23-0 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Corporate Finance Ross Westerfield ...

23-1

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

23-2


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.

23-3


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

23-4


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.)

23-5


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.

23-6


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.

23-7


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).

23-8


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

23-9


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.

23-10


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.

23-11



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

23-12



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

23-13



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.

23-14


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$529,6$

23-15


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.

23-16


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.

23-17


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

23-18


$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

23-19


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.

23-20


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

23-21



$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

23-22



$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

23-23



$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

23-24


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$

-$

23-25


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.

23-26


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.

23-27


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.

23-28



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.

23-29



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.

23-30



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:

23-31


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

23-32


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

23-33


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.

23-0 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Corporate Finance Ross Westerfield ...

Documents

Transcript of 23-0 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Corporate Finance Ross Westerfield ...