© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Chapter 22 Options and Corporate Finance: Extensions and Applications  Real Options  Follow Up Investments  Abandon  Wait  Vary Output or Production  Binomial Model  Value of the Maximum Price Guarantee

© 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. NPV with option = NPV w/o option + Value “Real 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 = Value 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 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 Risk-adjusted Probability (pseudo-probability) Up = p = (a - d)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 = 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 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

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Distribution of Memory Chip Prices S=$16 S=$10 S=$4 S=$13 S=$7 t=0 t=1 t=2

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Payoffs of the Maximum Price Guarantee V=$6 V=$0 t=0 t=1 t=2

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Value of the Maximum Price Guarantee  The risk-adjusted probability is: q = [($10) (1.03) - $7]/($13 - $7) =.55  The value of the option at t=1 is: V(S(U),t=1) = [(.55 ) ($6) + (.45) ($0)] / (1.03) = $3.20 per MB V(S(D),t=1) = [(.55 ) ($0) + (.45) ($0)] / (1.03) = $0.00 per MB  The value of the option at t=0 is: C(t=0) = [(.55 ) ($3.20) + (.45) ($0)] / (1.03) = $1.71 per MB Therefore the value of the price guarantee = $171 million