Abstract
This article examines the value of equity, optimal bankruptcy boundary, and optimal dividend policy in a continuous-time framework with finite time maturity. The model of equity value is formulated as a parabolic variational inequality, or equivalently, a free boundary problem, where the free boundary corresponds to the optimal bankruptcy boundary. We present an analytical approach to analyze the behaviors of the free boundary. The regularity of the value function and the optimal dividend policy are studied as well. The main feature and difficulty are the discontinuity of the coefficient in the variational inequality.
Highlights
The value of debt and equity and default covenants have long been interested in corporate finance literature
2 Formulation of the model we develop a model of equity value with finite time maturity at time T
The model of equity value is formulated as a parabolic variational inequality with discontinuous coefficient, or equivalently, a free boundary problem, where the free boundary corresponds to the optimal bankruptcy boundary
Summary
The value of debt and equity and default covenants have long been interested in corporate finance literature. In our formulation, as Fan and Sundaresan in [ ], dividends, or equivalently the total payout ratio, denoted by δ, are treated as a control variable in the firm’s cash flow generating process Stockholders will choose their dividend policies by acting to maximize their equity value. It is worthwhile pointing out that, without consideration of the dividend policy, Han et al in [ ] deduced that ∂xu ≥ , which plays an important role in the analysis of the regularities of the free boundary There exists a positive τ , such that h(τ ) < h( ) for any τ ≤ τ ; combining the condition h( ) < x∞ and limτ→+∞ h(τ ) = x∞, we know that the free boundary h(τ ) is not monotonic in the interval [ , +∞)
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