The discount rate for the tax shield depends on the risk of the tax shield. If the tax shield is risk-free, then the appropriate discount rate for the tax shield is the risk-free rate rf. If the debt is risky, then we must make the distinction between the contractual return and the expected...

In a recent paper, Loeffler (2001) showed that the Miles amp; Ezzell (M amp; E) WACC allows arbitrage if the cash flow process does not have a quot;certain growth ratequot;. To be specific, for a particular period, the set of up and down coefficients must be the same at all the nodes in a...

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 amp; M world with risk-free debt and without taxes. The structure of the presentation will facilitate the subsequent...

Risk-neutral valuation is simple, elegant and central in option pricing theory. However, in teaching risk-neutral valuation, it is not easy to explain the concept of 'risk-neutral' probabilities. Beginners who are new to risk-neutral valuation always have lingering doubts about the validity of...

The conventional wisdom about psi, the appropriate discount rate for the tax shield, is as follows. If the tax shield is risk-free, that is, the revenue is sufficient to ensure that the interest deduction will be used with full certainty in the relevant period, then the appropriate discount rate...

In the arena of valuation, the fanciful claims about the dethronement of the champion (a.k.a. NPV) by the concept of economic value added (EVA) have been greatly exaggerated, and it would be premature and unwise to abandon our reliable and trusted NPV. EVA is simply an interesting algebraic...

Recently, the residual income (RI) model has become very popular in valuation because it purports to measure quot;value addedquot; by explicitly taking into account the cost for capital in the income statement. Some proponents of the residual income approach have even suggested that the RI model...

This is a continuation of the simplified exposition of Discrete Option Pricing. In this teaching note, I discuss some of the determinants of the values for the call and put options. Second, I derive the put-call parity relationship. Third, as a practical application, the ideas of put and call...

It is widely accepted that the correct discount rate for the tax shield depends on whether the value of the debt is a fixed amount or is a proportion of the value of the firm. In this pedagogical note, using a simple two period numerical example, I assume a fixed amount of debt and demonstrate...

The objective of this teaching note is to present the basic principles of discrete option pricing in simple language, with detailed jargon-free explanation and rudimentary algebra. Simple numerical examples are used to illustrate the main ideas. The basic ideas for call and put options are...