Warrants on Preferred Stock: Is Black-Scholes Leading Us Astray?

Josh Schaeffer, PhD Nikhil Guruji

Private companies are known for their more complex financing arrangements, and with financing complexity comes valuation complexity. One piece we see quite often is warrants, which can be used as a sweetener for a transaction or otherwise used as an inducement.

When we look to value these warrants, one feature which can have a considerable impact is whether they’re issued on the company’s common or preferred stock. While seemingly very similar, the results of these two can be vastly different. Importantly, the Black-Scholes value—which we typically use to value warrants—may not be applicable if the underlying value is preferred. That often leaves companies scratching their heads over dealing with a more complicated model. The goal of this article is to provide an understanding of why these warrants require different valuation methodologies, what some of the underlying complexities are, and how one can approach solving them.

Understanding Black-Scholes

Just as it is for options, the Black-Scholes model is the most commonly-used tool for calculating the fair value of warrants. However, the model has a few assumptions that often prove less compatible with preferred stock.

To get a little technical, Black-Scholes calculates the value of warrants by treating them as a European call option, which can be exercised only at a fixed point in time. The model projects the stock price toward the end of the warrant term using a standard equation called a geometric Brownian motion. In layman’s terms, this means that we assume that the daily returns on a stock follow a bell-shaped normal distribution, and there’s always an equal chance of a positive and negative return on any given day.

Using this assumption, the geometric Brownian motion equation pulls a stock return from a normal distribution over the warrant period. This creates a “random walk” for the stock price where each day the stock price either moves up or down based on a random event. Further, the amount (as a percent) by which the stock moves up or down is the same at any time, regardless of where the stock price is and where it has moved in the past. Once the end of the stock price path is projected, the payoff of the call option is calculated based on the predefined strike price, and discounted back to the present date.

Preferred Stock Features

Generally, preferred stock has economic rights that don’t apply to common stock. As a result, their treatment and fair values can be vastly different from those for common stock. A couple of the features that make preferred stock unusual are:

  • Liquidation preference. Preferred stock has a senior claim on a company’s equity value, dividends, or other distributions. This means that in the event of a sale, merger, IPO, dissolution, or bankruptcy, preferred holders are paid an amount first, and common holders have to wait until this balance is paid. Companies often structure liquidation preferences to create different incentives and returns, and investors often use these to protect their capital and achieve a baseline return.
  • Conversion features. Most private company preferred shares include an option to convert the shares for a fixed number of common shares. Typically, when the value of the common stock at an exit event reaches a value high enough for liquidation preference to be less valuable than common stock, the preferred stockholders exercise their conversion feature. An alternative to conversion features are participation rights wherein preferred stock gets some of the upside along with common stock.

Due to these features, the capital structure of a company with multiple classes may get convoluted. (If this sounds familiar—or, on the other hand, too confusing—our article on complex capital structure has more information.) As a result of these terms, the payoff for preferred stock can be less “well-behaved” than Black-Scholes assumes. For example, if the company’s value is approaching its liquidation preference, preferred stock may bear all of the downside, but get no benefit of the upside.  On the other hand, if you’re above the conversion point, losses may be limited whereas gains are not.

Because the distribution doesn’t match the Black-Scholes assumptions, the formula can produce erroneous values, ranging from those marginally off to off by orders of magnitude depending on the situation.

Other Warrant Features

While the distribution of returns is a common problem, other features can cause some assumptions in the Black-Scholes model to give an inaccurate estimate of the fair value of warrants. Therefore, it is important to consider the terms carefully. For instance:

  • Do they have any protections? A down-round feature allows a reduction of the warrant strike price, which could also be limited to a predetermined floor. Some warrants also have anti-dilution provisions that protect the warrant holders from dilution due to future equity issuances.
  • What happens if there’s an IPO or change of control? Some warrants give the holders the right to exercise the warrants before the event occurs. Some warrants may even get terminated upon such an event.
  • Are there any circumstances other than the warrant expiration date that could trigger an exercise, such as call or redemption features? For example, many recent SPAC warrants have an exercise barrier wherein the holders have the option to exercise early if the stock price exceeds a certain threshold.

Selecting the Right Valuation Model

In the words of George Box, “All models are wrong, but some are useful.” In order to find the best fit for our warrants, we look at a class of option valuation models. These include the aforementioned Black-Scholes model, an option pricing method that looks to future values of the company and flows this down to various components, or a Monte Carlo simulation that looks at the future value based on a flexible framework of the company and/or the underlying stock.

To select the right model for valuing warrants, one needs to consider a number of factors:

  • What pieces result in potential value to the holders? This should reflect how beneficial the warrant is for the holders and issuers. Something like a down-round feature that is beneficial for the holder would increase its value. However, a call feature would reduce value as that gives issuers the ability to call the warrant.
  • Upon exercise, what class of shares will the holder receive? If the warrants are on preferred stock, then the liquidation preference for such preferred stock must be considered. However, in some cases, the exercise price is above the conversion price. In this case, we may be able to make a convenient assumption that the warrant is on common stock and the Black-Scholes model will apply.
  • Are there any other exotic features such as multiple exercise dates, the ability to gain more or less than target shares under different circumstances, or special treatment under a financing or a sale event? In all these cases, the recommendation is to simulate the scenarios under a Monte Carlo simulation model as this allows for the valuation specialist to apply all the necessary customizations to the valuation model.
  • What happens to the warrants at a liquidity event, like an IPO or a change of control? In this case, if all shares convert to common stock, then the value received by such warrants shall be determined by calculating the value of common stock under the full capital structure of the company. For example, at low equity values such as in the case of a dissolution, all of the proceeds would go to the preferred shareholders and the warrant holders would receive no value. Therefore, it’s important to consider the liquidation preferences for the full capital structure.
  • Are there any scenarios in which the warrant would pay different amounts? For example, a pharma company might issue warrants where the warrant holders get more shares if a certain drug receives regulatory approval, and fewer shares if the drug isn’t approved. In this scenario, the valuation specialist would use a probability-weighted expected return model that includes multiple models for each scenario.

When these factors are combined, a specialist can pick a model that captures all of the relevant economic features and, most importantly, fits the fact pattern for the warrants.