ch20

Chapter 20Options and Corporate Finance

Learning Objectives

1. Define a call option and a put option, and describe the payoff function for each of

these options.

An option is the right, but not the obligation, to buy or sell an asset for a given price on or

before a given date. The price is called the exercise or strike price, and the date is called

the exercise date or expiration date of the option. The right to buy the asset is known as a

call option. The payoff from a call option equals $0 if the value of the underlying asset is

less than the exercise price at expiration. If the value of the underlying asset is higher than

the exercise price at expiration, then the payoff from the call option is equal to the value

of the asset value minus the exercise price. The right to sell the asset is called a put

option. The payoff from a put option is $0 if the value of the underlying asset is greater

than the exercise price at expiration. If the value is lower than the exercise price, then the

payoff from a put option equals the exercise price minus the value of the underlying asset.

2. List and describe the factors that affect the value of an option.

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The value of an option is affected by five factors: the current price of the underlying

asset, the volatility of the value of the underlying asset, the time left until the expiration

of the option, the exercise price of the option, and the risk-free rate.

3. Name some of the real options that occur in business, and explain why traditional

NPV analysis does not accurately incorporate their values.

Real options that are associated with investments include options to defer investment,

make follow-on investments, change operations, and abandon projects. Traditional NPV

analysis is designed to make a decision to accept or reject a project at a particular point in

time. It is not designed to incorporate potential value associated with deferring the

investment decision. Incorporating the value of the other options into an NPV framework

is technically possible but would be very difficult to do because the rate used to discount

the cash flows would change over time with their riskiness. In addition, the information

necessary to value real options using the NPV approach is not always available.

4. Describe how the agency costs of debt and equity are related to options.

There are two principal classes of agency conflicts. The first is between stockholders and

lenders. When there is a risk of bankruptcy, stockholders may have incentives to increase

the volatility of the firm’s assets, turn down positive-NPV projects, or pay out assets in

the form of dividends. Stockholders have these incentives because their payoff functions

look like those for the owners of a call option.

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The other principal class of agency conflict is between managers and owners.

Managers tend to prefer less risk than stockholders and prefer to distribute fewer assets in

the form of dividends because their payoff functions are more like those of lenders than

those of stockholders. These preferences are magnified by the fact that managers are risk-

averse individuals whose portfolios are not well diversified.

5. Explain how options can be used to manage a firm’s exposure to risk.

A company can adjust its exposure to risks associated with commodity prices, interest

rates, foreign exchange rates, and equity prices by buying or selling options. For

example, a company that is concerned about the prices it will receive for products that

will be delivered in the future can purchase put options to partially or totally eliminate

that risk.

I. True or False Questions

1. A put option with a strike price of $20 is expiring today. The stock is currently selling at

$25. Based on this information, the put option should not be exercised.

a. True

b. False

2. A stock is selling for $50 today. A call option on the stock with a strike price of $50 is set

to expire next month. If the price of the stock goes down tomorrow we would expect the

price of the call option to go down as well.

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a. True

b. False

3. A call option can sometimes be priced higher than the underlying asset.

a. True

b. False

4. Neither a call nor a put option can have a negative price.

a. True

b. False

5. The current price of an asset is $75. A put option on the asset with a strike price of $100

expires one year from now. It is possible, without arbitrage, for this put option to be

priced at $24 today.

a. True

b. False

6. If the risk-free rate of interest increases, all else being equal, we would expect the value

of a call option to increase.

a. True

b. False

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7. In the binomial pricing model, an option is priced using a replicating portfolio that

typically consists of a risk-free bond and the asset underlying the option.

a. True

b. False

8. To price an option using the binomial pricing model, it is important that we know the

probability that the asset will increase in value.

a. True

b. False

9. When using the binomial pricing model to price an option, the volatility of the underlying

asset is represented by the difference between the two possible future values of the

underlying asset.

a. True

b. False

10. Consider a call option on a stock with a strike price of $60. If the stock price at expiration

is $50, the payoff from the call option is $10.

a. True

b. False

11. Consider a put option on a stock with a strike price of $60. If the stock price at expiration

is $50, the payoff from the put option is $10.

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a. True

b. False

12. Suppose you have sold a put option on a stock with a strike price of $25. If the stock

price at expiration is $30, your payoff will be $–5.

a. True

b. False

13. A portfolio consisting of one put option and one call option, both with the same exercise

price, is called a straddle. A straddle is a good investment strategy for investors who

don’t know whether an asset’s value is likely to go up or down, but think that the

volatility of the asset will increase.

a. True

b. False

14. If a project has a positive NPV, then the real options that affect the project are not

important to estimating the value of the project.

a. True

b. False

15. The option to defer investment can be characterized as the flexibility to wait and learn

more information about a project before committing resources to the project.

a. True

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b. False

16. Incorporating real options will not decrease the value of the project relative to the basic

NPV analysis.

a. True

b. False

17. After taking into account the value of real options, it is possible that some projects with a

negative NPV should be pursued.

a. True

b. False

18. A company is negotiating for the option to develop a platinum mine. Under the terms of

the option contract, the company would be able to purchase the development rights to the

mine one year from now for an exercise price specified today. If, during the negotiations

over the option contract, the volatility of the price of platinum increases, the company

should expect to pay a higher price for the development option.

a. True

b. False

19. The option to abandon a project can decrease its value.

a. True

b. False

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20. Kelvin’s Thermostats Co. sells equipment to residential and commercial customers. It is

considering whether or not to develop a new line of advanced commercial thermostats.

The discounted cash flows from commercial thermostat sales are not likely to cover the

development costs. However, the company has decided to pursue the project anyway. If

the commercial technology is successful, it might be applied to a new line of very

profitable residential thermostats. This is an example of the option to make follow-on

investments.

a. True

b. False

21. Consider a firm with a single loan. There are no interest payments on the loan, but the

principal and interest are all due in two years. It is uncertain whether the cash flow the

company will produce will be enough to pay off the debt. The payoff to stockholders in

this company resembles a call option.

a. True

b. False

22. Consider a company that is likely to go bankrupt in the next year. The bondholders may

encourage the company to pursue risky negative-NPV projects in hopes that the firm will

avoid financial distress.

a. True

b. False

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23. Consider a company that is likely to go bankrupt in the next year. Stockholders may wish

to pursue negative-NPV projects, even if there is no additional value to the project from

real options.

a. True

b. False

24. By designing compensation plans with performance bonuses, stock-based compensation

and stock options corporate boards are attempting to make the payoff function for

managers look similar to the payoff function for stockholders.

a. True

b. False

25. Financial options can be used to hedge risks such as interest rates and foreign exchange

rates.

a. True

b. False

26. Suppose the current spot price of wheat is $25 a bushel. A wheat farmer expects to

produce 1,000 bushels at the end of the season, and she wants to ensure that she gets at

least $19 a bushel. If a put option on 1,000 bushels of wheat with a strike price of

$20,000 and an expiration date at the end of the season is selling for $1,000, the farmer

can purchase the put option to guarantee she gets $19 a bushel.

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a. True

b. False

27. Suppose the current spot price of corn is $20 a bushel. A corn farmer expects to produce

2,000 bushels at the end of the season, and she wants to ensure that she gets at least $18

per bushel. Call options on 1,000 bushels of wheat with a strike price of $15,000 and an

expiration date at the end of the season are selling for $3,000. By selling call options on

her corn crop, the farmer can guarantee that she gets at least $18 per bushel.

a. True

b. False

28. Hedging is the process of using financial instruments such as options, forwards, futures,

and swaps to reduce the financial risks faced by a firm.

a. True

b. False

29. Socrates Motor Co. has a defined-benefit pension plan for its employees. To fund the

plan, the company makes periodic contributions to a stock investment fund. If the stock

market declines significantly, the company would have to make additional contributions

to make up for lost revenue. The company could hedge its risk of a market downturn by

periodically purchasing put options on the stock market.

a. True

b. False

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30. A small soybean farmer wants to hedge the price risk of his next crop, but he is

financially constrained. He can’t raise capital by either borrowing money or selling his

current assets. Instead, he sells call options on his soybean crop with a strike price of $14

per bushel at a premium of $0.50 a bushel. Using the process from selling the call

options, he buys put options on his soybean crop with a strike price of $11.00 per bushel

at a premium of $0.35 per bushel. The risk-free interest rate is 0 percent. By taking these

derivative positions, the farmer has guaranteed that he will earn somewhere between

$14.15 and $11.15 per bushel.

a. True

b. False

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II. Multiple-Choice Questions and Problems

31. An investor (the buyer) purchases a call option from a seller. On the expiration date of a

call option,

a. the buyer has the obligation to buy the underlying asset and the seller has the

obligation to sell it.

b. the buyer has the right to buy the underlying asset and the seller has the obligation

to sell it.

c. the buyer has the obligation to buy the underlying asset and the seller has the right

to sell it.

d. None of the above.

32. An investor (the buyer) purchases a put option from a seller. On the expiration date of a

call option,

a. the buyer has the obligation to sell the underlying asset and the seller has the right

to buy it.

b. the buyer has the obligation to sell the underlying asset and the seller has the

obligation to buy it.

c. the buyer has the right to sell the underlying asset and the seller has the obligation

to buy it.

d. None of the above

33. Which one of the following statements is NOT true?

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a. The value of a call option can never be negative.

b. The value of a call option can never be more than the value of the underlying

asset.

c. The value of a call option can never be worth less than the current value of the

asset minus present value of the strike price.

d. The value of a call option can never be worth more than the strike price.

34. Which one of the following statements is NOT true?

a. The value of a put option can never be negative.

b. The value of a put option can never be worth more than the underlying asset.

c. The value of a put option can never be less than the present value of the strike

price minus the current value of the underlying asset.

d. All the above statements are true.

35. Suppose you own a call option on a stock with a strike price of $20 that expires today.

The price of the underlying stock is $15. If you exercise the option and immediately sell

the stock,

a. you will earn $5.

b. you will lose $5.

c. you will lose $15.

d. you will earn $15.

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36. Suppose you own a put option on a stock with a strike price of $35 that expires today.

The price of the underlying stock is $25. If you purchase the stock and exercise the put

option,

a. you will earn $10.

b. you will lose $10.

c. you will earn $25.

d. you will lose $25.

37. Consider an option that gives the owner the right to buy a stock for $20 only on the third

Friday of May, next year. The option being described is

a. an American call option.

b. a European put option.

c. an American put option.

d. a European call option.

38. Consider an American and a European call option on a dividend-paying stock, with

otherwise identical features (same strike price, etc.). Which one of the following

statements is true?

a. The American call option will never be worth less than the European call option.

b. The European call option will never be worth less than the American call option.

c. Both options should always have the same value.

d. None of the above statements is true.

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39. A straddle is a combination of a put option and a call option on the same asset with the

same strike price. Which one of the following statements about a straddle is NOT true?

a. The owner of a straddle will receive a payoff if the price of the underlying asset is

higher than the strike price at expiration.

b. The owner of a straddle will receive a payoff if the price of the underlying asset is

lower than the strike price at expiration.

c. The owner of a straddle will never exercise the put and the call option at the same

time.

d. The owner of a straddle will receive a higher payoff if the price of the underlying

asset at expiration is near the strike price.

40. Which of the following changes, when considered individually, will increase the value of

a call option?

a. The value of the underlying asset becomes more volatile.

b. The price of the underlying asset goes down.

c. Getting closer to the expiration date (the passage of time).

d. A higher strike price.

41. Which of the following changes, when considered individually, will increase the value of

a put option?

a. An increase in the risk-free interest rate

b. Lower volatility of the price of the underlying asset

c. A higher strike price

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42. What happens to the value of call and put options if the volatility of the price of

underlying asset decreases?

a. Put options will be worth more, call options will be worth less.

b. Put options will be worth less, call options will be worth more.

c. Both call and put options will be worth more.

d. Both call and put options will be worth less.

43. If the price of the underlying asset increases, what happens to the value of call and put

options?

a. Put options will be worth more, call options will be worth less.

b. Put options will be worth less, call options will be worth more.



44. With everything else constant, as the expiration date gets closer, what happens to the

value of call and put options?

a. Call option will be worth more, put options will be worth less.

b. Call option will be worth less, put options will be worth more.



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45. With everything else held constant, what happens to the value of call and put options if

the risk-free interest rate increases?

a. Call options will be worth more, put options will be worth less.

b. Call options will be worth less, put options will be worth more.

c. Both call and put options will be worth less.

d. Both call and put options will be worth more.

46. The management at Socrates Motors considered the option to abandon when building

their new manufacturing plant. The design of the plant allows it to be easily converted to

manufacture other types of large machinery. If their new line of cars is poorly received,

their plant should be easy to sell to another manufacturing company. In this example, the

price at which they expect to sell the plant if things go poorly resembles

a. the premium of a put option on the plant.

b. the premium of a call option on the plant.

c. the strike price of a put option on the plant.

d. the strike price of a call option the plant.

47. Socrates Motors is very likely to enter financial distress. Without a dramatic change of

events over the next couple of years, the company will be unable to pay its lenders, who

will then gain control of the company’s assets. A group of stockholders has pressured the

company’s management to begin manufacturing and selling one of the company’s

concept cars in the hope that it will be a big hit. Concept cars are prototypes that are

developed to test new ideas and to show off at auto shows. Although elements of concept

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cars are often incorporated into product lines, rushing a concept car into production is

very risky. The best estimates about the concept car make it appear to be a negative-NPV

project. This is a good example of

a. the dividend payout problem.

b. the underinvestment problem.

c. the asset substitution problem.

d. the agency cost of equity.

48. Consider a CEO who holds neither stock nor stock options in the company she runs. Her

payoff function regarding the firm’s performance is most likely to resemble

a. stockholders.

b. lenders.

c. owners of a call option on the firm.

d. holders of a risk-free bond with coupon payments equal to her salary.

49. Which of the following compensation methods is NOT likely to reduce agency costs

between stockholders and managers?

a. Stock compensation—giving the CEO stock in the company as part of her salary.

b. A golden parachute—a guaranteed large lump-sum payment in the event that the

CEO is fired.

c. A higher salary than that of other CEOs in similar companies.

d. Performance bonuses—a higher bonus if the company’s cash flows are higher

then expected.

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50. Which of the following reasons is NOT a valid explanation of why managers sometimes

choose to take on negative-NPV Projects:

a. The NPV analysis does not include a valuable real option to expand the project if

things go well.

b. If the firm has debt, managers may create value for shareholders by taking on

some risky negative-NPV projects.

c. Managers’ payoff functions represent the payoffs of lenders. By taking negative-

NPV projects, the managers can create value for lenders.

d. All of the above descriptions are valid explanations for why managers sometimes

take on negative NPV projects.

51. As the manager of a sporting goods company, you are presented with a new golf project.

An inventor has recently patented the design for a new golf club that makes playing golf

much easier. Your company has made contact with the inventor, who is willing to sell the

exclusive rights to the technology, but if you don’t act fast he will sell the rights to a rival

company. You are not certain whether the new golf club will become popular, but your

analysts have completed a basic NPV analysis. Given the available information, the

project has a positive NPV. However, you know there are several real options associated

with the project, including the option to abandon the project and the option to make

follow-on investments. Which one of the following statements regarding the project is

correct?

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a. Based on the NPV analysis, you should accept the project. The value of the project

may be worth more than the NPV analysis but not less.

b. Based on the NPV analysis, you should accept the project. The NPV analysis contains

all the information about the value of the project.

c. Based on the NPV analysis, you should reject the project. Without additional

information about the value of the real options, there is no way to make a decision.

d. Based on the NPV analysis, you should reject the project. The NPV analysis contains

all the information about the value of the project.

52. A start-up company is making a decision on whether to develop a new internet social

networking site. The site will cost $1 million to develop, but it is unclear whether the new

technology critical to the site will work correctly. If development is successful, it will

cost an additional $20 million next year to advertise the site to Internet users. If the site

becomes popular with Internet users, it is expected to generate a present value of $100

million in advertising revenue. There is a 10 percent chance that the site will be both

successfully developed and subsequently become popular with Internet users. The

company’s cost of capital is 15 percent. Should the company pursue the project?

a. No, the project has a negative NPV.

b. Yes, the project has a positive NPV.

c. It doesn’t matter. The project has zero NPV.

d. There is not enough information to make a decision.

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53. The employment contracts for professional athletes often contain options for either the

player or the team. Consider one recent contract in Major League Baseball. The player’s

salary was guaranteed for the first couple years. However, after several years, the team

had the option to cancel the contract if the player became injured. If we think of each

player as a project for the team, this option feature of the contract is best described as

a. the option to defer investment.

b. the option to make follow-on investments.

c. the option to change operations.

d. the option to abandon projects.

54. RealEstates LLP is considering the construction of a new development of condominiums

in downtown Austin, Texas. The site for the new development is currently occupied by

an office building owned by the city. The project’s profitability will depend largely on

the population increase in Austin over the next several years. Rather than buy the site,

RealEstates has entered into an agreement with the city to pay $200,000 for the right to

purchase the site for $10 million two years from now. The real option embedded in this

contract is best described as




d. the option to abandon projects.

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55. Consider a new firm that is working on the first generation of long-awaited consumer jet

packs. The project will take a tremendous amount of R&D expenditure. Even if the

development is successful, manufacturing the first generation of jet packs is likely to be

so expensive that only a select few consumers will be able to afford them. The projected

sales of the first generation of jet packs almost certainly won’t cover the development and

manufacturing costs—the project has a negative NPV. Which of these reasons would

validate the firm’s decision to pursue the jet pack project?

a. If development is unsuccessful, it can abandon the project before spending money

on manufacturing.

b. If the project is successful, it may lead to a very profitable second project—a

cheaper jet pack that will be a positive-NPV project.

c. Because it is a high-tech firm, the cash flows generated by a project are not

important to valuing the company.

d. None of these reasons support the decision to pursue the project.

56. A local city government has awarded a contract to sequentially build five new elementary

schools over the next 10 years. The price for each school has been spelled out in the

contract, but at the beginning of each year the city can cancel the order for the remaining

schools. The city government is concerned that if the population of the town does not

grow as expected it may not need all of the schools. What sort of financial option does

the option to cancel the order resemble?

a. Owning a call option on the value of the new schools

b. Owning a put option on the value of the new schools

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c. Selling a call option on the value of the new schools

d. Selling a put option on the value of the new schools

57. Purchasing a house is a somewhat complicated process. Typically, if the buyer’s offer is

accepted by the seller, the transaction will not be completed or “closed” for several

weeks. During this time the buyer may gather more information about the house or

research other houses in the area. Some home purchase contracts include an option fee.

The buyer may pay the seller a few hundred dollars for the right to walk away from the

contract prior to closing for any reason. This option fee is best described as




d. a put option on the house.

58. The management at Socrates Motors considered the option to abandon when building

their new manufacturing plant. The design of the plant allows it to easily be converted to

manufacture other types of large machinery. If their new line of cars is poorly received,

their plant should be easy to sell to another manufacturing company. In this example, the

extra cost of building the plant in such a way that it can easily be converted for other uses

resembles

a. the premium of a put option on the plant.

b. the premium of a call option on the plant.

c. the strike price of a put option on the plant.

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d. the strike price of a call option on the plant.

59. Franklin Foods has made the decision to invest in a new line of organic microwave

dinners. The new line of dinners is a negative-NPV project; paying its suppliers to

convert to organic practices will be expensive. However, the company will be in a good

position to expand into more profitable lines of food if consumer demand for organic

foods grows more then expected. The negative value of the organic dinner project most

closely resembles:

a. the premium of a put option on future organic projects.

b. the premium of a call option on future organic projects.

c. the strike price of a put option on future organic projects.

d. the strike price of a call option on future organic projects.

60. Gnu Homes, Inc., is a developer of planned residential communities. It has entered into

an option contract with a land owner outside Austin, Texas. It will pay the land owner

$100,000 for the option to buy the land in two years at a price of $20 million. During that

time Gnu Homes will evaluate population and real estate trends in Austin. Their plan is to

buy the land if real estate prices in Austin increase enough that developing the land

would be worth more then the $20 million price. The $20 million purchase price

resembles

a. the premium price of a put option on the land.

b. the premium price of a call option on the land.

c. the strike price of a put option on the land.

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d. the strike price of a call option on the land.

61. The claim stockholders hold on cash flows in a company with outstanding debt is often

described as

a. a call option on the firm’s assets.

b. a put option on the firm’s assets.

c. an interest-free bond with the same value as the firm’s assets.

d. none of the above

62. Which of the following statements is NOT an example of the agency cost of debt?

a. ABC Co. shareholders pressure management to invest in very risky projects in

hopes that one of the investments might pay off. The company is highly

leveraged, so shareholders have little to lose.

b. ABC Co. has a large amount of debt but very few investment opportunities. The

board of directors decides to pay out a large special dividend, and the company

subsequently enters bankruptcy. Lenders collect about 60 percent of the face

value of the debt.

c. ABC Co. is very close to financial distress. The company has a positive-NPV

investment opportunity, but even with the project the company is likely to enter

bankruptcy. Investors refuse to invest the additional funds necessary to pursue the

project, even though it has a positive NPV.

d. Investors are unsure of the value for ABC Co. ABC Co. decides to issue equity to

pay down debt. The market assumes that ABC Co.’s managers are issuing equity

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because they think that the company’s stock is overvalued. As a result, the

company’s stock price falls when the equity issue is announced.

63. The claim lenders’ hold on cash flows in a company with outstanding risky debt is often

thought of as

a. holding a call option on the firm’s assets.

b. holding a put option on the firm’s assets.

c. selling a put option on the firm’s assets and holding a risk-free bond.

d. selling a call option on the firm’s asset and holding a risk-free bond.

64. Adding stock options and bonuses for performance to the compensation of a manager is

intended to closer align the interest of the manager with

a. stockholders.

b. lenders.

c. employees.

d. none of the above.

65. Option payoffs: What is the payoff for a call option with a strike price of $45 if the

underlying stock price at expiration is $75?

a. $30

b. $45

c. $75


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66. Option payoffs: What is the payoff for a call option with a strike price of $30 if the


a. $5

b. $25

c. $30


67. Option payoffs: What is the payoff for a put option with a strike price of $65 if the


a. $0

b. $33

c. $32

d. $65

68. Option payoffs: You own a put option on ABC. Co. stock with a strike price of $40. The

current stock price is $40. You will benefit if

a. the stock price goes up.

b. the stock price goes down.

c. the stock price stays the same.

d. It doesn’t matter; you are indifferent to changes in the stock price.

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69. Option payoffs: You have sold a call option on ABC Co. stock with a strike price of

$40. You do not intend to make any other transactions before the options expiration date.

The current stock price is $20. Which of the following statements best describes your

hopes for the stock?

a. You want the stock price to fall.

b. You want the stock price to rise.

c. You are indifferent, as long as the stock price stays under $40.

d. It doesn’t matter; you are indifferent to changes in the stock price.

70. Option payoffs: What is the payoff for a put option with a strike price of $20 if the price

of the underlying stock at expiration is $18?

a. $0

b. $2

c. $18

d. $20

71. Option valuation: Consider a call option with a strike price of $20, which expires in one

year. The risk-free rate of interest is 5 percent. The underlying stock price is $30. Without

arbitrage, which of the following is a possible price for the call option?

a. $0

b. $8

c. $15


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72. Option valuation: Consider a call option with a strike price of $10, which expires in one

year. The risk-free rate of interest is 10 percent. The current underlying stock price is

$30. Without arbitrage, which of the following is a possible price for the call option?

a. $0

b. $20.50

c. $21.00


73. Option valuation: Consider a put option with a strike price of $40, which expires in one

year. The risk-free rate of interest is 8 percent. The current underlying stock price is $20.

Without arbitrage, which of the following is a possible price for the put option?

a. $0.50

b. $16.50

c. $25.00


74. Option payoffs: Kelvin’s Thermostats, Inc., stock is currently trading at $20 per share.

There are two types of options written on the stock. Call options with a strike price of

$15, which expire next month, are currently trading at $6.00. Put options with a strike

price of $15 which expire next month are currently trading at $1.00. Steve invests $120

in common stock. Carol invests $120 in the call options. Paul invests $120 in the put

29

options. At the end of one month, the price of Kelvin’s Thermostats, Inc., is $23. Who

made the most money off of their investment?

a. Steve

b. Carol

c. Paul

d. Steve and Carol Tied

75. Option payoffs: Haumer Hardware Co. stock is currently trading at $20. There are two

types of options written on the stock. Call options with a strike price of $20, which expire

next year, are currently trading at $8. Put options with a strike price of $20, which expire

next year, are currently trading for $2. Steve invests $120 in common stock. Carol invests

$120 in the call options. Paul invests $120 in the put options. At the end of one year the

price of Haumer Hardware Co. stock is $18. Who made the most money off of their

investment?

a. Steve

b. Carol

c. Paul

d. Steve and Carol tied

76. Binomial pricing: Assume that the stock of Malcolm’s Mufflers, Inc,. is currently

trading for $18 and will either rise to $20 or fall to $14 in one year. The risk-free rate for

one year is 10 percent. What is the value of a call option with a strike price of $15?

a. $4.39

30

b. $3.33

c. $2.04

d. $0.83

77. Binomial pricing: Assume that the stock of Malcolm’s Mufflers, Inc., is currently


one year is 8 percent. What is the value of a call option with a strike price of $45?

a. $4.40

b. $5.84

c. $6.84

d. $7.17

78. Binomial pricing: ABC, Inc., stock is currently trading for $45 and will either rise to $47

or fall to $42 in one year. The risk-free rate for one year is 5 percent. You own a call

option with a strike price of $30, which expires in one year. What is the value of your call

option?

a. 0

b. 2.27

c. 12.05

d. 16.43

31

79. Binomial pricing: Assume that the stock of ABC, Inc., is currently trading for $17 and

will either rise to $23 or fall to $12 in one year. The risk-free rate for one year is 10

percent. What is the value of a call option with a strike price of $25?

a. $0

b. $6.23

c. $5.72




percent. What is the value of a put option with a strike price of $25?

a. $0

b. $1.85

c. $3.00

d. $4.85


will either rise to $50 or fall to $29 one year. The risk-free rate for one year is 4 percent.

What is the value of a put option with a strike price of $40?

a. $0

b. $2.14

c. $3.14

d. $5.54

32


will either rise to $23.50 or fall to $9 in one year. The risk-free rate for one year is 3

percent. What is the value of a put option with a strike price of $18 that expires in three

months?

a. $0

b. $2.75

c. $4.23

d. $5.73


will either rise to $32 or fall to $5 in one year. The risk-free rate for one year is 2 percent.


a. $0

b. $0.41

c. $1.78

d. $2.20




a. $0

b. $2

33

c. $5

d. $6

85. Binomial pricing: Assume that the stock of ABC, Inc., is currently trading for $2.60 and



a. $0

b. $2.35

c. $3.65

d. $3.70

86. Binomial pricing: You own a share of common stock in ABC, Inc., which is currently


one year is 0 percent. You also own an American put option on the stock with a strike

price of $20, which expires in one year. What is the value of the put option, and what

would be the net payoff from exercising the option now?

a. Option Value: $3.33 – Net Payoff $2

b. Option Value: $3.33 – Net Payoff $6

c. Option Value: $5.33 – Net Payoff $2

d. Option Value: $5.33 – Net Payoff $6

87. Binomial pricing: You are fortunate enough to own a put option with a strike price of

$50 on the stock of ABC, Inc. The current stock price is $4. When the option expires, you

34

expect the stock price to be either $2 or $5. The risk-free rate of interest is zero. What is

the value of your option?

a. 0

b. 45

c. 46

d. 48




a. $0

b. $2.00

c. $2.33

d. $5.00



percent. You own a portfolio that consists of one call option and one put option. Both

options have a strike price of $25, and both expire in one year. What is the value of your

portfolio?

a. $0

b. $25.00

c. $6.00

35

d. $6.50



You own a portfolio that consists of one call option and one put option. Both options

have a strike price of $15, and both expire in one year. What is the value of your

portfolio?

a. $0

b. $15

c. $21.40

d. $18.52

91. Binomial pricing: Consider two call options written on different stocks. Both call

options have a strike price of $15 and expire one year from today. The first option is

written on LowVol Co., whose current stock price is $16. One year from now, shares of

LowVol Co. will either rise to $18 or fall to $14. The second option is written on

HighVol, Inc., whose current stock price is also $16. One year from now shares of

HighVol Inc. will either rise to $22, or fall to $0. The risk-free interest rate is 0 percent.

Which call option is worth more?

a. The call option on LowVol is worth more.

b. The call option on HighVol is worth more.

c. They are both worth the same amount.

d. There is not enough information to make a comparison.

36

Value

Stock Price

$20

$40 $60 $80

92. Binomial pricing: Consider a call option and a put option both written on ABC, Inc.

stock. Both options have a strike price of $20 and expire in one year. The stock of ABC,

Inc., is currently selling for $20. In one month the stock will be at either $24 or $18. The

risk-free rate is 0 percent. Which is worth more, the put option or the call option?

a. The put option is worth more.

b. The call option is worth more.

c. They are worth the same.

d. There is not enough information.

93. Combining options: Suppose you are creating a portfolio that consists of zero-interest

bonds, stock from a single company, and call and put options on the stock. Holding

which of the following combination of securities will give the payoff shown in the

following diagram?

a. Buy one call option and one put option on the stock with a strike price of $60.

37

b. Buy one call option with a strike price of $60 and sell short one call option with a

strike price of $80. Buy one put option at a strike price at $60 and sell short one

put option with a strike price of $40.

c. Buy one share of the underlying stock. In addition, buy two call options, one with

a $40 strike price, and one with a $80 strike price.

d. Buy one share of the underlying stock, and a put option with a strike price of $60.

Sell short call two call options—one with a strike price of $40 and one with a

strike price of $80.




following diagram?

a. Buy $20 in risk-free bonds, and sell short one call option with a strike price of

$60.

b. Buy $20 in risk-free bonds, and buy one put option with a strike price of $60.

c. Buy one share of stock, and buy one call option with a strike price of $60.

d. Buy one share of stock, and sell one put option with a strike price of $60.

Value

Stock Price

$20

$60 $80

38




following diagram?

a. Buy one put option of the stock with a strike price of $60. Sell short a call option

with a strike price of $120.

b. Buy $60 in zero-interest bonds. Sell short one call option with a strike price of

$60. Sell short one put option with a strike price of $60.

c. Buy one share of stock. Sell one call option with a strike price of $120.

d. Buy one share of the stock. Sell short two call options with a strike price of $60.

Buy one call option with a strike price of $120.




following diagram?

Value

Stock Price

$60

$60 $120

39

a. Buy one call option with a strike price of $40 and one put option with a strike

price of $80.

b. Buy one call option with a strike price of $80 and one put option with a strike

price of $40.

c. Sell one call option with a strike price of $40 and one put option with a strike

price of $80.

d. Sell one call option with a strike price of $80 and one put option with a strike

price of $40.

97. Risk management: OilDog Co. is a privately owned oil drilling and hot dog producing

company with a significant amount of debt. Most of the company’s cash flows come

from the very safe hot dog unit of the business. With only the assets in place, the

company is very likely to avoid financial distress for the foreseeable future. Avoiding

financial distress is very important to the owners, who founded the company. The

company is considering a new oil field project, determined to have a positive NPV.

Because of the nature of oil prices, the project is very risky. At any oil price above $110

the project would add value to the company. However, if oil prices were to fall below $90

the losses could push the entire business into financial distress. The risk-free interest rate

Value

Stock Price

$40

$40 $80

40

is 0 percent. Which one of the following strategies would allow the firm to pursue the

positive-NPV project while hedging the oil price risk?

a. The firm purchases call options with a strike price of $120 for each barrel of oil it

expects to produce. Each call option costs $5.

b. The firm sells call options with a strike price of $120 on each barrel of oil it

expects to produce. Each option costs $5.

c. The firm purchases put options with a strike price of $120 on each barrel of oil it


d. The firm sells put options with a strike price of $120 on each barrel of oil it


98. Risk management: Consider a wheat farmer who expects to produce 50,000 bushels of

wheat at the end of this season. To hedge the risk associated with wheat prices, the farmer

purchases put options to cover his entire crop. The put options have a strike price of

$7.50 per and a premium of $0.30 per bushel. He also sells an equal amount of call

options with a strike price of $7.50 per bushel and a premium of $0.43 a bushel. Which of

the following statements is NOT correct?

a. From this transaction the farmer can pocket $6,500 immediately.

b. If wheat prices go up substantially, the farmer will earn more money.

c. The put options guarantee that the farmer will receive at least $7.50 per bushel at

the end of the season.

d. The farmer has guaranteed that he will sell his wheat for $7.50 a bushel.

41

99. Real options: Consider a lease agreement recently offered by a car dealership. The

agreement gives the customer the right to use a new SUV for three years in exchange for

payments of $550 per month. At the end of the lease, the customer can choose to

purchase the SUV for $15,000. What sort or option does this resemble?

a. A put option on the SUV with a strike price of $15,000

b. A call option on the SUV with a strike price of $15,000

c. A put option on the SUV with a strike price of $19,800

d. A call option on the SUV with a strike price of $19,800

100. Risk management: CoolHaus, Inc., is a manufacturer of residential air conditioning

equipment. Air conditioning equipment requires a lot of copper. In six months the

company will purchase its copper supply for the next two years. Management is very

concerned about the volatility of copper prices. Assume the risk-free rate of interest is 0

percent. Which of the following transactions will ensure the company does not have to

pay more then $8,100 per ton of copper six months from now?

a. The company purchases a put option for the necessary amount of copper with a

strike price of $8,000 per ton, a premium of $100 per ton, and an expiration date

six months from now.

b. The company purchases a call option for the necessary amount of copper with a

strike price of $8,000 per ton, a premium of $100 per ton, and an expiration date

six months from now.

42

c. The company sells a put option for the necessary amount of copper with a strike

price of $8,000 per ton, a premium of $100 per ton and an expiration date six

months from now.

d. The company sells a call option for the necessary amount of copper with a strike

price of $8,000 per ton, a premium of $100 per ton, and an expiration date six

months from now.

43

III. Essay Questions

101. Describe the difference between American call options and American put options.

Include in your answer a description of the option premium, the option strike price, the

expiration date, and the payoff function.

Answer: The buyer of an American call option pays the seller a premium for the right to

purchase the underlying asset at the strike price, before or on the expiration date. Because

the buyer of the option has the right, but not the obligation, to purchase the asset, he will

only exercise the option if the asset is worth more than the strike price. The payoff

function for a call option is zero until the value of the underlying asset reaches the strike

price. If the price of the underlying asset is above the strike price, the payoff function is

equal to the difference between the asset price and the strike price.

The buyer of an American put option pays the seller a premium for the right to

sell the underlying asset at the strike price, before or on the expiration date. Because the

buyer of the option has the right, but not the obligation, to sell the asset, he will only

exercise the option if the asset is worth less than the strike price. The payoff function for

a put option is zero if the value of the underlying asset is higher than the option’s strike

price. If the value of the underlying asset is lower than the strike price, the payoff of the

put option is equal to the difference between the strike price and the underlying asset

price.

44

102. Name the factors that affect the value of a call option and explain the direction of the

effects.

Answer: Five factors affect the value of a call option.

The Strike Price of the Option—All else equal, the lower the strike price of the call

option, the more valuable the option is. This is true because with a low strike

price, the underlying asset price will not have to be as high for the option to be “in

the money.”

The Price of the Underlying Asset—All else equal, the higher the price of the underlying

asset, the more valuable a call option on the asset is. If the price of the underlying

asset is higher, it is more likely to be above the strike price at the expiration date.

The Volatility of the Underlying Asset—All else equal, the higher the volatility of the

price of an asset, the more a call option is worth. With higher volatility, the price

of the underlying asset has a higher chance of going significantly down or up

before the expiration date. Because the call option will only be exercised if the

underlying asset price is above the strike price, the benefits from the upside of

volatility outweigh the negatives from the downside of volatility.

Time until Expiration of the Option—All else equal, the longer until an option expires,

the more it is worth. The effect of the time until expiration is similar to the effect

of volatility. With more time until maturity, the price of the underlying asset is

more likely to significantly increase or decrease.

The Risk-Free Interest Rate—The value of a call option increases with the risk-free

interest rate. The present value of the strike price decreases with the risk-free rate.

45

Since a call option involves paying the strike price in the future, a higher risk-free

rate increases the value of the option.

103. You’re brought in to consult on a project for Object Steel Corp., which is considering

whether or not to build a new high-tech manufacturing facility. Give four examples of

real options that you would consider when evaluating the project.

Answer: Real options fall into four categories: options to defer investment, options to

change operations, options to abandon projects, and to make follow-on investments.

Many examples of real options might be included in this steel project. The following list

gives one example from each category of real option.

The option to defer investment. The firm may consider postponing the project until it has

more information about the costs and benefits of the project. For example, the

company may learn that the plant will be less profitable then expected. Suppose

that during the next year costly environmental regulations are enacted, or the price

of steel goes down. The company should take these considerations into account

when deciding if now is the best time to build the plant.

The option to change operations. The company must consider whether it will have the

flexibility to change the way the plant is operated. For example, if the demand for

steel falls, it might be able shut down the plant temporarily and reduce costs.

Alternatively, it might be able to produce other metals, such as bronze or brass, if

it becomes more profitable to do so.

46

The option to abandon the project. The company should consider what it might be able to

do with the project if it fails or it becomes unprofitable to continue. It might

decide to construct the facility in such a way that it can accommodate other

manufactures in the event it has to liquidate the plant.

The option to make follow-on investments. The firm should consider whether any follow-

on investments may spring from this project. For example, it might consider

whether it can expand the plant to increase production if demand for steel is high.

It might also consider whether the new production process might be retrofitted to

its existing plants, if the project is successful.

104. What are agency costs in corporate finance, and how do they relate to options?

Answer: Agency costs arise when the interests of stockholders, lenders, and managers

are not perfectly aligned. These costs often arise because the payoff functions for these

different claimholders look like different types of options.

One broad category is the agency costs of debt. When the firm has debt, the

payoff function of stockholders looks similar to a call option on the firm’s assets. The

face value of debt is similar to the strike price on a call option. Because of this option-like

payoff function, the stockholders have an incentive to take actions that increase the value

of the stockholder’s claim, but may reduce the total value of the firm. Examples of

agency problems from debt include the dividend payout problem, the asset substitution

problem, and the underinvestment problem.

47

Another broad category of agency costs is the agency costs of equity. This

describes the difference between the interests of stockholders and managers. The payoff

function for a salary-only manager is similar to a portfolio consisting of a risk-free bond

and a put option. If the company performs well, the manager is not likely to see much

additional benefit. However, if the company enters financial distress, the manager is

likely to be fired and lose much of his or her future wealth. This option-like payoff gives

the managers an incentive to avoid risky projects that might increase the probability of

financial distress, even if the project has a positive NPV. Turning down positive-NPV

projects reduces the total value of the firm. Often the compensation for senior managers

contains additional payoffs for good performance to more closely align their incentives

with those of shareholders.

48

IV. Answers to True or False Questions

1. True

2. True

3. False

4. True

5. True

6. True

7. True

8. False

9. True

10. False

11. True

12. False

13. True

14. False

15. True

16. True

17. True

18. True

19. False

20. True

21. True

22. False

49

23. True

24. True

25. True

26. True

27. False

28. True

29. True

30. True

50

V. Answers to Multiple-Choice Questions

31. b

32. c

33. d

34. b

35. b

36. a

37. d

38. a

39. d

40. a

41. c

42. d

43. b

44. d

45. a

46. c

47. c

48. b

49. c

50. c

51. a

52. d

51

53. d

54. a

55. b

56. a

57. a

58. a

59. b

60. d

61. a

62. d

63. c

64. a

65. a

66. d

67. c

68. b

69. c

70. b

71. c

72. c

73. c

74. b

75. c

52

76. a

77. d

78. d

79. a

80. d

81. b

82. c

83. d

84. b

85. c

86. c

87. c

88. a

89. d

90. d

91. b

92. c

93. b

94. a

95. d

96. b

97. c

98. b

53

99. b

100. b

54

VI. Solutions to Multiple-Choice Problems

71. Solution:

Without arbitrage, the value of the option must fall between $10.96 and $30. Out of the

given choices, only $15 is a possible price for the option.

72. Solution:

Without arbitrage, the value of the option must fall between $20.91 and $30. Out of the

given choices, only $21 is a possible price for the option.

Value of Call Option

PV of Strike Price= 20/1.05 = $19.04

Current Value of Underlying Asset

$0

$30

$30

$10.96

55

The four limits tell us that the value of a call option prior to expiration will actually fall within this shaded area.

73. Solution:

Without arbitrage, the value of the put option must fall between $17.04 and $19.04. Out

of the given choices, only $25 is a possible price for the option.

Value of Call Option



$0

$30

$30

$20.91

Value of Put Option



$0

$37.04

The limits tell us that the value of a put option prior to expiration will actually fall within this area.

$17.04

$20

56

The four limits tell us that the value of a call option prior to expiration will actually fall within this shaded area.

74. Solution:

Steve holds ($120) / ($20) per share = 6 shares of stock. His gain is (6 shares) x ($23 per

share) – $120 = $18

Carol holds ($120) / ($6 per call option) = 20 call options. The final price of the

stock is above the $15 strike price, so her options are in the money. Her gain is ($23 –

$15) x (20 call options) – $120 = $40

Paul holds ($120) / ($1 per put option) = 120 put options. The final price of the

stock is above the $15 strike price, so his options are out of the money. He received no

payoff. His loss is –$120.

Carol made the most money.

75. Solution:

Steve holds ($120) / ($20) per share = 6 shares of stock. The stock went down, so Steve

lost money. His loss is (6 shares) × ($18 per share) – $120 = −$12.

Carol holds ($120) / ($8 per call option) = 15 call options. The final price of the

stock is below the $20 strike price, so her options are out of the money. There is no

payoff from her call options. Her loss is −$120.

Paul holds ($120) / ($2 per put option) = 60 put options. The final price of the

stock is below the $20 strike price, so his options are in the money. His gain is ($20 –

$18) × (60) − $120 = 0.

Paul broke even, the others lost money.

57

76. Solution:

The payoff from the call option is $5 if the stock price rises and $0 if the stock price falls.

From the binomial pricing model we can create a replicating portfolio with the following

two equations:

$5 = ($20 × x) + (1.10 × y)

$0 = ($14 × x) + (1.10 × y)

x = 0.83 shares of stock

y = –$10.51 of risk-free bonds

The value of the option is the value of the replicating portfolio:

(0.83 × $18) + (–10.51) = $4.39

77. Solution:

The payoff from the call option is $10 if the stock price rises and $0 if the stock price

falls. From the binomial pricing model we can create a replicating portfolio with the

following two equations:

$10 = ($55 × x) + (1.08 × y)

$0 = ($17 × x) + (1.08 × y)




(0.263 × $43) + (–4.14) = $7.17

78. Solution:

58

The payoff from the call option is $17 if the stock price rises and $12 if the stock price



$17 = ($47 × x) + (1.05 × y)

$12 = ($42 × x) + (1.05 × y)

x = 1 share of stock

y = –28.57 of risk free bonds


(1 × $45) + (–28.57) = $16.43

79. Solution:


This option will never payoff, so it has a value of $0.

80. Solution:

The payoff from the put option is $0 if the stock price rises and $7 if the stock price falls.


two equations:

$0 = ($31 × x) + (1.00 × y)

$7 = ($18 × x) + (1.00 × y)

x = –0.54 shares of stock

y = $16.69 of risk-free bonds


59

(-0.54 × $22) + ($16.69) = $4.85

81. Solution:

The payoff from the put option is $0 if the stock price rises and $11 if the stock price



$0 = ($50 × x) + (1.04 × y)

$11 = ($29 × x) + (1.04 × y)




(–0.52 × $44) + ($28.18) = $2.14

82. Solution:



two equations:

$0 = ($23.50 × x) + (1.03 × y)

$9 = ($9 × x) + (1.03 × y)




(–0.62 × $16) + ($14.16) = $4.23

60

83. Solution:




$0 = ($32 × x) + (1.02 × y)

$25 = ($5 × x) + (1.02 × y)




(–0.93 × $29) + ($29.05) = $2.20

84. Solution:



two equations:

$0 = ($30 × x) + (1.00 × y)

$3 = ($12 × x) + (1.00 × y)


y = $5 of risk-free bonds


(–0.167 × $18) + ($5) = $2

61

85. Solution:



two equations:

$0 = ($10 × x) + (1.01 × y)

$5 = ($0 × x) + (1.01 × y)




(–0.5 × $2.6) + ($4.95) = $3.65

86. Solution:

First, we can calculate the value of the put option with the binomial model. The payoff

from the put option is $0 if the stock price rises and $8 if the stock price falls. From the

binomial pricing model we can create a replicating portfolio with the following two

equations:

$0 = ($30 × x) + (1.00 × y)

$8 = ($12 × x) + (1.00 × y)




(–0.44 × $18) + ($13.33) = $5.33

62

The payoff from exercising the put option now is the option strike price minus the current

stock price: $20 – $18 = $2

87. Solution:


falls. When the put option pays off in either state, the value of the option is the PV of the

strike price minus the current stock price.

($50 / 1.00) – $4 = $46

88. Solution:


Either way the put option has no payoff. The value of this put option is $0.

89. Solution:

To calculate the value of this portfolio, we can use the binomial pricing model to

calculate that value of the call and the put. Then we can add the values together.



two equations:

$5 = ($30 × x) + (1.00 × y)

$0 = ($18 × x) + (1.00 × y)



63


(0.417 × $21) + (-7.5) = $1.25



two equations:

$0 = ($30 × x) + (1.00 × y)

$7 = ($18 × x) + (1.00 × y)

x = -0.583 shares of stock



(–0.583 × $21) + ($17.5) = $5.25

The total value of the straddle is $1.25 + $5.25 = $6.50

90. Solution:

To calculate the value of this portfolio, we can use the binomial pricing model to

calculate that value of the call and the put. Then we can add the values together.



two equations:

$35 = ($50 × x) + (1.08 × y)

$0 = ($2 × x) + (1.08 × y)



64


(0.729 × $16) + (–1.35) = $10.32




$0 = ($50 × x) + (1.08 × y)

$13 = ($2 × x) + (1.08 × y)




(–0.271 × $16) + ($12.54) = $8.20

The total value of the straddle is $10.32 + $8.20 = $18.52

91. Solution:

First we can price the LowVol call option. The payoff from the LowVol call option is $3

if the stock price rises and $0 if the stock price falls. From the binomial pricing model we

can create a replicating portfolio with the following two equations:

$3 = ($18 × x) + (1.00 × y)

$0 = ($14 × x) + (1.00 × y)


y = –$9.72 of risk free bonds


(0.75 × $16) + (-9.72) = $2.28

65

Next we can price the HighVol call option. The payoff from the HighVol call option is $7

if the stock price rises and $0 if the stock price falls. From the binomial pricing model we

can create a replicating portfolio with the following two equations:

$7 = ($22 × x) + (1.00 × y)

$0 = ($0 × x) + (1.00 × y)




(0.32 × $16) + ($0) = $5.09

The HighVol call option is worth more.

92. Solution:



two equations:

$4 = ($24 × x) + (1.00 × y)

$0 = ($18 × x) + (1.00 × y)


y = –$12 of risk-free bonds


(0.67 × $20) + (–12) = $1.33

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two equations:

$0 = ($24 × x) + (1.00 × y)

$2 = ($18 × x) + (1.00 × y)

x = -0.333 shares of stock



(–0.333 x $20) + ($8) = $1.33

The call and the put options are worth the same. Note that this is a special case where

interest rates are zero. With a positive interest rate, the call will be worth more than the

put.

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