Fundamentals of Corporate Finance/3e,ch21

Copyright 2004 McGraw-Hill Australia Pty Ltd PPTs t/a Fundamentals of Corporate Finance 3eRoss, Thompson, Christensen, Westerfield and JordanSlides prepared by Sue Wright

21-1

Chapter Twenty-one

Options, Corporate Securities and Futures


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


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.


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.


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.


21-6

Option Contract Characteristics

• Expiration month

• Option type

• Contract size

• Expiry

• Exercise price


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


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


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.


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


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.


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.


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.


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


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


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.


21-17

Example—Black–Scholes Option Pricing Model

• S0 = $25

• E = $20

• Rf = 8%

= 30%

• t = 0.5 years


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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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..


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.


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.


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


21-23

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.


21-24

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.


21-25

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.


21-26

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.


21-27

Forward Contracts

A. Buyer’s perspective B. Seller’s perspective

Payoffprofile

Payoffprofile

∆Poil ∆Poil

∆V ∆V


21-28

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.


21-29

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.


21-30

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.


21-31

Term Structure of Interest Rates


21-32

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.


21-33

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)

Fundamentals of Corporate Finance/3e,ch21

Economy & Finance

option equity

option terminology

option right

option beforeexpiration

option premium

european option

american option

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