2. My regression analysis of private fractional interest data.

Thus, in Chapter 10 we use three models for calculating the fractional

interest discount: the economic components model, the partnership pro-

¬les database regression, and the private data regression.

If any chapter may have rough edges to it, Chapter 7 is it. I hope to

be able to smooth those edges in future editions of this book. For now,

however, this chapter will have to remain as it is.

The calculation of the discount for lack of control in Chapter 9 is also

subject to further research and revision. Nevertheless, this is valuable and

novel material well worth the struggle through the quantitative parts.

I caution the reader not to get bogged down in the quantitative parts

of Chapter 7. Read it through lightly ¬rst for understanding the gist, and

do not worry about understanding every statistic in the academic articles.

The most important thing to get out of Chapter 7 in a ¬rst reading is an

understanding of why the acquisition premium data that we have been

using for the past 30 years tell us almost nothing useful about the value

of control of a private ¬rm and why we have to look elsewhere. It is then

worth a second reading to master the technical details.

PART 3 Adjusting for Control and Marketability 193

CHAPTER 7

Adjusting for Levels of Control

and Marketability

INTRODUCTION

THE VALUE OF CONTROL AND ADJUSTING FOR LEVEL OF

CONTROL

Prior Research”Qualitative Professional

Nath

Mercer (1990)

Bolotsky

Jankowske

Roach

Mercer (1998) and (1999)

Summary of Professional Research on Control Premiums

Prior Research”Academic

Schwert (1996)

Lease, McConnell, and Mikkelson (1983)

Megginson (1990)

My Conclusions from the Megginson Results

My Analysis of the Megginson Results

The Houlihan Lokey Howard & Zukin (HLHZ) Study

International Voting Rights Premia

Bradley, Desai, and Kim (1988)

Maquieira, Megginson, and Nail (1998)

Other Corporate Control Research

Menyah and Paudyal

My Synthesis and Analysis

Decomposing the Acquisition Premium

Inferences from the Academic Articles

The Disappearing Control Premium

The Control Premium Reappears

Estimating the Control Premium

DLOC

195

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DISCOUNT FOR LACK OF MARKETABILITY (DLOM)

Mercer™s Quantitative Marketability Discount Model

Kasper™s BAS Model

Restricted Stock Discounts

Regression of MPI Data

Using the Put Option Model to Calculate DLOM of Restricted

Stock

Annualized Standard Deviation of Continuously Compounded

Returns

Calculation of the Discount

Table 7-8: Black“Scholes Put Model Results

Comparison of the Put Model and the Regression Model

Empirical versus Theoretical Black“Scholes

Comparison to the Quantitative Marketability Discount Model

(QMDM)

Abrams™ Economic Components Model

Component #1: The Delay to Sale

Psychology

Black“Scholes Options Pricing Model

Other Models of Component #1

Abrams Regression of the Management Planning, Inc. Data

Limitations of the Regression

Component #2: Buyer Monopsony Power

Component #3: Transactions Costs

Table 7-11: Quantifying Transactions Costs for Buyer and Seller

Component #3 Is Different than #1 and #2

Developing Formulas to Calculate DLOM Component #3

A Simpli¬ed Example of Sellers™ Transactions Costs

Tables 7-12 and 7-13: Proving Formulas (7-9) and (7-9a)

Value Remaining Formula and the Total Discount

Table 7-14: Sample Calculation of DLOM

Evidence from the Institute of Business Appraisers

Mercer™s Rebuttal

Expected Growth and Expected Returns

Conclusion

My Counterpoints

Mercer™s Response

Conclusion

MATHEMATICAL APPENDIX

PART 3 Adjusting for Control and Marketability

196

INTRODUCTION

Adjusting for levels of control and marketability is a complicated and

very important topic. We will be discussing control premiums (CP), their

opposite, discount for lack of control (DLOC), and discount for lack of

marketability (DLOM).

Historically, these valuation adjustments have accounted for substan-

tial adjustments in appraisal reports”often 20“40% of the net present

value of the cash ¬‚ows”and yet valuation analysts may spend little to

no time calculating and explaining these adjustments.

This is a long chapter, with much data and analysis. It will be helpful

to break the discussion into two parts. The ¬rst part will deal with pri-

marily with control and the second part primarily with marketability. I

say primarily, because the two concepts are interrelated. The level of con-

trol of a business interest impacts its level of marketability. Therefore, it

is logical to begin with a discussion of control. Because of the interrela-

tionship, two academic articles that we will discuss in the section on

control relate more to marketability, yet they ¬t in better in the control

discussion.

THE VALUE OF CONTROL AND ADJUSTING FOR LEVEL

OF CONTROL

We will begin our analysis of the effects of control on value by reviewing

prior qualitative professional research and prior academic research. Then

we will present some additional data and come to some conclusions

about the magnitude of control premiums and DLOC.

The top portion of Figure 7-1 shows the traditional level of values

chart.3 The conventional wisdom represented in the traditional levels of

value chart holds that it is appropriate to add a control premium to the

F I G U R E 7-1

Traditional Levels of Value Chart

Level of Value Adjustment up To Adjustment Down To

Control interest Control premium NA

Marketable minority interest Reverse out DLOM DLOC

Private Minority Interest NA DLOM

Mercer™s Mercer (1998) modi¬ed traditional levels of value chart

Strategic value Value of synergies NA

Control value Control premium Eliminate synergies

Marketable minority interesta Reverse out DLOM DLOC

Private minority interest NA DLOM

a

Often referred to in the literature as the ˜˜as-if-freely-traded-value™™ for private ¬rms.

3. The bottom portion shows Chris Mercer™s modi¬ed traditional levels of value chart, which is

identical to the one above, except with the addition of the strategic value. We will cover this

later in the chapter.

CHAPTER 7 Adjusting for Levels of Control and Marketability 197

marketable minority interest value. There are signi¬cant opinions to the

contrary, i.e., that one should not add any control premium whatsoever.

Additionally, there is controversy over the appropriate magnitude of the

control premium among those who do add them to the marketable mi-

nority interest value. We will cover that in greater depth later in the chap-

ter. Of course, if the valuation method is a guideline company approach

using a database of sales of privately held ¬rms, the starting value is a

private control interest, and a control premium is inappropriate.

It is extremely important to understand that the valuation adjust-

ments in Figure 7-1 be appropriate to the valuation method used. If we

are valuing a control interest and we used a discounted cash ¬‚ow analysis

with discount rates calculated using New York Stock Exchange data, the

resulting value is a marketable minority interest, and a control premium

must be considered.4

The alternative levels of value chart is two tiered, i.e., it is a 2 2

chart (2 rows and 2 columns, versus the traditional chart, which is 3

1). It represents the four basic types of ownership interests, which are

combinations of public versus private and control versus minority inter-

est. Obviously, there are shades of gray in between the extremes. Bolotsky

(1991) was the ¬rst to propound this chart, although he used it for slightly

different purposes, which we discuss below. Much later in the chapter,

we will discuss Figure 7-3, which is my own extension of Bolotsky™s levels

of value chart to a 3 2 chart.

The traditional sources of control premiums are the Mergerstat and

the Houlihan Lokey Howard & Zukin (HLHZ) studies.5 Table 7-1, col-

umns B and C show Mergerstat™s compilation of average (mean) and

median ¬ve-day acquisition premiums from 1985“1997. The premiums

were measured as (POffer/P5Day) 1, where the numerator is the offering

price and the denominator is the minority trading price ¬ve days before

the announcement of the offer. Mean acquisition premiums have ranged

from 35“45%, with the average being 39.5% (B21), while median premi-

ums have ranged from 27“35%, with an average of 30.5% (C21).

F I G U R E 7-2

Two-Tiered Levels of Value Charta

Public Private

Control x x

Minority x x

a

Note: these are also the four basic types of ownership interests.

4. It is also important to make sure the measure of income is consistent with the interest valued.

When valuing a control interest, it is appropriate to add back excess salaries of the owners.

When valuing a minority interest that cannot force salaries lower, the add-back is

inappropriate.

5. HLHZ now owns Mergerstat, although the latter was previously owned by Merrill Lynch and

the W. T. Grimm Co.

PART 3 Adjusting for Control and Marketability

198

T A B L E 7-1

Synergies as Measured by Acquisition Minus Going-Private Premiums

A B C D E F G

5 Acquisition Going Private Difference

Premiums [1] Prem [2] Synergy?

6 Mean Median Mean Median Mean Median

7 1985 37.1% 27.7% 30.9% 25.7% 6.2% 2.0%

8 1986 38.2% 29.9% 31.9% 26.1% 6.3% 3.8%

9 1987 38.3% 30.8% 34.8% 30.9% 3.5% 0.1%

10 1988 41.9% 30.9% 33.8% 26.3% 8.1% 4.6%

11 1989 41.0% 29.0% 35.0% 22.7% 6.0% 6.3%

12 1990 42.0% 32.0% 34.3% 31.6% 7.7% 0.4%

13 1991 35.1% 29.4% 23.8% 20.0% 11.3% 9.4%

14 1992 41.0% 34.7% 24.8% 8.1% 16.2% 26.6%

15 1993 38.7% 33.0% 34.7% 20.0% 4.0% 13.0%

16 1994 41.9% 35.0% 41.9% 35.0% 0.0% 0.0%

17 1995 44.7% 29.2% 29.8% 19.2% 14.9% 10.0%

18 1996 36.6% 27.3% 34.8% 26.2% 1.8% 1.1%

19 1997 35.7% 27.5% 30.4% 24.5% 5.3% 3.0%

20 1998 40.7% 30.1% 29.1% 20.4% 11.6% 9.7%

21 Mean 39.5% 30.5% 32.1% 24.1% 7.4% 6.4%

[1] Mergerstat-1999, Chart 1-8, Page 23 (Mergerstat-1994, Figure 41, Page 98 for 1985-1988). Mergerstat is a division of Houlihan

Lokey Howard & Zukin.