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...

Llano-Ferro (2009) proposes a solution to avoid 'significant errors' when the Weighted Average Cost of Capital (WACC) obtained by the standard formula leads to significant errors in Net Present Value of the Firm calculations; particularly in those that apply to perpetual cash flow series. In...

Terminal value is critical for valuation purposes because very often it is a large part of what constitutes the value of a firm. In this short note I answer and clarify some typical questions and myths related to the calculation of terminal value. They are related to the use of non growing...

This paper shows that the notion of rate of return is best understood through the lens of the average-internal-rate-of-return (AIRR) model, first introduced in Magni (2010a). It is an NPV-consistent approach based on a coherent definition of rate of return and on the notion of Chisini mean, it...

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...

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....

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...