options and corporate securities chapter 25. 25-1 chapter outline options: the basics fundamentals...
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OPTIONS AND CORPORATE OPTIONS AND CORPORATE SECURITIESSECURITIES
Chapter 25
25-2
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