Valuation of Convertible Bonds with Sequential Conversion

Abstract

In this paper, we characterize optimal conversion strategies and the related values of convertible bonds and stocks under a sequential conversion policy. Contrary to the existing literature, we consider firms that have both subordinated debt outstanding and convertible bonds. The additional debt results in wealth transfers among the holders of stock, convertible bonds, and additional debt, depending on the conversion strategy. These wealth transfers lead to remarkable differences in the optimal conversion policy and for the values of convertible bonds and stocks. It is possible that only a fraction of outstanding convertibles are converted at the last conversion date, that the stock value is partly strictly decreasing in the firm value, and partly decreasing in the dividend payment. It is also possible that certain stock values cannot occur when block conversion takes place, and that the value of a block-convertible bond is below and never above the corresponding value of a convertible bond under unresticted conversion.