Credit risk and liquidation cost: Effects on prices of convertible bonds, as well as conversion and call strategies

This paper explores the issue of strategic debt service and its effect on the conversion and call strategies of convertible bondholders. Specifically, we consider a variant of the strategic debt service model of Anderson and Sundaresan (1996) in which the owner of the firm has a first-mover advantage, and strategically chooses the level of debt service. We first consider situations in which the convertible debt is concentrated in the hands of a single creditor. In these situations, it is possible that the convertible bondholder will convert the bond although the firm value is low. Furthermore, when liquidation costs are high, the firm will be less likely to call the bond and less likely to default. This is in contrast to existing models but consistent with the existing empirical evidence in the literature.; We also show when the debt is diffusely held by multiple non-cooperative creditors, convertible debt creates a free-rider problem among the debt holders that works to the advantage of the equity holders (or the owner-manager). Under some circumstances, it will be optimal for an individual bondholder to delay the conversion even though both bondholders benefit most from simultaneously converting the bonds. Specifically, the symmetric Nash equilibrium is such that all bondholders delay conversion relative to when they would in the absence of credit risk. As a result, convertible bond prices calculated ignoring this optimal delayed conversion are systematically biased. We show that for some parameters the bias can be as high as 10 percent.