# Option Valuation Concepts - Financial Management

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. Options are classified as either call or put options. A call is an option to buy a particular asset, whereas a put is an option to sell it.

Option Valuation Concepts

Suppose an investor is offered an opportunity to purchase a call option on one share of McKean Company stock. Consider the following sets of conditions:

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 2. 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
3. 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
4. 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 additional cost. Therefore,
Minimum value of a call option = 0

The results of these sets of conditions are shown in Figure

Variables Affecting Call Option Valuation

The examples in the previous section illustrate that the value of a call option is dependent on the relationship between the option’s exercise price, the price of the underlying stock, and the length of time before the option’s expiration date. Two other variables that influence the value of a call option are the level of interest rates and the expected volatility of the underlying stock’s price. A discussion of these four variables follows.

Relationship Between the Exercise Price and the Stock Price The effect of the exercise, or strike, price on option value is seen by examining Table 20.1, which lists a number of options quotations for Apple Computer. At the time (June 2004), Apple’s stock was selling at $32.91 a share. For options expiring in October 2004, the call option with a$30 exercise price sold at a higher price than the option with a $35 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. Therefore, the higher the exercise price, given the stock price, the lower the call option value, all other things being equal. Call Option Valuation at Different Stock Prices* Selected Call Option Prices for Apple Computer 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 The figures in Table show that an option expiring in January 2005 has a higher value than an option with an October 2004 expiration date because investors realize that Apple’s stock has a greater chance to increase in value with three additional months before expiration. Thus, 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.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. Option Valuation Models Financial researchers have made considerable progress in developing formal models to value options. Call Options on Bonds Many corporate bonds have a call feature included in the bond indenture. This call option gives the issuing company the right to redeem (call) the bonds prior to their scheduled maturity, usually with the payment of some premium, above the bond’s face value, to the bondholder. The most common circumstances that lead to the exercise of the call option by the bond issuer are (1) interest rates have fallen such that the issuer can sell new bonds at a lower interest rate (see Appendix 20B); or (2) the bonds are called as a way to force conversion of the bonds to common stock by the bondholders. 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 borrows$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 debtholders 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 debtholders 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 debtholders.