Copyright ©2003 South-Western/Thomson Learning Chapter 20 Financing with Derivatives.

Chapter 20Financing with Derivatives

Introduction

• This chapter examines the characteristics and valuation of options and option-related financing.

• It explores the concepts necessary to evaluate the impact that decisions to issue or purchase these type of securities have on shareholder wealth.

Classes of Derivatives: Securities

• Options are one of two important classes of so-called derivative securities – that is, securities whose value is derived from another asset.

• Another important class of derivative securities is forward-type contracts, such as futures contracts and forward contracts.

• Swaps are another important class of derivative securities.

Options

• Short-Term options

• Convertible fixed-income securities

• Warrants

• Rights offering

Options: Short-Term Options

• Short-term options on common stocks, stock market indexes (e.g., Standard & Poor’s 500 index), 30-year Treasury bonds (e.g., interest rate options), and foreign currency options (e.g., on the British pound and Japanese yen). These options are traded on organized exchanges, such as the Chicago Mercantile Exchange and the Chicago Board Options Exchange.

Options: Convertible Fixed-Income Securities

• Convertible fixed-income securities, such as debentures or preferred stocks, that may be exchanged for the company’s common stock at the holder’s option. By giving the fixed-income security holder an opportunity to share in any increase in its common stock value, the firm is able to reduce potential conflicts between the fixed-income security holders and stockholders, resulting in lower agency costs.

Options: Warrants

• Warrants, which are options issued by a company to purchase shares of the company’s common stock at a particular price during a specified period of time. Warrants are frequently sold to investors as part of a unit that consists of a fixed-income security with a warrant attached. As a result, warrants are issued by firms for similar reasons as convertible securities.

Options: Rights Offering

• A rights offering occurs when common stockholders are given an option to purchase additional shares of the company’s common stock, in proportion to the fraction they currently own, at a price below the market value.

Option Exchanges

• http://www.aantix.com/

• http://www.cboe.com/

• http://www.cbot.com/

• http://www.cme.com/

Option

CallCall

PutPut

Option to buybuy

Option to sell

Options to Buy and Sell

• An option is a security that gives its holder the right, but not the obligation, to buy or sell an asset at a set price (the exercise price) during a specified time period.

• A call is an option to buy a particular asset.

• A put is an option to sell a particular asset.

Call Option Valuation

• At expiration = Stock price – Exercise price

• Prior to expiration > Stock price – Exercise price

• Maximum value = Stock price

• Minimum value = 0

• Suppose an investor is offered an opportunity to purchase a call option on one share of McKean Company stock. Consider the following possible sets of conditions (see Figure 20.1):

• The option’s exercise price is $25; the McKean stock price is $30 a share; and the option’s expiration date is today. Under these conditions, the investor is willing to pay $5 for the option. In other words, the value of a call option is equal to the stock price minus the exercise price, or

Value of a call option at expiration = Stock price – Exercise price

• The option’s exercise price is $25; the McKean stock price is $30 a share; and the option expires in six months. Given these conditions, the investor is willing to pay more than $5 for the option because of the chance that the stock price will increase, thereby also causing the option to increase in value. Therefore,

Value of a call option prior to expiration > Stock price – Exercise price

• The option’s exercise price is $0.01; the McKean stock price is $30; and the option expires in six months. Under these somewhat unusual conditions, the option investor is willing to pay almost as much as the stock price. However, under no conditions should the investor be willing to pay more than the stock price. Therefore,Maximum value of a call option = Stock price

• The option’s exercise price is $25; the McKean stock price is $0.01; and the option expires today. The investor most likely is willing to pay nothing for the option given these conditions, but the investor also is not willing to pay someone to take the option “off his hands,” because it is an option and can be allowed to expire with no addition cost. Therefore,Minimum value of a call option = 0

Variables Affecting Value

VariablesVariablesaffectingaffecting

the value ofthe value ofan optionan option

Time to expiration date

Interestrates

Expected stockprice volatility

Exercise priceExercise priceStock priceStock price

Relationship Between the Exercise Price and the Stock Price

• For options expiring at the same time, the call option with a lower exercise price sell at a higher price than the option with a higher exercise price because buyers have to pay more money to exercise options with higher exercise prices. Thus, these options have less value to potential buyers.

Relationship Between the Exercise Price and the Stock Price

• The higher the exercise price, given the stock price, the lower the call option value, all other things being equal.

• Because an option’s value (payoff) is dependent, or contingent, on the value of another security (in this case, the underlying stock), an option is said to be a contingent claim.

Time Remaining Until Expiration Date

• An option with the longer time to expiration has a higher value than an option with the shorter time to expiration because investors realize that the underlying stock of the former has a greater chance to increase in value with the more time before expiration.

Time Remaining Until Expiration Date

• The longer the time remaining before the option expires, the higher the option value, all other things being equal. Because of this, an option is sometimes referred to as a “wasting asset.”

Interest Rates

• The buyer of common stock incurs either interest expense (explicit cost) if the purchase funds are borrowed or lost interest income (implicit cost) if existing funds are used for purchase. In either case, an interest cost is incurred.

Interest Rates

• Buying a call option is an alternative to buying stock, and by buying an option, the interest cost associated with holding stock is avoided. Because options are an alternative to ownership, option values are affected by the stock ownership interest costs. As a result, the higher the level of interest rates (and, hence, the interest cost of stock ownership), the higher the call option’s value, all other things being equal.

Expected Stock Price Volatility

• Suppose an investor has a choice of buying a call option on either stock S or stock V. Both stocks currently sell at $50 a share, and the exercise price of both options is $50. Stock S is expected to be the more stable of the two – its value at the time the option expires has a 50 percent chance of being $45 and a 50 percent chance of being $55 a share.

• In valuing the call option on stock S, the investor considers only the $55 price and its probability because if the stock goes to $45 a share, the call option with a $50 exercise price becomes worthless.

• Stock V is expected to be more volatile – its expected value at the time of option expiration has a 50 percent probability of being $30 and a 50 percent probability of being $70 a share. Similarly, in valuing the call option on stock V, the investor considers only the $70 price and its probability.

• The investor now has sufficient information to conclude that the call option on stock V is more valuable than the call option on stock S because a greater return can be earned by investing in an option that has a 50 percent chance of being worth $20 (stock price – exercise price = $70 – $50 = $20) at expiration than an option that has a 50 percent probability of being worth $5 (stock price – exercise price = $55 – $50 = $5) at expiration.

• Therefore, the greater the expected stock price volatility, the higher the call option value, all other things being equal.

The Foundations of Option Valuation

• The valuation of a call of option was determined to be a function of the following variables:– The current price of the asset underlying the

option. In the case of stock options this is the price of the common stock on which the option has been written.

– The exercise price of the option.

– The time remaining until the option expires.– The risk-free rate of interest.– The probability of the underlying asset, e.g.,

the share of stock on which the option was written.

• The Black-Scholes model was developed from the premise that a strategy of borrowing to buy stock can exactly equal the risk associated with the purchase of a call option. Because the price of a common stock is readily observable, as is the borrowing rate, they showed that it is possible to derive the theoretically correct value for a call option.

• The Black-Scholes model is based on the following assumptions:– The stock pays no dividends during the life

of the option. Although this might seem like a serious limitation of the model, other models have been developed that take dividends into account. A common way of adjusting the Black-Scholes model for the effect of dividends is to subtract the present value of expected dividend payments during the life of the option from the stock price variable in the model.

– The call option is a European option. European options can only be exercised at expiration, whereas American options can be exercised at any time up until the expiration date. This assumption is not important because few options are exercised prior to expiration.

When an option is exercised prior to expiration, the option holder loses the value of any premium (the difference between the market value of the option and option’s intrinsic value, which is defined as the difference between the stock price and the exercise price) that is contained in the option price.

– Stock prices are assumed to follow a random walk. Investors are assumed not to be able to predict the direction of the overall market or of any particular stock.

– There are no transaction costs in the buying and selling of options. This assumption is violated in reality, but transaction costs are low enough that this assumption is not a serious limitation of the model.

– The probability distribution of stock returns is normally distributed.

– Short-term, risk-free interest rates are assumed to be known and constant over the life of the option contract. The discount rate on 30-day U.S. government Treasury bills is often used as the risk-free rate in the Black-Scholes model.

– The variance of returns on the underlying stock is assumed to be constant and known to investors over the option’s life.

• With these assumptions, the “correct” market value of an option can be determined. If the price of an option differs from this theoretically “correct’ value, it is possible for investors to set up a risk-free arbitrage position and earn a rate of return is excess of the risk-free rate. Hence, it can be said that there are powerful market forces at work to keep actual market values of options consistent with their theoretical values.

The Black-Scholes Option Pricing Model

• The Black-Scholes model defines the equilibrium value of a call option to buy one share of a company’s common stock as:

where:

Ps = current stock valuet = time in years until the expiration of the option

1 2N( ) N( )s rt

EC P d d

E = exercise price of the call optionr = short-term annual, continuously compounded, risk-free rate of interestN(d) = the value of a cumulative normal density function; the probability that a standardized, normally distributed random variable will be less than or equal to the value de = the exponential value (2.71828)

σ = the standard deviation per year in the continuous return on the stock

In = natural logarithm

ln( ) ( )2

sP r tEd

Applying the Black-Scholes

• Consider the case of Queen Pharmaceuticals, Inc. Based on an analysis of past return for Queen’s common stock, the standard deviation of its stock returns has been estimated to be 0.3 or 30 percent. As of January 14, Queen’s stock price was Ps = $30. The exercise price of its call options was E = $29.

the short-term annual, continuously compounded interest rate was r = 0.06, and the time to expiration of the call option was t = 0.5 or one-half year. With this information, we can now compute the equilibrium value of these call options.

• Step 1: Compute the values for d1 and d2.

ln( ) ( )2

30 (0.3)ln( ) (0.06 )0.5

29 2 0.40740.3 0.5

0.4074 0.3 0.5 0.1953

sP r tEd

• Step 2: Compute N(d1) and N(d2).

Recall that the values in Table V are the probabilities of having a value greater than z (for positive standard normalized values such as d1 or d2 in this example) or less than z (for negative standard normalized values).

Because d1 and d2 are both positive, we can find the probability of a value greater than d1 or d2 directly from Table V and then subtract this probability from 1.0 to get the probability of a value less than d1 or d2 , as is required in the Black-Scholes model.

From Table V, the probability of a value greater than d1 (rounded to 0.41) is 0.3409. Hence the value for N(d1) will be 1.0 – 0.3409 or 0.6591. Similarly the probability of a value greater than d2 (rounded to 0.20) is 0.4207. Hence the value for N(d2), that is, the probability of a value less than d2, will be 1.0 – 0.4207 = 0.5793.

• Step 3: Calculate the value of C, the call option for Queen Pharmaceuticals stock.

(0.06)(0.5)

N( ) N( )

$29 $30(0.6591) (0.5793)

EC P d d

• Therefore, the Black-Scholes model indicates that an option to purchase one share of Queen Pharmaceuticals stock is worth approximately $3.47, given the assumptions presented above. Option values are especially sensitive to the estimates of stock return volatility that are input in the model.

Common Stock in an Options Framework

• Any firm with debt can be analyzed in an options framework. Suppose a start-up firm raises equity capital and also borrow $7 million, due two years from now. Then, suppose further that the firm undertakes a risky project to develop new computer parts. In two years, the firm must decide whether or not to default on its debt repayment obligation.

• Consider this example in an options context. The stockholders can be viewed as having sold this firm to the debt holders for $7 million when they borrowed the $7 million. But the stockholders retained an option to buy back the firm. The stockholders have the right to exercise their option by paying off the debt claim at maturity.

• Whether they do depends on the value of the firm at the time the debt is due. If the value of the firm is greater than the debt claim, the stockholders will exercise their option by paying off the debt. But if the value of the firm is less than the debt claim, the stockholders will let their option expire by not repaying the debt.

• This simplified example has interesting implications. Earlier in the options discussion, we showed that the greater the expected stock price volatility, the higher the call option value will be. Therefore, if the stockholders choose high-risk projects with a chance of very large payoffs, they increase the value of their option. But, at the same time, they also increase the likelihood of defaulting on the debt, thereby decreasing its value.

• Thus it is easy to see how potential conflicts between stockholders and debt holders can occur. These potential conflicts are discussed further in the next section on convertible securities. In fact, we shall see that giving the bondholders an equity stake in the firm decreases the potential for conflicts between stockholders and debt holders.

Option Valuation Calculator

• Check out the option valuation calculator at this Web site:http://www.numa.com/

Convertible Securities

• Both debentures and preferred stock can have convertibility or conversion features. When a company issues convertible securities, its usual intention is the future issuance of common stock.

• To illustrate, suppose the Beloit Corporation issues two million shares of convertible preferred stock at a price of $50 a share. After the sale, the company receives gross proceeds of $100 million. Because of the convertibility feature, the company can expect to issue shares of common stock in exchange for the redemption of the convertible preferred stock over some future time period. As a result, convertibles are sometimes described as a deferred equity offering.

In the case of Beloit’s convertible preferred, each $50 preferred share can be exchanged for two shares of common stock; that is, the holder has a call option to buy two shares of the company’s common stock at an exercise of $25 a share.

Therefore, if all the preferred shares are converted, the company in effect will have issued four million new common shares, and the preferred shares will no longer appear on Beloit’s balance sheet. No additional funds are raised by the company at the time of conversion.

Features of Convertible Securities

• As an introduction to the terminology and features of convertible securities, consider the $115 million, 25-year issue of 6.125 percent convertible subordinated debentures sold by Advanced Research, Inc. (ARI), a computer software company. Convertible securities are exchanged for common stock at a stated conversion price.

In the case of the ARI issue, the conversion price at the time of issue was $84. This means that each $1,000 debenture was convertible into common stock at $84 a share.

• The number of common shares that can be obtained when a convertible security is exchanged is determined by the conversion ratio, which is calculated as follows:

Par value of securityConversion ratio

Conversion price

• In the case of ARI’s convertible subordinated debentures, the conversion ratio at the time of issue was the following:

Conversion ratio = ($1,000)/($84) = 11.9

Thus, each $1,000 ARI debenture could be exchanged for 11.9 shares of common stock. Although the conversion ratio may change one or more times during the life of the conversion option (as it did for the ARI bonds), it is more common for it to remain constant.

• Normally, the conversion price is set about 15 to 30 percent above the common stock’s market price prevailing at the time of issue. For example, at the time ARI issued its convertible debentures, the market price of its common stock was about $65 a share. The $19 (=$84 – $65) difference between the conversion price and the market price represents a 29 percent premium.

Valuation of Convertible Securities

• Because convertible securities possess certain characteristics of both common stock and fixed-income securities, their valuation is more complex than that of ordinary nonconvertible securities. The actual market value of a convertible security depends on both the common stock value, or conversion value, and the value of a fixed-income security, or straight-bond or investment value.

Features of Convertible Securities: Conversion Value

• The conversion value, or stock value, of a convertible bond is defined as the conversion ratio times the common stock’s market price:

Conversion value

= Conversion ratio*Stock price

Features of Convertible Securities: Conversion Value

• To illustrate, assume that a firm offers a convertible bond that can be exchanged for 40 shares of common stock. If the market price of the firm’s common stock is $20 per share, the conversion value is $800. In the case of ARI’s convertible bonds, the conversion value was 11.9*$65 (the price per common share at the time of issue), or $774.

Features of Convertible Securities: Straight-Bond Value

• The straight-bond value, or investment value, of a convertible debt issue is the value it would have if it did not possess the conversion feature (option). Thus, it is equal to the sum of the present value of the interest annuity plus the present value of the expected principal repayment:

where kd is the current yield to maturity for nonconvertible debt issues of similar quality and maturity; t, the number of years; and n, the time to maturity.

Interest PrincipalStraight-bond value

(1+ ) (1 )

t nt k k

• Considering again ARI’s 6.125 percent, 25-year convertible debentures, the bond value at the time of issue is calculated as follows, assuming that 9 percent is the appropriate discount rate (and that interest is paid annually):

0.09, 25 0.09, 25

$61.25 $1,000Straight-bond value

(1.09) (1.09)

$61.25(PVIFA ) $1,000(PVIF )

$61.25(9.823) $1,000(0.116) $718

Features of Convertible Securities: Market Value

• The market value of a convertible debt issue is usually somewhat above the higher of the conversion or the straight-bond value; this is illustrated in Figure 20.2.

• The difference between the market value and the higher of the conversion or the straight-bond value is the conversion premium for which the issue sells.

• This premium tends to be largest when the conversion value and the straight-bond value are nearly identical. This set of circumstances allows investors to participate in any common stock appreciation while having some degree of downside protection because the straight-bond value can represent a “floor” below which the market value will not fall.

• The ARI convertible debentures described in this section were offered to the public at $1,000 per bond and quickly were bought up by investors. In this case, investors were willing to pay $1,000 for an issue having a conversion value of approximately $774 and a bond value of about $718. The $1,000 market value contained a premium of $226 over the conversion value (which was higher than the bond value).

• This premium can be thought of as the value of the implicit call option on a firm’s common stock associated with this convertible security. In practice, convertible securities are valued by adding the straight-bond value to the value of the conversion options to buy common stock. These conversion options can be valued using a variation of the Black-Scholes option pricing model.

Converting Convertible Securities

Conversion

Voluntary

Forced

Call privilegeCall privilege

Prior to expirationPrior to expiration

• Conversion can occur in one of two ways:– It may be voluntary on the part of the

investor.– It can be effectively forced by the issuing

company.

Whereas voluntary conversions can occur at any time prior to the expiration of a conversion feature, forced conversions occur at specific points in time.

The method most commonly used by companies to force conversion is the exercise of the call privilege on the convertible security.

Another way in which a company can encourage conversion is by raising its dividend on common stock to a high enough level that holders of convertible securities are better off converting them and receiving the higher dividend.

Convertible Securities and Earnings Dilution

• If a convertible security (or warrant) issue is ultimately exchanged for common stock, the number of common shares will increase and earnings per share will reduced (i.e., diluted), all other things being equal. Companies are required (by Accounting Principles Board Opinion 15) to disclose this potential dilution by reporting both primary and fully diluted earnings per shares.

• Primary earnings per share are calculated based on the number of common shares outstanding plus common stock equivalents. A common equivalent must meet certain tests, but it basically includes any convertible security that derives its value primarily from the common stock into which it can be converted.

• Fully diluted earnings per share are calculated based on the assumption that all dilutive securities are converted into common shares. In calculating primary or fully diluted earnings per share, earnings must be adjusted for the interest or preferred dividends saved as the result of conversion.

Reasons for Issuing Convertibles

• Make security more attractive

• Sell common stock in the future at higher price

• Allow time for investments to pay benefits

• Small, risky companies

• Lessen agency conflict

Warrants

• A warrant is a company-issued option to purchase a specific number of shares of the issuing company’s common stock at a particular price during a specific time period. Warrants are frequently issued in conjunction with an offering of debentures or preferred stock. In these instances, like convertibles, warrants tend to lower agency costs.

Features of Warrants

• Warrants are usually issued with other securities.

• The exercise price of a warrant is the price at which the holder can purchase common stock of the issuing company.– The exercise price is usually between 10

and 35 percent above the market price of the common stock prevailing at the time of issue.

– The exercise price normally remains constant over the life of the warrant. One exception is the case of a stock split. When this occurs, the exercise price of the warrant is adjusted to reflect the new number of shares and share price.

– Typically, the life of a warrant is between 5 and 10 years, although on occasion the life can be longer or even perpetual.

• With convertible securities such as convertible bonds or preferred stock, the company does not receive additional funds at the time of conversion.

• If a warrant is issued as part of a “unit” with a fixed-income security, the warrant is usually detachable from the debenture or preferred stock; this means that purchasers of the units have the option of selling the warrants separately and continuing to hold the debenture or preferred stock. As a result, other investors can purchase and trade warrants.

• Holders of warrants do not have the rights of common stockholders, such as the right to vote for directors or receive dividends, until they exercise their warrants.

Reasons for Issuing Warrants

• Lower agency costs

• Sell common stock in the future at higher price

• Sell common stock in the future without incurring significant costs at the time of sale

Valuation of Warrants

• The value of a warrant depends upon the same variables that affect call option valuation. Because a warrant’s value depends upon the price of the issuing company’s stock, it is a contingent claim, just like an option. In this connection, the formula value of a warrant (also called “the value at expiration”) is defined by the following equation:

Formula value of a warrant = Max{$0; (Common stock market price per share – Exercise price per share)*(number of shares obtainable with each warrant)}

Note that the market value of the warrant may not be equal to its formula value.

• At the time of issue, a warrant’s exercise price is normally greater than the common stock price. Even though the calculated formula value may be negative, it is considered to be zero because securities cannot sell for negative amounts.

• For example, at the time of issue, the Fannie Mae warrants had an exercise price of $44.25 and the firm’s common stock price was $33 per share. Each warrant entitled the holder to one share, and the formula value was zero:

Formula value

= Max {$0; ($33 – $44.25)(1)}

• Once the stock price rises above the exercise price of the warrant, the formula value will be greater than zero.

• For example, on February 24, 1989, Fannie Mae’s stock price was $59 and the warrant price was $19.375. At this point, the formula value of the warrant was Formula value = Max {$0; ($59 – $44.25)(1)} = $14.75

• On the expiration date of a warrant, the market price of the warrant should be equal to the formula value.

• For the Fannie Mae warrants on the expiration date, the market price of the stock (after the 3-for-1 stock split) was $45.375, and the market price of the warrants was $30.625. Note that the exercise price of the warrants was lowered from $44.25 to $14.75 as a result of the 3-for-1 stock split.

• As we see, the market price of the warrants was equal to the formula value:

• Formula value

= Max {$0; ($45.375 – $14.75)(1)}

= $30.625

Comparison of Warrants and Convertible Securities

• Assume that the warrants are issued as part of a fixed-income security offering. The similarities include the following:– Both warrants and convertibles tend to

lessen potential conflicts between fixed-income security holders and stockholders, thereby reducing agency costs.

– The intention is the deferred issuance of common stock at a price higher than that prevailing at the time of the convertible or warrant issue.

– Both the attachment of warrants and the convertibility option result in interest expense or preferred dividend savings for the issuing company, thereby easing potential cash flow problems.

• Some of the differences include the following:– The company receives additional funds at

the time warrants are exercised, whereas no additional funds are received at the time convertibles are converted.

– The fixed-income security remains on the company’s books after the exercise of warrants; in the case of convertibles, the fixed-income security is exchanged for common stock and taken off the company’s books.

– Because of the call feature, convertible securities potentially give the company more control than warrants over when the common stock is issued.

Warrants (W) and Convertible Securities (C)

Characteristic W C

Lessen Agency Conflicts

Deferred Issuance of C/S

Savings of Interest or Dividends

Company Receives Additional Funds

Two Securities on Books More Control

Analysis of Rights Offerings

• In a rights offering the firm’s existing stockholders are given an option to purchase a fraction of the new shares equal to the fraction they currently own, thereby maintaining their original ownership percentage.

• Hence, rights offerings are used in equity financing by companies whose charters contain the preemptive right. In addition, rights offerings may be used as a means of selling common stock in companies in which preemptive rights do not exist. The number of rights offerings has gradually declined over the years.

• The following example illustrates what a rights offering involves. The Miller Company has 10 million shares outstanding and plans to sell an additional 1 million shares via a rights offering. In this case, each right entitles the holder to purchase 0.1 share, and it takes 10 rights to purchase one share. (The rights themselves really are the documents describing the offer. Each stockholder receives one right for each share currently held.)

The company has to decide on a subscription price, which is price the right holder will have to pay per new share. The subscription price has to be less than the market price, or right holders will have no incentive to subscribe to the new issue. As a general rule, subscription prices are 5 to 20 percent below market prices. If the Miller Company’s stock is selling at $40 per share, a reasonable subscription price might be $35 per share.

Valuation of Rights

• Because a right represents an opportunity to purchase stock below its current market value, the right itself has a certain value, which is calculated under two sets of circumstances:– The rights-on case– The ex-rights case

Valuation of Rights

• A stock is said to “trade with rights-on” when the purchasers receive the rights along with the shares they purchase.

• In contrast, a stock is said to “trade ex-rights” when the stock purchasers no longer receive the rights.

Valuation of Rights

• For example, suppose the Miller Company announced on May 15 that shareholders of record as of Friday, June 20, will receive the rights. This means that anyone who purchased stock on or before Wednesday, June 18, will receive the rights, and anyone who purchased stock on or later than June 19 will not. (A stock purchaser become a “shareholder of record” two trading days after purchase.)

Valuation of Rights

The stock trades with rights-on up to and including June 18 and goes ex-rights on June 19, the ex-rights date. On that date, the stock’s market value falls by the value of the right, all other things being equal.

Valuation of Rights

• The theoretical value of a right for the rights-on case can be calculated using the following equation:

where R is the theoretical value for the right; M0, the rights-on market value of the stock; S, the subscription price of the right; and N, the number of rights necessary to purchase one new share.

Valuation of Rights

• In the Miller Company example, the right’s theoretical value is

$40 $35$0.455

Valuation of Rights

• The theoretical value of a right when the stock is trading ex-rights can be calculated by using the following equation:

where Me is the ex-rights market price of the stock; S, the subscription price of the right; and N, the number of rights necessary to purchase one new share.

Valuation of Rights

• If the Miller stock were trading ex-rights, the theoretical value of a right would be as follows:

• Note that Me is lower than M0 by the amount of the right; that is, $40 versus $39.545.

$39.545 $35$0.455

Valuation of Rights

• Some shareholders may decide not use their rights because of lack of funds or some other reason. These stockholders can sell their rights to other investors who wish to purchase them. Thus, a market exists for the rights, and a market price is established for them.

Valuation of Rights

• Generally, the market price is higher than the theoretical value until the time of expiration. The same factors discussed previously, which determine the value of a call option, also determine the value of a right, since a right is simply a short-term call option on the stock.

Valuation of Rights

• As with call options, investors can earn a higher return by purchasing the rights than by purchasing the stock because of the leverage rights provide. In general, the premium of market value over theoretical value decreases as the rights expiration date approaches. A right is worthless after its expiration date.

Valuation of Rights

• One can demonstrate that there is no net gain or loss to shareholders either from exercising the right or from selling the right at the theoretical formula value.

Valuation of Rights

• For example, suppose an investor owns 100 shares of the Miller Company common stock discussed earlier. The investor is entitled to purchase 10 (0.1*100) additional shares at $35 per share. Prior to the rights offerings, the 100 shares of Miller Company are valued at $4,000 (100 shares*$40 per share).

Valuation of Rights

Exercise of the rights will give the investor 10 additional shares at a cost of $35 per share, or a total cost of $350. These 110 shares will be valued at $4,350 (110*$39.545). Deducting the cost of these additional shares ($350) from the total value of the shares ($4,350), one obtains the same value ($4,000) as before the rights offering.

Valuation of Rights

Sale of the rights will yield $45.50 (100*$0.455) to the investor. Combining this value with the $3,954.50 (100*$39.545) value of the 100 shares still owned, one also obtains the same value ($4,000) as before the rights offering.

Interest Rate Swaps

• A financial swap is a contractual agreement between two parties (financial institutions or businesses) to make periodic payments to each other.

• There are two major types of swaps: interest rate swaps and currency swaps. This section will focus on interest rate swaps.

Interest Rate Swaps

• Interest rate swaps can be used to protect financial institutions and businesses against fluctuations in interest rates. Like futures contracts, swaps can be used to hedge against interest rate risk. Even though futures contracts are more effective in hedging against short-term risks (less than one year), swaps are more effective in hedging against longer-term risks (up to 10 years or more).

Interest Rate Swaps

• Of the many and various types of interest rate swaps, the most basic is one in which a party is seeking to exchange floating rate interest payments for fixed rate interest payments, or vice versa.

Interest Rate Swaps

• Consider the case of a finance company (e.g., Ford Credit) with floating rate debt (e.g., floating rate bonds) and fixed rate loans (e.g., automobile installment loans) that wants to protect itself against an increase in interest rates.

Interest Rate Swaps

• The finance company can enter into a swap contract with another party who agrees to pay the interest costs in excess of a specific rate (e.g., 7.5 percent) for a given period of time (e.g., three years). Should interest rates increase in the future, the finance company will receive rising payments from the other party to the swap agreement to cover its losses.

Interest Rate Swaps

• The other party to the swap agreement could be a bank, which borrows at fixed interest rates (e.g., certificates of deposit) and lends money to corporations at floating rates. The bank may desire t protect itself against a decline in interest rates. Should interest rates decline in the future, the bank will continue receiving fixed interest payments from the other party to the swap agreement.

Interest Rate Swaps

• This swap is illustrated in Figure 20.3. In most interest rate swaps, the floating rate used in computing the payments between the parties to the swap is tied to the London Interbank Offer Rate (LIBOR). (LIBOR is discussed in Chapter 2.) In this example it is 2.5 percentage points above LIBOR. Generally, in a swap agreement, the parties exchange only the interest differential, not the principal or actual interest payments.

Interest Rate Swaps

• Many financial institutions, such as investment banks, commercial banks, and non-financial companies, act as intermediaries in arranging swaps. Some intermediaries act as brokers and receive commissions for finding parties with matching needs. Other intermediaries act as dealers or market makers by offering themselves as a party to the swap until such time as they can arrange a match with another party.

Information on Swaps

• Check out the Chicago Board of Trade Web site as a source of information on swaps.http://www.cbt.com/

Copyright ©2003 South-Western/Thomson Learning Chapter 20 Financing with Derivatives.

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