Senin, 03 Desember 2012

The Integrated Theory of Business Valuation


The Integrated Theory of Business Valuation
by Z. Christopher Mercer, ASA, CFA
THE GORDON MODEL
The Gordon Model is a single-period income capitalization model, and is reflective of the way that securities are valued in the public markets. The Gordon Model is shown here as a beginning point for a discussion of an integrated theory of business valuation. 1 This integrated theory will be developed in the context of the conceptual levels of value.2
V = CF (1 + G)
R - G
Equation 1
The basic formulation of the Gordon Model can be interpreted as follows. Value today is equal to next period's (year's) expected cash flow (income measure) divided by (or capitalized by) a firm's discount rate less the expected (constant) growth rate of the measure of cash flow in the numerator. As we have previously shown, this formula is a summary of the basic discounted cash flow (future earnings) method of valuation under the following assumptions:
• The expected cash flows are growing at the constant rate of G, and

1 The actual beginning point for the discussion of an integrated theory is the basic discounted cash flow model. While business appraisers and finance professionals may disagree on many things, a large-scale poll of both would indicate virtual unanimity on this conceptual definition of the value of a business. In order to value a business today, then, we need the following:
• A forecast of all expected future cash flows or benefits to be derived from ownership of the business.
• An appropriate discount rate with which to discount the cash flows.
• A methodology for making the appropriate calculations to derive value.

These terms can be defined symbolically to facilitate discussion:
(1+r)3(1+r)4(1+r)nCF4CFnValue = Vo =++++…+(1+r)1(1+r)2CF1CF2CF3
Where: Vo is the intended result, the value of a business today
CF1 to CFn represent the expected cash flows (or benefits) to be derived for years 1 to n
r is the discount rate that converts future dollars of CF into present dollars of value
Professor Gordon proved that this basic model of valuation can be summarized as the “Gordon Model” as shown in Equation 1.
2 We use the term “integrated theory” in our discussion. The universality of the integrated theory has been previously recognized in an article in the ASA’s Valuation publication in June 1996. See C. Donald Wiggins, Dilip D. Kare, and Jeff Madura, “A Universal Valuation Model for Closely Held Businesses,” Valuation, June 1996. Wiggins, et al show in this article that the basic DCF formulation is a “universal valuation model” that can be reconciled with all other valuation methodologies.
© Z. Christopher Mercer, 2002 1 All rights reserved

All cash flows are reinvested in the firm at the discount rate, R (or are otherwise distributed and available for reinvestment at R).

Appraisers have been using the basic Gordon Model for many years. Some appraisers suggest that the appropriate measure of earnings (CF) to use is net cash flow, which is usually defined as follows:
Net Income
+ Depreciation/Amortization
+/- Net Changes in Working Capital
+/- Net Changes in Long-Term Debt
- Capital Expenditures
= Net Cash Flow
Other appraisers suggest that the appropriate measure of cash flow is that of net income. While over the long run, net income and net cash flow will be approximately equal, there can be significant differences over any short period of time. For a growing company, net cash flow, as defined above, will normally be less than net income because of working capital requirements of growth and investment in capital expenditures necessary to support growth.
Assume we know the next year’s expected net income, its expected net cash flow, and the value of the equity of an enterprise. Assuming equivalent expected growth, if net cash flow is less than net income, it should be clear that the discount rate applicable to net income must be different than that applicable to net cash flow in order to reach the same value using Equation 1. However, a 1992 article illustrates the difference as being relatively small over relevant ranges of assumptions about discount rates and expected growth.3
Appraisers develop discount rates for use with the Gordon Model by two primary means:
• Directly, based on the pricing of publicly traded securities
• Indirectly, using applications of the Capital Asset Pricing Model (CAPM) or the Adjusted Capital Asset Pricing Model (ACAPM)4

The cited net income/net cash flow article indicates that the magnitude of any adjustment between net income and net cash flow is within the range of judgments made by appraisers regarding expected growth, specific company risks, industry risks via the application of beta, and the selection of the base Treasury rate (using the CAPM, or ACAPM). It further suggests that appraisers who consistently use the ACAPM to develop discount rates for net income or net cash flow may be able to develop consistently credible results, regardless of the theoretical (or really, practical) controversy noted here. The Gordon Model is sufficiently well accepted to provide the basis for an integrated theory of business valuation.
3 Mercer, Z. Christopher, “Adjusted Capitalization Rates for the Differences Between Net Income and Net Free Cash Flow, Business Valuation Review, December, 1992.
4 Mercer, Z. Christopher, “The Adjusted Capital Asset Pricing Model for Developing Capitalization Rates: An Extension of Previous ‘Build-Up’ Methodologies Based Upon the Capital Asset Pricing Model,” Business Valuation Review, December, 1989.
© Z. Christopher Mercer, 2002 2 All rights reserved
THE GORDON MODEL AND THE LEVELS OF VALUE
The so-called levels of value chart first appeared in the valuation literature some time around 1990.5 However, the general concepts embodied in the chart were known by appraisers (and courts) prior to that time. To date, virtually all discussion regarding levels of value in the valuation literature has been at a conceptual level. There has been no published integration of the conceptual levels of value with and into current financial theory.6
The purpose of this discussion is to provide the theoretical integration of the Gordon Model, as a basic statement of how the markets (and appraisers) value companies with the levels of value. If we are to do this, we must accomplish the following:
• Explain each level of value in the context of the Gordon Model. In other words, we must adapt the Gordon Model to represent each conceptual level of value.
• Using the components of the Gordon Model, we must be able to define the conceptual adjustments between the levels of value, e.g., the control premium (and its inverse, the minority interest discount) and the marketability discount.
• Explain the differences in the levels of value (higher versus lower) in terms of the components of the Gordon Model.
• Explain why the integrated model is illustrative of pricing behavior in the marketplace for public securities (the marketable minority level), the market for entire companies (the controlling interest levels of value), and the "market" for illiquid, minority interests of private enterprises.

With these objectives in mind, we proceed with the development of an integrated theory of business valuation.
THE MARKETABLE MINORITY INTEREST LEVEL OF VALUE
It is generally accepted that the Gordon Model provides a short-hand representation of the value of public securities at the marketable minority interest level of value. For privately owned enterprises, it is indicative of the same level, i.e., the "as-if-freely-traded" level. In developing an integrated theory, we must discuss the Gordon Model in the context of the levels of value and understand how they 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 marketable minority interest level of value is defined in the context of the Gordon Model as follows:
Vmm = CFe(mm) or CF
(Rmm - Gmm) R - G
Equation 2
5 See Mercer Capital’s E-Law Business Valuation Perspective, Issue 2001-10, “Leveling with You About the Levels of Value,” November 19, 2001.
6 Such an integration has been presented in a number of speeches. See Z. Christopher Mercer, "Discounts and Premiums Meet the Levels of Value,” Internal Revenue Service, Fort Monmouth, NJ, 8/30/00. Same speech also given by Mercer at the 2000 AICPA National Business Valuation Conference, Miami, FL, 11/13/00 and the Litigation & Valuation Services Conference of the Florida Institute of Certified Public Accountants, Miami, FL, 01/12/01.
© Z. Christopher Mercer, 2002 3 All rights reserved
Equation 2 is defined as follows:
Vmm is the equity value of a public security at the marketable minority level of value (mm), and the value of a privately owned security at the same level, i.e., as-if-freely-traded. This is the benchmark, observable value for public securities. As developed more fully elsewhere, the as-if-freely-traded value for private enterprises is a hypothetical value. It does not exist by definition for illiquid interests of private enterprises, since there are no active, public markets for their shares. Appraisers develop indications of value at this level as a first step in estimating values at other levels of value.
CFe(mm) is equal to the cash flow (earning power) of the (public or as-if-public) enterprise at the marketable minority level for the next period. The marketable minority level of cash flow is assumed to be "normalized" for unusual or non-recurring events, and to have an expense structure that is market-based and designed to maximize returns to shareholders. Public companies attempt to keep the investment community focused on their "normalized" earnings. Many companies, for example, disclose pro forma earnings, or earnings after adjusting for unusual or nonrecurring (and sometimes not so non-recurring!) items.
Rmm is a public company's discount rate, or 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 the Adjusted Capital Asset Pricing Model.7
Gmm is the expected growth rate of earnings for the public security under the assumption that all earnings are distributed to shareholders. As shown previously, it is the compounding effect of reinvested earnings that enables a company to grow its value at rates in excess of its underlying earnings growth rate. Gmm is not equal to the expected growth rate of earnings published by stock analysts for public companies. The analysts' G includes the compounding effect of the reinvestment of cash flows on the expected growth of earnings.

At this point, we can begin to connect the basic 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. Figure 1 relates the conceptual math and the marketable minority level of value.
Vmm CFe(mm) Rmm- GmmMarketableMinority Conceptual Value Math RelationshipsImplicationsequals(GV = Rmm)
Figure 1
7 Mercer, Z. Christopher, “The Adjusted Capital Asset Pricing Model for Developing Capitalization Rates: An Extension of Previous ‘Build-Up’ Methodologies Based Upon the Capital Asset Pricing Model,” previously cited. Some writers make a distinction between the ACAPM and the so-called build-up method, which is identical to the ACAPM under the assumption that beta is equal to 1.0. This distinction is artificial, since it is apparent that the build-up method is based on the Capital Asset Pricing Model, just as is the ACAPM.
© Z. Christopher Mercer, 2002 4 All rights reserved
We define the marketable minority level of value as an enterprise level of value. We do so because CFmm is defined as the cash flow of the enterprise. The importance of this definition will become clear as the remaining mathematical relationships of the conceptual levels of value are built.
The marketable minority level of value is that level to which appraisers have often, 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 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 relates the controlling interest and marketable minority levels.
As pointed out clearly by Pratt, Reilly, Schweihs and others, no valuation premium or discount has meaning unless we understand the base to which it is applied.8 The marketable minority value is the base level of value for the enterprise in the integrated theory of business valuation.
A review of the valuation literature until the latter part of the 1990s yields little insight into the theoretical basis for applying the well-known conceptual premiums and discounts. Practically, appraisers applied control premiums because they were observable in the marketplace in which public companies changed control. And marketability discounts were applied because it was observed that restricted stocks of public companies traded at prices lower than their freely traded counterparts. Only in recent years have appraisers begun to understand and to articulate why control premiums and restricted stock discounts exist, and consequently, to understand the theoretical basis for their existence. The remainder of this discussion should be helpful in understanding the why behind the generally accepted valuation premiums and discounts.
THE FINANCIAL CONTROL LEVEL OF VALUE
There is a growing understanding that there are at least two conceptual levels of value above the marketable minority level:
Financial Control. The first level is referred to as the level of value that a financial buyer is willing and able to pay for control of a business. Financial buyers are those buyers in the marketplace who acquire companies based on their ability to extract reasonable (to them) rates of return through the acquisition of companies, often on a leveraged basis.
Strategic Control. The second control level is referred to as the strategic, or synergistic level of value. Strategic buyers, it is recognized, can (and do) pay more for companies than financial buyers because they expect to realize synergies from the acquisition (e.g., through eliminating duplicate expenses or achieving selling benefits). In addition, strategic buyers will often pay more than

8 Pratt, Shannon P., Reilly, Robert F., and Schweihs, Robert P., Valuing a Business: The Analysis and Appraisal of Closely Held Companies, Fourth Edition (New York, NY, McGraw-Hill 2000).
Pratt, Shannon P., Reilly, Robert F., and Schweihs, Robert P., Valuing a Business: The Analysis and Appraisal of Closely Held Companies, Third Edition (Chicago, IL, Irwin Professional Publishing 1996).
Pratt, Shannon P., Valuing a Business: The Analysis and Appraisal of Closely Held Companies, Second Edition (Homewood, IL, Dow Jones-Irwin 1988).
Pratt, Shannon P., Valuing a Business: The Analysis and Appraisal of Closely Held Companies, First Edition (Homewood, IL, Dow Jones-Irwin 1981).
Mercer, Z. Christopher, Valuing Financial Institutions (Homewood, IL, Business One Irwin, 1992), Chapter 12, pp. 193-206.
© Z. Christopher Mercer, 2002 5 All rights reserved

financial buyers for strategic reasons that relate, ultimately, to their ability to generate future cash flows.9

The growing realization, through observation in the whole-company transaction markets, has led to the appearance of conceptual levels of value charts with four, rather than three, levels. A comparison of the two charts is shown in Figure 2.
The Levels of ValueMarketabilityDiscountControlPremiumMarketable MinorityNonmarketable MinorityControl ValueMinorityInterestDiscountMarketabilityDiscountFinancialControlPremiumMarketable MinorityNonmarketable MinorityFinancial Control ValueMinorityInterestDiscountStrategic Control ValueStrategicControlPremiumTraditionalExpanded?
Figure 2
The left side of Figure 2 presents the traditional three-level chart, together with the conceptual premium and discounts that enable appraisers to relate the levels to each other. The right side of the figure presents the expanded, four-level chart. Note that the "financial control premium" on the right and the "control premium" on the left are the equivalent conceptual premiums.10 As a result, the minority interest discounts shown on the left and right sides of Figure 2 are the same conceptual discount. We have called the
9 Garber, Steven D., “Control vs. Acquisition Premiums: Is There a Difference?” Presentation given at the American Society of Appraisers 1998 International Appraisal Conference, Maui, Hawaii, June 22-24, 1998.
Mercer, Z. Christopher, “A Brief Review of Control Premiums and Minority Interest Discounts,” The Journal of Business Valuation Proceedings of the Twelfth Biennial Business Valuation Conference held in Toronto Canada, June 6-7, 1996, published by The Canadian Institute of Chartered Business Valuators, pp. 365-387.
Lee, M. Mark, “Premiums and Discounts for the Valuation of Closely Held Companies: The Need for Specific Economic Analysis,” Business Valuation Update, August 2001.
Pratt, Shannon P., DBA, CFA, CFP, ASA. "Discount Rates Based on CAPM Don't Always Lead to Minority Value," Shannon Pratt’s Business Valuation Update, March, 2001.
Pratt, Shannon P., DBA, CFA, CFP, ASA. "The Oxymoron of Control, Marketable," Shannon Pratt’s Business Valuation Update, October, 1999.
Pratt, Shannon P., DBA, CFA, CFP, ASA. "Public Market Values Inflated in Comparison with Private Companies," Shannon Pratt’s Business Valuation Update, November, 1997.
10 This flows from the general belief that fair market value is a financial concept based on the hypothetical negotiations of hypothetical willing buyers, and that the "strategic control premium" is reflective of the consideration of specific buyers to benefit from particular synergies or strategies. As indicated in Mercer, Z. Christopher and Brown, Terry S., “Fair Market Value vs. The Real World,” Valuation Strategies, March/April 1999, Volume 2, No. 4, the strategic control level of value might become the appropriate level for fair market value if the typical buyer is a strategic buyer. This situation existed during much of the 1990s in the consolidating banking industry and likely in numerous other consolidating industries.
© Z. Christopher Mercer, 2002 6 All rights reserved
conceptual premium relating the financial control value with the strategic control value the "strategic control premium."11 This term seems to incorporate sufficiently the concepts of strategies, synergies and control for our present purposes. Now note that no name is provided for the conceptual discount that would eliminate the strategic control premium relative to the financial control value. Further, note that this conceptual discount is not the minority interest discount relating the financial control value with the marketable minority level of value.
Careful review of most of the control premium (Pratt/Reilly Schweihs would suggest "acquisition premium") data available to appraisers suggests they generally result from transactions reflective of strategic or synergistic motivations. If this is observation is true, then the available control premium data is more generally reflective of the sum of the financial control premium and the strategic control premium. Our expanded conceptual understanding leads to what may be uncomfortable observations for many appraisers:12
• Use of available control premium studies as a basis for inferring minority interest discounts in a fair market value context is not conceptually correct, except where strategic buyers are the norm.
• Such use would tend to overstate the magnitude of minority interest discounts.
• Such discounts would not yield, when applied to financial control values, marketable minority interest levels of value, but something conceptually lower than that level (with no clear conceptual definition).
• And finally, The application of a "standard" marketability discount to that lower (and conceptually undefined) value would tend to understate the value of illiquid interests of private enterprises.

With this conceptual backdrop, we can now examine the controlling interest levels of value. Equation 3 introduces the conceptual math of the first control level of value – the financial control value.
As with the marketable minority level of value, we need to define the terms found in Equation 3 are defined as follows:
11 Pratt/Reilly/Schweihs call it the "strategic acquisition premium" in their chart. They state, regarding the chart:
The diagram presented in Exhibit 15-1 reflects the value influence of the ownership characteristics of control versus the noncontrolling stockholder's situation as discussed in Chapter 16. This schematic usually would represent the fair market value standard of value on a going-concern basis premise of value. In some cases, there may be yet another layer of value, which may reflect synergies with certain third-party buyers (as examples of: (1) reducing combined overhead by the consolidation of operations or (2) raising prices by reducing competition). There is not yet a widely used term for this additional layer of price premium over fair market, going-concern value. However, this price premium -- when combined with the ownership control premium -- is sometimes called an acquisition premium. The standard of value reflecting these synergies usually would be considered investment value. This is because it reflects the value to a particular buyer, generally referred to as the synergistic buyer, rather than value to the hypothetical willing buyer. This "hypothetical" typical willing buyer acquires the subject company strictly because of its financial merits, and is generally referred to as a financial buyer. (emphasis in original)
12 While others have concluded that strategic control premiums may overstate value in the context of developing financial control values, these observations follow the implications to their logical conclusions. See two articles that reach this same conclusion.
Mercer, Z. Christopher, “A Brief Review of Control Premiums and Minority Interest Discounts,” The Journal of Business Valuation, Proceedings of the Twelfth Biennial Business Valuation Conference of The Canadian Institute of Chartered Business Valuators, Toronto, Canada, June 6-7, 1996.
Mercer, Z. Christopher,” Understanding and Quantifying Control Premiums: The Value of Control vs. Synergies or Strategic Advantages, The Journal of Business Valuation, Proceedings of the Fourth Joint Business Valuation Conference of the Canadian Institute of Chartered Business Valuators and the American Society of Appraisers, Montreal, Canada, September 24-25, 1998. © Z. Christopher Mercer, 2002 7 All rights reserved

Ve(c,f) is the value of the equity of an enterprise from the viewpoint of typical purchasers of the entire enterprise (control) who do not have the expected benefit of synergies or strategic intent that could further increase value relative to the marketable minority value. This level of value is called the financial control level of value. Traditionally, appraisers have developed this level of value in two ways: 1) directly, by comparisons with change of control transactions of similar businesses (the guideline company change of control method); and 2) indirectly, by the application of a control premium to an indication of value at the marketable minority level of value.

Ve(c,f) = CFe(c,f)
[Rf - (Gmm + Gf)]
Equation 3
CFe(c,f) is equal to the cash flow of the enterprise from the viewpoint of the financial control buyer. The first step in developing CFe(c,f) is to derive CFe(mm) by normalizing the earnings stream as described elsewhere. (Note that the normalization of earnings is not a “control” process, but one of equating private company earnings to their as-if-public equivalent). The second step involves judgments regarding the ability of a control buyer to improve the earnings stream beyond the normalization process. This could involve the ability of a specific buyer to improve the existing operations, but might not be applicable in the context of fair market value, where the buyers are hypothetical, and where the typical buyer might not have that ability (or is unwilling to share that anticipated benefit with the seller).
Rf is the discount rate of the universe of financial buyers. In the real world, Rf may be identical to Rmm, as other writers have observed. We designate Rf specifically to allow for the fact that the leverage considered by a financial buyer could increase the discount rate somewhat above Rmm. This increase might be offset in the context of the total capital of the enterprise by the lower cost of a larger amount of debt than is considered normal in the public marketplace. However, in this discussion, we are dealing with the equity value of the enterprise, and not the value of the total capital.
(Gmm + Gf) is the expected growth rate of earnings for the financial control buyer. The first factor is the same Gmm found at the marketable minority level. The second factor is the increment in the growth rate of earnings that a control buyer may expect to generate. The second factor might not be relevant in a fair market value appraisal for two reasons: 1) the universe of hypothetical willing buyers may not expect such an increment in growth; and 2) a specific buyer who can accelerate growth may not share that expected benefit in a negotiation. Nevertheless, this component of expected growth needs to be specified in order to understand market behavior.

We now have a conceptual model to develop the value of the equity of an enterprise at the financial control level. That model is based on the conceptual model for value at the marketable minority level, which is based on the Gordon Model. The relationship between the two levels of value is illustrated in Figure 3.
© Z. Christopher Mercer, 2002 8 All rights reserved
VmmequalsCFe(mm)Rmm-GmmConceptualValueMathRelationshipsImplicationsFinancialControl ValueFinancialControl ValueMarketableMinorityMarketableMinorityCFe(c,f) >CFmmGf>0Rf>RmmCFe(c,f)Rf-[Gmm+ Gf]Ve(c,f) >Vmm
Figure 3
By examining Figure 3, the conceptual differences in value at the marketable minority and financial control levels of value can be discerned. The latter value can be greater than the former if one or more of the following conditions holds:
CFe(c,f) is greater than CFe(mm). This would be true if the typical buyer of the enterprise could be expected to improve the operations of the enterprise and would share that expected benefit with the hypothetical seller. Note that CFe(c,f) will not exceed CFe(mm) because of above-market salaries paid to owners of a business. Adjustments of that nature were required to arrive at CFe(mm).
Gf is greater than zero. If the typical financial control buyer expects to be able to augment the future growth of cash flows (and will share that benefit with the hypothetical seller), then Ve(c,f) can exceed Vmm, other things being equal.

The notation suggests that Rf could exceed Rmm. This could be true for a specific buyer; however, it is likely that market forces would tend to force the universe of buyers to accept Rmm as the basic discount rate.13 However, the conceptual model must include this distinction for an important reason. Many appraisers have observed that the value of an entire public company may be less than the freely traded market price of that company. The frequency of this observation increased dramatically during the dot.com era. The model now provides an explanation for the observation that the value of an enterprise as a whole may be less than the publicly traded price. This can be so if the universe of control buyers perceives more risk in a company than is reflected in speculative trading.
13 We have not included the possibility that Rf < Rmm in the notation above. If a buyer’s discount rate is less than the discount rate of the enterprise, use of that rate would tend to overstate financial control value. Such a buyer is likely a strategic buyer.
© Z. Christopher Mercer, 2002 9 All rights reserved
Financial Control Premium
At this point, the control premium that a financial control buyer might pay (CPf) can be specified in relationship to the value of a business at the marketable minority level.
CPf= Ve(c,f) - Ve(mm)Ve(mm)
CFe(c,f) CFe(mm) Rf - [Gmm + Gf] Rmm - Gmm-CPf= CFe(mm)Rmm - Gmm
Equation 4
Conceptually, the control premium of a financial control buyer must be the difference in value at the financial control level and at the marketable minority level in relationship to the marketable minority value. This is shown symbolically in the upper equation of Equation 4. The lower equation substitutes the right hand side of each value equation for each of the left hand values (see Figure 3).
Several important observations about the relationship between value at the marketable minority level and at the financial control level can now be made. Unless typical financial buyers can: 1) increase cash flows relative to normalized cash flows of the enterprise; 2) increase expected growth of cash flows of the enterprise, (and for both 1) and 2)), share that expected benefit with hypothetical sellers), or, 3) decrease the discount rate relative to Rmm (which most observers would consider unlikely):
• Ve(c,f) will be the same as Vmm.
• The control premium of the financial control buyer will be zero (or quite small)
• Guideline public company multiples applied to normalized earnings of privately owned enterprises will yield financial control values, or valued very close to this level. This will be true, of course, only if the public multiples are properly adjusted for fundamental differences in expectations (primarily for risk and growth) between the guideline public companies and the subject private enterprises.
• The marketable minority value will be equal to, or certainly, very close to, the financial control value.

We have come a long way since Eric Nath made this last, then-revolutionary observation in 1990.14 Suffice it to say that many appraisers thought his observation was nothing short of heresy. And I was in that group of appraisers!15
14 Nath, Eric W., “Control Premiums and Minority Interest Discounts in Private Companies,” Business Valuation Review, Vol. 9, No. 2, June 1990, pp. 39-46.
15 Mercer, Z. Christopher, “Do Public Company (Minority) Transactions Yield Controlling Interest or Minority Interest Pricing Data?” Business Valuation Review, Vol. 9, No. 4, December 1990, pp. 123-126.
© Z. Christopher Mercer, 2002 10 All rights reserved
Prerogatives of Control (Introduction to the Minority Interest Discount)
There is a corollary implication to the conceptual analysis thus far. The minority interest discount necessary to adjust a financial control value to a marketable minority value in an operating company may be zero, or quite small. This conclusion follows from the conceptual discussion surrounding Figure 2, and from the conceptual math of the integrated theory. The integrated theory is beginning to shake up some long-established and well-entrenched thinking. The difficulties of dealing with these issues absent an integrated theory can be illustrated by examining the discussion of control and noncontrol in the most recent edition of Pratt/Reilly/Schweihs. Many appraisers have cited the list of prerogatives of control found in each of the Pratt, Reilly, Schweihs books (and other books) as the reason for the application of a substantial minority interest discount.16 The prerogatives of control include:
1. Appoint or change operational management
2. Appoint or change members of the board of directors
3. Determine management compensation and perquisites
4. Set operational and strategic policy and change the course of the business
5. Acquire, lease, or liquidate business assets, including plant, property, and equipment
6. Select suppliers, vendors, and subcontractors with whom to do business and award contracts
7. Negotiate and consummate mergers and acquisitions
8. Liquidate, dissolve, sell out, or recapitalize the company
9. Sell or acquire treasury shares
10. Register the company’s equity securities for an initial or secondary public offering
11. Register the company’s debt securities for an initial or secondary public offering
12. Declare and pay cash and/or stock dividends
13. Change the articles of incorporation or bylaws
14. Set one’s own compensation (and perquisites) and the compensation (and perquisites) or related-party employees
15. Select joint venturers and enter into joint venture and partnership agreements
16. Decide what products and/or services to offer and how to price those products or services
17. Decide what markets and locations to serve, to enter into, and to discontinue serving
18. Decide which customer categories to market to and which not to market to
19. Enter into inbound and outbound license or sharing agreements regarding intellectual properties
20. Block any or all of the above actions

In short, the prerogatives of control indicate that the controlling shareholder is empowered with the rights and responsibilities to run a business enterprise for the benefit of the controlling shareholder. Appraisers (and courts) have long thought that control buyers pay control premiums for the prerogatives of control listed above. The Pratt/Reilly/Schweihs text concludes the presentation of this list, which first appears in Chapter 15, “Control and Acquisition Premiums,” with:
From the above list, it is apparent that the owner of a controlling interest in a business enterprise enjoys some very valuable rights that the owner of a noncontrolling ownership interest does not enjoy.17
The authors present two levels of value charts at the same point in the text. The first chart is one used for several years by Pratt/Reilly/Schweihs in editions of Valuing a Business and in other Pratt publications.
16 Pratt, et al., Valuing a Business, Fourth Edition, pp. 347-348. The list is growing with succeeding editions.
17 Ibid, p. 349.
© Z. Christopher Mercer, 2002 11 All rights reserved
The second is a reproduction of the right portion of Figure 2 above.18 This is important because it is clear from the charts that the control premium being discussed by Pratt/Reilly/Schweihs is the same conceptual premium as the financial control premium indicated in Figure 2.
We will see shortly that the above-quoted statement may be true as it relates to a controlling owner of a private company and a minority (noncontrolling) shareholder in the same company. It is likely not true (or is not relevant) as it relates to the managements and boards of directors of well-run public companies and the corresponding minority shareholders of their publicly traded stock.
The prerogatives of control list are repeated in the next chapter of Pratt/Reilly/Schweihs, “Discounts for Lack of Control.” Following the second list, we read:19
As the equityholder enjoys fewer and fewer of these elements of ownership control, his or her position changes from absolute control to relative control to lack of control to absolute lack of control. Along this spectrum: (1) The control premium begins to decrease, (2) then becomes zero, and finally (3) changes to a lack of control discount.
While I appreciate the range of values that the authors are attempting to describe, i.e., the range of value between financial control value and nonmarketable minority value, a careful reading of this conclusion in connection with a visual inspection of Figure 2 indicates that it is conceptually incorrect. The control premium referred to measures the value differential between the marketable minority value and the financial control value. If it is the prerogatives of control that give rise to this differential, then the elimination of the prerogatives (i.e., the case of a minority, or noncontrolling, investor) cannot give rise to a larger decrement in value than the value attributed to the prerogatives, i.e., the financial control premium. When the control premium decreases to zero, for whatever reason, we are at the marketable minority level of value. If the conceptual levels of value represented by the two charts found in Pratt/Reilly/Schweihs are a valid representation of economic and financial reality, any further decrement in value must result from factors other than the prerogatives of control.
The further reduction in value described in (3) in the quote above, where there is a change to a lack of control discount, is actually the decrement in value known as the marketability discount. Under this interpretation, the noncontrolling shareholder of a private enterprise may enjoy a lower value than either the hypothetical, marketable minority value or the financial control value. The conceptual name for this value is the nonmarketable minority (level of) value. In the context of the conceptual levels of value, it is not possible for the minority (lack of control) discount to become negative. The freely traded (marketable minority) value is the base to which the control premium is applied. If there is a positive value to the prerogative of control, it is not feasible for the control premium to be negative.20 The conceptual model outlined by Pratt/Reilly/Schweihs breaks down at this point. The lack of control discount in (3) above must be the marketability discount. We will discuss the concepts of lack of marketability and lack of control in more depth below.
18 Ibid, p. 347. Citing Fishman, Jay E., Pratt, Shannon P., et al, Guide to Business Valuations, 10th edition (Fort Worth, TX: Practitioners Publishing Company, 2000). Also, at p. 348, citing Mercer, Z. Christopher, “Understanding and Quantifying Control Premiums: The Value of Control vs. Synergies of Strategic Advantages, Part II,” The Journal of Business Valuation (Proceedings of the Fourth Joint Business Valuation Conference of The Canadian Institute of Chartered Business Valuators and the American Society of Appraisers, September 24 and 25, 1998) (Toronto: The Canadian Institute of Chartered Business Valuators, 1999), p. 51.
19 Ibid, p. 366.
20 We have observed that entire companies are sometimes worth less than their indicated, freely-traded values. If present, this difference could be termed a (negative) control premium.
© Z. Christopher Mercer, 2002 12 All rights reserved
A careful look at the conceptual math shown in Figure 4 reveals no payment for a single one of the above-listed prerogatives of control. What, then, is a control buyer paying for? Assume that Rf is equal to Rmm for purposes of the following attempt to answer this critical question. We can observe from Figure 4, which defines the control premium of a financial control buyer:
• The differential in value between the marketable minority level and the financial control value (i.e., the financial control premium) is created by any differential in cash flow that the typical control buyer is willing to price into a deal and any expectation for increased growth in those cash flows.
• In other words, the conceptual model suggests that a control buyer would pay a financial control price based only on the expectation of greater future cash flows than expected at the marketable minority level.
• The prerogatives of control are assumed in the valuation process of the control buyer, who will not pay a control price unless those prerogatives accompany the transfer of control. There is no separate payment for these prerogatives of control.
• There is no specific portion of the value of an enterprise that can be allocated to the so-called prerogatives of control.

It can therefore be concluded that the control premium is not the price paid for the prerogatives of control, but the price paid for control of the cash flows of an enterprise in cases where the typical buyer expects to augment those cash flows relative to the marketable minority level of cash flow.
We have observed thus far that unless the typical control buyer can expect to achieve augmented levels and growth of cash flows, the financial control premium could be zero, or at least, quite small. The reason is simple: if it were not so, if a substantial premium were paid with no expectation of augmented cash flows, then the control buyer would have to accept a lower than market return.
The Minority Interest Discount
We have defined the conceptual difference between the financial control value and the marketable minority value as the financial control premium (see Figure 2). If that premium is zero (or quite small), as observed above, it would also be true that the minority interest discount, which is also referred to as the lack of control discount, would be quite small.21 This issue will be explored further after we address the strategic control level. Before doing that, however, several observations about the relationships between the marketable minority and financial control levels of value should be summarized:
• There is no conceptual payment for the prerogatives of control at the financial control level. The payment is for the cash flows and the prerogatives are assumed.
• If the conceptual analysis is correct, there may often be little reason for a financial control premium to value at the marketable minority level – assuming that cash flows were properly normalized at that level.
• Minority shareholders of public companies lack control over the entities in which they invest. Control is vested with managements and boards of directors. Yet we have observed that the

21 American Society of Appraisers, Business Valuation Standards, Definitions (Revision dated February, 2001), pp. 21-27. This lack of control discount, unlike the term used in (3) above in Pratt/Reilly/Schweihs, is theoretically consistent with eliminating a financial control premium.
© Z. Christopher Mercer, 2002 13 All rights reserved

marketable minority value and the control financial value may be equal to or very closely equal to each other for many companies.
• The implication of this line of reasoning is that there is no (or very little) discount for lack of control considered in the pricing of public securities. This makes sense because investors in the public markets are not investing to gain control – they invest in companies and assume that managements will run them in the best interests of the shareholders. If it were not so, the shareholders would exercise the control they do have – selling their shares and putting downward pressure on market prices, creating opportunities for takeovers by financial buyers.
• Note that investors in public companies vest all of the prerogatives of control with their managements and directorate, reserving for shareholder vote only the election of the directorate and approval over certain major corporate events. The benefit or financial value of the prerogatives must either be a gift to management and directorate or, be reflected in pricing at the marketable minority value. Since rational investors are not in the business of making gifts, the value of prerogatives of control must be incorporated in marketable minority pricing. If it were not so, the shareholders would exercise the control they do have – selling their shares and putting downward pressure on market prices, creating opportunities for takeovers by financial buyers.
• Further, observe that value at the marketable minority level assumes that all the cash flows of public enterprises will be distributed to the shareholders in dividends or reinvested in the enterprises at their discount rates. There is no pricing penalty because minority shareholders do not control or have direct access to or control over enterprise cash flows. This is true because minority shareholders have access to the benefit of the market's capitalization of all expected future cash flows in the market price. At any time, a minority shareholder in a public enterprise can place a sale order and achieve current market value in three days.
• Conceptually, this suggests that the mechanism of the public securities markets eliminates any discount for lack of control of cash flows for minority shareholders.
• The logical inference is that if a private enterprise is valued at the hypothetical, marketable minority level of value, there is no imbedded minority interest discount, or discount for lack of control. Further, unless there are cash flow-driven differences in that enterprise’s financial control value and its marketable minority value, there will be no (or little) minority interest discount applicable at that level, either.22

The analysis suggests that use of the terms "lack of control discount" and "minority interest discount" may not be descriptive of the economic factors and issues that they are being used to describe. Rather than attempting to introduce new vocabulary at this point, we proceed with efforts to understand what the existing terms mean.
The financial control premium was defined in Figure 4. Basic algebra suggests that the related minority interest discount from the financial control value (MIDF)is defined as indicated at the top of Equation 5.
MIDF = [ 11 + CPF1 -]
22 The capital structure of an enterprise may include voting and nonvoting stock. If the vote is perceived to decrease risk somewhat relative to the nonvoting shares, voting shares may trade at a small premium to nonvoting shares. Stated alternatively, nonvoting shares may trade at a small discount to voting shares.
© Z. Christopher Mercer, 2002 14 All rights reserved
MIDF = [11 + Ve(c,f) - Ve(mm) Ve(mm) 1 -][]
Equation 5
Examination of the bottom portion of Equation 5 indicates that the minority interest discount will exist only if the typical control financial buyer can expect to augment cash flows from properly normalized cash flows at the marketable minority level. That is the only conceptual cause for Ve(c,f) to diverge from Ve(mm), which creates the financial control premium, which creates the so-called minority interest discount.23
Market discipline should cause most public companies to be run in reasonable fashion, with cash flows being optimized and either reinvested or distributed to achieve appropriate returns to shareholders. If it were not so, as Nath observed in 1990, there would be incentive for financial buyers to acquire underperforming companies and there would be considerably more merger and acquisition activity than was observed in the markets then or now.
The conceptual analysis thus far suggests that the appearance of Figure 2 should be modified to reflect the conceptual relationship between the financial control and marketable minority levels.
Strategic ValueMarketable MinorityNonmarketableMinorityControl ValueMarketabilityDiscountTraditionalExpanded, ModifiedNonmarketableMinorityControl ValueFreely TradableMarketabilityDiscountStrategic PremiumFCP?MID
Figure 4
The modified chart shows the much closer correspondence between the financial control and marketable minority levels of value suggested by the conceptual discussion and by the math of the levels of value.
The conceptual strategic control value will be developed to round out the enterprise levels before proceeding to the shareholder level represented by the nonmarketable minority value. However, before proceeding, a critical observation flows from Figure 4:
Assuming the conceptual analysis thus far is reasonably correct, the source of what can be large differences between enterprise values (financial control or marketable minority)
23 These observations are made in relationship to operating companies. Their relevance for asset holding entities needs to be addressed separately.
© Z. Christopher Mercer, 2002 15 All rights reserved
and the shareholder level, nonmarketable minority value is entirely (or at least substantially) found in the conceptual discount known as the marketability discount.
The analysis of the relationship between the financial control value and the marketable minority value can be recapped as follows:
• Value at the marketable minority level of value presumes that enterprise cash flows are normalized. If it were not so, market pressures would force such a process to occur, and/or takeovers would occur.
• Unless the typical financial control buyer will price an expectation for greater cash flows (level or expected growth) than the normalized earnings of an enterprise, there is no conceptual reason for there to be a distinction in value between the financial control and marketable minority levels.
• The financial control premium is not a payment to reflect the value of the so-called prerogatives of control. Those prerogatives are vested with managements and directorates of public entities, and are presumed vested for purposes of deriving private company values at the marketable (as-if-freely-traded) minority level of value.
• The minority interest discount is not a discount to reflect the absence of the so-called prerogatives of control. Lack of control on the part of minority shareholders is presumed in pricing at the marketable minority level.
• Application of strategic acquisition premiums may overstate overstate value in the context of fair market value.
• Use of strategic acquisition control premium data to infer minority interest discounts from financial control values will tend to overstate the magnitude of the appropriate discounts.
• The need to understand the conceptual nature of the marketability discount and the causes of often-observed large differences between marketable minority values and the values of illiquid securities of private (or public) enterprises rises in importance.

Thus far, the marketable minority and financial control levels of value have been examined, and we have drawn inferences about the other levels. This beginning of an integrated theory of business valuation has raised several questions about the value relationships reflected in the traditional three-level chart found in Figure 2.
© Z. Christopher Mercer, 2002 16 All rights reserved
STRATEGIC CONTROL LEVEL OF VALUE
Equation 6 introduces the conceptual math of the second control level of value – the strategic control value.
Ve(c,s) = CFe(c,s)
[ Rss - (Gmm + Gs) ]
Equation 6
As with the other levels, we need to define the terms in Equation 6 are defined as follows:
Ve(c,s) is defined as the value of the equity of an enterprise from the viewpoint of buyers of the entire enterprise (control) who may have the expected benefit of synergies or strategic intent that could increase value relative to the financial control value. This level is called the strategic control level of value. As noted in the quote from Pratt/Reilly/Schweihs above, the concept of strategic control value relates to value as perceived by particular buyers, rather than the typical buyers in the fair market value context. As such, Ve(c,s) is generally more akin to a concept of investment value rather than fair market value. Appraisers normally develop indications of value at the strategic control level in two ways: 1) directly, by capitalizing enterprise cash flows, as normalized and further adjusted to reflect the expected benefits or synergies or other strategic benefits; and 2) indirectly, by developing indications of value at the marketable minority level and applying a (strategic, or acquisition) control premium derived from one of the available control premium studies.
CFe(c,s) is equal to the cash flow of the enterprise from the viewpoint of a strategic control buyer(s). As with CFe(c,f), the first step in developing CFe(c,s) is to normalize earnings to derive CFe(mm). Additional adjustments may then be made: 1) to reflect the kinds of improvements that typical financial buyers might expect to make by running the company better; 2) concrete expectations of synergies (e.g., from eliminating overlapping functions or positions); or, 3) strategic benefits (e.g., from selling more of a purchaser's products through target's existing distribution chain). In other words, in addition to expectations of running a company better, strategic control buyers may take into consideration benefits expected by running the company differently.
Rss is the discount rate of potential strategic buyers. Rss can be lower than Rmm or Rf for at least two reasons: 1) Many strategic buyers are considerably larger in size than the smaller public and private companies that they may desire to acquire. As such their equity cost of capital may be lower than the discount rates appropriate for their smaller targets.24 2) A strategic acquirer of similar size may expect reduced risk as result of a strategic combination, and may therefore consider an Rss lower than its expected discount rate absent the acquisition.
(Gmm + Gs) is the expected growth rate of earnings for the strategic control buyer. The first factor is the same Gmm found at the marketable minority level. The second factor is the increment in the growth rate that a strategic control buyer may expect to be able to generate.

24 Whether strategic buyers should give benefit to their lower cost of capital in strategic acquisitions in a separate question. However, if the market consists of numerous strategic buyers that benefit may get reflected in value to selling companies. © Z. Christopher Mercer, 2002 17 All rights reserved
The conceptual model now incorporates the value of the equity of an enterprise at the strategic control level. It builds on the base created by the other two enterprise levels, marketable minority and financial control. The relations between the three enterprise levels of value is illustrated in Figure 5.
Ve(c,f) > VmmVe(c,s) > Ve(c,f) Conceptual Value Math RelationshipsImplicationsCFe (c,s) > CFe (c,f)GS > 0Rss < RmmVmm CFe(mm) Rmm- GmmControlControlStrategic/SynergisticStrategic/SynergisticValueValueControlControl(Value(Financial) ValueMarketableMarketableMinorityMinority CFe(c,s) Rss- [Gmm + Gs]CFe (c,f) > CFmmGf > 0Rf > Rmm CFe(c,f) Rf - [Gmm + Gf]equals(GV = Rmm)
Figure 5
The conceptual differences in value at the marketable minority, financial control and strategic control levels of value can be observed by examining Figure 5. The strategic control value can be greater than the financial control value if one or more of the following conditions holds:
CFe(s,c) is greater than CFe(f,c) (and greater than CFe(mm). This would be true if a strategic purchaser of the enterprise expects synergies or strategic benefits unavailable to the financial control buyer. Such benefits cannot automatically be considered in determinations of fair market value at the financial control level. A lone strategic buyer, for example, has no incentive to pay any more than $1 more (or just enough more to get the deal) than the highest price offered by a financial buyer.25
Gs is greater than zero. If a strategic control buyer expects to be able to augment the future growth of cash flows (and will share that benefit with the hypothetical seller), then value can be augmented above the financial control or marketable minority levels.
Rss is less than Rf or Rmm. If a strategic buyer considers its own discount rate, which may be lower than that of a target, in pricing an acquisition, strategic control value can be greater than at the other enterprise levels.

If a strategic control buyer is willing to consider expected cash flow enhancements (level and growth) and its own lower discount rate in pricing an acquisition, Ve(s,c) can be substantially higher than Vmm. If multiple strategic buyers are seeking the same (public or private) business, then strategic value is more likely to be achieved by that seller, and pricing can sometimes seem almost irrational.26
25 Mr. Gilbert A Matthews, ASA, currently of Sutter Securities, Inc. and for many years an investment banker with Bear, Stearns & Co., made this observation years ago. Its relevance in the context of fair market value determinations should now be clear based on this conceptual analysis.
26 I have often said in speeches that there are three kinds of buyers of businesses: financial buyers, strategic buyers, and irrational buyers. What every seller wants to find is an irrational buyer. Unfortunately, when they are really needed, they are hard to find. Fair market value is a rational concept, not an irrational one. Appraisers need to keep these concepts in mind when determining fair market value at the financial control level.
© Z. Christopher Mercer, 2002 18 All rights reserved
Strategic Control Premium
The control premium that a strategic control buyer might pay in relationship to the value of a business at the marketable minority level (CPs) can now be specified. We specify the premium in this way because there is no observable market for financial control values (other than if public companies are trading at their financial control values). Note that this premium would include any financial control premium available from typical financial buyers. CPs is specified in Equation 7.
CPs = Ve(c,s) - Ve(mm)Ve(mm)
CFe(c,f) CFe(mm) Rs - [Gmm + Gf5] Rmm - Gmm -CPs= CFe(mm) Rmm - Gmm
Equation 7
Conceptually, the control premium of a strategic buyer is the difference in value at the strategic control level and the marketable minority level in relationship to the marketable minority value. This is shown symbolically in the upper equation of Equation 7. The lower equation substitutes the symbolic definitions for each conceptual value into the upper equation.
Several important observations about the relationship between value at the marketable minority level and at the strategic control level can now be made. Unless a strategic buyer is willing to consider the potential for enhanced cash flows (level of flows and/ or growth rate) or the fact that Rs might be lower than Rmm:
• Ve(c,s) will be the same as Vmm (or the same as Ve(c,f) if the typical financial buyer does not expect to be able to enhance cash flows from the normalized, marketable minority level).
• The strategic control value, then, is not automatic, but is the result of negotiation between a seller and one or more strategic purchasers.
• The marketable minority value is the base from which strategic control values would be negotiated. This statement is true for publicly traded companies. Private company values tend to be negotiated directly, since there is no observable, freely traded value for companies. These principles would be imbedded within negotiated values in private transactions.
• Strategic control values will likely be received in transactions only if: 1) there is a single, motivated strategic buyer who is willing to share the expected synergistic or strategic benefits with a seller; 2) there are multiple strategic buyers who will compete in a bidding process; or 3) elements of motivation or irrationality enter into the bidding process.27
• Items 1) and 3) above are not elements of fair market value. Item 2) could represent fair market value if the indicated strategic buyers represent the typical buyers, as noted earlier.

27 Note that a target company that is not motivated to sell may be able to extract some or all of the potential stratgic control remium if there is only a single strategic buyer – if that buyer is motivated.
© Z. Christopher Mercer, 2002 19 All rights reserved

With the financial control buyer, there is no element in the symbolic representation of strategic control value in Figure 8 for any direct payment for the prerogatives of control. They simply come with the territory when a business is purchased.

Having developed the strategic control premium, the discount that would eliminate it from strategic control value can be briefly discussed. Refer to the right side of Figure 2 and note the question mark between the strategic control and financial control levels. We have already observed that the question mark is not the minority interest discount, which relates the financial control and marketable minority levels. However, the question mark discount would include or subsume the minority interest discount. It might represent the minority interest discount if strategic transactions are the norm for an industry. Rather than attempting to give this question mark discount a name at this time, we leave it for further consideration by appraisers in specific valuation situations.
MARKETABILITY DISCOUNT APPLICABLE TO CONTROLLING INTERESTS OF COMPANIES
Some appraisers have attempted to define a discount applicable to controlling interests of companies. This discount is often called a “marketability discount.” An examination of the conceptual relationships of the three enterprise levels of value in Figure 5 suggests that such a discount does not exist. Examination of the conceptual math for each enterprise level indicates that value is a function of expected cash flow, risk and expected growth. If an appraiser adequately measures expected cash flow and the risks and growth of those cash flows, the result is an enterprise value.28
ENTERPRISE LEVELS VS. THE SHAREHOLDER LEVEL OF VALUE
Thus far, the enterprise levels of value: marketable minority, financial control and strategic control have been addressed. These conceptual levels are called enterprise levels because each is determined based on differing market perceptions (and valuations) of the cash flows of the enterprise. A critical assumption of the Gordon Model is that value is a function of the expected cash flows of the enterprise, all of which are available for distribution or for reinvestment.
The fourth conceptual level of value is called the nonmarketable minority level. As opposed to an enterprise level of value, this level is referred to as the shareholder level of value. Value to a shareholder is determined based on the expectation of cash flows (or future benefits) to the shareholder. This is an important point, and the distinction is, unfortunately, lost by many observers. The levels of value in the context of enterprise and shareholder levels are illustrated in Figure 6.
28 See Quantifying Marketability Discounts (1997 version), Chapter 11, “Marketability Discounts and the Controlling Interest Level of Value.” This chapter primarily consisted of a reprint of a previous article: Mercer, Z. Christopher, “Should ‘Marketability Discounts’ be Applied to Controlling Interests of Private Companies?” Business Valuation Review, June 1994, pp. 55-65. These articles elaborated on a position taken in Valuing Financial Institutions (at p. 205), published in 1992, which concluded:
In any event, appraisers applying “marketability discounts” to controlling interest values should be clear as to the objective basis for their discounts or run the danger of having their discounts (and their valuation conclusions) considered illogical and/or arbitrary.
© Z. Christopher Mercer, 2002 20 All rights reserved
Marketable MinorityFinancial ControlEnterprise LevelsValue is a function of the Expected Cash Flows of the Enterprise (as capitalized by the public markets or controlling buyers)NonmarketableMinorityShareholder LevelShareholder LevelValue is a function of Cash Flows expected by Shareholders ( which are derived from the cash flows of the Enterprise, but may not be the same)Strategic ControlMarketable Control
Figure 6
Appraisers have called the conceptual difference between the marketable minority and nonmarketable minority levels of value the marketability discount for years. An alternative name for this concept is the discount for lack of marketability.29 As will be shown below, there is more to this discount than the mere absence of marketability, so it makes little sense to argue over which is the preferable term.
We recently wrote an article discussing the logical basis for the marketability discount. It focused on the distinction made between enterprise and shareholder values:30
There is almost unanimous agreement in the valuation profession that the value of a business, at the marketable minority level, where most valuations originate, is the present value of the expected future benefits to be generated by the business, discounted to the present at an appropriate, risk-adjusted discount rate. In other words, the value of a business depends on the expected cash flows of the business (including their expected future growth), and the risk of generating those cash flows (manifested in the discount rate).
Likewise, a nonmarketable minority interest in a business is a financial asset whose value must derive from the same factors determining the value of the business: expected cash flows (including their expected future growth), and the risk of generating those cash flows (as manifested in the discount rate).
• The expected cash flows to the holder of a nonmarketable minority business interest have as their source the cash flows generated by the business. The cash flows received by the nonmarketable minority investor may be less than, or equal to, but may be no greater than the cash flows generated by the business.

29 ASA Business Valuation Standards, Definitions (American Society of Appraisers, February 2001). The marketability discount is defined as: “an amount or percentage deducted from the value of an ownership interest to reflect the relative absence of marketability.”
30 Mercer, Z. Christopher, and Harms, Travis W., “Marketability Discount Analysis at a Fork in the Road,” Business Valuation Review , Volume 20, No. 4, December 2001, pp. 21-22.
© Z. Christopher Mercer, 2002 21 All rights reserved

Since the expected cash flows generated by the business are the source of the nonmarketable minority investor’s cash flows, the risks faced by the nonmarketable minority investor encompass the risk of the business generating those cash flows, as well as incremental risks arising from the illiquidity of the investment. Therefore, the embodiment of risk for valuation purposes, the relevant discount rate, must for nonmarketable investors be greater than or equal to, but cannot be less than, the discount rate applicable to the valuation of the business.
• From the standpoint of the nonmarketable minority investor, this confluence of circumstances (he may not receive all the cash flows of the business, and he faces additional risks not borne by the business) leads to the inevitable conclusions that his nonmarketable interest is worth less than (or possibly the same as) his pro rata share of the business. The difference in value is the “amount or percentage” from the definition of the marketability discount quoted above.
• The preceding discussion should make clear the logical and theoretical basis for the existence of a disparity between the value of illiquid business interests and the value of the corresponding business. Without any reference to empirical observation, the fact of marketability discounts is undeniable. Given any two investments, if it is known that one has both less cash flow (and corresponding growth) expectations and greater risk, its value will be lower than its counterpart.

The stage is now set to discuss the nonmarketable minority level of value and the marketability discount that separates it from the marketable minority level of value.
THE NONMARKETABLE MINORITY LEVEL OF VALUE
Equation 8 introduces the conceptual math of the shareholder level of value, which corresponds to the nonmarketable minority level of value.
Vsh = CFsh
(Rhp - Gv)
Equation 8
As with the other levels of value, the terms in the conceptual definition of value at the nonmarketable minority level are defined:
Vsh is the value of an equity interest in an enterprise that lacks an active market for its shares from the viewpoint of the shareholder of that interest. Appraisers typically develop indications of value at this level by subtracting a marketability discount from a marketable minority interest value. In the case of asset holding entities, appraisers often begin with a net asset value (deemed to be the financial control level) and then subtract minority interest and marketability discounts in sequence. Appraisers also examine transactions in the stock of companies without public markets as another means of developing indications of value at the nonmarketable minority level for their shares.
CFsh is equal to the portion of the cash flow to equity of an enterprise expected to be received by the shareholders of the enterprise. Consistent with the discounted future benefits method, CFsh represents

© Z. Christopher Mercer, 2002 22 All rights reserved

both interim cash flows (expected dividends or distributions) and any expected terminal value upon ultimate sale of an equity interest.31
Rhp is the discount rate of the minority investor in a nonmarketable equity security for the expected duration of the holding period, or the required holding period return. The concept of holding period risks is discussed in depth in the context of the QMDM. However, as noted above, logic suggests that Rhp will be equal to or greater than Rmm. This required return can be stated symbolically as in Equation 6, where HPP is the indicated holding period premium. Note that if HPP is equal to zero, and there are no holding period risks, as with a publicly traded security where liquidity can be achieved immediately, then Rhp is equal to Rmm.

Rhp = Rmm + HPP
Equation 9
Gv is the expected growth rate in value of the equity of the enterprise, which will yield the terminal value of the enterprise at the end of the expected holding period for the investment. The expected growth rate in value is equal to Rmm for a nondividend paying, publicly traded security. This occurs because cash flows assumed to be reinvested in at a firm’s discount rate enable the expected growth rate in earnings, the G of Equation 1, to compound and to yield a return of Rmm. If there is leakage of cash flow from the enterprise (e.g., as through the payment of above-market compensation to a controlling shareholder), then Gv will be less than Rhp. 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).32

We now have a conceptual model to develop the value of the equity of an enterprise at the nonmarketable minority level. The model anticipates that the appraiser will develop an indication of value at the marketable minority level. In so doing, there will be a thorough understanding of the expected cash flows, their expected growth, and their risks. Based on this analysis, the appraiser can then consider the expected benefits to be derived by the minority shareholder of the enterprise. This relationship can be seen symbolically as in Figure 7.
Vsh < Vmm Conceptual Value Math RelationshipsImplicationsVmmequals(GV = Rmm) CFe(mm) Rmm- GmmMarketableMarketableMinorityMinorityNonmarketableNonmarketableMinorityMinority CFsh Rhp - GvCFsh < CFmmGv RmmRhp > Rmm<
Figure 7
Examining the components of Figure 7, we can discuss the conceptual differences in value between the marketable minority and nonmarketable minority levels of value can be observed. The nonmarketable
31 CFsh 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, Equation 3-8 cannot be literally used to determine the value of a nonmarketable minority business interest.
32 For a more in-depth discussion of this issue, see Mercer, Z. Christopher, and Harms, Travis W., “Marketability Discount Analysis at a Fork in the Road,” Business Valuation Review , Volume 20, No. 4, December 2001, pp. 21-22. © Z. Christopher Mercer, 2002 23 All rights reserved
minority value, i.e., Vsh,, or value to the shareholder, will be less than Vmm if one or more of the following conditions holds:
CFsh is less than CFe(mm). The expected cash flow of a shareholder will be less than the expected cash flows of the enterprise in cases where less than all of its cash flows are distributed to shareholders. The cash flows may be reinvested in the business or paid out to controlling shareholders. Lower cash flow to shareholders yield lower value relative to the capitalized benefit of all cash flows in the public markets.
Gv is less than Rmm. The expected growth rate in value reflects the combined effect of the expected growth rate of earnings, or the G of the Gordon Model, and the reinvestment of those cash flows into the enterprise. If the reinvestment rate is equal to the discount rate, Gv will be equal to the discount rate, or Rmm. To the extent that cash flows are not reinvested in the enterprise or that they are reinvested suboptimally (at rates less than the discount rate), then Gv will be less than Rmm.33 A lower GV than Rmm implies a lower terminal value at the end of any holding period, and therefore, lower value.
Rhp is greater than Rmm. Few observers question that the owner of an illiquid asset bears greater risk than that borne by a shareholder of an otherwise identical asset with an active, public market.34 We have given a name to this incremental risk – the holding period premium, or HPP. HPP is comprised of numerous factors, including the potential for a long and indeterminate holding period and many other risks that flow from this holding period or from the factual situation in any appraisal. Greater risk implies lower value.

The circumstances under which the nonmarketable minority value will be less than the marketable minority value are now clear. The marketability discount, which is the name given to this result, can now be examined.
33 Note that the expectation of suboptimal reinvestment, and the accompanying lowering 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.
34 This should have been obvious to appraisers years ago (me 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.
© Z. Christopher Mercer, 2002 24 All rights reserved
THE MARKETABILITY DISCOUNT
Based on the conceptual model of an integrated theory of business valuation, the marketability discount (MD) that hypothetical (or real) investors might demand when purchasing illiquid interests of enterprises that do not have active public markets for their shares can be specified.
MD = VshVmm1 - MD = CFsh Rsh - Gv 1 -1 - CFmmRmm - Gmm
Equation 10
Conceptually, the first equation of Equation 10 illustrates that if the shareholder level value (Vsh) is equal to the marketable minority value (Vmm), there will be no marketability discount. To the extent that any of the three factors outlined in the previous section hold, there will be a marketability discount between the marketable minority value and the nonmarketable minority value.
Frequently, holders of illiquid securities of private enterprises are faced with expectations that include all three of these factors – cash flow to the shareholder less than that of the enterprise, expected growth in value less than the discount rate, and incremental risks of the expected holding period. In such cases, the marketability discounts that are appropriate relative to the marketable minority value 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 the result of a subtraction in value because of the prerogatives of control. The economic penalty that is the marketability discount is explained in terms of divergences between the expected cash flow of the enterprise and that to shareholders, expected growth in value from 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.
The public minority shareholder does have an element of control that the private minority shareholder lacks. He can obtain cash for his investment in three days through the institution of the public securities markets. In other words, he can control the timing of obtaining liquidity. And when liquidity is obtained, it occurs at the marketable minority level, which capitalizes all the expected cash flows of the enterprise into present value per share every day the markets are open.
© Z. Christopher Mercer, 2002 25 All rights reserved
AN INTEGRATED THEORY OF BUSINESS VALUATION
The four conceptual levels of equity value for a business, a business ownership interest, or equity security of a business observed by appraisers have now been examined in depth. Figure 12 incorporates all four levels into a single chart to present the conceptual math of the levels of value, and summarizes an integrated theory of business valuation.
CFe (c,s) > CFe (c,f)GS > 0Rss < RmmVmm CFe(mm) Rmm- Gmm Conceptual Value Math RelationshipsImplicationsControlStrategic/SynergisticValueControl(Financial) ValueMarketableMinorityNonmarketableMinority CFsh Rhp - GvVsh < Vmm CFe(c,s) Rss- [Gmm + Gs]Ve(c,s) > Ve(c,f)CFe (c,f) > CFmmGf > 0Rf > Rmm CFe(c,f) Rf - [Gmm + Gf]Ve(c,f) > Vmmequals(GV = Rmm)CFsh < CFmmGv RmmRhp > Rmm<
Figure 8
This integrated theory has accomplished several things that appraisers have previously been unable to do:
• Explained each level of value in the context of financial and valuation theory.
• Explained why value differs from level to level in financial and economic terms.
• Defined the conceptual adjustments relating the various levels of value in terms of that theory, i.e., in terms of discounted cash flow analysis summarized by the Gordon Model. Specifically, the financial control premium and the related minority interest discount, the strategic control premium, and the marketability discount have been defined in financial and economic terms.
• Explained why the integrated model is illustrative of pricing behavior observed in public and nonpublic markets for equity interests.
• Gained an increased level of understanding of the value of control, and conversely, the economic consequences of lack of control. Specifically, it should now be clear that an illiquid minority interest in a business is not worth less than its actual or hypothetical marketable minority value because of any lack of control, except over the timing of exit (which does not relate to a lack of control of the enterprise).
• Provided the economic explanation for Eric Nath’s observation in 1990 that the public market pricing of securities offers, at least in many instances, a controlling interest level of pricing. The integrated theory does not confirm his original premise that from the public/control price appraisers should take both a minority interest and marketability discount to arrive at the nonmarketable minority level of

© Z. Christopher Mercer, 2002 26 All rights reserved © Z. Christopher Mercer, 2002 27 All rights reserved

value.35 When public company earnings are reasonably optimized, there is no incentive for financial buyers to take them over to achieve greater earnings and value (and the implied minority interest discount is equal to zero). In this case, our conceptual analysis suggests that only one discount is appropriate – the marketability discount.

The integrated theory of business valuation presented in this discussion has accomplished a number of conceptual breakthroughs for business appraisers:
1. An integrated theory of business valuation has been presented for the first time. This theory is consistent with observed pricing behavior in the public markets and provides a framework within which to discuss the appraisal of privately held companies and interests therein.
2. The integrated theory should cause appraisers to focus more clearly on the relationship between financial control value and marketable minority value (as called for by Nath in 1990).
3. The integrated theory raises significant questions about the use of control premium data to estimate minority interest discounts.
4. And the integrated theory explains the relationship between the marketable minority and nonmarketable minority levels of value in financial and economic terms.
5. The Quantitative Marketability Discount Model has not been discussed at all. However, the analysis of the nonmarketable minority level of value provides the economic and financial rationale for quantitative, rate of return analysis (of which the QMDM is one example) to determine marketability discounts.
6. Importantly, the integrated theory of business does not confirm the conceptual rationale for another discount frequently used by appraisers – a marketability discount applicable to controlling interests of companies. If the conceptual math of the integrated theory is correct, there is no conceptual discount as a marketability discount applicable to controlling interests of companies. Financial control value should be estimated based on the economic factors outlined above. If a company has particular risks that might not be applicable to a hypothetical, freely traded security, those risks should be estimated in terms of the impact on its discount rate or expected returns.

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