1.  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

2. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 2 Topics Covered  Real Options  Follow Up Investments  Abandon  Wait  Vary Output or Production  Binomial Model

3. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 3 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

4. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 4 Intrinsic Value Option to Wait Option Price Stock Price

5. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 5 Intrinsic Value + Time Premium = Option Value Time Premium = Vale of being able to wait Option to Wait Option Price Stock Price

6. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 6 More time = More value Option to Wait Option Price Stock Price

7. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 7 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

8. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 8 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 2 120 (.6) 100 (.6) 90 (.4) NPV = 145 70 (.6) 50 (.4) 40 (.4)

9. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 9 Option to Abandon Year 0Year 1Year 2 120 (.6) 100 (.6) 90 (.4) NPV = 162 150 (.4) Option Value = 162 - 145 = $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?

10. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 10 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

11. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 11 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

12. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 12 Example Price = 36  =.40 t = 90/365  t = 30/365 Strike = 40r = 10% a = 1.0083 u = 1.1215 d =.8917 Pu =.5075 Pd =.4925 Binomial Pricing

13. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 13 40.37 32.10 36 Binomial Pricing

14. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 14 40.37 32.10 36 Binomial Pricing

15. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 15 50.78 = price 40.37 32.10 25.52 45.28 36 28.62 40.37 32.10 36 Binomial Pricing

16. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 16 50.78 = price 10.78 = intrinsic value 40.37.37 32.10 0 25.52 0 45.28 36 28.62 36 40.37 32.10 Binomial Pricing

17. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 17 50.78 = price 10.78 = intrinsic value 40.37.37 32.10 0 25.52 0 45.28 5.60 36 28.62 40.37 32.10 36 The greater of Binomial Pricing

18. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 18 50.78 = price 10.78 = intrinsic value 40.37.37 32.10 0 25.52 0 45.28 5.60 36.19 28.62 0 40.37 2.91 32.10.10 36 1.51 Binomial Pricing

19. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 19 50.78 = price 10.78 = intrinsic value 40.37.37 32.10 0 25.52 0 45.28 5.60 36.19 28.62 0 40.37 2.91 32.10.10 36 1.51 Binomial Pricing

20. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 20 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

21. © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 21- 21 How estimated call price changes as number of binomial steps increases No. of stepsEstimated value 148.1 241.0 342.1 541.8 1041.4 5040.3 10040.6 Black-Scholes40.5 Binomial vs. Black Scholes