Target zones on firm's value

In the present paper we extend the traditional literature on Dynamic Capital Structure initiated by Merton (1974) and Leland (1994) to a Target Zone & agrave; la Krugman (1991). The existing literature focuses on the effects caused by several type of restrictions in the bankruptcy state, without focusing on the evolution of the firm's value in good state. We show that the conditions excluding the explosive root of the differential equation solving debt and equity equation are in practice not sufficient to guarantee stability. The introduction of a Target Zone is in effect able to bound from above the value of the firm. We fully characterize the Target Zone of the firm's value and fully solve the dynamic system. The model delivers similar results to those obtained under Real Option approach. We extend our result to a mean reverting process leading revenue growth rate: this confirms all the conclusions from trade-off theory, as opposite to the case obtained with a simple arithmetic Brownian motion. The model is flexible enough to allow many further generalization.