1. 22-0 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Corporate Finance Ross  Westerfield  Jaffe Sixth Edition 22 Chapter Twenty Two Options and Corporate Finance: Basic Concepts Prepared by Gady Jacoby University of Manitoba and Sebouh Aintablian American University of Beirut

2. 22-1 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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

3. 22-2 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.

4. 22-3 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.

5. 22-4 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.

6. 22-5 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.

7. 22-6 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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 +

8. 22-7 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.

9. 22-8 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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 S T - E. If the call is out-of-the-money, it is worthless. C aT = C eT = Max[S T - E, 0] Where S T is the value of the stock at expiry (time T) E is the exercise price. C aT is the value of an American call at expiry C eT is the value of a European call at expiry

10. 22-9 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Call Option Payoffs -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option payoffs ($) Buy a call Exercise price = $50

11. 22-10 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Call Option Payoffs -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option payoffs ($) Write a call Exercise price = $50

12. 22-11 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Call Option Profits -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option profits ($) Write a call Buy a call Exercise price = $50; option premium = $10

13. 22-12 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 22.3 Put Options Put options give 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.

14. 22-13 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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 - S T. If the put is out-of-the-money, it is worthless. P aT = P eT = Max[E - S T, 0]

15. 22-14 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Put Option Payoffs -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option payoffs ($) Buy a put Exercise price = $50

16. 22-15 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Put Option Payoffs -20 1009080706001020304050 -40 20 0 -60 40 60 Option payoffs ($) write a put Exercise price = $50 Stock price ($)

17. 22-16 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Put Option Profits -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option profits ($) Buy a put Write a put Exercise price = $50; option premium = $10 10 -10

18. 22-17 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 22.4 Selling Options The seller (or writer) of an option has an obligation. The purchaser of an option has an option. -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option profits ($) Buy a put Write a put 10 -10 -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option profits ($) Write a call Buy a call

19. 22-18 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 22.5 Stock Option Quotations

20. 22-19 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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

21. 22-20 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.

22. 22-21 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 22.5 Stock Option Quotations On this day, 15 call options with this exercise price were traded.

23. 22-22 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.

24. 22-23 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.

25. 22-24 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 22.5 Stock Option Quotations On this day, there were 660 call options with this exercise outstanding in the market.

26. 22-25 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.

27. 22-26 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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 at expiry Value of stock at expiry

28. 22-27 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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 protection and upside potential $40 $0 -$40 $50 Value at expiry Value of stock at expiry

29. 22-28 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Covered Call Strategy Sell a call with exercise price of $50 for $10 Buy the stock at $40 $40 Covered call $40 $0 -$40 $10 -$30 $30$50 Value of stock at expiry Value at expiry

30. 22-29 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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

31. 22-30 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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

32. 22-31 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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 at expiry

33. 22-32 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Put-Call Parity Sell a put with an exercise price of $40 Buy the stock at $40 financed with some debt: FV = $X Buy a call option with an exercise price of $40 $0 -$40 $40-P 0 $40 Buy the stock at $40 -[$40-P 0 ] In market equilibrium, it mast be the case that option prices are set such that: Otherwise, riskless portfolios with positive payoffs exist. Value of stock at expiry Value at expiry

34. 22-33 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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. 22-34 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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 C 0 must fall within max (S 0 – E, 0) < C 0 < S 0. The precise position will depend on these factors.

36. 22-35 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Market Value, Time Value, and Intrinsic Value for an American Call C aT > Max[S T - E, 0] Profit loss E STST Market Value Intrinsic value S T - E Time value Out-of-the-moneyIn-the-money STST The value of a call option C 0 must fall within max (S 0 – E, 0) < C 0 < S 0.

37. 22-36 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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. 22-37 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Binomial Option Pricing Model Suppose a stock is worth $25 today and in one period will either be worth 15% more or 15% less. S 0 = $25 today and in one year S 1 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 S1S1 S0S0

39. 22-38 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Binomial Option Pricing Model 1.A call option on this stock with exercise price of $25 will have 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 S1S1 S0S0 C1C1 $3.75 $0

40. 22-39 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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 option’s payoff so the portfolio is worth twice the call option value. $25 $21.25 $28.75 S1S1 S0S0 debt - $21.25 portfolio $7.50 $0 ( - ) = = = C1C1 $3.75 $0 - $21.25

41. 22-40 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Binomial Option Pricing Model The levered equity portfolio value today is today’s value of one share less the present value of a $21.25 debt: $25 $21.25 $28.75 S1S1 S0S0 debt - $21.25 portfolio $7.50 $0 ( - ) = = = C1C1 $3.75 $0 - $21.25

42. 22-41 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Binomial Option Pricing Model We can value the option today as half of the value of the levered equity portfolio: $25 $21.25 $28.75 S1S1 S0S0 debt - $21.25 portfolio $7.50 $0 ( - ) = = = C1C1 $3.75 $0 - $21.25

43. 22-42 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited If the interest rate is 5%, the call is worth: The Binomial Option Pricing Model $25 $21.25 $28.75 S1S1 S0S0 debt - $21.25 portfolio $7.50 $0 ( - ) = = = C1C1 $3.75 $0 - $21.25

44. 22-43 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited If the interest rate is 5%, the call is worth: The Binomial Option Pricing Model $25 $21.25 $28.75 S1S1 S0S0 debt - $21.25 portfolio $7.50 $0 ( - ) = = = C1C1 $3.75 $0 - $21.25 $2.38 C0C0

45. 22-44 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Binomial Option Pricing Model the replicating portfolio intuition. Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities. The most important lesson (so far) from the binomial option pricing model is:

46. 22-45 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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(0), V(0) S(U), V(U) S(D), V(D) q 1- q

47. 22-46 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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 in the next period following an up move and a down move, respectively. q 1- q V(U) and V(D) are the values of the asset in the next period following an up move and a down move, respectively. q is the risk-neutral probability of an “up” move.

48. 22-47 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited The Risk-Neutral Approach to Valuation The key to finding q is 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 A minor bit of algebra yields:

49. 22-48 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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 is 5%. 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)

50. 22-49 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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)

51. 22-50 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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

52. 22-51 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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 $25,$2.38

53. 22-52 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited This risk-neutral result is consistent with valuing the call using a replicating portfolio. Risk-Neutral Valuation and the Replicating Portfolio

54. 22-53 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited The Black-Scholes Model The Black-Scholes Model is Where C 0 = the value of a European option at time t = 0 r = the risk-free interest rate. N(d) = Probability that a standardized, normally distributed, random variable will be less than or 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.

55. 22-54 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited The Black-Scholes Model Find the value of a six-month call option on 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 six 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.

56. 22-55 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited The Black-Scholes Model Let’s try our hand at using the model. If you have a calculator handy, follow along. Then, First calculate d 1 and d 2

57. 22-56 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited The Black-Scholes Model N(d 1 ) = N(0.52815) = 0.7013 N(d 2 ) = N(0.31602) = 0.62401

58. 22-57 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Assume S = $50, X = $45, T = 6 months, r = 10%, and  = 28%, calculate the value of a call and a put. From a standard normal probability table, look up N(d 1 ) = 0.812 and N(d 2 ) = 0.754 (or use Excel’s “normsdist” function) Another Black-Scholes Example

59. 22-58 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 22.9 Stocks and Bonds as Options Levered Equity is a Call Option. –The underlying asset comprises 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.

60. 22-59 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.

61. 22-60 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 22.9 Stocks and Bonds as Options It all comes down to put-call parity. 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

62. 22-61 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.

63. 22-62 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Balance Sheet for a Company in Distress AssetsBVMVLiabilitiesBVMV Cash$200$200LT bonds$300? Fixed Asset$400$0Equity$300? Total$600$200Total$600$200 What happens if the firm is liquidated today? The bondholders get $200; the shareholders get nothing.

64. 22-63 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Selfish Strategy 1: Take Large Risks (Think of a Call Option) The GambleProbabilityPayoff Win Big10%$1,000 Lose Big90%$0 Cost of investment is $200 (all the firm’s cash) Required return is 50% Expected CF from the Gamble = $1000 × 0.10 + $0 = $100

65. 22-64 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Selfish Stockholders Accept Negative 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.

66. 22-65 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 22.11 Mergers and Options This is an area rich with optionality, both in the structuring of the deals and in their execution.

67. 22-66 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.

68. 22-67 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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

69. 22-68 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited 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.