# Utilizing the Differential Put Method

An important step in determining the fair market value of a minority interest in the common stock for a privately-held company is to apply a discount for the lack of marketability (“DLOM”) of the private stock relative to a publicly traded common stock. Once an equity value is determined for a privately-held company using market and income approaches, another difference between a publicly-traded stock and privately-held one that needs to be accounted for is the difference in marketability of the two. A DLOM is appropriate to apply to account for the difference. There are various methods utilized to determine an appropriate DLOM including the restricted stock method, IPO method, and the option pricing method. The purpose of this piece is to focus on the application of the Differential Put Method, an option pricing method, to determine an appropriate DLOM.

The Differential Put Method is an option pricing method of quantitatively calculating a DLOM for the subject company used solely when there is a precedent transaction on another class of stock, typically a preferred round. The idea is that the preferred financing transaction has an implied discount for its lack of marketability in the price of the preferred shares. So when solving for the common stock based on the preferred price round, the resulting common value will already incorporate the discount implied in the preferred price. Therefore, the appropriate DLOM for the common is the incremental discount between the common and recently priced preferred DLOMs.

The Differential Put Method utilizes the protective put method to determine the specific DLOM for each class of stock based on the specific volatility for that class of stock. First, the volatility of each class of equity should be determined using Merton’s formula below1:

Class Volatility = Equity Volatility x [Equity Value x Class N(d1)]/Class Value

Once the class volatility is determined, the specific class DLOM can be calculated using the protective put method and the Black-Scholes-Merton formula. The Differential Put is then the incremental discount implied between the recently priced preferred stock and the common stock. Finally, the following formula can be used to determine the incremental discount between the preferred and the common:

Incremental DLOM = 1 – (1 – Common DLOM)/(1 – Preffered DLOM)

Some have calculated the incremental DLOM as the difference between the Common DLOM and Preferred DLOM. However, utilizing the difference between the two discounts will result in a lower incremental DLOM than the above formula. For example, assume we calculated a 10.0 percent DLOM for the Preferred Stock and a 30.0 percent DLOM for the Common Stock for a company with one class of preferred and common stock. Taking the difference will estimate an incremental DLOM of 20.0 percent, while the above formula results in a 22.2 percent incremental DLOM. Theoretically speaking, the above formula is the correct way to approach the calculation and simply taking the difference will underestimate the incremental DLOM. The larger the Preferred DLOM, the larger the difference between the two calculation methods.

In conclusion, the Differential Put Method is a useful tool to develop the incremental DLOM for the valuation of common stock in a privately held company on a minority interest basis. However, it should only be applied when there is a precedent transaction on another class of stock.

1 – American Institute of Certified Public Accountants, Inc.; Valuation of Privately-Held-Company Equity Securities Issued as Compensation, 2013.