Prepared by Professor Wei Wang Queen’s University © 2011 McGraw–Hill Ryerson Limited Options and Corporate Finance: Basic Concepts Chapter Twenty Three

2-1 © 2011 McGraw–Hill Ryerson Limited 23-1 Chapter Outline 23.1 Options 23.2 Call Options 23.3 Put Options 23.4 Selling Options 23.5 Stock Option Quotations 23.6 Combinations of Options 23.7 Valuing Options 23.8 An Option ‑ Pricing Formula 23.9 Stocks and Bonds as Options Capital-Structure Policy and Options Mergers and Options Investment in Real Projects and Options Summary and Conclusions

2-2 © 2011 McGraw–Hill Ryerson Limited 23-2 Options LO23.1 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.

2-3 © 2011 McGraw–Hill Ryerson Limited 23-3 Options Contracts: Preliminaries LO23.1 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.

2-4 © 2011 McGraw–Hill Ryerson Limited 23-4 Options Contracts: Preliminaries LO23.1 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.

2-5 © 2011 McGraw–Hill Ryerson Limited 23-5 Options Contracts: Preliminaries LO23.1 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.

2-6 © 2011 McGraw–Hill Ryerson Limited 23-6 Options Contracts: Preliminaries LO23.1 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 +

2-7 © 2011 McGraw–Hill Ryerson Limited 23-7 Call Options LO23.2 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.

2-8 © 2011 McGraw–Hill Ryerson Limited 23-8 Basic Call Option Pricing Relationships at Expiry LO23.2 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

2-9 © 2011 McGraw–Hill Ryerson Limited 23-9 Call Option Payoffs LO23.2 – – Stock price ($) Option payoffs ($) Buy a call Exercise price = $50 50

2-10 © 2011 McGraw–Hill Ryerson Limited Call Option Payoffs LO23.2 – – Stock price ($) Option payoffs ($) Sell a call Exercise price = $50 50

2-11 © 2011 McGraw–Hill Ryerson Limited Call Option Profits LO23.2 Exercise price = $50; option premium = $10 Sell a call Buy a call – – Stock price ($) Option payoffs ($) 50 –10 10

2-12 © 2011 McGraw–Hill Ryerson Limited Put Options LO23.3 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.

2-13 © 2011 McGraw–Hill Ryerson Limited Basic Put Option Pricing Relationships at Expiry LO23.3 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] where P aT is the value of an American call at expiry P eT is the value of a European call at expiry

2-14 © 2011 McGraw–Hill Ryerson Limited Put Option Payoffs LO23.3 – – Stock price ($) Option payoffs ($) Buy a put Exercise price = $50 50

2-15 © 2011 McGraw–Hill Ryerson Limited Put Option Payoffs LO23.3 – – –50 Stock price ($) Option payoffs ($) Sell a put Exercise price = $50 50

2-16 © 2011 McGraw–Hill Ryerson Limited Put Option Profits LO23.3 – – Stock price ($) Option payoffs ($) Buy a put Exercise price = $50; option premium = $10 –10 10 Sell a put 50

2-17 © 2011 McGraw–Hill Ryerson Limited Selling Options LO23.4 Exercise price = $50; option premium = $10 Sell a call Buy a call –40 40 Stock price ($) Option profits ($) Buy a put Sell a put The seller (or writer) of an option has an obligation. The purchaser of an option has an option (right). –10 10 Buy a call Sell a put Buy a put Sell a call

2-18 © 2011 McGraw–Hill Ryerson Limited Stock Option Quotations LO23.5

2-19 © 2011 McGraw–Hill Ryerson Limited Stock Option Quotations LO23.5 This option has a strike price of $8; A recent price for the stock is $9.35 June is the expiration month

2-20 © 2011 McGraw–Hill Ryerson Limited Stock Option Quotations LO23.5 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.

2-21 © 2011 McGraw–Hill Ryerson Limited Stock Option Quotations LO23.5 On this day, 15 call options with this exercise price were traded.

2-22 © 2011 McGraw–Hill Ryerson Limited Stock Option Quotations LO23.5 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.

2-23 © 2011 McGraw–Hill Ryerson Limited Stock Option Quotations LO23.5 Buying this CALL option costs $2.10. Since the option is on 100 shares of stock, buying this option would cost $210.

2-24 © 2011 McGraw–Hill Ryerson Limited Stock Option Quotations LO23.5 On this day, there were 660 call options with this exercise outstanding in the market.

2-25 © 2011 McGraw–Hill Ryerson Limited Combinations of Options LO23.6 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.

2-26 © 2011 McGraw–Hill Ryerson Limited Protective Put Strategy: Buy a Put and Buy the Underlying Stock: Payoffs at Expiry (Figure 23.4) LO23.6 Buy a put with an exercise price of $50 Buy the stock Protective Put payoffs $50 $0 $50 Value at expiry Value of stock at expiry

2-27 © 2011 McGraw–Hill Ryerson Limited Protective Put Strategy Profits LO23.6 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 -$10

2-28 © 2011 McGraw–Hill Ryerson Limited Covered Call Strategy Profits LO23.6 Sell a call with exercise price of $50 for $10 Buy the stock at $40 $40 Covered Call strategy $0 -$40 $50 Value at expiry Value of stock at expiry -$30 $10

2-29 © 2011 McGraw–Hill Ryerson Limited Long Straddle: Buy a Call and a Put LO Stock price ($) Buy a put with exercise price of $50 for $10 Buy a call with exercise price of $50 for $10 A Long Straddle only makes money if the stock price moves $20 away from $50. $50 –20 Value at expiry

2-30 © 2011 McGraw–Hill Ryerson Limited Short Straddle: Sell a Call and a Put LO23.6 – –40 Stock price ($) $50 This Short Straddle only loses money if the stock price moves $20 away from $50. Sell a put with exercise price of $50 for $10 Sell a call with an exercise price of $50 for $10 20 Value at expiry

2-31 © 2011 McGraw–Hill Ryerson Limited Long Call Spread LO23.6 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

2-32 © 2011 McGraw–Hill Ryerson Limited Bond Put-Call Parity: p 0 + S 0 = c 0 + E/(1+ r) T LO Stock price ($) Option payoffs ($) 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. Call Portfolio payoff Portfolio value today = c 0 + (1+ r) T E

2-33 © 2011 McGraw–Hill Ryerson Limited Put-Call Parity: p 0 + S 0 = c 0 + E/(1+ r) T LO Stock price ($) Option payoffs ($) Consider the payoffs from holding a portfolio consisting of a share of stock and a put with a $25 strike. Portfolio value today = p 0 + S 0 Portfolio payoff Put Stock

2-34 © 2011 McGraw–Hill Ryerson Limited Put-Call Parity: p 0 + S 0 = c 0 + E/(1+ r) T LO23.6 Since these portfolios have identical payoffs, they must have the same value today: hence Put-Call Parity: c 0 + E/(1+r) T = p 0 + S 0 25 Stock price ($) Option payoffs ($) 25 Stock price ($) Option payoffs ($) Portfolio value today = p 0 + S 0 Portfolio value today (1+ r) T E = c 0 +

2-35 © 2011 McGraw–Hill Ryerson Limited Valuing Options LO23.7 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.

2-36 © 2011 McGraw–Hill Ryerson Limited American Option Value Determinants LO23.7 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.

2-37 © 2011 McGraw–Hill Ryerson Limited Market Value, Time Value and Intrinsic Value for an American Call LO23.7 The value of a call option C 0 must fall within max (S 0 – E, 0) < C 0 < S 0. Call STST loss E $ STST Time value Intrinsic value Market Value In-the-moneyOut-of-the-money

2-38 © 2011 McGraw–Hill Ryerson Limited An Option ‑ Pricing Formula LO23.8 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.

2-39 © 2011 McGraw–Hill Ryerson Limited Binomial Option Pricing Model LO23.8 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 $ The risk-free rate is 5%. What is the value of an at-the-money call option? $25 $21.25 = $25×(1 –.15) $28.75 = $25×(1.15) S1S1 S0S0

2-40 © 2011 McGraw–Hill Ryerson Limited Binomial Option Pricing Model LO 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

2-41 © 2011 McGraw–Hill Ryerson Limited Binomial Option Pricing Model LO23.8 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

2-42 © 2011 McGraw–Hill Ryerson Limited Binomial Option Pricing Model LO23.8 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

2-43 © 2011 McGraw–Hill Ryerson Limited Binomial Option Pricing Model LO23.8 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

2-44 © 2011 McGraw–Hill Ryerson Limited Binomial Option Pricing Model LO23.8 If the interest rate is 5%, the call is worth: $25 $21.25 $28.75 S1S1 S0S0 debt - $21.25 portfolio $7.50 $0 ( - ) = = = C1C1 $3.75 $0 - $21.25

2-45 © 2011 McGraw–Hill Ryerson Limited Binomial Option Pricing Model LO23.8 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:

2-46 © 2011 McGraw–Hill Ryerson Limited Delta and the Hedge Ratio LO23.8 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: The delta of a put option is negative.  Swing of call Swing of stock

2-47 © 2011 McGraw–Hill Ryerson Limited Delta LO23.8 Determining the Amount of Borrowing: Value of a call = Stock price × Delta – Amount borrowed $2.38 = $25 × ½ – Amount borrowed Amount borrowed = $10.12

2-48 © 2011 McGraw–Hill Ryerson Limited The Risk-Neutral Approach to Valuation LO23.8 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) q S(D), V(D) 1- q

2-49 © 2011 McGraw–Hill Ryerson Limited The Risk-Neutral Approach to Valuation LO23.8 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.

2-50 © 2011 McGraw–Hill Ryerson Limited The Risk-Neutral Approach to Valuation LO23.8 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:

2-51 © 2011 McGraw–Hill Ryerson Limited Example of the Risk-Neutral Valuation of a Call: LO23.8 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)

2-52 © 2011 McGraw–Hill Ryerson Limited Example of the Risk-Neutral Valuation of a Call: LO23.8 The next step would be to compute the risk neutral probabilities $21.25,C(D) 2/3 1/3 $25,C(0) $28.75,C(D)

2-53 © 2011 McGraw–Hill Ryerson Limited Example of the Risk-Neutral Valuation of a Call: LO23.8 After that, find the value of the call in the up state and down state. $21.25, $0 2/3 1/3 $25,C(0) $28.75, $3.75

2-54 © 2011 McGraw–Hill Ryerson Limited Example of the Risk-Neutral Valuation of a Call: LO23.8 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

2-55 © 2011 McGraw–Hill Ryerson Limited Risk-Neutral Valuation and the Replicating Portfolio LO23.8 This risk-neutral result is consistent with valuing the call using a replicating portfolio.

2-56 © 2011 McGraw–Hill Ryerson Limited The Black-Scholes Model LO23.8 The Black-Scholes Option Pricing Model: Where C 0 = the value of a European option at time t = 0 r = the continuously-compounded 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.

2-57 © 2011 McGraw–Hill Ryerson Limited The Black-Scholes Model LO23.8 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 continuously-compounded 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.

2-58 © 2011 McGraw–Hill Ryerson Limited The Black-Scholes Model LO23.8 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

2-59 © 2011 McGraw–Hill Ryerson Limited The Black-Scholes Model LO23.8 N(d 1 ) = N( ) = N(d 2 ) = N( ) =

2-60 © 2011 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 ) = and N(d 2 ) = (or use Excel’s “normsdist” function) Another Black-Scholes Example

2-61 © 2011 McGraw–Hill Ryerson Limited Stocks and Bonds as Options LO23.9 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.

2-62 © 2011 McGraw–Hill Ryerson Limited Stocks and Bonds as Options LO23.9 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.

2-63 © 2011 McGraw–Hill Ryerson Limited Stocks and Bonds as Options LO23.9 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 c 0 = S 0 + p 0 – (1+ r) T E

2-64 © 2011 McGraw–Hill Ryerson Limited Capital-Structure Policy and Options LO23.10 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.

2-65 © 2011 McGraw–Hill Ryerson Limited Balance Sheet for a Company in Distress LO23.10 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. $200 $0

2-66 © 2011 McGraw–Hill Ryerson Limited Selfish Strategy 1: Take Large Risks (Think of a Call Option) LO23.10 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 = $100 NPV = –$200 + $100 (1.10) NPV = –$133

2-67 © 2011 McGraw–Hill Ryerson Limited Selfish Stockholders Accept Negative NPV Project with Large Risks LO23.10 Expected cash flow from the Gamble –To Bondholders = $300 × $0 = $30 –To Stockholders = ($ $300) × $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.

2-68 © 2011 McGraw–Hill Ryerson Limited Mergers and Options LO23.11 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.

2-69 © 2011 McGraw–Hill Ryerson Limited Mergers and Options LO23.11 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 $0 Value of General Mills in 1 year $42.55 $38 $4.55

2-70 © 2011 McGraw–Hill Ryerson Limited Mergers and Options LO23.11 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 $ –But the shareholders of Diageo sold a put with an exercise price of $38

2-71 © 2011 McGraw–Hill Ryerson Limited Mergers and Options LO23.11 $38 $0 Value of General Mills in 1 year $42.55 –$38 Own a put Strike $42.55 Sell a put Strike $38 – $38.00 $4.55 $42.55 Cash payment to newly issued shares

2-72 © 2011 McGraw–Hill Ryerson Limited Mergers and Options LO23.11 Value of a share $38 $4.55 $0 $42.55 Value of General Mills in 1 year Value of a share plus cash payment $42.55

2-73 © 2011 McGraw–Hill Ryerson Limited Investment in Real Projects & Options LO23.12 Classic NPV calculations typically ignore the flexibility that real-world firms typically have. The next chapter will take up this point.

2-74 © 2011 McGraw–Hill Ryerson Limited Summary and Conclusions LO23.13 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

2-75 © 2011 McGraw–Hill Ryerson Limited Summary and Conclusions LO23.13 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.

2-76 © 2011 McGraw–Hill Ryerson Limited Quick Quiz What is the difference between call and put options? What are the major determinants of option prices? What is put-call parity? What would happen if it does not hold? What is the Black-Scholes option pricing model? How can equity be viewed as a call option? Should management ever accept a negative NPV project? If yes, under what circumstances?