Corporate Debt Value And Optimal Capital Structure

Corporate debt value and optimal capital structure is the main problem of the firm fi-ance. Specifically, capital structure is the core problem of a firm's finance decision. In 1954, Modigliani and Miller gave the answer of the above problem under special conditions, but it was very difficult to application because of the very hash assumptions. So the problem has caused public concern by many scholars since then and considerable development has made in the theory of capital structure. The theories of capital structure are chiefly four:net earnings theory, Jing Ying Ye earnings theory, MM theory and agency theory. Except net earnings theory, the rest three kinds of theories consider that the optimal capital structure of the firm is exists because of the impact of interest tax shields and bankruptcy cost. In this paper we will use the method of contingent claim to consider the corporate debt value and optimal capital structure under two different models.The breakouts of this paper are that first we consider the firm's value in two kinds of situation exogenous and endogenous respectively, while previous studies are mostly in exogenous conditions. Second when the value of the firm is endogenous, we consider the case that due to the technology innovation, policy risks, emergencies and other factors, the firm's value have jump. The previous studies are mostly consider the case that the firm's value is continuous. While when the firm's value is endogenous, we consider the case that the underlying asset follows the mean reversion model. The studies of the problem under this model are rare. In this paper the optimal financing amount and the optimal leverage ratio is calculated, furthermore the related results of numerical analysis are given. The main models and results are summarized as following. When the firm's asset value follows The debt value satisfies D(V, t) the following equation we also have the results as following.Theorem 1 When the asset value of the firm follows the simple jump diffusion model, the corporate debt value, equity value and the total value of the firm respectively is furthermore we abtain the optimal financing account and the optimal leverage ratio are in which The numerical results under this model please see the second part of the paper.When the product price follows the simple mean reversion model To the questions we discussed we have the following results.Theorem 2 As to the all-equity-financing firm, when r=δ, the firm V(P) value and the abandonment trigger value P0 is Theorem 3 The value of the levered firm and the debt value is in which, PD=C+R-σ/(?).Theorem 4 When the firm uses the first good investment decisions, the value of the investment option F1(P) is While when the firm uses the second good investment decisions, the value of the investment option F2(P) is Then, the optimal financing account of the firm is here, the expression of VL(P) and E(P) is in Theorem 3. PA1 and PA2 satisfy the following equation...