Levered and Unlevered Beta

Abstract

We claim that in a world without leverage cost the relationship between the levered beta (BL) and the unlevered beta (Bu) of a company depends upon the financing strategy. For a company that maintains a fixed book-value leverage ratio, the relationship is Fernandez (2004): BL = Bu + (Bu - Bd) D (1 - T) / E. For a company that maintains a fixed market-value leverage ratio, the relationship is Miles and Ezzell (1980):BL = Bu + (D / E) (Bu - Bd) [1 - T Kd / (1 + Kd)]. For a company with a preset debt in every period, the relationship is Modigliani and Miller (1963):BL = Bu + [Bu - Bd] (D-VTS) / E, being the Value of Tax Shields (VTS) the present value of the future tax shields discounted at the cost of debt.

We also analyze alternative valuation theories proposed in the literature to estimate the relationship between the levered beta and the unlevered beta (Harris and Pringle (1985), Damodaran (1994), Myers (1974), and practitioners) and prove that all provide inconsistent results.

Keywords: unlevered beta, levered beta, asset beta, value of tax shields, required return to equity, leverage cost

JEL Classification: G12, G31, M21