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1、McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-0Executive Summary This chapter extends the analysis of options contained in Chapter 22. We describe four types of options found in common corporate finance decisions. Executive stock options The option to expa
2、nd embedded in a start-up. The option in simple business contracts. The option to shut down and reopen a project.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-1Chapter Outline23.1 Executive Stock Options23.2 Valuing a Start Up23.3 More on the Binomial Mode
3、l23.4 Shutdown and Reopening Decisions 23.5 Summary and ConclusionsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-223.1 Executive Stock Options Executive Stock Options exist to align the interests of shareholders and managers. Executive Stock Options are ca
4、ll options (technically warrants) on the employers shares. Inalienable Typical maturity is 10 years. Typical vesting period is 3 years. Most include implicit reset provision to preserve incentive compatibility. Executive Stock Options give executives an important tax break: grants of at-the-money op
5、tions are not considered taxable income. (Taxes are due if the option is exercised.)McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-3Valuing Executive Compensation FASB allows firms to record zero expense for grants of at-the-money executive stock options. H
6、owever the economic value of a long-lived call option is enormous, especially given the propensity of firms to reset the exercise price after drops in the price of the stock. Due to the inalienability, the options are worth less to the executive than they cost the company. The executive can only exe
7、rcise, not sell his options. Thus he can never capture the speculative valueonly the intrinsic value. This “dead weight loss” is overcome by the incentive compatibility for the grantor.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-4Top Stock Option GrantsC
8、ompanyCEOStock Option Award Citigroup, Inc.Sanford Weill$351,319,000American ExpressHarvey Golub$134,102,000Cisco Systems, Inc.John Chambers$132,100,000Bank of AmericaHugh McColl Jr.$104,300,000Honeywell Inc.Michael Bosignore$121,496,000ALCOAPaul ONeill$96,353,000McGraw-Hill/IrwinCopyright 2002 by T
9、he McGraw-Hill Companies, Inc. All rights reserved.23-523.2 Valuing a Start-Up An important option is the option to expand. Imagine a start-up firm, Campusteria, Inc. which plans to open private dining clubs on college campuses. The test market will be your campus, and if the concept proves successf
10、ul, expansion will follow nationwide. Nationwide expansion will occur in year four. The start-up cost of the test dining club is only $30,000 (this covers leaseholder improvements and other expenses for a vacant restaurant near campus).McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, In
11、c. All rights reserved.23-6Campusteria pro forma income statementInvestmentYear 0Years 1-4Revenues$60,000Variable Costs($42,000)Fixed Costs($18,000)Depreciation($7,500)Pretax profit($7,500)Tax shield 34%$2,550Net Profit$4,950Cash Flow$30,000$2,550We plan to sell 25 meal plans at $200 per month with
12、a 12-month contract.Variable costs are projected to be $3,500 per month.Fixed costs (lease payment) are projected to be $1,500 per month.We can depreciate our capitalized leaseholder improvements.84.916,21$)10. 1 (550, 2$000,30$41ttNPVMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc
13、. All rights reserved.23-723.2 Valuing a Start-Up Note that while the Campusteria test site has a negative NPV, we are close to our break-even level of sales. If we expand, we project opening 20 Capusterias in year four. The value of the project is in the option to expand. We will use the Black-Scho
14、les option pricing model to value this optionMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-823.2 Valuing a Start-Up with Black-ScholesThe Black-Scholes Model is)N()N(210dEedSCrTWhereC0 = the value of a European option at time t = 0r = the risk-free interes
15、t rate.TTrESd)2()/ln(21Tdd12N(d) = Probability that a standardized, normally distributed, random variable will be less than or equal to d.The Black-Scholes Model allows us to value options in the real world just as we have done in the 2-state world.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill
16、Companies, Inc. All rights reserved.23-923.2 Valuing a Start-Up with Black-ScholesWe need to find the value of a four-year call option on chain with an exercise price of $600,000 = $30,00020The interest rate available is r = 10%.The option maturity is four years.The volatility of the underlying asse
17、t is 30% per annum.The current value of the underlying assets is $110,418418,110$)10. 1 (14.663,161$)10. 1 ()10. 1 (550, 2$204441ttMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-1023.2 Valuing a Start-Up with Black-ScholesLets try our hand again at using th
18、e model. If you have a calculator handy, follow along.Then, TTrESd)5 .()/ln(21First calculate d1 and d245. 2430. 08544. 112Tdd8544. 1430. 04)30. 0(5 .10(.)000,600/418,110ln(21dMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-1123.2 Valuing a Start-Up with Bla
19、ck-ScholesN(d1) = N(-1.8544) =0.032N(d2) = N(-2.45) =0.007)N()N(210dEedSCrT03.718$007. 0000,600032. 0418,110$0410.0CeCThe option to expand, while valuable, is not as great as the negative NPV of opening the trial Campusteria. So we should not proceed. McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hi
20、ll Companies, Inc. All rights reserved.23-12The Option to Delay: Example Consider the above project, which can be undertaken in any of the next 4 years. The discount rate is 10 percent. The present value of the benefits at the time the project is launched remain constant at $25,000, but since costs
21、are declining the NPV at the time of launch steadily rises. The best time to launch the project is in year 2this schedule yields the highest NPV when judged today.YearCostPVNPV tNPV 0020,000$ 25,000$ 5,000$ 5,000$ 118,000$ 25,000$ 7,000$ 6,364$ 217,100$ 25,000$ 7,900$ 6,529$ 316,929$ 25,000$ 8,071$
22、6,064$ 416,760$ 25,000$ 8,240$ 5,628$ 2)10. 1 (900, 7$529, 6$McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-1323.3 More on the Binomial Model The binomial option pricing model is an alternative to the Black-Scholes option pricing modelespecially given the c
23、omputational efficiency of spreadsheets such as Excel. In some situations, it is a superior alternative. For example if you have path dependency in your option payoff, you must use the binomial option pricing model. Path dependency is when how you arrive at a price (the path you follow) for the unde
24、rlying asset is important. One example of a path dependent security is a “no regret” call option where the exercise price is the lowest price of the stock during the option life.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-14Three Period Binomial Option P
25、ricing Example There is no reason to stop with just two periods. Find the value of a three-period at-the-money call option written on a $25 stock that can go up or down 15 percent each period when the risk-free rate is 5 percent.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All
26、rights reserved.23-15Three Period Binomial Process: Stock Prices$2528.7521.252/31/3)15. 1 (00.25$2)15. 1 (00.25$)15.1)(15. 1 (00.25$2)15. 1 (00.25$)15.1 (00.25$3)15. 1 (00.25$)15.1 ()15. 1 (00.25$22)15.1 ()15. 1 (00.25$3)15.1 (00.25$33.0624.442/31/318.062/31/315.352/31/338.022/31/320.772/31/328.10Mc
27、Graw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-16$2528.7521.252/31/315.352/31/338.0228.102/31/320.772/31/333.0624.442/31/318.062/31/30 ,25$02.38max$),(3UUUC13.020 ,25$10.28max$),(),(),(333DUUCUDUCUUDC3.100 ,25$77.20max$),(),(),(333UDDCDUDCDDUC00 ,25$35.15max$
28、),(3DDDC0)05. 1 (10. 3$)31 (02.13$32),(2UUC9.25)05. 1 (0$)31 (10. 3$32),(),(22UDCDUC1.97)05. 1 (0$)31 (0$32),(2DDC0)05. 1 (97. 1$)31 (25. 9$32)(1UC6.50 )05. 1 (0$)31 (97. 1$32)(1DC1.254.52)05. 1 (25. 1$)31 (50. 6$320CThree Period Binomial Process: Call Option PricesMcGraw-Hill/IrwinCopyright 2002 by
29、 The McGraw-Hill Companies, Inc. All rights reserved.23-17Valuation 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 reset provision adds value, lets price
30、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/IrwinCopyright 2002 by The McGraw-Hill Compa
31、nies, Inc. All rights reserved.23-18Three Period Binomial Process: Lookback Call Option Prices$2528.7521.2533.0624.4418.0624.4415.3520.7728.1020.7720.7728.1038.0228.10McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-19Three Period Binomial Process: Lookback C
32、all Option Prices$2528.7521.2533.0624.4418.0615.3538.0220.7728.1028.1028.1024.4420.7720.770 ,25$02.38max$),(3UUUC13.02$3.1010. 30 ,25$10.28max$),(3DUUC$6.85$3.66 00 ,44.24$77.20max$),(3DDUC002.7100 ,06.1836.15max$),(3DDDC66. 30 ,44.24$10.28max$),(3UDUC85. 60 ,25.21$10.28max$),(3UUDC00 ,25.21$77.20ma
33、x$),(3DUDC71. 20 ,06.18$77.20max$),(3UDDCMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-20Three Period Binomial Process: Lookback Call Option Prices$2528.7521.2533.0624.4418.0615.3538.0220.7728.1028.1028.1024.4420.7720.7713.02$3.10$6.85$3.66 002.710)05. 1 (
34、10. 3$)31 (02.13$32),(2UUC9.25)05. 1 (0$)31 (66. 3$32),(2DUC)05. 1 (0$)31 (85. 6$32),(2UDC2.334.35)05. 1 (0$)31 (71. 2$32),(2DDC1.72McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-21Three Period Binomial Process: Lookback Call Option Prices$2528.7521.2533.06
35、24.4418.0615.3538.0220.7728.1028.1028.1024.4420.7720.7713.02$3.10$6.85$3.66 002.7109.252.334.351.72)05. 1 (33. 2$)31 (25. 9$32)(1UC6.61 3.31)05. 1 (72. 1$)31 (35. 4$32)(1DC)05. 1 (25. 1$)31 (50. 6$320C5.25McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-22Exc
36、el Applications of the BOPMThe BOPM is easily incorporated into Excel spreadsheets14% s28.75$ 1 Maturity25.00$ 1 n3.75$ 1 D tq25.00$ S025.00$ XStock Price25.00$ 5% rfExercise Price 25.00$ 1.1500 uOrdinary Call2.38$ 0.8500 d1.0500 a1- q66.67% Risk Neutral Prob21.25$ 33.33% 1- R.N. Prob25.00$ -$ McGra
37、w-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-2323.4 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
38、 around $30 million. The market capitalization is $240 million What could possibly explain 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/IrwinCopyright 2002
39、by The McGraw-Hill Companies, Inc. All rights reserved.23-24Discounted Cash Flows 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.OptNPVMA good example would be comparing t
40、he desirability of a specialized machine versus a more versatile machine. If they 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/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved
41、.23-25The Option to Abandon: Example Suppose that we are drilling an oil well. 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 un
42、successful payoff at time one is $0.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-26The Option to Abandon: Example failuregiven PayofffailureProb.successgiven PayoffsucessProb.payoffExpected 5 .287$05 . 0575$5 . 0payoffExpected64.38$)10. 1 (50.287$300$tNPV
43、Traditional NPV analysis would indicate rejection of the project.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-27The Option to Abandon: ExampleThe firm has two decisions to make: drill or not, abandon or stay.Do not drillDrill0$NPV500$FailureSuccess: PV =
44、$500Sell the rig; salvage value = $250 Sit on rig; stare at empty hole: PV = $0.Traditional NPV analysis overlooks the option to abandon.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-28The Option to Abandon: Example failuregiven PayofffailureProb.successgi
45、ven PayoffsucessProb.payoffExpected 50.412$0255 . 0575$5 . 0payoffExpected00.75$)10. 1 (50.412$300$tNPV When we include the value of the option to abandon, the drilling project should proceed:McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.23-29Valuation of the
46、 Option to Abandon Recall that 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.OptNPVMOpt64.3800.75$Opt64.3800.75$64.113$OptMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies
47、, Inc. All rights reserved.23-30Enrons Inefficient Plants In 1999 Enron planned to open gas-fired power plants in Mississippi and Tennessee. These plants were expected to sit idle most of the year, and, when operated to produce electricity at a cost of at least 50 percent higher than the most effici
48、ent state-of-the-art facility. Enron was buying a put option on electricity. They can sell electricity when electricity prices spike. Typical price is around $40 per megawatt-hour, but occasionally the price is several thousand dollars. Having a plant that was only economic to operate a few weeks a
49、year was a positive NPV investmentwhen you include the value of that option.Brealey, Myers, and Marcus Fundamentals of Corporate Finance, 3e. And “Exploiting Uncertainty: The “Real Options” Revolution in Decision Making” Business Week, June 7, 1999McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill C
50、ompanies, Inc. All rights reserved.23-3123.5 Summary and Conclusions Options appear in a variety of corporate settings. We describe four types of options found in common corporate finance decisions. Executive stock options The option to expand embedded in a start-up. The option in simple business co