We derive and present the formula for optimal debt under the assumption that tax shields are discounted at the cost of levered equity, Ke and cash flows are on perpetuity. The formulation is consistent and is derived from basic financial principles. This formulation is valid for non-growing...

This paper presents the derivation of non-circular formulas for the calculation of the cost of equity, WACC, equity value (as a function either of initial debt or leverage), and levered firm value, using some previous results and showing their consistency with other well-known expressions....

We present the derivation of cost of capital under the assumption of risky tax shields discounted with the cost of levered equity. We show that the formulation is consistent and is derived from basic financial principles. This formulation is valid for finite cash flows and non growing...

This paper presents a formal derivation of general expressions for Ke and 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, and are complemented with numerical examples of its application....

In this paper we propose an analytical solution to the circularity problem between value and cost of capital. Our solution is derived starting from a central principle of finance that relates value today to value, cash flow, and the discount rate for next period. We derive a general formulation...