Warrants are a little bit like a living memory of a long-past era of finance. Although relatively uncommon and out of favor in the United States, warrants have remained more popular in some areas of the world such as Hong Kong. However, they do still appear in the U.S. markets, and investors should know how to assess and value them. (For a background reading, see Warrants: A High-Return Investment Tool.)

What Is a Warrant?
In simple terms, a warrant is an option issued by a company that gives the holder the right to buy stock from the company at a specified price within a certain designated time period. Generally speaking, warrants are issued by the company whose stock underlies the warrant and when an investor exercises a warrant, he or she buys stock from the company and those proceeds are a source of capital for the firm.

Like an option, a warrant does not represent actual ownership in the stock of the company; it is simply the right (but not the obligation) to buy shares at a certain price in the future. Warrants typically have a much longer life than a call option - it is unusual for a warrant to be issued with less than a two-year term, and time periods of five to 10 years are not rare. In fact, some warrants are perpetual.

Although warrants are similar to options, there are several additional important differences. First, options are written by other investors or market-makers, while warrants are typically issued by companies. Warrants are often traded over-the-counter and do not have the standardized features of option contracts. Also, options are not dilutive to current shareholders, while warrants are.

Although there are several kinds of warrants, the most common types are detachable and naked. Detachable warrants are issued in conjunction with other securities (like bonds or preferred stock) and may be traded separately from them. Naked warrants are issued as is and without any accompanying securities.

Other less common types of warrants include wedded warrants (which can only be exercised if the attached bond/preferred stock is surrendered) and covered warrants (which are often issued by financial institutions and rarely issued by the underlying company). Companies will also occasionally issue put warrants to hedge employee option programs.

Why Are They Issued?
The most common reason for a company to issue warrants is to provide a "sweetener" for a bond or preferred stock offering. By adding the warrants, the company hopes to obtain better terms (lower rates) on the debt or preferred stock. Moreover, warrants represent a potential source of equity capital in the future and can thus offer a capital-raising option to companies that cannot, or prefer not to, issue more debt or preferred stock. In addition, there are certain accounting benefits - issuers can use the treasury stock method to calculate EPS (instead of the "if converted" method), and amortized warrant value can be allocated to the bond and increase the interest expense (and tax benefits).

Less commonly, warrants are issued as part of the recapitalization plan of a bankrupt company. While the holders of common stock are typically wiped out in a bankruptcy, issuing warrants for soon-to-be-worthless shares can not only give the company a future source of equity capital (if shareholders exercise those warrants), but preserve a little bit of goodwill in the former shareholder base.

Valuing Warrants with the Black-Scholes Model
Although there are several possible methods for valuing a warrant, a modified version of the Black-Scholes model is most common. This formula is for European-style options and, though American-style options are theoretically worth more, there is not much difference in price in practice.

In the Black-Scholes model, the valuation of a call option is expressed as:

C = S N(d1) - X e-rT N(d2)

Where:

C = price of the call option
S = price of the underlying stock
X = option exercise price
r = risk-free rate
T = time until expiration
N() = area under the normal curve
d1 = [ ln(S/X) + (r + σ2/2) T ] / σ T1/2
d2 = d1 - σ T1/2

Because of the dilution that warrants represent, the value of that call needs to be divided by (1 + q) where q is the ratio of warrants to outstanding shares, assuming each warrant is worth one share.

The Factors That Influence Warrant Prices
Beyond the calculation above, investors should consider the following factors when evaluating the price of a warrant.

Underlying Security Price
The higher the price of the underlying security, the more valuable the warrant becomes. After all, if the price of the stock is below the strike price of the warrant, there is no reason to exercise the warrant (it is cheaper to buy the stock on the open market).

Days to Maturity
Generally speaking, options and warrants are worth less as time goes on and expiration approaches. This phenomenon is also called "time decay", and it will accelerate as expiration approaches if the strike price is above the current price.

Dividend
Warrant-holders are not entitled to receive dividends, and the corresponding reduction in the stock price reduces the value of the warrant.

Interest Rate/Risk-Free Rate
Higher interest rates increase the value of options like warrants.

Implied Volatility
The higher the volatility, the higher the odds that the warrant will eventually be in the money and the higher the value of the warrant will be.

Additional Factors
In addition to those factors that are common between options and warrants, warrants have a few extra factors of their own:

Dilution: Because the exercise of a warrant will increase a company's outstanding shares, this dilution adds a twist to valuation that is not present in normal option valuation.

Premium: Warrants can be issued at premiums; the lower the premium the more valuable the warrant.

Gearing/leverage: Gearing is the ratio of the share price to the warrant premium, and it reflects how much the price of the warrant changes for a given change in the stock. The higher the gearing, the more valuable the warrant.

Restrictions on exercise: Though very difficult to quantify mathematically, any restrictions on the exercise of warrants will impact the value of a warrant, typically negatively. A common restriction (and one that is easy to quantify) is the difference between American-style and European-style warrants; American-style warrants permit exercise at any time, while European-style warrants can only be exercised on the expiration date.

The Bottom Line
Although warrants are not very common anymore, they are not all that hard to value in practice. After all, a warrant is basically just a long-term option issued by a company. Investors need to make a few adjustments for unique factors like dilution, but a basic Black-Scholes options pricing formula will produce a reasonable assessment of the warrant's value. (To learn more about how to price warrants, see ESOs: Using The Black-Scholes Model.)

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