Valuation for Mergers, Buyouts, and Restructuring, Second Edition

Appendix A

Financial Options

A.1 FINANCIAL OPTIONS IN M&A VALUATION

A number of applications presented in this book require the computation of options values that are provided by formulas developed for the pricing of financial options. The file Financial Options Calculator included in the Valuation Aids CD-ROM contains a number of easy-to-use Microsoft Excel spreadsheets for computing the value of these options. This appendix summarizes the valuation models included in the calculator, gives references to the sources where the original formulas were derived, and illustrates their application with examples. The general reference on financial options is Hull (2006). Note NA.2 shows the code of a program for valuing options using the Hewlett-Packard HP19-BII calculator. Although it does not incorporate some of the refinements included in the Financial Options Calculator, it permits valuing European calls, puts, and warrants. The problem section includes practice problems that can be solved using the calculators.

A.2 EUROPEAN CALLS AND PUTS AND AMERICAN CALLS

European options can be exercised only at expiration. European calls are valued with the Black-Scholes (1973) formula:

where P is the stock price, X is the exercise price, T is the expiration date, t is time, r is the riskless rate, N(d) is the normal distribution function,

and σ is the volatility (standard deviation of the rate ...