What is a Discount for Lack of Marketability (DLOM)?

Recall in the Options Pricing Model overview, we walked through the OPM to compute a per-share value of $3.05 on a fully marketable basis. In other words, if the company that we were valuing were publicly traded (i.e., fully marketable), then one would expect to pay $3.05 per share for every share of common stock in our example company, ABC, Inc.

When valuing closely-held (private) companies, however, valuators typically apply a discount for lack of marketability (DLOM) to the share price, to account for the fact that private company shares are not completely liquid. In other words, one should expect to pay less for a closely-held (private) share of stock than that same investor would pay for a publicly-traded, fully liquid security.

Marketability Defined

Marketability - “the ability to quickly convert property to cash at minimal cost, with a high degree of certainty of realizing the anticipated amount of proceeds.” 1,2

Discount for Lack of Marketability (DLOM) - “an amount or percentage deducted from the value of an ownership interest to reflect the relative absence of marketability.”1

What to Consider

The Carta 409A Valuation, in accordance with the parameters set forth in  Mandelbaum v. Commissioner,takes into account the following:

  • The value of the subject corporation's privately traded securities vis-a-vis its publicly traded securities (or, if the subject corporation does not have stock that is traded both publicly and privately, the cost of a similar corporation's public and private stock);
  • an analysis of the subject corporation's financial statements;
  • the corporation's dividend-paying capacity, its history of paying dividends, and the amount of its prior dividends;
  • the nature of the corporation, its history, its position in the industry, and its economic outlook;
  • the corporation's management;
  • the degree of control transferred with the block of stock to be valued; 
  • any restriction on the transferability of the corporation's stock;
  • the period of time for which an investor must hold the subject stock to realize a sufficient profit;
  • the corporation's redemption policy; 
  • the cost of effectuating a public offering of the stock to be valued, e.g., legal, accounting, and underwriting fees.

Summary of Approaches

The Carta 409A Valuation takes into account a number of different approaches to computing DLOM, loosely categorizable into the following:

  1. Benchmark study approaches
  2. Security-based approaches
  3. Analytical approaches
  4. Other approaches

Benchmark study approach

This approach estimates the appropriate DLOM based on restricted stock studies, as well as pre-Initial Public Offering (IPO) pricing studies. The Carta valuation considers the pre-IPO pricing studies a generally less-accurate indicator of private company DLOM for smaller, earlier-stage companies, thus only an overview of the restricted stock studies is provided below.

Restricted Stock Studies

Restricted stock - unregistered common stock of a corporation identical in every respect to its publicly traded shares, except that it has not been registered, and is therefore, not freely tradable.4

Valuators consider restricted stock studies because the effect of lack of marketability, one could argue, can be quantified by comparing the sale price of publicly traded shares to the sale price of so-called restricted shares of the same company that are identical in all rights and powers except for their ability to be freely marketed. Restricted stock studies are published, empirical studies, the most often cited of which are indicated below:

Restricted Stock Studies Attempting to
Measure the DLOM for Private Firms
Empirical Study Time Period Covered Mean DLOM
SEC overall average (a) Jan, 1966 - Jan, 1969 25.8%
SEC nonreporting OTC companies (a) Jan, 1966 - Jan, 1969 32.6%
Gelman (b) Jan, 1968 - Dec, 1970 33.0%
Trout (c) Jan, 1968 - Dec, 1972 33.5%
Moroney (d) Jan, 1969 - Dec, 1972 35.6%
Maher (e) Jan, 1969 - Dec, 1973 35.4%
Standard Research Consultants (f) Oct, 1978 - Jun, 1982 45.0% (median)
Willamette Management Associates (g) 1981 - 1984 31.2% (median)
Silber (h) Jan, 1981 - Dec, 1988 33.8%
FMV Opinions, Inc. (i) Jan, 1979 - Apr, 1992 23.0%
Management Planning, Inc. (j) Jan, 1980 - Dec, 1996 27.1%
Bruce Johnson Study (k) Jan, 1991 - Dec, 1995 20.0%
Columbia Financial Advisors (l) Jan, 1996 - Apr, 1997 21.0%
Columbia Financial Advisors (l) May, 1997 - Dec, 1998 13.0%
(a)Discounts Involved in Purchases of Common Stock (1966-1969), Institutional Investor Study Report of the Securities and Exchange Commission, H.R. Do. No. 92-64, Part 5, 92nd Congress, 1st Session, 1971, 2444- 2456.
(b)Gelman, Milton, An Economist Financial Analyst’s Approach to Valuing Stock of a Closely Held Company, Journal of Taxation, June 1972, 353-354.
(c)Trout, Robert R., Estimation of the Discount Associated with the Transfer of Restricted Securities, Taxes, June 1997, 381-384.
(d)Moroney, Robert E., Most Courts Overvalue Closely Held Stocks, Taxes, March 1993, 144-154.
(e)Maher, Michael J., Discounts for Lack-of-marketability for Closely Held Business Interests, Taxes, September 1976, 562-71.
(f)Pittock, William F., and Stryker, Charles H., Revenue Ruling 77-287 Revisited, SRC Quarterly Reports, Spring 1983.
(g)Willamette Management Associates study (unpublished)
(h)Silber, William L., Discounts on Restricted Stock: The Impact of Illiquidity on Stock Prices, Financial Analysts Journal, July-August 1991, 60-64.
(i)Hall, Lance S., and Timothy C . Polacek, “Strategies for Obtaining the Largest Valuation Discounts,” Estate Planning, January/February 1994. pp. 38-44.
(j)Oliver, Robert P. and Roy H Meyers, “Discounts Seen in Private Placements of Restricted Stock: The Management Planning, Inc., Long-Term Study (1980-1996)” (Chapter 5) in Robert F, Reilly and Robert P. Schweihs, eds, The Handbook of Advanced Business Valuations (New York: McGraw-Hill, 2000).
(k)Johnson, Bruce, "Restricted Stock Discounts, 1991-95", Shannon Pratt’s Business Valuation Update, Vol. 5, No. 3, March 1999, pp. 1-3. “Quantitative Support for Discounts for Lack of Marketability.” Business Valuation Review, December, 1999, pp. 152- 155.
(l)CFAI Study, Aschwald, Kathryn F., "Restricted Stock Discounts Decline as Result of 1-Year Holding Period – Studies After 1990 'No Longer Relevant' for Lack of Marketability Discounts", SHANNON PRATT'S BUSINESS VALUATION UPDATE, Vol. 6, No. 5, May 2000, pp. 1-5.

Securities-based approach

The Longstaff Approach 5

The Longstaff Approach relies on stock option pricing theory to estimate the DLOM for a privately held company, based on the price of a “ look back” option.  A “lookback” option differs from most other options in that the holder can look back at the end of the option’s life and retroactively exercise the option at the highest stock price (for a put option) during the holding period. The Longstaff study assumes an investor 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.

The Longstaff model should be considered the theoretical upper bound on an enterprise's DLOM, and it generally overstates the proper DLOM.

The Model


T = time to exit

σ = Volatility

N(.) = Standard normal cumulative distribution function

Representative DLOMs 

Volatility 25.00% 50.00% 75.00% 100.00% 125.00%
Time to exit
1 21.6% 46.6% 75.3% 108.1% 145.2%

2 31.5% 70.1% 116.7% 172.0% 236.9%

3 39.5% 90.0% 153.0% 229.9% 321.9%

4 46.6% 108.1% 186.8% 284.9% 404.0%

5 53.0% 125.0% 219.3% 338.4% 484.7%

Note: The Longstaff model outputs DLOMs in excess of 100% at very low volatilities, and as such is generally considered an inaccurate overestimation of a proper DLOM.  Thus, the Longstaff model should only be used as a guideline, but in most cases should not be used as the sole method to calculate a given DLOM.

The Chaffe Approach6

In 1993, David Chaffe authored a DLOM option pricing study in which he related the cost to purchase a European put option to the DLOM. In Chaffe's estimation, “if 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.”  Chaffe relied on the Black Scholes Option Pricing Model for a put option to determine the cost or price of the put option, and defined the DLOM as the cost of the put option divided by the market price.

According to Chaffe, this approach should be considered the theoretical lower bound on an enterprise's DLOM, since a European put option pricing formula does not take into account early exercise.  

The Model


S0 = Total Equity Value

= Equity Breakpoint Value

= continuously compounded dividend yield

= time to expiration (% of year)

σ = Volatility

r = risk-free rate

N(.) = Standard normal cumulative distribution function

Representative DLOMs 

  Volatility 25.00% 50.00% 75.00% 100.00% 125.00%
Time to exit            
1   9.25% 18.97% 27.48% 37.40% 45.86% 
2   12.61% 26.01% 37.41% 50.11% 60.25% 
3   14.97% 30.98% 44.20% 58.28% 68.81% 
4   16.81% 34.84% 49.30% 64.02% 74.35% 
5   18.32% 37.97% 53.50% 68.20% 78.00% 

The Finnerty Approach7

In 2002, John D. Finnerty conducted an extension of the Longstaff study, that “tests 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.” However, 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 general, the Finnerty model generates DLOMs that are relatively close to the average DLOMs reported in the empirical studies mentioned above. 

The Model



V0 = The value of the share of common stock without transfer restrictions

q = continuously compounded dividend yield

σ = Volatility

r = risk-free rate

N(.) = Standard normal cumulative distribution function

σ = Volatility

e = The mathematical constant = 2.71828...

Representative DLOMs 

  Volatility 25.00% 50.00% 75.00% 100.00% 125.00%
Time to exit            
1   5.72% 11.24% 16.34% 20.85% 24.62% 
2   8.04% 15.50% 21.84% 26.63% 29.74% 
3   9.79% 18.52% 25.26% 29.50% 31.49% 
4   11.24% 20.85% 27.54% 30.95% 32.05% 
5   12.49% 22.73% 29.10% 31.66% 32.22% 

Note: The Finnerty model has a mathematical asymptote at approximately 32%. Thus, for companies at higher volatilities, this model may understate the proper DLOM.

1 International Glossary of Business Valuation Terms, as adopted in 2001 by American Institute of Certified Public Accountants, American Society of Appraisers, Canadian Institute of Chartered Business Valuators, National Association of Certified Valuation Analysts, and The Institute of Business Appraisers.
2 Shannon P. Pratt, Alina V. Niculita, Valuing a Business, The Analysis and Appraisal of Closely HeldBusinesses, 5th ed (New York: McGraw Hill, 2008), p.39.
3 Mandelbaum v. Commissioner, T.C. Memo 1995-255, 36.
4 Securities Act of 1933 (Section 230.144). Note: Because the holder of restricted common stock is prohibited from selling any of the stock for full year (1997-2008, thereafter holding period is six months) and has additional constraints on the amounts that may be sold for an additional year, the restricted stock is significantly less liquid (and therefore less valuable) than its unrestricted counterpart.
5 Longstaff, Francis A., “How Much Can Marketability Affect Security Values?”, The Journal of Finance, Vol. L, No. 5 (1995), pp.1767-1774.
6 David B.H. Chaffe III, “Option Pricing as a Proxy for Discount for Lack of Marketability in Private Company Valuations,” Business Valuation Review (December 1993): 182–6. (Model corrected and updated in 2009; the Carta valuation uses the corrected, updated model)
John D. Finnerty, “The Impact of Transfer Restrictions on Stock Prices.” Analysis Group/ Economics (October 2002).