0. Options and Corporate Finance
Session 6
Options and Corporate Finance

1. Learning Objectives
LO 1: Explain the basic characteristics and terminology of options.
LO 2: Determine the intrinsic value of options at expiration date.
LO 3: Use the Black-Scholes Option Pricing Model to determine the fair value of an option before expiration.
LO 4: Explain how option pricing can be applied to corporate finance.

2. Outline Option Basics and Value at Expiration
The Black-Scholes Option Pricing Model
Applications of Options in Corporate Finance

3. 1. Option Basics and Value at Expiration
An option gives the holder the right, but not the obligation, to buy or sell a given quantity of an asset on (or before) a given date, at prices agreed upon today.
Exercising the Option
The act of buying or selling the underlying asset
Strike or Exercise Price
The fixed price in the option contract at which the holder can buy or sell the underlying asset
Expiration Date
The maturity date of the option

4. Option Basics European versus American options In-the-Money
European options can be exercised only at expiration date.
American options can be exercised at any time up to maturity date.
In-the-Money
Exercising the option would result in a positive payoff.
At-the-Money
Exercising the option would result in a zero payoff (i.e., stock price equals to exercise price).
Out-of-the-Money
Exercising the option would result in a negative payoff.
Call is in the money if spot price is greater than strike price (opposite for a put).

5. Call Options
Call options give 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.

6. Call Option Pricing at Expiration
At expiration, 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. Hence,
C = Max[ST – E, 0]
Where
ST is the stock price at expiration (time T)
E is the exercise/strike price.
C is the (intrinsic) value of the call option at expiration

7. Value of Call Option at Expiration60
Buy a call 40
Option value ($) 20 20 40 60 80
100
120 50
Stock price ($)
–20
Exercise price = $50

8. 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.

9. Put Option Pricing at Expiration
At expiration, 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. Hence,
P = Max[E – ST, 0]
where P is the (intrinsic) value of the put option at expiration

10. Value of Put Option at Expiration60 50
Buy a put 40
Option value ($) 20 20 40 60 80
100 50
Stock price ($)
–20
Exercise price = $50

11. 2. The Black-Scholes Option Pricing Model
The last section concerned itself with the value of an option at expiration.
This section considers the value of an option prior to the expiration date.
A much more interesting question.

12. Option Value Determinants
Call Put
Stock price –
Exercise price –
Interest rate –
Volatility in the stock price
Expiration date

13. The Black-Scholes Model
N(d) = Probability that a standardized, normally distributed, random variable will be less than or equal to d.
Where,
C0 = the value of a European option at time t = 0
S = current stock price
E = exercise price of call
r = annual risk-free rate of return, continuously compounded
σ2 = variance (per year) of the stock return
T = time (in years) to expiration date
e = the base of natural logarithm, equals …

14. P + S = C + PV(E) = C + e(-rT)*E
Put-Call Parity
If we know the intrinsic value of a call option, the intrinsic value of a put option with identical features (same maturity, exercise price, stock price, risk-free interest rate, and equity volatility) can be determined by the put-call parity:
P + S = C + PV(E) = C + e(-rT)*E
So P = C + e(-rT)*E - S

15. Example
Find the value of a six-month call and put option on Microsoft with an exercise price of $150.
The current price of Microsoft stock 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 stock is 30% per annum.

16. Example
We solve the value of the call option first. We then use the put-call parity to get the put option value.
First calculate d1 and d2
Then,

17. Example N(d1) = N(0.53) = 0.70194 N(d2) = N(0.32) = 0.62552
P = C + e(-rT)*E – S = $ e(-0.05*0.5)*$150 - $160 = $7.10

18. 3. Applications of Options in Corporate Finance
We can view bondholders, rather than shareholders as the owner of the firm.
Bondholders write a call option to shareholders.
The underlying asset is the asset of the firm.
The strike price is the payoff of the bond.
The expiration date of the call option is the debt maturity.

19. Stock As a Call Option
If at the maturity of the debt, the assets of the firm are greater in value than the debt (the strike price), 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.

20. Example Consider a company with the following characteristics:
MV assets = $40 million
Face value debt = $25 million
Debt maturity = 5 years
Asset return standard deviation = 40%
Risk-free rate = 4%
What is the market value of equity and debt?

21. Example S = $40 million, E = $25 million, T = 5, σ = 0.4, r = 0.04
First calculate d1 and d2
Then,

22. Example
N(d1) = N(1.20) =
N(d2) = N(0.30) =
Current market value of equity = $ million (using the NORMDIST function in EXCEL to calculate N(d1) and N(d2))
Current market value of debt = $ million
So the market value of equity is $22.75 million. The market value of debt = market value of firm – market value of equity = $40 million - $22.75 million = $17.25 million.

23. Readings
Chapter 17