OPTIONS AND CORPORATE SECURITIES Chapter 25

25-1 Chapter Outline Options: The Basics Fundamentals of Option Valuation Valuing a Call Option Employee Stock Options Equity as a Call Option on the Firm’s Assets Warrants Convertible Bonds Reasons For Issuing Warrants and Convertibles Other Options

25-2 Option Terminology 25.1 Call Put Strike or Exercise price Expiration date Option premium Option writer American Option European Option LO1

25-3 Stock Option Quotations Look at Figure 25.1 in the book ◦ Price and volume information for calls and puts with the same strike and expiration Things to notice ◦ Prices are higher for options with the same strike price but longer expirations ◦ 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 LO1

25-4 Option Payoffs – Calls 25.2 The value of the call at expiration is the intrinsic value ◦ C 1 = Max(0, S 1 - K) ◦ If S 1 <K, then the payoff is 0 ◦ If S 1 >K, then the payoff is S 1 – K Assume that the strike price is $30 LO1

25-5 Option Payoffs - Puts The value of a put at expiration is the intrinsic value ◦ P 1 = Max (0, K – S 1 ) ◦ If S 1 <K, then the payoff is E-S 1 ◦ If S 1 >K, then the payoff is 0 Assume that the strike price is $40 LO1

25-6 Work the Web Example Where can we find option prices? On the Internet, of course. One site that provides up-to-date option pricing information is the Montreal Exchange website. Click on the web surfer to go to the MX ◦ Follow the options link ◦ Look at the trading strategies that use options ◦ Check out the Options FAQ LO1

25-7 Call Option Bounds Upper bound ◦ Call price must be less than or equal to the stock price Lower bound ◦ 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 LO2

25-8 Figure 25.3 – Value of a call option before expiration LO2

25-9 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(K) If the call is worth something other than this, then there is an arbitrage opportunity LO2

25-10 What Determines Option Values? Stock price ◦ As the stock price increases, the call price increases and the put price decreases Exercise price ◦ As the exercise price increases, the call price decreases and the put price increases Time to expiration ◦ Generally, as the time to expiration increases both the call and the put prices increase Risk-free rate ◦ As the risk-free rate increases, the call price increases and the put price decreases LO2

25-11 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 LO2

25-12 Table 25.1 – Five factors that determine option values LO2

25-13 Employee Stock Options 25.4 Options that are given to employees as part of their benefits package Often used as a bonus or incentive ◦ Designed to align employee interests with stockholder interests and reduce agency problems ◦ Empirical evidence suggests that they don’t work as well as anticipated due to the lack of diversification introduced into the employees’ portfolios ◦ The stock just isn’t worth as much to the employee as it is to an outside investor LO4

25-14 Figure 25.4 – Executive stock options in Canada LO4

25-15 Equity: A Call Option 25.5 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 comes due, the option will be exercised and the stockholders retain ownership If the assets are worth less than the debt, the stockholders will let the option expire and the assets will belong to the bondholders LO3

25-16 Example: Equity as a Call Option ABC Company has a current value of $1,000 and debt outstanding consisting of a zero-coupon bond with a face value of $1,000 due in one year. The risk-free rate is 10% per year. Assume that the value of the firm’s asset will either increase to $1,500 or decrease to $500. What is the current value of the firm’s debt and equity? LO3

Example – continued UpDown Assets1, Debt1, Equity5000 If the value of the firm goes up to $1,500, then the debt will be paid off in full and the equity will be worth $500 If the value of the firm drops to $500, then the debt will only receive $500 and the equity would receive nothing LO3

Example – continued To find the current value of the debt and equity, we form a portfolio that replicates the firm’s assets which consists of an investment of $500 in a risk-free asset and a long position in two call options on the firm’s assets with a strike price of $1,000. How did we decide on the number of calls  Delta = ( ) =2  (500-0) LO3

Example – continued UpDown Assets1, Replicating Portfolio 1. Risk-free debt Two call options 2 max(0, ) =1,000 2 max(0, ) = 0 Total1, LO3

Example – continued If you have two portfolios that have the same payoff at some point in the future, then they have to be worth the same today PV of replicating portfolio = Current Value of Firm LO3

25-21 Example – continued The current value of the firm’s equity is $ V = D + E D = 1,000 – = Therefore, the value of the firm’s debt is $ LO3

25-22 Example: Equity as a Call Option Mega Company has a current value of $110 and debt outstanding consisting of a discount bond with a face value of $100 due in one year. The risk-free rate is 10% per year. Assume that the value of the firm’s asset will either increase to $160 or decrease to $55. What is the current value of the firm’s debt and equity? LO3

Example – continued UpDown Assets16055 Debt10055 Equity600 If the value of the firm goes up to $160, then the debt will be paid off in full and the equity will be worth $60 If the value of the firm drops to $55, then the debt will only receive $55 and the equity would receive nothing LO3

Example – continued To find the current value of the debt and equity, we form a portfolio that replicates the firm’s assets which consists of an investment of in a risk-free asset that will have FV of $55 (out of the money outcome) and a long position in N call options on the firm’s assets with a strike price of $100 (FV of debt). How did we decide on the number of calls  Delta = (160-55) =1.75  (60-0) LO3

Example – continued UpDown Assets16055 Replicating Portfolio 1. Risk-free debt call options 1.75 max(0, ) =105 2 max(0, ) = 0 Total16055 LO3

Example – continued If you have two portfolios that have the same payoff at some point in the future, then they have to be worth the same today PV of replicating portfolio = Current Value of Firm LO3

25-27 Example – continued The current value of the firm’s equity is $34.29 V = D + E D = 110 –34.29 = Therefore, the value of the firm’s debt is $75.71 Cost of debt =? LO3

25-28 Warrants 25.6 A security that gives the holder the right to purchase shares of stock at a fixed price over a given period of time It is basically a call option issued by corporations in conjunction with other securities to reduce the yield Usually included with a new debt or preferred shares issue as a sweetener or equity kicker LO5

25-29 Differences between warrants and traditional call options Warrants are generally very long term They are written by the company and exercise results in additional shares outstanding The exercise price is paid to the company and generates cash for the firm Warrants can be detached from the original securities and sold separately LO5

25-30 Convertible Bonds 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. It is the dollar amount of a bond’s par value that is exchangeable for one share of stock LO5

25-31 Convertibles – continued The conversion ratio is the number of shares received when the bond is converted Conversion Premium – The difference between the conversion price and the current stock price divided by the current stock price Straight Bond Value – The value of a convertible bond if it could not be converted into common stock LO5

25-32 Convertibles – continued Floor Value – Either the straight bond value or the conversion value Convertible bonds will be worth at least as much as the straight bond value or the conversion value, whichever is greater LO5

Figure 25.5 – Minimum value of a convertible bond versus the value of the stock for a given interest rate LO5

25-34 Figure 25.6 – Value of a convertible bond versus value of the stock for a given interest rate LO5

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 = ◦ Conversion ratio = 1000/100 = 10 ◦ Conversion value = 10*110 = 1100 ◦ Minimum price = $1100 LO5

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 LO5

Table 25.3 – The case for and against convertibles LO5

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 LO5

Other Options continued Over allotment 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 LO5

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?

Summary 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

Key Concepts and Skills Know 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 Know how to value a firm’s equity as an option on the firm’s assets and use option valuation to evaluate capital budgeting projects Understand the basics of employee stock options and their benefits and disadvantages Understand convertible bonds and warrants and how to value them