Warrants: Features and Valuation

1. The Anatomy of a Warrant

A warrant gives its holder the right, but not the obligation, to purchase a company's shares at a fixed price (the strike or exercise price) on or before a specified date (the expiry date). Think of it as a long-term call option issued directly by the company itself.

This last point is the most crucial distinction. While a standard call option is a contract between two investors, a warrant is a contract between an investor and the company. This structural difference has important consequences that we will explore throughout this lesson.

To start, let's get a clear overview of what a warrant is and why a company might issue one.

As the video highlighted, the two main purposes for issuing warrants are:

• As a "sweetener": Companies often attach warrants to other financing, such as a bond issuance or private placement, to make the offering more attractive to investors. This allows the company to, for instance, pay a lower interest rate on its bonds.
• As compensation: Warrants can be a form of long-term incentive for executives and key employees, aligning their interests with those of shareholders.

Key Features and Terminology

Warrants share much of their terminology with options. Let's define the essential terms, using the comprehensive "MANUAL FOR THE INVESTOR IN WARRANTS" as a reference.

The image below provides a concise summary comparing warrants to the options you might be more familiar with.

2. The Impact of Exercise: Dilution

The most significant consequence of a warrant being a contract with the company stems from what happens upon exercise. When you exercise a standard call option, you buy existing shares from another investor. When you exercise a warrant, you pay the exercise price directly to the company, and in return, the company issues new shares.

This increases the total number of shares outstanding, which leads to dilution. Each existing share now represents a smaller percentage of the company, and the value per share is diluted by the influx of new shares issued at the (typically lower) exercise price.

Let's examine this concept more formally.

As the paper explains, let's say a company has $n$ shares outstanding with a stock price of $S_t$. The total value of the firm's equity is $V_t=n\times S_t$. If one warrant is exercised at a strike price of $K$, the company receives $K$ in cash, and the number of shares increases to $n+1$.

The new equity value is $V_{t+}=V_t+K=n{S}_t+K$, and the new share price is:

Since an investor will only exercise if the stock price is greater than the strike price ($S_t>K$), we can see that:

Thus, the new share price $S_{t+}$ is always lower than the pre-exercise price $S_t$, demonstrating the dilutive effect. This is a fundamental feature of warrants. The concept is also explained very intuitively in the following video.

3. Calculating the Value of a Warrant Upon Exercise

Now, let's turn to the core calculation. The "value upon exercise" is the gross profit an investor realizes by exercising their warrant. This is also known as the warrant's intrinsic value. A rational investor will only exercise if this value is positive.

For a call warrant, which gives the right to buy, the intrinsic value is the difference between the current market price of the stock and the warrant's strike price.

As the reading shows, for a single share (ratio = 1), the intrinsic value of a call warrant is:

The max(0, ...) simply ensures that the value cannot be negative, as you would not exercise a warrant to buy a share for more than its market price.

A Practical Example

Let's see how this works in a detailed scenario, accounting for the initial cost of the warrant.

Let's recap the profitable scenario from the video:

• Initial cost of warrant (premium): $0.27
• Exercise price: $0.95
• Total cost per share if exercised: $0.27 + $0.95 = $1.22
• Market price of the stock at expiration: $3.00
• Profit per share: $3.00 (sale price) - $1.22 (total cost) = $1.78

This demonstrates the leverage inherent in warrants. The initial investment was only $0.27, but it controlled an asset that generated a profit of $1.78, a return of over 600%.

A More Formal Calculation with Dilution

For your CB1 exam, you should also be prepared to calculate payoffs in a scenario that explicitly models dilution. Let's work through a more formal problem.

Let's break down the logic of Exercise 2 from the paper:

• Data:
  • Shares outstanding ($n$): 1,000
  • Warrants outstanding ($m$): 250
  • Strike price ($K$): $120
  • Total firm value at maturity ($Y$): This is the variable we are interested in.
• Exercise Condition: The warrants will only be exercised if the resulting share price is greater than the strike price. If they are not exercised, the share price is simply $Y/n$. If they are exercised, the new share price becomes $(Y+mK)/(n+m)$. The exercise condition simplifies to whether the total firm value $Y$ exceeds the total strike price needed for all original shares, i.e., $Y>nK=1000\times 120=\$120,000$.
• Payoff Calculation (if exercised):
  • The total value of the firm becomes $Y+mK=Y+(250\times 120)=Y+30,000$.
  • The total number of shares becomes $n+m=1,000+250=1,250$.
  • The new price per share is $(Y+30,000)/1,250$.
  • The value of one warrant upon exercise is the value of the share received minus the cost to exercise: $$\text{Value per Warrant}=\frac{Y+30,000}{1,250}-120$$

This type of calculation, which incorporates the dilutive impact on the entire firm, demonstrates a full understanding of how warrants function.

Conclusion

In this lesson, we have dissected the features and valuation of warrants, completing our survey of long-term financing instruments. We have established that while they appear similar to options, their direct issuance by a company creates the crucial feature of dilution upon exercise.

Key Takeaways:

• A warrant is a security issued by a company that gives the holder the right to buy stock at a fixed price and date.
• Unlike exchange-traded options, exercising a warrant involves paying new capital to the company in exchange for newly issued shares.
• The issuance of new shares causes dilution, reducing the value of each existing share.
• The value of a call warrant upon exercise (its intrinsic value) is the amount by which the stock's market price exceeds the strike price, calculated as $\max (0,\text{Stock Price}-\text{Strike Price})$.
• The total profit from a warrant position must also account for the initial premium paid to acquire the warrant.

This lesson concludes our module on long-term financing. In our next session, we will begin a new module, "Short-Term and Alternative Financing", starting with a comparison of two fundamental sources of short-term cash for a business: bank overdrafts and term loans.