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 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...

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...

I identify three sources of risk for the tax shields: two of them associated to the risk of debt and one associated to the operating risk. I present a set of conditions for defining risky debt associated to cash flow and not to accounting earnings. I explain why realization of tax shields for...

This article (1) identifies three sources of risk for tax shields (TS): Two of them are associated with debt risk and one is associated with operating risk. (2) A set of conditions for defining risky debt associated with cash flow, not with earnings, is presented. (3) It further shows that...

This paper questions the idea that the deduction of debt interest is always a good policy instrument in order to spur investment. Particularly, it analyzes the investment choice in a "financing hierarchy" framework with an exogenous constraint on the amount of the debt that the firm can...