Deciphering Complex Capital Structures

DECIPHERING COMPLEX CAPITAL STRUCTURES

Many venture funded companies have multiple classes of equity, each with particular provisions that materially affect their fair value.

Many venture funded companies have multiple classes of equity, each with particular provisions that materially affect their fair value. For example, preferred stock may have voting, liquidation and conversion rights that must be considered.  In addition, early investors may use convertible debt that has the economic character of preferred stock.

The valuation of preferred equity or convertible debt presents a technical challenge that can often be solved through the use of option pricing methods. One of the most important innovations in finance is the development of a set of tools to help value options contracts. These tools range from relatively simple formulas to more complex numerical procedures. Particularly useful is the Black-Scholes formula for the valuation of a European call option, which gives option values as a function of five inputs: the underlying stock price, the estimated volatility of its return, the risk free interest rate, the time until option expiration, and the exercise price of the option. The most typical use of option valuation formulas is to determine the value of an options contract that has a stock as the underlying security.

In the valuation of business interests, we can sometimes apply the Black-Scholes formula by viewing each investment in a company as an option or portfolio of options on the value of the underlying enterprise. For example, if a company’s enterprise value consists of only one debt issue and common equity, we might be able to model the common stock as a call option on the overall enterprise value with a strike price equal to the face value of the debt.

 

An illustration

To demonstrate, we start with a simple hypothetical example in which we are tasked with determining the value of some common shares. Imagine a firm with two classes of shares, common and preferred, with a million shares of each outstanding. The preferred shares have a liquidation preference of $1 per share and are participating and thus share equally with common shareholders on all incremental value greater than $1 per share. This implies that the first $1 million of liquidation proceeds is captured by preferred shareholders, but any proceeds beyond that million dollars will be split equally between the two types of shareholders. So if the company were sold for $1.5 million, then preferred shareholders would get $1.25 million and common shareholders $250,000.

Now that our firm’s capital structure is laid out, we can add a critical ingredient: uncertainty. We cannot be certain, ahead of time, what the eventual value of the firm will be. The core of option pricing theory is that ability to incorporate uncertainty. To avoid getting into the nitty-gritty of the Black-Scholes formula, we create a three scenario valuation model that incorporates uncertainty. Our three liquidation scenarios are: $6 million, $1.5 million, and $250,000. Using the distributional logic described in the prior paragraph, these liquidation scenarios result in common stock prices of $2.5, 0.25 and $0 per share, respectively. If we assume that each scenario has an equal probability, we can average these three values to get an estimated common stock payoff of $0.92. Depending on the timing of the liquidation scenarios and the methods we used to develop the scenario probabilities, this value may need to be discounted to account for time or risk preference.

 

Option Pricing in Theory and Practice

We can formalize the example above by using option pricing methods rather than the simple three scenario model. Option pricing offers several advantages. First, it specifies that the distribution of outcomes is lognormal and is a function of a volatility parameter that is relatively easy to estimate. This means we can avoid enumerating and applying values to discrete scenarios. Second, these methods allow us to avoid the messy task of estimating risk adjusted discount rates. Instead, option pricing formulas rely on no-arbitrage foundations, meaning they can be applied with fewer subjective assumptions.

While option pricing methods present some advantages, applying them to certain companies with moderately complex capital structures requires great care. Typically, a venture firm that has progressed through several rounds of fundraising may have common shares and common stock options, as well has several classes of preferred stock. Take for example a company with two rounds of preferred stock, A and B. In this case, the B shares will likely have liquidation preference of over Preferred A shares, which will in turn have preference over common shares. Setting up a model for such a firm requires an understanding of how various classes of stock will be paid out under each liquidation scenario. A chart like the one shown below shows how the various classes of investment might participate in capturing value for increasing enterprise values.