Determining a Reasonable Volatility Assumption for the OPM

It can be difficult to value privately held equity securities, especially when the company is an early stage firm with no revenue. Traditional methods like the market approach, income approach, and cost approach may not be relevant or provide a reasonable value. However, when an early stage company has raised some form of financing, whether in preferred equity or convertible debt, valuation professionals can determine an implied value of the common equity based on the facts and terms of the financing using the Option-Pricing Method (OPM).

The AICPA’s Practice Aid Valuation of Privately Held Company Equity Securities Issued as Compensation (“Practice Aid”) discusses the OPM. The OPM treats common stock and preferred stock as call options on the enterprise’s equity value, with exercise prices based on the liquidation preference of the preferred stock. Under this method, the common stock has value only if the funds available for distribution to shareholders exceed the value of the liquidation preference at the time of a liquidity event (for example, a merger or sale) — assuming the enterprise has funds available to satisfy liquidation preferences.1 We commonly used the Black-Scholes model to price the call option. The Black-Scholes model requires a number of assumption inputs, including: risk-free rate, volatility, time to exit, exercise price, and current price. In an OPM analysis, these are: the risk-free rate, volatility, time to liquidity event, liquidation preferences, and equity value (or enterprise value in cases where the OPM includes debt).

The purpose of this article is to discuss the volatility assumption used on the OPM. The starting point is to determine the historical equity volatilities over the assumed time horizon for a group of comparable companies to the subject company being valued. In some cases, the valuator may stop there and use the determined equity volatility in their OPM analysis. However, if comparable companies have capital structures with varying levels of debt or preferred equity (which typically has many preferences to the common equity), the equity volatility may be inconsistent and not a good match for the subject company. In these cases, it may be necessary to un-lever the equity volatility to remove the effect of leverage and determine the asset volatility for each of the comparable companies. Using asset volatility removes the differences in capital structure between the comparable and subject companies and leads to a more consistent application of volatility in the OPM.

The general relationship between equity value and asset value can be expressed as follows:

Equity Value = Total Asset Value × N(d1) – Book Value of Debt (or Preferred Equity) × exp(–rT) × N(d2)

In this equation, r is the risk free rate, T is the time to liquidity, and d1 and d2 have their standard Black- Scholes definitions based on the asset’s volatility. In addition, the relationship between equity volatility and asset volatility can be written as follows:

Equity Volatility = (Total Asset Value × N(d1) × Asset Volatility) / Total Equity Value

Using the equation above, you can solve for the asset volatilities for each of the comparable companies. Then, the asset volatility should be applied for the volatility input assumption within the OPM analysis in situations where all levels of capital are accounted for the in the OPM. In a case where the subject company has both debt and preferred equity but the OPM only incorporates preferred and common equity, it is then important to re-lever the volatility based on the subject company’s capital structure to determine the volatility for equity as a whole. In this way, the volatility assumption utilized is consistent with the capital that is being allocated in the OPM.

1. American Institute of Certified Public Accountants, Inc., Working Draft Practice Aid “Valuation of Privately Held Company Equity Securities Issued as Compensation”, 2011.