Discounts for Lack of Marketability
Consideration for Closely Held Securities‚ÄĒDLOM Theoretical Models (Part II of II)
This article summarizes the factors (and the empirical evidence) that the analyst may consider in the measurement of a discount for lack of marketability (DLOM) valuation adjustment associated with non-controlling securities of a closely held company. This security-level DLOM is different from the entity-level DLOM that is applied at the closely held company level. This second part of the article focuses on theoretical DLOM measurement models: the option pricing and DCF models.
- DCF models
Option Pricing Models
OPMs are based on the premise that the cost to purchase a stock option is related to the DLOM. ¬†The following discussions summarize published DLOM studies that rely on OPMs.
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David Chaffe published a study that related the cost to purchase a European put option to the DLOM. ¬†Chaffe concluded, ‚Äúif one holds restricted or non-marketable stock and purchases an option to sell those shares at the free market price, the holder has, in effect, purchased marketability for those shares. ¬†The price of that put is the discount for lack of marketability.‚ÄĚ
Chaffe relied on the Black-Scholes OPM to estimate the option price. ¬†The inputs in the Black-Scholes model are as follows:
- Stock price
- Strike price
- Time to expiration
- Interest rate
In the Chaffe model, the stock price and strike price equal the marketable value of the closely held company stock as of the valuation date. ¬†The time to expiration equals the time the securities are expected to remain nonmarketable. ¬†The interest rate is the cost of capital. ¬†And, volatility is a judgmental factor based on volatility of selected guideline publicly traded company stocks.
To apply an OPM to the subject closely held security, each of these variables is determined. ¬†Some variables, such as the interest rate and strike price, are relatively easy to estimate. ¬†Other variables, such as the holding period and volatility, are more difficult to estimate.
According to the study, the appropriate DLOM for a closely held security with a two-year required holding period, and a volatility between 60% and 90%, is between 28% and 41%.
According to Chaffe, ‚Äúconsidering that volatility for shares of most smaller, privately held companies fit the ‚ÄėVOL 60%-70%-80%-90%‚Äô curves, a range of put prices of approximately 28% to 41% of the marketable price is shown at the two-year intercept. ¬†At the four-year intercept, these ranges are 32% to 49%, after which time increases do not substantially change the put price.‚ÄĚ
Francis Longstaff published a study that relies on stock options to estimate the DLOM. ¬†While Chaffe based his study on avoiding losses, Longstaff based his study on unrealized gains. ¬†Another difference between the two studies is that the Longstaff study provides an estimate for the upper limit on the value for marketability. ¬†The Longstaff study is based on the price of a hypothetical ‚Äúlookback‚ÄĚ option.
The Longstaff study assumes the owner has a single-security portfolio, perfect market timing, and trading restrictions that prevent the security from being sold at the optimal time. ¬†The value of marketability, based on these assumptions, is the payoff from an option on the maximum value of the security, where the strike price of the option is stochastic.
Exhibit 1 summarizes the Longstaff study results.
Upper Bounds for Implied DLOM
|Marketability Restriction Period||Standard Deviation
So for a five-year holding period and 30% standard deviation, the implied DLOM is over 65%. ¬†Longstaff analyzed securities with a volatility between 10% and 30% because ‚Äúthis range of volatility is consistent with typical stock return volatilities.‚ÄĚ
John Finnerty published an option-pricing study that ‚Äútests the relative importance of transfer restrictions on the one hand, and information and equity ownership concentration effects on the other in explaining private placement discounts.‚ÄĚ
The Finnerty option-pricing study is an extension of the Longstaff study. ¬†Unlike Longstaff, Finnerty did not assume that investors have perfect market timing ability. ¬†Instead, Finnerty modeled the DLOM as the value of an average strike put option.
In addition to analyzing stock options, Finnerty analyzed 101 restricted stock private placements that occurred between January 1, 1991, and February 3, 1997. ¬†The Finnerty private placement study concluded price discounts of 20.13% and 18.41% for the day prior to the private placement and for 10 days prior to the private placement, respectively.
Long-Term Equity Anticipation Securities (LEAPS) Studies
Each of these LEAPS studies was conducted using a similar research design. ¬†A long-term equity anticipation security is essentially a long-term stock option that offers price protection for up to two years into the future. ¬†Therefore, an investor who desires protection against stock price declines can purchase a LEAPS put option.
The LEAPS studies examined the cost of buying LEAPS put options and concluded that the cost of the LEAPS put option divided by the stock price indicates the DLOM. ¬†Trout examined nine LEAPS as of March 2003 with options expiring January 2005. ¬†The nine LEAPS were for large companies with actively traded securities.
According to Trout, ‚ÄúThe data concerning the relative cost of puts as an insurance premium indicate an insurance premium cost equal to about 24% of the price. ¬†This finding suggests that the minimum discount that one should assign for the lack of marketability of holding privately held stock is at least 24%.‚ÄĚ
The 2013 Seaman study updated and extended the Trout study through November 2012. ¬†The Seaman study considered the relationship between the price of the LEAPS (i.e., the price discount) and the following variables:
- Company size
- Company risk
- Latest year profit margins
- Latest year return on equity
- Company industry
The Seaman study reached the following conclusions:
- Company size: Revenue size has a major effect on the cost of price protection with smaller levels of revenue associated with larger discounts.
- Company risk: Company risk has a large effect on discounts, with higher risk companies, as measured by a company‚Äôs beta, associated with a larger discount.
- Latest year profit margin: Company profitability has a mild (but not a major) effect on marketability discounts.
- Latest year return on equity: The company‚Äôs latest year return on equity has some effect on discounts particularly at the lower end of returns. For positive returns on equity, there is a minor effect on discounts.
- Company industry: The size of the discount varies by industry, but the discounts vary even more by the individual company.
The LEAPS studies concluded that the observed DLOMs were minimum price discounts when applied to the value of closely held companies. ¬†This conclusion is based on the following observations:
- The underlying securities on which the LEAPS were based are often much larger than the subject closely held company.
- The underlying securities on which the LEAPS were based are marketable.
- The LEAPS themselves can be sold at any time during the holding period.
- There is a known liquidity event (i.e., the sale of the underlying security) for LEAPS.
The OPM studies indicate similar price discounts to the above-described empirical studies. ¬†In the Chaffe, Longstaff, and Finnerty studies, the indicated DLOM for a closely held company (given certain volatility assumptions) reaches 65%. ¬†In the LEAPS studies, the price discount is much lower, but the authors of the two sets of studies conclude that the indicated discount represents a minimum DLOM.
Discounted Cash Flow Models
The DCF method is based on the principle that value equals the present value of future income. ¬†Christopher Mercer and Travis Harms described how the DCF model relates to the DLOM:
Quantitative analyses therefore estimates the value of illiquid interests based on the expectation of benefits (distributions or dividends and proceeds of ultimate sales) over relevant expected holding periods using appropriate discount rates to equate with present values. ¬†The process of doing this analysis, in the context of valuing a business at the marketable minority interest level, determines the applicable marketability discount.
The Quantitative Marketability Discount Model (QMDM)
The QMDM is a shareholder-level DCF model that uses a quantitative analysis to calculate the DLOM. ¬†The QMDM is based on:
- The expected growth rate in subject company value
- The expected interim cash flow
- The expected holding period
- The required holding period return
In the QMDM, the analyst values the closely held company at the entity level, resulting in a marketable security value. ¬†Next, the analyst estimates shareholder value. ¬†The shareholder value represents the nonmarketable security value.
To calculate the shareholder value, the analyst increases the closely held company value by the growth rate during the expected holding period. ¬†Next, the analyst discounts the future company value using the required holding period return. ¬†The resulting value equals the shareholder value. ¬†The calculation of one minus the ratio of shareholder value to entity value equals the DLOM.
The Tabak Model
David Tabak developed a DCF model to estimate the DLOM based on the capital asset pricing model. ¬†The Tabak model ‚Äúfocuses on the extra risks imposed on the owner of a security or interest in a business enterprise, and not on the lack of access to capital. ¬†In brief, the theory uses market data on the additional return that investors require in order to hold a risky asset, measured by the equity risk premium, to extrapolate the extra return that the holder of an illiquid asset would require.‚ÄĚ
Security-Specific Transferability Restrictions
Many of the above-listed empirical studies indicate that company size, block size, and dividends affect the DLOM. ¬†Other factors affect closely held securities that are not measurable in the above-listed empirical studies. ¬†These factors include contractual restrictions, such as a shareholder agreement, right of first refusal, buy-sell agreement, and the like. ¬†Contractual restrictions can severely limit the marketability of closely held securities.
The following list presents some contractual restrictions that may affect the DLOM:
- Buy-sell agreements
- Shareholder or partnership agreements
- Rights of first refusal
- Other contractual transferability restrictions
The more restrictive the agreement or provision, the greater the appropriate DLOM, all else equal.
Summary and Conclusion
Analysts may be asked to value noncontrolling securities in closely held companies for various transaction, financing, taxation, planning, and litigation reasons. ¬†Depending on the business valuation approaches and methods applied, and on the benchmark empirical data used, the analyses may initially conclude the security value on a marketable (as if traded on an organized stock exchange) basis. ¬†In such instances, the analyst may apply a valuation adjustment to conclude the final (nonmarketable level) security value. ¬†This discussion summarized the factors (and empirical evidence) that the analyst may consider in the DLOM measurement related to the valuation of noncontrolling securities in a closely held company.¬†
 European options have a single exercise date. ¬†In contrast, the holder of an American option can exercise the option at any time during the existence of the option.
 David B.H. Chaffe III, ‚ÄúOption Pricing as a Proxy for Discount for Lack of Marketability in Private Company Valuations,‚ÄĚ Business Valuation Review (December 1993): 182‚Äď6.
 Ibid.: 184.
 Francis A. Longstaff. ‚ÄúHow Much Can Marketability Affect Security Values?‚ÄĚ The Journal of Finance (December 1995): 1767‚Äď74.
 A ‚Äúlookback‚ÄĚ option differs from most other options in that the holder can look back at the end of the option‚Äôs life and retroactively exercise the option at either the lowest stock price (for a call option) during the holding period or the highest stock price (for a put option) during the holding period.
 Longstaff, ‚ÄúHow Much Can Marketability Affect Security Values?‚ÄĚ: 1771.
 John D. Finnerty, ‚ÄúThe Impact of Transfer Restrictions on Stock Prices,‚ÄĚ Analysis Group/Economics (October 2002).
 Robert R. Trout, ‚ÄúMinimum Marketability Discounts,‚ÄĚ Business Valuation Review (September 2003).
 Ronald M. Seaman, ‚ÄúLatest LEAPS Study Sheds Light on Company Size and DLOMs,‚ÄĚ Business Valuation Update 19, no. 9 (September 2013).
 Companies examined included Amazon, Ford Motor, General Motors, Morgan Stanley, Microsoft, Nextel, Qlogic, Qualcom, and Tyco.
 Trout, ‚ÄúMinimum Marketability Discounts‚ÄĚ: 124‚Äď5.
 Seaman, ‚ÄúMinimum Marketability Discounts‚ÄĒ5th Edition,‚ÄĚ March 2010.
 Z. Christopher Mercer and Travis W. Harms, ‚ÄúMarketability Discount Analysis at a Fork in the Road,‚ÄĚ Business Valuation Review (December 2001): 23.
 David Tabak, ‚ÄúA CAPM-Based Approach to Calculating Illiquidity Discounts,‚ÄĚ NERA Economic Consulting publication (November 11, 2002), www.nera.com.
Robert Reilly, CPA, ASA, ABV, CVA, CFF, CMA, CBA, is a managing director of Willamette Management Associates based in Chicago. His practice includes business valuation, forensic analysis, and financial opinion services. Throughout his notable career, Mr. Reilly has performed a diverse assortment of valuation and economic analyses for an array of varying purposes.
Mr. Reilly is a prolific writer and thought leader who can be reached at (773) 399-4318, or by e-mail to email@example.com.