Risk-Neutral Valuation: A Gentle Introduction (2)

Abstract

This teaching note is a continuation of the previous teaching note on risk-neutral valuation. In Section One, we estimate the value of levered equity in a levered company in an M & M world with risk-free debt and without taxes. The structure of the presentation will facilitate the subsequent analysis with taxes. We find the value of the levered firm in two ways. First, we use the replicating portfolio method. Second, we use the risk-neutral approach, which is equivalent to the replicating portfolio method.

In Section Two, we analyze risky debt in a world without taxes. In Section Three, we introduce taxes. However, we continue to assume risk-free debt. The risk of the tax shield is indeterminate. In Section Four, we analyze risky debt in the presence of taxes and derive the relevant expressions for the returns to the equity and debt holders.

Keywords: Risk-neutral valuation, Cost of Capital

JEL Classification: D61, G31, H43