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Slides by Matthew Will

Principles of Corporate Finance Brealey and Myers Sixth Edition. Real Options. Slides by Matthew Will. Chapter 21. Irwin/McGraw Hill. The McGraw-Hill Companies, Inc., 2000. Topics Covered. Real Options Follow Up Investments Abandon Wait Vary Output or Production Binomial Model.

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Slides by Matthew Will

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

  2. Topics Covered • Real Options • Follow Up Investments • Abandon • Wait • Vary Output or Production • Binomial Model

  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. Option to Wait Intrinsic Value Option Price Stock Price

  5. Option to Wait Intrinsic Value + Time Premium = Option Value Time Premium = Vale of being able to wait Option Price Stock Price

  6. Option to Wait More time = More value Option Price Stock Price

  7. Option to Abandon 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%

  8. Option to Abandon 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? Year 0 Year 1 Year 2 120 (.6) 100 (.6) 90 (.4) NPV = 145 70 (.6) 50 (.4) 40 (.4)

  9. Option to Abandon 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? Year 0 Year 1 Year 2 120 (.6) 100 (.6) 90 (.4) NPV = 162 150 (.4) Option Value = 162 - 145 = $17 mil

  10. Corporate Options 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

  11. Binomial Pricing Probability Up = p = (a -d) Prob Down = 1 - p (u - d) a = erD t d =e-s [D t].5 u =es [D t].5 Dt = time intervals as % of year

  12. Binomial Pricing Example Price = 36 s = .40 t = 90/365 D t = 30/365 Strike = 40 r = 10% a = 1.0083 u = 1.1215 d = .8917 Pu = .5075 Pd = .4925

  13. Binomial Pricing 40.37 32.10 36

  14. Binomial Pricing 40.37 32.10 36

  15. Binomial Pricing 50.78 = price 40.37 32.10 25.52 45.28 36 28.62 40.37 32.10 36

  16. Binomial Pricing 50.78 = price 10.78 = intrinsic value 40.37 .37 32.10 0 25.52 0 45.28 36 28.62 40.37 32.10 36

  17. Binomial Pricing 50.78 = price 10.78 = intrinsic value 40.37 .37 32.10 0 25.52 0 45.28 5.60 36 28.62 The greater of 40.37 32.10 36

  18. Binomial Pricing 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

  19. Binomial Pricing 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

  20. Expanding the binomial model to allow more possible price changes Binomial vs. Black Scholes 1 step 2 steps 4 steps (2 outcomes) (3 outcomes) (5 outcomes) etc. etc.

  21. How estimated call price changes as number of binomial steps increases Binomial vs. Black Scholes No. of steps Estimated value 1 48.1 2 41.0 3 42.1 5 41.8 10 41.4 50 40.3 100 40.6 Black-Scholes 40.5

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