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chapter 22 options and corporate finance basic concepts and understandings
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Corporate FinanceRoss Westerfield Jaffe
Sixth Edition
22
Chapter Twenty Two
Options and Corporate
Finance: Basic Concepts
Instructor: AJAB KHAN BURKI
For Download: tinyurl.com/burki09
http://www.theoptionsguide.com
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Chapter Outline
22.1 Options
22.2 Call Options
22.3 Put Options
22.4 Selling Options
22.5 Stock Option Quotations
22.6 Combinations of Options
22.7 Valuing Options
22.8 An Option-Pricing Formula
22.9 Stocks and Bonds as Options
22.10 Capital-Structure Policy and Options
22.11 Mergers and Options
22.12 Investment in Real Projects and Options
22.13 Summary and Conclusions
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22.1 Options
Many corporate securities are similar to the stockoptions that are traded on organized exchanges.
Almost every issue of corporate stocks and bonds
has option features.
In addition, capital structure and capital budgeting
decisions can be viewed in terms of options.
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22.1 Options Contracts: Preliminaries
An option gives the holder the right, but not the obligation,to buy or sell a given quantity of an asset on (or perhaps
before) a given date, at prices agreed upon today.
Calls versus Puts
Call options gives the holder the right, but not theobligation, tobuya given quantity of some asset at some
time in the future, at prices agreed upon today. When
exercising a call option, you call in the asset.
Put options gives the holder the right, but not theobligation, to sella given quantity of an asset at some
time in the future, at prices agreed upon today. When
exercising a put, you put the asset to someone.
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22.1 Options Contracts: Preliminaries
Exercising the Option
The act of buying or selling the underlying asset through the
option contract.
Strike Price or Exercise Price
Refers to the fixed price in the option contract at which theholder can buy or sell the underlying asset.
Expiry
The maturity date of the option is referred to as the
expiration date, or the expiry.
European versus American options
European options can be exercised only at expiry.
American options can be exercised at any time up to expiry.
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Options Contracts: Preliminaries
In-the-Money The exercise price is less than the spot price of the
underlying asset.
At-the-Money
The exercise price is equal to the spot price of the
underlying asset.
Out-of-the-Money
The exercise price is more than the spot price of theunderlying asset.
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In The Money
1. For a call option, when the option's strike price isbelow the market price of the underlying asset.
2. For a put option, when the strike price is above
the market price of the underlying asset.
Being in the money does not mean you will profit, it
just means the option is worth exercising. This is
because the option costs money to buy.
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In The Money (Con)
In the money means that your stock option is worthmoney and you can turn around and sell or exercise
it. For example, if John buys a call option on ABC
stock with a strike price of $12, and the price of the
stock is sitting at $15, the option is considered to be
in the money. This is because the option gives John
the right to buy the stock for $12 but he could
immediately sell the stock for $15, a gain of $3. If
John paid $3.50 for the call, then he wouldn't
actually profit from the total trade, but it is still
considered in the money.
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Out Of The Money - OTM
A call option with a strike price that is higher thanthe market price of the underlying asset, or a put
option with a strike price that is lower than the
market price of the underlying asset. An out of the
money option has no intrinsic value, but only
possesses extrinsic or time value. As a result, the
value of an out of the money option erodes quickly
with time as it gets closer to expiry. If it still out of
the money at expiry, the option will expire
worthless.
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At The Money
A situation where an option's strike price is identicalto the price of the underlying security. Both call and
put options will be simultaneously "at the money."
For example, if XYZ stock is trading at 75, then the
XYZ 75 call option is at the money and so is theXYZ 75 put option. An at-the-money option has no
intrinsic value, but may still have time value.
Options trading activity tends to be high when
options are at the money.
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At The Money (Con)
"At the money" is one of three terms used todescribe the relationship between an option's strike
price and the underlying security's price, or option
"moneyness." The other two are "in the money,"
meaning the option has some intrinsic value, and"out of the money," meaning the option has no
intrinsic value. Also, sometimes the term "near the
money" is used to describe an option that is within
50 cents of being at the money
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Options Contracts: Preliminaries
Intrinsic Value The difference between the exercise price of the option
and the spot price of the underlying asset.
Speculative Value
The difference between the option premium and the
intrinsic value of the option.
Option
Premium=
Intrinsic
Value
Speculative
Value+
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22.2 Call Options
Call options gives the holder the right, but not theobligation, tobuya given quantity of some asset
on or before some time in the future, at prices
agreed upon today.
When exercising a call option, you call in the
asset.
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Basic Call Option Pricing Relationships at Expiry
At expiry, an American call option is worth the same asa European option with the same characteristics.
If the call is in-the-money, it is worth ST-E.
If the call is out-of-the-money, it is worthless.
CaT= CeT=Max[ST -E, 0]
Where
STis the value of the stock at expiry (time T)
E is the exercise price.
CaTis the value of an American call at expiry
CeT is the value of a European call at expiry
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Call Option Payoffs
-20
100908070600 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
Optionpayoffs($)
Buy a call
Exercise price = $50
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Call Option Payoffs
-20
100908070600 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
Optionpayoffs($)
Write a call
Exercise price = $50
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Call Option Profits
-20
100908070600 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
Optionprofits
($)
Write a call
Buy a call
Exercise price = $50; option premium = $10
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22.3 Put Options
Put options give the holder the right, but not theobligation, to sella given quantity of an asset on
or before some time in the future, at prices
agreed upon today.
When exercising a put, you put the asset to
someone.
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Basic Put Option Pricing Relationships at Expiry
At expiry, an American put option is worth thesame as a European option with the same
characteristics.
If the put is in-the-money, it is worthE - ST
.
If the put is out-of-the-money, it is worthless.
PaT=PeT=Max[E - ST, 0]
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Put Option Payoffs
-20
100908070600 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
Optionpayoffs($)
Buy a put
Exercise price = $50
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Put Option Payoffs
-20
100908070600 10 20 30 40 50
-40
20
0
-60
40
60
Optionpayoffs($)
write a put
Exercise price = $50
Stock price ($)
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Put Option Profits
-20
100908070600 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
Optionprofits(
$)
Buy a put
Write a put
Exercise price = $50; option premium = $10
10
-10
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22.4 Selling Options
The seller (or writer) of anoption has an obligation.
The purchaser of an option hasan option.
-20
100908070600 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
Option
profits($)
Buy a put
Write a put
10
-10
-20
100908070600 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
Optionprofits($)
Write a call
Buy a call
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22.5 Stock Option Quotations
Stk Exp P/C Vol Bid Ask Opint
Nortel Networks (NT) 9.35
9 Mar C 446 0.50 0.55 24619 Mar P 155 0.20 0.30 841
8 June C 15 1.95 2.10 660
8 June P 35 0.55 0.65 1310
11 Sept C 11 1.10 1.25 459
11 Sept P 5 2.65 2.80 279
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Stk Exp P/C Vol Bid Ask Opint
Nortel Networks (NT) 9.35
9 Mar C 446 0.50 0.55 24619 Mar P 155 0.20 0.30 841
8 June C 15 1.95 2.10 660
8 June P 35 0.55 0.65 1310
11 Sept C 11 1.10 1.25 459
11 Sept P 5 2.65 2.80 279
22.5 Stock Option Quotations
This option has a strike price of $8;
A recent price for the stock is $9.35
June is the expiration month
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22.5 Stock Option Quotations
This makes a call option with this exercise price in-the-money by $1.35 = $9.35$8.
Puts with this exercise price are out-of-the-money.
Stk Exp P/C Vol Bid Ask Opint
Nortel Networks (NT) 9.35
9 Mar C 446 0.50 0.55 24619 Mar P 155 0.20 0.30 841
8 June C 15 1.95 2.10 660
8 June P 35 0.55 0.65 1310
11 Sept C 11 1.10 1.25 459
11 Sept P 5 2.65 2.80 279
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Stk Exp P/C Vol Bid Ask Opint
Nortel Networks (NT) 9.35
9 Mar C 446 0.50 0.55 24619 Mar P 155 0.20 0.30 841
8 June C 15 1.95 2.10 660
8 June P 35 0.55 0.65 1310
11 Sept C 11 1.10 1.25 45911 Sept P 5 2.65 2.80 279
22.5 Stock Option Quotations
On this day, 15 call options with this exercise price were traded.
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Stk Exp P/C Vol Bid Ask Opint
Nortel Networks (NT) 9.35
9 Mar C 446 0.50 0.55 24619 Mar P 155 0.20 0.30 841
8 June C 15 1.95 2.10 660
8 June P 35 0.55 0.65 1310
11 Sept C 11 1.10 1.25 45911 Sept P 5 2.65 2.80 279
22.5 Stock Option Quotations
The holder of this CALL option can sell it for $1.95.
Since the option is on 100 shares of stock, selling this option
would yield $195.
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Stk Exp P/C Vol Bid Ask Opint
Nortel Networks (NT) 9.35
9 Mar C 446 0.50 0.55 24619 Mar P 155 0.20 0.30 841
8 June C 15 1.95 2.10 660
8 June P 35 0.55 0.65 1310
11 Sept C 11 1.10 1.25 45911 Sept P 5 2.65 2.80 279
22.5 Stock Option Quotations
Buying this CALL option costs $2.10.
Since the option is on 100 shares of stock, buying this option
would cost $210.
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Stk Exp P/C Vol Bid Ask Opint
Nortel Networks (NT) 9.35
9 Mar C 446 0.50 0.55 24619 Mar P 155 0.20 0.30 841
8 June C 15 1.95 2.10 660
8 June P 35 0.55 0.65 1310
11 Sept C 11 1.10 1.25 45911 Sept P 5 2.65 2.80 279
22.5 Stock Option Quotations
On this day, there were 660 call options with this exercise
outstanding in the market.
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22.6 Combinations of Options
Puts and calls can serve as the building blocksfor more complex option contracts.
If you understand this, you can become a
financial engineer, tailoring the risk-return
profile to meet your clients needs.
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Protective Put Strategy: Buy a Put and Buy
the Underlying Stock: Payoffs at Expiry
Buy a put with an exercise
price of $50
Buy the
stock
Protective Put strategy has
downside protection and
upside potential
$50
$0
$50
Value atexpiry
Value of
stock at
expiry
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Protective Put Strategy Profits
Buy a put with
exercise price of
$50 for $10
Buy the stock at $40
$40
Protective Put
strategy has
downside protectionand upside potential
$40
$0
-$40
$50
Value at
expiry
Value of
stock at
expiry
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Covered Call Strategy
Sell a call withexercise price of
$50 for $10
Buy the stock at $40
$40
Coveredcall
$40
$0
-$40
$10
-$30
$30 $50
Value of stock at expiry
Value at
expiry
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Long Straddle: Buy a Call and a Put
Buy a put with an
exercise price of
$50 for $10
$40
A Long Straddle only makes money if the
stock price moves $20 away from $50.
$40
$0
-$20$50
Buy a call with an
exercise price of
$50 for $10
-$10
$30
$60$30 $70
Value of
stock at
expiry
Value at
expiry
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Short Straddle: Sell a Call and a Put
Sell a put with exercise price of$50 for $10
$40
A Short Straddle only loses money if the stock
price moves $20 away from $50.
-$40
$0
-$30
$50
Sell a call with an
exercise price of $50 for $10
$10
$20
$60$30 $70
Value of stock at
expiry
Value at
expiry
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Long Call Spread
Sell a call with exercise
price of $55 for $5
$55
long call spread$5
$0
$50
Buy a call with an
exercise price of
$50 for $10
-$10-$5
$60
Value of
stock at
expiry
Value atexpiry
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Put-Call Parity
Sell a put with an
exercise price of $40
Buy the stock at $40
financed with somedebt: FV = $XBuy a call option with
an exercise price of $40
$0
-$40
$40-P0rT
Xe40$
$40
Buy the
stock at $40
040$ C)40($ rTXe
-[$40-P0]
0C
0P
In market equilibrium, it mast be the case that option prices
are set such that:000 SPXeC rT
Otherwise, riskless portfolios with positive payoffs exist.
Value of
stock at
expiry
Value at
expiry
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22.7 Valuing Options
The last sectionconcerned itself with the
value of an option at
expiry.
This section considersthe value of an option
prior to the expiration
date.
A much moreinteresting question.
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Option Value Determinants
Call Put
1. Stock price +
2. Exercise price +
3. Interest rate +
4. Volatility in the stock price + +5. Expiration date + +
The value of a call option C0must fall within
max (S0E,0) < C0 < S0.
The precise position will depend on these factors.
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Market Value, Time Value, and Intrinsic
Value for an American Call
CaT>Max[ST- E, 0]
Profit
lossE ST
Market Value
Intrinsic valueTime value
Out-of-the-money In-the-money
The value of a call option C0must fallwithin max (S0E,0) < C0 < S0.
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22.8 An Option-Pricing Formula
We will start with abinomial option pricing
formula to build our
intuition.
Then we will graduateto the normal
approximation to the
binomial for some real-
world option valuation.
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Binomial Option Pricing Model
Suppose a stock is worth $25 today and in one period willeither be worth 15% more or 15% less. S0= $25 today and in
one year S1 is either $28.75 or $21.25. The risk-free rate is
5%. What is the value of an at-the-money call option?
$25
$21.25
$28.75
S1S0
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Binomial Option Pricing Model
1. A call option on this stock with exercise price of $25 willhave the following payoffs.
2. We can replicate the payoffs of the call option. With a
levered position in the stock.
$25
$21.25
$28.75
S1S0 C1
$3.75
$0
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Binomial Option Pricing Model
Borrow the present value of $21.25 today and buy one share.
The net payoff for this levered equity portfolio in one period is
either $7.50 or $0.
The levered equity portfolio has twice the options payoff so
the portfolio is worth twice the call option value.
$25
$21.25
$28.75
S1S0 debt- $21.25
portfolio$7.50
$0
( - ) ==
=
C1$3.75
$0- $21.25
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Binomial Option Pricing Model
The levered equity portfolio value today istodays value of one share less the present valueof a $21.25 debt:
)1(
25.21$25$
fr
$25
$21.25
$28.75
S1S0 debt- $21.25
portfolio$7.50
$0
( - ) ==
=
C1$3.75
$0- $21.25
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Binomial Option Pricing Model
We can value the option today ashalf of the value of the levered
equity portfolio:
)1(
25.21$25$
2
10
frC
$25
$21.25
$28.75
S1S0 debt- $21.25
portfolio$7.50
$0
( - ) ==
=
C1$3.75
$0- $21.25
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If the interest rate is 5%, the call is worth:
The Binomial Option Pricing Model
38.2$24.2025$2
1
)05.1(
25.21$25$
2
10
C
$25
$21.25
$28.75
S1S0 debt- $21.25
portfolio$7.50
$0
( - ) ==
=
C1$3.75
$0- $21.25
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If the interest rate is 5%, the call is worth:
The Binomial Option Pricing Model
38.2$24.2025$2
1
)05.1(
25.21$25$
2
10
C
$25
$21.25
$28.75
S1S0 debt- $21.25
portfolio$7.50
$0
( - ) ==
=
C1$3.75
$0- $21.25
$2.38
C0
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Binomial Option Pricing Model
the replicating portfolio intuition.
Many derivative securities can be valued by
valuing portfolios of primitive securitieswhen those portfolios have the same
payoffs as the derivative securities.
The most important lesson (so far) from the binomialoption pricing model is:
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The Risk-Neutral Approach to Valuation
We could value V(0) as the value of the replicating portfolio.An equivalent method is r isk-neutral valuation
S(0), V(0)
S(U), V(U)
S(D), V(D)
q
1- q
)1(
)()1()()0(
fr
DVqUVqV
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The Risk-Neutral Approach to Valuation
S(0) is the value of the
underlying asset today.
S(0), V(0)
S(U), V(U)
S(D), V(D)
S(U) and S(D) are the values of the asset inthe next period following an up move and adown move, respectively.
q
1- q
V(U) and V(D) are the values of the asset in the next periodfollowing an up move and a down move, respectively.
qis the risk-neutral
probability of an
up move.
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The Risk-Neutral Approach to Valuation
The key to finding qis to note that it is already impounded
into an observable security price: the value of S(0):
S(0), V(0)
S(U), V(U)
S(D), V(D)
q
1- q
)1(
)()1()()0(
fr
DVqUVqV
)1()()1()()0(
frDSqUSqS
A minor bit of algebra yields:)()(
)()0()1(
DSUS
DSSrq
f
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Example of the Risk-Neutral Valuation of a Call:
$21.25,C(D)
q
1- q
Suppose a stock is worth $25 today and in one period will
either be worth 15% more or 15% less. The risk-free rate is5%. What is the value of an at-the-money call option?
The binomial tree would look like this:
$25,C(0)
$28.75,C(D)
)15.1(25$75.28$
)15.1(25$25.21$
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Example of the Risk-Neutral Valuation of a Call:
$21.25,C(D)
2/3
1/3
The next step would be to compute the risk neutral
probabilities
$25,C(0)
$28.75,C(D)
)()(
)()0()1(
DSUS
DSSrq
f
3250.7$
5$
25.21$75.28$
25.21$25$)05.1(
q
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Example of the Risk-Neutral Valuation of a Call:
$21.25, $0
2/3
1/3
After that, find the value of the call in the up state and down
state.
$25,C(0)
$28.75, $3.75
25$75.28$)( UC
]0,75.28$25max[$)( DC
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Example of the Risk-Neutral Valuation of a Call:
Finally, find the value of the call at time 0:
$21.25, $0
2/3
1/3
$25,C(0)
$28.75,$3.75
)1(
)()1()()0(
fr
DCqUCqC
)05.1(
0$)31(75.3$32
)0(
C
38.2$)05.1(
50.2$)0( C
$25,$2.38
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This risk-neutral result is consistent with valuing the callusing a replicating portfolio.
Risk-Neutral Valuation and the Replicating Portfolio
38.2$24.2025$2
1
)05.1(
25.21$25$
2
10
C
38.2$05.150.2$
)05.1(0$)31(75.3$320 C
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The Black-Scholes Model
The Black-Scholes Model is
)N()N( 210 dEedSC rT
Where
C0= the value of a European option at time t= 0
r= the risk-free interest rate.
T
T
rESd
)2
()/ln(2
1
Tdd 12
N(d) = Probability that a
standardized, normally
distributed, random
variable will be less thanor equal to d.
The Black-Scholes Model allows us to value options in the
real world just as we have done in the two-state world.
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The Black-Scholes Model
Find the value of a six-month call option on Microsoft with anexercise price of $150.
The current value of a share of Microsoft is $160.
The interest rate available in the U.S. is r= 5%.
The option maturity is six months (half of a year).The volatility of the underlying asset is 30% per annum.
Before we start, note that the intrinsicvalueof the option is
$10our answer must be at least that amount.
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The Black-Scholes Model
Lets try our hand at using the model. If you have a calculatorhandy, follow along.
Then,
T
TrES
d
)5.()/ln( 2
1
First calculate d1and d2
31602.05.30.052815.012 Tdd
5282.05.30.0
5).)30.0(5.05(.)150/160ln( 2
1
d
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The Black-Scholes Model
N(d1) = N(0.52815) = 0.7013
N(d2) = N(0.31602) = 0.62401
5282.01d
31602.02d
)N()N( 210 dEedSC rT
92.20$
62401.01507013.0160$
0
5.05.
0
C
eC
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22.9 Stocks and Bonds as Options
Levered Equity is a Call Option.
The underlying asset comprises the assets of thefirm.
The strike price is the payoff of the bond.
If at the maturity of their debt, the assets of the firmare greater in value than the debt, the shareholdershave an in-the-money call, they will pay the
bondholders, and call in the assets of the firm.
If at the maturity of the debt the shareholders havean out-of-the-money call, they will not pay thebondholders (i.e.,the shareholders will declarebankruptcy), and let the call expire.
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22.9 Stocks and Bonds as Options
Levered Equity is a Put Option.
The underlying asset comprise the assets of the firm.
The strike price is the payoff of the bond.
If at the maturity of their debt, the assets of the firm
are less in value than the debt, shareholders havean in-the-money put.
They will put the firm to the bondholders.
If at the maturity of the debt the shareholders have
an out-of-the-money put, they will not exercise the
option (i.e.,NOT declare bankruptcy) and let the
put expire.
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22.9 Stocks and Bonds as Options
It all comes down to put-call parity.
Value of acall on the
firm
Value of aput on the
firm
Value of arisk-free
bond
Value of
the firm= +
TreXPSC 00
Stockholders
position in terms
of call options
Stockholders
position in terms
of put options
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22.10 Capital-Structure Policy and Options
Recall some of the agency costs of debt: they canall be seen in terms of options.
For example, recall the incentive shareholders in
a levered firm have to take large risks.
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Balance Sheet for a Company in Distress
Assets BV MV Liabilities BV MVCash $200 $200 LT bonds $300 ?
Fixed Asset $400 $0 Equity $300 ?
Total $600 $200 Total $600 $200
What happens if the firm is liquidated today?
The bondholders get $200; the shareholders get nothing.
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Selfish Strategy 1: Take Large Risks
(Think of a Call Option)
The Gamble Probability PayoffWin Big 10% $1,000
Lose Big 90% $0
Cost of investment is $200 (all the firms cash)
Required return is 50%
Expected CF from the Gamble = $1000 0.10 + $0 = $100
133$
50.1
100$200$
NPV
NPV
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p g
NPV Project with Large Risks
Expected cash flow from the Gamble To Bondholders = $300 0.10 + $0 = $30
To Stockholders = ($1000 - $300) 0.10 + $0 = $70
PV of Bonds Without the Gamble = $200
PV of Stocks Without the Gamble = $0
PV of Bonds With the Gamble = $30 / 1.5 = $20
PV of Stocks With the Gamble = $70 / 1.5 = $47
The stocks are worth more with the high risk project because
the call option that the shareholders of the levered firm hold
is worth more when the volatility is increased.
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22.11 Mergers and Options
This is an area rich with optionality, both in thestructuring of the deals and in their execution.
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22.12 Investment in Real Projects & Options
Classic NPV calculations typically ignore theflexibility that real-world firms typically have.
The next chapter will take up this point.
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22.13 Summary and Conclusions
The most familiar options are puts and calls.Put options give the holder the right to sell stock
at a set price for a given amount of time.
Call options give the holder the right to buy stock
at a set price for a given amount of time.
Put-Call parity
00 PSeXC Tr
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22.13 Summary and Conclusions
The value of a stock option depends on six factors:1.Current price of underlying stock.2. Dividend yield of the underlying stock.
3. Strike price specified in the option contract.
4. Risk-free interest rate over the life of the contract.5. Time remaining until the option contract expires.
6. Price volatility of the underlying stock.
Much of corporate financial theory can be
presented in terms of options.1. Common stock in a levered firm can be viewed as a call
option on the assets of the firm.
2. Real projects often have hidden options that enhance
value
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