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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