CREDIT SCORING AND RELATIONSHIP LENDING: THE CASE OF ... · 4 Von Thadden (1995) shows that a long-term line of credit with a termination clause can balance the costs of the hold-up

CREDIT SCORING AND RELATIONSHIP LENDING:

THE CASE OF GERMAN SME

Patrick Behr, University of Frankfurt1

André Güttler, University of Frankfurt2

Dankwart Plattner, KfW Group3

Version 16. March 2004

Abstract

We estimate a logit scoring model for the prediction of the probability of default of Ger-

man SME using a unique dataset on SME loans in Germany provided by Germany’s big-

gest, governmental owned SME financier, the KfW Group. Our scoring model allows

SME to compute their default risk which, in turn, can be used to approximate their risk

adequate cost of debt. This knowledge is likely to lead to a detection of hold-up problems

German SME might be confronted with in their bank relationships. Furthermore, it can

influence their future financing decisions towards capital market based financing.

Keywords: SME, relationship banking, hold-up problem, credit scoring

JEL classification: G21, G32, G33

1 Patrick Behr, Chair of International Banking and Finance, University of Frankfurt, Mertonstr. 17, 60054 Frank-furt, Germany, tel. +49 6979823984, fax +49 6979828272, [email protected] (contact author). 2 André Güttler, Chair of Banking, University of Frankfurt, Mertonstr. 17, 60054 Frankfurt, Germany. 3 Dr. Dankwart Plattner, KfW Group, Palmengartenstraße 5-9, 60325 Frankfurt, Germany. The views expressed in this article are solely those of the authors and do not necessarily reflect official positions of the KfW Group.

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1. Introduction

Bank financing is the dominating source of external financing for German Small and Medium

Sized Enterprises (SME). On the other hand, equity ratios of German SME spread within a

wide range but, according to most available sources, do not exceed 20% on average which

illustrates the need of other sources of financing. Since SME usually don’t have access to

organized capital markets bank financing often remains the only alternative. In capital-market

based financial systems, i.e. USA or UK, bank lending takes place at arm-length. In contrast

to that, bank lending in Germany, a country that is well-known for its bank-based financial

system, is generally exercised through close, long-term relationships between banks and their

customers.1 This way of providing companies with bank loans is widely known as the Haus-

bank principle. One major characteristic of the Hausbank principle is that companies with a

Hausbank typically don’t have multiple bank relationships. This puts Hausbanks in the posi-

tion to exert market power that can lead to hold-up problems for the borrower. The change of

a bank relationship is costly for the debtor because a new bank does not have the same

amount and quality of information on her that the former Hausbank has and will therefore

charge the debtor a risk premium that accounts for the lack of information. These so-called

switching costs2 allow Hausbanks to extract higher margins that do not necessarily correspond

to the risk inherent in a loan but are likely to exceed this risk adequate cost of debt. Further-

more, banks do not have incentives to provide their debtors with detailed information about

the way they calculate the individual loan risk. The asymmetric information problem in a

bank-customer relationship can be effectively reduced when the bank that finances a com-

pany’s corporate activities is a Hausbank. The reduction of information asymmetry is, how-

ever, only one-sided: it remains in the customer-bank direction. Since this puts the Hausbank

in a situation where she can exert monopolistic market power she has no incentive to increase

the level of transparency about the way loan risk is measured and incorporated in the loan

price. An effective reduction of this lack of transparency could put the debtor in a position to

renegotiate loan conditions on the basis of a larger set of information on her, it could lead to

reduced switching costs by increasing the probability of successfully changing the bank rela-

tionship at better terms or it could open ways for alternative sources of financing thus enlarg-

ing the scope of the firm’s financing decisions.

Based upon a unique dataset on loans to German SME provided by the KfW Group, the big-

gest, governmental owned supplier of SME financing in Germany, we estimate a scoring

1 See Allen and Gale (2001) for an overview of prevailing financial regimes in different countries. 2 Switching costs do not only incorporate the risk margin but also search costs for a new bank and other internal costs associated with a new bank relationship.

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model applying logit analysis to the dataset. This model allows SME to calculate their ex-

pected Probability of Default (PD), which we argue to be a good proxy for individual loan

risk as measured by internal bank ratings (and rating agencies).3 In homage to the well-known

Z-Score introduced by Altman (1968) we refer to our model as the German Z-Score.

The impact of the knowledge of the German Z-Score or the approximate risk adequate cost of

debt, respectively, by SME can be twofold: First, it potentially leads to a detection of hold-up.

This strengthens the position of SME in future negotiations of their debt conditions and re-

duces the costs for the search of new lenders. Second, it can be a first step towards an external

rating that opens the way for alternative sources of external debt financing thus reducing the

prevailing financing restrictions German SME face. We argue that both impacts widen the set

of financing decisions German SME can opt for.

The main contribution of this paper to the existing literature lies in trying to build a bridge

between the credit scoring literature that is of rather practical relevance and its application to

phenomena such as hold-up in relationship lending. The particular value of our empirical

analysis arises from the fact that it is based upon a unique dataset on SME loans in Germany

that, in this form, can only be provided by the KfW Group.

The paper is organized as follows: In chapter 2 we give an overview of related literature on

relationship lending and its negative sides as well as of literature on financing restrictions of

SME. Chapter 3 is devoted to the description of the financing situation of German SME in

order to point out the dominant role of bank financing. In chapter 4 we describe the dataset

and conduct the empirical analysis. The impacts of the German Z-Score on SME lending in

Germany are discussed in chapter 5. Chapter 6 summarizes our findings.

2. Literature Overview

Hausbanks may be defined as the premier lender of a firm having more detailed and timelier

information about their customers than a comparable arm’s-length bank. A Hausbank can

effectively reduce the information asymmetry in the bank-customer-relationship (Elsas and

Krahnen (1998)). Borrowers with Hausbanks benefit from increased credit availability (Peter-

sen and Rajan (1994 and 1995)) and are less likely to pledge collateral (Harhoff and Körting

(1998)). However, there is also a dark side in relationship banking. The proprietary borrower

information that Hausbanks obtain as integral part of their relationships may result in an in-

3 According to Basle II loan risk measuring should be based on predictions of the PD, Loss given Default (LGD), Exposure at Default (EAD) and Effective Maturity (M). Banks using the foundation Internal Ratings-based Approach will be provided fixed values for LGD, EAD and M by bank regulation authorities. The PD estima-tion, on the other hand, will be conducted by means of applying internal rating systems.

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formation monopoly (Boot (2000)) which, in turn, might lead to hold-up problems that mate-

rialize in Hausbanks charging interest rates on loans that are ex-post too high (Sharpe (1990),

Rajan (1992), Weinstein and Yafeh (1998)). Such loan conditions do not properly reflect the

true loan risk of a borrower and therefore do not lead to a “fair” credit price. Degryse and Van

Cayseele (2000) find that loan rates of small Belgian firms increase with the endurance of a

bank-firm relationship. Angelini et al. (1998) come to the same conclusion for customers of

non-cooperative banks in Italy. These findings suggest that the hold-up problem is more emi-

nent in the bank-based financial systems that can be found throughout Europe. To reduce the

hold-up effect firms can opt for multiple bank relationships (Rajan (1992), Houston and

James (1996), Farinha and Santos (2002), Howorth et al. (2003)).4 However, in accessing a

new source of bank financing, the firm faces an adverse selection problem, arising because of

new lenders having less information than relationship lenders (Detragiache et al. (2000)).

Hence, a new bank might suspect the borrower to incorporate a high default risk and would

charge a higher interest rate than the rate adequately reflecting the default risk of this bor-

rower. This allows Hausbanks to extract higher margins at the cost of their borrowers.

Closely related to the relationship banking literature, there is a fast growing strand of litera-

ture on financing constraints of SME. Their non-corporate form, higher business and financial

risks and the higher degree of information asymmetry limit the availability of alternative ex-

ternal sources of financing (e.g. Apilado and Millington (1992)), especially in bank-

dominated countries like Germany. SME thus depend heavily on bank loans to finance their

corporate activities. If their Hausbanks tighten loan volumes, SME are likely to face financing

trouble (Haron and Shanmugam (1994)). The on-going consolidation of the banking industry

may also lead to a decrease in the amount of credit available to SME. Some researchers (e.g.

Keeton (1995)) have raised concerns that such consolidation indeed reduces credit availability

to SME.5

3. The role of bank financing for German SME

Bank loans play an important role in the external financing of corporate activities of German

SME (Plattner (2003)). The German Central Bank finds that for companies with an annual

turnover of EUR 12.5 to 50 million bank loans accounted for almost a fourth of the overall

4 Von Thadden (1995) shows that a long-term line of credit with a termination clause can balance the costs of the hold-up problem and the benefits of ex-post competition. Such a line of credit generally stipulates that the lender may terminate the lending relationship but, if she chooses to continue it, she should do so at pre-specified terms. This combination of a termination clause and the possibility to continue only at pre-specified terms gives the lender limited bargaining power. Thus, multiple bank relationships may not be needed. 5 Though other researchers found little reason to argue in this direction (e.g. Peek and Rosengren (1998)).

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financing (Deutsche Bundesbank (2000)). For smaller firms, having an annual turnover of less

than EUR 12.5 million, the share of bank loans ranged from 33% to 40% of total liabilities in

1996. Since the share of bank loans as a source of (overall) financing declines as the company

size increases, the relative importance of bank financing for SME is higher than for bigger,

publicly listed companies that surely have access to other sources of external debt financing.

In contrast to that, corporate bonds play a negligible role as a source of SME financing. SME

generally do not obtain a costly external rating to build up reputation and signal their credit-

worthiness to investors. Besides, the required volumes for public debt issuances usually

amount to volumes beyond EUR 100 million which does not seem to be suitable for SME.

This leads to the conclusion that the importance of bank loans is extraordinarily high thus

underlining the dependence of German SME on their bank relationships. In times where eco-

nomic downturns result in a tightening of the overall volume of credit available, SME will

face severe financing problems that increase the default risk of those companies. Most re-

cently, German banks reported record high losses in their commercial credit business forcing

some of the major German banks to announce a cutback of their supply of credit. According

to the time series database of the Deutsche Bundesbank, the four biggest private banks cut

back their supply of commercial loans between the maximum volume in mid-2001 and end-

2003 by 15.8%.6 Even though public sector banks might have closed this financing gap to

avoid a credit crunch in the German economy, a change of the bank relationship is costly for

companies who suffer from the cutback of credit supply. Since at the same time the impor-

tance of bank financing increased substantially7 the strong dependence of German SME on

bank loans becomes ever more obvious.

As bank financing plays such a dominant role in financing German SME, their equity ratios

are relatively low. According to a study by the KfW Group the weighted average (median)

equity ratio of German companies amounts to 28% (17%). For smaller firms the values are

even lower (Plattner (2003)).8 Dufey and Hommel (1999) observed that average equity ratios

for German SME fell from 31% to 17% during the period 1967-94.

Given the high dependence on bank financing and the low equity ratios one way to change

this financing situation could be to strengthen the equity base. A straightforward solution for 6 Hommel and Schneider (2003) underline this observation. In their survey 42% (37%) of the participating com-panies reported a reduction in short-term (long-term) loan availability in 2002. Firms of smaller size were par-ticularly affected by this. Plattner (2003) reports that the number of companies with a worsening in loan condi-tions was significantly higher than the number of firms with improved loan conditions. These figures are even looking worse for small firms. 7 According to a survey of the German Chamber of Commerce (DIHK) 28% of the participants in the survey reported an increased importance of bank loan financing (DIHK (2002)). 8 The Deutsche Bundesbank reports a somewhat similar figure of 25% which declines with firm size (Deutsche Bundesbank (2003)).

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this is to raise equity by means of initial public offerings (IPO). But the downturn of equity

markets that started in September 2001 dried out the German IPO market: The official statis-

tic of the German Stock Exchange reported that in 2002 only three companies went public, in

2003 not even one. Besides, even if there still were a well-functioning equity market the great

majority of German SME would not feel eligible to issue equity. According to a survey by

Hommel and Schneider (2003) on the financing situation of German SME almost 90% of the

interviewed firms indicated they would not feel ready yet for an IPO. Private equity (PE)

might be a solution but there is strong reason to argue that it is only suitable for a minor part

of German SME given the high required returns of PE-investors and the reluctance of com-

pany owners in Germany to give away control rights (Hommel and Schneider (2003), Plattner

(2003)). We conclude from these observations that neither public nor private equity seems to

play an important role in strengthening the weak equity base of German SME and to change

the prevailing financing patterns.9 Summing up these observations we come to the conclusion

that the financing situation of SME in Germany can be characterized by a strong dependence

on bank loans, and a minor relevance of alternative forms of external financing.

The more important bank financing, relative to other sources of financing, the higher the de-

pendence of firms on their bank relationships thus increasing the weight of information mo-

nopolies of Hausbanks. Since bank financing often remains the only obtainable source of ex-

ternal financing, in addition to the potential hold-up problems, German SME face severe

financing restrictions that are likely to increase the degree of hold-up exerted by Hausbanks

on their customers. Therefore it might be desirable for German SME to have a mechanism

that allows the widening of their scope of financing decisions.

4. Empirical Analysis

4.1. Dataset

The sample for the empirical analysis is based on a database of the KfW Group which is

Germany’s biggest promotional bank. One of the main aims of the KfW is to finance German

SME. To achieve this, the KfW does not grant loans directly to SME but rather to banks who

pass the money on to the SME that requires the loan. That is, if a SME requires fresh money

to finance investment activities she demands a KfW-loan from her (Haus)bank while the bank

refinances herself by means of borrowing money from the KfW. A potential moral hazard

problem is avoided by the fact that in most cases banks are fully liable for these credits. Since

all German banks – private banks, co-operative banks and public sector banks – can forward 9 This is mainly due to the underdeveloped German equity markets. Another reason might be that the German tax system in the past discriminated building up equity by withholding profits (e.g. Hommel and Schneider (2003)).

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their customers’ loan demands to the KfW the data sample does not contain any selection bias

in that direction. All companies in the dataset were, at the time of their loan application, in a

stable financial situation. There is no adverse selection with respect to the most needy SME

debtors. Every German firm with less than EUR 500 million in annual sales (including affili-

ated companies), that fulfills common creditworthiness criterions of commercial banks, can

apply for a KfW loan. Hence, we view KfW`s debtors to be neither a positive nor a negative

selection of German firms.10 The KfW-Database contains balance sheet and P+L statement

data of German SME based on standardized application forms including up to 30 different

variables. Most companies in the sample are represented by at least two accounts. At the time

of their loan application the average account is not older than 14 months. The database origi-

nally contained 129,922 annual accounts from 73,467 companies.11

Datasets with missing values and implausible information were eliminated from the sample.12

In case of a loan default of a company the banks are obliged to inform KfW about the default

event. Many of those defaults were accompanied by an insolvency in the legal sense. The

balance sheet data of the companies in the KfW-Database might, at the time of default, be

several years old. For the model estimation we therefore only included companies that re-

ported data not having a time gap greater than three years between the end of the last report-

ing year and the year of the loan default. The resulting sample contained 760 default observa-

tions from 485 companies. Annual accounts of solvent companies were included in the

sample in all cases in which they were not older than 1992. After these adjustments the sam-

ple contained 88,402 annual accounts from 40,154 companies. There is reason to assume that

the data adjustments led to significant differences between the original database and the sam-

ple we used for the analysis. Therefore we tested for mean differences between both samples.

The results of the test are summarized in table 1:

< table 1 about here >

As the results suggest there are significant mean differences of the return on sales level vari-

able, the depreciation ratio and temporary liquidity problems. We, however, argue that the

biases that arose from the adjustments do not provide ground for material critique. The further

10 A comparison to other available datasets (Deutsche Bundesbank, German Association of Public Sector Banks, BACH) has further shown that our sample does not contain a bias towards companies that are in a bad financial situation. 11 2,500 annual accounts of housing associations are not included in the KfW-Database because their balance sheet and P+L characteristics are too different from the rest of the database. 12 We are well aware that from a methodical point of view there are superior solutions to deal with the problem of missing values than elimination, namely (multiple) imputation. However, we believe that given the overall stability of the sample’s structure the application of this advanced technique would not lead to better results.

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analysis will show that neither the absolute level of the return on sales nor the absolute level

of the depreciation ratio have a strong economic impact on the default risk of German SME.

Moreover, we show that the estimated model delivers robust results as compared to the de-

fault risk measured by S&P and Moody’s.

Since neither the original KfW database nor the sample that resulted after the adjustments is

fully representative for the population of all German companies with regard to sector, legal

form, and size of the companies we compared our sample to the German VAT statistic which

is the best proxy for the whole population of German companies (table 2).

<table 2 about here>

The comparison shows that the Retail/Wholesale sector is underrepresented in our sample,

whereas the manufacturing sector is considerably overrepresented. Moreover, the size struc-

ture of our sample is biased towards larger companies because companies of sole proprietor-

ship are underrepresented in the sample. Such a bias may arise due to the fact that bigger

companies are assumed to have better information about the loan programs of the KfW. The

true reason is, however, not clear. Besides the better information argument it may be that

large companies are more likely to be economically active and need more loans to finance

their activities. Another possible explanation is that those companies invest more steadily.

This should lead to an increase in the demand for loans.

4.2. Methodology

Statistical credit scoring models try to predict the probability that a loan applicant or existing

borrower will default over a given time-horizon, that is, they measure the individual default

risk of a borrower – usually over a time-horizon of one year.13 As data input for the prediction

serve historical data a bank obtains from her customer relationships. These data are supposed

to contain information on the default risk of a borrower and are transformed into a credit score

that aims at isolating the effects of various borrower characteristics on her probability of de-

fault. The model produces a score the bank takes to rank her actual and potential borrowers

according to their individual credit risk. To construct a scoring model historical data on the

performance of all loans in the loan portfolio have to be statistically analyzed in order to de-

termine the borrower characteristics that are useful in predicting whether a loan will perform

well or poorly. Hence, a well-designed14 model should result in a higher percentage of high

13 According to the Basle Committee on Banking Supervision (BCBS) banks are required to measure the one-year probability of default for the calculation of the equity exposure of loans (BCBS (2003)). 14 The term design refers to the sharpness of the model in this context.

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scores for borrowers whose loans will perform well and a higher percentage of low scores for

borrowers whose loans will perform poorly. Moreover, the model should be well-calibrated.

A well-calibrated model yields – in the ideal case – as many realized defaults as predicted by

the model.

Historically, discriminant analysis and linear regression have been the most widely used

methods for constructing scoring systems (Hand and Henley (1997)). Altman (1968), who

was the first to use a statistical model to predict default probabilities of firms, calculated his

well known Z-Score using a standard discriminant model solely based on five financial vari-

ables. Almost a decade later Altman et al. (1977) modified the Z-Score by extending the data-

set to larger-sized and distressed firms. The model parameters, however, remained unchanged.

This model was for many years one of the most prominent models for the calculation of a

borrower’s credit risk and the first one that aimed at objectifying the credit risk evaluation of

banks’ borrowers. Besides this basic method, more accurate ones such as logistic regression,

neural networks, smoothing nonparametric methods and expert systems have been developed

and are now widely used for practical and theoretical purposes in the field of credit risk meas-

urement (Hand and Hanley (1997)).

In this study we use a binary logistic regression model, which, in our view, is a suitable

method of measuring individual credit risk.15 The dependent variable in a logistic regression

is a dummy variable that takes the value 1 if a borrower defaulted in the observation period

and 0 otherwise. Independent variables are all potentially relevant parameters that may drive

credit risk. Among these are firm specific characteristics and soft facts. The basic logit model

takes the form

( )[ ] eBXaPD1PD/In ++=− (1)

where PD is the probability that a firm goes bankrupt; a is the coefficient of the constant term;

B is a vector of coefficients of the independent variables; X is a vector of independent vari-

ables and e is the error term that is log-normally distributed by assumption. The coefficient of

the constant and the vector B are estimated through maximum likelihood estimation.16 The

transformation of the dependent variable constrains PD to be in the interval [0;1].17 This stan-

15 Frerichs and Wahrenburg (2003) and Plattner (2002) use a logit model to predict the default risk of German companies. The use of a discriminant model to measure credit risk has not been considered here because of several problems that can occur when using this method. See Eisenbeis (1977) for a discussion of these prob-lems. 16 All estimations have been run using the econometrics package Stata 8.2. 17 By solving the logit function for p one can see that all values of p cannot lie outside the interval [0;1].

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dardization is one of the main advantages of logit regression models and allows for the com-

putation of the probability of default of a borrower by just plugging the borrower specific

variable values into the estimated logit function. According to the data and methodology we

applied the result of the logit regression is the three year cumulative default rate (PD_cum3)

( )[ ])1BX)*((aexp113PD_cum −++= (2)

This three-year default rate can be transformed18 into the one-year default rate (Moody’s

(1995))

( ) 31311 /cum_PDPD −−= (3)

We refer to the outcome of this transformation as the so called German Z-Score.

4.3. Hypotheses and variables

The dependent variable of our logistic regression model is the observed credit default of a

company. In the majority of those cases, an insolvency was associated with the credit default.

The independent variables and their expected influences on the default risk are:

1. Equity ratio of the firm (Equity/Assets * 100)

Following the argumentation in chapter 3 we expect a higher equity ratio to lead to a decrease

of the default risk of a SME.

2. Equity ratio growth (1, if the average growth rate was positive; 0, else)

A positive equity growth rate over time signals an improvement of the financial situation that

is likely to lead to more stability. Therefore it should result in a decrease of the default risk.

3. Return on sales (Profits after taxes/Sales * 100)

The higher the return on sales the lower the default risk. Since a high return on sales is a posi-

tive signal for a good market position of the firm it should reduce the default risk.

4. Return on sales growth (1, if the average growth rate was positive; 0, else)

A positive return on sales growth rate should have the same impact as the equity growth rate.

Again, a growth of the return on sales gives rise for the assumption that the company becomes

more stable which, in turn, reduces the default risk.

5. Depreciation ratio (Depreciation/Sales * 100) 18 We assume that the marginal default rates are constant over all years.

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The higher the depreciation ratio, the lower the default probability. Depreciations of fixed

assets are due to former investments. As these are, i.e., new machines and the like, the firm

should be better prepared for the future.

6. Temporary liquidity problems (1, if the bank reported temporary liquidity problems of the

borrower to KfW at the time of the loan application; 0, else)

Temporary liquidity problems indicate a higher default probability. If a firm faces an in-

creased demand for liquidity because, for instance, of lower sales the firm has a higher default

risk even if her bank is providing a new loan.

7. External equity financing (1, if the external equity provider refinanced the equity invest-

ment through the KfW; 0, else)

Firms with external equity financing need additional capital, primarily for innovative and

risky projects. The higher risk of these projects leads to a higher default risk since equity in-

vestors are likely to abstain from providing new money in case the company can’t earn the

promised rate of return.

8. Size (according to six classes of annual sales)

Smaller companies have a higher default risk due to more severe restrictions with regards to

capital- and credit markets financing compared to larger firms (liability of smallness).

9. Business sector (according to the four classes construction, service, retail/wholesale, and

manufacturing)

Firms of the construction sector are expected to have a higher default probability. The con-

struction sector in Germany is experiencing an economic crisis that began in the mid-nineties

of the last century. The end of this crisis is not yet foreseeable. The difficult economic situa-

tion of firms from the construction sector should lead to a higher default risk of those firms.

10. Location of Headquarter (Eastern or western part of Germany)

Firms with their headquarter in the eastern part of Germany face a higher default risk. They

are on average younger, have worse cost structures and act in a more difficult economic envi-

ronment. Furthermore, banks are very strict in providing loans to companies located in that

region.

11. Legal form (according to the three classes sole proprietorship, partnership, and corpora-

tion)

Companies that are organized as partnerships and corporations are expected to bear a higher

default risk. This is due to the liability of those companies. Whereas the owner of a sole pro-

prietorship company is liable with her private wealth, some partnerships – and all corpora-

tions – are organized as limited liability companies. A single, fully liable owner can be as-

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sumed more disposed to provide the company with new equity in an attempt to avoid a loan

default. In a limited liability company this should be less likely to occur.

4.4. Results

The results of the estimated logit-model are summarized in table 3. The outcomes for the eq-

uity ratio growth and the return on sales growth as well as both level variables confirm our

expectations. The results show clearly that an improvement in both variables leads to a more

stable company situation and therewith reduces default risk. The result for the depreciation

ratio is in line with our hypothesis. A high amount of depreciation demonstrates a high degree

of investments that are likely to positively influence the economic future of a company. A

company with external equity financing is usually riskier than a comparable company without

external equity, again confirming our expectations. Thus, the default risk of such companies

should be higher than for ones without external equity. It is important to note that the coeffi-

cient is of high economic relevance but of lesser statistical significance. The coefficient for

actual liquidity problems is the highest among the group of independent variables. The results

also show the regional factor to be an important driver of a German SME’s default risk, con-

firming the assumption that companies in the eastern part of Germany are substantially riskier

than their western Germany counterparts. This difference can not be tied back to structural

problems of some business sectors because structural effects have been controlled for in the

regression (interaction terms have not been significant during the model-building stage). The

results for the size variables are surprising because they do not verify our hypothesis.19 Com-

panies of medium and bigger size in the sample bear a higher default risk than small compa-

nies. This stands in contrast to other empirical studies that found small companies to be more

likely to default. The common argument for this finding is that such companies have less di-

versified production and distribution markets and more serious financing problems. Audretsch

(1995) found that, further to the actual company size, the size at the point of opening the

business is a key determinant of the default risk, that is, the bigger the size of the company at

the point of opening the smaller the default risk.20 However, most of the studies analyzing the

influence of company size on the default risk lack an appropriate number of company indi-

vidual influence factors with the consequence that these factors are reflected in the company

size. In our study we were able to explicitly measure the impact of company individual vari-

ables such as equity or depreciation ratio and therefore the results are easier to interpret.

19 They do not change if we use other variables than the yearly earnings as a proxy for the company size. 20 Dunne and Hughes (1994) come to a different conclusion. In their study company size and defaults are nega-tively correlated.

13

Companies of the construction sector are riskier than companies from one of the other three

sectors, confirming our expectation. Companies organized as partnerships have a higher de-

fault risk than ones with only one proprietor. Since owners of sole proprietorship companies

are liable with their entire wealth in case of a default they might have stronger incentives to

put additional equity at the company’s disposal to avoid a default. In contrast to that, in a

partnership there may be a severe coordination problem. Furthermore, partnerships in Ger-

many are often (but not necessarily) organized as limited liability companies thus the costs of

a default are smaller and the avoidance of an insolvency event is less desirable. The same

applies to corporations that are solely organized as limited liability companies.

< table 3 about here >

The absolute height of the coefficients of a logit model do not allow to directly infer the

strength of the influences of the independent variables but only the direction of influence and

its relative strengths. We therefore computed the marginal effects of all independent variables

used in the model for a selected reference company. The results that are given in table 4 are

thus only valid for that particular company21:

<table 4 about here>

A positive sign means that the PD increases with the variable, a negative one has the opposite

effect on the PD. The absolute levels of the equity ratio and of the return on sales are of minor

relevance whereas the growth dummies have a much bigger impact on the PD of a German

SME. As the coefficients of the logit model suggested the strongest influence on the PD of a

German SME comes from temporary liquidity problems. Everything else equal, the reference

company with temporary liquidity problems has a 1.33% higher PD than the reference com-

pany without such problems. This does not change if the Hausbank views the liquidity prob-

lems to be only of temporary character. The result is somewhat surprising. Even though the

bank views the liquidity problems to be temporary and provides the company with new capi-

tal it seems to be difficult to recover from these problems.

4.5. Model accuracy

We are well aware that a model solely using quantitative data might not be regarded to be of

good predictive accuracy relative to more complex rating systems using the same data plus

additional information on the borrowers in the sample, i.e. rating systems of external rating

agencies or complex internal bank rating systems. Therefore we tested the accuracy of the

German Z-Score on a sample of 37 large German companies that by the end of 2002 were 21 In the appendix we provide a comparison of the effects of varying equity ratios, return on sales ratios and depreciation ratios on the PD of five different types of companies.

14

externally rated by either Moody’s or Standard & Poor’s or both.22 Surprisingly, the mean PD

obtained through the application of the German Z-Score nearly met the mean of the average

PD estimated by the two external rating agencies. Moreover, we did not find a statistical

difference of the mean PD of the German Z-Score compared to the mean average PD derived

by Moody’s and Standard & Poor’s ratings.

< table 5 about here >

According to this, our model appears to be well-calibrated relative to complex rating systems

such as the ones of Moody’s and Standard & Poor’s.

To test the sharpness of the default predictions of the German Z-Score we applied the Re-

ceiver Operating Characteristic (ROC) curve methodology, which is a widely used validation

technique for rating systems (Sobehart and Keenan (2001)). For validation purposes the size

of the area below a ROC curve is of particular interest. The construction of a ROC curve can

best be explained by two possible distributions of continuous scores for non-defaulting and

defaulting debtors. For well-designed rating systems the distribution of the non-defaulting

debtors should have better scores on average compared to the distribution of defaulting debt-

ors. To decide which debtors will survive during the next period and which debtors will de-

fault a value C has to be introduced. Each debtor with a score lower than C is classified as a

defaulter and each debtor with a higher score as a survivor. If the score is below this so-called

cut-off value and the debtor defaults later on, the classification was correct. Otherwise a non-

defaulter was incorrectly classified as a defaulter. The same procedure applies to the group of

non-defaulters. We define the hit rate HR(C) as:

( ) ( )DNCHCHR = (4)

where H(C) is the number of correctly classified defaulters with the cut-off value C, and ND is

the total number of defaulters in the sample. The false alarm rate FAR(C) is defined as:

( ) ( )NDNCFCFAR = (5)

22 We did not include any banks in this sample. Banks can not be easily compared to industrial companies for they have totally different balance sheet and P+L structures. To calculate the German Z-Score of the selected companies we assumed all corporations to have external equity financing, all companies not organized as part-nerships to not have external equity financing. We further assumed that no company was in temporary liquidity problems. Since all companies in the sample are publicly listed and have an external rating they can be assumed to have easy access to various sources of liquidity.

15

where F(C) is the number of false alarms, that is, the quantity of non-defaulters that were mis-

takenly classified as defaulters according to their cut-off value. The total number of non-

defaulters in the sample is denoted by NND. Hence, the ROC curve is constructed as follows.

For all cut-off values C that are contained in the range of the scores the quantities HR(C) and

FAR(C) are calculated. The ROC curve is a plot of HR(C) versus FAR(C). The larger the area

under the ROC curve, which is defined as AUC

( ) ( )∫=1

0

FARdFARHRAUC (6)

the better the model’s performance in predicting defaults. For a random model without dis-

criminative power the area under the ROC curve is 0.5 (the dotted line in figure 1), it is 1 for

an ideal model and between 0.5 and 1 for any rating model in practice. Using the probability

of default based on the account data until the end of the year 2001 and credit default dummies

up to the year 2003 we find an AUC value of 85.16%. Whereas one can not compare this

measure easily between different portfolios of debtors (Hamerle et al. (2003)), our model

seems not only to be well-calibrated but also of a relatively high sharpness (see figure 1).23

< Figure 1 about here >

Another, more qualitative argument arises from the review of several studies comparing rat-

ing systems with and without the inclusion of qualitative variables (i.e. management quality).

Grunert et al. (2004) and Lehmann (2002) compare the accuracy of two internal rating sys-

tems, one using only quantitative and the other additionally qualitative data. The combined

use of quantitative and qualitative variables results in significantly more accurate default pre-

dictions than the inclusion of only quantitative data. A study by Blochwitz and Eigermann

(2000) incorporates a variable for accounting behavior (progressive versus conservative) in

addition to traditional financial ratios. Their findings confirm that the inclusion of soft factors

slightly enhances the accuracy of default predictions. Since there is only a slight enhancement

of default prediction accuracy we argue that a rating system using solely quantitative vari-

ables as data input is a good proxy for a more complex rating system. Frerichs and Wahren-

burg (2003) emphasize that banks with a small dataset face severe problems in setting up an

own internal rating system. As we use a huge dataset, our scoring model is likely to be better

in predicting a borrower’s PD than more complex rating system of banks that face the small

dataset problem. This assertion stems mainly from the fact that our dataset includes data from

23 Particularly if one compares the German Z-Score to a random model.

16

more than one bank. Therefore our pool of information is much larger than the information of

one single bank which, if she applies an inaccurate model, will draw misleading inferences

from the model outcome. The diversification over several banks exempts us from this draw-

back. Both, quantitative and qualitative assessments of our model give rise to the assumpion

that the German Z-Score contains a reasonable enough amount of information on a bor-

rower’s default risk to draw sound inferences from it.

5. Implications

Any SME-borrower can easily calculate her PD by plugging her specific variable values into

the estimated logit function. The knowledge of a borrower’s individual credit risk as meas-

ured by the German Z-Score allows a company to derive her (approximate) risk adequate cost

of debt. By mapping the PD to historic default data provided by external rating agencies and

actual bond yields the cost of debt corresponding to the measured PD can be computed as

follows: A German Z-Score of, say, 2% can be translated into a BB- rating class according to

the S&P rating table (table 6) that shows a long-term average one year default rate of compa-

nies rated by S&P of about 2.07%24 and a corresponding smoothed bond spread of about

3.7%.

< Table 6 about here >

The implications of the knowledge of the German Z-Score for a SME can be twofold: First of

all, it can lead to a detection of hold-up problems and secondly to an improvement – in the

sense of enlarging the set of financing sources SME can choose from – of the financing situa-

tion by removing prevailing financing restrictions.

5.1. Detection of hold-up problems

Theoretical work (Sharpe (1990), Rajan (1992)) and empirical findings based on European

data (Degryse and Van Cayseele (2000), Angelini et al. (1998)) both indicate that SME with

long term bank relationships might face hold-up problems. The proprietary information about

borrowers that Hausbanks obtain as integral part of their relationships can result in an infor-

mation monopoly. This leads to significant switching costs for SME. Non-Hausbanks have

less information than relationship lenders and a new lender bank might therefore suspect that

the firm which is applying for a loan incurs a high default risk. Thus, the new lender will

charge an interest rate of rnl = rc + rr where rc is the risk adequate cost of debt and rr is a risk 24 Further to the PD, a bank’s operational, funding and opportunity costs of equity provisioning should be re-flected in the interest rate of a loan.

17

margin that accounts for the lack of information. Therefore, the Hausbank is given a range of

chargeable interest rates in the interval [rc; rsc] where rsc is the sum of the risk adequate cost of

debt and switching costs minus some infinitesimal amount ε. As long as rsc is below the inter-

est rate a new lender will charge it does not pay for the borrower to switch her bank relation-

ship. Since a new lender will charge the borrower a risk margin the borrower will neither ob-

tain the “fair” rate of interest – that is the risk adequate cost of debt – from her Hausbank nor

from a new lender. This leads to the conclusion that a Hausbank has no incentives to fully

disclose the information about the borrower and the loan pricing mechanism therefore keep-

ing the borrower’s knowledge about her creditworthiness on a level too low to allow for the

(re)negotiation of loan conditions with her Hausbank or to search for a new lender. Assuming

that hold-up stems to a significant degree from this one-sided asymmetric distribution of in-

formation, an improved knowledge of the borrower’s creditworthiness would put the bor-

rower in the position to detect hold-up. The detection of hold-up will, however, not automati-

cally lead to Hausbanks reducing their interest rates. As long as a new lender will not offer the

loan at a cheaper price a rational Hausbank has no incentive to counteroffer, that is, to de-

crease her interest rates. Since any new lender may be assumed to have the proper technology

to efficiently measure the default risk of a SME, the knowledge of the German Z-Score might

not have the power to change this setting. The benefit lies elsewhere. The knowledge of the

individual creditworthiness accompanied by the detection of hold-up exerted by the SME’s

Hausbank is likely to stimulate the search for a new lender that offers a loan at a better price.

Whereas the search for a new lender without the knowledge of the German Z-Score might not

be a sound decision, the search process will become more efficient if the SME knows about

her creditworthiness. Thus, search costs for a new lender can be reduced. With the knowledge

of the German Z-Score it only pays to try to change the bank relationship if the SME can de-

tect hold-up.

5.2. Alternative sources of external debt financing

The second major benefit of the knowledge of the German Z-Score is that more information

about the default risk of a borrower has the potential to enhance the use of alternative sources

of external debt financing in order to substitute bank financing. As we pointed out in section

three, German SME face serious financing restrictions bounding them to their banks. For Ja-

pan, another bank-based financial system that is often compared to Germany for its great im-

portance of bank financing, Hoshi et al. (1993) reported an increasing importance of external

(non-bank) debt financing for Japanese companies at the beginning of the 1990s as a result of

18

deregulation. However, for Germany until now this has not been the case. A necessary pre-

requisite for debt financing in the capital market is usually an external rating which is costly.

Besides the relatively high costs – especially for SME – that could be a significant obstacle

themselves, the quality of the rating is ex-ante not known. German companies, and to a larger

extent SME, thus might fear to obtain a bad credit rating.25 This, among others, might be a

reason why one can hardly observe public debt issuances of German SME. A self-estimation

of the creditworthiness of a borrower – by means of the calculation of the German Z-Score –

could therefore positively influence the decision to obtain an external rating which aims at

issuing debt at some future point in time. We argue that SME with low default risk, that is a

low German Z-Score, by knowing about their default risk, might consider to issue external

debt in order to substitute bank financing by a new source of debt financing, independent of

their bank relationship.26 Since the financing needs of a SME usually do not reach the vol-

umes that would be necessary for the issuance of costly public debt, we view a private place-

ment of certificates of debt (Schuldscheindarlehen) to be a feasible alternative. Besides, these

private placements of debt, which often amount to volumes between EUR 10 and 100 million,

do not obligatorily need a costly external rating but can be based on an internal rating by the

bank involved in the issuing process. Prior research in this area (e.g. Krishnaswami et al.

(1998)) found that private debt is more likely to be issued by firms with a higher degree of

asymmetric information distribution. SME surely fall into this category (Elsas and Krahnen

(2003)). The issuer of private debt generally has to demonstrate her credit quality, thus the

German Z-Score might do a good job in influencing managerial decisions towards raising

external debt by means of a private placement. Since external debt is very likely to limit the

monopolistic market power a (Haus)bank can exert on her customers (Houston and James

(1996)) it is supposed to lead to reduced switching costs and hold-up problems. The benefit of

the knowledge of the German Z-Score in this context falls into the category of directly influ-

encing a firm’s financing decisions and widening the scope of obtainable financing sources.

6. Summary

The main objective of this paper was the estimation of a logit function for the measurement of

default risk of German SME. We argue that this function delivers a good approximation of

their default risk relative to the default risk measured by other rating systems such as internal

bank rating systems. Therefore, it allows a valid self-assessment of the creditworthiness of a

25 According to Hommel and Schneider (2003) only 5-10% of the companies with a turnover of EUR 10 to 40 million consider an external rating. 26 However, companies with high default risk will stick to their bank relationship.

19

SME. Since German SME depend heavily on bank loans as the main source of financing they

might face serious hold-up problems exerted by their Hausbanks. There is strong theoretical

and empirical evidence that supports this hypothesis. Furthermore, the high dependence on

bank loans is due to the severe financing constraints German SME face. The knowledge of the

individual default risk measured by the German Z-Score allows for the calculation of a bor-

rowers approximate risk adequate cost of debt and can thus lead to a detection of potential

hold-up situations. This may lead to more efficient decisions on when and how to search for

new lenders. Furthermore, it could boost the issuance of private debt that seems to be well

suited for German SME. This is likely to reduce switching costs and thus hold-up problems,

and adds significantly to the dismantling of financing restrictions German SME face. Summa-

rized, the knowledge of the Z-Score by German SME might influence managerial decisions

towards new sources of external financing by widening the scope of possible financing deci-

sions.

We did not spent anything on whether SME desire to liberate from the strong relationships

with their Hausbanks. Putting both, the advantages and the disadvantages of Hausbank rela-

tionships, on a balance, we are not in the position to finally judge on that. This issue is left

open for future resarch.

20

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23

Table 1: Mean-difference tests for the sample adjustment

Mean KfW-Databasea Mean samplea Differencea t-Value Return on salesb 3.3544 3.1719 0.1825 *** -9.37 Equity ratioc 27.4567 27.4710 -0.0143 0.20 Depreciation ratiob 4.8742 4.7252 0.1490 *** -7.34 Companies with return on sales growth 51.7696 51.4900 0.2795 -1.66 Companies with equity ratio growth 53.3186 53.2700 0.0486 -0.29 Equity financing 1.6956 1.6380 0.0577 -1.33 Temporary liquidity problems 9.2063 8.7362 0.4701 *** -4.83

aAll figures in %. bMean weighted with turnover. cMean weighted with total assets.

24

Table 2: Structure of the KfW-Database, the sample and comparison to the official German tax statistic (in %)

KfW-Database Sample Tax statistica I. Sector Construction 12.6 11.65 15.81 Services 16.87 15.94 13.39 Retail/Wholesale 26.57 27.36 56.56 Manufacturing 43.96 45.05 14.24 Total 100 100 100 II. Annual sales (EUR million) < 1 42.66 39.72 89.43 1 - 2.5 22.06 22.54 2.5 – 10 22.15 23.56 9.29

10 – 50 10.57 11.48 1.01 50 – 250 2.37 2.52 0.22 250 – 500 0.19 0.17 0.05b Total 100 100 100 III. Legal form Sole proprietorship 46.89 46.22 71.03 Partnership 21.59 22.68 12.82 Corporation 31.52 31.1 16.15 Total 100 100 100 IV. Region (headquarter of the firm) Eastern Germanyc 18.27 16.19 17.57 Western Germany 81.73 83.81 82.43 Total 100 100 100

aAll quantities of the German tax statistic were provided by the Federal Statistic Office (www.destatis.de), and

given for the year 2001. bThis quantity is calculated for all German companies with annual sales of more than EUR 250 million. cEastern Germany refers to the newly-founded states after the reunification of the then German Democratic

Republic and Western Germany in 1990 including Berlin.

25

Table 3: Determinants of default frequencies

Independent variables Coefficienta Standard Errorb

Intercept -4.3261 *** 0.1894 Return on sales growth -0.2156 ** 0.1013 Equity ratio growth -0.2603 ** 0.1046 Return on sales -0.0354 *** 0.0105 Equity ratio -0.0052 *** 0.0009 Depreciation ratio -0.0254 *** 0.0091 Equity financing 0.4822 * 0.2631 Temporary liquidity problems 2.2626 *** 0.1066 Eastern Germany (reference group) c Western Germany -0.8857 *** 0.1094 Sales < 1 EUR million (reference group) c Sales 1 - 2.5 EUR million 0.1357 0.1384 Sales 2.5 - 10 EUR million 0.5631 *** 0.1383 Sales 10 - 50 EUR million 0.8647 *** 0.1768 Sales 50 - 250 EUR million 0.9321 ** 0.3761 Sales 250 - 500 EUR million 0.7938 1.0241 Construction (reference group) c Services -0.4502 ** 0.1807 Retail/Wholesale -1.2178 *** 0.1604 Manufacturing -0.4432 *** 0.1273 Sole proprietorship (reference group) c Partnership 0.3479 ** 0.1681 Corporation 0.6108 *** 0.1480 Sizes χ2 (degrees of freedom) d 33.75 *** (5) Sectors χ2 (degrees of freedom) d 57.84 *** (3) Legal forms χ2 (degrees of freedom) d 17.48 *** (2) Akaike information criterion 0.081 McFadden's adjusted R2 0.187 Observationse 88,402 Log Likelihood -3,539

a***,**,* Denote significance at the 1%, 5%, and 10% levels, respectively. bStandard errors are calculated using robust Huber/White variance estimators. cFirms with annual sales less than EUR 1 million, headquartered in the eastern part of Germany, from the con-

struction sector, and managed under sole proprietorship are the respective reference groups. All other combina-

tions of these control variables are modeled by Dummy variables. dThe Wald tests have been conducted in order to test the joint significance of the respective dummy variable

group. eSince there can be several balance sheets of one firm in the sample, we only assume independence of balance

sheets of different firms.

26

Table 4: Marginal Effects on the PD (in %)

Independent variables Marginal Effecta, b Standard Error

Return on sales growth -0.038 * 0.020 Equity ratio growth -0.047 ** 0.020 Return on sales -0.006 *** 0.002 Equity ratio -0.001 *** 0.000 Depreciation ratio -0.004 ** 0.002 Equity financing 0.097 0.070 Temporary liquidity problems 1.329 *** 0.235 Western Germany -0.222 *** 0.050 Sales 1 - 2.5 EUR million 0.023 0.024 Sales 2.5 – 10 EUR million 0.118 *** 0.037 Sales 10 - 50 EUR million 0.215 *** 0.064 Sales 50 - 250 EUR million 0.240 0.148 Sales 250 - 500 EUR million 0.189 0.352 Services -0.057 *** 0.020 Retail/Wholesale -0.110 *** 0.020 Manufacturing -0.087 *** 0.030 Partnership 0.065 * 0.035 Corporation 0.132 *** 0.039

aMarginal effects are calculated for a reference company with head office in Western Germany, sales smaller

than EUR 1 million, from the manufacturing sector, organized as sole proprietorship, with positive equity and

return on sales ratio growth, without external equity financing or temporary liquidity problems. The equity ratio,

return on sales and depreciation ratio are set at the sample median. b***,**,* Denote significance at the 1%, 5%, and 10% levels, respectively.

27

Table 5: Mapping of one year average default rates with empirical and smoothed empirical bond spreads (in %)

Ratings Default ratesa

Smoothed default ratesb

Bond spreadsc

Smoothed bond spreadsb

AAA 0.0000 0.0042 0.3140 0.3040 AA+ 0.0000 0.0071 0.3460 0.3750 AA 0.0000 0.0120 0.4500 0.4610 AA- 0.0200 0.0203 0.5390 0.5680 A+ 0.0600 0.0344 0.7240 0.7000 A 0.0500 0.0581 0.9170 0.8620 A- 0.0400 0.0983 1.0650 1.0610 BBB+ 0.3500 0.1662 1.4240 1.3070 BBB 0.3400 0.2810 1.2200 1.6090 BBB- 0.4300 0.4750 2.4880 1.9810 BB+ 0.5200 0.8030 3.1640 2.4400 BB 1.1600 1.3576 2.2220 3.0050 BB- 2.0700 2.2952 4.1250 3.7000 B+ 3.2900 3.8804 4.4860 4.5560 B 9.3100 6.5602 5.9880 5.6110 B- 13.1500 11.0909 6.0940 6.9100

aOne year average long-term default rates where obtained from the annual default report of Standard & Poor’s

(S&P (2003)). bSmoothed default rates and bond spreads were calculated by exponential ols-fitting (Bluhm et al. (2002), p. 36)

to get well behaving, monotonously increasing, default rates and spreads. cBond spreads are based on a database of spreads of 3,403 Eurobond issues during the period 1990 to 2001

(Gabbi and Sironi (2002)).

28

Table 6: Mean-difference test for the average PD of Moody’s and S&P and the PD of the German Z-Score

Observations Mean Average PDa of Moody’s and S&P

Mean PDb of the German Z-Score

Difference p-Value

37 0.6532 0.6046 -0.0486 0.8239 aBoth means and the difference between the means are in %. One year average long-term default rates where

obtained from the annual default reports of Moody’s and Standard & Poor’s of 2003. To get well behaving,

monotonously increasing, default rates they were smoothed by exponential ols-fitting (Bluhm et al. (2002), p.

36). bCompany data for the German Z-Score were obtained from the annual reports of 2001 and 2002.

29

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

False alarm rate

Hit

rate

German Z-Score Random model

Figure 1: ROC curve of the German Z-Score

30

Appendix

Figure A1a and A1b: Sensitivity of different return on sales ratios on the PD (in %)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Return on sales

PD

Reference company Type 2 Type 3

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30Return on sales

PD

Type 4 Type 5

All sensitivities are calculated for a reference company with head office in Western Germany, sales smaller than

EUR 1 million, from the manufacturing sector, organized as sole proprietorship, with positive equity and return

on sales ratio growth, without external equity financing or temporary liquidity problems. The equity ratio and

depreciation ratio are set at the sample median. Characteristics of company type 2: like reference company, but

with negative return on sales ratio growth; Characteristics of company type 3: like reference company, but with

negative return on sales and equity ratio growth; Characteristics of company type 4: like reference company, but

with negative return on sales and equity ratio growth, with headquarter in eastern Germany and external equity

financing; Characteristics of company type 5: like reference company, but with temporary liquidity problems

Figure A1c and A1d: Sensitivity of different depreciation ratios on the PD (in %)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Depreciation ratio

PD

Reference company Type 2 Type 3

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Depreciation ratio

PD

Type 4 Type 5

All sensitivities are calculated for a reference company with head office in Western Germany, sales smaller than

EUR 1 million, from the manufacturing sector, organized as sole proprietorship, with positive equity and return

on sales ratio growth, without external equity financing or temporary liquidity problems. The return on sales

ratio and the equity ratio are set at the sample median. Company types 2 to 5 are defined as above.

31

Figure A1e and A1f: Sensitivity of different equity ratios on the PD (in %)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

-5 -3 -1 1 3 5 7 9 11 13 15 17 19 21 23 25

Equity ratio

PD

Reference company Type 2 Type 3

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

-5 -3 -1 1 3 5 7 9 11 13 15 17 19 21 23 25Equity ratio

PD

Type 4 Type 5

All sensitivities are calculated for a reference company with head office in Western Germany, sales smaller than

EUR 1 million, from the manufacturing sector, organized as sole proprietorship, with positive equity and return

on sales ratio growth, without external equity financing or temporary liquidity problems. The return on sales

ratio and the depreciation ratio are set at the sample median. Company types 2 to 5 are defined as above.