Allocating Value Among Different Classes of Equity

All companies with preferred stock need to be fluent in the application of an option-pricing method since it is often used to determine the per-share value of their common or preferred securities. An understanding of option-pricing models is no longer the exclusive domain of a small group of accountants. Now, board members, executive officers, CFOs, auditors and private equity investors should have an awareness and understanding of the option-pricing models.

Today, companies are being financed with hybrid forms of capital that go well beyond plain-vanilla common equity and interest-bearing debt. It is not unusual for a business to carry debt that can be converted to equity or equity that is entitled to a liquidation preference. To complicate matters further, some rounds of financing incorporate caps, accrued dividends, performance warrants and other valuation complexities. An understanding of these financial structures and their effect on value is essential for several interested parties:

Valuation analysts need to understand the ramifications of a company’s capital structure on the value of its equity securities.

Executive management needs to know the effect that a round of financing may have on the fair value of a company’s existing securities and capital structure.

Private equity investors need to understand the effect that their investment has on the fair value of other equity securities in order to better structure their transactions.

Accordingly, we have presented an example to help valuation analysts, senior executives and investors through the structured-finance maze.

ALLOCATING EQUITY VALUE BETWEEN DIFFERENT CLASSES OF EQUITY
In 2004, the AICPA released its Practice Aid titled Valuation of Privately-Held-Company Equity Securities Issued as Compensation (please note that due to changes made to professional standards since this practice aid was originally issued, it is out of print and no longer available for purchase through the AICPA Web site). The guide summarizes many of the valuation standards and procedures that have been adopted by the profession. The guide also describes three methods of allocating value between preferred and common equity, which include:

Current Value Method (“CVM”)

Probability Weighted Expected Return Method (“PWERM”)

Option-Pricing Method (“OPM”)

The CVM has practical limitations on its use. Specifically, it should be used in two cases: (1) when a liquidity event is imminent and (2) when the business is at such an early stage of development that there is no material progress on the company’s business plan and there is no reasonable basis to estimate value beyond the preferred preference.

The PWERM is especially difficult to apply due to the significant level of subjectivity it requires. The probability of various exit scenarios and the value of the business at such exit events is very difficult to support.

As a result, the OPM is a commonly used method for allocating equity value between common and preferred shares. The OPM is more quantitative as it relies on the Black-Scholes-Merton model. Although the Black-Scholes formula was not designed for private companies, the accounting profession applies it in various situations, ranging from stock options to common equity valuation, and it continues to be the basis for the OPM.

OVERVIEW OF KEY STEPS FOR THE OPTION-PRICING METHOD
Below, we have summarized the steps and general processes in applying the option-pricing method.

Step 1—Determine Business Value and Black-Scholes Assumptions

Business Value—As the OPM values invested capital as a call option on a company’s value, the analyst must first determine which value to use. Conceptually, this value should be the amount claimholders would receive in a liquidity event. Accordingly, it is reasonable to estimate this value by using the implied enterprise value derived from the market-based and income-based analyses as of the valuation date. Since the fair value of interest-bearing debt (net of excess cash) is typically known, it can be subtracted from enterprise value.

Time to Liquidity Event—This is one of many assumptions that can be difficult to pin down, but the question that it raises is a significant one: How much time exists until there is a planned or likely liquidity event, such as a sale, public offering or other exit event? Of course, no company has a crystal ball and many professionals are often frustrated trying to defend the assumption. Interaction at the board level is often warranted.

Risk-Free Rate—The risk-free rate is the most obvious assumption. Typically, it is the rate available on a government security whose term matches the assumed time to liquidity. The analyst must then compute a continuously compounded equivalent rate for the Black-Scholes calculation.

Volatility—This measure should be based on the standard deviation of quoted market prices. In the case of a public company, volatility can be derived easily from the company’s historical stock prices. For private companies, volatility can be estimated by analyzing comparable public companies’ historical stock performances. It should be noted that the range of the stock returns sampled should cover the same period as the estimated time to liquidity. The OPM is highly sensitive to volatility and great care should be taken in estimating the volatility factor.

Step 2—Understanding the Capital Structure

Convertible debt and preferred stock come in many flavors, shapes and sizes. It is critical to invest the time to properly understand any conversion features. For example, some private equity firms structure preferred rounds that are effectively debt but labeled as preferred stock for tax purposes (the preferred never converts, instead it simply accrues a dividend). Whereas, other more common preferred rounds may have a choice of both realizing their preferences and then participating with common shareholders. Other preferred stock may be structured to either convert to common or be paid its preference, but not both. It is important to understand the subtle differences of preferred stock.

Step 3—Setting the Strike Prices for the Different Classes of Equity

In general, classes of invested capital convert in a sequential manner. Conversion starts with the invested capital with the lowest price per common stock equivalent (“CSE”). Subsequent conversion of other invested capital will follow this pattern.

Step 4—Allocating Value

Value is then allocated to each equity class based on each class’s ownership at different equity levels, as determined by call options.

COMPREHENSIVE EXAMPLE

Step 1—Determine Business Value & Black-Scholes Assumptions

For this example, we will look at a hypothetical company (“XYZ” or “the Company”) and assume an enterprise value of $50 million. We have arbitrarily chosen the time to liquidity (two years), volatility (50%), and the risk-free rate (5%). Defining and properly supporting these assumptions are paramount to a proper allocation of value.

Standard interest-bearing debt that calls for periodic interest and principal payments is typically valued at its face amount (which is reasonable if the interest rates reflect market rates). In our example, we have assumed a net debt obligation of $1 million. Consequently, the debt’s amount, net of any excess cash, is subtracted from the company’s enterprise value to determine the underlying value used in the OPM. XYZ’s enterprise value of $50 million less its net debt of $1 million results in an underlying value attributable to remaining invested capital of $49 million.

Step 2—Understanding the Capital Structure

The hypothetical preferred rounds were structured so that Preferred A benefits from its liquidation preference and its conversion to common. In contrast, Preferred B is entitled to either its liquidation preference or its conversion to common. The Company’s capital structure in terms of CSEs is summarized in Exhibit 1.

Step 3—Setting the Strike Prices for the Different Classes of Equity

Under the OPM, the point at which each class of equity becomes “in-the-money” is viewed as a call option. It is therefore necessary to determine the underlying value where each class would receive value, known as the strike price.

Value for Payoff to Common Shareholders

Conceptually, payoff begins to accrue to common equity when all other contractual obligations have been fulfilled. In our example, XYZ’s common shareholders will start receiving some proceeds when the Company’s debt and amounts owed to preferred shareholders have been paid. We used the preferred shares’ liquidation value as of the time to liquidity, which includes any accrued and accumulated dividends. Doing so allows for the preferred shares’ respective dividend rate to affect the value attributed to each equity class. Consequently, common shareholders will be able to receive value after the preferred stockholders and convertible debt holders have received their preferences.

For XYZ, the underlying value for payoff to the common shareholders is $13.5 million, which is the total after $1 million of convertible debt, $6 million of Preferred A (face value plus two years of accumulating dividends), and $6.5 million of Preferred B (face value plus two years of accumulating dividends). Accordingly, common equity will be modeled with a call option with a $13.5 million strike price.

Analyzing the Participation of Each Equity Class

After common stock and fully participating securities, the additional classes of invested capital will convert based on their respective price per common stock equivalent, with the lowest converting first. Exhibit 2 summarizes the strike price or equity value when each class of equity will participate.

Preferred A

Preferred A is participating as it benefits from both its liquidation preference and also its automatic conversion to common after its liquidation preference has been realized. Preferred A’s value is derived from a combination of call options. First, its liquidation preference is modeled with a call option with a strike price of $1 million on the underlying value since Preferred A is paid after the convertible debt. Then, the value of its automatic conversion feature is estimated using a call option that has a strike price of $13.5 million, or the underlying value necessary for payoff to begin to common shareholders. Lastly, the dilution from the subsequent conversion of the remaining invested capital will be taken into account as detailed in our final allocation of value.

Options

Options differ from other types of invested capital in that these securities carry a strike price. Consequently, the exercise of options will not only dilute a company’s equity, but also provide cash proceeds. As with other forms of invested capital that carry an option to buy a company’s equity, the necessary enterprise value for exercise must first be assessed. It is assumed that vested and non-vested options as of the valuation date will be exercised upon a liquidity event. All granted options should typically be included in the model.

In the example, there are 100,000 vested and non-vested options at a strike price of $0.20. The payoff to common shareholders starts at $13.5 million, with both converted Preferred A and common shares outstanding, for a total of 600,000 CSEs outstanding. However, at $13.5 million, the common stock equivalents have a $0 per-share price. Options will be exercised only if the 700,000 outstanding shares (CSEs and options) have a per-share price of at least $0.20, the options’ exercise price. Accordingly, the underlying value must be $140,000 over the $13.5 million floor for the 700,000 common stock equivalents to have a per-share price of $0.20.

Also, the cash proceeds from the exercise of options must be taken into account. At an underlying value of $13,640,000, 100,000 options will be exercised providing $20,000 in cash proceeds. Accordingly, the floor level of $13,640,000 for the exercise of options should be reduced by $20,000 to $13,620,000.

Convertible Debt

In the example, XYZ has a $1 million debt liability that can convert to 100,000 common shares, while 700,000 CSEs are currently outstanding (common, Preferred A, and options). For the debt to convert, the per-share price of the Company’s CSEs must be at least $10 so that the value of the converted shares equals $1 million. At $10 per share and 800,000 outstanding shares (700,000 CSEs and 100,000 from the debt’s conversion), the underlying value must be $20,480,000 [the $13.5 million starting point for payoff to common, plus an additional $8 million (or $10 per share with 800,000 CSEs outstanding), less the $20,000 of cash proceeds from the options, less the forgiven $1 million debt]. It should be highlighted that if the debt converts, the Company is no longer responsible for the original $1 million liability.

Preferred B

Preferred B is modeled in a similar way to the convertible debt. As it can only benefit from its liquidation preference or its conversion to common, we need to calculate the value at which the Preferred B would convert. For Preferred B to participate in the equity of the Company for a value greater than its preference, the underlying value must be $64,480,000 [the $13.5 million starting point for payoff to common, plus an additional $58.5 million (or $65 per share with 900,000 CSEs outstanding), less the $20,000 of cash proceeds from the options, less the forgiven $1 million of convertible debt, and less the forgiven Preferred B preference]. Similar to the convertible debt, if Preferred B converts, it will not benefit from its preference.

Step 4—Allocating Value

The next step is to allocate XYZ’s enterprise value between its different classes of equity. First, Exhibit 3 summarizes the key assumptions to the model.

XYZ’s equity structure is illustrated in Exhibit 4. In this example, all proceeds up to $1 million would go to convertible debt. The next $6 million (the tranche from $1 million to $7 million) would be paid to Preferred A. Similarly, the next $6.5 million would be received by Preferred B. Then the next $120,000 (the tranche from $13.5 million to $13.62 million) would be split between Preferred A, receiving 17%, and common shareholders, who would receive 83%.

Once we understand the capital structure and the behavior of the equity classes at different levels of value, we then derive the value of the respective call options by using the Black-Scholes model. The value of each equity tranche represents the difference between each call option price (or the incremental change in value for each option). Exhibit 5 summarizes the value for each option based on the strike price for each equity class.

Next, we allocate the value of each equity tranche to the equity classes that participate in it, based on their respective percentage of ownership, as summarized in Exhibit 6 (note, totals may not recompute due to rounding).

Based on the information presented above, we are able to model each class of invested capital as a combination of call options. The total value for the various classes of equity must total the $49 million value of the respective invested capital.

CONCLUSION
Like many issues in business valuation today, best practices are evolving and there are disparities among professionals. Many issues in valuation are still unresolved and subject to debate (such as reflecting voting and non-voting rights, applicability of discounts for lack of marketability, etc.), and the applications and underlying details of the option-pricing method are no exceptions. Valuation models must be tailored to the specific facts and circumstances of the company and the securities being valued.