32、Companies, Inc. All rights reserved. 23-18 $25 28.75 21.25 2/3 1/3 15.35 2/3 1/3 38.02 28.10 2/3 1/3 20.77 2/3 1/3 33.06 24.44 2/3 1/3 18.06 2/3 1/3 0 ,25$02.38max$),( 3 UUUC 13.02 0 ,25$10.28max$ ),(),( ),( 33 3 DUUCUDUC UUDC 3.10 0 ,25$77.20max$ ),(),( ),( 33 3 UDDCDUDC DDUC 0 0 ,25$35.15max$ ),(。

33、3 DDDC 0 )05. 1 ( 10. 3$)31 (02.13$32 ),( 2 UUC 9.25 )05. 1 ( 0$)31 (10. 3$32 ),(),( 22 UDCDUC 1.97 )05. 1 ( 0$)31 (0$32 ),( 2 DDC 0 )05. 1 ( 97. 1$)31 (25. 9$32 )( 1 UC 6.50 )05. 1 ( 0$)31 (97. 1$32 )( 1 DC 1.25 4.52 )05. 1 ( 25. 1$)31 (50. 6$32 0 C Three Period Binomial Process: Call Option Prices 。

34、 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 23-19 Valuation of a Lookback Option When the stock price falls due to the stock market as a whole falling, the board of directors tends to reset the exercise price of executive stock options. To see how this r 。

35、eset provision adds value, lets price that same three-period call option (exercise price initially $25) with a reset provision. Notice that the exercise price of the call will be the smallest value of the stock price depending upon the path followed by the stock price to get there. McGraw-Hill/Irwin 。

36、 Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 23-20 Three Period Binomial Process: Lookback Call Option Prices $25 28.75 21.25 33.06 24.44 18.06 24.44 15.35 20.77 28.10 20.77 20.77 28.10 38.02 28.10 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rig 。

37、hts reserved. 23-21 Three Period Binomial Process: Lookback Call Option Prices $25 28.75 21.25 33.06 24.44 18.06 15.35 38.02 20.77 28.10 28.10 28.10 24.44 20.77 20.77 0 ,25$02.38max$),( 3 UUUC 13.02 $3.10 10. 30 ,25$10.28max$),( 3 DUUC $6.85 $3.66 00 ,44.24$77.20max$),( 3 DDUC 0 0 2.71 0 0 ,06.1836. 。

38、15max$),( 3 DDDC 66. 30 ,44.24$10.28max$),( 3 UDUC 85. 60 ,25.21$10.28max$),( 3 UUDC 00 ,25.21$77.20max$),( 3 DUDC 71. 20 ,06.18$77.20max$),( 3 UDDC McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 23-22 Three Period Binomial Process: Lookback Call Option Pric 。

39、es $25 28.75 21.25 33.06 24.44 18.06 15.35 38.02 20.77 28.10 28.10 28.10 24.44 20.77 20.77 13.02 $3.10 $6.85 $3.66 0 0 2.71 0 )05. 1 ( 10. 3$)31 (02.13$32 ),( 2 UUC 9.25 )05. 1 ( 0$)31 (66. 3$32 ),( 2 DUC )05. 1 ( 0$)31 (85. 6$32 ),( 2 UDC 2.33 4.35 )05. 1 ( 0$)31 (71. 2$32 ),( 2 DDC 1.72 McGraw-Hil 。

40、l/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 23-23 Three Period Binomial Process: Lookback Call Option Prices $25 28.75 21.25 33.06 24.44 18.06 15.35 38.02 20.77 28.10 28.10 28.10 24.44 20.77 20.77 13.02 $3.10 $6.85 $3.66 0 0 2.71 0 9.25 2.33 4.35 1.72 )05. 1 ( 33.。

41、2$)31 (25. 9$32 )( 1 UC 6.61 3.31 )05. 1 ( 72. 1$)31 (35. 4$32 )( 1 DC )05. 1 ( 25. 1$)31 (50. 6$32 0 C 5.25 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 23-24 Excel Applications of the BOPM The BOPM is easily incorporated into Excel spreadsheets 14% s28.7 。

42、5$ 1 Maturity25.00$ 1 n3.75$ 1 D tq 25.00$ S0 25.00$ XStock Price25.00$ 5% rfExercise Price 25.00$ 1.1500 uOrdinary Call2.38$ 0.8500 d 1.0500 a1- q 66.67% Risk Neutral Prob21.25$ 33.33% 1- R.N. Prob25.00$ -$ McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 23- 。

43、25 23.4 Shutdown and Reopening Decisions Can easily be seen as options. The “Woe is Me” gold mine is currently closed. The firm is publicly held and trades under the ticker WOE. The firm has no debt and has assets of around $30 million. The market capitalization is $240 million What could possibly e 。

44、xplain why a firm with $30 million in assets and a closed gold mine that is producing no cash flow at all has this kind of market capitalization? Options. This firm has them in spades. McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 23-26 Discounted Cash Flow 。

45、s and Options We can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project. OptNPVM A good example would be comparing the desirability of a specialized machine versus a more versatile machine. If t 。

46、hey both cost about the same and last the same amount of time the more versatile machine is more valuable because it comes with options. McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 23-27 The Option to Abandon: Example Suppose that we are drilling an oil w 。

47、ell. The drilling rig costs $300 today and in one year the well is either a success or a failure. The outcomes are equally likely. The discount rate is 10%. The PV of the successful payoff at time one is $575. The PV of the unsuccessful payoff at time one is $0. McGraw-Hill/Irwin Copyright 2002 by T 。

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