第二十三章 期权与公司理财：推广与应用

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1. Executive SummaryThis 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 expand embedded in a start-up. The option in simple business contracts. The option to shut down and reopen a project.
2. Chapter Outline23.1 Executive Stock Options 23.2 Valuing a Start Up 23.3 More on the Binomial Model 23.4 Shutdown and Reopening Decisions 23.5 Summary and Conclusions
3. 23.1 Executive Stock OptionsExecutive Stock Options exist to align the interests of shareholders and managers. Executive Stock Options are call options (technically warrants) on the employer’s 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 options are not considered taxable income. (Taxes are due if the option is exercised.)
4. Valuing Executive CompensationFASB allows firms to record zero expense for grants of at-the-money executive stock options. However 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 exercise, not sell his options. Thus he can never capture the speculative value—only the intrinsic value. This “dead weight loss” is overcome by the incentive compatibility for the grantor.
5. Top Stock Option GrantsCompanyCEOStock 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.$104,300,000 Honeywell Inc.Michael Bosignore $121,496,000 ALCOAPaul O’Neill $96,353,000
6. 23.2 Valuing a Start-UpAn 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 successful, 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).
7. Campusteria 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 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.
8. 23.2 Valuing a Start-UpNote 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-Scholes option pricing model to value this option
9. 23.2 Valuing a Start-Up with Black-ScholesThe Black-Scholes Model isWhere C0 = the value of a European option at time t = 0r = the risk-free interest rate.N(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.
10. 23.2 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 = $30,000×20 The interest rate available is r = 10%. The option maturity is four years. The volatility of the underlying asset is 30% per annum. The current value of the underlying assets is $110,418
11. 23.2 Valuing a Start-Up with Black-ScholesLet’s try our hand again at using the model. If you have a calculator handy, follow along.Then, First calculate d1 and d2
12. 23.2 Valuing a Start-Up with Black-ScholesN(d1) = N(-1.8544) =0.032 N(d2) = N(-2.45) =0.007The option to expand, while valuable, is not as great as the negative NPV of opening the trial Campusteria. So we should not proceed.
13. The Option to Delay: ExampleConsider 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 are declining the NPV at the time of launch steadily rises. The best time to launch the project is in year 2—this schedule yields the highest NPV when judged today.
14. 23.3 More on the Binomial ModelThe binomial option pricing model is an alternative to the Black-Scholes option pricing model—especially given the computational 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 underlying 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.
15. Three Period Binomial Option Pricing ExampleThere 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.
16. Three Period Binomial Process: Stock Prices$2528.7521.252/31/333.0624.442/31/318.062/31/315.352/31/338.022/31/320.772/31/328.10
17. $2528.7521.252/31/315.352/31/338.0228.102/31/320.772/31/333.0624.442/31/318.062/31/313.023.10009.251.9706.50 1.254.52Three Period Binomial Process: Call Option Prices
18. Valuation of a Lookback OptionWhen 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, let’s 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.
19. Three Period Binomial Process: Lookback Call Option Prices$2528.7521.2533.0624.4418.0624.4415.3520.7728.1020.7720.7728.1038.0228.10
20. Three 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
21. Three 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$3.66 002.7109.252.334.351.72
22. Three 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$3.66 002.7109.252.334.351.726.61 3.315.25
23. Excel Applications of the BOPMThe BOPM is easily incorporated into Excel spreadsheets
24. 23.4 Shutdown and Reopening DecisionsCan 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 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.
25. Discounted Cash Flows and OptionsWe 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. A good example would be comparing the 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.
26. The Option to Abandon: ExampleSuppose 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 unsuccessful payoff at time one is $0.
27. The Option to Abandon: Example Traditional NPV analysis would indicate rejection of the project.
28. The Option to Abandon: ExampleThe firm has two decisions to make: drill or not, abandon or stay.Do not drillDrillFailureSuccess: PV = $500Sell the rig; salvage value = $250 Sit on rig; stare at empty hole: PV = $0.Traditional NPV analysis overlooks the option to abandon.
29. The Option to Abandon: Example When we include the value of the option to abandon, the drilling project should proceed:
30. Valuation of the Option to AbandonRecall 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.
31. Enron’s Inefficient PlantsIn 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 efficient 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 year was a positive NPV investment—when 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, 1999
32. 23.5 Summary and ConclusionsOptions 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 contracts. The option to shut down and reopen a project. We have the methodology to value them.