A Capital Structure Model (CSM) with Tax Rate Changes

Abstract

Perpetuity gain to leverage (GL) research originates in Modigliani and Miller (1963) and was extended by Miller (1977) to incorporate personal taxes. This research analyzes GL when issuing debt to retire unlevered equity. Hull (2007,2010, 2012) extended this research by developing the Capital Structure Model (CSM) that demonstrates how the costs of borrowing affect GL and the optimal debt-equity ratio (ODE). The CSM research, like the mainline capital structure research originating in Modigliani and Miller (1958, 1963) has a shortcoming: it fails to address the effect on GL and ODE when a leverage change alters corporate and personal tax rates. To overcome this shortcoming, we derive new CSM equations that allow tax rates to be dependent on leverage. The directions of how tax rates change with leverage are based on arguments we supply. Through the derivational process, we discover a new "alpha" variable to add to the prior "alpha" variable discovered by Miller and his predecessors. One of our new equations uses the original Hull (2007) CSM framework that assumes an unlevered situation, no growth and discount rates that change with leverage. Another new equation adds complexity by using the more recent CSM framework of Hull (2012) for levered firm with growth and a wealth transfer. We use two of our new equations to illustrate the role of changing tax rates. Our illustrations suggest managers cannot ignore even relatively small changes in tax rates. In particular, they cannot ignore the new "alpha" variable we discover.