The literature on capital structure commenced with the seminal paper by Mo-digliani and Miller (1958), who argued that in a frictionless market the value of the firm is independent of its capital structure. Hence, there is no optimal capi-tal structure and the firm's weighted average cost of capital remains constant regardless of the composition of debt and equity. The main mechanism behind these results originates from the assumption of the absence of frictions. Since investors can trade promptly in financial markets and causelessly alter their personal portfolios it follows that any modification in the firm's capital struc-ture can be undone by investors trading on their own account (Modigliani and Miller, 1958). This was clearly a far too restrictive setting, and when the as-sumption of no frictions is relaxed Modigliani and Miller (1963) show that tax-deductible interest payments give rise to an optimal capital structure consist-ing solely of debt (Modigliani and Miller 1963). Evidently, neither of these two extremes can be reconciled with empirically observed leverage ratios. In anoth-er classic paper Miller (1977) is making the setting more akin to the real world by considering a richer tax structure with both personal and corporate taxes that determine an economy-wide leverage ratio, but renders capital structure irrelevant for any individual firm. The aggregate equilibrium leverage ratio is determined by a clientele effect where high tax bracket investors who prefer income in the form of capital gains invest in low-leverage firms, whereas inves-tors in the other end of the scale invest in high-leverage firms. Thus, Miller uses an equilibrium argument to obtain the irrelevance proposition (Miller 1977).
After the contributions by Modigliani and Miller (1958,1963) the literature has been characterized by a dominant separation between (i) asymmetric infor-mation models based on information discrepancies between corporate insiders and informationally disadvantaged outside financiers and (ii) trade-off models where the firm trades off the tax benefits of debt with bankruptcy costs.
Meyes and Majluf (1984) provide an important contribution to the category of articles concerning asymmetric information. With the assumption that manag-ers have inside information and act in the interest of existing passive share-holders the firm might forego positive NPV-projects when outside financing is required to undertake a transitory real investment. Managers will prefer to issue debt rather than new equity, because investors correctly anticipate man-agement's desire to issue new shares when the stock is overpriced. In turn, prospective shareholders will be willing to pay a lower price for new shares and thereby reduce the proceeds from an equity issue, which dilutes existing share-holders (Meyes and Majluf, 1984). Hence, a descending pecking order consisting of retained earnings, debt, and equity emerges. Notice the assumption of pas-sive existing shareholders that ensure the firm's financial decisions cannot be undone through trading on the shareholders' own account. Other important contributions to this category of models include Ross (1977) where debt is used as a signaling device for firm quality and Leland and Pyle (1977) where the entrepreneur's willingness to invest in his own project reveals its quality to external financiers. In short, asymmetric information models point to a number of factors that might influence the capital structure decision, but a clear weak-ness is the lack of any explicit advice on optimal capital structure.
One of the first trade-off models is written by Kraus and Litzenberger (1973) who consider a firm that trades off the benefits with the costs of debt. The benefits consist of tax-deductible interest payments that reduce the firm's tax-able income, whereas the cost arise from direct and indirect bankruptcy costs. An optimal capital structure that maximizes the market value of the firm is determined by this fundamental trade-off (Kraus and Litzenberger 1973). Mey-ers (1984) compares the two approaches to capital structure and makes the additional observation that if the firm incurs adjustment costs it might be op-timal to deviate from its optimal capital structure. Adjustment costs then im-plies an optimal range of leverage ratios and can potentially explain the wide variation in empirically observed leverage ratios (Meyers, 1984).
The empirical literature on the pecking order theory versus the trade-off theo-ry is at best mixed. Frank and Goyal (2003) find that net equity issues track the firm's financing deficit closer than net debt issues contrary to the pecking order theory. They do, however, obtain some evidence that suggests large firms to some extent display features consistent with the pecking order theory, but conclude that it is not a robust theory. In an international comparison Wald (1999) documents that the most profitable firms have the lowest leverage, which contradicts the trade-off theory given that profitable firms should use more debt to shield earnings. Cotei and Farhat (2009) present evidence con-sistent with aspects of both pecking order and trade-off theory, which implies that the two frameworks are not mutually exclusive. Other authors tend to gravitate towards the trade-off theory e.g. Ju et al (2005) conclude that this framework performs fairly well in terms of predicting typical leverage levels. In addition, Strebulaev (2007) convincingly shows using a simulated cohort of firms based on an assumed underlying trade-off model that this synthetic dataset gives rise to several of the empirical regularities that are commonly interpreted as evidence against the trade-off theory. Similar to Meyers (1984) the key in-sight behind these results lies in the observation that in any cross section firms' actual and optimal leverage differ due to adjustment costs.
The breakthrough in contingent claims pricing pioneered by Black and Scholes (1973) and Merton (1974), which marked the inception of continuous-time capi-tal structure models. The ensuing continuous-time models can be distinguished by (i) structural models and (ii) reduced-form models. One of the main dimen-sions that motivate this distinction is in terms of modeling default. Structural models commence with an assumption on the dynamics governing the state variable and determine default as the first time the state variable hits (or falls below) a specified bankruptcy barrier. In contrast, reduced-form models assume the default event is a stochastic event driven by a default intensity while leav-ing aside the question of what actually triggers default. Another often men-tioned difference between the two approaches is the assumed information set available to the modeler. Strictly speaking, most structural models assume a comprehensive information set similar to what is observed by the manager, whereas reduce-form models require a limited information set closer to what is observed in the market. The reduced-form framework has proven particularly successful for modeling bonds and credit derivatives where examples include Jarrow et al (1997), Lando (1998) and Duffie and Singleton (1999) among many others. Duffie and Lando (2001) develop a structural model where bond inves-tors imperfectly observe the firm's asset value and obtain a default-arrival in-tensity process consistent with reduced-form representation. Hence, their con-tribution bridges the two types of model frameworks. In a nutshell, reduced-form models are to a greater extent concerned with the pricing of corporate debt, whereas structural models focus on optimal structure.
This thesis will focus on structural models. The true power of structural models rests in the ability to jointly consider the valuation of corporate securities and the choice of financial structure by the firm. In the structural framework capi-tal structure affects the value of securities by way of altering cash flows and in turn the value of securities affect the choice of capital structure. Hence, there is an inherently dialectic relationship at the heart of structural models. Struc-tural models can be distinguished by (i) single-period static models and (ii) multiple-period dynamic models. The models typically assume a stationary debt level, which will also be the case in our model.
In the empirical literature some general consensus has emerged. But predicted optimal leverage ratios in structural models remain too high and predicted changes in leverage seem inconsistent with the data (e.g. Lemmon et al. 2008). Trying to reconcile the predictions of structural models with empirical regulari-ties several avenues have been pursued in the literature. A branch of literature focuses on the strategic debt renegotiation where shareholders act strategically and use the threat of bankruptcy to force renegotiation with debt holders when default is imminent. It has also been explored how alternative stochastic pro-cesses for the state variable affect the firm’s capital structure, e.g. Sarkar and Zapatero (2003) model the firm’s EBIT process with mean-reversion. Most structural models assume exogenous state variable, which is typically either unlevered assets or EBIT referred to as the firm fundamental. Consequently, capital structure implications remain challenging to reconcile with empirical regularities. This is to some extent my ambition in the thesis.
Before we develop the new model, one of the central existing capital structure models by Leland (1994) is reviewed. The models presented throughout the thesis share a set of general assumptions, which are explained in the section below.