0. Chapter 24 Options and Corporate Finance
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin

1. Key Concepts and Skills
Understand the basics of call and put options
Be able to determine option payoffs and pricing bounds
Understand the major determinants of option value
Understand employee stock options
Understand how a firm’s equity can be viewed as a call option on the firm’s assets
Understand how option valuation can be used to further evaluate capital budgeting projects
Understand warrants and convertible securities and how to determine their value
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2. Option Terminology Call Put Strike or Exercise price Expiration date
Option premium
Option writer
American Option
European Option
Call – right to buy
Put – right to sell
Strike or exercise price – fixed price at which the underlying asset may be bought (or sold) Expiration date – the last day that the option can be exercised Option premium – price paid to the option writer for the right
Option writer – seller of the option (obligation)
American option – the option can be exercised any time up to and including the expiration date European option – the option can only be exercised on the expiration date
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3. Stock Option Quotations
Look at Table 24.1 in the book
Price and volume information for calls and puts with the same strike and expiration is provided on the same line
Things to notice
Prices are higher for options with the same strike price but longer expirations
Call options with strikes less than the current price are worth more than the corresponding puts
Call options with strikes greater than the current price are worth less than the corresponding puts
Lecture Tip: You might want to point out that the strike prices in listed options are standardized. The various exchanges offer contracts in $2.50 and $5.00 increments for individual stocks. Cheap stocks have $2.50 increments, and higher priced stocks traded in $5 increments. Indexes can trade with varying strike price increments depending on the “size” of the contract.
Lecture Tip: You may wish to emphasize the symmetrical nature of options transactions by contrasting the positions of options buyers and options writers. For example, call buyers hope that the value of the underlying asset rises before their option expires. Their potential gain is unlimited, while their loss is limited to the price paid (the premium) for the option contract. Call writers, on the other hand, hope that the value of the underlying asset falls (or, at least, doesn’t rise); their gain is limited to the premium received, while their potential (opportunity) loss is unlimited. Writers of covered calls possess the underlying asset at the time the call is written, so the cost of delivering the underlying asset, should it become necessary, is known. However, the opportunity cost of having to sell the asset at a below market price is unknown and unlimited. Writers of naked calls do not own the underlying asset and must purchase it at the prevailing market price if the option is exercised. Their actual potential cost (the amount of cash they have to come up with) is unknown and unlimited. For this reason, many people view writing naked options as much riskier than writing covered options.
Lecture Tip: There has been a great deal of innovation in the derivatives field over the years. In the options area, a number of interesting twists on the standard option contract provide interesting class discussion topics. Consider the growing credit derivatives sector. A couple of examples are “price/spread” options, which are triggered by changes in the spread between the value of emerging market debt and U.S. Treasuries and “default puts,” for which payment occurs upon the default of a third party. Lecture Tip: Students are often fascinated by the topics of hedging and speculation. Options provide an excellent opportunity to introduce the differences between these terms. Hedging occurs when you use options (or some other security) to offset a position you already have. For example, if you own 100 shares of GM stock and the price has risen nicely, you might want to hedge against a price decline by buying a put option contract. Speculators do not hold offsetting positions. Instead, they take a stand-alone derivatives position hoping the price will move in the direction they want. If you expect the price of GM to decline, you could buy put options and then profit if you are correct. If you are incorrect, then your loss is limited to the price that you paid for the options.
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4. Option Payoffs – Calls
The value of the call at expiration is the intrinsic value
Max(0, S-E)
If S<E, then the payoff is 0
If S>E, then the payoff is S – E
Assume that the exercise price is $30
S is the underlying asset price
E is the exercise price
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5. Option Payoffs - Puts
The value of a put at expiration is the intrinsic value
Max(0, E-S)
If S<E, then the payoff is E-S
If S>E, then the payoff is 0
Assume that the exercise price is $30
Lecture Tip: Although the concepts are similar for puts and calls, students generally have more difficulty working with puts. An example showing what happens to the intrinsic value of both a put and a call when the stock price changes may be helpful. As such, an example is provided in the IM.
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6. Call Option Bounds Upper bound Lower bound
Call price must be less than or equal to the stock price
Lower bound
Call price must be greater than or equal to the stock price minus the exercise price or zero, whichever is greater (i.e., the option’s intrinsic value)
If either of these bounds are violated, there is an arbitrage opportunity
Lecture Tip: The phrase “intrinsic value” is important in the field of finance, but it has more than one meaning. In this context, it refers to the lower bound on options. In the investments area, however, it is used by fundamental analysts to refer to the “true” value of a financial asset.
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7. Figure 24.2
Lecture Tip: You may want to discuss the importance of arbitrage in the valuation of options. The classic definition of arbitrage is trading in more than one market simultaneously to earn a riskless profit. It is designed to exploit price discrepancies between markets. Risk arbitrage, on the other hand, is used to exploit the apparent mispricing of stocks involved in a takeover. The “risk arbitrageur” buys the stock of the firm being acquired and shorts the stock of the acquiring firm. The goal is to profit from the tendency of target firm prices to increase and acquiring firm prices to decrease. The difference here is that there is risk involved because there is no guarantee that the prices will move “normally.”
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8. A Simple Model
An option is “in-the-money” if the payoff is greater than zero
If a call option is sure to finish in-the-money, the option value would be
C0 = S0 – PV(E)
If the call is worth something other than this, then there is an arbitrage opportunity
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9. What Determines Option Values?
Stock price
As the stock price increases, the call price increases and the put price decreases
Exercise price
As the exercise price increases, the call price decreases and the put price increases
Time to expiration
Generally, as the time to expiration increases, both the call and the put prices increase
Risk-free rate
As the risk-free rate increases, the call price increases and the put price decreases
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10. What about Variance?
When an option may finish out-of-the-money (expire without being exercised), there is another factor that helps determine price
The variance in underlying asset returns is a less obvious, but important, determinant of option values
The greater the variance, the more the call and the put are worth
If an option finishes out-of-the-money, the most you can lose is your premium, no matter how far out it is
The more an option is in-the-money, the greater the gain
The owner of the option gains from volatility on the upside, but don’t lose any more from volatility on the downside
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11. Table 24.2
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12. Employee Stock Options
Options that are given to employees as part of their benefits packages
Often used as a bonus or incentive
Designed to align employee interests with stockholder interests and reduce agency problems
Empirical evidence suggests that they don’t work as well as anticipated due to the lack of diversification introduced into the employees’ portfolios
The stock isn’t worth as much to the employee as it is to an outside investor because of the lack of diversification – this suggests that options may work in limited amounts, but not as a large part of the compensation package
Lecture Tip: The idea behind using stock options to align management interests with stockholder interests is a noble one. Many companies have embraced it wholeheartedly because it seems so logical. However, overusing ESOs and other employee stock grants may backfire. We saw in previous chapters that holding a diversified portfolio is important because we are only rewarded for bearing non-diversifiable risk. If a substantial portion of an employee’s portfolio is tied up in company stock, then s/he may have difficulty diversifying fully. This lack of diversification leads to a higher required return by employee-owners than outside owners. The higher required return leads employees to place a lower value on the stock than outside stockholders. Recent research indicates that this does tend to be the case. Therefore, stock options may not provide as much incentive as it would appear at first glance. Employers need to be careful about overusing this incentive or it loses its value.
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13. Equity: A Call Option
Equity can be viewed as a call option on the company’s assets when the firm is leveraged
The exercise price is the face value of the debt
If the assets are worth more than the debt when it comes due, the option will be exercised and the stockholders retain ownership
If the assets are worth less than the debt, the stockholders will let the option expire and the assets will belong to the bondholders
Lecture Tip: Option valuation can explain how a company that has filed for Chapter 11 could still have a positive equity value, even though it is unlikely to be able to pay off its creditors. Consider the example in the IM.
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14. Capital Budgeting Options
Almost all capital budgeting scenarios contain implicit options
Because options are valuable, they make the capital budgeting project worth more than it may appear
Failure to account for these options can cause firms to reject good projects
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15. Timing Options
We normally assume that a project must be taken today or forgone completely
Almost all projects have the embedded option to wait
A good project may be worth more if we wait
A seemingly bad project may actually have a positive NPV if we wait due to changing economic conditions
We should examine the NPV of taking an investment now, or in future years, and plan to invest at the time that the project produces the highest NPV
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16. Example: Timing Options
Consider a project that costs $5,000 and has an expected future cash flow of $700 per year forever. If we wait one year, the cost will increase to $5,500 and the expected future cash flow will increase to $800. If the required return is 13%, should we accept the project? If so, when should we begin?
NPV starting today = -5, /.13 =
NPV waiting one year = (-5, /.13)/(1.13) =
It is a good project either way, but we should wait until next year
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17. Managerial Options
Managers often have options that can add value after a project has been implemented
It is important to do some contingency planning ahead of time to determine what will cause the options to be exercised
Some examples include
The option to expand a project if it goes well
The option to abandon a project if it goes poorly
The option to suspend or contract operations particularly in the manufacturing industries
Strategic options – look at how taking this project opens up other opportunities that would be otherwise unavailable
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18. Warrants
A call option issued by corporations in conjunction with other securities to reduce the yield required on the other securities
Differences between warrants and traditional call options
Warrants are generally very long term
They are written by the company, and warrant exercise results in additional shares outstanding
The exercise price is paid to the company, generates cash for the firm, and alters the capital structure
Warrants can normally be detached from the original securities and sold separately
Exercise of warrants reduces EPS, so warrants are included when a firm reports “diluted EPS”
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19. Convertibles
Convertible bonds (or preferred stock) may be converted into a specified number of common shares at the option of the bondholder
The conversion price is the effective price paid for the stock
The conversion ratio is the number of shares received when the bond is converted
Convertible bonds will be worth at least the straight bond value or the conversion value, whichever is greater
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20. Valuing Convertibles
Suppose you have a 10% bond that pays semiannual coupons and will mature in 15 years. The face value is $1,000, and the yield to maturity on similar bonds is 9%. The bond is also convertible with a conversion price of $100. The stock is currently selling for $110. What is the minimum price of the bond?
Straight bond value = 1,081.44
Conversion ratio = 1,000/100 = 10
Conversion value = 10*110 = 1,100
Minimum price = $1,100
Straight bond value: N = 15*2 = 30; I/Y = 9/2 = 4.5; PMT = .1(1000)/2 = 50; FV = 1000; CPT PV
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21. Other Options Call provision on a bond Put bond
Allows the company to repurchase the bond prior to maturity at a specified price that is generally higher than the face value
Increases the required yield on the bond – this is effectively how the company pays for the option
Put bond
Allows the bondholder to require the company to repurchase the bond prior to maturity at a fixed price
Insurance and Loan Guarantees
These are essentially put options
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22. Ethics Issues
It has been reported that during the internet boom in the late 1990s, technology firms were increasing their earnings by selling put options on their own stock.
When is this practice beneficial for the firm?
Why do you think this practice was significantly reduced in the year 2000?
Is there any ethical implication of this practice?
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23. Comprehensive Problem
A convertible bond has a straight bond value of $1,050. The conversion ratio is 24, and the stock price is $49 per share. What is the value of the option to convert?
What is the intrinsic value of a call and a put, each with an exercise price of $40, if the stock price is currently $50?
What if the stock price is $20?
Conversion value = 24 x $49 = $1,176
Value of the option to convert = $1,176 - $1,050 = $126 (This is the minimum value. Due to the speculative premium, an investor may be willing to pay more than this for the option.)
Stock price = $50:
Call option intrinsic value = $50 – $40 = $10
Put option intrinsic value = $0
Stock price = $20:
Call option intrinsic value = $0
Put option intrinsic value = $40 - $20 = $20
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24. End of Chapter
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