Dynamic Debt Negotiation

8/9/2019 Dynamic Debt Negotiation

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Topic 7 – Dynamic Debt RenegotiationCorporate Finance (Part 1)

Pierre Mella-Barral

Edhec Business School

[email protected]

Ph.D. in Finance – Corporate Finance (Part 1) Topic 7 – Dynamic Debt Renegotiation Page 1


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Overview

Default versus Liquidation Timing: Debt Renegotiation

Debt Forgiveness and Strategic Debt Service Valuing Bargaining Power



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When a firm enters a debt contract, debt-holders are toreceive a series of payments (coupon).

These promises are credible, to the extend that if

share-holders repudiate the debt contracts, i.e. do not fulfilltheir debt service obligations, debt-holders are entitled toinvoke debt collection law to seize the assets of the firms:They can force liquidation and request the Absolute Priority

Rule to be applied.



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Debt opens the following sequence of decisions:

1. Share-holders have residual control rights, defined as the rightto decide all usages of the real assets in any way notinconsistent with the contract.

In particular they decide when to abandon, in anon-cooperative fashion, i.e only maximizing the value of theirclaim (equity).That is share-holders hold a limited liability call option.

2. In the event of repudiation, debt-holders recover the control of the firm.

They can decide to force bankruptcy, but will only do so if it isin their best interest.



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Consider more carefully decision 2

Debt-holders can force bankruptcy, but bankruptcy is not optimal because as residual claimants the debt-holders bearall the costs of bankruptcy.→ prefer to renegotiate with share-holders.

This further decision is also taken non-cooperatively, but thistime by the debt-holders, i.e only maximizing the value of their claim (debt).

Debt-holders hold a liquidation call option which onlybecomes active once shareholders exercise their limited liability

call option. This is an embedded (or compound) option.

This illustrates the fact that corporate decision making mostoften involves sequences of decision which are taken bydifferent players.



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We have considered decision 1 (the limited liability option)but ignored decision 2.

That is, we have considered that in the event of repudiation,debt-holders always respond triggering liquidation. Leland(1994).

Amounts to assuming that the debt-holders’ option not toseize the assets of the firm (and renegotiate) is equal to zero.



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Debt suffers from the following moral hazard problem:

Default versus Liquidation Timing:

The ex-ante (cooperative) optimal time of liquidationdiffers fromDebtors’ ex-post optimal time of default.

Renegotiating the contract is pareto-optimal. Debt-holders’ optimal decision 2 does not consist of

immediately forcing bankruptcy.



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Debt contract concessions can be

◦ temporary, or◦ permanent

Notice:

◦ Does not assume asymmetric information.◦ Trading occurs continuously in perfect and frictionless markets.◦ Management acts in debtors’ interest.



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Empirical Evidence on Debt Renegotiation

Deviations from the priority of creditors claim on thepre-liquidation cash-flows of the firm:

◦ Firms emerge from debt restructuring with lower debt-equityratios.Leverage

◦ Firms re-enter restructuring within a few years aftercompleting restructuring.Sequences of debt reorganizations.

Deviations from the priority of creditors claim on thepost-liquidation (residual) value of the firm:

◦ Departures from the Absolute Priority Rule in liquidation(Debtors get a share of the proceeds of a liquidation sale, eventhough creditors are not completely paid-off).



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Model

Framework: Mella-Barral (1999)

Firm status described by a summary state variable, reflectingeconomic fundamentals, x t , which follows a diffusion process

dx t = µ(x t ) dt + σ(x t ) dB t .

where B is a standard Brownian motion.

Assume risk-neutrality, and a constant borrowing and lending

safe rate, ρ.



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Model

The incumbent can operate the physical assets:−→ yields a period income flow (which maybe negative insome range),

π(x t )

Alternatively, the incumbent can liquidate the physical assets:

−→ In the hands of competitors, the physical assets couldyield an income flow,

π∗(x t )

Assumption

1. At entry, π(x 0) > π∗(x 0) (otherwise already in liquidation).

2. The functions π(x ) and π∗(x ) have a single crossing point,

3. the corresponding state, x ∗, is smaller than x 0.



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Model

A representation of the set-up is as follows:



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Valuation, under the First Best Policy

Denote Π(x ) and Π∗(x ) the unlimited liability value of aperpetual claim on the income flows π(x ) and π∗(x )

Π(x ) ≡ E

∞τ

π(x s ) e −ρs ds | x τ = x

.

Π∗(x ) ≡ E ∞

τ

π∗(x s ) e −ρs ds | x τ = x .

Then the value of the firm:

U (x t ) ≡ Π(x t ) + [Π∗(x ) − Π(x )] P (x t → x ) ,

where P (x t → x ) is the Laplace transform of f t (T x ), the

density of T x , the first time at which x t hits the level x . The ex-ante optimal liquidation trigger level, x , solves the first

order condition

∂ U (x t )

∂ x = 0 .



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Valuation, under the First Best Policy

A representation of the set-up in terms of values is as follows:



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“Benchmark” Model of Debt

Creditors are a cohesive group: abstracting from the“hold-out” problem, in the presence of multiple creditors .

Tax advantage of debt is set to zero .

The status is observable to both parties, but not verifiable tooutsiders, thus cannot be part of an enforcable contract, as in

Hart Moore (1989). Debtors select their time of default in an unconstrained

fashion.

◦ Liquidity problems do not influence debtors’ decision to default.◦ No debt protective covenants imposes liquidation to the

debtors.

Infinite maturity debt contract.

Contracts can be perfectly and costlessly renegotiated.



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Debt: Standard Debt Contract

Debtors, D, promise to their creditors, C ,

1. δ : Coupon payment every unit of time. Infinite maturity .

◦ Debtors can at any time decide to repudiate the contract anddefault on their contractual obligations.

◦ If the contract is not serviced, creditors can take legal action,going to court, and force a liquidation sale.

2. C (x ): Claim on the residual value of the firm in liquidation.

◦ If the Absolute Priority Rule is applied, creditors are paid first,out of the proceeds of a liquidation sale, up to a par value, P .

◦ Then, C (x ) = min{Π∗(x ); P }).

Debt contract: C ( δ ; C (x ) )

Pre-liquidation Post-liquidation

cash flows cash flows


V l i d h S d B P li


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Valuation under the Second Best Policy

No Reorganization, as in Leland (1994):

Debtors’ claim (Equity):

D (x t | δ ) = Π(x t ) − δ

ρ +

Π∗(x D) − C (x D) − Π(x D) +

δ

ρ

Creditors’ claim (Bonds):

C (x t | δ ) = δ

ρ +

C (x D) − δ

ρ P (x t → x D)

where

P (x t → x D) =

∞t

e −ρ(T x D−t )f t (T x D

)d T x D

.

Debtors’ non-cooperative (unconstrained) optimal defaulttrigger level, x D, solves

∂ D (x t | δ )

∂ x D= 0 .


E P E A O i l Ti i


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Ex-Post versus Ex-Ante Optimal Timing

The ex-ante optimal (first-best) liquidation trigger level, x ,consists of balancing

◦ a pre-liquidation rent, π(x ), against◦ an alternative rent, π∗(x ).

whereas

Debtors’ ex-post optimal (second-best) default trigger level,x D, consists of balancing

◦ a pre-default rent, π(x ) − δ , against

◦ an alternative post-default rent, π∗

(x ) − ρ C (x ).


E P E A O i l Ti i


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The second best choice can therefore lead to eitherinefficiently early liquidations,



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E P t E A t O ti l Ti i


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Consequently,

There exists a unique level of debt service obligations, δ̃ , such thatx equals x D.

This, for any given liquidation sharing rule, C (x ), such as theAPR. Hence with the APR, there exists a unique level of

borrowings for which debtors’ optimal decision is not ill-timed .




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Renegotiation is pareto-optimal. There are two dimensions to it:

1. Leverage (as we have just see);2. Bargaining power (who internalizes the surplus to be gained in

reorganizations).


First Dimension: Leverage


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First Dimension: Leverage

Case (a): For higher levels of leverage (δ > δ̃ ),

x D > x , −→ “Early” default.It will becomes in creditors’ interest to make “deferring”concessions, prior to forcing liquidation. With respect to the

debt contract C(δ ; C (x )):

−→ Reducing the coupon δ (self-imposed debt write-off).−→ Rationale for Debt Forgiveness.

Case (b): For lower levels of leverage (δ > δ̃ ),x D < x , −→ “Late” default.It will becomes in creditors’ interest to make an “inducive”

concession, in order to have liquidation earlier. With respectto the debt contract C(δ ; C (x )):

−→ Concession on C (x ), the residual claim.−→ Rationale for Departures from the APR, in liquidation.


Second Dimension: Bargaining Power


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We have developed the intuition when creditors makeself-imposed concession.

However, instead of passively accepting or rejecting suchconcessions, debtors can actually obtain more.

Debtors’ may behave opportunistically , given creditors’willingness to avoid bearing the costs of an ill-timedliquidation (strategic debt service).

So it is important to consider the relative bargaining power

between debtors and creditors in reorganizations (afterdefault), denoted BDC .




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Consider the two limiting cases (Stackelberg equilibria).Case (i): the creditors make take-it-or-leave-it offers to thedebtors :

−→ Self-imposed concessions, BD=0C=1 .

Case (ii): vice-versa:

−→ Forced concessions, BD=1C=0 .

The surplus to be gained in reorganizations is

U (x ) − [ D (x t | δ ) + C (x t | δ ) ]

First Best Second Best

(with x ) (with x D )


Debt Renegotiation


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Debt Renegotiation

Out of the four possible cases, we now only examine

Case (a) (i): Creditors deferring, self-imposed concessions

To highlight the importance of bargaining power, we thenbriefly contrast it with

Case (a) (iI): Creditors deferring, forced concessions


Creditors deferring self-imposed concessions


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Creditors deferring, self-imposed concessions

Case (a): Higher levels of outstanding debt, leading to an“early ” default:

◦ Reorganizing the debt contract, C(δ ; C (x )), consists of

“deferring” concessions−→ Debt Forgiveness: decreasing the coupon obligation, δ .

Case (i): Creditors make take-it-or-leave-it offers to thedebtors .



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Creditors deferring, self-imposed concessions


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Creditors deferring, self imposed concessions

Separating planes, yields “corporate” debt relief Laffer curves:


Creditors deferring, forced concessions


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Creditors deferring, forced concessions

Consider now Case (a) (ii): Creditors deferring, forcedconcessions:

Shareholders essentially blackmail their creditors. Strategicdebt service

Concessions can be permanent (as discussed here), but theycould be temporary, as with debt holidays.


Case (a) (ii): Creditors deferring, forced concessions


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( ) ( ) g,

The sequence of renegotiations represented on one graph is:


Contrasting Reorganization Timing


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g g g

Strategically forced concessions occur well before creditor

self-imposed ones:


Value of Bargaining Power


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g g

Such real option models permit to measure the importance of renegotiation bargaining power (here in debt pricing).

The bond’s default risk premium with self imposed

concessions is

p C(x t , x̌ t ) ≡ δ (x̌ t ) − ρ Č C(x t , x̌ t ) ,

and similarly, with forced concessions it is

p D(x t , x̌ t ) ≡ δ (x̌ t ) − ρ Č D(x t , x̌ t ) .



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Readings

– Mella-Barral, P., and W.R.M. Perraudin, 1997, Strategic DebtService, Journal of Finance 52, 531-556.

– Mella-Barral, P., (1999) “The Dynamics of Default and Debt

Reorganization,” Review of Financial Studies , Vol. 12, No. 3,pp 535-578.


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Dynamic Debt Negotiation