Executive Summary

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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 employers 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 valueonly the intrinsic value.
• This dead weight loss is overcome by the
  incentive compatibility for the grantor.

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Top Stock Option Grants
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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
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.
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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

Where C0 the value of a European option at
time t 0
r 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 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 30,00020
• 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

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23.2 Valuing a Start-Up with Black-Scholes

• Lets try our hand again at using the model. If
  you have a calculator handy, follow along.

First calculate d1 and d2
Then,
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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
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
  2this schedule yields the highest NPV when
  judged today.

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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
  modelespecially 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
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Three Period Binomial Process Call Option Prices
38.02
13.02
2/3
33.06
2/3
9.25
1/3
28.75
28.10
2/3
3.10
2/3
6.50
1/3
25
24.44
4.52
2/3
1.97
1/3
1/3
21.25
20.77
2/3
0
1.25
1/3
18.06
0
1/3
15.35
0
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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, 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.

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Three-Period Binomial Process Lookback Call
Option Prices
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Three-Period Binomial Process Lookback Call
Option Prices
38.02
13.02
33.06
28.10
3.10
28.75
28.10
3.66
24.44
20.77
0
25
28.10
6.85
24.44
20.77
0
21.25
20.77
2.71
18.06
15.35
0
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Three-Period Binomial Process Lookback Call
Option Prices
38.02
13.02
33.06
9.25
28.10
3.10
28.75
28.10
3.66
24.44
20.77
0
2.33
25
28.10
6.85
24.44
20.77
0
4.35
21.25
20.77
2.71
18.06
1.72
15.35
0
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Three-Period Binomial Process Lookback Call
Option Prices
38.02
13.02
33.06
9.25
28.10
3.10
28.75
28.10
3.66
6.61
24.44
20.77
0
2.33
25
5.25
28.10
6.85
24.44
20.77
0
4.35
21.25
3.31
20.77
2.71
18.06
1.72
15.35
0
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Excel Applications of the BOPM

• The BOPM is easily incorporated into Excel
  spreadsheets

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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.

• 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
Traditional NPV analysis would indicate rejection
of the project.
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The Option to Abandon Example
Traditional NPV analysis overlooks the option to
abandon.
The firm has two decisions to make drill or not,
abandon or stay.
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The Option to Abandon Example

• 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.

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Enrons 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
  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, 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.