This is an annotated appendix that accompanies the paper. In this note, we provide detailed commentary on a numerical example that illustrates the ideas that we discuss in the main paper. The numerical example is in Table18.10, Chapter 8, page 656, of the third edition of Corporate Finance,...

In this note, we extend a numerical example in the textbook by Berk & DeMarzo that matches methods for only when K_TS is equal to K_D. We show that there is a generalized formulation for the return to levered equity K_E that works for any value of K_TS, the appropriate discount rate for the tax...

In this short note, we present a nontechnical retrospection on the unbearable longevity of the classic WACC (Weighted Average Cost of Capital) for the Free Cash Flow (FCF) in perpetuity. Over the past two decades, researchers in finance have increased greatly our understanding of the properties...

In this note, we present a simple numerical example, with a finite cash flow, to illustrate the concept of the Optimal Capital Structure (OCS). First, we assume that the discount rate for the tax benefits K_TB equals the return to unlevered equity K_U. The cost of debt K_D is a simple linear...

In this note, we comment on and discuss the weirdness and absurdity of the idea that Professor Fernandez has argued for. The weirdness or absurdity of a theory does not automatically disqualify a theory; however, perhaps another review of the implications of the theory may have some merit. It...

In this note, we discuss two fundamental principles for Cash Flow Valuation (CFV). We hope that adherence to these two principles will improve the practice of CFV. These principles are general, relatively uncontroversial, and should be acceptable as starting points for cash flow valuation....

This paper presents three different approaches for calculating the levered annual values for a finite cash flow profile. In the first approach, we use K_U, the return to unlevered equity to calculate the annual tax savings and use K_U to calculate the (present) value of the tax savings. In the...

In this note, we present a simple numerical example to illustrate the case where the growth rate for the Free Cash Flow (FCF) gU is greater than but different from the growth rate for the Cash Flow to Debt (CFD) gD. Here we assume that the value of the appropriate discount rate for the tax...

There are methods to match value added approaches (Residual Income Method, RIM and Economic Value Added, EVA) with discounted cash flow methods, DCF. In this note we use a real life case from an emerging country to illustrate the matching, with complexities such as unpaid taxes, losses carried...

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...