2007 Page 1 F. MICHAUX CORPORATE FINANCE Financial and Real Options

2007 Page 2 F. MICHAUX GENERAL AGENDA Financial and Real Options

2007 Page 3 F. MICHAUX TOPICS COVERED Calls, Puts and Shares Financial Alchemy with Options What Determines Option Value Option Valuation Real Options –Follow Up Investments –Abandon –Wait –Vary Output or Production Binomial Model

2007 Page 4 F. MICHAUX OPTION TERMINOLGY Call Option Right to buy an asset at a specified exercise price on or before the exercise date. Put Option Right to sell an asset at a specified exercise price on or before the exercise date.

2007 Page 5 F. MICHAUX OPTION OBLIGATIONS

2007 Page 6 F. MICHAUX The value of an option at expiration is a function of the stock price and the exercise price. OPTION VALUE

2007 Page 7 F. MICHAUX The value of an option at expiration is a function of the stock price and the exercise price. Example - Option values given a exercise price of $85 OPTION VALUE

2007 Page 8 F. MICHAUX Call option value (graphic) given a $85 exercise price. Share Price Call option value $20 OPTION VALUE

2007 Page 9 F. MICHAUX Put option value (graphic) given a $85 exercise price. Share Price Put option value $5 OPTION VALUE

2007 Page 10 F. MICHAUX Call option payoff (to seller) given a $85 exercise price. Share Price Call option $ payoff 85 OPTION VALUE

2007 Page 11 F. MICHAUX Put option payoff (to seller) given a $85 exercise price. Share Price Put option $ payoff 85 OPTION VALUE

2007 Page 12 F. MICHAUX Protective Put - Long stock and long put Share Price Position Value Long Stock OPTION VALUE

2007 Page 13 F. MICHAUX Protective Put - Long stock and long put Share Price Position Value Long Put OPTION VALUE

2007 Page 14 F. MICHAUX Protective Put - Long stock and long put Share Price Position Value Protective Put Long Put Long Stock OPTION VALUE

2007 Page 15 F. MICHAUX Protective Put - Long stock and long put Share Price Position Value Protective Put OPTION VALUE

2007 Page 16 F. MICHAUX Straddle - Long call and long put - Strategy for profiting from high volatility Share Price Position Value Long call OPTION VALUE

2007 Page 17 F. MICHAUX Straddle - Long call and long put - Strategy for profiting from high volatility Share Price Position Value Long put OPTION VALUE

2007 Page 18 F. MICHAUX Straddle - Long call and long put - Strategy for profiting from high volatility Share Price Position Value Straddle OPTION VALUE

2007 Page 19 F. MICHAUX Straddle - Long call and long put - Strategy for profiting from high volatility Share Price Position Value Straddle OPTION VALUE

2007 Page 20 F. MICHAUX Strip – 1 Long call and 2 long put - Strategy for profiting from high volatility Share Price Position Value Long call OPTION VALUE

2007 Page 21 F. MICHAUX Strip – 1 Long call and 2 long put - Strategy for profiting from high volatility Share Price Position Value 2 Long put OPTION VALUE

2007 Page 22 F. MICHAUX Strip – 1 Long call and 2 long put - Strategy for profiting from high volatility Share Price Position Value Strip OPTION VALUE

2007 Page 23 F. MICHAUX Strip – 1 Long call and 2 long put - Strategy for profiting from high volatility Share Price Position Value Strip OPTION VALUE

2007 Page 24 F. MICHAUX Strap – 2 Long call and 1 long put - Strategy for profiting from high volatility Share Price Position Value 2 Long call OPTION VALUE

2007 Page 25 F. MICHAUX Strap – 2 Long call and 1 long put - Strategy for profiting from high volatility Share Price Position Value Long put OPTION VALUE

2007 Page 26 F. MICHAUX Strap – 2 Long call and 1 long put - Strategy for profiting from high volatility Share Price Position Value Strap OPTION VALUE

2007 Page 27 F. MICHAUX Strap – 2 Long call and 1 long put - Strategy for profiting from high volatility Share Price Position Value Strap OPTION VALUE

2007 Page 28 F. MICHAUX Upper Limit Stock Price OPTION VALUE

2007 Page 29 F. MICHAUX Upper Limit Stock Price Lower Limit (Stock price - exercise price) or 0 whichever is higher OPTION VALUE

2007 Page 30 F. MICHAUX Components of the Option Price 1 - Underlying stock price 2 - Striking or Exercise price 3 - Volatility of the stock returns (standard deviation of annual returns) 4 - Time to option expiration 5 - Time value of money (discount rate) OPTION VALUE

2007 Page 31 F. MICHAUX Black-Scholes Option Pricing Model O C = P s [N(d 1 )] - S[N(d 2 )]e -rt OPTION VALUE

2007 Page 32 F. MICHAUX O C = P s [N(d 1 )] - S[N(d 2 )]e -rt O C - Call Option Price P s - Stock Price N(d 1 ) - Cumulative normal density function of (d 1 ) S - Strike or Exercise price N(d 2 ) - Cumulative normal density function of (d 2 ) r - discount rate (90 day comm paper rate or risk free rate) t - time to maturity of option (as % of year) v - volatility - annualized standard deviation of daily returns Black-Scholes Option Pricing Model

2007 Page 33 F. MICHAUX (d 1 )= ln + ( r + ) t PsSPsS v22v22 v t N(d 1 )= Black-Scholes Option Pricing Model

2007 Page 34 F. MICHAUX (d 1 )= ln + ( r + ) t PsSPsS v22v22 v t Cumulative Normal Density Function (d 2 ) = d 1 -v t

2007 Page 35 F. MICHAUX CALL OPTION Example What is the price of a call option given the following? P = 36r = 10%v =.40 S = 40t = 90 days / 365

2007 Page 36 F. MICHAUX (d 1 ) = ln + ( r + ) t PsSPsS v22v22 v t (d 1 ) = N(d 1 ) = =.3794 Example What is the price of a call option given the following? P = 36r = 10%v =.40 S = 40t = 90 days / 365 CALL OPTION

2007 Page 37 F. MICHAUX (d 2 ) = N(d 2 ) = =.3065 (d 2 ) = d 1 -v t Example What is the price of a call option given the following? P = 36r = 10%v =.40 S = 40t = 90 days / 365 CALL OPTION

2007 Page 38 F. MICHAUX O C = P s [N(d 1 )] - S[N(d 2 )]e -rt O C = 36[.3794] - 40[.3065]e - (.10)(.2466) O C = $ 1.70 Example What is the price of a call option given the following? P = 36r = 10%v =.40 S = 40t = 90 days / 365 CALL OPTION

2007 Page 39 F. MICHAUX Intrinsic Value OPTION TO WAIT Option Price Stock Price

2007 Page 40 F. MICHAUX Intrinsic Value + Time Premium = Option Value Time Premium = Vale of being able to wait Option Price Stock Price OPTION TO WAIT

2007 Page 41 F. MICHAUX More time = More value Option Price Stock Price OPTION TO WAIT