Agency Cost, Capital Structure and Credit Risk∗ Luigi Malachini† Current Draft: April 2007, please do not distribute.

Extended Abstract The relation between external finance and investment decisions has occupied the finance literature for the last fifty years. In their seminal work, Modigliani and Miller (1958) prove that if capital markets are perfect and investment decisions are fixed, then the value of the firm does not depend on its financing decisions. Jensen and Meckling (1976), however, dispute the assumption that investment decisions can be taken independent of financing decisions. Their argument is that since equityholders do not bear the full cost of low returns, they have incentives to take riskier projects, potentially extracting value from the debtholders. This conflict of interest between the equityholders and the debtholders is referred to as the asset substitution problem. In addition to that, Myers (1977) shows that equityholders of a leveraged firm will underinvest because a fraction of the results of their investment will accrue to debtholders. The broad consensus at present is that the use of debt financing affects investment decisions, producing substantial inefficiencies. Moreover, another source of agency cost is the equityholders-managers relation, as documented in two papers that differs according to the specific way in which this conflict arises and in how debt alleviates the problem. In Harris and Raviv (1990) managers are assumed to want always to continue the firm’s current operations even if liquidation of the firm is preferred by investors. In Stulz (1990), managers are assumed to want always to invest all ∗

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Work developed under the supervision of Andrea Gamba. University of Verona and SAFE center.

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available funds even if paying out cash is better for investors. In both cases, it is assumed that the conflict cannot be resolved through contracts based on cash flow and investment expenditure. Debt mitigates the problem in the first model by giving debtholders the option to force liquidation if cash flows are poor. In the second model, as in Jensen (1986), debt payments reduce free cash flow. A large number of performance related wage incentives has been proposed in order to align the manager’s objective function with that of equityholders. Among these incentive methods the most popular are the equity based compensation plans1 . The exploitation of these incentive methods have indeed fed the problem of overvalued equity, as stated in Jensen (2004). The goal of this paper is to shed some light on the relation between capital structure decisions, manager compensation and how this translates into credit risk, in a firm driven by a manager paid with equity and cash. We also look at the effects of a change in the payment structure of the manager, such as the monetary wage and the percentage of the firm owned by the manager, analysing specifically the dynamic of agency costs. Another important issue we want to understand is the relation between agency costs and capital structure decisions with the manager’s risk aversion. A natural starting point is the Merton (1974) model based on the Black and Scholes (1973) option pricing model. The development of option-pricing techniques and the application to the study of corporate liabilities is where the modeling of credit risk has its foundations. While there was of course research out before this, the option-pricing literature, which views the value of stock and bonds issued by a firm as contingent claims on the firm’s assets, is the first to give us a strong link between a statistical model describing default and a financial model. Since the work of Merton, the option-pricing machinery has expanded significantly. The development of Merton (1974) model is related with some problems and questions that arise when using the machinery to price corporate debt. Merton models the simplest case of corporate debt pricing: he consider a single class of risky discount bonds while the model takes two key contractual provisions exogenously indeed the lower reorganization boundary (which is the threshold value of the firm at which the control of the firm transfers from the stockholders to the bondholders) is specified, and the compensation to be received by creditors upon reaching the lower reorganization boundary as taken as given. Past attempts to fit the Merton model on US corporate bonds proved unsatisfactory (Jones et al. (1984)). The model tended to systematically underestimate observed yields when realistic values of asset volatility were employed. This shortcoming has motivated the research for more accurate 1

See Tirole (2006) and Smith and Watts (1982).

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theoretical models that could deliver results and implications consistent with the empirical findings. A natural prerequisite is that their assumptions allow for realistic economic consideration , i.e., they came close to reality in capturing as many important factors as possible. In an attempt to improve accuracy, many authors have extended the original model in several directions, first of all introducing corporate taxation2 (Leland (1994), Leland and Toft (1996), Mauer and Ott (2000)) as well as personal taxation (Kane et al. (1985), Goldstein et al. (2001), Dangl and Zechner (2003), Hennessy and Whited (2004)). Another way would be the introduction of stochastic interest rate (Longstaff and Schwartz (1995)). On the side of bond indenture, some authors like Fischer et al. (1989), Leland and Toft (1996), Goldstein et al. (2001), Collin-Dufresne and Goldstein (2001), Christensen et al. (2002), or Dangl and Zechner (2003), Hennessy and Whited (2005), and Titman and Tsyplakov (2005) relax debt covenants allowing for financial restructuring and endogenizing capital structure decisions as a function of issuance and bankruptcy costs. Looking closer at the issue of what triggers default, there are some authors such as Fischer and Zechner (1989), Leland (1994), Leland and Toft (1996), Fan and Sundaresan (2000), Goldstein et al. (2001), Christensen et al. (2002), or more recently, Dangl and Zechner (2003), Titman and Tsyplakov (2005) that allow managers decide the threshold in the sole interest of equityholders so that the firms equity value is maximized. Another issue that has been studied by Anderson and Sundaresan (1996), Kane et al. (1985), Leland (1994), Leland and Toft (1996) and Mauer and Ott (2000) is the influence of bankruptcy costs. Anderson and Sundaresan (1996) demonstrate that properly accounting for costly bankruptcy can better explain observed credit spreads, and introduce strategic debt services through a game-theoretic model of the bankruptcy process that allows to point out the determinants of deviations from absolute priority. A closely related approach treats the liquidation decision as on option (see Mella-Barral and Perraudin (1997)) followed by the more recent paper of Christensen et al. (2002). The main results that arise from the numerical analysis of the models below can be summarized as follows. If we concentrate on the side of the bond indenture, the main conclusion of Dangl and Zechner (2003) is that as long as transaction costs associated with debt repurchase are low the adoption of a dynamic recapitalization policy increases credit spreads, and that the excess in credit spreads is more pronounced for high-risk firms and for firms with high growth rates. In addition, it is extremely sensitive to the size of bankruptcy costs. However, Titman and Tsyplakov (2005) and Goldstein The primary goal of several paper cited below is the study of capital structure. Nevertheless they include some references on the issue of yield spreads. 2

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et al. (2001) find that the opposite result holds, i.e., dynamic recapitalization reduces the credit spread. Higher credits spreads are delivered from an exogenous bankruptcy policy than for an endogenous one as reported in Leland and Toft (1996) and Dangl and Zechner (2003). A remarkable effort for measuring to what extent strategic debt service bears on the premium of risky debt is made by Mella-Barral and Perraudin (1997). They found that when a firm is not renegotiating the debt service, the proportion of the debt premium attributable to the possibility of strategic debt service is a constant, independent of the state variable. For typical parameter values this proportion is sizable, being around 30% to 40%. For firms with relatively low asset value volatility, this percentage increases substantially. If we look at the main comparative statics the credit spread is an increasing function of the leverage level (Merton (1974), Leland (1994), Anderson and Sundaresan (1996)), the volatility of the firm (Merton (1974), Fischer and Zechner (1989), Anderson and Sundaresan (1996), Leland (1998), Goldstein et al. (2001)) and the liquidation costs (Anderson and Sundaresan (1996)). As demonstrated in Merton (1974), Longstaff and Schwartz (1995), Leland and Toft (1996), Goldstein et al. (2001) the only variable that is negatively related to the credit spread is the riskless interest rate. As highlighted by several authors such as Merton (1974), Longstaff and Schwartz (1995), Leland and Toft (1996), there exist a link between the shape of the term structure of credit spreads and the leverage of a firm. Indeed for bonds with high ratings (low leverage) the term structure of credit spread is increasing in the issuance maturity date; for bonds with moderate-to-high leverage levels (i.e., intermediate term debt offers higher yields than either very short or very long term debt) it become humped shaped; finally, decreasing for high leverage values. Several of the models above have been implemented empirically to unveil the correspondence degree between the theoretical credit spread and the real ones. The first to implement the Merton’s model were Jones et al. (1984) and Ogden (1987), while Lyden and Saraniti (2000) add up Longstaff and Schwartz (1995) model. Anderson and Sundaresan (2000) formulate a general model which include: Merton (1974), Leland (1994), Anderson and Sundaresan (1996), and Mella-Barral and Perraudin (1997). They find that the models incorporating endogenous bankruptcy fit only slightly better than the original Merton model. Eom et al. (2004) compare five structural bond pricing models (Merton (1974), Geske (1977), Longstaff and Schwartz (1995), Leland and Toft (1996) and Collin-Dufresne and Goldstein (2001)); Huang and Huang (2002)). The conclusion of Eom et al. (2004) is that Longstaff and Schwartz (1995) and Collin-Dufresne and Goldstein (2001) models when compared with the mod4

els of either Merton or Geske produces higher predicted spreads, but this comes at a substantial expense to accuracy. These authors find that all these five models tend to generate extremely low spreads on the low leverage bonds and low business risk, and to generate very high spreads on the bonds considered to be very risky. Huang and Huang (2002) compare Longstaff and Schwartz (1995) (with stochastic interest rates), Leland and Toft (1996) (with endogenously determined default boundaries), Anderson and Sundaresan (1996), Anderson et al. (1996), Mella-Barral and Perraudin (1997) (with strategic defaults), and Collin-Dufresne and Goldstein (2001) (with mean-reverting leverage ratios policy). They find that these models, however, may not adequately capture the intuition that the credit risk premium can be potentially very high if we consider the fact that some special states of the economy associated with high default probabilities may also require high market risk premia. In a more recent paper, Ericsson et al. (2005) develop a simple pricing formula for credit default swaps that is applied to three distinct structural models: Leland (1994), Leland and Toft (1996) and Fan and Sundaresan (2000). Finally, the general conclusions of Huang and Huang (2002) and Ericsson et al. (2005) are in correspondence with those of the literature. A crucial assumption of both Merton model and all the subsequent structural credit risk models considered above is that the Modigliani-Miller theorem holds: investment is assumed to be exogenous, therefore independent of capital structure decisions of the firm. This is implemented through the assumption that exogenous variable that drives uncertainty in the model is not affected by financing decisions. This one could be either the market value of unlevered firm (Kane et al. (1985), Fischer and Zechner (1989), Leland (1994), Leland and Toft (1996), Fan and Sundaresan (2000)) or as in the work of Goldstein et al. (2001), the cash flow EBIT machine (Goldstein et al. (2001), Christensen et al. (2002), Dangl and Zechner (2003)). However, if we take a closer look at how investment decision influence financing decision, it is reasonable to argue that when a firm faces new investments the cash flows generated affects the need of raising capital to finance the business. Here we follow the framework of Aranda, Gamba and Poiega (2006) that adds investment flexibility to the general model by allowing stakeholders to choose the investment level. Past efforts of endogeneizing investment decisions (see, among others Mello and Parsons (1992), Mauer and Ott (2000)) treats capital structure as given. Several papers have recently analyzed the interplay between investment and financial flexibility. First, Hennessy and Whited (2004), Hennessy and Whited (2005), Gomes (2001) and Gamba and Triantis (2005) provide models that analyze the interactions between firms investment and financing policy where the lender imposes a collateral 5

constraint, ensuring that the firm can always meet its repayment obligations. Since debt is riskless, these models do not concentrate on credit risk. Titman and Tsyplakov (2005) present a structural model for risky debt, analyzing the credit spread and the probability of default as well. Yet, in their model, an increase in assets is completely financed by issuing additional debt, but doing this they restrict investment financing to debt. Financial and investment flexibility have been analyzed in the past models, now we add to this literature a new feature: the agency costs that comes from the employment of a manager in the decisional process of the firm. Management, specifically the CEO, has their own objectives to pursue. The classical ones are empire-building, risk averse investments and manipulating financial figures to optimize bonusses and stockprice-related options. The latter may be just outright fraudulent, but the first two certainly aren’t. They erode the stockholders value, but a risk averse strategy is not by definition fraudulent. This paper extends the existing literature of Structural Credit Risk Models by exploring within an infinite horizon discrete-time stochastic framework the joint effects of dynamic capital and investment decisions on capital structure decisions and credit spreads, in a framework where the principal actor of the model is a manager that controls the stochastic process driving the firm value. The organization of the article is as follows: section 1 introduces the discussion, section 2 is a review of the literature, section 3 describes the setup of the model, section 4 discusses the preliminary results.

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