The Gordon Model is a single-period income capitalization model that provides a summary interpretation of how securities are valued in the public markets. The Gordon Model is often used to estimate the terminal value in a Discounted Cash Flow (DCF) valuation method, as we saw in an earlier post. The basic formulation of the Gordon Model defines the value of a business or interest as next period’s expected cash flow divided by an appropriate discount rate less the expected growth rate of the specified cash flow. This formula is a summary of the discounted cash flow method of valuation under the following conditions:

• The cash flows are expected to grow into perpetuity at the constant rate of g, and
• All cash flows are distributed to shareholders or are reinvested in the firm at the discount rate,

The discounted cash flow model as summarized by the Gordon Model provides an ideal basis for discussing what we call an integrated theory of business valuation, which is fully developed in my book (with Travis Harms), Business Valuation: An Integrated Theory (2nd Edition). We begin with a bit of introduction for perspective.

The Original Levels of Value Chart

The so-called levels of value chart first appeared in the valuation literature around 1990.  However, the general concepts embodied in the chart were known by appraisers and courts prior to that time.  While the general concepts were known, there was very little understanding of what the levels meant in terms of valuation theory. Even today, most discussions of the levels of value are very general and lack any compelling logic or rationale regarding the factors giving rise to value differences at each level.  As we have seen, the early levels of value chart showed three conceptual levels. We see three conceptual adjustments between the levels in the chart above:

• Control Premium (CP). The conceptual control premium moves from a marketable minority level of value (center of chart above) to the control level (top level).  Historically, control premiums have been observed in the public market place when public companies are acquired.  Normally, the acquiring company pays a premium over the price before the announcement in order to induce the selling company to sell.  Appraisers began to value companies on a controlling interest basis by adding control premiums to marketable minority values.
• Minority Interest Discount (MID).  The minority interest discount moves conceptually from the control level of value to the marketable minority level of value.  The minority interest discount was considered to be the mirror of the control premium, so appraisers looked at market evidence from control premiums (where the price is effectively (1 + CP)) to estimate minority interest discounts using a formula: MID = 1 – (1 / (1 – CP).  So if the average observed control premium was 40%, the corresponding minority interest discount was 28.6%, i.e., (1 – (1 / (1 + 40%))).
• Marketability Discount (MD or DLOM).  The marketability discount is often called a discount for lack of marketability, or DLOM, although I most often use the first term.  The MD moves from the marketable minority level of value (center above) to the nonmarketable minority interest level of value (bottom level above).  Marketability discounts were estimated historically by reference to restricted stock studies of transactions involving public companies selling blocks of their restricted (under SEC Rule 144) shares.  The restricted blocks of shares typically sold at discounts, often substantial discounts, to the publicly traded prices of companies prior to the restricted share transactions.  The medians of the early restricted stock studies tended to be in a broad range of around 25% to 45% or so, and marketability discounts for private companies often were found by appraiser to be in the range of 35% or so, and often larger, based solely on references to the restricted stock studies.

The marketable minority level of value is key in the three level chart above. It is the base from which the marketability discount is taken and to which the control premium is applied. We know that the value of a business is based on its expected cash flow, the growth of the expected cash flows, and the risks associated with achieving the expected cash flows.  The value of an interest in a business is similarly related to its expected cash flows (and their growth) and the risks associated with achieving those cash flows (i.e., interim distributions over an expected holding period and a terminal value upon an assumed liquidity event). Note that in the discussion of the traditional levels of value chart above, we did not mention either excepted cash flow, growth or risk. By the mid-1990s, a number of appraisers began to realize that the control premiums reflected in control premium studies typically involved strategic (or synergistic) transactions on the part of acquirers.  As a result, there was a growing recognition that the observed control premiums were measuring something other than “the value of control.” Upon reflection and observation, it is clear that strategic or synergistic transactions are actually measuring the value of expected synergies or strategic benefits (i.e., expected post-acquisition incremental cash flows and growth) as well as the acquirers’ perceived risks in achieving the synergistic benefits. Upon further reflection and observation, it is also clear that illiquid minority interests are worth less (i.e., the nonmarketable minority level above) than freely traded (or as-if freely traded for private companies) shares because of similar reasons. The Gordon Model capitalizes all expected cash flows of a business into present value at an appropriate discount rate.  The holder of an illiquid interest will typically pay less for it than for a liquid interest. Why is this?  Because the cash flows to an interest are often less than the cash flows of the enterprise, and the risks associated with achieving those cash flows are greater than the risks of the enterprise. I wrote a book titled Quantifying Marketability Discounts in 1997, which recognized these facts.  This book introduced the Quantitative Marketability Discount Model (QMDM), which is a shareholder-level discounted cash flow model, to estimate marketability discounts based on expected cash flows (and growth) and risks associated with illiquid interests. In 2004, I published another book, The Integrated Theory of Business Valuation, which introduced, as the title suggested, an integrated theory of business valuation.  Between the mid-1990s and 2004, we developed a second conceptual levels of value chart that had four levels, and related those levels to the expected cash flows, risks and growth associated with interests at the respective levels. All of the ideas from both books are included in our current book, Business Valuation: An Integrated Theory Second Edition. The updated levels of value chart is shown below for reference. As we continue this series on statutory fair value and business valuation, we will examine the cash flow and risk characteristics associated with each of the four levels above in detail.

Statutory Fair Value and an Integrated Theory of Business Valuation

Guided by the discussion in Business Valuation: An Integrated Theory (2nd Edition), we will begin a process of integrating the Gordon Model with a discussion of how the markets value public companies as we continue in the statutory fair value series. And, we will frame this discussion within the conceptual framework of the levels of value. The end game of this series on statutory fair value and business valuation is to create a theoretical framework and vocabulary with which we can talk about the valuation concepts that arise in statutory fair value determinations. As we proceed with developing an integrated theory of business valuation, we will:

• Describe the four level, levels of value chart previously shown in earlier posts.
• Use the components of the Gordon Model to define the conceptual adjustments between the levels of value, including the strategic and financial control premiums, 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).
• Use the integrated theory of business valuation to discuss statutory fair value concepts such as the implicit minority discount in Delaware case law, the use of a marketability discount in statutory fair value determinations in New York, and other concepts of value that appear in historical and emerging cases relating to statutory fair value.

Begin with the Marketable Minority Level of Value

Remember, no valuation premium has any meaning unless the base to which it is applied is specified. And no valuation discount has any meaning unless the base from which it is taken is specified. The marketable minority interest level of value is the middle level in the three level, levels of value chart above. It is the base from which marketability discounts are applied and to which control premiums are added.  And this level is also in the middle of the four level chart.  As such, an understanding of the marketable minority level of value is pivotal to our developing knowledge of valuation concepts. With these objectives in mind, we proceed in the next post with the development of the integrated theory of business valuation and with our discussion of statutory fair value. The next post in this series will discuss the benchmark level of value known as the marketable minority interest. Be well, Chris