第二十三章 期权与公司理财：推广与应用

20 4 $2,550
t1 (1.10)t (1.10) 4

$161,663.14 (1.10) 4

$110,418
McGraw-Hill/Irwin
• 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-Scholes option pricing model to value
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.
• This “dead weight loss” is overcome by the incentive compatibility for the grantor.
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Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Honeywell Inc.
Michael Bosignore
ALCOA
Paul O’Neill
Stock Option Award $351,319,000 $134,102,000 $132,100,000 $104,300,000 $121,496,000 $96,353,000
McGraw-Hill/Irwin
McGraw-Hill/Irwin
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
23-9
23.2 Valuing a Start-Up with Black-Scholes
We need to find the value of a four-year call option on chain with an exercise price of $600,000 = $30,000×20
Year 0 –$30,000
Years 1-4 $60,000
($42,000) ($18,000) ($7,500) ($7,500)
$2,550 –$4,950
$2,550
We plan to sell 25 meal plans at $200 per month with a 12-month contract.
• 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.)
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
23-5
23.2 Valuing a Start-Up
• An important option is the option to expand. • Imagine a start-up firm, Campusteria, Inc. which
23-4
Top Stock Option Grants
Company
CEO
Citigroup, Inc.
Sanford Weill
American Express
Harvey Golub
Cisco Systems, Inc. John Chambers
Bank of America
Hugh McColl Jr.
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23-2
23.1 Executive Stock Options
• Executive Stock Options exist to align the interests of shareholders and managers.
• 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.
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).
• 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.
Where
C0 S N(d1) EerT N(d2 )
C0 = the value of a European option at time t = 0 r = the risk-free interest rate.
ln( S / E) (r σ 2 )T
d1
2
T
d2 d1 T
this option
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23-8
23.2 Valuing a Start-Up with Black-Scholes
The Black-Scholes Model is
23-0
Executive 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 expand embedded in a start-up. – The option in simple business contracts. – The option to shut down and reopen a project.
NPV $30,000 4 $2,550 $21,916.84
t1 (1.10)t
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23-7
23.2 Valuing a Start-Up
• 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.
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Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
23-1
Chapter Outline
23.1 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