 Real Options Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will Chapter 21 © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Topics Covered  Real Options  Follow Up Investments  Abandon  Wait  Vary Output or Production  Binomial Model

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Corporate Options 4 types of “Real Options” 1 - The opportunity to make follow-up investments. 2 - The opportunity to abandon a project 3 - The opportunity to “wait” and invest later. 4 - The opportunity to vary the firm’s output or production methods. Value “Real Option” = NPV with option - NPV w/o option

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Intrinsic Value Option to Wait Option Price Stock Price

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Intrinsic Value + Time Premium = Option Value Time Premium = Vale of being able to wait Option to Wait Option Price Stock Price

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill More time = More value Option to Wait Option Price Stock Price

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Example - Abandon Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option? Use a discount rate of 10% Option to Abandon

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Example - Abandon Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option? Option to Abandon Year 0Year 1Year (.6) 100 (.6) 90 (.4) NPV = (.6) 50 (.4) 40 (.4)

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option to Abandon Year 0Year 1Year (.6) 100 (.6) 90 (.4) NPV = (.4) Option Value = = $17 mil Example - Abandon Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option?

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Reality  Decision trees for valuing “real options” in a corporate setting can not be practically done by hand.  We must introduce binomial theory & B-S models Corporate Options

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Probability Up = p = (a - d)Prob Down = 1 - p (u - d) a = e r  t d =e -  [  t].5 u =e  [  t].5  t = time intervals as % of year Binomial Pricing

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Example Price = 36  =.40 t = 90/365  t = 30/365 Strike = 40r = 10% a = u = d =.8917 Pu =.5075 Pd =.4925 Binomial Pricing

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Binomial Pricing

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Binomial Pricing

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill = price Binomial Pricing

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill = price = intrinsic value Binomial Pricing

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill = price = intrinsic value The greater of Binomial Pricing

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill = price = intrinsic value Binomial Pricing

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill = price = intrinsic value Binomial Pricing

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Expanding the binomial model to allow more possible price changes 1 step 2 steps 4 steps (2 outcomes) (3 outcomes) (5 outcomes) etc. Binomial vs. Black Scholes

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill How estimated call price changes as number of binomial steps increases No. of stepsEstimated value Black-Scholes40.5 Binomial vs. Black Scholes