Chapter 25
OPTIONS AND CORPORATE
SECURITIES
Chapter Outline
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Options: The Basics
Fundamentals of Option Valuation
Valuing a Call Option
Employee Stock Options
Equity as a Call Option on the Firm’s Assets
Warrants
Convertible Bonds
Reasons For Issuing Warrants and Convertibles
Other Options
25-1
LO1
Option Terminology 25.1
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Call
Put
Strike or Exercise price
Expiration date
Option premium
Option writer
American Option
European Option
25-2
LO1
Stock Option Quotations

Look 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
25-3
LO1
Option 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 – K

Assume that the strike
price is $30
LO1
Option 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
LO1
Work the Web Example
Where 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
25-6
LO2
Call Option Bounds

Upper 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
25-7
LO2
Figure 25.3 – Value of a call option
before expiration
25-8
LO2
A Simple Model
An option is “in-the-money” if the payoff
is greater than zero
 If a call option is sure to finish in-themoney, the option value would be

◦ C0 = S0 – PV(K)

If the call is worth something other than
this, then there is an arbitrage
opportunity
25-9
LO2
What Determines Option 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 increases

Time 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
25-10
LO2
What about Variance? 25.3
When 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
25-11
LO2
Table 25.1 – Five factors that
determine option values
25-12
LO4
Employee Stock Options 25.4
Options that are given to employees as part of
their benefits package
 Often 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
25-13
LO4
Figure 25.4 – Executive stock options
in Canada
25-14
LO3
Equity: A Call Option 25.5
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 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

25-15
LO3
Example: Equity as a Call Option

ABC 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?
25-16
LO3
Example – continued
•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
Up Down
Assets 1,500 500
Debt
1,000 500
Equity 500
0
2517
LO3
Example – 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)
2518
LO3
Example – continued
Assets
Replicating 1. Risk-free
debt
Portfolio
2. Two call
options
Total
Up
Down
1,500
500
500
500
2 max(0,
2 max(0,
1500-1000) 500-1000)
=1,000
=0
1,500
500
2519
LO3
Example – 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

500
 2c  1,000
1.10
1
500 
c  1,000 
2
1.10 
c  272.73
2520
LO3
Example – continued
The current value of the firm’s equity is
$272.73
V=D+E
 D = 1,000 – 272.73 = 727.27
 Therefore, the value of the firm’s debt is
$727.27

25-21
LO3
Example: Equity as a Call Option

Mega 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?
25-22
LO3
Example – continued
•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
Assets
Debt
Equity
Up
160
100
60
Down
55
55
0
2523
LO3
Example – 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)
2524
LO3
Example – continued
Up
Down
Assets
160
55
Replicating 1. Risk-free
debt
Portfolio
55
55
2. 1.75 call
options
Total
1.75 max(0, 2 max(0,
160-100)
55-100)
=105
=0
160
55
2525
LO3
Example – 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

500
 2c  1,000
1.10
1
500 
c  1,000 
2
1.10 
c  272.73
2526
LO3
Example – continued
The current value of the firm’s equity is
$34.29
V=D+E
 D = 110 –34.29 = 75.71
 Therefore, the value of the firm’s debt is
$75.71
 Cost of debt =?

25-27
LO5
Warrants 25.6
A 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

25-28
LO5
Differences between warrants and
traditional call options
Warrants are generally very long term
 They 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

25-29
LO5
Convertible Bonds 25.7
Convertible 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

25-30
LO5
Convertibles – continued
The 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

25-31
LO5
Convertibles – continued
Floor 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

25-32
LO5
Figure 25.5 – Minimum value of a convertible bond
versus the value of the stock for a given interest
rate
LO5
Figure 25.6 – Value of a convertible bond versus
value of the stock for a given interest rate
25-34
LO5
Valuing Convertibles

Suppose you have a 10% bond that pays semiannual 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
LO5
Reasons for Issuing Warrants and
Convertibles 25.8
They 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

LO5
Table 25.3 – The case for and against
convertibles
LO5
Other Options 25.9

Call 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
LO5
Other Options continued

Over 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
Quick Quiz
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What 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 25.10
The 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 Skills
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Know the basics of call and put options and how to
calculate their payoffs and profits
Understand 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