Cost of Equity and Weighted Average Cost of Capital for Perpetuities, with Constant Growth

This article presents a formal derivation of general expressions for cost of equity (Ke) and weighted average cost of capital (WACC) in perpetuities with constant growth, which do not make any assumption on what the proper discount rate is to be applied to the firm's tax shield. The formulas are complemented with numerical examples of their application. Furthermore, because the most widely known approaches to firm's market value and equity estimation make either an implicit or explicit assumption on the value the mentioned rate should take, expressions of the adequate rate on each one of those cases are presented. In addition, a formula for the calculation of the impact on the firm and equity value of a variation on the discount rate for tax shield is proposed, which yields exact results for changes of any size.