t
W 1 )dt
(
W 1 . Using (6), we have
and x =
dIt + (dY^t
dt):
With the identity
Bt + W 1 = Wt , we get back the law of motion for Wt under the optimal
contract: dWt = Wt dt dIt + (dY^t
dt).
For C~ L
Bt < C L , from (7) and (8), we have i =
Using (6), we have
dBt =
( + )Bt dt
= ( + )
(
W1
+
and x =
W1 +
Rdt + (dY^t
Bt + W 1 dt
R)dt
W1
(W 1
R).
dDivt + dY^t
dt):
With the identity
Bt + W 1 = Wt , we get back the law of motion for Wt under the optimal
contract in the search region: dWt = ( + )Wt dt
Rdt + (dY^t
dt).
12
This shows that if the agent follows the proposed policy, he does as well as in the optimal
contract. That he cannot do better follows by contradiction. If he could, we’d be able to
construct a diversion policy Y^ that would give the agent a higher payo¤ also under the optimal
contract, which contradicts the incentive compatibility property of that contract.
The interest rate on the credit line and the long-term debt payment are adjusted when the
…rm’s …nancial position Bt crosses the distress threshold C~ L . The rate i goes up, as in most
performance pricing contracts. The payment to long-term debt is stepped down.
One way to implement an automatic decrease in payment x at the distress threshold is to
issue two classes of long-term debt at date 0: a regular perpetuity with face value D =
r 1(
W1
(W 1 R)) and the coupon rate r, resulting with a permanent payment of
W1
xd =
(W 1
R);
and a perpetual, contingent, noncumulative bond with face value Dcd = r 1 (W 1 R) and
the coupon rate r. The contingency feature of this bond suspends (i.e., eliminates without the
obligation to pay back later) its coupon payments whenever the …rm is …nancially distressed,
i.e., when Bt > C~ L . Together, these two bonds replicate the structure of optimal payment
to long-term debt holders, x(Bt ). In …nancially sound conditions, Bt C~ L , the total coupon
W 1 . In …nancial
‡ow, i.e., the sum of coupon payments to the two types of debt, is
distress conditions, Bt > C~ L , the total coupon ‡ow is reduced by
xcd =
(W 1
R);
as the coupons to the contingent bond become automatically suspended.
Figure 2 illustrates the joint e¤ect of the contingency feature of debt and the performancepricing feature of the credit line. It shows total debt service costs as a function of the draw
on the credit line, Bt . In the baseline model of DS, the total debt service costs, represented
by the red line, have an a¢ ne structure. The constant component is the constant payment
to long-term debt, and a linear component is the interest payment on the …rm’s credit line,
which has a constant slope of . In our model, total debt service costs are discontinuous at
the …nancial distress threshold, C~ L . The payment to long-term debt declines, but the slope of
the variable component, i.e., the interest rate on the revolving balance Bt , increases from to
+ . As shown in Figure 2, the joint e¤ect of the contingency feature and the performance
pricing feature is positive for the …rm everywhere in the …nancial distress region. In fact, the
optimal amount of contingent debt the …rm issues is determined at the level that ensures the
…rm receives a debt service cost relief in the distress region. Indeed,
xcd =
(W 1
R) >
W1
Wt
13
= Bt for all Bt 2 [C~ L ; C L );
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
12
Figure 2: Total debt service costs.
i.e., the suspension of payments to contingent debt outweighs the additional interest charged
on the credit line under performance pricing.
In the distress region, the …rm also searches for an opportunity to reorganize. The search costs,
, represent preparation costs for bankruptcy reorganization. In particular, the …rm must line
up …nancing to cover negative cash ‡ows during the bankruptcy reorganization stage.
In bankruptcy itself, the monitoring and reorganization ‡ow costs are B . Upon transition
to bankruptcy, the manager is dismissed with a severance payment of zero. The value of
the manager’s equity stake in the …rm is zero, as equity is extinguished in bankruptcy and
debt holders become …rm owners, which gives the manager the total continuation value of just
R. The value of the …rm in bankruptcy is M , which is allocated to long-term debt holders,
contingent debt holders, and the revolving debt holders in the order of seniority. Operating
losses are covered by external, prearranged …nancing. This …nancing problem is free of the
agency friction, thanks to the costly monitoring activities exerted during bankruptcy. As soon
as the …rm has an opportunity to transition back to the agency stage, a new manager is hired
and a new capital structure is set up with the initial value b0 to the owners, and the value of W0
14
to the new manager. The time spent in bankruptcy captures the delay in creditor negotiations
and search for a new manager.
5.1
Alternative capital structures
In this capital structure, contingent debt is similar to (noncumulative) preferred equity. The
distinction between the two comes from the ex ante commitment by the …rm to make payments
to this liability class everywhere in the non-distress region, Bt 2 [0; C~ L ), even when common
equity dividends are zero. This distinction, however, is not essential. In the Appendix, we
provide an alternative capital structure under which the manager prefers to make payments
to this liability class whenever not distressed even if the only consequence for not paying is an
onset of search for restructuring.
Provision of …nancial relief to the …rm in distress combined with an increased incentive to
pay revolving debt o¤ are essential features of our model. As we have shown, these can be
implemented with performance pricing on revolving debt combined with a contingent liability
similar to noncumulative contingent debt or preferred equity. Our model, therefore, gives an
e¢ ciency-based explanation for why these features are observed in corporate capital structures.
6
Security values and comparative statics
In order to compute security values and obtain comparative statics results, we follow the
approach of DS. The following lemma adapts their method to our model by allowing for the
possibility of a jump to a state M .
Lemma 3 Let Wt follow the equilibrium law of motion for the manager’s continuation value
until a stopping time = minf L ; M g. Let g be a ‡ow return function de…ned on [R; W 1 ]
and k and FM be real numbers. Then the same function G de…ned on [R; W 1 ] solves both
rG(W ) = g(W ) + ( W + 1W
~
W
(W
R))G0 (W ) +
1
2
2 2
G00 (W ) + 1W
with boundary conditions G(R) = FL and G0 (W 1 ) = k, and
Z
Z
rt
G(W0 ) = E
e g(Wt )dt k
e rt dIt + e r (1
0
0
Proof Follows the martingale argument of DS.
15
=
L
FL + 1
~
W
=
(FM
M
FM ) :
G(W ))
6.1
Market value of securities
Let us denote market value of security 2 fe; d; cd; clg conditional on the current draw on the
credit line B by V (B), where e stands for equity, d for long-term debt, cd for contingent debt,
and cl for the credit line. Let us …x the liquidation payo¤s at some nonnegative constants
P
FL; such that
FL; = L, and the reorganization payo¤s at some non-negative constants
P
FM; such that
FM; = M , where the constants respect some speci…c seniority structure of
claims. With these terminal payo¤s, the values of securities are as follows:
Z
e rt dDivt + e r (1 = L FL;e + 1 = M FM;e ) ;
Ve (Bt ) = Et
0
Z
e rt xd dt + e r (1 = L FL;d + 1 = M FM;d ) ;
Vd (Bt ) = Et
Z0
Vcd (Bt ) = Et
e rt 1B C~ L xcd dt + e r (1 = L FL;cd + 1 = M FM;cd ) ;
0
Z
Z
Vcl (Bt ) = Et
e rt d(Yt Divt )
e rt (xd + 1Bt C~ L xcd
0
+1Bt >C~ L )dt + e
0
r
(1
=
L
FL;cl + 1
=
M
FM;cl ) :
These values can be computed using the general formula in Lemma 3.
In particular, to compute the value of long-term debt, we use formula of Lemma 3 with the ‡ow
return function g(W ) = xd at all W , the value of k = 0, and terminal payo¤s Md = minfD; M g
and Fd = minfD; Lg, where D = xrd . For contingent debt, we use g(W ) = 1W >W
~ xcd , and
k = 0. Because we have assumed contingent debt to be junior to regular long-term debt, the
terminal values for contingent debt are Mcd = minfDcd ; Mc g and Fcd = minfDcd ; Fd g, where,
we recall, Dcd = xrcd . Having veri…ed Mcd < Dcd and Fcd < Dcd , the terminal payo¤s for both
security classes junior to contingent debt, i.e., the unsecured credit line and equity, are zero.
To compute the value of the credit line, we use g(W ) =
xd 1W >W
1W W
~ , and
~ xcd
1
.
k = 1. For equity we use g(W ) = 0 at all W and k =
Figure 3 presents a computed example. In this example, the seniority structure is as follows:
long-term debt, contingent debt, credit line, equity. Under the parameter values of this example, long-term debt becomes riskless, as its face value D is below both M and L. Contingent
debt is risky, with face value Dcd higher than M (and hence also L). In both liquidation and
reorganization, the short-term unsecured line of credit recovers zero, as does equity.
Figure 4 uses the same parametrized example to compute security values in the DS model. In
that model, the optimal capital structure has only one kind of long-term debt. In this example,
this debt is risky. The introduction of the possibility of monitoring increases the total debt
capacity of the …rm, as D + Dcd > DDS , and the optimal credit line is shorter.
16
60
50
40
30
20
10
0
0
2
4
6
8
10
12
Figure 3: Security values.
Security values are highly sensitive to the order of seniority in bankruptcy. In our model, in
particular, it is easy to see that if both forms of long-term debt are pari-passu to each other,
then regular long-term debt is no longer risk-free. The total …rm value, however, as determined
by the optimal contract, is independent of the order of seniority of debt claims.
6.2
Comparative statics
In this section, we use the approach of Lemma 3 to compute comparative statics of the model.
We present the derivation of the comparative statics with respect to the search friction parameter . The comparative statics with respect to other parameters of the model, presented in
Table 1 below, are obtained using the same methodology.
The e¤ect of the search friction parameter, , on the …rm’s pro…t can be found by di¤erentiating
the HJB equation and its boundary conditions. Starting in the no-search region, we have
r
@bN S; (W )
@ @bN S; (W ) 1
= W
+
@
@W
@
2
17
2 2
@ 2 @bN S; (W )
:
@W 2
@
60
50
40
30
20
10
0
0
2
4
6
8
10
12
Figure 4: Security values in the model without monitoring.
Using the Feynman-Kac formula of Lemma 3, this can be simpli…ed to
~)
@bN S; (W )
@bS; (W
~ ; W 1 ],
=
GS (W ) for all W 2 [W
@
@
where
GS (W )
E e
r
S
jW0 = W
~ ; W 1 ],
for all W 2 [W
and S is the stopping time indicating the …rm’s …rst entrance into the search region, i.e.,
~
S = minft : Wt = W g.
~]
Similarly, in the search region we have for all W 2 [R; W
~)
@bN S; (W
@M
GM (W )+
GN S (W ) ;
@
@
(10)
~ ],
where M is the …rm value in the monitoring stage with parameter , and, for all W 2 [R; W
Z
G (W )
E[
e (r+ )t (Wt R) b0S; (Wt ) dtjW0 = W ];
@bS; (W )
@M
1
= G (W )+
M +
@
r+
r+ @
(1
G (W )) +
0
G (W )
E[1
e
(r+ )
jW0 = W ];
18
GM (W )
E e
r
GN S (W )
E e
r
E e
r
GL (W )
1
=
M
jW0 = W ;
1
=
NS
1
=
L
jW0 = W ;
jW0 = W ;
where = minf N S ; M ; L g is the stopping time indicating the …rm’s …rst exit from the
search region due to either …nancial recovery ( = N S ), or transition to monitoring ( = M ),
or liquidation ( = L ). Thus, we have
G (W ) = GN S (W ) + GM (W ) + GL (W ) :
(11)
Finally, from the de…nition of the value in monitoring, M , we have
~)
@bS; (W
GS (W ):
@
@M
=
@
r+
The following lemma signs the comparative statics for the value functions and the boundary
conditions.
@b
(W )
Lemma 4 N S;@
su¢ ciently small.
Proof
> 0,
@bS; (W )
@
> 0,
@M
@
> 0 and
@W 1
@
< 0. Further,
From the de…nition, obviously, we have GS (W )
~)
(W
@b
@b
~
@W
@
< 0 if
0, thus the sign of
is
@bN S; (W )
@
~)
(W
. Suppose S;@
0. Again from the de…nition of
is the same as the sign of S;@
0
~ ) < 0. At the super-contact point W = W
~ , we have
~ ) = 1 and G (W
GS (W ), we have GS (W
S
~)
~)
~)
~) 0
@bS; (W
@bN S; (W
@ 2 bS; (W )
@ 2 bN S; (W
@bS; (W
~ ) 0. So for an arbitrarily
=
and
=
=
G (W
@
@
small " > 0 we have
~)
@bS; (W
@
@W @
@W @
~ ")
~)
@bS; (W
@bS; (W
and
@
@
~
G (W
+
") +
1
M
r+
S
@
hence
~
G (W
1
~)
@bS; (W
GS (W )
@
r+
") +
~
G (W
1
r+
~)
@bS; (W
~
GN S (W
@
~
") + GM (W
")
") :
Rearranging and using (11), we obtain
~)
@bS; (W
~
GL (W
@
~
G (W
") +
") + 1
1
M
r+
1
r+
~
G (W
r+
GS (W )
1
~
G (W
") + 1
r+
~
GS (W ) GM (W
") :
(12)
@b
~)
(W
The left side of (12) is negative under the premise S;@
0. By Lemma 2, b0S; (W ) > 0 for
~ ], which implies G (W
~ ") > 0. Thus, the right side of (12) is strictly positive,
all W 2 [R; W
which is a contradiction.
19
")
Table 1: Comparative statics for the captial structure.
dC L
d
d
d
d B
dL
dR
d
d 2
Also, since we have
from (10).
dD
dDcd
+
+
dW
db0
+
+
+
+
+
+
+
+
+
+
+
+
+
@bN S; (W )
@
> 0, we must have
@M
@
=
r+
@bN S; (W )
@
> 0 and
@bS; (W )
@
>0
Di¤erentiating the boundary condition rbN S; (W 1 ) + W 1 = , we have
@W 1
=
@
r
Di¤erentiating the indi¤erence condition
0
B
~
@W
1
B
=
B
00
~
~
@
W bN S; (W ) @
~
+ (W
~)
@bS; (W
GS (W 1 ) < 0:
r
@
~
= (W
~ ) + (W
~
R)b0N S (W
~)
@b0N S; (W
+
R)
GS (W )
@
r+
{z
}
|
|
{z
<0
<0
~ )), we have
bN S (W
1
1
}
~ )C
@bN S; (W
C
C;
@
A
~ (by Lemma 2 again), GS (W
~ ) = 1 and GS (W ) is decreasing.
where GS (W ) 1 since W > W
~
Thus, we have @@W < 0 if is su¢ ciently small.
Lemma 4 can now be used to derive comparative statics for the optimal capital structure.
Recall that the credit line satis…es C L = 1 (W 1 R) and the distress threshold is C~ L =
1
~ ). Long-term debt is D = 1
(W 1 W
W1
(W 1 R) and the contingent bond is
r
Dcd = r (W 1 R). Applying the lemma to these expressions, we obtain comparative statics
for the capital structure. Table 1 summarizes these results for the credit line, long-term debt,
contingent debt, the value for a new manager, and the value of the …rm in the agency stage.
The comparative statics for the distress threshold C~ L are nonmonotone. When search frictions
are very severe, for example when = is very large, the …rm will only search in a small
20
neighborhood of liquidation, which means C~ L is close to C L and the …rm’s value function b
is close to the DS value function bL over almost all of the domain [R; W 1 ] with a boundary
condition at R approaching L. When search friction are very light, for example when is very
high, the …rm does not search much either because it can …nd transition to monitoring quickly.
In this case, C~ L is also close to C L and value function is represented by bN S over almost all
of the domain [R; W 1 ] with a boundary condition at R approaching M > L. At intermediate
levels of search costs, the …rm commences the search for a bankruptcy opportunity early, i.e.,
the ratio C~ L =C L is lowest.
7
Conclusion
Asquith et al. (2005) and Manso et al. (2010) document that, broadly de…ned, performance
pricing on debt instruments is a feature used commonly in the practice of corporate …nance. In
this paper, we show that performance pricing arises as a part of an optimal credit arrangement
when …rms can use a …nancial reorganization procedure similar to Chapter 11 bankruptcy. In an
optimal contract, management is dismissed with no severance and the value of equity is wiped
out as the …rm enters bankruptcy reorganization. This discrete loss of value is compensated
by giving the …rm a relief in its debt service costs during …nancial distress, when the arrival
rate of bankruptcy is positive. The role of performance pricing on the …rm’s debt obligations
is to implement this relief.
Appendix
Capital structure with preferred stock
In this Appendix, we discuss a modi…ed capital structure under which the …rm is not committed ex ante to the payment of contingent debt coupons in the non-distress region. Rather,
payments to the contingent liability class are optional, at the discretion of the manager, with a
covenant attached dictating that the …rm searches for a bankruptcy reorganization whenever
the optional payment to this liability class is skipped. This payment optionality feature makes
this contingent liability class very similar to preferred equity.
Consider the following capital structure consisting of a long-term bond, preferred equity, common equity, a primary revolving credit line, and a secondary revolving credit line.
Long-term debt pays a constant coupon rate xd . The preferred equity dividend rate is p. The
primary revolving credit line charges the interest rate on the balance outstanding, which is
21
denoted by At , and has the credit limit A. The secondary revolving credit line charges the
interest rate + on the outstanding balance Bt , and has the limit B.
The covenant structure attached to the above liabilities is as follows. Missing a coupon payment to long-term debt triggers liquidation. Preferred equity dividends p are non-cumulative,
i.e., can be paid out at the manager’s discretion. Although missing a payment p does not
cause default, it triggers the search for reorganization at all times at which p is not paid out.
Resumption of preferred dividend payments stops the search. Likewise, a positive balance Bt
on the secondary credit line triggers the search for reorganization. The primary credit line can
be used at the manager’s discretion, up to the limit A, with no triggers attached.
The manager holds the fraction of common equity. The manager chooses the common equity
cumulative dividend process, Divt , the preferred equity cumulative dividend process, Divtp , a
process of drawing upon the secondary credit line, bt , and the cash ‡ow reporting process Y^t .
The manager maximizes
E
Z
e
t
( d(Yt
Y^t ) + dDivt ) + e
r
R
0
subject to
dAt =
At dt + xd dt + dDivt + dDivtp
dBt = ( + )Bt dt + dbt ;
Y^t
where = min f
zation.
L; M g
dY^t
dbt ;
(13)
(14)
Yt ;
is the stopping time indicating liquidation or transition to reorgani-
Proposition 2 Suppose
p =
~
(W
W1
xd =
A =
B =
R);
W1
~
W
22
~
W
R
:
;
(15)
p;
(16)
(17)
Then the strategy
Y^t = Yt ;
(
dDivtp =
dbt =
(
1
Divt =
pdt if At < A and Bt = 0;
0 otherwise,
0 if At < A and Bt = 0;
Adt + xd dt dYt otherwise,
It ;
solves the manager’s problem, and the implied revolving credit balance processes At and Bt
satisfy
(
W1
At ; if At < A and Bt = 0;
Wt =
(18)
~
W
Bt ; otherwise,
where (Wt ; t 0) is the manager’s value process obtained as the solution to the optimal contracting problem.
Proof First, we check that if the manager follows the proposed strategy, then (18) holds.
With the credit limits (16) and (17), we have the following boundary conditions. With At =
~ . With At = A and
Bt = 0, we have Wt = W 1 . With At = A and Bt = 0, we have Wt = W
Bt = B, we have Wt = R.
For all At 2 [0; A) and Bt = 0, the proposed strategy implies Y^t = Yt , dDivtp = pdt and dbt = 0.
W 1 dt dYt . Under this
Hence (14) implies dBt = 0 and (13) implies dAt = At dt + dt
~ ; W 1 ] because
law of motion, the balance processes satisfy (18) at all Wt 2 (W
d(W 1
At ) =
dAt
=
At dt +
W 1 dt + (dYt
At + W 1 )dt +
=
(
=
Wt dt +
dt)
dZt
dZt ;
which replicates the law of motion for Wt determined by the optimal contract in the no-search
~ ; W 1 ] and the boundary condition for At = Bt = 0 matches the boundary
region Wt 2 (W
condition Wt = W 1 .
For At = A and Bt 2 [0; B), the proposed strategy implies Y^t = Yt , dDivtp = 0 (so the …rm
searches for a transition to monitoring), dbt = Adt+xd dt dYt , from which we obtain dAt = 0
(with At remaining at A as long as Bt is positive), and, using, (14), dBt = ( + ) Bt dt+ Adt+
23
~
(
W1
(W
R))dt dYt . Under this law of motion, the balance processes satisfy (18)
~
at all Wt 2 (R; W ] because
~
d(W
Bt ) =
=
=
=
dBt
( + ) Bt dt +
~
W
W1
( + ) Bt dt +
~
W
dt + (
dt + (
~ dt + ( (W
~
( + ) Bt dt + W
= ( + )
~ dt
Bt dt + W
= ( + )Wt dt
Rdt +
~
(W
W
~
(W
1
R))dt
R))dt + (dYt
Rdt + (dYt
(dYt
R))dt
dt)
!
dYt
!
dt)
dt)
dZt
which replicates the law of motion for Wt determined by the optimal contract in the search
~ ] and the boundary condition for At = A, Bt = 0 matches the boundary
region Wt 2 (R; W
~.
condition Wt = W
Now we show that the proposed strategy is optimal to the manager. Due to the higher interest
rate and the search trigger associated with the secondary line of credit, it is clearly optimal
for the manager to not use it unless At = A. Further, since the maxing out the primary credit
line triggers search already, the manager has no longer an incentive to pay preferred dividends
p when At = 0 and Bt > 0. As in DS, the manager has no incentive to pay common dividends
when balance on revolving lines is positive because he owns fraction of both the dividends
and the slack on the credit lines. For the same reason, the manager has no incentive to divert
the cash ‡ow.
Further, we need to check that the manager prefers to pay the noncumulative preferred dividend
p whenever At < A. Suspending the payment of pdt triggers search in dt, which costs the
manager the expected loss of dt(Wt R), but, on the other hand, it allows the manager to
reduce the balance At at the rate pdt, which increases the manager’s value Wt at the rate pdt.
We need to check that the loss is weakly larger than the gain whenever A < A. Since the
manager’s loss is monotone in Wt , it is su¢ cient to check the case with the smallest Wt in the
~ , which takes place when At = A. Thus,
preferred dividend payment region, i.e., at Wt = W
we need to check that
~
~
(W
R);
(W
R)
p=
which is true, by (15).
This shows that if the manager follows the proposed policy, he does as well as in the optimal
contract. That he cannot do better follows by contradiction. If he could, we’d be able to
24
construct a diversion policy Y^ that would give the manager a higher payo¤ also under the
optimal contract, which contradicts the incentive compatibility property of that contract.
References
Antill, S. and S. Grenadier (2018). Optimal capital structure and bankruptcy choice: Dynamic
bargaining vs liquidation. Journal of Financial Economics forthcoming.
Antinol…, G. and F. Carli (2015). Costly monitoring, dynamic incentives, and default. Journal
of Economic Theory 159, 105–119.
Asquith, P., A. Beatty, and J. Weber (2005). Performance pricing in bank debt contracts.
Journal of Accounting and Economics 40 (1-3), 101–128.
Biais, B., T. Mariotti, G. Plantin, and J. Rochet (2007). Dynamic security design: Convergence
to continuous time and asset pricing implications. Review of Economic Studies 74, 345–390.
Bris, A., I. Welch, and N. Zhu (2006). The costs of bankruptcy: Chapter 7 liquidation versus
chapter 11 reorganization. The Journal of Finance 61 (3), 1253–1303.
Chen, M., P. Sun, and Y. Xiao (2017). Optimal monitoring schedule in dynamic contracts.
Working paper, Duke University.
Chen, N., P. Glasserman, B. Nouri, and M. Pelger (2017). Contingent capital, tail risk, and
debt-induced collapse. The Review of Financial Studies 30 (11), 3921–3969.
Corbae, D. and P. D’Erasmo (2017). Reorganization or liquidation: Bankruptcy choice and
…rm dynamics. Working Paper 23515, National Bureau of Economic Research.
DeMarzo, P. and Y. Sannikov (2006). Optimal security design and dynamic capital structure
in a continuous-time agency model. The Journal of Finance 66 (6), 2681–2724.
DeMarzo, P. M. and M. J. Fishman (2007). Optimal long-term …nancial contracting. The
Review of Financial Studies 20 (6), 2079–2128.
Du¢ e, D., N. Gârleanu, and L. H. Pedersen (2005). Over-the-counter markets. Econometrica 73 (6), 1815–1847.
Flannery, M. J. (2005). No pain, no gain? e¤ecting market discipline via reverse convertible
debentures. In H. S. Scott (Ed.), Capital adequacy beyond Basel: Banking, securities, and
insurance, pp. 171–196. Oxford University Press Oxford, UK.
25
Flannery, M. J. (2014). Contingent capital instruments for large …nancial institutions: A
review of the literature. Annual Review of Financial Economics 6 (1), 225–240.
Gale, D. and M. Hellwig (1985). Incentive-compatible debt contracts: The one-period problem.
Review of Economic Studies 52(4), 647–663.
Hanson, S. G., A. K. Kashyap, and J. C. Stein (2011). A macroprudential approach to …nancial
regulation. Journal of economic Perspectives 25 (1), 3–28.
Jacobs Jr, M., A. K. Karagozoglu, and D. N. Layish (2012). Resolution of corporate …nancial
distress: an empirical analysis of processes and outcomes. Journal of portfolio management 38 (2), 117.
Jensen, M. C. (1986). Agency costs of free cash ‡ow, corporate …nance, and takeovers. The
American Economic Review 76 (2), 323–329.
Leland, H. E. (1994). Corporate debt value, bond covenants, and optimal capital structure.
The Journal of Finance 49 (4), 1213–1252.
Manso, G., B. Strulovici, and A. Tchistyi (2010). Performance-sensitive debt. The Review of
Financial Studies 23 (5), 1819–1854.
Monnet, C. and E. Quintin (2005). Optimal contracts in a dynamic costly state veri…cation
model. Economic Theory 26 (4), 867–885.
Mortensen, D. T. and C. A. Pissarides (1994). Job creation and job destruction in the theory
of unemployment. The Review of Economic Studies 61 (3), 397–415.
Piskorski, T. and M. M. Wester…eld (2016). Optimal dynamic contracts with moral hazard
and costly monitoring. Journal of Economic Theory 166, 242–281.
Tchistyi, A. (2016). Security design with correlated hidden cash ‡ows: The optimality of
performance pricing. Working paper, University of Illinois at Urbana-Champaign.
Townsend, R. M. (1979). Optimal contracts and competitive markets with costly state veri…cation. Journal of Economic Theory 21 (2), 265–293.
Varas, F., I. Marinovic, and A. Skrzypacz (2017). Random inspections and periodic reviews:
Optimal dynamic monitoring. Working paper, Stanford University.
Wang, C. (2005). Dynamic costly state veri…cation. Economic Theory 25 (4), 887–916.
26
@FedFRASER