1. . Chapter Twenty Derivative securities Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 1

2. . Chapter Organisation 20.1Options: the basics 20.2Fundamentals of option valuation 20.3Valuing a call option 20.4Black–Scholes option pricing model 20.5Equity as a call option on the firm’s assets 20.6Types of equity option contracts 20.7 Futures contracts 20.8Term structure of interest rates Summary and conclusions Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 2

3. . Chapter Objectives Understand the basics of call and put options, and how to calculate their payoffs and profits. Understand the factors that affect option values, and how to price call and put options using no arbitrage conditions. Understand the famous Black–Scholes option pricing model and its uses. Understand how the five factors in the Black–Scholes formula affect the value of an option. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 3

4. . Chapter Objectives (cont’d) Understand how the Black–Scholes model can be used to value the debt and equity of a firm. Understand the exposures of risk in a company’s business, and how a company could choose to hedge these risks. Understand the similarities and differences between futures and forward contracts, and how these contracts are used to hedge risk. Understand the payoffs of option contracts, and how they are used to hedge risk. Understand the basics of convertible bonds and warrants, and how to value them. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 4

5. . Option Terminology Call option –Right to buy a specified asset at a specified price, on or before a specified date. Put option –Right to sell a specified asset at a specified price, on or before a specified date. European option –An option that can only be exercised on a particular date (on expiry). American option –An option that can be exercised at any time up to its expiry date. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 5

6. . Option Terminology (cont’d) Striking price or exercise price –The contracted price at which the underlying asset can be bought (call) or sold (put). Expiration date – The date at which an option expires. Option premium –The price paid by the buyer for the right to buy (call) or sell (put) an asset –The price received by the seller for the obligation to sell (call) or buy (put) an asset. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 6

7. . Option Terminology (cont’d) Exercising the option –The act of buying or selling the underlying asset via the option contract. Option writer –The writer of an option is the seller of the option. The writer is obligated to perform according to the terms of the option if and when an exercise is enforced. Option buyer –The buyer of an option is the taker or holder of the option. The option buyer obtains the right conveyed by the option and only the option buyer has a right to exercise an option. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 7

8. . Australian Options Market Contract Characteristics Expiration month –The month in which the option expires. Option type –All options are American options so that they can be exercised at any time prior to expiration. Contract size –The standard contract size is 1 000 shares. –When a share on which there exists a traded option undergoes a capital issue (bonus issue, share split, etc.) an adjustment is made to one or more of the:  Exercise price  The number of options outstanding  The number of shares to which each option contract relates. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 8

9. . Australian Options Market Contract Characteristics (cont’d) Expiry –The maturity date for an option series is the last Friday of the expiration month, or if not a business day, the next business day. Exercise price –A new series is generally opened for trading approximately nine months prior to the expiration month. –Exercise prices are set ‘reasonably close’ to the prevailing market price of the underlying share. –Additional exercise prices are added by the Exchange on an ad hoc basis, depending upon price movements of the underlying share. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 9

10. . A Sample Newspaper Listing of Call Options Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 10

11. . Work the Web Example Where can we find option prices? On the Internet, of course. One site that provides option prices is the ASX Click on the web surfer to go to the ASX Website –Enter a ticker symbol to get a basic quote Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 11

12. . Clearing and Margining Premium payable in full by buyer (taker) and credited to account of seller (writer) at time of trade. At the same time, seller must lodge a deposit with the Clearing House to ensure performance in the event of price movement adverse to the position of seller. Deposit levels vary depending on value of underlying shares, and extent to which share price changes. The margin is comprised of two components: –Premium margin –Risk margin. –Premium reflects the value of the contract, and risk margin reflects amount by which the value could change in a day. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 12

13. . Option Valuation S 1 = share price at expiration S 0 = share price today C 1 = value of call option on expiration C 0 = value of call option today E = exercise price on the option Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 13

14. . Value of Call Option at Expiration Option is out of the money. Option is in the money. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 14

15. . Value of Call Option at Expiration Share price at expiration (S 1 ) Call option value at expiration (C 1 ) S 1  E S 1 > E Exercise price (E) 45 ° Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 15

16. . Call Option Boundaries Upper bound —a call option will never be worth more than the share itself: C 0  S 0 Lower bound —share price cannot fall below 0, and to prevent arbitrage, the call value must be the larger of 0 or (S 0 – E). Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 16

17. . Call Option Boundaries (cont’d) Opportunities for riskless profits are called arbitrages. In a well-organised market, significant arbitrages are rare. Option price = Intrinsic value + Time value. Intrinsic value: what the option would be worth if it were about to expire = lower bound Time value: the amount investors will pay for the possibility of making a profit. For example, XYZ shares are $5.00, exercise price is $4.75, and option price is $0.59 ($0.25 intrinsic value + $0.34 time value). Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 17

18. . Value of a Call Option Before Expiration Share price (S 0 ) Call price (C 0 ) Exercise price (E) 45° Lower bound C 0  S 0 – E C 0  0 Upper bound C 0  S 0 Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 18

19. . Factors Determining Option Values The value of a call option depends on four factors: –Share price –Exercise price –Time to expiration –Risk-free rate. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 19

20. . Another Factor to Consider? The above four factors are relevant if the option is to finish in the money. If the option can finish out of the money, another factor to consider is volatility. The greater the volatility in the underlying share price, the greater the chance the option has of expiring in the money. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 20

21. . The Factors that Determine Option Value Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 21

22. . Black–Scholes Option Pricing Model Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 22

23. . Black–Scholes Option Pricing Model (continued) Note: The risk-free rate, the standard deviation and the time to maturity must all be quoted using the same time units. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 23

24. . Example—Black–Scholes Option Pricing Model S 0 = $25 E = $20 R f = 8%  = 30%  t = 0.5 years Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 24

25. . Example—Black–Scholes Option Pricing Model (continued) Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 25

26. . Example—Black–Scholes Option Pricing Model (continued) From the cumulative normal distribution table: N(d 1 ) = N(1.34) = 0.9099 N(d 2 ) = N(1.13) = 0.8708 Therefore, the value of the call option is: Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 26

27. . Equity as a Call Option on the Firm’s Assets Equity can be viewed as a call option on the company’s assets when the firm is leveraged. The exercise price is the value of the debt. If the assets are worth more than the debt when it becomes due, the option will be exercised and the shareholders retain ownership. If the assets are worth less than the debt, the shareholders will let the option expire, and the assets will belong to the bondholders. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 27

28. . Equity Option Contracts Types of equity option contracts offered in Australia: –Exchange-traded put and call options on company shares (called ‘share options’ or ‘stock options’). –Exchange-traded long dated contracts issued by a financial institution to holders who can then trade them (called ‘warrants’ in Australia). –Over-the-counter options on company shares (called ‘company options’ in Australia, but ‘warrants’ on international markets). –Convertible notes issued by companies, comprising both a debt and an equity component. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 28

29. . Warrants Warrants are a financial instrument issued by banks and other financial institutions, and are traded on the ASX. They are tradeable securities that give the holder the right to purchase the underlying security at a fixed price, for a fixed period of time. Like options, there are both call and put warrants. Basically, warrants are long-term options. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 29

30. . Warrants (continued) Types of warrants available: –Equity warrants –Fractional warrants –Basket warrants –Fully covered warrants –Index warrants –Instalment warrants –Low exercise price warrants –Endowment warrants –Currency warrants. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 30

31. . Company Options A company option is a security that gives the holder the right to purchase shares in a company at a specified price over a given period of time. Usually offered as a ‘sweetener’ or ‘equity kicker’ to a debt issue. These options are often detached, and sold separately. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 31

32. . Company Options versus Exchange Traded Options Company options have longer maturity periods, and are often European-type options. Company options are issued as part of a capital-raising program and are therefore limited in number. The clearing house has no role in the trading of company options. Company options are issued by firms. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 32

33. . Earnings Dilution Put and call options have no effect on the value of the firm. Company options do affect the value of the firm. Company options cause the number of shares on issue to increase when: –the options are exercised –the debts are converted. This increase does not lower the price per share, but EPS will fall. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 33

34. . Forward Contracts A contract where two parties agree on the price of an asset today to be delivered and paid for at some future date. Legally binding on both parties. Can be tailored to meet the needs of both parties. Positions: –Long —agrees to buy the asset at the future date –Short —agrees to sell the asset at the future date. Can be used to reduce or eliminate uncertainty by setting a buying or selling price in advance. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 34

35. . Futures Contracts An agreement between two parties to exchange a specified asset at a specified price at a specified time in the future. A futures contract is a special type of forward contract that is standardised and traded on an organised exchange. Do not need to own an asset to sell a future contract. Either buy before delivery, or close out position with an opposite market position. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 35

36. . Futures Markets Enable buyers and sellers to avoid risk in commodities (and other) markets with high price variability → hedging. Deposit required by all traders to guarantee performance. Adverse price movements must be covered daily by further deposits called margins (‘marked to market’). Futures also available for short-term interest rates, to protect against interest rate movements. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 36

37. . Futures Quotes Commodity, exchange, size, quote units –The contract size is important when determining the daily gains and losses for marking-to-market. Delivery month –Open price, daily high, daily low, settlement price, change from previous settlement price, contract lifetime high and low prices, open interest –The change in settlement price multiplied by the contract size determines the gain or loss for the day:  Long—an increase in the settlement price leads to a gain  Short—an increase in the settlement price leads to a loss. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 37

38. . Example—Hedging with Wool Futures It is August and Jill Farmer expects to have 5 000 kg of wool to sell in December. Wool futures for December delivery are currently trading at 945 cents per kg. Jill would like to get a price close to that. One standardised contract equals 2 500kg To lock in that price, Jill will need to sell two December futures delivery contracts now (August). The value of her open position will be: 5000kg x 945 cents = $47 250 Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 38

39. . Example—Hedging with Wool Futures (continued) It is now December. The price of wool at auction is 910 cents/kg and December wool futures are also selling for 910 cents/kg. What does Jill do? Jill will now need to close out her position by buying two December wool futures: 5 000kg x 910 cents = $45 500 This gives her a profit on futures of $1 750. Jill will also sell her wool at auction: 5 000kg x 910 cents = $45 500 Her net proceeds are $1 750 + $45 500 = $47 250, or 945 cents/kg, which is the price she wanted. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 39

40. . Example—Hedging with Wool Futures (continued) What if, in December, the price of wool at auction is 975 cents/kg and December wool futures are also selling for 975 cents/kg. What does Jill do this time? Jill will still need to close out her position by buying December wool futures: 5 000kg x 975 cents = $48 750 This time she has a loss on futures of $1 500. Jill will also sell her wool at auction for $48 750. 5 000kg x 975 cents = $48 750 Net proceeds are $48 750 – 1 500 = $47 250, or 945 cents/kg, which again is the price she wanted. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 40

41. . Term Structure of Interest Rates Yield curve shows the different interest rates available for investments of different maturities, at a point in time. The relationship between interest rates of different maturities is called the term structure. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 41

42. . Term Structure of Interest Rates Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 42

43. . Factors Determining the Term Structure Risk preferences —borrowers prefer long- term credit, whereas lenders prefer short- term loans (explains upward-sloping yield curve only). Supply  demand conditions —segmented capital markets can cause supply  demand imbalances (explains all yield curve shapes). Expectations about future interest rates (most favoured explanation). Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 43

44. . Quick Quiz What is the difference between a call option and a put option? What is the intrinsic value of call and put options, and what do the payoff diagrams look like? What are the five major determinants of option prices and their relationships to option prices? What are some of the major capital budgeting options? How would you value a convertible bond? Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 44

45. . Summary and Conclusions Options takers have the right, but not the obligation, to sell (puts) or buy (calls) ordinary shares at a given price during a specified period. Option writers have an obligation to sell (calls) or buy (puts) ordinary shares at a given price during a specified period. The value of any option depends on only five factors: –The price of the underlying asset –The exercise price –The expiration date –The interest rate on risk-free debt –The volatility of the underlying asset’s value. A futures contract can be used to hedge prices. Copyright  2011 McGraw-Hill Australia Pty Ltd PPTs to accompany Fundamentals of Corporate Finance 5e, by Ross, et al. Slides prepared by Tim Whittaker 20 - 45