Valuation: Measuring and Managing the Value of Companies, Fifth Edition

APPENDIX D

Levering and Unlevering the Cost of Equity

In Chapter 6, we value a company using adjusted present value (APV). One key input for APV is the unlevered cost of equity. In this appendix, we derive various formulas that can be used to compute the unlevered cost of equity under different assumptions.

Chapter 10 details a second application for the unlevered cost of equity. To determine the cost of equity for use in a company’s cost of capital, we do not use raw regression results (because of estimation error). Instead, we rely on an unlevered industry beta that is relevered to the company’s target capital structure. To build an unlevered industry beta, we use techniques identical to those used for building the unlevered cost of equity. We discuss both in this appendix.

UNLEVERED COST OF EQUITY

Franco Modigliani and Merton Miller postulated that the market value of a company’s economic assets, such as operating assets (V_u) and tax shields (V_txa), should equal the market value of its financial claims, such as debt (D) and equity (E):

(D.1)

A second result of Modigliani and Miller’s work is that the total risk of the company’s economic assets, operating and financial, must equal the total risk of the financial claims against those assets:

(D.2)

where

k_u = unlevered ...