Is the diversification discount caused by the book value bias of debt?

Journal of Banking & Finance 34 (2010) 2307–2317

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Is the diversification discount caused by the book value bias of debt? q Markus Glaser a,*, Sebastian Müller b a b

Chair of Business Administration, esp. Corporate Finance, Department of Economics, University of Konstanz, Germany Chair of Business Administration and Finance, esp. Banking, University of Mannheim, Germany

a r t i c l e

i n f o

Article history: Received 4 December 2008 Accepted 18 February 2010 Available online 23 February 2010 JEL classification: G12 G13 G14 G31 Keywords: Diversification Diversification discount Conglomerate discount Internal capital markets Option pricing Debt valuation Merton model Corporate governance Ownership structure

a b s t r a c t We analyze whether the diversification discount is driven by the book value bias of corporate debt. Book values of debt may be a more downward biased proxy of the market value of debt for diversified firms, relative to undiversified firms, as diversification leads to lower firm risk. Thus, measures of firm value based on book values of debt undervalue diversified firms relative to focused firms. Our paper complements recent literature which uses market values to test the risk reduction hypothesis for a subsample of firms for which debt is traded. Alternatively, we employ market value of debt estimates for the whole firm universe. Consistent with the above hypothesis, we show that the use of book values of debt underestimates the value of diversified firms. There is no discount for mainly equity financed firms and lower distress risk and equity volatility for diversified firms. More concentrated ownership increases firm valuation. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction The benefits and costs of corporate diversification have been the subject of extensive empirical and theoretical research.1 Weston (1970) suggests that diversified firms have the ability to use economies of scale because they provide more efficient operations and more profitable lines of business when compared to stand-alone

q We would like to thank an anonymous referee and Martin Artz, Sreedhar T. Bharath, Jannis Bischof, Wolfgang Breuer, Holger Daske, Ike Mathur (the editor), Ernst Maug, Volker Vonhoff, Thomas Wenger, David Yermack, and seminar participants at the Workshop on Corporate Governance and Executive Compensation 2009 at the University of Mannheim, the Tagung des Verbandes der Hochschullehrer für Betriebswirtschaft (Pfingsttagung 2009) in Nürnberg, and the 16th annual meeting of the German Finance Association (DGF) in Frankfurt for valuable comments and insights. Furthermore, we would like to thank Andreas Dzemski and Peter Kahlcke for excellent research assistance. Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged. * Corresponding author. Tel.: +49 (0)7531 88 5346; fax: +49 (0)7531 88 5347. E-mail addresses: [email protected] (M. Glaser), mueller@ bank.BWL.uni-mannheim.de (S. Müller). 1 Recent surveys of this literature are Hellwig et al. (2002), Maksimovic and Phillips (2007), Martin and Sayrak (2003), and Stein (2003).

0378-4266/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2010.02.017

firms. Lewellen (1971) argues that diversified firms enjoy greater debt capacity and debt tax shields relative to single-line firms due to lower firm risk. Furthermore, diversification can create internal capital markets that enable firms to pool and reallocate corporate resources more efficiently through ‘‘winner picking” than through external financing, which may increase investment efficiency (see, e.g., Stein, 1997). The negative impacts of corporate diversification are often described in terms of inefficient investments due to cross-subsidization between divisions. Rajan et al. (2000), for example, model distortions caused by internal power struggles among the divisions of a diversified firm in the course of the resource allocation process. Other costs of diversification include investments in lines of businesses with poor investment opportunities (e.g., Stulz, 1990). Jensen (1986) argues that diversified firms invest more in negative cash flow projects than their segments would if operated independently. This argument is reinforced by the influence cost model of Meyer et al. (1992), in which lower-level managers of a firm attempt to lobby top management to increase the investment flows available to their business segment, even if the business segment has poor future growth prospects. Compared to focused firms, lobbying leads to inefficiencies in diversified organizations.

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Scharfstein and Stein (2000) suggest that rent-seeking behavior by divisional managers undermines the functioning of internal capital markets and leads to inefficient investments. Overall, the published literature on corporate diversification suggests that conglomeration is associated with greater agency costs. These agency costs are manifested in the form of accepting negative net present value projects, which reduce the value of a firm. The empirical literature mainly documents a so-called ‘‘diversification discount”. As developed by Lang and Stulz (1994) and Berger and Ofek (1995), the diversification discount compares the market value of a diversified firm to the imputed stand-alone values of its individual segments. These imputed values are based on multiples (such as price-to-book value or price-to-sales) of comparable pure-play firms in the same industry as the corresponding diversified firm’s segments. Using data from the US, these authors find substantial mean discounts on the order of 15%, which they interpret as evidence of value destruction of diversified firms. This work has been extended to a variety of other sample periods and countries by Servaes (1996), Lins and Servaes (1999), or Lins and Servaes (2002). Results suggest that the diversification discount is a pervasive phenomenon. However, a number of other papers cast doubt on the interpretation that the diversification discount reflects value destruction. Campa and Kedia (2002), Chevalier (2004), Graham et al. (2002), and Villalonga (2004) all argue in one way or another that the discount is driven by endogeneity bias, as relatively weak firms are the ones that choose to diversify in the first place. A balanced reading of these papers suggests that accounting for this endogeneity bias reduces – though does not eliminate – the discount. Overall, the diversification discount seems to be such a stable fact that consulting firms base their strategy suggestions on these findings. For example, the Boston Consulting Group (2006) writes how diversified firms can create value. Even textbooks pick up the arguments of the early literature and state that the diversification discount is likely to be the consequence of agency problems and inefficient resource allocation in conglomerates (see, e.g., Hill and Jones, 2007). Despite the vast amount of literature on the diversification discount one aspect of the Berger and Ofek (1995) excess value measure is hardly addressed: the risk effects of conglomeration and its subsequent impact on firm value. While diversification reduces shareholder value, it enhances bondholder value due to a reduction in firm risk. Mansi and Reeb (2002) is the only published study which makes this point. They obtain the market values of both debt and equity for a subset of US firms and examine the bias of using book values of debt to compute excess values. Consistent with the hypothesis that diversification leads to lower firm risk, they find that book values of debt are a more downward biased proxy of the market value of debt for diversified firms, relative to undiversified firms. This finding suggests that measures of firm values based on book values of debt systematically undervalue diversified firms. When considering the joint impact of diversification on debt and equity holders, they find that, on average, corporate diversification is insignificantly related to excess firm value. Their conclusion is that diversification reduces shareholder value, increases bondholder value, and has no significant impact on total firm value. Given that several theoretical papers examine the consequences of corporate diversification by explicitly assuming that it leads to lower firm risk, it is surprising that Mansi and Reeb (2002) is the only published empirical study dealing with the risk effect of corporate diversification and its impact on firm value that we are aware of. For example, Lewellen (1971) argues that diversified companies enjoy higher debt capacities as their default risk is lower. As a consequence, the value of the company’s tax shield increases, which enhances the company’s overall value as well. Amihud and Lev (1981) argue that managers engage in corporate

diversification, even if it reduces shareholder value, to reduce their human capital risk. The assumption is that corporate diversification lowers firm risk. In a contingent claims framework, lowering firm risk should lower shareholder value and increase bondholder value. Our analysis complements the study of Mansi and Reeb (2002). In principal, there are two ways to test the risk reduction hypothesis of corporate diversification. One way is suggested by Mansi and Reeb (2002). They use actual market values of debt which they obtain from the Lehman Brothers Fixed Income database and analyze the diversification discount for a subsample of firms for which debt is traded (13% of all US firms). Our study follows an alternative approach and tests the risk reduction hypothesis for the whole listed firm universe in a country (in our case a sample of all German non-financial CDAX firms from 2000 to 2006), which goes at the cost that market values of debt have to be estimated. This is due to the fact that even if one has access to a research database to infer the market price of debt, most corporate debt is not traded. This is especially true for bank-based systems like Germany. In this case one either has to use estimates of market values or to rely on book values. As a solution to this problem, we employ several specifications of the Merton (1974) bond pricing model which were previously used in different research contexts to estimate the market value of the firm’s assets. Our estimation procedure, which will be described in detail below, requires only very little additional information and can thus be implemented for almost all focused and diversified companies for which an excess value based on debt book values can be calculated. Eberhart (2005) shows that applications of the Merton (1974) model provide more accurate debt value estimates than the book value approximation. Our study is related to a recent working paper by Ammann et al. (2008) who treat the entire long-term debt on the books of firms as one coupon bond with the coupon set equal to the interest expenses on all debt. They then value this coupon bond at the current cost of debt for the company approximated by the yield of a bond portfolio with the same credit rating. As Compustat provides an official credit rating from S&P only for a very limited subset of their sample, they alternatively construct an artificial credit rating based on the interest coverage ratio. Their sample consists of all firms with data reported on both the Compustat Industrial Annual and Segment data files and covers the period from 1998 to 2005. Ammann et al. (2008) show with their approximation of the market value of debt that the potential effect of accounting for differences between the market and book value of debt on the conglomerate discount in the US is limited. Our main findings can be summarized as follows. In a first step, we document that German conglomerates trade at a significant discount of 15% when the traditional Berger and Ofek (1995) measure is used. Consistent with the risk reduction hypothesis and in line with Mansi and Reeb (2002), we provide evidence that the use of book values of corporate debt in the computation of the excess value underestimates the firm value of diversified firms when compared to focused ones. Additional tests are also consistent with the risk reduction hypothesis of corporate diversification (no discount for firms which are barely financed with debt, lower distress risk and lower equity volatility for diversified firms). Moreover, we show that ownership structure affects the diversification discount. We therefore conclude that the book value of debt bias is an important, but not the only explanation for the diversification discount. The remainder of the study is organized as follows. In Section 2, we describe the data set, the identification of focused and diversified firms, and the excess value measure. In Section 3, we outline the precise procedure of how we estimate market values of debt. Furthermore, we assess the quality of our estimation by comparing market value of debt estimates with actual bond prices for a subset

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of our initial firm sample. Section 4 presents the results and the last section concludes. 2. Construction of the data set 2.1. Sample of firms and data set The starting point of our analysis is the sample of all CDAX firms from 2000 to 2006. The reason for starting in the year 2000 is that from this year on reliable business segment data is available as it is the first year in which German firms have to disclose segment information comparable to US accounting rules. To construct our final data set, we proceed as follows. From Datastream/Worldscope, we download business segment information for all German (financial and non-financial) firms that have been members of the CDAX index in at least one year during the period 2000 and 2006.2 The CDAX covers all German firms whose shares were admitted to the Prime Standard and General Standard segments of the German Stock Exchange. Before the introduction of these segments in the year 2003, the CDAX contained all firms whose shares were members of the segments Amtlicher Handel, Geregelter Markt, and Neuer Markt. The CDAX index reflects the full spectrum of the German equity market, and is consequently well suited for academic purposes. To identify the firms in the CDAX, we obtain end of year lists of the index members from the Karlsruher Kapitalmarktdatenbank (KKMDB) maintained by the University of Karlsruhe in Germany. The number of firms listed in the CDAX during the sample period varies between 678 and 790. The number of firms generally decreases over time indicating that several firms were delisted after the stock market boom around the year 2001. In 2006, the number of listed firms slightly increases. For our empirical analysis, we clean the data set in the following way. Some firms appear twice in our CDAX list as they are listed with more than one type of stock (e.g., common stock and preferred stock). Therefore, we delete all duplicate observations. Firms in the remaining data set are identified by their ISIN of the common stock. A firm is categorized as a firm with business segment information if one of the following variables is available for at least one (operating or non-operating) segment: segment assets (Worldscope data item wc19503), segment sales (wc19501), or segment description (wc19500). To construct our final data set, we merge the business segment data with the complete CDAX list. We then drop all financial firms as their balance sheet data is not comparable to non-financial firms. We identify financial firms by their primary SIC code (Worldscope data item wc07021) and delete all firms with SIC codes between 6000 and 6999. 2.2. Identification of operating segments and classification procedure to obtain focused and diversified firms We classify all firms without business segment information as focused firms. A firm is treated as diversified if the number of operating segments which operate in different 2-digit SIC codes is 2 or higher.3 All other firms are also classified as focused. To obtain this classification, we disregard all non-operating segments. We define a segment as non-operating if one of the following criteria is met: – The segment description (Worldscope code wc19500 ‘‘Product Segment 1 – Description” to wc19590 ‘‘Product Segment 10 – 2 Datastream/Worldscope is an often used data source in empirical corporate finance research. Another recent example is Croci and Petmezas (2010). 3 This classification procedure is standard for non-US countries. Note, that we do not analyze geographic diversification. For an analysis of the effects of geographic diversification see, e.g., Dos Santos et al. (2008) and Kim and Mathur (2008).

Description”) contains strings which indicate that the segment is a non-operating segment.4 – The segment SIC code provided by Worldscope (Worldscope code wc19506 ‘‘Product Segment 1 – SIC Code” to wc19596 ‘‘Product Segment 10 – SIC Code”) is 9999 (nonclassifiable establishments). – Segment assets (Worldscope code wc19503 ‘‘Product Segment 1 – Assets” to wc19593 ‘‘Product Segment 10 – Assets”) are 0 or negative (because such segments can be regarded as adjustment segments). – Segment sales (Worldscope code wc19501 ‘‘Product Segment 1 – Sales” to wc19591 ‘‘Product Segment 10 – Sales”) are 0 or negative (because such segments can be regarded as adjustment segments). Whenever we refer to a focused firm, we mean (i) firms with only one operating segment, (ii) firms with more than one operating segment which all operate in the same two-digit SIC code industry or (iii) firms without business segment information at all.5 Consistent with the literature (see, e.g., Rajan et al., 2000, p. 54), we ensure that no data item is calculated using data spread over multiple years. One reason for this convention is that it is impossible to identify the respective business segment of the last year for a given business segment due to potential name changes or reorganizations. Furthermore, we collect data on several other variables which are described in Table 1. 2.3. Measuring the excess value The excess value of a company is the natural logarithm of the ratio of a firm’s actual value to its imputed value. A firm’s imputed value is the sum of the imputed values of its segments, with each segment’s imputed value being equal to the segment’s sales multiplied by its industry median ratio of total capital (market value of equity plus book value of debt or market value estimate of debt) to sales. More precisely, excess value EV i and imputed value IðVÞi of company i, are defined as



 Vi ; and IðVÞi n X AIij  ðmultiple of segment j of firm iÞ; IðVÞi ¼

EV i ¼ ln

ð1Þ with

ð2Þ

j¼1

V = total capital (market value of equity plus book value of debt or market value estimate of debt) multiple of segment j of firm i = median ratio of V to accounting item (sales ratio) of focused firms in industry of segment j AIij = accounting item of segment j of firm i n = number of segments of firm i Note that it is also possible to calculate the excess value measure for focused (single segment) firms, i.e., firms with ‘‘only one segment”. In other words, some focused firms may trade at a premium while others might trade at a discount. However, the median focused firm has, by construction, an excess value of 0. 4 Such strings are, for example, holding, central division, central services, corporate, corporate center, corporate services, other & holding, consolidated, consolidation, intercompany, inter-company, intergroup, intersegment, intra-group, intragroup, adjustment, unallocated, not allocated, transfer, and administration. The search for these strings is case insensitive and spaces are ignored, i.e., we classify a segment as non-operating when the segment description contains the strings holding, Holding, central services, or centralservices, for example. 5 All results are robust with respect to the definition of focused and diversified firms. Furthermore, the results are unchanged when we drop all firms without business segment information from our sample.

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Table 1 Definition of variables. Variable

Worldscope code

Diversified firm (dummy) Assets Operating income Capital expenditures Total liabilities Total debt Current liabilities Short-term debt Long-term debt Interest expense Accounting standard (dummy)

wc02999 wc01250 wc04601 wc03351 wc03255 wc03101 wc03051 wc03251 wc01251 wc07536

Altman’s Z

wc18191 wc01001 wc03495 wc03151 wc02999 wc08021

Closely held shares Volatility

Description Firms with two or more operating segments which operate in different industries (based on two-digit segment SIC codes) Total assets

Interest expense on debt Three dummy variables Each dummy variable is set equal to 1 when a specific accounting standard is used and 0 otherwise Firms are grouped into US-GAAP, local GAAP (HGB), and IFRS based on this Worldscope variable (3.3  earnings before interest and taxes + 1.0  net sales or revenue + 1.4  retained earnings + 1.2  working capital)/ Total assets Closely held shares (in %) This variable represents shares held by insiders Standard deviation of daily stock returns over the past 125 trading days

This table summarizes and defines the variables used in this paper.

The contribution of this paper is that we do not only calculate the traditional Berger and Ofek (1995) excess value measure in which the total capital of a firm is calculated as market value of equity plus book value of debt, but also substitute the book value of debt by market value of debt estimates that are based on implementations of the Merton (1974) model. We will describe our estimation procedure in the next section.

3. Estimation of market values of debt 3.1. Detailed estimation procedure for market values of debt Merton (1974) shows that under certain assumptions the equity of a firm can be regarded as a call option on the underlying value of the firm. Details of his model can be found in Appendix A. We can use his insights to estimate market values of debt by solving a system of nonlinear equations for the firm value, V, and the volatility of the firm, rV (see Eqs. (A.2) and (A.5) in Appendix A). Therefore, we need values for the remaining variables in the system of nonlinear equations: stock return (equity) volatility ðrE Þ, time to maturity (T), the risk-free rate (r), the face value of debt (F), and the market capitalization (E). We use the set of input parameters suggested by three recent studies (Bharath and Shumway, 2008; Eberhart, 2005; Vassalou and Xing, 2004). Table 2 shows a summary of the input parameters used in this paper to estimate market values of debt, which are based on the three papers mentioned above.6 It is possible to use historical returns data to estimate rE . Furthermore, several studies assume a forecasting horizon of 1 year ðT ¼ 1Þ, and take the book value of the firm’s total liabilities to be the face value of the firm’s debt. Assuming a time to maturity of T ¼ 1 is quite common (see, e.g., Bharath and Shumway, 2008; Campbell et al., 2008; Crosbie and Bohn, 2003; Vassalou and Xing, 2004). However, this assumption is an oversimplification. Consequently, we also use and prefer the Eberhart (2005) parametrization. He explicitly takes the amount of long-term debt into account. As an approximation of the time to expiration for the cap6 All results presented in this paper remain unchanged when we use total debt instead of current liabilities þ 12  long-term debt as face value of debt in the parametrization of Bharath and Shumway (2008) and Vassalou and Xing (2004).

ital structure presumed in the Merton (1974) model, he estimates the weighted average of the duration for the firm’s short-term debt and long-term debt as 0.6  (short-term debt ratio) +6.3  (longterm debt ratio). Thus, Eberhart (2005) assumes a short-term debt duration of 0.6 years and long-term debt duration of 6.3 years.7 The next step is to collect values of the risk-free rate and the market equity of the firm. Then, we have values for each of the variables in the two equations except for V and rV , the total value of the firm and the volatility of firm value, respectively. The last step is to solve the system of nonlinear equations numerically to obtain the market value of debt estimates. There are widespread applications of the Merton (1974) model such as pricing of credit risk (see, e.g., Duffie and Singleton, 2003) or forecasting of corporate default (see, e.g., Bharath and Shumway, 2008).8 Koutsomanoli-Filippaki and Mamatzakis (2009) calculate bank default risk using the Merton (1974) model. A popular implementation of the model is the commercial KMV model (see Crosbie and Bohn, 2003).9 3.2. Quality of estimation In the remainder of this subsection, we address the question of how good the Merton (1974) model works. To do this, we first summarize evidence found in the literature. In a second step, we compare the market value estimates obtained by using the above parametrizations with real bond prices of a subset of our firm sample. Eberhart (2005) performs two series of tests comparing the Merton (1974) model to the book value of debt approximation. Using stock and bond data, he finds consistent evidence that the Merton (1974) model provides more accurate debt value estimates than the book value of debt approximation. Second, he shows that 7 Eberhart (2005) estimates the debt duration for short-term (long-term) debt using the weighted average durations of bonds with durations of 1 year or less (more than 1 year) in the Lehman corporate bond database. We find a very similar long-term debt duration of 5.6 years in our corporate bond database, which is presented in detail in the next subsection. Therefore, we retain the parameter values of Eberhart (2005) to calculate the time to maturity in the implementation of his model. 8 Other recent studies which use the Merton (1974) model are Duffie et al. (2007) and Campbell et al. (2008). 9 Moody’s KMV is the world’s leading provider of quantitative credit analysis tools to lenders, investors, and corporations.

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M. Glaser, S. Müller / Journal of Banking & Finance 34 (2010) 2307–2317 Table 2 Estimation of market values of debt: summary of input parameters. Input parameters

Eberhart (2005)

Vassalou and Xing (2004) and Bharath and Shumway (2008) Standard deviation of daily stock returns over the past 125 trading days 1

Stock return (equity) volatility Time to maturity

rE

Standard deviation of daily stock returns over the past 125 trading days

T

Risk-free rate Face value of debt

r F

0.6  short-term debt ratio +6.3  long-term debt ratio 1-year Fibor

Market capitalization

E

Total debtð1 þ iÞT with i = coupon rate (interest expense divided by total interest bearing debt) Market capitalization (stock price times shares outstanding)

1-year Fibor Current liabilities þ 12  long-term debt (KMV assumption) Market capitalization (stock price times shares outstanding)

This table shows a summary of the input parameters used in this paper to estimate market values of debt. To estimate market values of debt, we solve Eqs. (A.2) and (A.5) of Appendix A, a system of nonlinear equations, for V and rV . Therefore, we need values for the remaining variables: stock return (equity) volatility (rE ), time to maturity (T), the risk-free rate (r), the face value of debt (F), and the market capitalization (E). We use the set of input parameters suggested by three recent studies (Bharath and Shumway, 2008; Eberhart, 2005; Vassalou and Xing, 2004).

the Merton (1974) model is an easily estimated alternative to the book value of debt approximation as it only requires standard data available in data bases like CRSP or Compustat. Therefore, he concludes that the book value of debt approximation not only leads to severe biases, but is also an unnecessary simplification. Eom et al. (2004) empirically test several structural models of corporate bond pricing, among them the Merton (1974) model. They implement the models using a sample of 182 bond prices from firms during the period from 1986 to 1997. They find that more sophisticated structural models of corporate bond pricing do not outperform the Merton (1974) model. Schaefer and Strebulaev (2008) show that structural models of credit risk provide quite accurate predictions of the sensitivity of corporate bond returns to changes in the value of equity (hedge ratios). The main result of this paper is that even the simplest of the structural models, the Merton (1974) model, produces hedge ratios that are not rejected in time-series tests. To evaluate the accuracy of the debt market value estimates for the two different model parametrizations shown in Table 2, we obtain bond prices from the iBoxx EUR Corporates database for a subset of our firm sample. The data is provided by Deutsche Börse AG, which calculates and disseminates the iBoxx EUR index family. Those indices aim at representing the investment grade fixed-income market for Euro-denominated bonds. They comprise all bonds issued in the Euro-zone by central and local governments, banks, and private corporations. A bond must have a predetermined cash flow structure (e.g., plain vanilla bonds or zero coupon bonds), a time to maturity of at least one year, and a minimum amount outstanding of 500 million euros to be included. Moreover, an investment grade rating for the bond must be provided by at least one rating agency (Moody’s, S&P, or Fitch). The iBoxx EUR Corporates database contains information such as market value, nominal amount, coupon, yield, and maturity of the bonds. We obtain the constituent lists for the period from December 2000 to December 2006 and match them with our CDAX sample. While the iBoxx index series is biased towards larger bonds being rated, it is, to the best of our knowledge, the most comprehensive database on bond prices for Euro-denominated bonds. It is managed with a philosophy to reflect the investable fixed income universe. As a result, market values of debt should not be distorted by illiquidity constraints. Table 3 shows the number of firms in our sample with tradable debt securities, separated by year and diversification degree. Within the total CDAX universe only eight firm-year observations classified as focused can be matched with bond data. In contrast, diversified firms are bond-financed to a larger extent as indicated by the 313 diversified firm-year observations with bond data. Still, this number is rather small compared to the total firm universe.

Moreover, an inspection of Columns 4 and 5, which relate the amount outstanding to total debt and long-term debt, shows that most corporate debt in our sample is not traded. The average ratio is 13.6% for total debt and 20.0% for long-term debt. The last column presents the average excess values for the firms having traded debt outstanding in the respective year. Excess values are calculated using book values of debt. Given the fact that most firms are classified as diversified, we should expect a negative mean excess value in the sample. Apparently, this is not the case. The mean excess value of 0.15 indicates that bond-financed firms have an above-average valuation compared to the total firm sample. This finding is consistent with Santos and Winton (2008), who report a positive relationship between a firm’s market-to-book ratio and its access to the bond market. The description of the bond database clearly suggests that it is necessary to estimate market values of debt if one wants to test the validity of the book value bias of debt argument, at least for bank-based systems like Germany. Most importantly, considering the high average excess values for firms with bonds outstanding, using a smaller sample with market values of debt available instead, may lead to a sample selection bias in our case. Although it is not possible (or not appropriate) to test the book value bias of debt using market values of debt in our case, the question remains how accurate the estimation methods (i.e., parametrizations) are. In the following, we provide information on this issue. To do so, we compare the market-to-book ratios of total firm debt using the market value estimates and the observed ratios of the bonds outstanding.

Table 3 Bond price data: descriptive statistics. No. of firms diversified

Year

No. of firms focused

2000 2001 2002 2003 2004 2005 2006

0 0 1 3 1 1 2

17 23 42 58 49 59 65

Total Mean

8

313

Average of bond value in % of total debt [wc03255]

Average of bond value in % of long-term debt [wc03251]

Average excess value

28.0 12.2 21.7 16.0 13.1 8.0 8.3

47.4 17.3 31.5 24.0 18.7 10.8 12.0

0.35 0.36 0.17 0.24 0.09 0.25 0.10

13.6

20.0

0.15

This table shows the number of firms in our sample with tradable debt securities, separated by year and diversification degree and the relation of the bond amount outstanding to total, respectively, long-term firm debt. The last column presents the average excess value measure of the firms with bonds outstanding in the respective year.

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Table 4 Cross sectional distribution of bond prices and market value of debt estimates. Method

Mean

Min.

p25

Median

p75

Max.

N

Actual (bonds) Eberhart (2005) Vassalou and Xing (2004) and Bharath and Shumway (2008)

1.08 1.09 0.97

0.95 0.93 0.95

1.03 0.98 0.96

1.07 1.06 0.97

1.10 1.12 0.98

1.46 1.38 0.98

321 318 318

This table presents the cross-sectional distribution of market-to-book values using observed bond prices and market value of debt estimates based on the different parametrizations.

Table 5 Estimation error of the market value of debt estimates. Year

Book values of debt

Eberhart (2005) estimation

Vassalou and Xing (2004) and Bharath and Shumway (2008) estimation

2000 2001 2002 2003 2004 2005 2006

0.03 0.05 0.08 0.09 0.11 0.09 0.04

0.02 0.05 0.08 0.00 0.01 0.03 0.01

0.08 0.08 0.11 0.11 0.14 0.12 0.08

Mean

0.08

0.01

0.11

This table presents the estimation errors of the different approaches. See Section 3 for details on the calculation of the estimation error.

Table 4 depicts the cross-sectional variation in bond market values to face values and market-to-book ratios for total firm debt for both estimation methods. There is a considerable variation in bond prices, which highlights the potential benefit of using market value estimates instead of book values. While the mean bond market value to face value is 1.08, the highest value is 1.46 and the lowest value is 0.95.10 However, if we look at the relation of market value estimates to book values, we find that the Bharath and Shumway (2008) and Vassalou and Xing (2004) parametrization is not capable of replicating this observed cross-sectional heterogeneity. Since both studies use unadjusted book values of debt as face values, it is not surprising that market value estimates are lower than book values and that the market-to-book ratio is always below 1. However, it is remarkable how similar minimum, mean, and maximum market-to-book ratios are for this parametrization. In contrast, the Eberhart (2005) model, which adjusts the book value of debt in order to obtain face values, produces a dispersion in market-to-book ratios which is very similar when compared to the observed distribution of bond market-to-face value ratios. The mean ratio is 1.09, the minimum is 0.93, and the maximum is 1.38. In Table 5, we compare the estimation error based on the two different market estimates, which is defined as follows:

Estimation Error ¼

  Actual Market Value Face Value Bond   Estimated Market Value  : Book Value Firm

ð3Þ

Hence, we compare the market-to-book ratio based on observed bond prices with the market-to-book ratio based on market value estimates for each firm-year observation.11 We also calculate the 10 The fact that most bonds are traded above their face values may reflect the decline of the yield curve over the sample period as well as the investment-grade quality of the bond issuers. 11 Note that this procedure assumes that the outstanding bonds are representative for total firm debt, which is a simplifying but necessary assumption.

estimation error of replacing market value estimates by book values to assess the bias in using book values for firm debt and start with an examination of this issue in Column 2 of Table 5. Over the complete sample period, there is a considerable book bias of 0.08 or 8%, indicating that book values of debt are a downward biased proxy for market values. The mean estimation error varies over time, but exists in all years. However, as shown in Column 4, the model of Bharath and Shumway (2008) and Vassalou and Xing (2004) produces an even larger estimation error (11%) suggesting that it does not lead to better estimates. In contrast, the Eberhart (2005) parametrization produces a much lower mean estimation error (0.01), which is also much lower than the mean estimation error using book values. In fact, the obtained market-to-book ratios based on debt value estimates are very close to the observed bond market-to-book ratios.12 To summarize, a considerable variation in market-to-book ratios can be observed for tradable debt in our firm sample. The only parametrization which is capable of reproducing this variation and also reduces the estimation error compared to using book values of debt is based on the Eberhart (2005) model, which also seems to be the most realistic parametrization ex ante (e.g., it uses a realistic time to maturity). It is interesting to note that some parametrizations of the Merton (1974) model lead to higher estimation errors when compared to book values of debt. In the following, we therefore focus on a comparison between the excess value measure which uses book values of debt and an excess value measure which is based on market value estimates obtained by using the Eberhart (2005) assumptions.

4. Results 4.1. Basic results Table 6, Panel A, presents the median excess value measures for focused and diversified firms. Furthermore, the table contains the number of observations in each group as well as the p-value of a Wilcoxon rank-sum test (Mann–Whitney test). Null hypothesis is that the two samples are from populations with the same distribution. There are two main observations. First, replacing the book value of debt by market value of debt estimates leads to a reduction of the diversification discount. This is in line with our prediction and consistent with Mansi and Reeb (2002). The discount is reduced from 15% to 5% (see Result (1)), i.e., to one third of the original discount which is based on the traditional Berger and Ofek (1995) measure in which the book value of debt is used. Second, even when we use the Eberhart (2005) parameter values to estimate market values of debt, the resulting discount of 5% remains significant. Table 7 shows coefficient estimates from pooled OLS (Regressions (1) and (2)) and fixed effects panel regressions (Regressions (3) and (4)) of excess value on a diversified firm indicator and control variables such as in Mansi and Reeb (2002). Control variables are the natural logarithm of total assets, operating income divided by total assets, and capital expenditures divided by total assets. In Regressions (1) and (3), the excess value is based on the traditional Berger and Ofek (1995) measure which uses book values of debt. In Regressions (2) and (4), book value of debt is replaced by market 12 We also repeat the analysis using the absolute estimation error and the mean squared error to assess the quality of the estimation procedures. In line with the results reported in Table 5, we find that the Eberhart (2005) application also yields the lowest absolute and mean squared error.

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M. Glaser, S. Müller / Journal of Banking & Finance 34 (2010) 2307–2317 Table 6 Excess value measures, Altman’s Z, and volatility for focused and diversified firms. Panel A: Excess value measures Sample

Debt measure

N

Median foc.

N

Median div.

p-value (Wilcoxon)

(1)

Full sample

(2)

All-equity

(3)

High proportion of long-term debt

(4)

Low proportion of long-term debt

Book value Eberhart (2005) Book value Eberhart (2005) Book value Eberhart (2005) Book value Eberhart (2005)

1411 1029 582 386 565 424 846 605

0 0 0.216 0.224 0.058 0.025 0.056 0.026

2375 2021 588 493 1403 1199 972 822

0.147 0.051 0.273 0.346 0.226 0.123 0.019 0.111

<0.0001*** 0.019** 0.713 0.672 0.0003*** 0.219 0.013** 0.872

Sample

Distress measure

N

Median foc.

N

Median div.

p-value (Wilcoxon)

Full sample

Altman’s Z (lower value = more distressed)

1133

Sample

Risk measure

N

Full sample

Volatility

1630

Panel B: Altman’s Z

(5)

1.443

2086

0.005***

1.499

Panel C: Volatility

(6)

Median foc. 0.440

N

Median div.

2551

p-value (Wilcoxon) <0.0001***

0.376

This table presents median excess value measures (Panel A). Excess value measures are shown for our full sample (Result (1)), for ‘‘all-equity firms” (Result (2)) as well as for firms with a high (Result (3)) and a low proportion of long-term debt (Result (4)). We define a firm as all-equity financed if leverage is below 5% with leverage computed as the ratio of book value of debt (short-term debt plus long-term debt) to book value of debt plus book value of equity. A firm is classified as having a high (low) proportion of long-term debt if the amount of long-term debt relative to the sum of equity and long term as well as short-term debt is above (below) the sample median. Moreover, the table shows median Altman’s Z scores (Panel B) as well as the annualized volatility (Panel C) for focused and diversified firms. Altman’s Z score is defined in Table 1. Volatility is measured as standard deviation of daily stock returns over the past 125 trading days. Furthermore, the table contains the number of observations in each group as well as the p-value of a Wilcoxon rank-sum test (Mann–Whitney test). Null hypothesis is that the two samples are from populations with the same distribution. ** Significance at 5%. *** Significance at 1%.

Table 7 Determinants of excess value. Dependent variable: excess value

Pooled OLS

Debt measure

Book value (1)

Eberhart (2005) estimation (2)

Book value (3)

Eberhart (2005) estimation (4)

Diversified firm (dummy)

0.139*** (0.000) 0.004 (0.509) 0.097 (0.336) 1.117*** (0.001) 0.059 (0.516)

0.082** (0.020) 0.001 (0.891) 0.182 (0.139) 1.327*** (0.001) 0.127 (0.278)

0.077** (0.014) 0.007 (0.561) 0.273*** (0.005) 0.769** (0.026) 0.234 (0.169)

0.067* (0.087) 0.002 (0.885) 0.547*** (0.000) 1.001*** (0.008) 0.169 (0.422)

Firm fixed effects Year fixed effects Accounting standard fixed effects

No Yes Yes

No Yes Yes

Yes Yes Yes

Yes Yes Yes

Observations Firms (clusters)

4070

3118

4070 812

3118 628

Adjusted R-squared R-squared within model R-squared overall model R-squared between model

0.031

0.030 0.020 0.014 0.003

0.032 0.017 0.007

ln(total assets) Operating income/total assets Capital expenditures/total assets Constant

Panel regressions

This table shows coefficient estimates from pooled OLS (Regressions (1) and (2)) and fixed effects panel regressions (Regressions (3) and (4)) of excess value on a diversified firm indicator and control variables such as in Mansi and Reeb (2002). Excess value is the natural logarithm of the ratio of a firm’s actual value to its imputed value. A firm’s imputed value is the sum of the imputed values of its segments, with each segment’s imputed value being equal to the segment’s sales multiplied by its industry median ratio of capital to sales. Control variables are the natural logarithm of total assets, operating income divided by total assets, and capital expenditures divided by total assets. In Regressions (1) and (3), the excess value is based on the traditional Berger and Ofek (1995) measure which uses book values of debt. In Regressions (2) and (4), book value of debt is replaced by market value of debt estimates that are based on implementations of the Merton (1974) model suggested by Eberhart (2005). Time period is 2000–2006. Year dummies and accounting standard dummies are included. See Table 1 for details on the definition of variables. Variables are winsorized at the 1% level. Robust p-values are in parentheses. * Significance at the 10% level. ** Significance at the 5% level. *** Significance at the 1% level.

value of debt estimates that are based on implementations of the Merton (1974) model suggested by Eberhart (2005). The results are similar to those presented in Mansi and Reeb (2002). Table 7 shows, for example, that operating income has a

positive effect on excess value. When excess value is calculated using the traditional Berger and Ofek (1995) measure (Regressions (1) and (3)), the diversified dummy is significantly negative at least at the 5% level even in a regression with firm fixed effects. In

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M. Glaser, S. Müller / Journal of Banking & Finance 34 (2010) 2307–2317

Regression (4), the coefficient of the diversified dummy variable is only marginally significant at the 10 % level. In connection with the results of Table 6 we can conclude that replacing the book value of debt with market value of debt estimates leads to a reduction of the diversification discount. However, the discount does not completely vanish. The book value of debt bias, therefore, does not completely explain the diversification discount. We further analyze this phenomenon in several robustness checks. We find, for example, that the accounting standards used do not affect the valuation difference between focused and diversified firms although they may affect the absolute valuation of firms (see, e.g., Daske et al., 2008). We also find that our main results shown in Table 7 are not driven by industry effects. To do this, we include industry dummies instead of firm fixed effects in the regressions and calculate industry-adjusted standard errors. 4.2. Further results supporting the risk reduction hypothesis The results presented so far are consistent with the risk reduction hypothesis. In this subsection, we show further tests to better understand whether the risk reduction hypothesis holds. To directly address the risk reduction hypothesis, we compute the median excess value for focused and diversified firms within several sub-samples. In Table 6, Panel A, we do not only show excess value measures for our full sample but also for ‘‘all-equity” firms (see Result (2)) as in Mansi and Reeb (2002). The difference in excess values for focused and diversified firms is insignificant implying that there is no diversification discount among ‘‘all-equity” firms supporting the risk reduction argument. Moreover, we separately compute the median excess values for sub-samples of firms with a high proportion and firms with a low proportion of long-term debt (see Results (3) and (4) of Table 6, Panel A). In line with the risk reduction hypothesis, we find a significant difference in the excess values of focused and diversified firms using book values of debt. This difference renders insignificant when we compute the excess value based on the Eberhart (2005) specification. Furthermore, these results indicate that the maturity of debt plays a role in the shareholder diversification discount as the discount tends to be larger the higher the proportion of long-term debt. This may indicate that book values are more likely to diverge from market values the longer the time to maturity. This in turn has implications for the computation of the diversification discount. However, we are not able to replicate the results of the regression of the book value error (= book value of debt  market value of debt) on the multi-segment variable (diversified dummy) and control variables presented in Table IV of Mansi and Reeb (2002). In unreported results, we find that, although the coefficient of the multi-segment variable is negative (like in Mansi and Reeb, 2002), it is not significant. This might be due to the relatively small sample with only 318 firm-year observations in our bond sample. Looking at Panel B, we compute the median value of Altman’s Z (see Agarwal and Taffler, 2008; Altman, 1968) for focused and diversified firms.13 Further supporting our risk reduction argument, we find a significant difference of the respective median values, implying that focused firms tend to be more financially distressed. In addition, we look at the equity volatility of focused as well as diversified firms in Panel C. Supporting previous findings, we find a significantly lower volatility of diversified firms. To summarize, we presented several additional results in this subsection, which are consistent with the risk reduction hypothe13

Note that, for Altman’s Z score, a lower value means a higher degree of financial distress. See Table 1 for a definition of Altman’s Z score. Coefficients are based on Sufi (2009).

Table 8 Determinants of excess value: the influence of ownership structure. Dependent variable: excess value Debt measure

Pooled OLS Book value (1)

Eberhart (2005) estimation (2)

Book value (3)

Eberhart (2005) estimation (4)

Diversified firm (dummy) ln(total assets)

0.170*** (0.000) 0.001 (0.945) 0.108 (0.308) 0.986*** (0.006) 0.117 (0.106) 0.067 (0.438)

0.178*** (0.002) 0.014* (0.090) 0.187 (0.130) 1.040** (0.013) 0.110 (0.222) 0.230** (0.027)

0.118** (0.014) 0.010 (0.494) 0.315*** (0.002) 0.596* (0.090) 0.030 (0.678) 0.076 (0.338)

0.106* (0.090) 0.010 (0.517) 0.544*** (0.000) 0.757** (0.045) 0.002 (0.978) 0.086 (0.385)

0.061 (0.557)

0.296** (0.016)

0.259 (0.183)

0.289 (0.181)

Firm fixed effects Year fixed effects Accounting standard fixed effects

No Yes Yes

No Yes Yes

Yes Yes Yes

Yes Yes Yes

Observations Firms (clusters)

3750

3040

3750 753

3040 618

Adjusted R-squared R-squared within model R-squared overall model R-squared between model

0.028

0.030 0.019 0.019

0.032 0.019

0.011

0.009

Operating income/total assets Capital expenditures/ total assets Closely held shares (in %) Closely held shares (in %) X diversified firm (dummy) Constant

Panel regressions

This table shows coefficient estimates from pooled OLS (Regressions (1) and (2)) and fixed effects panel regressions (Regressions (3) and (4)) of excess value on a diversified firm indicator and control variables such as in Mansi and Reeb (2002). Excess value is the natural logarithm of the ratio of a firm’s actual value to its imputed value. A firm’s imputed value is the sum of the imputed values of its segments, with each segment’s imputed value being equal to the segment’s sales multiplied by its industry median ratio of capital to sales. Control variables are the natural logarithm of total assets, operating income divided by total assets, and capital expenditures divided by total assets. In Regressions (1) and (3), the excess value is based on the traditional Berger and Ofek (1995) measure which uses book values of debt. In Regressions (2) and (4), book value of debt is replaced by market value of debt estimates that are based on implementations of the Merton (1974) model suggested by Eberhart (2005). In contrast to the regressions presented in Table 7, we also include the percentage of closely held shares as a measure of the ownership structure of a firm as well as an interaction term between ownership structure and the diversification dummy variable. Time period is 2000–2006. Year dummies and accounting standard dummies are included. See Table 1 for details on the definition of variables. Variables are winsorized at the 1% level. Robust p-values are in parentheses. * Significance at the 10% level. ** Significance at the 5% level. *** Significance at the 1% level.

sis of corporate diversification. ‘‘All-equity” firms and firms with a low proportion of long-term debt do not show or show only a weak diversification discount. In contrast, firms with a high proportion of long-term debt exhibit a strong diversification discount. Furthermore, focused firms are riskier, as measured by volatility, and exhibit a higher degree of financial distress, as measured by Altman’s Z score.

4.3. The influence of ownership structure Moreover, we analyze the effects of the ownership structure of a firm as a measure of corporate governance on the diversification discount. In line with several recent papers (see, e.g., Doidge et al., 2007), we use the Worldscope variable ‘‘closely held shares”

M. Glaser, S. Müller / Journal of Banking & Finance 34 (2010) 2307–2317

as a measure of ownership structure.14 A higher degree of closely held shares is usually regarded as better corporate governance (see, e.g., Singh et al., 2004). Results are presented in Table 8. The table shows that all coefficient estimates of the diversification dummy variable are larger when we control for ownership. Furthermore, the interaction coefficient between ownership and the diversification dummy is positive in all regressions and significant in Regression (2). These results are broadly consistent with those of Hoechle et al. (2009) and Kim and Mathur (2008). For US firms, for example, Hoechle et al. (2009) also find that the negative value impact of diversification is amplified by adverse governance variables such as low CEO ownership. Kim and Mathur (2008) find that firms with a higher insider ownership percentage are associated with a higher excess value. Two recent working papers (Anderson et al., 2009, Faccio et al., 2009) shed light on why ownership structure may have an influence on the degree of diversification. Both studies show that large shareholders can have a strong impact on the nature of corporate investment.

5. Discussion and conclusion Prior literature documents that diversified firms trade at a discount relative to the sum of imputed values for their business segments. However, theoretical arguments suggest that corporate diversification has both a positive and a negative impact on value. Empirical research on the value impacts of corporate diversification suggests that firm value is decreasing in diversification. In this paper, we argue that there is actually much less evidence of a general loss of investor wealth associated with corporate diversification. Our major line of reasoning is that the excess value concept suggested by Berger and Ofek (1995) underestimates the firm value of diversified firms compared to focused ones. And since most later studies which analyze potential causes of the diversification discount follow the Berger and Ofek (1995) procedure, they may also contain a systematic measurement bias and overestimate the discount. One of the obvious consequences of corporate diversification (apart from any potentially increasing inefficiencies in the internal capital budgeting process) is that it should lead to lower firm risk if business units with cash flows which are not perfectly positively correlated are grouped together. In terms of the Merton (1974) model of debt valuation, lower firm risk (lower volatility of the firm’s asset value) will increase bondholder’s value at the expense of shareholder’s value. The argument is that the equity of a firm can be viewed as a call option on the firm’s assets because shareholders are the residual claimants on the firm’s assets after any obligations have been met. Thus, there is reason to believe that book values of corporate debt are a more downward biased measure of market values for diversified companies. The traditional Berger and Ofek (1995) excess value measure compares the firm value of a company computed as the market value of equity plus the book value of debt to its imputed value as if its segments operated as stand-alone firms. Book values of debt are used as a proxy for market values of debt because most corporate 14 We compare this variable with hand-collected ownership data of our sample firms. German companies are required to report the holdings of all shareholders who own more than 5%. We hand-collect this information from annual reports. Based on this information, we construct three widely used ownership measures: the sum of the shareholdings of all owners who own more than 5% of a firm, a Herfindahl index of the individual ownership stakes as a measure of ownership concentration, and the stake of the firm’s largest shareholder (if the shareholder owns more than 5%). We find that all three ownership structure variables are highly significantly positively correlated with the Worldscope variable ‘‘closely held shares” [wc08021] with correlation coefficients of more than 0.7. To ensure that our results can be replicated easily, we decide to use the Worldscope variable ‘‘closely held shares” instead of the hand-collected data.

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debt is not traded implying that market values are not observable. Under the assumption that book values are reasonably close to market values of debt and that any differences are not systematically related to the degree of corporate diversification this approach is not problematic. However, this is unlikely to be the case as we describe above. This argument was first put forward by Mansi and Reeb (2002), who compute the excess value for a subset of diversified firms using market values of debt. They find that there is no significant diversification discount if one relies on the market price of debt. While Mansi and Reeb (2002) use actual market prices of debt from about 13% of the original sample of US firms, we employ a different method to assess the magnitude of the bias in the excess value computation. We replace the book value of debt by market value of debt estimates that are based on the implementation of the Merton (1974) model suggested by Eberhart (2005). This procedure is possible for all firms in our sample. To summarize, Mansi and Reeb (2002) use the true measure of the value of debt (the actual market price) for a subsample of firms whereas our study uses estimates of the market values for the whole firm universe. As estimates may be noisy, we extensively address how noisy our estimates actually are. It turns out that they are quite precise. Furthermore, we stress that our way of testing the risk reduction hypothesis is better suited for bank-based countries like Germany for which bank credit is important and where market prices of debt barely exist. In line with Mansi and Reeb (2002), the diversification discount is reduced. Additional tests are also consistent with the risk reduction hypothesis of corporate diversification. Both the Mansi and Reeb (2002) and our study suggest that the risk reduction hypothesis plays an important role in explaining the size of the discount in studies using the traditional Berger and Ofek (1995) excess value measure. Our results differ from those of Mansi and Reeb (2002) because there remains a small but statistically significant discount in our firm sample. We cannot rule out the possibility that this small difference is driven by the fact that our market value estimates are measured with error. Note, that we are only able to show that our estimation procedure works quite well for firms which have bonds outstanding. Given that we also show that ownership structure affects the diversification discount, we conclude that the book value of debt bias is unlikely to be the sole explanation for the diversification discount. Future research should therefore analyze which economic factors additionally drive the diversification discount. Recently proposed factors are managerial optimism, managerial power, corporate governance, or efficiency of internal capital allocation. Appendix A. Sketch of the Merton model In the appendix, we describe the Merton (1974) bond pricing model.15 The Merton (1974) model makes the following assumptions. The first is that the total value of a firm follows a geometric Brownian motion,

dV ¼ lV dt þ rV V dW;

ðA:1Þ

where V is the total value of the firm, l is the expected continuously compounded return on V, rV is the volatility of firm value and dW is a standard Wiener process. The second assumption of the Merton (1974) model is that the firm has issued just one discount bond maturing in T periods. Under these assumptions, the equity of the firm is a call option on the underlying value of the firm with a strike price equal to the face value of the firm’s debt and a time-to-maturity of T. Moreover, the 15

The following paragraphs are based on Bharath and Shumway (2008).

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value of equity as a function of the total value of the firm can be described by the Black–Scholes–Merton formula. Symbolically, the Merton model states that the equity value of a firm satisfies

E ¼ VNðd1 Þ  erT FNðd2 Þ;

ðA:2Þ

where E is the market value of the firm’s equity, F is the face value of the firm’s debt, r is the risk-free rate, NðÞ is the cumulative standard normal distribution function, d1 is given by

d1 ¼

ln

V  F

þ ðr þ 0:5r2V ÞT pffiffiffi ; rV T

ðA:3Þ

pffiffiffi and d2 is d1  rV T . The Merton (1974) model makes use of two equations. The first is the Black–Scholes–Merton Eq. (A.2) which expresses the value of a firm’s equity as a function of the value of the firm. The second relates the volatility of the firm’s value to the volatility of its equity (see Eq. (A.5)). Under the assumptions in Merton (1974), the value of equity is a function of the value of the firm and time, so it follows from Itô’s lemma that

rE ¼

  V @E rV : E @V

ðA:4Þ

In the Black–Scholes–Merton model, it can be shown that ¼ Nðd1 Þ, so that under the assumptions in the Merton (1974) model, the asset volatility of the firm and its equity volatility are related by

@E @V

rE ¼

  V Nðd1 ÞrV ; E

ðA:5Þ

where d1 is defined as in Eq. (A.3). In the Merton (1974) model, the value of the option is observed as the total value of the firm’s equity, while the value of the underlying asset (the total value of the firm) is not directly observable. Thus, while V must be inferred, E is easy to calculate by multiplying the firm’s shares outstanding by its current stock price (market capitalization). Similarly, in the Merton (1974) model, the volatility of equity, rE , can be estimated while the volatility of the underlying firm, rV , must be inferred. To obtain the market value estimates of debt, one has to subtract the market capitalization E from the inferred total firm value V. The first step in implementing the Merton (1974) model is to estimate rE from historical stock returns data. The second step is to choose a forecasting horizon and a measure of the face value of the firm’s debt. The third step is to collect values of the risk-free rate and the market equity of the firm. Then, we have values for each of the variables in Eqs. (A.2) and (A.5) except for V and rV , the total value of the firm and the volatility of the firm value, respectively. The next step in implementing the model is to solve Eqs. (A.2) and (A.5) numerically for values of V and rV . References Agarwal, V., Taffler, R., 2008. Comparing the performance of market-based and accounting-based bankruptcy prediction models. Journal of Banking and Finance 32, 1541–1551. Altman, E.I., 1968. Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance 23, 589–609. Amihud, Y., Lev, B., 1981. Risk reduction as a managerial motive for conglomerate mergers. Bell Journal of Economics 12, 605–617. Ammann, M., Hoechle, D., Schmid, M., 2008. Is there really no conglomerate discount? Working paper, Swiss Institute of Banking and Finance, University of St. Gallen. Anderson, R., Duru, A., Reeb, D., 2009. R&D spending and capital expenditure decisions: The influence of ownership structure. Working paper. Berger, P.G., Ofek, E., 1995. Diversification’s effect on firm value. Journal of Financial Economics 37, 39–65. Bharath, S.T., Shumway, T., 2008. Forecasting default with the Merton distance to default model. Review of Financial Studies 21, 1339–1369.

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