Fundamentals of corproate finance 3e chapter 21

Chapter Twenty-one
Options, Corporate Securities
and Futures

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21-1


Chapter Organisation
21.1
21.2
21.3
21.4
21.5
21.6
21.7
21.8
21.9

Options: The Basics
Fundamentals of Options Valuation
Valuing a Call Option
Black–Scholes Option Pricing Model
Equity as a Call Option on the Firm’s Assets
Types of Equity Option Contracts
Futures Contracts
Term Structure of Interest Rates
Summary and Conclusions

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21-2


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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21-3

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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21-4

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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21-5

Option Contract Characteristics
• Expiration month
• Option type
• Contract size
• Expiry
• Exercise price

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21-6


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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21-7


Value of Call Option at Expiration
Call option value

at expiration (C1)

S1 ≤ E

S1 > E

45 °
Exercise price (E)

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Share price
at expiration (S1)

21-8


Value of Call Option at Expiration
C1 = 0 if ( S1 − E ) ≤ 0
Option is out of the money.

C1 = S1 − E if ( S1 − E ) > 0
Option is in the money.

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21-9

Value of a Call Option Before
Expiration

Call price

Upper bound

Lower bound

(C0)

C0 ≤ S0

C0 ≥ S0 – E
C0 ≥ 0

45 °

Share price (S0)

Exercise price (E)

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2110


Call Option Boundaries

•

Upper bound—a call option will never be worth more than the
share itself:
C0 ≤ S 0

•

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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Factors Determining Option Values
Call option value = Share price − PV of exercise price
C0 = S 0 − E/ (1 + R f )

t

The value of a call option depends on four factors:

•

share price

•

exercise price

•

time to expiration

•

risk-free rate.

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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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The Factors that Determine Option
Value
Factor

Calls

Puts

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 (+)

(+)

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2114


Black–Scholes Option Pricing Model
C0 = S 0 × N ( d 1 ) − E

(1 + R )

t

× N ( d2 )

f

C0 = option value
S 0 = share price

N ( d1 ) = some probability the share price is relevant

E/ (1 + R f ) = PV exercise price
t

N ( d 2 ) = some probability the exercise price is paid

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2115


Black–Scholes Option Pricing Model


1

2
1n ( S 0 /E ) +  R f + 2 × σ  × t 


 
d1 = 
σ× t

(

)

d 2 = d1 − σ × t
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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2116


Example—Black–Scholes Option
Pricing Model

• S0 = $25

∀ σ = 30%

• E = $20

• t = 0.5 years

• Rf = 8%

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2117


Example—Black–Scholes Option
Pricing Model (continued)


1

2
1n ( 25 / 20 ) +  0.08 + 2 × 0.3  × 0.5



d1 = 
0.3 × 0.5
= ( 0.223 + 0.0625) / ( 0.212)
= 1.34

(

(

d 2 = 1.34 − 0.3 × 0.5

= 1.34 − 0.212
= 1.13

)

)

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2118


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:

C0 = 25 ( 0.9099) −

20

( 0 .08 )( 0 .5 )

e
= 22.7475 − 16.7331

( 0.8708)

= $6.01
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2119


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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2120

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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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
fractional warrants
basket warrants
fully covered warrants
index warrants
instalment warrants

low exercise price warrants
endowment warrants
currency warrants

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2122


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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2123


Company Options versus Exchangetraded 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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2124


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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