Download - Fundamentals of Corporate Finance/3e,ch21
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21-1
Chapter Twenty-one
Options, Corporate Securities and Futures
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21-2
21.1 Options: The Basics
21.2 Fundamentals of Options Valuation
21.3 Valuing a Call Option
21.4 Black–Scholes Option Pricing Model
21.5 Equity as a Call Option on the Firm’s Assets
21.6 Types of Equity Option Contracts
21.7 Futures Contracts
21.8 Term Structure of Interest Rates
21.9 Summary and Conclusions
Chapter Organisation
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21-3
Chapter Objectives
• Understand the key terminology associated with options.
• Outline the five factors that determine option values.• Price call options using the Black–Scholes option
pricing model.• Discuss the types of equity option contracts offered.• Outline the types of warrants available to investors.• Discuss the characteristics of future contracts.• Understand the term structure of interest rates.
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Copyright 2004 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 3eRoss, Thompson, Christensen, Westerfield and JordanSlides prepared by Sue Wright
21-4
Option Terminology
• Call option– Right to buy a specified asset at a specified price on or
before a specified date.
• Put option– Right to sell a specified asset at a specified price on or
before a specified date.
• European option– An option that can only be exercised on a particular date
(on expiry).
• American option– An option that can be exercised at any time up to its
expiry date.
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21-5
Option Terminology• Striking price
– The contracted price at which the underlying asset can be bought (call) or sold (put).
• Expiration date– The date at which an option expires.
• Option premium– The price paid by the buyer for the right to buy or sell an
asset.
• Exercising the option– The act of buying or selling the underlying asset via the
option contract.
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21-6
Option Contract Characteristics
• Expiration month
• Option type
• Contract size
• Expiry
• Exercise price
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21-7
Option Valuation
• S1 = share price at expiration
• S0 = share price today
• C1 = value of call option on expiration
• C0 = value of call option today
• E = exercise price on the option
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21-8
Share price
at expiration (S1)
Call option value
at expiration (C1)
S1 E S1 > E
Exercise price (E)45 °
Value of Call Option at Expiration
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21-9
Value of Call Option at Expiration
0if01 E S C 1
Option is out of the money.
0if 111 E S E S C
Option is in the money.
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21-10
Share price (S0)
Call price
(C0)
Exercise price (E)
45 °
Lower bound
C0 S0 – E
C0 0
Upper bound
C0 S0
Value of a Call Option Before Expiration
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21-11
Call Option Boundaries
• Upper bound—a call option will never be worth more than the share itself:
C0 S0
• Lower bound—share price cannot fall below 0 and to prevent arbitrage, the call value must be (S0 – E):
The larger of 0 or (S0 – E)
• Intrinsic value—option’s value if it was about to expire = lower bound.
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21-12
Factors Determining Option Values
tfR E/ S C
100
price exercise ofPV price Sharevalue option Call
The value of a call option depends on four factors:
• share price
• exercise price
• time to expiration
• risk-free rate.
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21-13
Another Factor to Consider?
• The above four factors are relevant if the option is to finish in the money.
• If the option can finish out of the money, another factor to consider is volatility.
• The greater the volatility in the underlying share price, the greater the chance the option has of expiring in the money.
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21-14
The Factors that Determine Option Value
Current value of the underlying asset (+) ( )
Exercise price on the option ( ) (+)
Time to expiration on the option (+) (+)
Risk-free rate (+) ( )
Variance of return on underlying asset (+) (+)
Factor Calls Puts
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21-15
Black–Scholes Option Pricing Model
paid is price exercise they probabilit some dN
RE/
dN
S
C
dN R
E dN S C
2
tf
tf
1
price exercise PV1
relevant is price share theyprobabilitsome
price share
ueoption val
1
1
0
0
200
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21-16
Black–Scholes Option Pricing Model
t d d
t
t R /ES
df
12
20
1
21
n1
Note: The risk-free rate, the standard deviation and the time to maturity must all be quoted using the same time units.
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21-17
Example—Black–Scholes Option Pricing Model
• S0 = $25
• E = $20
• Rf = 8%
= 30%
• t = 0.5 years
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21-18
Example—Black–Scholes Option Pricing Model (continued)
131
2120341
5030341
341
2120062502230
5030
503021
0802025n1
2
2
1
.
. .
. . . d
.
./. .
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d
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21-19
Example—Black–Scholes Option Pricing Model (continued)
• From the cumulative normal distribution table:
N(d1) = N(1.34) = 0.9099
N(d2) = N(1.13) = 0.8708
• Therefore, the value of the call option is:
016$
733116747522
8708020
9099025500800
.
. .
. e
. C..
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21-20
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 value of the debt.• If the assets are worth more than the debt when it
becomes due, the option will be exercised and the shareholders retain ownership.
• If the assets are worth less than the debt, the shareholders will let the option expire and the assets will belong to the bondholders.
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21-21
Equity Option Contracts
• Types of equity option contracts offered in Australia:
– Exchange traded put and call options on company shares
– Exchange traded long dated contracts issued by a financial institution that can then trade them (warrants)
– Over-the-counter options on company shares
– Convertible notes issued by companies, comprising both a debt and an equity component.
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21-22
Warrants
• A long-lived option that gives the holder the right to buy shares in a company at a specified price.
• Types of warrants available:equity warrants low exercise price warrants
fractional warrants endowment warrants
basket warrants currency warrants
fully covered warrants
index warrants
instalment warrants
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Company Options
• A holder is given the right to purchase shares in a company at a specified price over a given period of time.
• Usually offered as a ‘sweetener’ to a debt issue.
• These options are often detached and sold separately.
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Company Options versus Exchange-traded Options
• Company options have longer maturity periods and are often European-type options.
• Company options are issued as part of a capital-raising program and are therefore limited in number.
• The clearing house has no role in the trading of company options.
• Company options are issued by firms.
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Earnings Dilution
• Put and call options have no effect on the value of the firm.
• Company options do affect the value of the firm.• Company options cause the number of shares on
issue to increase when:– the options are exercised– the debts are converted.
• This increase does not lower the price per share but EPS will fall.
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Forward Contracts
• A contract where two parties agree on the price of an asset today to be delivered and paid for at some future date.
• Forward contracts are legally binding on both parties.• They can be tailored to meet the needs of both parties and
can be quite large in size.• Positions
– Long—agrees to buy the asset at the future date– Short—agrees to sell the asset at the future date
• Because they are negotiated contracts and there is no exchange of cash initially, they are usually limited to large, creditworthy corporations.
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Forward Contracts
A. Buyer’s perspective B. Seller’s perspective
Payoffprofile
Payoffprofile
∆Poil ∆Poil
∆V ∆V
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Futures Contracts
• An agreement between two parties to exchange a specified asset at a specified price at a specified time in the future.
• Do not need to own an asset to sell a future contract.
• Either buy before delivery or close out position with an opposite market position.
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Futures Markets
• Enable buyers and sellers to avoid risk in commodities (and other) markets with high price variability → hedging.
• Involves standardised contracts.• Deposit required by all traders to guarantee
performance.• Adverse price movements must be covered daily
by further deposits called margins (‘marked to market’).
• Futures also available for short-term interest rates, to protect against interest rate movements.
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Futures Quotes• Commodity, exchange, size, quote units
– The contract size is important when determining the daily gains and losses for marking-to-market.
• Delivery month– Open price, daily high, daily low, settlement price, change
from previous settlement price, contract lifetime high and low prices, open interest
– The change in settlement price multiplied by the contract size determines the gain or loss for the day:
Long—an increase in the settlement price leads to a gain Short—an increase in the settlement price leads to a loss
• Open interest is how many contracts are currently outstanding.
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Term Structure of Interest Rates
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Term Structure of Interest Rates
• Yield curve shows the different interest rates available for investments of different maturities, at a point in time.
• The relationship between interest rates of different maturities is called the term structure.
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Factors Determining the Term Structure
• Risk preferences—borrowers prefer long-term credit whereas lenders prefer short-term loans (explains upward-sloping yield curve only).
• Supplydemand conditions—segmented capital markets can cause supplydemand imbalances (explains all yield curve shapes).
• Expectations about future interest rates (most favoured explanation)