[Note: This is a lengthy post. You might want to print to read.]
In the second post in this series on statutory fair value, we provided background information on the Gordon Model.
The Gordon Model is a single-period income capitalization model that summarizes the way securities are valued in the public markets, and is a beginning point for continuing our discussion of an integrated theory of business valuation.
The basic formulation of the Gordon Model defines the value of a business or interest as the next period’s expected cash flow divided by an appropriate discount rate less the expected growth rate of the specified cash flow. As we have previously shown, this formula is a summary of the discounted cash flow method of valuation under the following conditions:
- The cash flows are expected to grow at the constant rate of g, and
- All cash flows are distributed to shareholders or are reinvested in the firm at the discount rate, r.
The discounted cash flow model as summarized by the Gordon Model provides an ideal basis for an integrated theory of business valuation.
Early Views of the Levels of Value
The so-called levels of value chart first appeared in the valuation literature some time around 1990. However, the general concepts embodied in the chart were known by appraisers (and courts) prior to that time. Even today, most discussions regarding levels of value in the valuation literature are very general, lacking any compelling logic or rationale regarding the factors giving rise to value differences at each level.
The early levels of value chart showed three conceptual levels, as indicated below, and discussed in the third post in this series. The chart is so important to an understanding of valuation concepts that analysts at Mercer Capital have included it, or an evolving version with four levels (introduced in the fifth post in this series) in virtually every valuation report since about 1992.
We, like most appraisers in the 1990s, assumed the existence of the conceptual adjustments referred to as the control premium, the minority interest discount, and the marketability discount. We relied on market evidence from control premium studies to help ascertain the magnitude of control premiums (and minority interest discounts). And we relied on certain benchmark studies, the so-called Pre-IPO Studies and the Restricted Stock Studies, as the basis for estimating the magnitude of marketability discounts. Such reliance contributed then, and unfortunately, continues to do so today, to a failure to understand the basis for the valuation premiums and discounts being estimated.
By the early 1990s, we grew increasingly uncomfortable with the bold adjustments that we and other appraisers made. In 1994, I introduced the Quantitative Marketability Discount Model (QMDM) to develop marketability discounts based on the expected cash flows (and growth) and risks associated with minority interests. This marked the beginnings of an integrated theory of business valuation. Quantifying Marketability Discounts was published in 1997 (now, see Business Valuation: An Integrated Theory, 2nd Edition).
The Gordon Model, An Integrated Theory of Business Valuation, and Statutory Fair Value
One purpose of this series of posts is to integrate the Gordon Model (and how the markets value companies) and the conceptual framework of the levels of value. In so doing, we will discuss an integrated theory of business valuation, which will help as we continue our discussion of statutory fair value.
We will proceed to:
- Provide a conceptual description of each level of value in the context of the Gordon Model.
- Use the components of the Gordon Model to define the conceptual adjustments between the levels of value, the control premium (and its inverse, the minority interest discount), and the marketability discount.
- Reconcile the resulting integrated valuation model to observed pricing behavior in the market for public securities (the marketable minority level), the market for entire companies (the controlling interest level(s) of value), and the market for illiquid, minority interests in private enterprises (the nonmarketable minority level of value).
- Begin a discussion of this conceptual framework in the context of statutory fair value generally.
- Discuss specific statutory fair value cases and issues in the context of an integrated theory of business valuation.
With this background, we will develop the marketable minority interest level of value, or the middle level in the three-level chart, as the benchmark level of value from which other levels of value are developed and understood.
The Gordon Model provides a shorthand representation of the value of public securities at the marketable minority interest level of value. We call normal pricing in the public securities market “marketable minority” because interests being traded there are both marketable and minority in nature. For privately owned enterprises, this conceptual level is referred to with the same name.
In developing an integrated theory, we use the Gordon Model to analyze how the levels of value relate to each other. To do so, we introduce a symbolic notation to designate which elements of the model relate to each level of value.
The following equation introduces conceptual (annotated) math for the benchmark level of value – the marketable minority value.
We just described the marketable minority level of value as the “benchmark” level of value. Control premiums are added to it to develop controlling interests indications of value. Marketability discounts are subtracted to develop nonmarketable minority indications of value. These are the traditional concepts in relationship to the marketable minority level of value. The annotated Gordon Model consists of the following components:
- Vmm is the equity value of a company at the marketable minority level of value, whether public or private. This is the benchmark, observable value for public securities. For private companies, this level is often called the “as-if-freely-traded” value. We say “as-if-freely-traded” because for a private company, it is a hypothetical value. By definition, it is not observable for nonmarketable interests of private enterprises since there are no active, public markets for their shares. Appraisers develop indications of value at the marketable minority level as a first step in determining other levels of value. Such indications of value are developed either by direct reference to the public securities markets (using the guideline public company method), or indirectly, using what I call the Adjusted Capital Asset Pricing Model or other build-up methods (see Chapter 6 of Business Valuation: An Integrated Theory, 2nd Edition).
- CFe(mm) is the expected cash flow (to equity) of the enterprise at the marketable minority level for the next period. The marketable minority level of cash flow reflects enterprise earnings, “normalized” for unusual or non-recurring events. These cash flows consider expense structures that are market-based, at least in terms of owner/key shareholder compensation (see the tenth and eleventh posts in the series on normalization of earnings). Public companies attempt to keep investors focused on their “normalized” earnings. Many public companies, for example, disclose pro forma earnings, or earnings after adjusting for unusual or nonrecurring (and sometimes not so non-recurring) items. The need to adjust for unusual or non-recurring items should be intuitively apparent. Unfortunately, too many appraisers fail to grasp this essential element of valuation.
- Rmm is the discount rate at the marketable minority level of value. While it is not directly observable, it can be inferred from public pricing or estimated using the Capital Asset Pricing Model or other models. For private companies, Rmm is most often estimated using one of several build-up approaches.
- Gmm is the expected growth rate of core earnings for the enterprise under the assumption that all earnings are distributed to shareholders (or ge from our discussion in the second post on discounted cash flow). However, earnings are often reinvested in businesses. It is the compounding effect of reinvested earnings that enables a company to grow its reported earnings (and value) at rates (g*) in excess of its underlying core earnings growth rate. So, Gmm is not equal to the expected growth rate of earnings published by stock analysts for public companies. The analysts’ g (g*) includes the compounding effect of the reinvestment of cash flows on the expected growth of earnings.
The Conceptual Math of the Marketable Minority Level of Value
At this point, we can begin to connect the mathematics of valuation theory with the conceptual levels of value chart. The marketable minority level of value is the conceptual value from which other levels of value are derived. The following figure presents the conceptual math of the marketable minority level of value.
We refer to the marketable minority level of value as an enterprise level of value. We do so because CFe(mm) is defined as the cash flow of the enterprise to equity holders. We hope to expand the integrated theory to embrace valuation at the total capital level in the near future.
All the shareholders of a publicly traded enterprise, controlling or minority, share the benefit of all of its cash flows (as they are capitalized in the public stock markets every day). The importance of this definition will become clear as the remaining mathematical relationships of the conceptual levels of value are developed.
The conceptual math of the marketable minority level indicates that, as we have discussed previously, value is a function of expected cash flows (next period and expected growth) and risk. The figure shows an important relationship regarding the expected growth in value in the middle column. The Gordon Model is a dividend discount model. CFe(mm) is the expected cash flow available for distribution.
- Expected returns to shareholders come in two forms, distribution or dividend yield and capital gains. Dividends provide current income, and reinvested earnings provide the potential for future growth in value and for capital gains.
- If there are no dividends, then CFe(mm) is equal to the net income of an enterprise. Intuitively, that is why the long-term growth rate used in the Gordon Model is typically fairly low, quite often in the low single digits. If all earnings are distributed, growth is limited to inflation and productivity increases. Owners get substantial current returns and limited expected capital gains. If all earnings are paid out to shareholders, then the expected growth in value is the long-term growth of core earnings.
- If some earnings are retained to finance growth, then two things occur. First, owners get a current return in the form of current dividends and a portion of expected returns relates to the more rapid growth (than long term core growth) because of the compounding effect (at the discount rate) of reinvested earnings.
- The point is that expectations for growth in value of an enterprise are related to distribution policy. If all earnings are retained in the enterprise, the expected growth in value is the discount rate. If all earnings are distributed, the expected growth in value is the long-term core (slow) growth in earnings. For distribution policies in between 0% and 100%, the expected growth in value is discount rate (Rmm) minus the dividend yield. This is true because shareholders expect to get their expected return either in the form of dividends or capital gains (and are assumed to be indifferent between the two forms of return).
Finally, the right side of the figure above indicates that the Gordon Model provides a benchmark for comparison to other levels of value. The marketable minority level of value is that level to which appraisers have almost automatically applied control premiums to develop controlling interest indications of value. It is also the level from which appraisers have subtracted marketability discounts to derive indications of value at the nonmarketable minority level of value.
The Levels of Value Revisited
Referring again to the three-level, levels of value chart, the control premium and the marketability discount are conceptual adjustments enabling appraisers to relate the marketable minority level of value with the controlling interest level (control premium) and the nonmarketable minority level (marketability discount). The minority interest discount also relates the controlling interest and marketable minority levels.
No valuation premium or discount has meaning unless we understand the base to which it is applied. The marketable minority value is the benchmark (base) level of value for the enterprise in the integrated theory of business valuation. Unless we understand this basic fact, we cannot understand or make proper use of the conceptual valuation adjustments typically used by appraisers.
A review of the valuation literature prior to the latter part of the 1990s yields little insight into the theoretical basis for applying the well-known conceptual premiums and discounts.
- Appraisers applied control premiums because they were observed when public companies changed control.
- Marketability discounts were applied because it was observed that restricted stocks of public companies traded at prices lower than their freely traded counterparts.
- There was virtually no discussion regarding what caused the differences in observed values.
Only in recent years have appraisers begun to understand and to articulate why control premiums and restricted stock discounts exist. The integrated theory explains the why behind the generally accepted valuation premiums and discounts.
What Does Any of This Have to Do with Statutory Fair Value?
Statutory fair value is an interesting area of valuation. The legislatures in virtually all states have passed laws regarding the kind of value that should be available to minority shareholders in dissenting shareholder or shareholder oppression matters. In most cases, this value is called fair value.
However, as previously noted, with a couple of exceptions (Mississippi being one), fair value is not defined statutorily. As a result, it is up to the courts of the various states to provide judicial interpretations of the concept. We have briefly discussed fair value in Delaware and New York (here, here and here) in prior posts, and will continue the discussion in the future.
I hope that this series of posts on statutory fair value will begin to provide a basis for reasonable judicial interpretations of fair value in the context of solid valuation theory.
I also hope that the discussion will encourage appraisers to present their valuations in the context of solid valuation theory.
If courts have good financial, economic and valuation evidence, the chances are improved for statutory fair value decisions that make economic sense.