The first four posts in this series introduced the marketability discount, or discount for lack of marketability, and set the direction for the next several posts. This post addresses the marketability discount in the context of the income approach to valuation. The next post will discuss the market approach.

Many appraisers do not think of valuation approaches when valuing minority interests in businesses. Such interests are often referred to as “partial interests.” For example, as we learn in Procedural Guideline, or PG-2 — Valuation of Partial Ownership Interests (Para IV.A) in the ASA Business Valuation Standards:

Appraisers should consider all three approaches to value (asset-based, income and market) when valuing partial interests. If an approach is excluded in an assignment the appraiser should explain the reason for such exclusion in the appraisal report.

This post regarding the income approach to marketability discounts is long and somewhat theoretical. In fact, it clocks in at almost 2,500 words which I know is a blogging sin; however, the topic demands it. Therefore, you might want to print this post rather than read it on screen.

Forewarned is forearmed. Here we go.

**The Nonmarketable Minority Level of Value**

It wouldn’t be proper to begin a discussion of the nonmarketable minority level of value without presenting the Levels of Value chart.

The first equation below introduces conceptual math describing the shareholder – or nonmarketable minority – level of value — expressed in the context of the Gordon Model. The expression is imperfect because, unlike the valuation of businesses, which is a perpetuity concept (i.e., the expected cash flows go on forever), minority investments are typically made with finite investment horizons. We deal with this below.

The terms in the conceptual definition of value at the nonmarketable minority level are defined:

**V**_{sh}**CF**is the portion of the enterprise cash flow expected to be received pro rata by the shareholders, including both interim distributions and any expected terminal value. CF_{sh }_{sh}is a symbolic notation to describe all expected interim cash flows and any expected terminal value at the end of the holding period for the investment. In other words, the equation cannot be literally used to determine the value of a nonmarketable minority business interest. Actual notation for the two stage, shareholder level DCF model can be shown as follows:

The left portion of the equation represents the present value of interim cash flows (PVICF) for a finite expected holding period ending in year *f*. The right portion of the equation represents the present value of the terminal value (PVTV), which is, for purposes of this discussion, the marketable minority (enterprise) value at the end of year f. Rational investors do not enter into a minority investment absent the expectation of achieving the objective of the investment, which is an enterprise value at some point, even an indeterminable point, in the future.

**R**is the discount rate of the minority investor in a nonmarketable equity security for the expected holding period, or the_{hp }*required holding period return*. Logic suggests that R_{hp}will be equal to or greater than R_{mm}. It makes sense that a minority shareholder’s investment is exposed to risks that are incremental to those of the entire business. This incremental required return can be stated symbolically as in the next equation, where HPP is the indicated*holding period premium*. What we are suggesting is that the required holding period return is the sum of the enterprise discount rate and the holding period premium. Note that if HPP is equal to zero, meaning there are no holding period risks, as with a liquid, publicly traded security, then R_{hp }is equal to R_{mm}.

**G**is the_{v}*expected growth rate in value*of the enterprise, which yields the terminal value of the enterprise at the end of the expected holding period. The objective of every investor (dare I be absolute here?) is to sell his or her investment at an enterprise level and to receive the benefits of the risks that were endured during the holding period for the investment.**Tennis??**is the second statement of this premise and I repeat it because it is so important.

If we work with the Gordon Model, we can see that for a publicly traded security, the expected growth rate in value is equal to R_{mm} less the dividend yield. If not all enterprise cash flows are distributed to, or invested for the benefit of, the minority shareholders (if, for example, above-market compensation is paid to a controlling shareholder), then G_{v }will be less than R_{mm} (adjusted for the dividend yield).

The same result will occur if a company’s expected reinvestment rate is less than its discount rate (e.g., as with the accumulation of low-yielding cash assets, vacation homes, or other assets providing no yield or a yield less than the discount rate).

For a more in-depth discussion of this issue, see Z. Christopher Mercer and Travis W. Harms, “Marketability Discount Analysis at a Fork in the Road,” *Business Valuation Review*, Vol. 20, No. 4 (2001): pp. 21-22.

**Enterprise Value vs. Shareholder Value**

Enterprise valuation is a perpetuity concept. Value today is the present value of all expected cash flows attributable to an enterprise discounted to the present at an appropriate discount rate.

In contrast, shareholder level values depend on expected holding periods. Investors expect finite holding periods, even if the precise holding period is not known or knowable. The expected growth in value is the means of estimating the future exit value of the investment.

Assume for a moment that the appropriate discount rate is 16% and expected growth in earnings (long term) is 6%. Assume that the expected earnings per share are $0.10 per share. Applying the Gordon Model, the marketable minority value is therefore $1.00 per share ($0.10/(16%-6%)).

Now assume that, contrary to the assumptions of the Gordon Model, that there are no distributions to minority shareholders, perhaps as a result of non prorata distributions to a controlling shareholder (e.g., above-market compensation).

Expected growth in value will be 6%, since there will be no reinvestment. Now assume that the expected holding period for nonmarketable investment is exactly 10 years, and that the minority investor’s discount is 20% (HPP is equal to 4%). The minority investor’s present value (and the implied marketability discount) can be illustrated graphically.

Value grows from the current value of $1.00 per share to $1.79 per share at the end of 10 years ($1.00 x ( 1 + 6 )^{10} ). The present value of the expected future value of $1.79 per share is $0.29 per share ( $1.79 / ( 1 + 20% )^{10} ). The implied marketability discount of 71% is determined by these two values, or MD = (1 – $0.29/$1.00 ),

Obviously, the purpose of this example is not to illustrate that all marketability discounts should be 71%. An examination of the various restricted stock studies in future posts will show, however, that discounts of this magnitude are within the realm of observation. Such examination will also show that very small DLOMs, or even positive discounts (i.e., premiums) are also possible. The purpose of our discussion is to understand why such variations occur and how, as appraisers, we can differentiate between them in different valuation or investment situations.

**Conceptual Model to Describe the Nonmarketable Minority Level of Value**

We now have a conceptual model to describe the nonmarketable minority level of value. The model anticipates that the appraiser will initially develop an indication of value at the marketable minority level. In so doing, we will have developed a thorough understanding of the expected enterprise cash flows, their expected growth, and their risks. Grounded in this analysis, the appraiser can then assess the expected benefits to be derived by the minority shareholder of the enterprise. We will further develop this conceptual model in future posts in the context of our discussion of methods for determining discounts for lack of marketability.

Relying on the framework presented in the discussion above, we can analyze the conceptual differences between the marketable minority and** **nonmarketable minority levels of value. The nonmarketable minority value, or value to the shareholder (V_{sh}), will be less than V_{mm }if, all else equal, one or more of the following conditions hold:

*CF*The expected shareholder cash flows will be less than the expected enterprise cash flows if the enterprise cash flows are either reinvested in the business or distributed on a non-pro rata basis to certain shareholders. Recall that the benchmark marketable minority value is determined under the assumption that all cash flows are paid out to shareholders pro rata or reinvested in the enterprise to achieve a return equal to the discount rate. After this determination is made, the appraiser then estimates CF_{sh}is less than CF_{e(mm)}._{sh}, which may be less than or substantially less than the cash flow of the enterprise (CF_{e(mm)}).*G*The expected growth rate in value is a function of the expected growth rate of core earnings, and the effect of reinvestment of enterprise cash flows. If the reinvestment rate is equal to the discount rate, then, G_{v}is less than R_{mm}._{v}will be equal to the discount rate, or R_{mm}(adjusted for dividend yield). To the extent that cash flows are not reinvested in the enterprise or are reinvested suboptimally (at rates less than the discount rate), then G_{v }will be less than R_{mm,}resulting in a lower expected terminal value and lower nonmarketable minority value. Note that the expectation of suboptimal reinvestment, and the accompanying reduction of expected growth in value impacts both controlling and noncontrolling shareholders. The difference between the two situations is that the controlling shareholder can change the reinvestment and/or distribution policies in order to maximize value while the noncontrolling shareholder cannot make those changes. Said another way, the value, today, of a business to a controlling shareholder can exceed the value of the expected business plan.- R
Few observers question that the owner of an illiquid asset bears greater risk than the owner of an otherwise identical asset with an active, public market. This should have been obvious to appraisers years ago (Mercer included) based on the restricted stock studies and their observed discounts on average. If the restricted shares were identical in all respects save restrictions (for a period of time) under Rule 144, the only reason for discounts to market prices of freely traded shares relates to perceived incremental risk over the time horizon until restricted shares become marketable. We have given a name to the compensation necessary for an investor to accept this incremental risk – the holding period premium, or HPP. HPP accounts for numerous risks, including the potential for a long and indeterminate holding period and many other risks that flow from the holding period or from the factual situation in any valuation. Other things being equal, greater risk implies lower value._{hp}is greater than R_{mm}.

Using an income approach (i.e., discounted cash flow in symbolic form), we have examined certain circumstances under which the nonmarketable minority value will be less than the marketable minority value. Said another way, we have described certain circumstances under which the appropriate discount for lack of marketability, or DLOM, would be greater than zero.

Asset will see in future posts, the appropriate marketability discount for specific valuation situations can be estimated using valuation methods under either the income approach or the market approach.

**The Marketability Discount **

The marketability discount (MD) that investors demand when purchasing nonmarketable minority interests in enterprises is defined:

This equation confirms that if the shareholder level value (V_{sh}) is equal to the marketable minority value (V_{mm}) there is no marketability discount. Frequently, owners of nonmarketable securities anticipate each potential source of diminished value:

- Cash flow to the shareholder (CF
_{sh}) less than that of the enterprise (CF_{e(mm)}); - Expected growth in value less than the discount rate (adjusted for dividend yield); and,
- Incremental risks associated with illiquidity during the expected holding period.

In such cases, the appropriate marketability discounts can be quite large. In other cases, however, as with fully distributing entities, or in cases where the expected growth rate in value is relatively high and holding period risks are not large, the appropriate marketability discounts can be quite small.

Conceptually, no portion of the marketability discount is attributable to not possessing the prerogatives of control. The marketability discount reflects, rather, differences between the expected cash flows of the enterprise and those to shareholders, expected growth in value less than the underlying discount rate, and holding period risk in excess of the risks associated with the enterprise.

Note that the minority investor in a public company has no more direct control over the enterprise than does the minority investor in a private company. However, the public minority shareholder does have an element of *personal control* that the private minority shareholder lacks. He has the ability to sell his investment and receive cash in three days through the public securities markets at the marketable minority level (the present value of all expected cash flows of the enterprise).

**So, What Does All This Mean?**

The conceptual logic regarding the income approach is difficult to refute. What can cause expected cash flows to minority shareholders to be less than the expected cash flows of the enterprise? What can cause the expected growth in value, from the minority shareholder’s perspective, to be less than the expected growth in value for the enterprise from the viewpoint of a purchaser today? What factors create additional risks for minority shareholders, in addition to the need to bear the risks of the enterprise?

The answers to these questions lie in a myriad of factors influencing marketability, many of which were summarized in the *IRS DLOM Job Aid*. With the background laid for future discussion, we move in the next post to a discussion of the market approach when valuing illiquid minority interests, to be followed by an overview of the *IRS DLOM Job Aid*, first, providing an overview, and then, focusing on the factors influencing marketability.

We will then take a look at the marketability discount, again conceptually, from the viewpoint of valuation standards.

With our growing base of knowledge and understanding, we will then begin to examine the various methods used by appraisers to develop marketability discounts, analyzing them in light of the conceptual understanding we are developing as this series continues.