Introduction

Warrants are financial instruments that grant the holder the right, but not the obligation, to buy a company’s common stock at a specified price (exercise price) within a predetermined period. They are often used as a means to raise additional capital for the company. In this chapter, we will delve into the concept of warrants, how to calculate their value, and understand the potential dilution they can bring to existing shareholders.

Warrants

Warrants can be thought of as call options issued by the company on its own stock. They are typically attached to other securities, such as bonds or preferred stock, as a sweetener to attract investors. When an investor exercises a warrant, they purchase shares of the company’s stock at the predetermined exercise price, thus providing additional capital to the company.

Calculating the Value of a Warrant

The value of a warrant is calculated using the Black-Scholes-Merton option pricing model, similar to how options are priced. The key variables in this calculation include:

• Current stock price (S): The market price of the company’s stock
• Exercise price (K): The price at which the warrant holder can buy the stock
• Time to expiration (T): The remaining time until the warrant expires
• Volatility $(\sigma)$: The stock’s volatility, which measures the uncertainty of its future price movements
• Risk-free interest rate (r): The rate of return that could be earned on a risk-free investment

The formula for valuing a warrant is:

$$W=S-\frac{K}{(1+r)^T}$$

Example: Suppose a warrant has an exercise price of USD 50, the current stock price is USD 60, the time to expiration is one year, the stock’s volatility is 20%, and the risk-free rate is 5%. Using the formula, the warrant’s value would be calculated as:

$$W = 60 - \frac{50}{(1+0.05)^1} = \text{USD 9.52}$$

Dilution Cost of Warrants

When warrants are exercised, new shares are issued by the company. This issuance can dilute the ownership percentage of existing shareholders, as the total number of shares outstanding increases. The dilution cost measures the impact of warrant exercise on existing shareholders.

The formula for dilution cost is:

$$\text{Dilution Cost} = \frac{X}{S}$$

Where:

• $X$ is the number of shares issued upon warrant exercise
• $S$ is the total number of shares outstanding before exercise

Example: Let’s say a company has 1 million shares outstanding, and an investor exercises warrants for an additional 50,000 shares. Using the formula, the dilution cost would be:

$$\text{Dilution Cost} =\frac{50,000}{1,000,000}=5$$