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Corporate Liquidity Management under Moral Hazard

Barney Hartman-Glaser Simon Mayer Konstantin Milbradt§ September 30, 2020

Abstract

We present a model of dynamic liquidity management in which an insider designs and sells long-term claims on a financially constrained firm to outside investors. The insider maintains control of the firm and is subject to moral hazard. Risk-sharing can cause the insider’s perfor- mance sensitivity to be above the minimum required for incentives. Agency conflicts prevent some firms from attracting initial financing, while others may only do so with future liquidation risk. Volatile cash flows exacerbate moral hazard and thus may reduce target cash holdings.

Depending on fundamentals, the insider either contributes or extracts cash at the initial round of financing. Periodic access to capital markets allows refinancing and decreases liquidation risk, but not the firm’s ability to attract initial financing. Agency conflicts lead to state-dependent flotation costs and potential cash bonuses to the insider upon refinancing. We approximate the optimal contract with cash reserves, equity, and an insider-provided credit line.

We thank Simon Board, Jean Paul D´ecamps, Mike Fishman, Sebastian Gryglewicz, Alexander Guembel, Zhiguo He, Julien Hugonnier, Erwan Morellec, Stavros Panageas, Adriano Rampini, Alejandro Rivera, and St´ephane Vil- leneuve for helpful comments and discussions. We also thank seminar audiences at University of Houston, EPFL, Kellogg Northwestern, Toulouse School of Economics, Copenhagen Business School, University of North Carolina Chapel Hill, the 2020 Western Finance Association Meetings, the Spring 2019 Finance Theory Group Meetings, EIEF, CUHK Shenzhen, and McGill University. A previous version of this paper was circulated under the title “Cash and Dynamic Agency”.

UCLA Anderson. E-mail: bhglaser@anderson.ucla.edu

Erasmus University Rotterdam. E-mail: mayer@ese.eur.nl.

§Northwestern University and NBER. E-mail: milbradt@northwestern.edu

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Financial constraints play a key role in the investment, compensation and payout decisions of both firms (Campello, Graham, and Harvey 2010) and investment funds, such as private equity and venture capital funds (Robinson and Sensoy 2013). The inability to raise external funds gives rise to internal liquidity management, in that firms accumulate cash (Bates, Kahle, and Stulz 2009) and structure compensation packages (Michelacci and Quadrini 2009) to avoid financial distress.

At the same time, internal cash holdings exacerbate agency conflicts as they serve as a larger pool from which insiders can divert cash (Jensen 1986).

In this paper, we study how a firm optimally designs payout policies when it faces both financing and agency frictions. To do so, we develop a continuous-time model in which a risk-averse insider operates a firm co-financed by dispersed risk-neutral outside investors. The firm has risky cash flows and faces financial constraints. Specifically, the firm can only access capital from outside investors at inception. As a result, the firm must finance operating losses with internal cash or with contributions from the insider. Both forms of liquidity management are costly: internal cash earns a return below the risk-free rate due to an internal carry cost of cash, while financing from the insider must compensate her for bearing risk. In the event the firm cannot cover a negative cash-flow shock, which occurs when cash reserves are exhausted and the insider provides no further financing, it must liquidate. The firm is also subject to an agency problem. Specifically, the insider can privately divert cash for her own consumption. The firm’s capital structure, cash holdings, and insider compensation contract are intertwined. The insider chooses the firm’s dynamic liquidity management policy to maximize the value of the securities sold to outsider investors, while ensuring that she has incentives to truthfully report cash flow. We interpret the insider–outsider relationship broadly. For example, the insider can be an entrepreneur who raises funds from outside investors.

Alternatively, the insider can also represent a large shareholder (such as a private equity or hedge fund) that affects the firm’s performance.

Under the optimal payout agreement, risk-sharing and agency frictions are closely related. When the firm has large cash reserves, the optimal payout agreement exposes the insider to the minimal amount of cash-flow risk that is sufficient to provide her with incentives to truthfully return cash flow. In contrast, when the firm has low cash reserves, risk-sharing considerations determine the insider’s exposure to cash-flow risk. In detail, the payout agreement stipulates that the insider bears risk in excess of pure incentive considerations, specifically requiring her to inject funds into the firm to help cover cash shortfalls and lower the volatility of the firm’s cash holdings. When the firm’s net present value (NPV) is high, the insider fully absorbs cash-flow volatility and thus any

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risk of liquidation.1 When the firm’s NPV is low, the insider never fully absorbs cash-flow volatility and the firm faces the risk of liquidation.

We show that a capital structure consisting of cash reserves, standard equity, and a variable- interest credit line provided the insider implements the optimal contract to a first order. During the initial round of financing, the insider issues standard equity and sells a fraction to outside investors.

She retains the remaining equity to guarantee she has incentives to truthfully return cash flow. The insider also commits to provide a credit line with an interest rate that varies with its balance. The credit line allows the firm to shift risk onto the insider when cash-flow shocks deplete its cash reserves. While our implementation bears some similarities to those found in the literature, for example, that of DeMarzo and Sannikov (2006) and Biais, Mariotti, Plantin, and Rochet (2007), it has some novel and realistic features. First, our implementation includes two forms of internal liquidity — the cash reserves and the credit line — that the firm uses simultaneously when low on cash. In addition, the insider, rather than outside investors, provides the credit line.

We next explore conditions under which the firm is able to attract initial financing. Even when we consider only positive NPV firms, agency conflicts keep some firms from attracting initial financing from outside investors, while others are financed only under risk of subsequent liquidation.

Interestingly, which firms can attract initial financing does not depend on the severity of financial constraints, but rather on the severity of agency conflicts. In contrast, which firms are at risk of liquidation only depends on whether the insider would be willing to run the firm in the absence of any outside investors. If so, the insider provides inside financing under financial distress to avert liquidation. As a result, firms with high NPV receive sufficient outside and inside financing and are not at the risk of liquidation. Firms with moderate NPV attract outside financing, but do not receive sufficient inside financing. These firms are financed under risk of subsequent liquidation.

Firms with low (but positive) NPV are not financed at all, due to agency conflicts.

We then study the optimal payout policy. This policy is characterized by an upper bound on the firm’s cash balance at which dividends are paid to outside investors. Interestingly, this target cash balance, which is also the firm’s optimal starting cash position, is hump-shaped in cash-flow volatility, as an increase in cash-flow volatility has two opposing effects. An increase in cash-flow volatility boosts the firm’s motive to accumulate precautionary cash holdings, but exacerbates agency conflicts and therefore reduces the marginal value of cash within the firm and

1Here, we use NPV to mean the first-best value of the firm when outsiders are unconstrained and insiders have no moral hazard; i.e., the perpetuity value of expected cash flow.

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accelerates payouts. Note that the magnitude of the target cash balance determines whether the insider contributes cash (i.e., co-invests) or extracts cash at the initial round of outside financing.

Specifically, the insider extracts cash when cash-flow volatility and the target cash balance are low, while she contributes cash otherwise.

To complete our analysis, we extend the model and consider the insider can raise capital from outside investors after the inception of the firm. Specifically, the firm has infrequent and stochastic access to frictionless capital markets. We find that such refinancing opportunities are subject to an endogenous and state-dependent flotation cost due to moral hazard. For high levels of cash reserves, the firm may not refinance to its target cash balance as the insider’s agency problem requires additional payoffs. This result contrasts with models of pure liquidity management, in which refinancing to the target balance is always the optimal policy in the absence of refinancing costs. For low levels of cash reserves, refinancing to the target balance can be optimal, in which case, the insider receives a cash bonus. The intuition is that promising bonus payments conditional on refinancing lowers the payouts required outside of refinancing opportunities, thus preserving liquidity.

We then explore the implications of refinancing on the firm’s liquidation risk and its ability to attract initial financing. We find that the presence of refinancing opportunities does not change the set of firms able to attract initial financing. However, refinancing opportunities increase the set of firms that are never at risk of liquidation. Further, for firms that are at risk of liquidation, refinancing opportunities reduce such risk. In other words, in the presence of refinancing opportu- nities, liquidation risk depends on both firm fundamentals and financial frictions. The intuition is that improved access to outside financing also improves the insider’s willingness to provide inside financing, which ultimately mitigates liquidation risk.

Our work connects two related strands of the corporate finance literature. First, our paper adds to the literature on dynamic incentive problems. Recent contributions include DeMarzo and Sannikov (2006, 2016), Biais, Mariotti, Plantin, and Rochet (2007), Sannikov (2008), Biais, Mariotti, Rochet, and Villeneuve (2010),Williams(2011),He(2011),DeMarzo, Fishman, He, and Wang(2012),Zhu(2012), Ai and Li(2015), Miao and Rivera(2016),Marinovic and Varas (2019), Malenko (2019), and Gryglewicz, Mayer, and Morellec (2020). The innovation in our paper is that we consider a financially constrained principal; i.e., the outside investors in our model. This assumption further connects this literature to empirical research. Ward and Ying(2020) present a numerical solution of a model of moral hazard and financial constraints with a risk-neutral agent.

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Second, our model is linked to the theoretical literature on dynamic liquidity management.

Here, Bolton, Chen, and Wang (2011,2013), D´ecamps, Mariotti, Rochet, and Villeneuve (2011), Gryglewicz (2011), Hugonnier, Malamud, and Morellec (2015), Decamps, Gryglewicz, Morellec, and Villeneuve (2016), Hugonnier and Morellec (2017), and Abel and Panageas (2020) are the closest references. Unlike our paper, these papers do not study dynamic compensation schemes and insider incentives. Importantly, Decamps, Gryglewicz, Morellec, and Villeneuve (2016) and Abel and Panageas (2020) demonstrate that an increase in persistent cash-flow risk may increase or decrease target cash holdings. Unlike these papers, we find that the relationship between target cash holdings and risk is non-monotonic in a stationary cash-flow environment if moral hazard is sufficiently severe. Our paper is also closely related to Bolton, Wang, and Yang (2019), who analyze how to optimally structure compensation, investment, and payout policies. Unlike ours, their framework does not feature agency conflicts and the risk of negative cash-flow realizations.

In addition, important empirical and structural papers on corporate cash management and fi- nancial constraints include Whited and Wu (2006), Almeida and Campello (2007), Bates, Kahle, and Stulz (2009), Nikolov and Whited (2014), and Nikolov, Schmid, and Steri (2019). Our pa- per also adds to the literature analyzing risk-sharing between firms and their workers, such as the theoretical studies of Berk, Stanton, and Zechner (2010) or Hartman-Glaser, Lustig, and Xi- aolan (2019) or the empirical study ofGuiso, Pistaferri, and Schivardi(2005), who document that firms only partially insure their workers against cash-flow risk. Howell and Brown (2019) provide empirical evidence in support of a mechanism in line with our results. They find that financially constrained firms borrow from insiders by promising payouts in response to positive cash-flow shock in the future. Viewed through the lens of our model, one can interpret their findings as a form of risk-sharing.

The remainder of the paper is structured as follows. Section 1presents the setup of the model and Section 2 presents the heuristic model solution. Section 3 analyzes the model and derives its implications. Section 4 extends the baseline model and introduces refinancing opportunities.

Section 5discusses another model extension andSection 6concludes the paper. All technical details and proofs can be found in the Appendix.

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1 Model Setup

We consider a firm that produces volatile cash flows and is owned by a risk-averse agent whom we call the insider. To share risk with competitive and risk-neutral outside investors (i.e., outsiders), the insider designs at time zero a payout agreement that includes a security (called outside equity) she sells to outside investors and an inside stake within the firm that she retains. We interpret the insider–outsiders relationship broadly. For instance, the insider can be an entrepreneur who raises funds from outside investors. The insider can also represent a large shareholder of the firm, such as a hedge fund if the firm is public, or a private equity fund if the firm is private, while the outside investors are the firm’s dispersed shareholders. Alternatively, the insider may represent the general partners within a private equity or venture capital fund that owns a target firm and raises funds from the outside investors acting as the limited partners.

1.1 Cash Flows, the Payout Agreement, and Corporate Liquidity

Time t is continuous on [0, ∞). The firm generates cash flows dXt with mean µ and volatility σ

dXt= µdt + σdZt, (1)

where Z is a standard Brownian Motion. The insider designs a payout agreement (i.e., contract) C = (Div, I) that stipulates cumulative dividend payouts Divtto outside investors and cumulative payouts It to the insider, including dividends and payouts at the time of founding (i.e., at time t = 0). We assume that it is not possible to raise external funds from either new or existing outsider investors after the founding of the firm at time t = 0, for example, by issuing equity.

That is, we assume dDivt≥ 0 for all t ≥ 0, which may reflect that outside investors are themselves financially constrained.2 Note that outside investors can provide funds at time t = 0, in which case dDiv0 < 0.

The insider perfectly observes cash flows while the outside investors do not. As in DeMarzo and Sannikov (2006), the insider can divert cash dbt for her own by underreporting cash flows to outside investors. She receives λ ∈ [0, 1) per dollar she diverts so that cash diversion is inefficient.

As we verify later, the insider never finds it valuable to inject cash into the firm by overreporting cash flow and setting dbt< 0. We thus impose dbt≥ 0 to simplify the notation.

The firm’s financial constraints together with the fact that cash-flow shocks can be negative

2We introduce refinancing opportunities inSection 4.

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imply that the firm must accrue a cash balance. Specifically, the outside investors are unable to inject cash so that all operating losses dXt < 0, dividends dDivt ≥ 0, and transfers to and from the insider dIt must come out of the firm’s internal cash balance, which we denote by Mt. We normalize the cash balance at t = 0 to zero (i.e., M0 = 0). In contrast to outside investors, the insider can inject cash into the firm and provide inside financing, dIt < 0, but this source of financing is costly and limited because the insider is risk averse.3 The cash within the firm accrues interest at the rate r − δ where r is the common discount rate and δ > 0 represents a carrying cost of cash.4 In Appendix H.1, we demonstrate how these costs can arise endogenously as a result of agency conflicts. The dynamics of Mtare thus given by

dMt= [µ + (r − δ)Mt] dt + σdZt− dbt− dDivt− dIt. (2)

Cash holdings cannot be negative; i.e., Mt ≥ 0, ∀t ≥ 0. This implies that if Mt attains zero, the insider must either inject funds or liquidate the firm, as outside investors cannot inject funds into the firm after time zero. Liquidation thus occurs at some stopping time τ ∈ [0, ∞], and dDivt= dIt= dXt = 0 for all t > τ . For tractability, we assume that the liquidation value of the firm is zero.

1.2 Preferences

The common discount rate is r > 0. The firm’s outside investors are risk neutral, reflecting that outside investors are diversified. The insider is risk averse with CARA preferences, with the instantaneous utility of consumption c given by

u(c) = −1

ρexp(−ρc),

and with a risk-aversion coefficient of ρ > 0. Risk aversion reflects the notion that the type of insiders we consider in this paper typically have undiversified exposure to the firm.

Both the outside investors and the insider have limited commitment. Thus, the outside investors’

(the insider’s) continuation value from following the payout agreement must at any time t ≥ 0 exceed the outside investors’ (the insider’s) outside option, which we normalize to zero. As payouts

3Appendix H.3discusses the model solution when the insider is financially constrained in the sense that payouts to the insider must be positive; i.e., dIt≥ 0 for all t ≥ 0.

4The assumption is standard in the literature and is needed to preclude degenerate solutions, in which dividend payouts are indefinitely delayed and the firm saves itself from the liquidity problem.

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to outside investors are positive after time zero, outside investors always derive positive value from following the payout agreement, so their limited-commitment constraint is always satisfied.

The insider can maintain private savings, denoted by St. Savings accrue interest at rate r and are subject to changes induced by the payouts she receives from the firm dIt, diverted cash dbt≥ 0, and consumption ct, so that

dSt= rStdt + λdbt+ dIt− ctdt. (3) Endowing the insider with the possibility to accumulate savings ensures that she can smooth her consumption beyond any time at which she will no longer receive payouts from the firm.

Consumption ct and savings balance St can both take positive and negative values. We normalize the balance of the savings account at t = 0to zero (i.e., S0= 0). Finally, savings must satisfy the standard transversality condition limt→∞Ee−rtSt = 0, ruling out Ponzi schemes. For simplicity, the insider’s savings are not subject to the carrying cost of cash δ > 0. In Appendix H.2, we demonstrate that the results of our analysis remain largely unchanged if the insider’s savings are subject to the interest rate r − δ rather than r.

1.3 The Optimal Security Design Problem.

The payout agreement (i.e., contract) C can be written conditional on all publicly observable vari- ables and outcomes. Cash holdings Mt and changes in cash holdings dMt, as well as payouts to the outside investors dDivt and to the insider dIt, are publicly observable and contractible. In contrast, cash-flow shocks dZt, cash-flow realizations dXt, the insider’s savings St, and the insider’s cash diversion dbt are privately observed by the insider, not observable to outside investors, and not contractible. Thus, observing the cash dynamics dMtand payouts (dIt, dDivt) and anticipating zero cash diversion dbt= 0, outside investors impute the cash flow realization

d ˆXt≡ dMt− (r − δ)Mtdt + dDivt+ dIt. (4)

In other words, the imputed cash flows d ˆXtare publicly observable and contractible but the actual cash flows dXt are not.5

Given C, the insider chooses consumption c and diversion policies b to maximize her lifetime

5Equivalently, one can interpret d ˆXt as reported cash flows, like inDeMarzo and Sannikov(2006). If the insider were to report cash flows d ˆXt to outside investors, then (4) is the only report that is consistent with zero diversion, the observed dynamics of cash, and the observed payouts to the insider and the outside investors.

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utility. Let U (C) be the insider’s indirect utility for a given contract C; i.e.,

U0= U (C) = max

ct,bt

E

Z 0

e−rtu(ct)dt



. (5)

We call a payout agreement incentive compatible if it induces zero cash diversion so that d ˆXt= dXt for all t ≥ 0, and if it respects the outside investors’ and the insider’s limited commitment. In what follows, we restrict our attention to incentive-compatible payout agreements.

We can then write the optimal security design problem as

maxC U (C) (6)

such that C is incentive compatible. At firm inception at time t = 0, the outside investors contribute a total of −dDiv0 dollars and the insider contributes −dI0 dollars.6

Note that because the outside investors are competitive and have zero outside option, their initial cash contribution −dDiv0 must equal the expected present value of their stream of dividends. We can interpret this quantity as the competitive price P0 of the security (i.e., outside equity) that the insider issues and write

P0 = E

Z τ 0

e−rtdDivt



= −dDiv0. (7)

As M0 = S0= 0, the initial cash balance is given by

M0 = −dDiv0− dI0 = P0

|{z}

Cash from outsiders

+ (−S0).

| {z }

Cash from the insider

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Note that the insider’s initial cash contribution to the firm can be either positive or negative.

When S0 < 0, the insider is contributing cash to the firm, whereas when S0 > 0 the insider is extracting cash from the firm by transferring some of the sale proceeds into her savings account.

However, regardless of the sign of S0, the insider will always have skin in the game— i.e., a positive stake in the firm—due to promised future payouts.

6Because the insider has concave utility and access to savings, she will smooth consumption so that dI0 = S0− S0 = S0.

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2 Model Solution

In this section, we solve the model and derive the optimal payout agreement. First, we analyze the insider’s problem and characterize conditions for the payout agreement to be incentive compatible.

Next, we show how to collapse the state space of the problem. We then provide a heuristic argu- ment that the security design problem we give in equation (6) is equivalent to one in which the insider maximizes the value of the outside equity claim she sells to outside investors. Finally, we characterize the dynamic optimization problem by an ordinary differential equation (ODE).

2.1 Continuation Value and Incentive Compatibility Define the insider’s continuation value at time t by

Ut:= Et

Z t

e−r(s−t)u(cs)ds



. (9)

To provide incentives, the insider’s continuation value is sensitive to firm performance in that

dUt= rUtdt − u(ct)dt + βt(−ρrUt)(d ˆXt− µdt), (10)

where βt captures the insider’s exposure to cash-flow shocks. Because we focus on incentive- compatible payout agreements, there is no diversion (i.e., dbt= 0) in optimum, leading to dXt= d ˆXt

and hence d ˆXt− µdt = σdZt.

First, note that because the insider has access to a savings technology, she optimally smooths her consumption, implying that her marginal utility is a martingale. As shown inAppendix C, the insider’s first-order condition with respect to consumption given the access to a savings account implies that u0(ct) = −ρrUt> 0. Because, in addition, u0(ct) = −ρu(ct), it follows that u(ct) = rUt, so that by (10), the insider’s continuation utility Ut is a martingale. Second, let us define the certainty equivalent Wtas the amount of wealth needed that would result in utility Utif the insider only consumed interest on her wealth rWt; i.e.,

Wt:= − ln(−ρrUt)

ρr . (11)

Note that Wtis the insider’s continuation value in monetary (dollar) terms while Utis the insider’s continuation value in utility terms. One can also derive that due to u(ct) = rUt, it follows that

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ct= rWt, in that the insider optimally consumes the “interest” on her current certainty equivalent.

Applying Ito’s Lemma to Wt, we obtain

dWt= ρr 2 (βtσ)2

| {z }

risk premium

dt + βt(d ˆXt− µdt) (12)

Because her payouts are sensitive to cash-flow shocks d ˆXt = dXt, the insider demands a risk premium, in that Wthas a drift equal to the required risk premium.

Note that the insider’s certainty equivalent payoff Wt consists of two sources. First, the insider has the savings Stshe has accumulated up to time t. Second, the insider expects to receive payouts from the firm after time t, which we she values at Yt. That is, the value of the insider’s deferred payouts (i.e., deferred compensation) is defined as Yt= Wt− St. In Proposition 1 below, we show that Yt is the expected present value of the insider’s future payouts dIs for s ≥ t adjusted for risk so that

Yt= Et

Z t

e−r(s−t)



dIs−ρr

2 (βsσ)2ds



(13) and

dYt=

rYt+ρr

2 (βtσ)2

dt + βt(d ˆXt− µdt) − dIt. (14) We refer to Equation (14) as the promise-keeping constraint. It means that current transfers dIt must be accompanied by a commensurate change in future promised transfers dYt (i.e., dYt/dIt=

−1) to deliver the promised value at time t (i.e., Yt) to the insider.

We can now characterize the incentive compatibility conditions that guarantee zero cash di- version. Importantly, the insider can divert cash two ways. First, she can divert a small (i.e., infinitesimal) amount of cash, which we refer to as diversion from the cash flow. In this case, dbt

is infinitesimal and of the order dt, and outside investors attribute the loss of cash to adverse cash flow realizations d ˆXt< dXt rather than diversion dbt, in that the diversion dbt is not observed by outside investors. Thus, cash flow diversion induces a similar moral hazard problem as inDeMarzo and Sannikov(2006). If the insider diverts dbt= 1dt dollars from the cash flow at time t, she gains λdt dollars but also reduces imputed cash flows d ˆXt by 1dt dollars, so that her continuation value (in monetary terms) Wt falls by βtdt dollars (see (12)). Thus, the payout agreement implements zero diversion from the cash flow at time t if and only if:

βt≥ λ. (15)

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Likewise, the insider does not find it optimal to boost cash flow through dbt< 0 as long as βt≤ 1.

Second, the insider can divert a larger (i.e., non-infinitesimal) amount of cash, which we refer to as diversion from the cash stock. Note that diversion from the cash stock with non-infinitesimal dbt∈ (0, Mt] induces a downward discontinuity, or jump, in the firm’s cash holdings Mt. Thus, the outside investors can perfectly detect and observe diversion from the cash stock because without diversion, cash-flow shocks dZt would lead to a continuous sample path for Mt. Hence, diversion from the cash stock is publicly observable and to some extent contractible.

While the payout agreement can punish the insider for the diversion from the cash stock, the scope of these punishments is constrained by the insider’s limited commitment, as the insider can always leave the firm and receive zero future payouts. That is, the loss of the deferred compensation Yt is the harshest punishment possible for the insider’s cash diversion. Thus, the insider does not find it optimal to divert from the cash stock if and only if Yt ≥ λdbt for all dbt ∈ [0, Mt]. As the right-hand side of the above inequality is maximized for dbt = Mt, the incentive constraint is equivalent to

Yt≥ λMt. (16)

The interpretation is that if the insider absconds with the entire cash balance Mt, she gains λMt

dollars but triggers immediate firm liquidation, which renders her stake within the firm worthless and leads to a loss of her deferred compensation Yt. Alternatively, (16) can also be seen as a limited-commitment constraint, as in Ai and Li (2015). That is, Yt is the insider’s incremental value derived from continuing to operate the firm and following the payout agreement and λMt is the insider’s endogenous outside option obtained by leaving the firm.

Proposition 1summarizes the behavior of the different representations of the continuation value of the insider, U, W, Y , the insider’s optimal consumption ct, as well as the incentive constraints associated with the flow (β) and the stock of cash.

Proposition 1. Under an incentive-compatible payout agreement C, the following holds:

1. U follows (10) and W follows (12). Optimal Consumption satisfies ct= rWt. 2. Y follows (14) with integral representation (13).

3. βt∈ [λ, 1] for all t ≥ 0.

4. Yt≥ λMt for all t ≥ 0.

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2.2 The Autarky and Second-Best Benchmarks

To gain intuition, it is useful to establish two benchmarks. First, we consider the autarky benchmark in which there are no outside investors or outside financing. Next, we consider the second-best benchmark in which the firm can freely access outside investors at all points in time with no financing frictions. In both cases, the firm holds no cash as the internal carry-cost δ makes it inefficient to do so.

The Autarky Benchmark. In the case of autarky, the insider must absorb all cash flow fluctu- ations, i.e., dIt= dXt= µdt + σdZt, and because the model is stationary, βt= 1 is required to yield a constant Y in (14). The firm (once initiated) is never liquidated and the insider’s deferred payout Yt is time-stationary so that Yt= YAfor some constant YA. Plugging into (13) and evaluating the expectation under the assumption of no default yields

YA= µ r −ρσ2

2 . (17)

Also note that the insider will operate the firm in autarky if and only if the net present value (NPV)

µ

r of the project is in excess of her required risk compensation ρσ22 for fully owning the firm; i.e., if and only if YA≥ 0.7

The Second-Best Benchmark. In the second-best case, the outsider investors can freely con- tribute cash to the firm. Given that these outsider investors are risk neutral, it is optimal to expose the insider to minimal risk subject to incentive compatibility (15) as such exposure is costly, and thus β = λ. The firm (once initiated) is never liquidated and the insider’s deferred payouts Yt

and the outside equity value Pt are both time-stationary, so that Yt = YSB and Pt= PSB for all t ≥ 0 for some constants YSB and PSB. Further, the insider sells as much of the firm as she can, so there is no inside financing (i.e., Y0 = 0) and P0 > 0.8 Setting (13) equal to zero, the insider’s compensation dI must have a drift of µI = ρr(λσ)2 2 to compensate for her risk exposure. Thus, as the outsider investors are the direct claimants to the residual cash flows (recall there is no cash in the firm) and the firm never defaults (incentives are from local variation in transfers dI and not

7Our convention is that NPV refers to the valuation of risk-neutral financially unconstrained investors.

8Note that Y0 = 0 does not imply that the insider has no exposure to firm risk — she does, as β > 0. It simply states that her expected value going forward from participating in the firm is 0.

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from default), we have

YSB = 0 and PSB = µ

r −ρ (λσ)2

2 . (18)

Only firms with PSB > 0 receive financing. It is clear that a firm that does not receive financing in the second-best scenario without financial constraints, also does not receive financing in the baseline scenario with financial constraints. To make the analysis interesting, we make — unless otherwise mentioned — the following assumption:

Assumption 1. The parameters of the model satisfy

PSB = µ

r −ρ (λσ)2

2 > 0. (19)

.

When there are no agency frictions and λ = 0, the insider does not absorb any risk and the second-best price PSB is equal to the firm’s net present value N P V = µr. Thus, an interpretation of Assumption 1is that the (first best) NPV of the firm is sufficiently positive.

2.3 The Optimal Payout Agreement

In the following sections, we analyze the full problem in the presence of outside investors and financial constraints. We derive an expression for the value of outside equity that depends on the three endogenous state variables of the problem: the insider’s certainty equivalent Wt, the insider’s savings St, and the firm’s cash holdings Mt,

2.3.1 Reduction of the State Space

We now provide a heuristic argument to reduce the state space of the problem. We verify this argument in the proof ofProposition 2 in theAppendix D. Given the insider’s continuation value Wt, the insider’s savings St, and the firm’s cash holdings Mt, the value of outside equity under the optimal payout agreement is given by a function ˆP (Mt, Wt, St). Because of the insider’s CARA preferences, there are no wealth effects. As such, Wt and St do not separately enter the problem and only their difference Yt = Wt− St matters. Thus, we are left with the two state variables (Mt, Yt), and the outside equity value under the optimal payout agreement can be written in the form ˆP (Mt, Wt, St) = ˜P (Mt, Yt).

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Next, consider a state (Mt, Yt) = (M, Y ) with positive cash M > 0. Observe that at any time t with (Mt, Yt) = (M, Y ), the payout agreement can stipulate that the insider either receives payouts M ≥ dIt > 0 from the cash balance or injects cash into the firm; i.e., dIt < 0. The insider is indifferent between all such transfers so long as they are accompanied by a compensating change in Yt. In state (Mt, Yt) = (M, Y ), the promise-keeping constraint (14) implies that the insider’s total payoff at time t, which is given by St+ Yt+ dYt+ dIt+ o(dt) and consists of her savings St, current payouts dIt, the present value of future payouts Yt+ dYt= Yt− dIt+ o(dt), and infinitesimal remainder terms o(dt), is independent of dIt. Because payouts dI change the cash balance M by dI, the insider is indifferent between remaining at a point (M, Y ) in the state space and receiving a payout dI while moving to the point (M − dI, Y − dI), as long as M − dI ≥ 0. As payouts dI do not affect the insider’s payoff, they cannot affect the outsiders’ value function ˜P (M, Y ) under the optimal payout agreement either, in that ˜P (M, Y ) = ˜P (M − dI, Y − dI). Otherwise, payouts dI would lead to a Pareto improvement and ˜P (M, Y ) could not be the outside investors’ payoff under the optimal payout agreement.

Next, we introduce the variable C as the net cash position of the firm equal to the cash balance of the firm less the insider’s deferred payouts:

C = M − Y. (20)

Thus, we can write ˜P (Y, M ) = p(C, Y ) for some function p. Note that because payouts dI reduce both cash balance M and deferred payouts Y by the same amount, dI, they do not affect the net cash position C = M − Y . Therefore, we are left with

p(C, Y ) = ˜P (Y, M ) = ˜P (Y − dI, M − dI) = p(C, Y − dI), (21)

with M ≥ dI ≥ 0 and M > 0. As a result, ∂Y p(C, Y ) = 0, implying that the outside equity value is independent of the current value of Y . This means that we can express the outside equality value under the optimal payout agreement p(C, Y ) as a function of C only, so that P (C) = p(C, Y ) = ˜P (Y, M ) for all (M, Y ) in the state space with M > 0. By continuity, it also follows that P (C) = ˜P (Y, M ) for all (M, Y ) in the entire state space.

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2.3.2 The Optimal Security Design Problem Revisited

To translate the security design problem into a standard dynamic programming problem, we argue that maximizing the insider’s payoff is equivalent to maximizing the initial value of outside equity, P0 = P (C0). The insider maximizes her lifetime utility (5) or equivalently her lifetime payoff in monetary terms W0 = W (C, S0). Hence, the insider’s problem at time zero reads:

maxC W (C, S0). (22)

Recall that her savings at time zero are equal to the difference between the amount she raises from outside equity and the initial cash balance of the firm S0 = P0− M0. Now note that the insider’s total payoff is equal to the sum of her savings and her deferred payouts; i.e., W0 = S0+ Y0, and the net cash position of the firm is equal to the difference between the firm’s cash balance and the insider’s deferred payouts; i.e., C0 = M0− Y0. Using these relations, the insider’s problem is then equivalent to

maxC P (C0) − C0. (23)

To solve this problem, we first dynamically maximize the outside equity value P (C0) for a given level of initial net liquidity C0 and then determine the optimal level of initial net liquidity.

2.3.3 The Hamilton–Jacobi–Bellman equation

We can now derive a Hamilton–Jacobi–Bellman (HJB) equation for the outside equity value and use it to solve for the optimal payout agreement and liquidity policy. We begin by determining the dynamics of net liquidity Ct. Using equations (2), (14), Mt = Ct+ Yt, noting that by optimality dbt= 0 and ct= rWt, we have

dCt=h

µ + (r − δ)Ct− δYt−ρr

2 (βtσ)2i

dt + (1 − βt)σdZt− dDivt. (24)

Two features of the dynamics of net liquidity Ctare important to note. First, note that we can rewrite the incentive constraint given in Equation (16) as

Yt

 λ

1 − λ



Ct. (25)

While deferring payments to the insider through setting Y > 0 is necessary to maintain incentive

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compatibility, it requires the firm to hold more cash, which leads to an additional carry cost of cash δY dt reflected in the dynamics of Ct. Second, as cash-flow shocks affect both cash holdings and the present value of the insider’s payouts, exposing the insider’s compensation to cash-flow shocks through βt > 0 reduces the volatility of net liquidity below the level of cash-flow volatility σ, in that

dCt dXt

= 1 − βt< 1 = dMt dXt

. (26)

For example, a dollar cash-flow loss, dXt= −1, reduces both cash holdings Mt by one dollar and the insider’s deferred payouts Ytby βtdollars, so the firm’s net liquidity Ct falls by 1 − βtdollars.9 We conjecture that dividend payouts only occur at some upper payout boundary C, i.e., dDiv = max{C − C, 0}, so that Ct≤ C at all times t. Further, for simplicity, we impose that net liquidity C cannot become negative and thus stipulate a lower boundary C = 0 so that Ct≥ C = 0 at all times t ≥ 0. As Section 5discusses in more detail, it may be optimal under certain circumstances that net liquidity C takes negative values in that C < 0.10

On [0, C], there are no dividend payouts and an application of Ito’s formula yields the HJB equation

rP (C) = max

β≥λ,Y ≥1−λλC

 P0(C)

h

µ + (r − δ)C − δY −ρr 2 (βσ)2

i

+ P00(C) σ2(1 − β)2 2



. (27)

The dividend boundary satisfies the standard smooth pasting and super contact conditions

P0(C) = 1 and P00(C) = 0. (28)

Notably, P0(C) ≥ 1 and P00(C) < 0 for C < C, and P0(C) = 1 for C ≥ C. The concavity of the outside equity value reflects that the outside investors become effectively risk averse due to the possibility of financial distress when the firm’s liquidity reserves dwindle. Note that the concavity of P (C) and P0(C) = 1 for C ≥ C imply

C = arg max

C0≥0P (C0) − C0. (29)

Thus, C0 = C is the firm’s optimal initial level of net liquidity attained during the initial financing

9Any possible cash infusions from the insider via dItincrease Mtand Ytby the same amount. After “netting-out”

those increases, we see that the reaction of Ct to dXt remains as described.

10One could micro-found the constraint C ≥ 0 by modelling shareholders’ limited commitment, as inAi and Li (2015).

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round. Section 3.5discusses the initial financing round at time t = 0 in more detail.

As payouts to the insider dI leave the level of C unchanged but change the level of Y by

−dI (see (14)), choosing the insider’s payouts dI is equivalent to choosing the insider’s deferred compensation Y . Thus, we formulate the dynamic optimization such that Y instead of dI enters (27) as control variable. Section 3.2then determines the payouts to the insider that implement the optimal level of deferred compensation Y (C). From (27) we observe that it is costly to give the insider excess deferred compensation because of constraint (16) and the presence of a carry cost of cash. Thus, the incentive constraint (16) (i.e., (25)) is binding and we have

Y = Y (C) =

 λ

1 − λ



C and M = M (C) =

 1 1 − λ



C. (30)

Maximizing with respect to the insider’s incentives β, the first-order condition and the incentive- compatibility constraint (15) imply that

β(C) = max{λ, β(C)} where β(C) := −P00(C)

ρrP0(C) − P00(C) < 1. (31) Increasing β = β(C) not only provides incentives but also transfers risk to the insider and thus reduces the volatility of C, reducing liquidity risks. Therefore, it may be optimal to raise β(C) beyond the level λ needed to maintain incentive compatibility.

Finally, let us investigate the behavior at the lower boundary C = 0. Note that C = 0 implies M = Y = 0 (compare (30)), in that the firm has run out of cash when C = 0. As the firm does not have access to financing from outside investors after time zero, the following two scenarios are possible as C approaches zero. First, the firm relies on inside financing provided by the insider and thus never liquidates. Second, the insider does not provide sufficient financing and the firm liquidates when it reaches C = 0 with zero liquidation value.

Let us check under which condition the firm never liquidates; i.e., the first scenario holds.

For the firm to survive as C approaches zero, we need to make sure the firm’s net cash balance C cannot go negative; i.e., dC ≥ 0 as C approaches zero. This requires the volatility of dC, σC(C) = σ(1 − β(C)), to vanish so that limC→0σC(C) = 0 ⇐⇒ limC→0β(C) = 1, while the drift of dC,

µC(C) = µ + (r − δ)C − δY (C) −ρr

2 (β(C)σ)2,

stays positive so that limC→0µC(C) ≥ 0. Evaluating µC(C) in the limit C → 0 and plugging

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in limC→0β(C) = 1 and limC→0Y (C) = 0, we see that the condition for limC→0µC(C) ≥ 0 is equivalent to YA ≥ 0, with YA defined in (17). In other words, the insider is willing to provide inside financing to the firm as C approaches zero if and only if she is willing to operate the firm with a zero cash balance and no access to risk-sharing with outside investors. As limC→0β(C) = 1 is equivalent to limC→0P00(C) = −∞ (compare equation (31)), we thus have11

C→0lim P00(C) = −∞ if YA≥ 0, (32a)

P (0) = 0 otherwise. (32b)

Although there is no risk of liquidation when YA≥ 0, allowing C to approach zero is still costly for the firm because as it must rely on financing from the insider, which in turn requires a risk premium. As a result, the firm accumulates cash to reduce the chance that it must rely on costly financing from the insider. In contrast, for YA < 0, the insider is unwilling to provide sufficient inside financing, so the firm is liquidated when C = 0 and therefore accumulates cash to prevent early liquidation.12

Proposition 2summarizes our findings on the outside equity value function P (C), the dividend payout boundary C, as well as the behavior of the firm as C approaches zero.

Proposition 2. Stipulate that Ct ≥ C = 0. Then, under the optimal payout agreement C, the following holds:

1. The outside equity value P (C) solves (27) subject to P0(C) − 1 = P00(C) = 0. P (C) is strictly concave on [0, C), and P000(C) > 0.

2. Optimal dividends satisfy dDiv = max{C − C, 0}, with payout boundary C.

3. The optimal controls satisfy (30) and (31).

4. As C approaches zero, the firm is either:

(i) kept afloat by the insider if YA≥ 0, so that limC→0P00(C) = −∞ and limC→0β(C) = 1, (ii) liquidated if YA< 0, so that P (0) = 0 and β(0) < 1.

11In the knife-edge case YA= 0 in which both σC(C) → 0 and µC(C) → 0 as C → 0, it follows that limC→0P00(C) =

−∞ is equivalent to limC→0P (C) = 0 (seeProposition 2).

12Using (32) in (27) and then plugging into (31), we see that YA< 0 also implies β(0) < 1 — when liquidation is imminent, transferring all risk onto the risk-averse insider is too expensive in the absence of the upside of continued operation.

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0 0.05 0.1 0.15 0.2 0.25 0

0.05 0.1 0.15 0.2

0 0.05 0.1 0.15 0.2

0.86 0.88 0.9 0.92 0.94 0.96 0.98 1

Figure 1: Numerical illustration of the value function and optimal cash flow risk borne by the insider β(C). The parameters are such that PSB > 0 > YA, and consequently the firm is liquidated at C = 0. Appendix Adiscusses the choice of parameters for the numerical analysis.

5. When YA > 0, then C = 0 is never reached and limC→0P (C) = P0(C)YA > 0. When YA= 0, limC→0P (C) = 0.13

3 Analysis

3.1 Incentive Provision: Moral Hazard and Liquidity Management

In this section, we analyze the quantity of cash-flow risk β(C) borne by the insider under the optimal payout agreement. In standard agency models, for exampleDeMarzo and Sannikov(2006), optimal incentive provision determines this quantity. In our model, two forces are at work. To see this, let us look at the following two extreme cases. First, consider the second-best benchmark in which the outside investors are financially unconstrained and can inject funds into the firm at any time.

In this case, the insider is exposed to the minimum amount of cash-flow risk that maintains her incentives (i.e., β = λ), so the moral hazard problem determines the insider’s incentives, as is the case in DeMarzo and Sannikov(2006).

Second, consider the case in which there is no moral hazard problem (i.e., λ = 0), but outside investors are financially constrained and cannot inject funds into the firm after time zero. Even though there is no moral hazard, the insider is exposed to cash-flow risks; i.e., β(C) > 0. The reason is that transferring cash-flow risk to the insider reduces the volatility of liquidity reserves, which in turn reduces the risk of the firm running out of liquidity. At the same time, the insider requires

13To determine whether C reaches zero in the knife-edge case YA= 0 (i.e., to determine whether zero is accessible or not), one can employ the Feller test for explosions. However, it does not matter (for outside equity value) whether zero is accessible or not, as — either way — the boundary condition limC→0P (C) = 0 applies when YA= 0.

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compensation for the additional risk she bears. Put differently, β(C) in this case reflects optimal risk-sharing with the insider. While the insider has constant risk aversion ρ, the outside investors have state-dependent effective risk aversion captured by −P00(C). As liquidity reserves dwindle and the firm undergoes financial distress, the outside investors’ effective risk aversion increases;

i.e., −P00(C) increases, and it becomes optimal to transfer more risk to the insider. Therefore, the insider’s exposure to cash-flow risk increases as C decreases.

When both financial constraints and moral hazard are present, the optimal choice of β(C) reflects both liquidity management considerations and incentive provision (i.e., the moral hazard problem). When β(C) = β(C) > λ, liquidity management considerations dominate, whereas when β(C) = λ > β(C), incentive considerations dominate. Figure 1provides a numerical example of the model solution and illustrates these effects. The choice of the baseline parameters for the numerical analysis follows prior contributions in the literature and is discussed inAppendix A. As the middle panel of Figure 1 illustrates, liquidity management considerations dominate for low values of C, while incentive considerations dominate for higher values of C; therefore, β(C) decreases in C (for low C). We present our analytical findings regarding risk-sharing and incentives in the following corollary.

Corollary 1. Under the optimal payout agreement, the following holds:

1. There exists C0∈ [0, C) with ∂β∂C(C) < 0 on [C0, C].

2. For λ > 0 small, we have β(C) > λ for C close to zero and β(C) = λ for C close to C.

3.2 Inside and Outside Financing via Standard Securities

In this section, we demonstrate how to interpret the contributions of the insider and outside in- vestors to the firm’s cash balance as a form of financing by providing an implementation of the optimal payout agreement in terms of standard securities.

First, we describe in more detail the payouts to the insider. Note that payouts dI to the insider are implicitly defined as the residual that implements Y (C) = 1−λλC and ensures the incentive-

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compatibility constraint in Equation (16) binds. As shown in theAppendix E.2, we have

dI = µI(C)dt + σI(C)dZ + ξIdDiv (33) where µI(C) = 1

1 − λ

 ρr

2 (β (C) σ)2+ δ λ

1 − λC − λµ

 , σI(C) = β (C) − λ

1 − λ



σ, (34)

ξI = λ 1 − λ.

We emphasize that while payouts to the insider dI can become negative, in which case the insider injects funds into the firm, she is perfectly willing to provide such financing. In fact, at any point in time t ≥ 0, the insider is indifferent across different levels of payouts to herself, dI, and dividend payouts to the outside investors, dDiv.14 Thus, we can effectively delegate payout decisions to the insider. Observe that the insider partially covers cash-flow losses dZ < 0 when σI(C) > 0, which occurs when β(C) > λ; i.e., when the insider’s incentives are high powered. The intuition is that when the firm is low on liquidity and β(C) > λ, the insider provides inside financing to the firm. We formalize this intuition by demonstrating that the provision of inside financing can be implemented by a credit line that the insider grants to the firm.

As a first step towards implementation, let us split the transfers dIt into a credit line part, which is defined below, and which is utilized only on C < ˆC where

C := infˆ C ≥ 0 : β(c) = λ for all c ∈ [C, C] .

and a residual part dIt = 1{C

t≥ ˆC}dIt, which we will split further into preferred and standard equity.15

On C < ˆC, all transfers from (to) the insider operate through drawdowns (repayments) of the credit line. To this end, define the credit line balance as Dt = D(Ct) with an endogenous limit D and state-dependent interest rate rD(Ct), where

dDt= µD(Ct)dt + σD(Ct)dZt. (35)

Intuitively, when C < ˆC, the firm should cover cash-flow losses dZ < 0 partially by drawing on

14At any point in time, the insider solves maxdIt,dDivt≥0dIt+ dYt. By (14), the insider’s objective does not depend on dIt and dDivt, so the insider is indifferent to the choice of dIt and dDivt.

15Here, 1{·} denotes the indicator function, which equals one if {·} is true and zero otherwise.

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0 1 2 3 0

0.5 1 1.5 2 2.5

0 1 2 3

0 0.05 0.1 0.15 0.2 0.25

0 1 2 3

0 0.05 0.1 0.15

0 1 2 3

-2 -1 0 1 2

10-3

Figure 2: A simulated path of cash flow shocks that leads to default. The top left panel shows the path of cash reserves Mt, the top right panel shows the path of the credit line balance Dt, the bottom left panel shows the dividend payments to the insider ξIdDivt, and the bottom right panel shows the dividend payments of preferred equity held by the insider, µI(Ct)dt. The firm is liquidated once cash holdings Mt reach zero (at t ≈ 3.25) and the credit line Dt is exhausted.

Appendix A discusses the choice of parameters for the numerical analysis.

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its credit, whereas positive cash-flow shocks dZ > 0 should lead to repayment of the credit line balance. To construct the balance, note that when the firm loses σ dollars, i.e., dZ = −1, the reduction in cash holdings M and the increase the credit line balance D must add up to σ, so that σM(C) + σD(C) = σ where σM(C) is the volatility of cash holdings M = M (C). As M (C) = 1−λC , σM(C) = σ(1−β(C))1−λ and we can directly solve for

σD(C) = − β(C) − λ 1 − λ



σ = −σI(C). (36)

Alternatively, using Itˆo’s Lemma on the function D(C), we get a second expression for σD(C), that is, σD(C) = D0(C)σ(1 − β(C)). Setting these expressions equal, we can solve for

D0(C) = − β(C) − λ

(1 − λ)(1 − β(C)) = (1 − λ)P00(C) + λρrP0(C)

(1 − λ)ρrP0(C) . (37)

where for the second equality we used (31). Imposing the boundary condition D( ˆC) = 0, we can solve for

D(C) = 1{C≤ ˆC} 1 ρr

h

log P0(C) − log P0( ˆC) i

− λ

1 − λ

 ˆC − C



. (38)

Note that as σD(C) = 0 for C ≥ ˆC, we have a zero balance for all C ∈ [ ˆC, C]. As D0(C) ≤ 0, the credit line limit is defined by D = D(0). Lastly, note that in case the firm liquidates at C = 0, it also defaults on its credit line.

To complete the characterization of the credit line, we now construct its interest rate rD(C), so the flow interest payments on the credit line are rD(C)D(C). Recall that for C < ˆC, all transfers from and to the insider flow through the credit line; i.e., dDiv = dI = 0. Simple accounting then requires the interest payments rD(C)D(C) to account for all (smooth) changes to the credit line balance, which come from the natural drift µD(C) in the balance induced by C and the smooth part µI(C) of the transfers to and from the agent dI:

rD(C)D(C) = µD(C) − µI(C). (39)

Note that the interest paid on the credit line is state dependent, and may become (slightly) negative, something we deem optimal debt forgiveness. The insider is willing to forgive debt as the insider’s other claims—i.e., those that arise from possible future payments dI— increase more in value than the losses on the credit line.

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For C ≥ ˆC, the credit line balance D(C) is identically zero and thus has been completely paid down. With the indicator function 1{·}, the insider’s residual payouts dI(C) = 1{C≥ ˆC}dI(C) consist of

(i) smooth payouts

µI(C)dt = 1 1 − λ

 ρr

2 (λσ)2+ δ λC

1 − λ− λµ



dt (40)

that can be thought of as preferred equity with a variable rate µI(C) held exclusively by the insider, and

(ii) lumpy payouts ξIdDiv > 0 that occur exactly when outside equity is being paid out; as ξI = 1−λλ , these dividend payouts to the insider can be implemented by requiring the insider to hold a constant fraction λ of the firm’s outstanding standard equity.16

To summarize the implementation, when liquidity reserves are low, i.e., C < ˆC, the firm covers cash-flow shortfalls by drawing on both its cash reserves and its credit line, i.e., taking inside financing, while making no payments towards any form of equity. This is in contrast to other implementations in the literature (such as the ones in DeMarzo and Sannikov (2006) and Biais, Mariotti, Plantin, and Rochet(2007)), in which the firm usually either uses its cash balance or its credit line for liquidity. Also, neither the credit line nor the cash balance of the firm operate for the sake of incentives. Rather, both instruments act as hedges against financial constraints. In contrast, when liquidity reserves are high, i.e., C > ˆC, the firm covers all cash-flow shortfalls from its cash balance, while also continuously paying preferred equity. Because the insider’s incentives β(C) are highest for low values of C, the firm increasingly relies on credit line financing when in financial distress.

Figure 2uses a sample path of cash flow realizations dX and displays the resulting paths of cash holdings Mt (top left panel), credit line balance Dt(top right panel), dividend payouts accruing to the insider ξIdDivt (bottom left panel), and the payouts to preferred equity held by the insider, µI(Ct)dt (bottom right panel) under our implementation. Indeed, when the firm’s cash reserves are high, there are occasional payouts to the insider and the outside investors and the credit line balance Dt is zero. Note that the firm draws on the credit line in response to negative cash-flow shocks until the credit line and the cash reserves are exhausted, leading to liquidation.

16For a given dividend payout to outside investors dDiv, define the firm’s total dividend at C as dDiv= dDiv1−λ, where fraction λ (i.e., λdDiv1−λ ) accrues to the insider and fraction 1 − λ (i.e., dDiv) accrues to outside investors.

References

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