0. Options and Corporate Finance: Basic Concepts
CHAPTER 22
Options and Corporate Finance: Basic Concepts

1. Chapter Outline 22.1 Options 22.2 Call Options 22.3 Put Options
22.4 Selling Options
22.5 Reading The Wall Street Journal
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

2. 22.1 Options
Many corporate securities are similar to the stock options 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.

3. 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 the obligation, to buy a 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 the obligation, to sell a 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.

4. 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 the holder 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.

5. 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 the underlying asset.

6. 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 +

7. 22.2 Call Options
Call options gives the holder the right, but not the obligation, to buy a 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.

8. Basic Call Option Pricing Relationships at Expiry
At expiry, an American call option is worth the same as a 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:
C = Max[ST – E, 0]
Where
ST is the value of the stock at expiry (time T)
E is the exercise price.
C is the value of the call option at expiry

9. Call Option Payoffs Exercise price = $50 Buy a call 60 4020 20 40 60 80
100
120 50
Stock price ($)
–20
Exercise price = $50
–40

10. Call Option Payoffs Exercise price = $50 Sell a call 60 4020 20 40 60 80
100
120 50
Stock price ($)
–20
Exercise price = $50
Sell a call
–40

11. Call Option Profits Exercise price = $50; option premium = $10
–20
120 20 40 60 80
100
–40
Stock price ($)
Option payoffs ($)
Buy a call 10 50
–10
Exercise price = $50; option premium = $10
Sell a call

12. 22.3 Put Options
Put options gives the holder the right, but not the obligation, to sell a 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.

13. Basic Put Option Pricing Relationships at Expiry
At expiry, an American put option is worth the same as a European option with the same characteristics.
If the put is in-the-money, it is worth E – ST.
If the put is out-of-the-money, it is worthless.
P = Max[E – ST, 0]

14. Put Option Payoffs Exercise price = $50 Buy a put 60 50 4020
Buy a put 20 40 60 80
100 50
Stock price ($)
–20
Exercise price = $50
–40

15. Put Option Payoffs Exercise price = $50 Sell a put 4020
Sell a put 20 40 60 80
100 50
Stock price ($)
–20
Exercise price = $50
–40
–50

16. Put Option Profits Exercise price = $50; option premium = $1060 40
Option payoffs ($) 20
Sell a put 10
Stock price ($) 20 40 50 60 80
100
–10
Buy a put
–20
–40
Exercise price = $50; option premium = $10

17. 22.4 Selling Options
The seller (or writer) of an option has an obligation.
The purchaser of an option has an option. 40
Buy a call
Option payoffs ($)
Buy a put
Sell a call 10
Sell a put
Stock price ($) 50
Buy a call 40 60
100
–10
Buy a put
Sell a put
Exercise price = $50; option premium = $10
Sell a call
–40

18. 22.5 Reading The Wall Street Journal

19. 22.5 Reading The Wall Street Journal
This option has a strike price of $135;
a recent price for the stock is $138.25
July is the expiration month

20. 22.5 Reading The Wall Street Journal
This makes a call option with this exercise price in-the-money by $3.25 = $138¼ – $135.
Puts with this exercise price are out-of-the-money.

21. 22.5 Reading The Wall Street Journal
On this day, 2,365 call options with this exercise price were traded.

22. 22.5 Reading The Wall Street Journal
The CALL option with a strike price of $135 is trading for $4.75.
Since the option is on 100 shares of stock, buying this option would cost $475 plus commissions.

23. 22.5 Reading The Wall Street Journal
On this day, 2,431 put options with this exercise price were traded.

24. 22.5 Reading The Wall Street Journal
The PUT option with a strike price of $135 is trading for $.8125.
Since the option is on 100 shares of stock, buying this option would cost $81.25 plus commissions.

25. 22.6 Combinations of Options
Puts and calls can serve as the building blocks for more complex option contracts.
If you understand this, you can become a financial engineer, tailoring the risk-return profile to meet your client’s needs.

26. Value of stock at expiry
Protective Put Strategy: Buy a Put and Buy the Underlying Stock: Payoffs at Expiry
Protective Put payoffs
Value at expiry
$50
Buy the stock
Buy a put with an exercise price of $50 $0
Value of stock at expiry
$50

27. Protective Put Strategy Profits
Value at expiry
Buy the stock at $40
$40
Protective Put strategy has downside protection and upside potential $0
-$10
$40
$50
Buy a put with exercise price of $50 for $10
Value of stock at expiry
-$40

28. Value of stock at expiry
Covered Call Strategy
Value at expiry
Buy the stock at $40
$10
Covered Call strategy $0
Value of stock at expiry
$40
$50
Sell a call with exercise price of $50 for $10
-$30
-$40

29. Long Straddle: Buy a Call and a Put40
Buy a call with exercise price of $50 for $10
Option payoffs ($) 30
Stock price ($) 40 60 30 70
Buy a put with exercise price of $50 for $10
–20
$50
A Long Straddle only makes money if the stock price moves $20 away from $50.

30. Long Straddle: Buy a Call and a Put
This Short Straddle only loses money if the stock price moves $20 away from $50.
Option payoffs ($) 20
Sell a put with exercise price of
$50 for $10
Stock price ($) 30 40 60 70
$50
–30
Sell a call with an
exercise price of $50 for $10
–40

31. Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T
Portfolio value today = c0 +
(1+ r)T E
Portfolio payoff
Call
Option payoffs ($)
bond 25 25
Stock price ($)
Consider the payoffs from holding a portfolio consisting of a call with a strike price of $25 and a bond with a future value of $25.

32. Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T
Portfolio payoff
Portfolio value today = p0 + S0
Option payoffs ($) 25
Stock price ($) 25
Consider the payoffs from holding a portfolio consisting of a share of stock and a put with a $25 strike.

33. Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T25
Stock price ($)
Option payoffs ($)
Portfolio value today = p0 + S0
Portfolio value today
(1+ r)T E
= c0 +
Since these portfolios have identical payoffs, they must have the same value today: hence
Put-Call Parity: c0 + E/(1+r)T = p0 + S0

34. 22.7 Valuing Options
The last section concerned itself with the value of an option at expiry.
This section considers the value of an option prior to the expiration date.
A much more interesting question.

35. Option Value Determinants
Call Put
Stock price –
Exercise price –
Interest rate –
Volatility in the stock price
Expiration date
The value of a call option C0 must fall within
max (S0 – E, 0) < C0 < S0.
The precise position will depend on these factors.

36. Market Value, Time Value and Intrinsic Value for an American Call
Profit ST
Call
Option payoffs ($) 25
Market Value
Time value
Intrinsic value ST E
Out-of-the-money
In-the-money
loss
The value of a call option C0 must fall within max (S0 – E, 0) < C0 < S0.

37. 22.8 An Option‑Pricing Formula
We will start with a binomial option pricing formula to build our intuition.
Then we will graduate to the normal approximation to the binomial for some real-world option valuation.

38. Binomial Option Pricing Model
Suppose a stock is worth $25 today and in one period will either be worth 15% more or 15% less. S0= $25 today and in one year S1is either $28.75 or $ The risk-free rate is 5%. What is the value of an at-the-money call option? S0
$21.25 = $25×(1 –.15)
$28.75 = $25×(1.15) S1
$25

39. Binomial Option Pricing Model
A call option on this stock with exercise price of $25 will have the following payoffs.
We can replicate the payoffs of the call option. With a levered position in the stock. S0 S1 C1
$28.75
$3.75
$25
$21.25 $0

40. Binomial Option Pricing Model
Borrow the present value of $21.25 today and buy 1 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 option’s payoff so the portfolio is worth twice the call option value. S0
( – ) = S1
debt
portfolio C1
$28.75
– $21.25 =
$7.50
$3.75
$25
$21.25
– $21.25 = $0 $0

41. Binomial Option Pricing Model
The value today of the levered equity portfolio is today’s value of one share less the present value of a $21.25 debt: S0
( – ) = S1
debt
portfolio C1
$28.75
– $21.25 =
$7.50
$3.75
$25
$21.25
– $21.25 = $0 $0

42. Binomial Option Pricing Model
We can value the call option today as half of the value of the levered equity portfolio: S0
( – ) = S1
debt
portfolio C1
$28.75
– $21.25 =
$7.50
$3.75
$25
$21.25
– $21.25 = $0 $0

43. The Binomial Option Pricing Model
If the interest rate is 5%, the call is worth:
$2.38 C0 S0
( – ) = S1
debt
portfolio C1
$28.75
– $21.25 =
$7.50
$3.75
$25
$21.25
– $21.25 = $0 $0

44. Binomial Option Pricing Model
the replicating portfolio intuition.
The most important lesson (so far) from the binomial option pricing model is:
Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities.

45. Delta and the Hedge Ratio
This practice of the construction of a riskless hedge is called delta hedging.
The delta of a call option is positive.
Recall from the example:
D =
Swing of call
Swing of stock
The delta of a put option is negative.

46. Delta Determining the Amount of Borrowing:
Value of a call = Stock price × Delta – Amount borrowed
$2.38 = $25 × ½ – Amount borrowed
Amount borrowed = $10.12

47. The Risk-Neutral Approach to Valuation
We could value V(0) as the value of the replicating portfolio. An equivalent method is risk-neutral valuation
S(U), V(U) q
S(0), V(0)
1- q
S(D), V(D) ) 1 ( f r D V q U + - =

48. The Risk-Neutral Approach to Valuation
S(U), V(U) q
q is the risk-neutral probability of an “up” move.
S(0), V(0)
1- q
S(0) is the value of the underlying asset today.
S(D), V(D)
S(U) and S(D) are the values of the asset in the next period following an up move and a down move, respectively.
V(U) and V(D) are the values of the asset in the next period following an up move and a down move, respectively.

49. The Risk-Neutral Approach to Valuation
S(0), V(0)
S(U), V(U)
S(D), V(D) q
1- q ) 1 ( f r D V q U + - =
The key to finding q is to note that it is already impounded into an observable security price: the value of S(0): ) 1 ( f r D S q U + - =
A minor bit of algebra yields:

50. Example of the Risk-Neutral Valuation of a Call:
Suppose a stock is worth $25 today and in one period will either be worth 15% more or 15% less. The risk-free rate is 5%. What is the value of an at-the-money call option?
The binomial tree would look like this:
$21.25,C(D) q
1- q
$25,C(0)
$28.75,C(D) ) 15 . 1 ( 25 $ 75 28 = 21 -

51. Example of the Risk-Neutral Valuation of a Call:
The next step would be to compute the risk neutral probabilities ) ( 1 D S U r q f - + = 3 2 50 . 7 $ 5 25 21 75 28 ) 05 1 ( = - q
$28.75,C(D)
2/3
$25,C(0)
1/3
$21.25,C(D)

52. Example of the Risk-Neutral Valuation of a Call:
After that, find the value of the call in the up state and down state. 25 $ 75 . 28 ) ( - = U C
$28.75, $3.75
2/3
$25,C(0) ] , 75 . 28 $ 25
max[$ ) ( - = D C
1/3
$21.25, $0

53. Example of the Risk-Neutral Valuation of a Call:
Finally, find the value of the call at time 0: ) 1 ( f r D C q U + - = ) 05 . 1 ( $ 3 75 2 + = C
$21.25, $0
2/3
1/3
$25,C(0)
$28.75,$3.75 38 . 2 $ ) 05 1 ( 50 = C
$25,$2.38

54. Risk-Neutral Valuation and the Replicating Portfolio
This risk-neutral result is consistent with valuing the call using a replicating portfolio.
The replicating portfolio consists of buying one share of stock today and borrowing the present value of $ The payoffs to the portfolio are twice those of the call, therefore the portfolio is worth twice as much as a call. Since we can value the portfolio, we can value the call.

55. The Black-Scholes Model
The Black-Scholes Model is ) N( 2 1 d Ee S C rT - =
Where
C0 = the value of a European option at time t = 0
r = the risk-free interest rate. T σ r E S d s ) 2 ( /
ln( 1 + =
N(d) = Probability that a standardized, normally distributed, random variable will be less than or equal to d. T d s - = 1 2
The Black-Scholes Model allows us to value options in the real world just as we have done in the 2-state world.

56. The Black-Scholes Model
Find the value of a six-month call option on the Microsoft with an exercise 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 6 months (half of a year).
The volatility of the underlying asset is 30% per annum.
Before we start, note that the intrinsic value of the option is $10—our answer must be at least that amount.

57. The Black-Scholes Model
Let’s try our hand at using the model. If you have a calculator handy, follow along.
First calculate d1 and d2 T σ r E S d s ) 5 . ( /
ln( 2 1 + =
5282 . 5 30 ). ) ( 05 (.
150 /
160
ln( 2 1 = + d
Then,
31602 . 5 30
52815 1 2 = - T d s

58. The Black-Scholes Model) N( 2 1 d Ee S C rT - =
5282 . 1 = d
N(d1) = N( ) =
N(d2) = N( ) =
31602 . 2 = d 92 . 20 $
62401
150
7013
160 5 05 = - C e

59. Another Black-Scholes Example
Assume S = $50, X = $45, T = 6 months, r = 10%,
and  = 28%, calculate the value of a call and a put. ( )
884 . 50 28 2 10 45 ln 1 = ÷ ø ö ç è æ + - d
686 . 50 28
884 2 = - d
From a standard normal probability table, look up N(d1) = and N(d2) = (or use Excel’s “normsdist” function) 32 . 8 $ )
754 ( 45
812 50 10 5 = - e C
125 . 1 $ 45 50 32 8 ) ( 10 = + - e P

60. 22.9 Stocks and Bonds as Options
Levered Equity is a Call 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 greater in value than the debt, the shareholders have 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 have an out-of-the-money call, they will not pay the bondholders (i.e. the shareholders will declare bankruptcy) and let the call expire.

61. 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 have an 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.

62. 22.9 Stocks and Bonds as Options
It all comes down to put-call parity.
c0 = S0 + p0 –
(1+ r)T E
Value of a call on the firm
Value of a put on the firm
Value of a risk-free bond
Value of the firm = + –
Stockholder’s position in terms of call options
Stockholder’s position in terms of put options

63. 22.10 Capital-Structure Policy and Options
Recall some of the agency costs of debt: they can all be seen in terms of options.
For example, recall the incentive shareholders in a levered firm have to take large risks.

64. Balance Sheet for a Company in Distress
Assets BV MV Liabilities BV MV
Cash $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?
$200 $0
The bondholders get $200; the shareholders get nothing.

65. Selfish Strategy 1: Take Large Risks
The Gamble Probability Payoff
Win Big 10% $1,000
Lose Big 90% $0
Cost of investment is $200 (all the firm’s cash)
Required return is 50%
Expected CF from the Gamble = $1000 × $0 = $100
NPV = –$200 +
$100
(1.10)
NPV = –$133

66. Selfish Stockholders Accept Negative NPV Project with Large Risks
Expected CF from the Gamble
To Bondholders = $300 × $0 = $30
To Stockholders = ($1000 – $300) × $0 = $70
PV of Bonds Without the Gamble = $200
PV of Stocks Without the Gamble = $0
$20 =
$30
(1.50)
PV of Bonds With the Gamble:
$47 =
$70
(1.50)
PV of Stocks With the Gamble:
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 of the firm is increased.

67. 22.11 Mergers and Options
This is an area rich with optionality, both in the structuring of the deals and in their execution.
In the first half of 2000, General Mills was attempting to acquire the Pillsbury division of Diageo PLC.
The structure of the deal was Diageo’s stockholders received 141 million shares of General Mills stock (then valued at $42.55) plus contingent value rights of $4.55 per share.

68. 22.11 Mergers and Options
The contingent value rights paid the difference between $42.55 and General Mills’ stock price in one year up to a maximum of $4.55.
Cash payment to newly issued shares
$4.55
$38 $0
$42.55
Value of General Mills in 1 year

69. 22.11 Mergers and Options
The contingent value plan can be viewed in terms of puts:
Each newly issued share of General Mills given to Diageo’s shareholders came with a put option with an exercise price of $42.55.
But the shareholders of Diageo sold a put with an exercise price of $38

70. 22.11 Mergers and Options Cash payment to newly issued shares
Own a put
Strike $42.55
$42.55
– $38.00
$4.55
$42.55 $0
Sell a put
Strike $38
$42.55
Value of General Mills in 1 year
$38
–$38

71. 22.11 Mergers and Options Value of General Mills in 1 year
Value of a share
Value of a share plus cash payment
$42.55
$4.55 $0
Value of General Mills in 1 year
$38
$42.55

72. 22.12 Investment in Real Projects & Options
Classic NPV calculations typically ignore the flexibility that real-world firms typically have.
The next chapter will take up this point.

73. 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
c0–
(1+ r)T E
= S0 + p0

74. 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.
Common stock in a levered firm can be viewed as a call option on the assets of the firm.
Real projects often have hidden option that enhance value.