Dynamical Corporate Finance

The way in which leverage and its expected dynamics impact on firm valuation is very different from the assumptions of the traditional static capital structure framework. The purpose of this book is to re-characterize the firm’s valuation process within a dynamical capital structure environment, by drawing on a vast body of recent and more traditional theoretical insights and empirical findings on firm evaluation, also including asset pricing literature. We offer a new setting in which practitioners and researchers are provided with new tools to anticipate changes in capital structure and setting prices for firm’s debt and equity accordingly.

This chapter has the fundamental role to introduce the reader to the basics of corporate finance. Broadly speaking, corporate finance is the branch of economic science which deals with the financing and investment decisions of firms, and how these decisions affect the value of corporate securities and their financial returns. A security is a contingent claim liability issued by a company, which attributes certain control rights to its holders. Control rights include, but are no restricted to, receiving certain cash flow streams. For instance, common stocks attribute the right to shareholders to receive dividends, as well as equal voting rights. Firms are not directly tradable, while their liabilities are. The set of the outstanding securities characterizes the ensemble of the control rights, and therefore the set of individuals that are entitled to split the (free) cash flows generated by the firm. Accordingly, the value of a firm is defined as the market value of its securities, net of cash and other equivalent risk-free assets. Netting for liquidity allows to identify the going concern value of the business, which is generally higher than the accounting book value of invested capital (fixed assets plus trade working capital).

This chapter deals with dynamic capital structure models with risk-free debt. This class of models is based on the presence of a borrowing constraint ensuring debt holders being always paid back in full. Namely, we consider the case of secured debt, in which a collateral constraint limits the amount of debt outstanding to the minimum resale price of the pledged assets, net of total interest expenses. Contrary to the case of unsecured debt, in which the firm borrows against cash flows, debt capacity is directly tight to the size of its balance sheet.

In the previous chapter we studied equilibrium investment and financing decisions in the case of perfect competition in the firm’s product market. A counterfactual result of the model is that the wedge between the expected firm’s profitability and the cost of capital is entirely driven by the size of investment adjustment costs. Namely, the larger \(||\theta \left (I_{t}\right )||\), the wider is the spread between the return on invested capital (RoIC), which is the ratio between operating earnings and the total capital stock, and the firm’s WACC, holding everything else constant.

This chapter is dedicated to continuous time methods in corporate finance, focusing on capital structure models in which the firm is assumed to be financed by equity and unsecured debt. The major difference with the discrete time setting is that investment and financing decisions take place at each \(t\in \mathbb {R}\), with free cash flows and payments on outstanding securities accruing continuously. Admittedly, while continuous time models are based on this purely theoretical abstraction, they are notwithstanding useful to characterize the occurrence of default episodes. We use the standard Ito’s processes to model the sources of randomness affecting free cash flows dynamics. Ito’s processes can be extended to include jumps, that is, a set of countable discontinuities occurring at deterministic or random Poisson times. In order to keep the discussion self-contained, jumps are excluded from both the exogenous processes driving the firm’s free cash flows, as well as discrete or lump sum payments to the firm claimholders, with the only possible exceptions of (i) the date at which the firm is established, say t = 0, and (ii) the date in which a default episode takes place.

The static trade-off theory of capital structure is based on the unsatisfactory premise that firms do not adjust debt over time. While alternative forms of commitment could be considered, of which the target interest coverage ratio is an example, there is a clear problem of time-consistency that must be taken into account. To clarify this point, consider again the case of the Leland model, in which shareholders commit to never issue additional debt in the future. Absent legal constraints preventing shareholders to adjust debt in the future, will they maintain their commitment?

In this chapter we extend in several ways the models developed in the previous chapters. Section 7.1 presents a more general version of the model of imperfect competition we discussed in Chap. 4. In particular, we introduce the presence of investment adjustment costs, production costs other than the consumption of inventories as well as the possibility for the firm to issue unsecured debt. The model does not admit a closed-form solution, but we will show that, within the class of Markov Perfect Equilibria, the capital structure of the firm is a combination of the results we obtained in the previous chapters.