Restricted Stock Benchmarkers Beware

Benchmark Analysis Will Not Work for Even a Single Asset Holding Company

You have been asked to determine the fair market value of a 10% member interest in a limited liability company that holds a single asset, an income-producing commercial building.   All you have to do is slap on a couple of discounts with the largest discount based on benchmark analysis based on dated restricted stock studies.  Right?  Wrong!  Absolutely wrong!

The example for this post is a single asset holding company holding an income-producing property.  The example is about as basic as it can be.  There is no debt and few other complicating factors.  This post outlines the basic analysis necessary to develop a credible, Standards-compliant marketability discount in the context of a fair market value determination.

The Building and the Holdco

The building is a rental industrial building located in Industrial, Tennessee (“Building”).  Building is ten years old, is located in a reasonably good commercial area of town, and is of average condition.  Building is leased by a single tenant who has occupied it from the beginning.  The lease has just renewed for a ten-year period.

Building is owned in fee simple by Single-Asset Holdco, LLC. (“Holdco”).

The picture above is taken from the real estate appraisal.  The mortgage taken out on Building upon its completion has just been retired.  Note the “wrapper” around Building is Holdco, the legal entity that owns it.  Building and Holdco are not the same things.

The Real Estate Appraisal

Building was recently appraised by Compass, LLC, a qualified real estate appraisal firm familiar with Industrial, Tennessee.  The valuation date was March 31, 2021 and the report was dated June 30, 2021.

The appraisal’s conclusion of market value for Building was $2,495,000.  The 10% interest is worth $249,500 at pro rata value.  What else can we learn from the real estate appraisal?  A brief summary of key information and assumptions is found in the next table.

The table above summarizes key information about the real estate appraisal. The standard of value (market value) and valuation date (March 31, 2021) are on Rows 1 and 2.  The appraiser concluded that the highest and best use of the property was “as is,” and that the market value of Building is $2,495,000 (Rows 3 and 4).  The square footage of Building and the lot are found on Rows 5 to 10.

Net operating income is summarized through Row 14 and is $192,964.  The capitalization rate used in the appraisal is a range of 7.50% to 8.0%.  As a check, we divide the net operating income by the mid-point cap rate and get $2,490,000, which is close to the conclusion.  That is corroborated with a Sales (Market) Approach with an indication of $2,500,000.  With equal weights, the appraiser concludes the midpoint, or $2,495,000.

We will touch on Rows 22 to 25 below.

Holdco Analysis and the Market Value Balance Sheet

Holdco has been in operation for ten years.  Building has been depreciated for ten years, so the book value of Building on Holdco’s balance sheet is less than its original cost.  It is necessary to take a close look at Holdco in order to begin to think about the fair market value of a 10% member interest.  An overview of the analytical process is outlined in the next figure. The analysis would, of course, include any other relevant facts or information pertaining to the value of Holdco and the 10% member interest.

Holdco, like every limited liability company, has an operating agreement.  The terms of that agreement can have an impact, and sometimes a material impact, on the fair market value of illiquid minority interests.  It is necessary for the appraiser to summarize the primary terms of Holdco’s operating agreement and identify those terms that have a potential impact on fair market value.  These might include restrictions on transfer, an adverse clause in the “buy-sell agreement” portion of the agreement, and others, as applicable.  Assume there are significant restrictions on transfer of owners’ interests.

The history of distributions and the outlook for future distributions are important investor considerations that have a potential impact on value.  For example, other things being equal, an interest in an entity paying a regular distribution (above taxes) is worth more that an otherwise identical interest in an entity that makes no distributions.  It can also be important to analyze the relationship between the actual history of operating income and the pro forma net operating income utilized in the real estate appraisal.

The appraiser should be able to understand the reasons for significant differences.  Holdco has not made distributions other than for taxes since its inception.  However, the mortgage on Building has just been retired, so the expectation is that all future available cash flow will be distributed.  The lease on Building is a triple net lease, so there are few expenses to impinge on distributable cash flow.

Given the ownership and management of Holdco, what are reasonable expectations for the business plan for the entity?  What are the prospects for liquidity through an eventual sale or refinancing of Building?  The analyst must make a good faith effort to estimate the likely holding period for the investment.  This, of course, can seldom be known with precision, but the holding period is not forever and must be estimated (or a range must be estimated) based on information available at the valuation date.  Assume that the expected holding period is in the range of five to ten years.  The controlling owner is 65 years old and there seems to be a good chance that he will be interested in selling Building within that timeframe, which would likely provide a liquidity event for all owners of Holdco.

What are the prospects for growth in value of Holdco?  In this case, value growth is based on the expected growth in the real estate appraisal, which is about 3% per year.  Holdco has historical balance sheets that should also be analyzed, if available.  The balance sheets will show the progression of key items over time and the current book values of all assets and liabilities.  Are there any other assets or liabilities whose carrying values differ from their market values?  In the case of Holdco, there are no assets other than Building, and there are no liabilities.

The objective of this analysis of the operating agreement and the historical financial statements is to identify items that can influence value and to comply with the Uniform Standards of Professional Appraisal Practice (USPAP) relative to the valuation of interests in businesses, which is exactly what a 10% member interest in Holdco is.  The need for the analysis suggested in this section is affirmed by the Uniform Standards of Professional Appraisal Practice.

USPAP Requirements for Analysis

Standard 9 of USPAP is titled “Business Appraisal, Development.”  Many business appraisers and most real estate appraisers are not aware of the quite specific requirements for analysis provided in Standards Rules 9-4(c) and 9-4(d) regarding interests in businesses.  That guidance is quoted below.

The guidance of USPAP is clear.  Appraisers must analyze the effect on value, if any, of a number of factors that influence the perceptions of hypothetical or real investors for interests like the 10% member interest of Holdco. In just over eleven lines of text, appraisers are admonished to analyze the effect on value four times.  In fact, appraisers are instructed by Standards Rules 9-4(c) and 9-4(d) to analyze the effect on value of a number of factors, including:

  • Buy-sell and option agreements
  • Investment letter stock restrictions
  • Restrictive corporate charter or partnership agreement clauses
  • Other similar features or factors
  • Extent to which the interest contains elements of ownership control
  • Extent to which the interest is marketable and/or liquid
  • Holding period, i.e., from the valuation date, a reasonable range of expected holding periods for the interest
  • The concept of holding period implies that there is a terminal event in which the interest or the underlying asset or both are sold.  In other words, there is a future event at which time the investor expects to obtain the benefits of the investment being made on the valuation date.  The implication for Holdco is that the appraisers must estimate the expected growth in value of Building to anticipate its value upon a terminal event.
  • Interim benefits, i.e., the history of and expectations for future distributions
  • Difficulty of marketing the subject interest
  • The degree of control and/or liquidity or lack thereof depends on a broad variety of facts and circumstances that must be analyzed when applicable

The analysis of Holdco described in the section above is essentially mandated by USPAP.

Given this very specific guidance from USPAP, which has been in the standards for a number of years now, it is surprising that some business appraisers who are benchmarkers still believe they can look at a handful of restricted stock studies and “divine” marketability discounts.  More on that below.

Understanding Fair Market Value

In recent years, I have been using a graphic to discuss the standard of value known as fair market value with some success.  The graphic is shown now and will be discussed below the figure.

The key to the graphic is that hypothetical investors (buyers and sellers) with the characteristics shown above engage in hypothetical negotiations.  At the upper right of the figure, we see that they negotiate over the economics of investments and, specifically regarding the expected cash flow from a business or interest (over an expected holding period), the growth in that cash flow (and the expected growth in value of the underlying assets), and the risks associated with achieving those cash flows.

Buyers want the lowest possible price.  Sellers want the highest possible price.  Neither desire is fair market value, which occurs at the intersection of these hypothetical negotiations and is, inherently, a range concept.  But the hypothetical negotiations narrow the range considerably, as indicated in the figure.

Importantly, the factors of analysis in USPAP above mirror this concept.  They definitely require examination of expected cash flow and its growth, the required holding period and the risks associated with long periods of illiquidity, and the expected growth in value for an interest or an asset.  In the case of Holdco, there is an expectation for a good distribution yield going forward from the valuation date.

Rows 21 to 25 in the summary of the appraisal above indicate that the simple yield implied by net operating income and market value of Building is 7.73% based on the appraised value.  Hypothetical buyers would be interested in that yield, and would love to buy it on the cheap.  However, hypothetical sellers understand the value of a yield of that magnitude in the current low interest rate environment.  Both would be aware of the growth in value expectations from the real estate appraisal.

The point is that a business appraisal report should mirror the hypothetical negotiations of the buyers and sellers of the fair market value world.  Both the sellers and the buyers must be present.

The Minority Interest Discount

It is generally accepted and understood in the business appraisal community that the various control premium studies reflect, for the most part, strategic or synergistic acquisitions.  Market participants pay strategic control premiums for the benefit of merging acquired companies or assets into their businesses to generate strategic or synergistic cash flow benefits.  The implication of this fact is that control premium studies cannot be used to estimate minority interest discounts like most appraisers did historically and like some continue to do today. In other words we cannot use the following equation to estimate minority interest discounts.

MID = 1 – (1 / (1 + CP))

Control premiums represent capitalized expectations of strategic or synergistic benefits and do not measure the value of control.  This should be clear from the following quote from The Measurement and Application of Market Participant Acquisition Premiums, issued by The Appraisal Foundation, published in 2017.

The Working Group believes that MPAPs should be supported by reference to either enhanced cash flows or a lower required rate of return from the market participant perspective. The referenced economic benefits should be sufficient to provide market participants with an adequate return on the concluded fair value of the controlling interest. The Working Group anticipates that in many instances such benefits will not be reliably identifiable, resulting in either no, or a small, premium.

We reached the same conclusion years prior in previous (and the current) edition of Business Valuation: An Integrated Theory (Mercer and Harms).  See this book’s Appendix 7-A.  No control premiums to what the MPAP guidance calls the foundation value, which comports with the marketable minority / financial control level of value discussed repeatedly on this blog, implies  no (or very small) minority interest discounts.

Asset holding entities have no strategic value component.  So net asset value is the financial control level of value, as seen in the figure below.

To the extent that there is a minority discount at all, it would be small.  The best available market evidence regarding the extent of the minority interest discount for asset holding entities is found in the public market for closed-end funds.  Publicly-traded close-end funds hold portfolios of (mostly) publicly-traded debt and equity securities.  Over time, these funds trade on average at discounts to their net asset values, typically on the order of 5% to 10%, plus or minus a bit.  Individual discounts can be much larger or negative (i.e., priced at premiums to NAV).

Some have argued that closed-end fund discounts have nothing to do with lack of control and should not be used as a basis to estimate minority interest discounts.  My response is that private asset holding entities (whether holding a single-asset like Holdco or a portfolios of assets) are similar to publicly-traded closed-end funds.  Closed-end funds provide ready and ample evidence that entities holding portfolios of assets tend to trade at discounts to their NAVs.  The comparison is far from perfect, but it is the best evidence available in the current market environment.

To the extent that appraisers employ minority interest discounts, and we will use that name with attribution to tradition, when valuing asset holding entities, they should be small, or on the order of 5% to 10%.  The old logic of there being a large penalty for “lack of control” does not work anymore.  However, many benchmarkers still remember the days of minority discounts ranging from 20% to 30% or so, and still believe that such discounts should be significant because of the lack of control for minority interest owners.

The Marketability Discount

We discussed the minority interest discount in the section above.  We repeat the levels of value chart now to focus on the marketability discount.

Before addressing the marketability discount, we look at two definitions of value:

  • The value of a business is the present value of all expected future cash flows from the business (including growth into the indefinite future) discounted to the present at a discount rate reflective of the risks associated with their expected receipt.  This is a perpetuity concept.
  • The value of an interest in a business is the present value of all expected future cash flows to the interest discounted to the present at a discount rate reflective of the risks associated with their expected receipt over the relevant expected holding period (i.e., the expected investment horizon).

In the real estate appraisal of Building, the cash flows (NOI) of Holdco were capitalized at an effective capitalization rate of 7.75%.  Assume there are no other cash flows available to Holdco.  The capitalized cash flows (including growth) created the $2,495,000  market value of Building.

  • As we have seen already, there are no other cash flows in Holdco, no other assets, and no debt. The $2,495,000 net asset value of Holdco is developed by capitalizing all expected future cash flows from the business.
  • The question is, what are the cash flows available to the 10% subject member interest?  The managing member could pay non pro rata management fees to herself, which would not be available to the subject interest.  That is a risk, but it is not the expectation.
  • In Holdco’s case, the mortgage has recently been paid off.  This means that the entire $192,964 of net operating income should be available for distribution.  The subject interest’s share would be $19,296, which is the going forward expectation.  However, the risk of a change in distribution policy to the detriment of the minority owner  is one reason for the need for a marketability discount.
  • The cap rate of 7.75% in the appraisal assumed growth of, say, 3.0%, so the effective discount rate was 10.75%, reflecting the risks associated with the cash flows of Building per the real estate appraiser.  The risks to an investor in a 10% interest of Holdco, however, are greater than those of Building, itself.  There are restrictions on transfer that are not present for Building.  There is the potential that the managing member will not distribute all available cash flows on a pro rata basis.  The analysis above may highlight other risks.  The discount rate for the interest will necessarily be higher than the discount rate for Building over the expected holding period, providing additional evidence for the need for a marketability discount.

The point here is not to provide a definite conclusion for the marketability discount for Holdco.  The objective is to show that there is substantially more involved in determining the appropriate marketability discount for a minority interest in a fairly straightforward single asset holding company than simply applying a discount by reference to restricted stock studies.

The Restricted Stock Studies

The restricted stock studies can be examined in light of the necessary analysis and the USPAP requirements discussed above.

Based on the BV Resources DLOM Survey, which I wrote about here, a significant number of business appraisers do little more than reference a few restricted stock studies, quote a range of “typical” discounts (like 25% to 45% or 35% to 45%), and conclude their discounts for illiquid minority interests in closely held businesses.  It is not that easy.  In fact, that method can only achieve reasonable results by chance.  And chance is not good enough.

The following table summarizes information about the majority of known restricted stock studies.  It is from Chapter 8 in Business Valuation: An Integrated Theory, Third Edition (Mercer and Harms).

The sources for the studies are found in the second part of the figure in Chapter 8.

Look at Rows 1 to 6 above.  Six restricted stock studies are cited and highlighted.  These six are the most frequently cited studies found in many appraisal reports.  Note the following:

  • The studies were published between 1971 and 1993, or roughly, between 30 and 50 years ago.
  • Assuming no duplication of transactions, which is not a good assumption, the so-called “benchmark range” of 35% to 45% is based on a total of 794 transactions.  Eliminate the SEC Study (Row 1) and appraisers have been relying on studies involving 366 transactions  performed many years ago and without any tests of statistical significance (thank you Ashok Abbot!).
  • While the averages/medians are in the range of 24% to 45%, the actual range of discounts is from a 91% discount to a 30% premium.  The available standard deviations are from 18% to 24%, which does not indicate a close fit.
  • Looking at Rows 7 to 16, there is no information that supports a benchmark range of 25% or 35% to 45%.  As the SEC Rule 144 restricted stock required holding period has been reduced from two years (or more) prior to April 1997, to one year at that date, and subsequently, to six months, the measures of central tendency have been lower than the famous benchmark range.

What we see in the figure and glean in the observations above is all the information that is available from the restricted stock studies.  It should be apparent that it is simply not possible to engage in the rigorous analysis required for even a single asset holding company interest based on any comparisons to the information above.

Reaching a Conclusion of Fair Market Value

The following is not a formal valuation of Holdco or the 10% subject member interest, although it reaches a conclusion.  The calculations are made for perspective only to show that not all marketability discounts should be in the benchmark range of 35% to 45% or so.

The market value of Building is $2,495,000.  There are no other assets. With assets with a market value of $2,495,000 and no liabilities, the net asset value of Holdco is $2,495,000.  In an actual appraisal, the net asset value would be developed in the mark-to-market balance sheet.

Assume that, based on an analysis of closed end funds holding real estate and related assets, we estimate the minority interest discount to be 5.0%.

The marketability discount could be developed using the Quantitative Marketability Discount Model, or another shareholder level discounted cash flow model.  In this case, however, we will estimate the marketability discount based on the level of discount necessary to provide a 2.5% premium in return relative to the implied discount rate for the underlying real estate.  In this example, the marketability discount is 20.6%.

The implied premiums to discount rates from actual restricted stock transactions range from 2% to 3% on the low side to 5% to 6% or more (often considerably more).  The 2.5% premium assumed in this example falls within this range. For some actual calculations of these returns, see my recent article in the ASA’s Business Valuation Review, “A Current View of the Restricted Stock Studies and Restricted Stock Discounts.” The general rule is that more attractive companies tend to have lower required holding period premiums than riskier, less attractive companies.  Holdco is an attractive entity providing a significant expected distribution yield for hypothetical buyers.

The “valuation” table is broken into two parts for ease of discussion.  The first part provides the value of 100% of Holdco at the nonmarketable minority level of value.

Rows 1 to 3 develop the net asset value (NAV) of Holdco, which is $2,495,000.  The minority interest discount of 5% is applied on Row 4, yielding the Marketable Minority Value of $2,370,250 on Row 5.

The marketability discount was calculated on Row 6 to provide a 2.5% premium return to the discount rate of Building (shown in the second portion of the table below). This yields a nonmarketable minority value for 100% of Holdco of $1,881,979 on Row 7, which represents a 24.6% discount to the net asset value of Holdco.  We always make this calculation as one form of sanity check on the resulting conclusion.  Row 9 provides the net operating income of $192,964 for perspective.  Before reading further, look at the relationship of net operating income and the nonmarketable minority value.

The value of the 10% subject interest of $188,198 is calculated on Row 10 (10% of the value on Row 7 above).  The expected distribution for the subject interest of $19,296 is calculated on Row 11 (10% of NOI on Row 9).  Dividing the expected distribution by the value of the interest implies a distribution yield of 10.25% (Row 12).  Row 14 is the sum of the distribution yield of 10.25% and the expected growth in value from the real estate appraisal, or 13.25%.  Compare this indication of expected holding period return with the discount from the appraisal of Building (10.75%) and we see that the “valuation” using a 20.6% marketability discount provides a 2.5% premium in return to that implied for Holdco itself.

Recall the figure showing fair market value from above.  It should be clear that there are risks associated with owning an 10% interest in Holdco that are in excess of the risks of Holdco itself.  Those risks require that the hypothetical seller make a concession by offering a premium in return to the base discount rate to induce the hypothetical buyer into purchasing.  The hypothetical buyer desires a very high premium return (lower value and higher marketability discount).  The question is, what is the premium that will induce both the hypothetical buyer and seller to transact?  In this case, we started with a relatively low premium over the discount rate and used expected cash flow and growth to calculate the marketability discount

This is a short-form version of more detailed calculations in models like the QMDM.

This example has been created to talk about marketability discounts in a particular way.  It has also been created to illustrate why appraisers cannot use restricted stock benchmark analysis to determine marketability discounts.  We do so in the next section.

Restricted Stock Benchmark Analysis for Holdco

Examining the figure of restricted stock studies above, we showed a range of discounts from 25% to 45%.  Virtually no one uses the 25% figure in benchmark analysis, so the benchmark range is more normally 30% to 45% or 35% to 45%.  Assume that the benchmark range is 35% to 45% for the hypothetical “benchmarker” appraiser for this example.

How do we apply this benchmark range to Holdco?  We can say that restrictions on transfer (relative to restricted shares of public companies) should warrant a “higher” discount.  We can further say that the longer expected holding period of 5 to 10 years (relative to the two year Rule 144 period of restriction) should also warrant a “higher” discount.  And we can say that the expected distribution yield should warrant a “lower” discount, but virtually none of the restricted stock issuers paid dividends, so what does this mean?  And, how can we quantify any of this?  The sad truth is, we cannot using this form of analysis.

Assume that a benchmarker looks at the information on Holdco from above and concludes that the minority interest discount should be 15% and that the marketability discount should be 40%.  That sounds pretty “normal” or “typical,” so the benchmarker applies them in the following figure, which replicates the analysis above.

The benchmarker concludes that the nonmarketable minority value for 100% of Holdco is $1,272,450.  In most applications of similar benchmark analysis I have seen, the appraisers stop there, at Row 7.  As before, look at the visual relationship between net operating income and the nonmarketable minority value. We now proceed to the “valuation” of the interest and make comparisons similar to the ones above.

The 10% subject interest is valued at $127,245 (Row 10).  The implied distribution ($19,296) and distribution yield (15.16%) are on Rows 2 and 3.  If the benchmarker had made the yield calculation, he might have had second thoughts about his choice of discounts. The implied holding period return after adding the expected growth in value is 18.16% (Row 14).  That’s a 7.41% premium to the base discount rate (Row 16).

Recall the discussion of fair market value above.  The hypothetical seller was not present in the “negotiation” suggested by the benchmarker.  No rational, uncompelled, knowledgeable and hypothetical (or real) seller would sell the subject interest that is expected to yield in excess of 10% plus growth (from above) at a price that would yield an 18.16% return to the hypothetical buyer.  There would be no transaction because the benchmarker’s “valuation” does not represent fair market value, or a value where the interests of buyers and sellers could intersect.


What have we learned from this walk through the “valuation” of a single asset holding company?  We summarize with the following observations:

  • The asset in a single asset holding entity is different from the entity itself.  The same would be true, of course, for entities holding multiple assets.  In this example, Building is owned by Holdco as its only asset, so the value of Holdco flows directly from the value of Building.
  • It is necessary to read and understand the real estate appraisal for the asset owned by the holding entity.  It is good practice to summarize the major assumptions and results for readers of valuation reports.
  • Analysis must be conducted regarding the asset holding entity itself.  Appraisers should review the operating agreement, examine historical financial statements, and tax returns.
  • Discussions should be held with management of the asset holding entity to assess the business plan for the entity, prospects for distributions, and prospects for future liquidity through a sale of the underlying asset.
  • Create a market value balance sheet and develop the net asset value of the entity.
  • Conduct appropriate analysis to determine the appropriate minority interest discount, if applicable.  However, control premium studies cannot be used for this purpose since they do not measure the value of control, but rather the value of expected strategic or synergistic benefits.
  • Conduct appropriate analysis to develop an appropriate marketability discount. Since the expected benefits to be derived from an interest in a single asset holding company (or any company) are quantifiable (distributions and expected terminal values), it is necessary to quantify their impact on value.  This cannot be done using benchmark analysis.
  • Standards Rules 9-4(c) and 9-4(d) essentially require the type of analysis described in this post.
  • Any marketability discount developed using the benchmarking method can be reverse-engineered so that the implied economic assumptions and implied returns become apparent.

Benchmarkers beware.  The days of using benchmark analysis as a primary method for developing marketability discounts are rapidly going away.  Benchmarking alone cannot be supported and is not standards compliant based on Standards Rules 9-4(c) and 9-4(d) of USPAP.  For even more detailed guidance for the valuation of partial interests, see the ASA Business Valuation Standards, “PG-2 – The Valuation of Partial Ownership Interests.”  More on that in a future post.

In the meantime, be well.  And purchase your copy of Business Valuation: An Integrated Theory Third Edition (Mercer and Harms) while supplies last.  If you purchase a book, give it an honest review on Amazon.


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2 thoughts on “Restricted Stock Benchmarkers Beware

  1. In the restricted studies there are segments within the data that can provide an improve level of comparison to the valuation subject. (Sort Example: Size, Profitability) Application of refined data in this manner has some “benefit” to the analyst. Once accomplished the results should be tested to determine the implied rate of return. The “test return” should be in a defensible range based on market observations to conclude that the “studies” yielded discounts that were properly applied and the conclusion appropriate in the given situation.

    As noted in the article…the ultimate test is the “market rate” of return for the acquirer…that is acceptable to a willing seller. That noted, I believe there is still some analytical value to be found in the restricted studies…even though they are small data sets and now much older than might be desired.

    • Richard,
      Thanks for your comment! The problem is that most of the transactions involved small public companies that were not profitable. If one sorts on size and profitability, the next sorts would logically be on line of business and date of transactions. At this point there is little left for “comparability” with any subject company.

      We can calculate the implied rates of return from the restricted stock transactions if we have the appropriate data. The market price and the transaction price set the discount. The estimated holding period (based on block size and dribbling out after two years) can then be used to estimate the required return implied by the pricing. That provides an implied discount rate, or required holding period return. We estimate the discount rate for the public companies and compare this required holding period return to estimate the implied holding period premiums. This information is used as a basis for testing the reasonableness of required returns used in the QMDM.

      If you are estimating a required return, you are on the right track. This post stands for the fact that appraisers cannot use averages of the studies and “Kentucky windage” to estimate marketability discounts. Anything beyond that is a step in the right direction.