In the most recent post in this series on appraisal review, we began a discussion of fair market value and the integrated theory of business valuation.  We introduced the integrated theory and developed the strategic control and marketable minority/financial control levels of value.

In this post, we continue the discussion of the integrated theory and focus on the nonmarketable minority level of value.

The nonmarketable minority level of value is the lowest conceptual level on the chart.  The chart above has two premiums: the financial control premium and the strategic control premium.  And there are two discounts, the minority interest discount, and the marketability discount, also known as the discount for lack of marketability (DLOM). We will address premiums and discounts in our next post.

The Nonmarketable Minority Level of Value

We now examine the conceptual math of the nonmarketable minority level of value and the marketable minority level of value, just as with differences between the marketable minority and financial control levels and between the financial control and strategic control levels.  As with the other levels, differences in values at these two levels relate to differences in expectations for cash flow, growth, and risk from investors’ perspective at each level.

The nonmarketable minority level of value reflects investors’ view of illiquid, minority interests of businesses.  The base or benchmark to which the nonmarketable minority level of value is compared is the marketable minority level of value, or the “as-if-freely-traded” value.  The initial understanding of the relationship between these two levels came from observing the public securities markets.  Some publicly traded companies, beginning in the latter 1960s, began to issue blocks of shares to investors which had restrictions on transfer for a period of time under Rule 144 of the Securities and Exchange Commission.  Two prices were observed:

• The publicly traded price of the companies on the issuance date.
• The generally lower price at which the blocks of restricted shares were issued.
• The difference in pricing was called the restricted stock discount.

These restricted stock transactions were the subject of a number of restricted stock studies, which examined the differences in transaction prices for restricted shares relative to the counterpart freely traded shares.  In late 2020 and early 2021, I wrote a series of posts beginning here on the restricted stock studies and implications for appraisers. I elaborated on this series in an article for the Business Valuation Review titled “A Current View of the Restricted Stock Studies and Restricted Stock Discounts” (Summer 2021 issue).  Email me for a copy of the article (mercerc@mercercapital.com ).

Appraisers focused on the restricted stock studies and used them to infer the magnitude of what came to be called the marketability discount (or DLOM).  The logic used suggested that illiquid (restricted) interests of public companies sell at discounts to their freely-trading prices, then illiquid minority interests of a business should similarly sell at discounts from their marketable minority or as-if-freely-traded” prices.

Conceptual Math

Examining the conceptual math of the marketable minority and nonmarketable minority levels of value, we see that the reasons for restricted stock discounts and marketability discounts lie in differences in expected cash flow, growth, and risk from the viewpoint of investors at one level or the other.

Implications of Conceptual Math

The upper left equation is the familiar Gordon Model, which we refer to as the fundamental valuation equation.  Expected cash flow to equity is capitalized by dividing it by the equity discount rate less the expected growth in earnings.

The cash flow to be capitalized has been normalized to eliminate the effect of agency costs on cash flow.  Unusual or non-recurring items are initially normalized.  Then owner compensation and perquisites are normalized to market levels.  The normalized cash flows are “as-if-public equivalents.”  The market value of equity at the marketable minority level of value is the benchmark to which all other levels of value are compared.  It bears noting that when appraisers develop valuation indications at the marketable minority level of value, the indications are hypothetical in nature since no active markets exist for the shares of private businesses.

There are appraisers who still believe that it is a matter of “judgment” whether to normalize earnings or not when valuing minority interests. I know, I know. The minority investor cannot change owner compensation so that’s the supposed rationale for not normalizing.  The problem is that there is a theoretical basis for exercising such “judgments.” Normalizing is not a matter of judgment at all.  It is a basic valuation theory.  Suppose earnings are not normalized to the marketable minority level in the first step of valuing a minority interest. In that case, there is no appropriate base value from which to consider a marketability discount.   Valuation premiums and discounts have no meaning unless the base value to which they are applied or from which they are taken is specified.  The appropriate base value for the application of a marketability discount is, of course, the marketable minority level of value. Not normalizing business cash flows in the process of valuing minority interests is, I believe, wrong.

We look now at the conceptual math at the nonmarketable minority level. The shareholder equation from the larger figure above is repeated The equation examines expected cash flows, risk, and growth at the shareholder level.  This equation is a conceptual representation.  Minority interest investments are made for finite (even if indeterminate) expected holding periods. The actual math for V_{sh is} a discounted cash flow model, just as is the actual math of the fundamental equation above. The conceptual representation is sufficient for initial comparisons with the marketable minority level of value and the fundamental valuation equation.

An Initial Look at Restricted Stock Discounts

We take a brief diversion (not really) before examining the conceptual math at the nonmarketable minority level of value to talk about restricted stock transactions.  These transactions began to occur in the late 1960s, and have continued in one form or another for decades.  Restricted stock transactions typically occurred at discounts to the freely traded prices of the issuers.  Why?  The answer is in this blog in a series I wrote in late 2020 and early 2021 (pandemic months for sure):

• RSD-1 Background on Restricted Stock Discounts. In this first post, we defined the restricted stock discount and provided some background into how appraisers began to think that all marketability discounts are 35%, give or take a bit.

• RSD-2: Why Are Illiquid Minority Values Always (Almost) Lower Than Marketable Minority Values?   That is a good question.  The answer lies in differences in expected cash flows, risk and growth between the two levels of value.

• RSD-3: Restricted Stock Discounts and the Guideline Transactions Method.  The third post observes that the use of averages of restricted stock discounts from historical studies is a flawed use of the guideline transaction method.

• RSD-4: Restricted Stock Discounts Are Not Valuation Ratios. Restricted stock discounts measure only the difference between two prices and contain no economic or valuation information.

• RSD-5: Restricted Shares of Public Companies are Identical to Freely Traded Shares, But…  Restricted shares have the same expectations for future cash flows, risk, and growth as do freely traded shares, so why is there a price difference?

• RSD-6: The Expected Holding Period Premium for Restricted Stock Investors Is Caused by Incremental Risk Relative to Publicly Traded Shares of Issuers.  Investors in restricted stocks impose higher than business-level risks and lower than freely traded pricing to negotiate restricted stock discounts.

I elaborated on this series in an article for the Business Valuation Review titled “A Current View of the Restricted Stock Studies and Restricted Stock Discounts” (Summer 2021 issue).  Email me for a copy, paid subscription is required (mercerc@mercercapital.com).

I offer these posts as an expanded discussion of conceptual or theoretical math.  Three equations from the above series prove with irrefutable logic the cause of restricted stock discounts.  With little discussion, the equations are presented here.  The first equation defines the restricted stock discount in terms of the freely traded price of issuers on the day of issuance less the restricted stock discount.  To the extent that a restricted stock discount is observed, the restricted share price will be less than the freely traded price.

The second equation considers why the restricted stock issuance prices might be lower than the freely traded price of the issuers.  Since the same public companies are involved with restricted stock transactions and freely trading shares in the public markets, the expected cash flows are exactly the same for restricted shares and freely trading shares (see the numerator below).  Similarly, the expected growth for the restricted shares is identical to that of the freely trading shares (see the right element of the denominator). There are no differences in expected cash flows or expected growth to cause restricted stock discounts. This is not a matter of judgment, but of valuation theory and logic.

The only possible cause for restricted stock discounts is the fact that restricted stock issuers imposed higher discount rates than those applicable to the public company issuers over their expected holding periods for the restricted investments. The theoretical math is clear. This is not a matter of judgment but one of theoretical clarity. The third equation carries the logic one step further.

Restricted stock investors imposed holding period premiums to the discount rates, which we name HPP in the equation above. We should have been examining relative risk these many years rather than absolute restricted stock discounts, which carry no valuation meaning.

Differences Between the Marketable Minority and Nonmarketable Minority Levels of Value

Move now to the world of private businesses. Why would an illiquid minority interest of a business tend to trade at a discount to the marketable minority value of the same business? As with the other levels of value, we examine the three valuation components:

• Cash flow.  At the marketable minority level, CF_equity represents all of the normalized, expected cash flow of a business. Alternatively, CF_sh represents the expected cash flow to be received each year by a minority interest in the same business, which often is lower or even considerably lower than CF_equity.  This is a conceptual comparison.  Minority interest investments are made for finite but often indeterminate expected holding periods and business valuation is a perpetuity concept.  Unlike the restricted transactions discussed above, there are numerous reasons why shareholder cash flow would be less than cash flow to equity.  One obvious reason is reinvestment.  Cash flows reinvested in a business are not available for distribution to minority owners.  Hopefully, they contribute to the rate of return achieved by minority investors.  Cash flows devoted to non-pro rata distributions to controlling owners are not available for distributions to minority owners. Other agency costs can serve to decrease cash flows available to minority shareholders. By this time, the point should be clear: lower expected cash flows for an illiquid minority interest (relative to the expected cash flow of the business) lead to lower minority interest values relative to the marketable minority level of value.
• Growth.  G_earnings at the marketable minority level of value reflects the required return of a business less the expected dividend yield assuming all non-distributed cash flows are reinvested in the business at its discount rate.  In valuing businesses, the assumption is generally made that all expected cash flows are reinvested in the business at the discount rate, so the expected growth in value is the discount rate, R_equity.  At the nonmarketable minority level, the expected growth in value (Gv) may be less than the growth in value for the business as result of what we have already discussed, agency costs.  Agency costs include non-pro-rata distributions (i.e., bonuses or other benefits to controlling owners and suboptimal reinvestment of cash flows into low-yielding cash, land or other non-operating assets.  The point here should be clear: lower expected growth in value for an interest (relative to the expected growth of the business excluding agency costs) leads to lower values at the nonmarketable minority level of value relative to the marketable minority level.
• Risk.  The risk of the business at the marketable minority level of value is the equity discount rate, R_equity.  For a public company, risk is mitigated by the ability to sell stock if investors have a change in investment attitude or a need for liquidity.  Public pricing reflects the existence of an active public market for shares.  When appraisers value at the marketable minority level of value for a private business, the hypothetical assumption is made that an active public market exists for shares. The risk of holding illiquid minority interests is intuitively greater than the risks at the marketable minority level.  Recall the discussion of the holding period premium for restricted shares above. So R_hp will be greater than R_equity in most instances.  Again, the point is clear: greater risks for illiquid minority interests relative to the risks of the business at the marketable minority level lead to lower values at the nonmarketable minority level relative to the marketable minority level.
• Combination of factors.  As with the other levels of value, combinations of these three valuation drivers can lead to lower values.

Implications for Fair Market Value and Appraisal Review

We draw at least two implications from this discussion of differences between the marketable minority and nonmarketable minority levels of value.  These are:

1. Normalize business earnings.  When valuing illiquid minority interests at the nonmarketable minority level, appraisers use a two-step process: 1) Develop valuation indications at the marketable minority level; and 2) From that base level of value, consider an appropriate marketability discount to determine the nonmarketable minority value indication.  In fair market value determinations, it is necessary to normalize business earnings to develop value indications at the marketable minority level of value.  Suppose an appraiser fails to normalize earnings (for non-recurring and unusual items and for agency costs). In that case, the concluded value will be at something other than the marketable minority level of value. Refer to that as valuation limbo.  The base value for developing nonmarketable minority indications of value is the marketable minority level.  Appraisal reviewers should be sure to determine whether appropriate normalizing adjustments have been made.  If they have not been made, the use of “standard” tools to develop marketability discounts will not be applicable, since they have all been developed from marketable minority base pricing levels.  The conclusion of value would be reasonable only by chance, which is not good enough.
2. Recognize that value differences between the nonmarketable minority level and the marketable minority level are created by differences in expected cash flow, risk, and growth.  In fair market value determinations, marketability discounts should be developed based on an analysis of differences between expected cash flows, risk, and growth between the two levels of value and from the perspective of investors at those levels.  Any appraisal applying “standard” techniques, like basing marketability discounts on average discounts from restricted stock studies or pre-IPO studies, is incorrect from a theoretical viewpoint. It is impossible to analyze differences in expected cash flows, risk, and growth between a subject business at the marketable minority and nonmarketable minority levels of value using averages from these studies.  This conclusion is based on valuation theory and will be troubling and controversial to many appraisers.  The fact that “others are doing it” does not make the use of such studies reasonable or appropriate.  In terms of appraisal review, if an appraiser’s report is under review and does not provide a reasonable analysis of the basic valuation elements that give rise to value at the nonmarketable minority level of value, the report is flawed.

In the next post in this series, we will begin to examine the valuation premiums and discounts that “move” between the various levels on the levels of value chart.

In the meantime, be well.

Please feel free to comment on this post or any post in the series.

Chris