OPTIONS AND CORPORATE OPTIONS AND CORPORATE SECURITIESSECURITIES

Chapter 25

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Chapter OutlineChapter OutlineOptions: The BasicsFundamentals of Option ValuationValuing a Call OptionEmployee Stock OptionsEquity as a Call Option on the Firm’s

AssetsWarrantsConvertible BondsReasons For Issuing Warrants and

ConvertiblesOther Options

25-3

Option Terminology 25.1Option Terminology 25.1CallPutStrike or Exercise priceExpiration dateOption premiumOption writerAmerican OptionEuropean Option

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Stock Option QuotationsStock Option QuotationsLook at Figure 25.1 in the book

◦ Price and volume information for calls and puts with the same strike and expiration

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

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Option Payoffs – Calls 25.2Option Payoffs – Calls 25.2

The value of the call at expiration is the intrinsic value◦ C1 = Max(0, S1 - K)◦ If S1<K, then the

payoff is 0◦ If S1>K, then the

payoff is S1 – KAssume that the

strike price is $30

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Option Payoffs - PutsOption Payoffs - Puts

The value of a put at expiration is the intrinsic value◦ P1 = Max (0, K – S1)◦ If S1<K, then the

payoff is E-S1

◦ If S1>K, then the payoff is 0

Assume that the strike price is $40

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Work the Web ExampleWork the Web ExampleWhere can we find option prices?On the Internet, of course. One site

that provides up-to-date option pricing information is the Montreal Exchange website.

Click on the web surfer to go to the MX◦ Follow the options link◦ Look at the trading strategies that use

options◦ Check out the Options FAQ

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Call Option BoundsCall Option BoundsUpper 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

If either of these bounds are violated, there is an arbitrage opportunity

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Figure 25.3 – Value of a call Figure 25.3 – Value of a call option before expirationoption before expiration

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A Simple ModelA Simple ModelAn option is “in-the-money” if the

payoff is greater than zeroIf a call option is sure to finish in-

the-money, the option value would be◦C0 = S0 – PV(K)

If the call is worth something other than this, then there is an arbitrage opportunity

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What Determines Option What Determines Option Values?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 increasesTime 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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What about Variance? What about Variance? 25.325.3When 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◦ You gain from volatility on the upside, but don’t lose

anymore from volatility on the downside

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Table 25.1 – Five factors that Table 25.1 – Five factors that determine option valuesdetermine option values

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Employee Stock Options Employee Stock Options 25.425.4Options that are given to employees

as part of their benefits packageOften 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 just isn’t worth as much to the employee as it is to an outside investor

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Figure 25.4 – Executive stock Figure 25.4 – Executive stock options in Canadaoptions in Canada

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Equity: A Call Option 25.5Equity: A Call Option 25.5Equity can be viewed as a call option on

the company’s assets when the firm is leveraged

The exercise price is the value of the debtIf 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

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Example: Equity as a Call Example: Equity as a Call OptionOptionABC Company has a current value

of $1,000 and debt outstanding consisting of a zero-coupon bond with a face value of $1,000 due in one year. The risk-free rate is 10% per year. Assume that the value of the firm’s asset will either increase to $1,500 or decrease to $500. What is the current value of the firm’s debt and equity?

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Example – continuedExample – continued

Up Down

Assets 1,500 500

Debt 1,000 500

Equity 500 0

•If the value of the firm goes up to $1,500, then the debt will be paid off in full and the equity will be worth $500

•If the value of the firm drops to $500, then the debt will only receive $500 and the equity would receive nothing

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Example – continuedExample – continued

To find the current value of the debt and equity, we form a portfolio that replicates the firm’s assets which consists of an investment of $500 in a risk-free asset and a long position in two call options on the firm’s assets with a strike price of $1,000.

How did we decide on the number of calls

Delta = (1500-500) =2 (500-0)

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Example – continuedExample – continued

Up Down

Assets 1,500 500

Replicating

Portfolio

1. Risk-free debt

500 500

2. Two call options

2 max(0, 1500-1000)

=1,000

2 max(0, 500-1000)

= 0

Total 1,500 500

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Example – continuedExample – continued

If you have two portfolios that have the same payoff at some point in the future, then they have to be worth the same today

PV of replicating portfolio = Current Value of Firm

73.272

10.1

500000,1

2

1

000,1210.1

500

c

c

c

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Example – continuedExample – continuedThe current value of the firm’s

equity is $272.73V = D + ED = 1,000 – 272.73 = 727.27Therefore, the value of the firm’s

debt is $727.27

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Example: Equity as a Call Example: Equity as a Call OptionOptionMega Company has a current value

of $110 and debt outstanding consisting of a discount bond with a face value of $100 due in one year. The risk-free rate is 10% per year. Assume that the value of the firm’s asset will either increase to $160 or decrease to $55. What is the current value of the firm’s debt and equity?

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Example – continuedExample – continued

Up Down

Assets 160 55

Debt 100 55

Equity 60 0

•If the value of the firm goes up to $160, then the debt will be paid off in full and the equity will be worth $60

•If the value of the firm drops to $55, then the debt will only receive $55 and the equity would receive nothing

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Example – continuedExample – continued

To find the current value of the debt and equity, we form a portfolio that replicates the firm’s assets which consists of an investment of in a risk-free asset that will have FV of $55 (out of the money outcome) and a long position in N call options on the firm’s assets with a strike price of $100 (FV of debt).

How did we decide on the number of calls Delta = (160-55) =1.75 (60-0)

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Example – continuedExample – continued

Up Down

Assets 160 55

Replicating

Portfolio

1. Risk-free debt

55 55

2. 1.75 call options

1.75 max(0, 160-100)

=105

2 max(0, 55-100)

= 0

Total 160 55

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Example – continuedExample – continued

If you have two portfolios that have the same payoff at some point in the future, then they have to be worth the same today

PV of replicating portfolio = Current Value of Firm

73.272

10.1

500000,1

2

1

000,1210.1

500

c

c

c

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Example – continuedExample – continuedThe current value of the firm’s

equity is $34.29V = D + ED = 110 –34.29 = 75.71Therefore, the value of the firm’s

debt is $75.71Cost of debt =?

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Warrants 25.6Warrants 25.6A security that gives the holder the

right to purchase shares of stock at a fixed price over a given period of time

It is basically a call option issued by corporations in conjunction with other securities to reduce the yield

Usually included with a new debt or preferred shares issue as a sweetener or equity kicker

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Differences between warrants Differences between warrants and traditional call optionsand traditional call optionsWarrants are generally very long termThey are written by the company and

exercise results in additional shares outstanding

The exercise price is paid to the company and generates cash for the firm

Warrants can be detached from the original securities and sold separately

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Convertible Bonds 25.7Convertible Bonds 25.7Convertible bonds (or preferred

stock) may be converted into a specified number of common shares at the option of the security holder

The conversion price is the effective price paid for the stock. It is the dollar amount of a bond’s par value that is exchangeable for one share of stock

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Convertibles – continuedConvertibles – continuedThe conversion ratio is the

number of shares received when the bond is converted

Conversion Premium – The difference between the conversion price and the current stock price divided by the current stock price

Straight Bond Value – The value of a convertible bond if it could not be converted into common stock

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Convertibles – continuedConvertibles – continuedFloor Value – Either the straight

bond value or the conversion value

Convertible bonds will be worth at least as much as the straight bond value or the conversion value, whichever is greater

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Figure 25.5 – Minimum value of a Figure 25.5 – Minimum value of a convertible bond versus the value of the convertible bond versus the value of the stock for a given interest ratestock for a given interest rate

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Figure 25.6 – Value of a convertible bond Figure 25.6 – Value of a convertible bond versus versus value of the stock for a given interest ratevalue of the stock for a given interest rate

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Valuing ConvertiblesValuing ConvertiblesSuppose you have a 10% bond that

pays semi-annual 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 = 1081.44◦ Conversion ratio = 1000/100 = 10◦ Conversion value = 10*110 = 1100◦ Minimum price = $1100

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Reasons for Issuing Warrants Reasons for Issuing Warrants and Convertibles 25.8and Convertibles 25.8They allow companies to issue

cheap bonds by attaching sweeteners to the new bond issue. Coupon rates can then be set at below market rate for straight bonds

They give companies the chance to issue common stock in the future at a premium over current prices

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Table 25.3 – The case for and Table 25.3 – The case for and against convertiblesagainst convertibles

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Other Options 25.9Other Options 25.9Call provision on a 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◦Gives the bondholder the right to

require the company to repurchase the bond prior to maturity at a fixed price

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Other Options continuedOther Options continuedOver allotment option

◦Underwriters have the right to purchase additional shares from a firm in an IPO (chapter 15)

Insurance and Loan Guarantees◦These are essentially put options

Managerial options

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Quick QuizQuick QuizWhat is the difference between a call

option and a put option?What is the intrinsic value of call and

put options and what do the payoff diagrams look like?

What are the five major determinants of option prices and their relationships to option prices?

What are some of the major capital budgeting options?

How would you value a convertible bond?

Summary 25.10Summary 25.10The most familiar options are puts and

calls. The holder has the right, but not the obligation, to sell (buy) the underlying asset at a given price on or before a given date

There are five factors that impact an options value: price of underlying, exercise price, expiration date, risk-free interest rate, and volatility

Warrants given the holder the right to buy shares directly from the company at a fixed price for a specified period of time

Convertible bonds are a combination of a straight bond and a call option, both of which will affect the minimum value of the bond

Key Concepts and SkillsKey Concepts and SkillsKnow the basics of call and put options and

how to calculate their payoffs and profitsUnderstand the factors that affect option

values and how to price call and put options using no arbitrage conditions

Know how to value a firm’s equity as an option on the firm’s assets and use option valuation to evaluate capital budgeting projects

Understand the basics of employee stock options and their benefits and disadvantages

Understand convertible bonds and warrants and how to value them