Convertibles or Stock: A Cash Flow Comparison Model with Credit Risk

Abstract

While much theoretical and empirical research examines the issuer’s choice between straight debt and equity, little attention has been paid to the choice relating to convertible bonds. The aim of this work is to propose a rational model that will aid managers or issuers to decide between convertibles and stock in raising a required amount of money by comparing the cash flow streams of both the alternatives with the aim of maximizing the value for the present shareholders. Indeed given the hybrid nature of convertibles, the comparison cannot be conducted by simply comparing dividend yield and coupon’s rate but it need a unified framework that, among other variables, take at least into account for the probability of conversion. The framework follows the works of Stone (1976) and Bierman (1973) with a suitable extension for considering convertible bonds instead of warrants. After outlining a basic model in a world without default risk, credit risk is then introduced by an intensity based approach with an internal corporate variable similar to the work of Madan and Unal (2000). Even if the results of the model are not available in closed form they can be easily approximated by a numerical integration.