Dynamic optimal restructuring policies under debt renegotiation with positive externalities

• Published date: 01 November 2022
• Author: Pengfei Luo,Yingxian Tan,Jinqiang Yang
• Date: 01 November 2022
• DOI: http://doi.org/10.1111/eufm.12341

DOI: 10.1111/eufm.12341

ORIGINAL ARTICLE

Dynamic optimal restructuring policies under

debt renegotiation with positive externalities

Pengfei Luo

1

|Yingxian Tan

2

|Jinqiang Yang

3

1

School of Finance and Statistics, Hunan

University, Changsha, China

2

School of Finance, Jiangxi University

of Finance and Economics,

Nanchang, China

3

School of Finance, Shanghai University

of Finance and Economics,

Shanghai, China

Correspondence

Yingxian Tan, School of Finance, Jiangxi

University of Finance and Economics,

Nanchang, China

Email: yxtan6@163.com

Abstract

This paper develops a debt renegotiation model with

positive externalities using the Nash bargaining game

and explores dynamic optimal downward debt

restructuring policies in times of financial distress. We

derive closed‐form expressions for the optimal

restructuring policies. Moreover, we provide theore-

tical support for the advantages of debt renegotiation

with positive externalities. In addition, our model

could explain the violation of the absolute priority rule

for firms in financial distress. Finally, we find that debt

renegotiation is facilitated among firms with relatively

low risk and a high leverage ratio, as documented by

empirical evidence.

KEYWORDS

asset substitution, debt renegotiation, dynamic capital structure,

positive externalities

JEL CLASSIFICATION

G13, G31, G32

Eur Financ Manag. 2022;28:1227–1259. wileyonlinelibrary.com/journal/eufm © 2021 John Wiley & Sons Ltd.

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The authors would like to thank Editor John Doukas and two anonymous referees for their constructive comments,

which greatly helped in improving the paper. The authors are grateful for helpful comments from Aifan Ling,

Xuezhong (Tony) He, Yanchu Liu, and conference participants at the 15th Chinese Finance Annual Meeting

(Guangzhou) and 13th Chinese Management Annual Meeting (Hangzhou). The research reported in this paper was

supported by National Natural Science Foundation of China (Project Nos. 71901111, 71862012, and 72001074), the

Humanities and Social Sciences Foundation of Chinese Ministry of Education (19YJC630152), China Postdoctoral

Science Foundation (2018M630421), Social Science Planning Project of Jiangxi Province (19YJ38), Key Research Base

Project of Humanities and Social Science of Jiangxi Province (JD19030), Science and Technology Research Project of

Jiangxi Province(GJJ200508) and Hunan Provincial Natural Science Foundation of China (2021JJ40132).

1|INTRODUCTION

Debt restructuring is an efficient way to resolve firms' financial distress (see Gilson et al., 1990;

Sudarsanam & Lai, 2001). When a firm faces financial distress, creditors and equityholders

usually agree to enter into debt renegotiation (Chapter 11) and restructure the firm's capital

(debt), thereby allowing it to continue operating. For example, the US bankruptcy court system

received nearly 38,000 commercial bankruptcy filings in 2016, of which 80% were handled

under Chapter 11 for publicly traded firms (Corbae & D'Erasmo, 2021). Thus, debt re-

structuring is an important and extensively studied issue in corporate finance. In particular,

patterns of reorganization have been discussed from strategic debt service (Anderson &

Sundaresan, 1996; Fan & Sundaresan, 2000; Sundaresan & Wang, 2007) to debt‐to‐equity swaps

(Fan & Sundaresan, 2000; Sarkar, 2013) and pure debt‐to‐debt swaps (Mella‐Barral, 1999;

Moraux & Silaghi, 2014). To the best of our knowledge, however, the externalities of debt

restructuring are underexamined in the literature. In this paper, we therefore examine the

impact of the externalities of debt restructuring on financial policies.

We find, as shown in Table 1, that debt renegotiation (e.g., distress exchange offer in

Sarkar, 2013)

1

can cause negative externalities (i.e., lower value) for both creditors and society

since they suffer negative external losses owing to the debt restructuring offered by share-

holders (equityholders' economic activities). Using the same parameter values as Sarkar (2013),

we calculate the values obtained by creditors and shareholders under different scenarios, such

as formal bankruptcy (without debt renegotiation) as well as failed and successful debt re-

negotiation.

2

As seen in Table 1, when debt renegotiation fails, the benefit (i.e., liquidation

value) obtained by creditors, 6.6306, is less than that without renegotiation (i.e., formal

bankruptcy), 8.7276, while the benefit obtained by shareholders, 0, is also lower than that

without renegotiation, 0.7752. In other words, debt renegotiation results in significant dead-

weight losses for creditors and shareholders. Moreover, even if debt renegotiation is successful,

when shareholders have relatively strong bargaining power (e.g.,

η

=0.

6

), the value obtained

by creditors, 8.4023, is still less than that without renegotiation, 8.7276. That is to say, even if

the debt renegotiation does succeed, it can lead to losses for creditors. In fact, Sarkar (2013)

supposes that shareholders can force concession from creditors by focusing on the default

liquidation threat when the firm is in financial distress. However, the shareholders make the

distress exchange offer before they would declare bankruptcy. Namely, the restructuring

threshold provided by shareholders is above the default threshold under formal bankruptcy.

Thus, Sarkar (2013) rules out the argument that the liquidation threat for renegotiation might

not be a credible threat for creditors since it would be better for shareholders to continue

servicing the existing debt,

3

and Silaghi (2018) makes a similar argument in the introduction.

Meanwhile, a failed renegotiation offer results in the forced liquidation of the firm (Christensen

et al., 2014), which leads to losses for both shareholders and creditors, as displayed in Table 1.

1

The distress exchange offer of debt restructuring in Sarkar (2013) consists of two parts: the coupon level will be

reduced from the initial coupon

c

to a lower coupon

b

and creditors will be given a fraction

ρ

of the restructured firm's

equity, where equity stake

ρ

depends on their relative bargaining power.

2

Incorporating renegotiation frictions, debt renegotiation can fail with a certain probability and lead to early default, as

discussed by Davydenko and Strebulaev (2007), Favara et al. (2012), Morellec et al. (2014), and Antill and

Grenadier (2019).

3

Similarly, the debt renegotiation model for strategic debt service in Sundaresan and Wang (2007) also exists the threat

becomes non‐credible given that equity holders threaten to liquidate the firm. Because we find that the shareholders

make the strategic debt service before they would declare bankruptcy.

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LUO ET AL.

In a word, from the above analysis, the debt renegotiation described by Sarkar (2013) can result

in negative externalities for both creditors and society.

Since the debt renegotiation pattern mentioned above can cause significant negative ex-

ternalities, revising debt restructuring to a greater extent, such that it always has positive

externalities, could be socially optimal.

4

In other words, a new debt renegotiation pattern

provided by the shareholders should benefit the creditors (or society) and that they will not

need to pay the cost. In times of financial distress, renegotiating at a later time instead of earlier

would be beneficial to both creditors and shareholders because this strategy not only can create

higher tax shield interest and lower bankruptcy loss costs, but also alleviate and even mitigate

deadweight losses if the renegotiation fails. In the extreme case, when the restructuring

threshold is much closer to the default level of formal bankruptcy, creditors and shareholders

receive only the liquidation value and zero, respectively, which does not create any losses for

them even though the restructuring has failed. Hence, the debt renegotiation offered by

shareholders might not cause any negative externalities in this case. Furthermore, both cred-

itors and shareholders always obtain a partial net surplus from debt renegotiation, but only if

the two parties possess a certain amount of bargaining power. Thus, positive externalities and

Pareto improvement are involved. Our study examines this debt renegotiation pattern with

positive externalities.

5

In contrast to the studies mentioned above, we present a debt renegotiation model with

positive externalities through a Nash bargaining game and investigate dynamic downward debt

restructuring policies when a firm is in financial distress. We assume a firm has assets in place,

that are already financed with straight bonds (bank loans) and equity, as well as debt re-

negotiation options to restructure debt levels when in financial distress. A novel feature of our

new debt renegotiation model is positive externalities. We assume that creditors have an op-

portunity to decide whether to accept or reject the debt restructuring proposal offered by

shareholders. If it is refused, shareholders will continue running the firm and will pay the

promised coupon until the conditions become even worse. In other words, creditors accept only

credible debt restructuring offers that benefit themselves. The distribution of the benefits from

TABLE 1 Debt renegotiation described by Sarkar (2013).

μ

rσα τc= 0, = 0.06, = 0.2, = 0.35, = 0.2, =

1

η

=0.

6

may cause negative externalities for both creditors and society

Sarkar (2013)

Debt renegotiation Without With (successful) With (failed)

Value obtained by creditors 8.7276 8.4023 6.6306

Value obtained by shareholders 0.7752 2.6577 0

4

An externality is an economic term referring to the fact that the behaviour of an economic agent (country, enterprise,

or individual) directly affects other economic agents without any corresponding payment or compensation. An

externality can be either positive or negative. A positive externality suggests that the economic activities of an

individual benefit others or society and that the beneficiaries do not need to pay the cost. Conversely, a negative

externality suggests that the economic activities of an individual harm others or society but the individual in question

does not bear the cost. Some studies have investigated how externalities affect firms' business policies in corporate

finance. For example, Dcamps and Mariotti (2004) and Kwon et al. (2015) investigate the effects of externalities on

investment decisions.

5

We consider shareholders and creditors to be two different economic entities in our paper. Since debt restructuring

provided by shareholders can benefit the creditors and society, we use positive externalities to describe it.

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