Post on 13-Jan-2016
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McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited
Corporate Finance Ross Westerfield Jaffe Sixth Edition
23Chapter Twenty Three
Options & Corporate Finance: Extensions & Applications
Prepared by
Gady JacobyUniversity of Manitoba
and
Sebouh AintablianAmerican University of Beirut
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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.
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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
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23.1 Executive Stock Options
• Executive 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 three 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.)
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Valuing Executive Compensation
• Canadian tax laws allow 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.
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Top Stock Option Grants
Company CEO Stock Option Award
U.S. 1999
Citigroup, Inc. Sanford Weill $351,319,000 U.S.
American Express Harvey Golub $134,102,000
Cisco Systems, Inc. John Chambers $132,100,000
Bank of America Hugh McColl Jr. $104,300,000
Honeywell Inc. Michael Bosignore $121,496,000
ALCOA Paul O’Neill $96,353,000
Canada 2000
Nortel Networks John Roth $89,010 Cdn.
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23.2 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 university campuses.
• The test market will be your campus, and if the concept proves successful, expansion will follow nationwide.
• Nationwide expansion will occur in year 4.• 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).
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Campusteria pro forma income statement
Investment Year 0 Years 1-4
Revenues $60,000
Variable Costs ($42,000)
Fixed Costs ($18,000)
Depreciation ($7,500)
Pretax profit ($7,500)
Tax shield 34% $2,550
Net Profit –$4,950
Cash Flow –$30,000 $2,550
We 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 $1,500 per month.
We can depreciate our capitalized leaseholder improvements.
84.916,21$)10.1(
550,2$000,30$
4
1
t
tNPV
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23.2 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 Campusterias in year 4.
• The value of the project is in the option to expand.
• We will use the Black-Scholes option pricing model to value this option.
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23.2 Valuing a Start-Up with Black-Scholes
The Black-Scholes Model is
)N()N( 210 dEedSC rT
Where
C0 = the value of a European option at time t = 0r = the risk-free interest rate.
T
Tσ
rESd
)2
()/ln(2
1
Tdd 12
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 two-state world.
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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
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 $110,418
418,110$)10.1(
14.663,161$
)10.1(
)10.1(
550,2$20
44
4
1
tt
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23.2 Valuing a Start-Up with Black-Scholes
Let’s try our hand again at using the model. If you have a calculator handy, follow along.
Then,
T
TσrESd
)5.()/ln( 2
1
First calculate d1 and d2
45.2430.08544.112 Tdd
8544.1430.0
4))30.0(5.10(.)000,600/418,110ln( 2
1
d
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23.2 Valuing a Start-Up with Black-Scholes
N(d1) = N(-1.8544) =0.032
N(d2) = N(-2.45) =0.007
)N()N( 210 dEedSC rT
03.718$
007.0000,600032.0418,110$
0
410.0
C
eC
The option to expand, while valuable, is not as great as the negative NPV of opening the trial Campusteria. So we should not proceed.
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The Option to Delay: Example
• Consider the above project, which can be undertaken in any of the next four years. The discount rate is 10-percent. The present value of the benefits at the time the project is launched remains constant at $25,000, but since costs are declining the NPV at the time of launch steadily rises.
• The best time to launch the project is in year 2—this schedule yields the highest NPV when judged today.
Year Cost PV NPV t NPV 0
0 20,000$ 25,000$ 5,000$ 5,000$ 1 18,000$ 25,000$ 7,000$ 6,364$ 2 17,100$ 25,000$ 7,900$ 6,529$ 3 16,929$ 25,000$ 8,071$ 6,064$ 4 16,760$ 25,000$ 8,240$ 5,628$
2)10.1(
900,7$529,6$
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23.3 More on the Binomial Model
• The 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.
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Three-Period Binomial Option Pricing 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.
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Three Period Binomial Process: Stock Prices
$25
28.75
21.25
2/3
1/3
)15.1(00.25$
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$ 2
2)15.1()15.1(00.25$
3)15.1(00.25$
33.06
24.44
2/3
1/3
18.06
2/3
1/3
15.35
2/3
1/3
38.02
2/3
1/3
20.77
2/3
1/3
28.10
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$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$35.15max[$
),,(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$320
C
Three Period Binomial Process: Call Option Prices
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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 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.
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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
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McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited
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
10.3]0,25$10.28max[$),,(3 DUUC
$6.85
$3.66
0]0,44.24$77.20max[$),,(3 DDUC0
0
2.71
0]0,06.1836.15max[$),,(3 DDDC
66.3]0,44.24$10.28max[$),,(3 UDUC
85.6]0,25.21$10.28max[$),,(3 UUDC
0]0,25.21$77.20max[$),,(3 DUDC
71.2]0,06.18$77.20max[$),,(3 UDDC
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McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited
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
$3.66
0
0
2.71
0
)05.1(
10.3$)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
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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
$3.66
0
0
2.71
0
9.25
2.33
4.35
1.72
)05.1(
33.2$)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$320
C
5.25
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Excel Applications of the BOPM
The BOPM is easily incorporated into Excel spreadsheets
14% s 28.75$ 1 Maturity 25.00$ 1 n 3.75$ 1 D t q
25.00$ S 0
25.00$ X Stock Price 25.00$ 5% r f Exercise Price 25.00$
1.1500 u Ordinary Call 2.38$ 0.8500 d1.0500 a 1- q
66.67% Risk Neutral Prob 21.25$ 33.33% 1- R.N. Prob 25.00$
-$
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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 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.
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Discounted 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.
OptNPVM
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.
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The 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 unsuccessful payoff at time one is $0.
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The Option to Abandon: Example
failuregiven
Payoff
failure
Prob.
successgiven
Payoff
sucess
Prob.
payoff
Expected
5.287$05.0575$5.0payoff
Expected
64.38$)10.1(
50.287$300$
tNPV
Traditional NPV analysis would indicate rejection of the project.
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The Option to Abandon: Example
The firm has two decisions to make: drill or not, abandon or stay.
Do not drill
Drill
0$NPV
500$
Failure
Success: PV = $500
Sell the rig; salvage value
= $250
Sit on rig; stare at empty hole:
PV = $0.
Traditional NPV analysis overlooks the option to abandon.
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The Option to Abandon: Example
failuregiven
Payoff
failure
Prob.
successgiven
Payoff
sucess
Prob.
payoff
Expected
50.412$0255.0575$5.0payoff
Expected
00.75$)10.1(
50.412$300$
tNPV
• When we include the value of the option to abandon, the drilling project should proceed:
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Valuation of the 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.
OptNPVM
Opt 64.3800.75$
Opt 64.3800.75$
64.113$Opt
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Enron’s 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 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
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23.5 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 contracts.
– The option to shut down and reopen a project.
• We have the methodology to value them.