1. © 2003 The McGraw-Hill Companies, Inc. All rights reserved. Options and Corporate Securities Chapter Twenty-Five

2. 25.1 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Option Terminology 25.1 Call Put Strike or Exercise price Expiration date Option premium Option writer American Option European Option

3. 25.2 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Options: The Basics An option gives the owner of the option the right, but not the obligation, to buy or sell a certain asset at a fixed price (the strike price or exercise price) during a specified period of time. Options on stock and other assets are examples of derivative securities. The value of an option is derived from the price and other features of the underlying assets. The act of purchasing or selling the underlying asset, as specified in the option contract, is referred to as exercising the option. The maturity date of the option is called the expiration date; the owner of the option cannot exercise the option after the expiration date.

4. 25.3 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Options: The Basics (cont.) An American option can be exercised anytime up to the expiration date. A European option can be exercised only on the expiration date. Options on stocks and bonds are traded on several exchanges, the largest of which is the Chicago Board Options Exchange (CBOE). Option trading in Canada began in 1975 on the Montreal Exchange.

5. 25.4 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Stock Option Quotations Things to notice –Prices are higher for options with the same strike price but longer expirations (why?) –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 –C = Max(0, S - E), P = Max (0, E – S)

6. 25.5 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Variable Explanation S 1 = Stock price at expiration (in one period) S 0 = Stock price today C 1 = Value of the call option on the expiration date (in one period) C 0 = Value of the call option today P 1 = Value of the put option on the expiration date (in one period) P 0 = Value of the put option today E = Exercise price on the option

7. 25.6 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Option Payoffs – Calls 25.2 The value of the call at expiration is the intrinsic value –C 1 = Max(0, S 1 - E) –If S 1 <E, then the payoff is 0 –If S 1 >E, then the payoff is S 1 – E Assume that the exercise price is $35

8. 25.7 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example 1 Suppose that on October 1, an investor purchases a call option to buy 100 shares of The Bank of Montreal (BOM) common stock: the expiration date is the third Friday in December; the exercise price is $30; the price of the option is quoted as $1½; the current market price of BOM stock is $27½. How much does the investor pay for the option? What is the investor’s gain (or loss) if the price of BOM stock declines to $25 between October 1 and the third Friday in December? What is the investor’s gain (or loss) if the price of BOM stock increases to $32.75?

9. 25.8 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example 1 (cont.) The price of the option is $1½ per share, or a total cost of $150 (i.e., the option contract costs $1½ x 100 = $150). If the price of BOM stock declines to $25, the investor would not exercise the option (i.e., he would not choose to purchase 100 shares of stock at $30 per share at a time when the market price of the stock is less than $30 per share). When the market price of the stock is less than the exercise price of the call option, the option is said to be “out of the money.” If on the expiration date, the market price of the stock is less than the exercise price of the option, then the option is worthless; the investor has lost $150 on the transaction, the purchase price of the option, because the option expired out of the money.

10. 25.9 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example 1 (cont.) If the price of the stock exceeds the exercise price, then the option is “in the money.” When the price of the stock is $32.75 on the expiration date; the owner of the option could exercise the option for a profit. The investor can exercise the option and purchase 100 shares of stock for ($30x100) $3,000, and then immediately sell the shares for ($32.75x100) $3,275. The investor’s profit is ($3,275 - $3,000) $275, less the $150 purchase price of the option, for a net profit of ($275 - $150) $125.

11. 25.10 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Option Payoffs - Puts The value of a put at expiration is the intrinsic value –P 1 = Max (0, E – S 1 ) –If S 1 <E, then the payoff is E-S 1 –If S 1 >E, then the payoff is 0 Assume that the exercise price is $35

12. 25.11 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example 2 On October 1, an investor purchases a Times Mirror December 30 put, currently quoted at $3. The market price of Times Mirror stock is $27½. What is the investor’s gain (or loss) if the price of Times Mirror stock declines to $25 between October 1 and the third Friday in December? What is the investor’s gain (or loss) if the price of Times Mirror stock increases $32?

13. 25.12 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example 2 (cont.) A put is “in the money” if the market price is less than the exercise price and is “out of the money” if the market price exceeds the exercise price. If the market price of Times Mirror stock is $25 on the expiration date, the investor will exercise the option That is to say, he will buy 100 shares in the market for ($25x100) $2,500, and then sell the 100 shares for the writer of the call option for ($30x100) $3,000). The profit from this transaction is ($3,000 - $2,500) $500. Since the purchase price of the option is ($3x100) $300, the investor’s net profit is ($500 - $300) $200.

14. 25.13 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example 2 (cont.) The writer of the option incurs a loss of $500 when the put is exercised; he is obligated to purchase, for $3,000, stock with a market value of only $2,500. This loss is partially offset by the $300 he received when he sold the option, so that his net profit is ($300 - $500) -$200, or a $200 loss. If the market price exceeds the exercise price, the put owner will not exercise the option. If the market price is $32 on the expiration date, the owner of the option would not choose to exercise an option to sell, at $30 per share, stock which can be sold in the market for $32 per share.

15. 25.14 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example 2 (cont.) Consequently, the option expires out of the money; the buyer of the option loses the $300 he paid to acquire the option., while the option writer has a net profit of $300.

16. 25.15 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Call Option Bounds Upper bound –Since a call option is simply the right to buy the stock, the option cannot be worth more than the stock. –Call price must be less than or equal to the stock price –C 0 ≤ S 0

17. 25.16 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Call Option Bounds (cont.) Lower bound –The lower bound on the value of a call option depends on whether the option is in or out of the money. –The value of the call option at expiration is equal to zero if the option is out of the money. –A call that is in the money prior to expiration is worth at least the difference between the value of the stock and the exercise price of the call. –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

18. 25.17 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Figure 25.3 – Value of a call option before expiration

19. 25.18 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. 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-the-money, the option value would be C 0 = S 0 – PV(E) = S 0 – [E / (1+R f )] If the option expires in t time periods C 0 = S 0 – [E / (1+R f )]^t If the call is worth something other than this, then there is an arbitrage opportunity

20. 25.19 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example 3 Suppose a share of stock is currently selling for $100, and the risk-free rate (R f ) is 10%. Also assume that, one year from now, the stock price will be either $105 or $120. A call option with expiration in one year has an exercise price of $100. Suppose that in addition to buying the option today, you also lend an amount equal to the present value of the exercise price. How much is the call worth today?

21. 25.20 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example 3 (cont.) One year from now, the stock will be worth either $105 or $120. If you buy the option today, you will have either ($105 - $100) $5 or ($120 - $100) $20 one year from now. Since you also lend an amount equal to the present value of the exercise price: ($100 / 1.10) = $90.91. At the end of the year, you have $100 from the repayment of the loan and either $5 or $20 from the exercise of the option. The total return is either ($100+$5) $105 or ($100+$20) $120. The strategy of buying and lending $90.91 has the same possible future returns as does the strategy of simply buying the stock. Since the two strategies have the same future returns, they must have the same value today.

22. 25.21 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example 3 (cont.) Therefore, the value of the call option plus the present value of the exercise price must be the same as the price of the stock: C 0 + $90.91 = $100 C 0 = $9.09 Therefore, the value of the call option is $9.09

23. 25.22 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. What Determines Option Values? Stock price –As the stock price (S 0 ) increases, the call price increases and the put price decreases Exercise price –As the exercise price (E) increases, the call price decreases and the put price increases Time to expiration (t) –Generally, as the time to expiration increases both the call and the put prices increase since this provides the holder of the option a longer period of time during which to exercise it.

24. 25.23 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. What Determines Option Values? (cont.) Risk-free rate –As the risk-free rate (R f ) increases, the call price increases and the put price decreases –The purchase of a call option will pay the exercise price at some future date –The higher the interest rate, the lower the present value of this future amount –Thus, the higher the interest rate, the more the call option is worth

25. 25.24 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. 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

26. 25.25 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Table 25.1 – Five factors that determine option values

27. 25.26 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Employee Stock Options 25.4 An Employee Stock Option (ESO) gives an employee the right to purchase shares of a stock at a fixed price for a fixed period. ESOs are quite common; one study found that at the end of 1994, 90% of firms listed on the Toronto Stock Exchange used stock options.

28. 25.27 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Employee Stock Options Features ESOs are call options, but include several unique features. ESOs tend to have longer lives than regular options, typically 10 years. For a period of time known as the “vesting” period the ESO cannot be exercised. Holders of ESOs may be forced to exercise following resignation from the company. Firms grant ESOs to align shareholder and management interests and to motivate employees.

29. 25.28 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Employee Stock Options Features (cont.) Executives granted many ESOs can become very wealthy if the firm does well. Firms grant ESOs when they do not have enough cash to pay ordinary wages. Since ESOs do not require any cash outlay upfront, they provide a tempting alternative form of compensation.

30. 25.29 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Employee Stock Options Repricing When issued, the strike price associated with the ESO is equal to the stock price. The ESO is “underwater” in situations where the stock price falls significantly. ESO repricing may occur in such situations, through designating a new strike price. Repricing occurs to maintain the incentive associated with the ESOs. Some critics argue that repricing represents an award for failing, effectively undercutting the motivational benefits associated with ESOs.

31. 25.30 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Figure 25.4 – Executive stock options in Canada

32. 25.31 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Equity: A Call Option The financial decision-making process can often be reformulated in terms of options. Corporate securities can be viewed as options on the value of the firm. Suppose a firm has a single debt issue coming due in one year. At that time, the shareholders will have a choice. If the value of the firm (V 1 ) exceeds the face value of the debt (D 1 ), then the shareholders will payoff the debt and the stock will be worth S 1 = (V 1 - D 1 ). By paying off the debt, the shareholders own the assets of the firm.

33. 25.32 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Equity: A Call Option (cont.) If V 1 is less than D 1, then the shareholders will not exercise their option to acquire the firm’s assets, and the bondholders will own the firm. The stock (equity) is worth zero in this case. Consequently, the equity in a firm with debt can be viewed as a call option on the assets of the firm. The bondholder’s own the firm and they have written a call option against the value of the firm, with an exercise price equal to the value of the debt.

34. 25.33 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example A firm has a $500 debt issue due in one year. The risk-free rate is 10%, and the current market-value of the firm’s assets is $475. What is the value today of the equity in the firm?

35. 25.34 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example (cont.) The firm’s shareholders own a call option on the firm’s assets. The exercise price of the option is $500. C 0 = S 0 – [E / (1+R f )]^t = $475 - $500 / (1.10) = $20.45 Therefore, the firm’s equity is worth $20.45

36. 25.35 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Warrants A warrant gives the holder the right to buy common stock directly from the company at a fixed price during a specified time period. To the holder, a warrant is essentially a call option, although warrants usually have longer maturities. Typically, warrants are attached to the bond with which they are issued; however, some warrants are detachable, which means the warrants can be sold separately from the bond.

37. 25.36 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Difference between Warrants and Call Options To a firm, a warrant is substantially different from a call option. -A call option sold on the firm’s stock is a private transaction between investors, in which the firm is not directly involved. -When a call option is exercised, existing stock merely changes hands, but when a warrant is exercised, the firm must issue new stock (i.e., exercise results in additional shares outstanding so the earnings per share will be diluted) -In case of warrants, the exercise price is paid to the company and generates cash for the firm -Warrants are generally very long term. -Warrants can be detached from the original securities and sold separately

38. 25.37 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Convertibles 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 The conversion ratio is the number of shares received when the bond is converted Convertible bonds will be worth at least as much as the straight bond value or the conversion value, whichever is greater

39. 25.38 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Figure 25.5 – Minimum value of a convertible bond versus the value of the stock for a given interest rate

40. 25.39 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Figure 25.6 – Value of a convertible bond versus value of the stock for a given interest rate

41. 25.40 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Valuing Convertibles Suppose you have a 10% bond that pays semi-annual 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

42. 25.41 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. 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

43. 25.42 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Table 25.3 – The case for and against convertibles

44. 25.43 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. 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 Overallotment 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

45. 25.44 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. 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