Principles of Corporate Finance Brealey and Myers Sixth Edition Real Options Slides by Matthew Will Irwin/McGraw Hill Chapter 21 ©The McGraw-Hill Companies, Inc., 200 21- Topics Covered Real Options Follow Up Investments Abandon Wait Vary Output or Production Binomial Model Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- Corporate Options types of “Real Options” - The opportunity to make follow-up investments - The opportunity to abandon a project - The opportunity to “wait” and invest later - The opportunity to vary the firm’s output or production methods Value “Real Option” = NPV with option - NPV w/o option Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- Option to Wait Intrinsic Value Option Price Stock Price Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- Option to Wait Intrinsic Value + Time Premium = Option Value Time Premium = Vale of being able to wait Option Price Stock Price Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- Option to Wait More time = More value Option Price Stock Price Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- 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% Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- 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 Year Year 120 (.6) 100 (.6) 90 (.4) NPV = 145 70 (.6) 50 (.4) 40 (.4) Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- 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 Year Year 120 (.6) 100 (.6) 90 (.4) NPV = 162 Option Value = 150 (.4) Irwin/McGraw Hill 162 - 145 = $17 mil ©The McGraw-Hill Companies, Inc., 200 21- 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 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- 11 Binomial Pricing Probability Up = p = a = er∆ t d =e-σ (a - d) (u - d) [∆ t].5 Prob Down = - p u =eσ [∆ t].5 ∆t = time intervals as % of year Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- 12 Binomial Pricing Example Price = 36 σ = 40 t = 90/365 ∆ t = 30/365 Strike = 40 r = 10% a = 1.0083 u = 1.1215 d = 8917 Pu = 5075 Pd = 4925 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- 13 Binomial Pricing 40.37 P0 × U = PU 36 × 1.1215 = 40.37 36 32.10 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- 14 Binomial Pricing 40.37 36 × 1.1215 = 40.37 P0 × D = PD1 36 32.10 Irwin/McGraw Hill P0 × U = PU 36 × 8917 = 32.10 ©The McGraw-Hill Companies, Inc., 200 21- 15 Binomial Pricing 45.28 50.78 = price Pt × U = Pt +1 40.37 36 40.37 36 32.10 32.10 28.62 25.52 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- 16 Binomial Pricing 45.28 50.78 = price 10.78 = intrinsic value 40.37 40.37 36 37 36 32.10 32.10 28.62 25.52 Irwin/McGraw Hill 0©The McGraw-Hill Companies, Inc., 200 21- 17 Binomial Pricing The greater of 45.28 50.78 = price 5.60 10.78 = intrinsic value 40.37 40.37 36 36 37 32.10 32.10 28.62 [ ( Ou × Pu ) + (U d × Pd ) ] × ( e− r∆t ) Irwin/McGraw Hill 25.52 0©The McGraw-Hill Companies, Inc., 200 21- 18 Binomial Pricing 45.28 50.78 = price 5.60 10.78 = intrinsic value 40.37 40.37 2.91 36 37 19 36 1.51 32.10 10 32.10 28.62 0 [ ( Ou × Pu ) + (U d × Pd ) ] × ( e− r∆t ) Irwin/McGraw Hill 25.52 0©The McGraw-Hill Companies, Inc., 200 21- 19 Binomial Pricing 45.28 50.78 = price 5.60 10.78 = intrinsic value 40.37 40.37 2.91 36 37 19 36 1.51 32.10 10 32.10 28.62 0 [ ( Ou × Pu ) + (U d × Pd ) ] × ( e− r∆t ) Irwin/McGraw Hill 25.52 0©The McGraw-Hill Companies, Inc., 200 21- 20 Binomial vs Black Scholes Expanding the binomial model to allow more possible price changes step steps steps (2 outcomes) (3 outcomes) (5 outcomes) Irwin/McGraw Hill etc etc ©The McGraw-Hill Companies, Inc., 200 21- 21 Binomial vs Black Scholes How estimated call price changes as number of binomial steps increases No of steps Estimated value 48.1 41.0 42.1 41.8 10 41.4 50 40.3 100 40.6 Black-Scholes 40.5 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 ... 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% Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- Option... 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)... Companies, Inc., 200 21- 13 Binomial Pricing 40.37 P0 × U = PU 36 × 1. 1215 = 40.37 36 32.10 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 21- 14 Binomial Pricing 40.37 36 × 1. 1215 = 40.37 P0