Private Information and Debt Renegotiation

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Private Information and Debt Renegotiation

Collateraland Restructuring Know How as Sorting Devices

Dorothea Schäfer

Version vom 29th February 2000

Abstract

What is the role of collateral and restructuring know how in a framework of debt renegotiation and a priori private information? We show that the result in the literature according to which debt renegotiation implies that the highrisk borrower is more inclined to pledge collateral than the lowrisk borrower does not hold with unobservability of borrowers' risk class. In that scenario collateral either plays the usual role under perfect competition and enables the lowrisk entrepreneur to select himself or has no sorting potential at all. In addition, we show that the way collateral is used in debt contracts may induce investment in restructuring know how. If selfselection via collateral is working restructuring know how reduces the amount of collateral needed for separation. If collateral gives rise to pooling restructuring know how may restore sorting.

Keywords: Collateral, Debt Renegotiation, Restructuring Know How, Sorting Device JEL: G33

I am grateful for comments from participants at a conference of the DFG and in particular to my discussants Günter Bamberg and Marcel Tyrell. I thank Anette Boom, Franz Hubert and Roland Strausz for helpful suggestions and the DFG for nancial assistance.

Freie Universität Berlin Department of Banking and Finance Boltzmannstr. 20 14195 Berlin email: dorosch@zedat.fuberlin.de

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1. Introduction

The paper explores the role of restructuring know how and collateral in a framework of two dimensional asymmetric information. We model banks that lend to borrowers of a priori unknown type nancing projects with ex post unobservable outcomes. The debt contract contains a bankruptcy clause that enables the creditor to take hold of the entrepreneur's assets. But as the bank is the less ecient manager of the rm the entrepreneur has an incentive to default strategically and renegotiate his debt. To weaken this incentive the creditor may either force the owner to pledge outside collateral or invest upfront in restructuring know how. If the latter option was chosen the bank can take over eciently in the event of default. Our primary focus is on analyzing what scale of bankrm disparity in collateral's valuation counts for a separating or pooling equilibrium and how an alternative sorting device at hand inuences the nature of the credit market equilibrium.

Our research makes two points. The rst is to show that selfselection of the lowrisk borrower by pledging collateral may also arise in a framework of costlystateverication. This contra- dicts the Bester [1994] result that unobservability of project's returns leads to collateralization primarily by the highrisk entrepreneur. In fact observability of risks is crucial to Bester's conclusion. Building on Bester's framework and assuming that borrower's type is unknown we nd that collateral acts as a sorting device and thus the lowrisk borrower is more inclined to secure his debt than the highrisk borrower. Since we are in line with most of the theoretical research then, debt securization primarily by the lowrisk type seems to be a rather robust theoretical result. This is, however, somewhat puzzling if one considers the empirical literature. The main part revolving around the question as to whether the high- or the lowrisk borrower has to post more collateral points in the opposite direction (see Carey/Post/Sharpe [1998], Berger/Udell [1995] or Elsas/Krahnen [1998] and the table below).

Based on our ndings we suggest that this puzzle might be due to the fact that theoretical and empirical research concentrate on dierent stages of the creditordebtorrelationship. At the starting point of this relationship the risk class of the newcomerborrower is always somewhat blurry. Banks are therefore obliged to allow for selfselection even if debt securization is extremely expensive. As the creditor, however, learns about his clients the urge for self selection vanishes gradually. Then the collateral's potential to force proper repayment becomes the dominant motivation for debt securization and the creditor will demand collateral from the highrisk type in the rst place. By relying implicitly on the sortingbyobservedrisk paradigm (Berger/Udell [1990]), empirical research presumably captures only the second, more mature stage of this relationship. This explanation of the disparity between theory and empiricism is backed up by a empirical study of Cressy [1996]. Analyzing the nancing of business start ups the author provides evidence that lowrisk entrepreneurs indeed pledge more collateral and pay lower interest rates than highrisk borrowers.

Our second main point refers to the ongoing struggle of banks to establish eective restructuring entities and once in place to enhance permanently their eciency. We suggest that the investment in restructuring know how is not only driven by the increased default risk but also by the way collateral is used in debt contracts. First, according to our ndings workout

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Empirical Evidence:

Who has to post more collateral?

Author(s) low risks high risks

Large rms

Ewert/Schenk [1998] x x

Machauer/Weber [1998] x

Elsas/Krahnen[1998] x

Carey/Post/Sharpe [1997] x

Small rms

Harho/Körting [1998] x

Blackwell/Winters [1997] x

Berger/Udell [1995] x

Very small rms

Degryse/van Cayseele [1998] x

Cressy [1996] x

know how may economize on extremely inecient but for reasons of selfselection neverthe- less inevitable pledging of collateral. Second, if selfselection is not obtainable via collateral restructuring know how may play the role of an alternative sorting mechanism. Interestingly in such a separating equilibrium banks may earn positive prots even though there is perfect competition.

In preparation for making these main points we outline initially a model where banks know a priori the type but cannot observe the project returns directly. There are a few surprises here.

As highrisk borrowers are more inclined to default strategically than lowrisk borrowers their motivation to secure the debt is stronger. For the same reason banks do have a greater incentive to invest ex ante in restructuring know how if dealing with the highrisk borrower.

This changes, however, when we turn to twodimensional information asymmetry in the bank rm relationship. Neglecting the option to invest in restructuring know how at rst and focusing on collateral only we observe that a priori private information alters the borrower's incentive to secure his debt. It is no longer the highrisk type who posts collateral in the rst place since his threshold in terms of the bank's valuation of private nonliquid assets is lower. Instead, if (and only if) collateral's value is below that threshold a lowrisk borrower can use his non liquid endowment to separate himself. That is equivalent to saying that with unobservability of types the lowrisk entrepreneur is more inclined to secure his debt than the highrisk one.

Should collateral's value be high, distinction of types by means of collateral is not attainable.

As selfselection fails both types secure their debt and pool at one contract.

Since restructuring know how is benecial for the bad borrower in the rst place it aects both

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kinds of equilibria. If selfselection works anyway the upfront investment increases the bad borrower's prot and therefore reduces the amount of collateral needed for separation. This is certainly eciencyimproving as debt securization is extremely costly here. If collateral only gives rise to pooling restructuring know how may withdraw the high risks from the uniform contract and restore sorting. In the resulting equilibrium banks may earn positive prots. This is due to the fact that within a certain range of restructuring costs any variation of repayment or/and collateral would instantly give rise to a lossmaking pooling allocation.¹

Our paper is close in spirit to Chan/Thakor [1987] and Boot/Thakor/Udell [1991], who also studied a problem of twodimensional information asymmetry. They focus at private information about creditor's type in combination with unobservability of action choice, whereas we concentrate on ex ante private information and unobservability of project returns, the latter directly providing the entrepreneur in case of success with a strong incentive to renegotiate his debt. In addition, Chan/Chakor as well as Boot/Thakor/Udell only consider collateral whereas we allow for restructuring know how as a second instrument to weaken borrowers' ex post opportunism. Showing that in this case unconstrained availability of collateral is neither a necessary nor a sucient condition for a separating equilibrium (Bester [1985]), our paper is also related to Besanke/Thakor [1987] and Bester [1987], who used the rationing probability as an alternative sorting device. In contrast to ours, however, these papers are exclusively based on a priori private information.

Restructuring know how serves the creditor only in case of declared default. So, our approach counts for the fact that banks neither can assess new loan applicants so carefully in advance that bad projects are entirely ruled out nor do they have an incentive and the legal permission to interfere directly into the rms aairs during a quiet lifetime of a loan contract. Staying passive as long as the loan behaves normally is a rather ecient habit for the creditor (see Franks/Mayer/Renneboog [1997]). However, once default is declared passivity is no longer recommendable. Then the option to take a leading role in determining the rms actions is suddenly at hand. So, in our view default is always the turning point in the history of a bank rm relationship and the bank has certainly the highest incentive to getting itself ready to use the foreclosure option in a protable way.

Interpreting the incentives of banks to protect themselves from creditors' opportunism in this way, we contradict a recent paper of Manove/Padilla/Pagano [1998]. Like us they study the separation of highrisk and lowrisk rms and use a framework in which an eciencyenhancing upfront investment may take place. Their upshot, however, is the establishment of a screening technology that enables the bank directly to rule out all the negative netpresent value projects in advance. Suggesting that banks may be lazy, that is, they do not screen out the bad projects of lowrisk debtors as these types select themselves by posting collateral, the authors propose a weakening of creditors' rights to repossess collateral. This conclusion, however, builds heavily on the authors' assumption of a fully liquid collateral. Introducing liquidation costs in their framework, one would get results, which are in some way comparable with our own ndings.

That is, banks may use upfront investments to economize on inecient pledging of collateral

1The result of sustainable positive prots even though there is perfect competition among agents has also been developed in Bester [1995].

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which is inevitable as the lowrisk debtors do not want to be pooled with the highrisk ones.

The reminder of the paper is organized as follows. In section 2 we develop the basics of the model. Section 2.2 derives the equilibria given unobservable project returns only. In section 2.3 the twodimensional information asymmetry case is analyzed. At rst, we explore the credit market equilibria when collateral is the only instrument to restrict creditors opportunism. Then, we study the impact of restructuring know how on the dierent equilibria. We conclude in section 3. All proofs are relegated to the appendix.

2. Model description

Project and entrepreneurs

Consider a riskneutral economy. Banks are asked to nance protable risky projects since the entrepreneurs do not possess liquid funds. Each entrepreneur, however, has known non liquid private wealth ^W, which may be used as collateral ^C. The project demands the initial investment ^I and given the entrepreneur is in charge yields the high return ^xh if it is successful and^x_l otherwise. The project's returns are private information to the entrepreneur.

The creditor can only observe the true outcome after transfer of control. Depending on the entrepreneur's type ^j the probability that the projects succeeds is either ^pg or ^pb, where ¹ ^>

pg ^>^pb ^>⁰. Each borrower knows his own type.

Banks

The bank cannot distinguish among borrowers. It only knows that a fraction of the entrepreneurs are lowrisk types ^g (good borrowers) and that ⁽¹^;⁾ are highrisk borrowers

b (bad borrowers). Moreover, banks are a priori the less ecient managers. So if default is declared and the right to foreclose is exercised, the creditor has to bear a transfer related loss of ⁽¹^;i⁾ ^xi, where ⁱ ² ^fl;^hg. However, the creditor may get around this takeover costs if he chooses to invest ^S ex ante and build up restructuring know how. We assume that the upfront investment in restructuring know how is eective only if the declared failure is true. In that case it lowers the takeover cost to zero.² Denoting the creditor's decision by^k ²^f0;^Sgwe dene

k

1 if^k⁼^S

l if^k⁼^0:

We assume that an unsuccessful project can never yield higher returns than a successful project even though the bank has invested^S,

h^xh^>^xl^:

2Both assumption are without loss of generality. It can be shown that due to economies of specialization the creditor always concentrates on workouts of truly defaulting companies. In addition, allowing the take over cost to vary in the range^](1^;l^)xl^;^0]does not change the qualitative results.

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The bank may also demand collateral. If the outstanding debt has been secured and default occurs the bank liquidates the collateral at a cost of⁽¹^;⁾^C.

Consider the bank's situation if it has not invested ^S. Suppose at rst the project turns out to be unsuccessful and default is declared. The bank not knowing the true nature of state can either take possession of the entrepreneur's assets or renegotiate and forgive a portion of the outstanding debt. Since take over would depress the asset's value to_l^x_l, the creditor's dominant strategy is to reduce the repayment obligation to^xl, the maximal amount the entrepreneur pretends to have. Since ^R^;^x_l^;^C^>⁰this prospect of a lowered repayment obligation, however, creates a strong incentive to default in the good state as well. Suppose now the creditor has invested ^S. Then there is no takeover related loss in the bad state. Consequently debt forgiveness is always inferior. Facing the transfer of the rm's control to the bank with certainty the entrepreneur's incentive to default strategically vanishes.

Banks are perfectly competitive and face a perfectly elastic supply of funds. For reasons of simplicity we normalize the interest rate to zero. We do not allow for safe credits,^I ^>^xl⁺^W. Game

Figure 1 illustrates the game. In ^t ⁼ ⁰ the banks credit policy consists of the credit ^I, the (observable) upfront investment ^S, the face value ^R ^> ^I, and the amount of collateral ^C. In

t=1 the return^x_h or ^x_l is realized. Given ^x_l the owner must default. With success, however, the entrepreneur has two options. He can either repay ^R or pretend failure. In the rst case the entrepreneur receives^xh^;^Rand the creditor's net payo is^R^;^I^;^k. Mixed strategies are allowed. So, the entrepreneur may take the second option with probability ^d_jk ²^[0;^1]. Given default has been declared the lender either reduces the repayment to^xlor imposes bankruptcy.

In the rst case the owner keeps control over the project and receives ^xh^;^xl^;^C in strategic and ^;C in liquidity default, respectively. The bank's payo is^x_l⁺^C^;^I^;^k.

In case of bankruptcy the owner loses the project and the collateral. The bank's payo is

h^xh^+C^;^I^;k if the project has succeeded and_k^x_l⁺^C^;^I^;^kotherwise. The probability that the creditor actually imposes bankruptcy is denoted by^tjk²^[0;^1].

Equilibrium strategies

We solve the game of twodimensional information asymmetry by applying the concept of the perfect Bayesian equilibrium (Bester [1994]). For a start suppose ^k ⁼⁰ and the bank knows that the borrower is of type ^g. When default is declared the lender still lacks the information about the project's outcome. Let the lender expect that the entrepreneur always declares falsely,

dg⁰ ⁼¹. Since the posterior probability that^xh has been realized is^pg^dg⁰^=(pg^dg⁰⁺¹^;^pg⁾ the lender's expected payo from takeover is given by

pgh^xh⁺⁽¹^;^pg⁾l^xl⁺^C^>^xl⁺^{C :}

This implies an optimal takeover probability of^tg⁰⁼¹. Given^xh^;^R^>^;C the entrepreneur's best response to ^tg⁰ ⁼ ¹ is ^dg⁰ ⁼ ⁰. The expectation of truthtelling, however, makes the

Private Information and Debt Renegotiation